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By the sixth week of pregnancy, the baby is in the embryo stage and developing fast.
The baby is just the size of a sweet pea at 6 weeks of pregnancy. It initiates the development of various organs of the baby. Various symptoms of pregnancy start to show by now.
These self-care measures should be adopted at 6 weeks gestation for a healthy pregnancy.
The doctors usually perform some diagnostic tests and prescribe medications and lifestyle changes based on the diagnosis. The doctors may perform a physical examination, blood tests, urine tests, and prenatal genetic screening to evaluate your health. A folic acid multivitamin medications are recommended at this stage for all women. The doctors also advise the childbearing women to have a healthy diet, thoroughly cooked meals and keep intake of caffeine to only 200 mg per day. Alcohol and tobacco are to be completely avoided.
It is best to reach out to your gynecologist at 6 weeks gestation pregnancy for routine checkup and to ensure good health. At Mfine, we provide integrated treatment plans for a healthy body under the guidance of the qualified specialists. | https://www.mfine.co/gynecologists/conditions/6-weeks-into-pregnancy/ |
Wind turbine blades are subjected to a higher number of complex loading cycles not experienced in other applications of composite structures. These loads can lead to structural failure through various mechanisms such as a crack initiated at a flaw or structural detail such as an adhesive joint. Predicting how blade materials will behave under realistic loading and environmental conditions and how damage initiates and progresses is critical information which enables designers, manufacturers and materials developers to improve blade manufacturing, performance and cost leading to a lower cost of energy.
Since 1989, Sandia has partnered with Montana State University to test and analyze mechanical properties and trends of fiber-reinforced polymers (composites) and other materials used to construct wind-turbine blades. These data, representing over 12,000 tests, are collected and published annually in a public database available here. Supporting publications can be found at the Montana State University Composite Technologies Research Group website.
Recent work has focused on a variety of industry-relevant areas including:
• Testing the effects of common flaws in composites on properties in fatigue loading
• Characterizing new materials such as urethane resins, aligned strand material forms, and carbon fiber composites
• Studying crack growth and delamination in adhesive and core materials
• Establishing full 3-D properties of thick laminates
• Developing substructure testing capabilities in order to capture the realistic and complex loading experienced by modern wind-turbine blades. | https://energy.sandia.gov/programs/renewable-energy/wind-power/blade-reliability/blade-materials-and-substructures-testing/ |
The Model for Improvement begins with three questions designed to clarify the following concepts:
Aims, measures, changes
Applying the Model for Improvement to the clinic’s improvement goal, which of the following is the most reasonable aim statement?
Increase the number of patients reporting they are “very satisfied” with the clinic’s scheduling by 50 percent within six months.
What is the team’s next step?
Test their change plan using the PDSA cycle.
The orthopedic clinic plans the change to improve scheduling, and then it carries out a small test of change with three patients on Tuesday morning. What’s the next thing the clinic’s improvement team should do?
Measure to see if the change led to improvement.
When trying to improve a process, one reason to use PDSA cycles rather than a more traditional version of the scientific method (such as a randomized, controlled trial) is that:
Both C and D
Having a clear aim statement is important in quality improvement work because:
Aim statements provide a clear and specific goal for the organization to reach.
An aim statement should include the following:
Numeric goals, specific time frame, patient population or system affected
Which of the following is the most effective aim statement for this project?
Within three months, the emergency department will administer all pain medications within 45 minutes of order time.
The charge nurse in the emergency room asks Brenda to assemble a team to improve the delivery of pain medication. As she considers who to place on the team, Brenda should:
Review the aim statement to make sure the team includes representatives of all processes affected by the team’s aim.
During Brenda’s first group meeting, the members ask to review the aim statement to make sure they agree it addresses the current problem. With Brenda’s approval, they all decide to rewrite it. However, when they meet to consider what would be a better aim statement, the group loses direction. In order to help them, Brenda might want to:
Remind the team of the Institute of Medicine’s dimensions of health care quality.
What would you identify as the outcome measure for the project?
Percent of patients that are readmitted to the hospital
Which of the following is an example of a process measure that you may collect as part of this improvement effort?
The percent of patients receiving a call within 48 hours of discharge
Why might you consider collecting balancing measures?
To make sure you did not unintentionally damage other aspects of the unit’s work
What else should you add to the graph to best explain the work your unit has done?
Annotations to show when specific changes were tested
Gathering and reviewing data during an improvement project—that is, measuring—helps you answer which of the three questions of the Model for Improvement?
How will we know that a change is an improvement?
You’re a medical assistant at a community health clinic. Sometimes, patients with unresolved problems need to come in for follow-up appointments. However, you notice that it’s a real challenge to schedule these follow-ups within a week of the initial appointments. Which of the following techniques might be most useful as you search for a good idea for change?
Review the process for scheduling these appointments with colleagues to identify opportunities for improvement.
What’s the main benefit of using change concepts to come up with improvement ideas?
Using change concepts can help you develop specific improvement ideas that might not have occurred to you initially.
You notice that it’s very easy to confuse medications at the community health center where you’re working. They are lined up on the shelf and the labels are very similar. You decide that it’s worth a try to highlight parts of drug names on certain labels to reduce confusion. Which change concept are you using?
Design Systems to Prevent Errors
Which of the following changes falls under the heading of “eliminating waste”?
Physicians type all consult responses directly into a computer rather than writing them in a patient’s chart, thus saving paper.
As you recall, the IHI staff member’s change idea involves leaving work by 5:30 PM each workday. Which of the following is an example of using technology to help her do so?
Scheduling a reminder into her work calendar that pops up daily at 5:15 PM with the message, “Leave!”
The care protocol was successful at the other hospital. Why would it be important to test this proven change at your hospital?
Because this change may not be as effective in your hospital.
After several tests, you decide to try implementing a modified version of the protocol at your institution. Which of the following might you do within the “S” portion of your next PDSA cycle?
Analyze information collected.
Based on the recommendations in this lesson, what should you do next?
Work on improving both the schedule and communication at the same time.
Starting with small tests of change:
Improves the likelihood of buy-in from opinion leaders
Which of the following statements is true?
While not all changes lead to improvement, all improvement requires change. | https://clikngo.com/qi-102-how-to-improve-with-the-model-for-improvement-flashcard-example-26678/ |
The role or usefulness of imperialism, colonialism and postcolonialism, as terms with a modernist historical baggage, to the understanding of pre-modern societies has been the source productive discussion. On these matters, however, the Byzantine world, broadly conceived has lagged somewhat behind.
This event will seek to critically asses the usefulness of the frameworks of imperialism, colonialism and postcolonialism to the study of the Byzantine world. It will do so from a range of perspectives, historical, archaeological, literary, historiographical, and through a discussion-led approach.
Location: St Luke’s Chapel, Radcliffe Humanities Quarter, Oxford
Timetable:
- 09.00 – 09.30 Arrival & Coffee
- 09.30 – 10.00 Welcome & Introduction Mirela Ivanova – Balliol College, Oxford , Matthew Kinloch – Austrian Academy of Sciences, Vienna
- 10.00 – 11.30 Session 1: Imperialism and Colonialism in Byzantium Chair: Catherine Holmes
- Beyond Methodological Imperialism: Medieval New Rome from a Subaltern Perspective Nicholas Matheou – Institute of Historical Research, London
- Byzantine Subalterns from an Archaeological Perspective Sophie Moore – Cardiff University
- 11.30 – 12.00 Coffee Break
- 12.00 – 13.30 Session 2: Imperialism and Colonialism in Byzantine Studies Chair: Averil Cameron
- Byzantium and OrientalismJules Gleeson – University of Vienna
- The Postcolonial Turn in Medieval Studies, False Starts and New Horizons Alexandra Vukovich – St Edmund’s College, Oxford
- 13:30 – 14:30 Lunch
- 14:30 – 16:30 Session 3: Can the Byzantine World be Postcolonial? Discussion with Robert J.C. Young
- Discussion readings:
- General R.J.C. Young, ‘Introduction’, Empire, Colony, Postcolony (Chichester, 2015) pp.1-6.
- E. Said, Orientalism (London, 1978), pp. 1-73.Medieval HistoryJ.
- J. Cohen ‘Introduction. Midcolonial’ in ed. The Postcolonial Middle Ages (Basignstoke, 2000), pp. 1-18.S.
- Gaunt, ‘Can the Middle Ages be Post-Colonial?’ Comparative Literature 61 (2009), pp. 160-76. | https://royalhistsoc.org/calendar/imperialism-colonialism-and-postcolonialism-in-the-byzantine-world/ |
PLEASE NOTE: Some or all instruction for all or part of Academic Year 20-21 may be delivered remotely. Tuition and mandatory fees have been set regardless of the method of instruction and will not be refunded in the event instruction occurs remotely for any part of the Academic Year.
Ph.D Student
Biblia’s research interests include mental health and mental health service use; health disparities, and the intersections of race, religion/spirituality, and health. Her current work focuses on Korean American church-goers and clergy in Southern California and the contextual and structural pathways to their intentions to seek mental health services.
Ph.D Student
My research examines how policies and structural factors correspond with mental health and suicidality among vulnerable populations. I am interested in the relation between structural racism within the criminal justice system and mental health outcomes in minority populations. Additionally, I investigate whether firearm policies and gun culture precede increases in suicidal behavior. I utilize econometric methods (i.e., fixed effects, difference-in-difference, time series) with longitudinal and panel data to measure changes over time.
Ph.D Student
Samantha’s research focuses on advancing the understanding of mechanisms contributing to Latino health disparities and intervening with efficacious health behavior interventions utilizing health communication strategies. Her work focuses on developing, implementing and testing community-based interventions using mixed methods research. Her dissertation work investigates individual, interpersonal and structural drivers of HPV-vaccination disparities among Mexican American young adults.
Ph.D Student
My research interests lie in infectious diseases, particularly neglected tropical diseases and public health responses to infectious disease outbreaks in low-resource settings. My interests are informed from my educational background at The London School of Economics where I studied for a BSc and then an interdisciplinary MSc in African Development during which I researched the barriers to the international response to the Ebola outbreak in Sierra Leone. Building from this previous work, I am now trying to research how local and international health responses coexist, interact and how they influence health behavior in outbreak situations
Ph.D Student
I have a broad interest in the epidemiology and prevention of infectious diseases, with a focus on healthcare-associated infections and drug-resistant pathogens. For my dissertation, I seek to quantify and address barriers to the prevention of SARS-CoV-2 in nursing homes.
Ph.D Student
I am a PhD student in Public Health with a concentration in Disease Prevention at UCI. My research interests include coping mechanisms for distress, dietary patterns, structural discrimination, and social determinants of mental health among Asian American populations. I am also passionate about suicide prevention, support networks, and interdisciplinary approaches to health equity. Prior to entering UCI, I worked as a project manager/research analyst at the UCLA Center for Health Policy Research and volunteered as a crisis line counselor at the Didi Hirsch Suicide Prevention Center. I completed my MPH in Epidemiology/Biostatistics at UC Berkeley and received my BS in Human Biology and Society at UCLA. During my undergraduate education, I was involved in a nonprofit organization that funds health clinic services and scholarships to villagers in Vietnam. My master's capstone research paper focused on obesity and metabolic outcomes among patients in a safety-net health system.
Ph.D Student
My research interests lie broadly in global health and vector-borne disease epidemiology. I aim to apply my previous experiences in materials science, bioengineering, and translational research towards my current research, which focuses on developing a better understanding of the transmission dynamics and drivers of malaria infection in malaria elimination settings.
Ph.D Student
My research interests lie in better understanding vaccination behaviors among African American and Latinx communities and improving health disparities as they relate to infectious diseases. I am interested in intervention design, mixed methods approaches, and health communication strategies as ways to address these disparities. My interests originate from my academic background in microbiology and global health, my previous research in vaccine development and food insecurity among vulnerable populations, as well as my professional career as a Public Health Microbiologist. My current work is focused on investigating COVID-19 vaccine hesitancy among parents and understanding risk perceptions via mask-wearing discussions on social media.
Ph.D Student
I have a passion for protecting the health of mothers and babies. My current research interests include understanding the role of physiologic biomarkers of maternal allostatic load on birth outcomes and subsequent child development. In addition, I am interested in the racial patterning of perinatal allostatic load. In the long term I seek to translate findings of physiologic stress that contribute to perinatal disparities into tangible public health results.
Ph.D Student
Erika’s research interests include mental health and chronic diseases among the Khmer community as well as health disparities among underserved populations, particularly within the Asian American community. Her academic and cross-cultural experiences in research, volunteering abroad, and interning on a federal level solidified her passions in addressing health disparities through research, policy, health education, program interventions and community organization. She aspires to design, implement, and improve health programs and policies that leverage abilities of health research and education to improve minority health.
Ph.D Student
My current research focuses on understanding how maternal substance exposure during pregnancy alters the brain and endocrine development in children. I am a physician by training from Bangladesh. My interest in public health research ignited during my time of work in the International Center for Diarrhoeal Diseases Research, Bangladesh, where I explored several public health issues like childhood stunting, malnutrition and antimicrobial resistance. Prior to joining UC Irvine, I completed a Master’s in Nutrition from the University of Nevada, Reno with a research thesis on postmortem hypertensive human brain to disentangle the brain mechanisms of blood pressure regulation.
Ph.D Student
Vida is a Ph.D. student studying the impact of epidemiological, clinical, and laboratory findings seen in children exposed to certain prenatal conditions, including preeclampsia and maternal substance use, to understand subsequent effects on childhood developmental risks. Her interests also include using salivary biomarkers to elucidate endocrine/environmental disruptors in mother-child dyads. The overarching aim of her research is to help contribute to the strengthening of health systems globally on maternal and child health outcomes. Vida has previously worked with the United Nations Foundation to address global health issues, such as child vaccination coverage. She has also worked with health care institutions in the US and India as a physical therapist and patient safety specialist in CQI procedures to improve the quality of health care, increase patient safety and reduce healthcare-associated infections.
Ph.D Student
Connie Valencia's research interests are focused on the role that structural, individual and environmental factors impact health disparities and health equity among low income Latino communities. Connie's dissertation work focuses on understanding the impact ambient air pollution has on obesity and factors that impact civic engagement among predominantly Latino communities. Connie earned her BS from UCLA and an MPH from Cal State Fullerton.
Ph.D Student
My research focuses on the way structural factors, in particular work, influence population-level patterns in preventive health behaviors. In my dissertation, I am applying quantitative methods to existing datasets to examine how employment status and working conditions relate to racial disparities in breastfeeding. I have an MPH in Community Health Sciences and a BA in Social Welfare.
Ph.D Student
Yachen Zhu is a PhD student on the global health track. She has a master's degree in Statistics. Her research uses a variety of statistical methods to examine how PFAS in the environment relates to maternal and infant health. | https://publichealth.uci.edu/ph/_graduate/phd_student_profiles |
RELATED APPLICATION(S)
BACKGROUND
SUMMARY
DETAILED DESCRIPTION
This application claims the benefit of Korean Patent Application No. 10-2014-0177136, filed on Dec. 10, 2014, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference.
The present disclosure relates to a method and apparatus for calculating a rotation angle of a device, and more particularly, to a method and apparatus for calculating an inclination angle of a device with respect to a moving direction of the device.
Pedestrian dead-reckoning (PDR) may be used for estimating a position by using devices such as smartphones. In PDR, an inclination angle of the device substantially affects position estimation performance. When the inclination angle of the device is miscalculated, an error may still be present even though a moving distance has been accurately calculated.
In particular, when a user of a small device such as a smartphone moves while gripping the device in his/her hand, an inclination angle of the device with respect to a moving direction of the device may change arbitrarily depending on user convenience or an intention of the user. For example, assuming that the user is moving while gripping the smartphone in a vertical direction (portrait mode) or a horizontal direction (landscape mode), when the user is moving while the smartphone is inclined in a yawing direction by about 60° with respect to a moving direction, it may be difficult to calculate an inclination angle of the smartphone with respect to the moving direction of the user by only using a built-in accelerometer of the smartphone. Due to inaccurate calculation, position calculation results may have many errors.
It is difficult to calculate the inclination angle of the device with respect to the moving direction of the device because an accelerometer in the device senses gravitational (gravity axis) acceleration, information about acceleration in a direction in which the user is moving, and vertical acceleration information, but cannot distinguish between the acceleration components.
According to the related art, an inclination angle of a device with respect to a moving direction of a user may be calculated by interpreting acceleration information, which is sensed by using an accelerometer, a gyroscope, and a geomagnetic sensor, in a frequency range or by using movement dynamics of the user.
When the inclination angle of the device is calculated by using a reaction acceleration vector at which the user takes a step, the inclination angle of the device with respect to the moving direction of the user may have an error because the reaction acceleration vector may not be easily distinguished due to sensor noise. Although final calculated angle information may be filtered by a low pass filter to reduce errors, calculation time may be delayed due to the filtering process.
The present disclosure provides a method of efficiently distinguishing between gravitational acceleration, vertical acceleration, and horizontal acceleration based on information sensed by only an accelerometer, by recognizing movement characteristics of the user as the user moves. By distinguishing the gravitational acceleration from acceleration information, the inclination angle of the device with respect to the moving direction of the user may be more accurately calculated compared to methods in the related art. This technology may increase position calculation accuracy of mobile phones, and perform position calculation using low power by reducing sensing power consumption.
Provided is a method of determining an angle between a moving direction of a user and a heading direction of a device, and a rotation angle of the device may be accurately calculated by using an acceleration component.
Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the presented exemplary embodiments.
According to an aspect of an exemplary embodiment, a method of determining a rotation angle of a device with respect to a proceeding direction of the device, includes obtaining, from an accelerometer of the device, acceleration information related to movements of the device, transforming coordinates of the acceleration information of the device, filtering the acceleration information on the transformed coordinates of the device, and determining the rotation angle of the device with respect to the proceeding direction of the device by using gravitational acceleration of gravity information on the transformed coordinates. The gravitational acceleration information is derived by using information about a time point when a vertical acceleration component at the transformed coordinates of the device has a maximum value, from among the acceleration information.
The time point when the vertical acceleration component at the transformed coordinates of the device has the maximum value may be the same as a time point when a magnitude of acceleration of the obtained acceleration information has a maximum value.
A minimum value of the vertical acceleration component at the transformed coordinates may be derived by using the information about the time point when the vertical acceleration component at the transformed coordinates has the maximum value.
A horizontal acceleration component included in the acceleration information may correspond to acceleration information with respect to the proceeding direction of the device, and the vertical acceleration component may be an acceleration component between the device and a horizontal plane.
The transforming of the coordinates of the acceleration information may include transforming the acceleration information from coordinates on a coordinate system based on the device into coordinates on a coordinate system based on a direction of gravity.
The coordinate system based on the direction of gravity may include three axes that are perpendicular to one another, and a first axis from among the three axes may be parallel to a gravitational acceleration direction.
A second axis from among the three axes may be defined by rotating an axis of the coordinate system based on the device at a roll angle, and a third axis from among the three axes may be defined by rotating another axis of the coordinate system based on the device at a pitch angle.
The vertical acceleration component and a horizontal acceleration component at the transformed coordinates may change according to an identical cycle.
The vertical acceleration component and a horizontal acceleration component at the transformed coordinates may have a phase difference of 90°.
The vertical acceleration component may lead the horizontal acceleration component by 90°.
The vertical acceleration component may lag the horizontal acceleration component by 90°.
The gravitational acceleration information may be derived by averaging a magnitude of the vertical acceleration component and a magnitude of a horizontal acceleration component at the transformed coordinates of the device with respect to a plurality of cycles.
The filtering of the acceleration information may include transforming the acceleration information into a frequency range.
The filtering of the acceleration information may include band-pass filtering the acceleration information.
The band-pass filtering may include filtering the acceleration information that is transformed into the frequency range, based on a central frequency that is determined by using dynamics of the device.
The dynamics of the device may be obtained according to a position of a user of the device walking in the proceeding direction.
According to an aspect of another exemplary embodiment, a device configured to determine a rotation angle of the device with respect to a proceeding direction of the device, includes an accelerometer configured to obtain acceleration information related to movements of the device, a storage unit configured to store the acceleration information, and a controller configured to transform coordinates of the acceleration information, filter the acceleration information at the transformed coordinates, and determining the rotation angle of the device with respect to the proceeding direction of the device by using gravitational acceleration information at the transformed coordinates. The gravitational acceleration information is derived by using information about a time point when a vertical acceleration component at the transformed coordinates of the device has a maximum value, from among the acceleration information.
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. Sizes or thicknesses of components in the drawings may be exaggerated for convenience of description and clarity. Expressions such as “at least one of,” when preceding a list of elements, modify the entire list of elements and do not modify the individual elements of the list.
In the present disclosure, a “rotation angle” of a device refers to an angle related to a position in a 3-dimensional (3D) space based on a coordinate system. “Rotation angle” may have the same meaning as “inclination angle” in the 3D space, and both terms may be used in the present disclosure. Also, the term “rotation angle” may refer to an angle between axes in a random coordinate system. In the present disclosure, a “body frame” refers to coordinates of x-, y-, and z-axes based on a device, the x-, y-, and z-axes being perpendicular to one another. The x-axis corresponds to a major axis direction of the device, the y-axis corresponds to a minor axis direction of the device, and the z-axis corresponds to a direction determined according to the right-hand rule based on the x- and y-axes. When four fingers of the right hand are rolled in a direction of the x-axis toward the y-axis, a direction indicated by the thumb corresponds to the z-axis. That is, the body frame is a coordinate system in which the z-axis is defined as a direction from top to bottom of a device, such as a smartphone.
In the present disclosure, a “local frame” refers to a 3D coordinate system. In relation to the body frame, properties of the local frame are as below. First, when the device is rotated by ‘−1*roll angle’ about the x-axis of the body frame, the y-axis of the body frame is located at a y′-axis in a plane perpendicular to a gravitational acceleration direction. When the device is rotated by ‘−1*pitch angle’ about the y′-axis, the x-axis is located at an x′-axis in a plane perpendicular to a gravitational acceleration direction. Therefore, the local frame is a coordinate system in which three axes are defined; that is, the determined x′- and y′-axes may be respectively defined as an x-axis and a y-axis of the local frame, and a z-axis may be defined according to the right-hand rule based on the x- and y-axes.
In the local frame, the z-axis is a direction parallel to the gravitational acceleration direction, the x-axis indicates 0° when the x-axis is the same as a proceeding direction of the device, and the y-axis is determined according to the determined x- and z-axes. The three axes are perpendicular to each other. Therefore, the local frame may be understood as a coordinate system that includes features described in the present disclosure, from among coordinate systems having three axes which are perpendicular to one another in the 3D space.
FIGS. 1 to 20
Hereinafter, a method of calculating a rotation angle of a device according to exemplary embodiments will be described with reference to .
FIG. 1
100
is a diagram of a rotation axis of a device , according to an exemplary embodiment.
100
100
100
100
100
100
Since the device moves in a 3D space, the device may be located in any direction at any angle. All devices have a ‘physical center’ and three axes based on the physical center. The term ‘physical center’ may refer to the center of gravity, a geometrically defined center, a position of an accelerometer, and the like. Three axes may be present based on the center of the device in a front-back direction, a left-right direction, and an up-down direction. The three axes may be randomly defined axes that are perpendicular to each other, and may vary according to a physical structure of the device . For example, when the device is rectangular cuboid-shaped, such as a smartphone, a display unit displaying images may be set as a front surface and three axes may be defined about the display unit. Alternatively, when the device is spherical-shaped and a front surface cannot be determined, the three axes may be defined based on any direction.
FIG. 1
100
100
As shown in , the three axes of the device, i.e., x-, y-, and z-axes, may be defined about the center of the device , based on a portrait direction in which a display unit (not shown) of the device is toward the front and vertically positioned.
100
100
100
B
B
B
The x-, y-, and z-axes that are configured based on the device may be perpendicular to each other and referred to as a body frame. The x-, y-, and z-axes of the body frame may be fixed with respect to the device and change as a position of the device changes in the 3D space. In the present disclosure, the x-, y-, and z-axes may be respectively indicated by X, Y, and Z, wherein the subscript ‘B’ refers to the first letter of “body frame.”
FIGS. 2 to 4
100
100
are diagrams of an inclined angle of the device with respect to a proceeding direction of the device , according to an exemplary embodiment.
More people are travelling because of the development of transportation (e.g., automobiles, subways, etc.). When travelling, people tend to carry devices such as smartphones, tablet PCs, etc. Device users may utilize services when travelling by using various applications that are executed in the devices. A location based service (LBS) may allow the users to immediately identify services that may be used at the current location while travelling and select to use a desired service. Also, the users may reproduce content, such as games or movies, in the devices regardless of the current location.
100
100
100
100
100
When a user uses a navigation application, different information may be displayed on the device according to a proceeding direction and moving velocity of the device . Alternatively, when the user is using a game application, control settings and display settings may vary depending on whether the user is using the device in a portrait mode or a landscape mode. Therefore, a method of accurately measuring an inclination angle of the device may be valuable. The inclination angle of the device refers to an angle between two vectors, i.e., an angle between a vector in a proceeding direction of the user and a heading vector of the device with respect to a plane that is perpendicular to a gravity vector.
FIG. 2
100
100
100
100
As shown in , the user may grip the device while having the proceeding direction of the user to be the same as a major axis of the device . The user may move while gripping the device and watching a screen of the device in a portrait (a direction corresponding to the major axis direction of the device ) mode.
For example, when the user is moving while being guided by a navigation application of a device, the user may match the heading vector of the device with a proceeding direction of the user (or the device).
FIG. 3
FIG. 2
100
100
100
100
100
100
As shown in , the user may match the heading vector of the device with a direction perpendicular to the proceeding direction of the user (or the device ), and move while watching the screen of the device in a landscape (a direction corresponding to the minor axis direction of the device ) mode. In this case, a rotation state of the device with respect to the proceeding direction of the user (or the device ) may be different from the case described with reference to .
FIG. 4
100
100
100
100
100
100
As shown in , the user may be moving while the proceeding direction of the user (or the device ) is not matched with an axis of the device and the device maintains a random inclination angle. For example, the user may be carrying the device in a bag or a pocket, and walking while using an audio direction guide service from a navigation application. In this case, the heading vector of the device in a bag or a pocket may be not corresponding to the proceeding direction of the user (or the device ).
FIGS. 5A through 5D
are diagrams of a coordinate system that may be applied to an exemplary embodiment.
In order to calculate an inclination angle of a device, information may be received via various sensors in the device, and desired angle information may be obtained by processing the received information. The angle information may be shown by using various coordinate systems, and an angle measurement criterion may vary according to which coordinate system is used. Therefore, it may be valuable to process various pieces of information shown by using various coordinate systems such that the various pieces of information are compatible to one another.
An example of a coordinate system of pedestrian dead reckoning (PDR may include a body frame or a local frame. Various coordinate systems are present, and exemplary embodiments in the present disclosure are not limited to the two coordinate systems described herein. The two coordinate systems are provided only as an example for convenience of description.
FIG. 5A
FIG. 5A
FIG. 5B
FIG. 5B
FIG. 5C
L
B
B
B
B
L
B
B
B
L
B
B
B
L
B
B
B
L
shows a body frame that is randomly positioned to define a local frame, according to an exemplary embodiment. In , a Yaxis of the local frame may be defined as a vector parallel to a plane in which a Yaxis of a body frame is perpendicular to a direction of gravity when the Yaxis and a Zaxis of the body frame is rotated about an Xaxis of the body frame. That is, the Yaxis of the local frame may be perpendicular to a gravitational acceleration vector. In this case, rotation may be performed in two ways, the Yaxis and a Zaxis of the body frame may be rotated in a direction such that an angle between a Zaxis of the rotated body frame and the gravitational acceleration vector does not exceed 90°, as shown in . An Xaxis of the local frame may be defined as a vector parallel to a plane in which the Xaxis of the body frame is perpendicular to the direction of gravity when the Xaxis and the Zaxis of the body frame is rotated about the Yaxis of the local frame of . In this case, rotation may be performed in two ways, and the Xaxis and the Zaxis of the body frame may be rotated such that the Zaxis of the rotated body frame matches with the gravitational acceleration direction. Therefore, a Zaxis of the local frame is the same as the gravitational acceleration direction, as shown in .
L
L
L
L
L
FIG. 5C
The origin of the local frame is the same as the origin defined in the body frame. The subscript ‘L’ of X, Y, and Zof the local frame may indicate the first letter of ‘local frame.’ Therefore, since the Zaxis of the local frame is parallel to a gravitational acceleration axis as shown in , only gravitational acceleration of the Zaxis may be sensed. Three axes of the local frame may be perpendicular to each other. Based on inclined position information between the local frame and the body frame in a 3D coordinate system, a direction and an inclination angle of a device with respect to a proceeding direction of a user may be shown on a horizontal plane that is perpendicular to the gravitational acceleration direction.
In order to identify a position in the local frame and the body frame, a roll angle, a pitch angle, and a yaw angle may be defined based on the local frame. With regard to the roll angle, ‘rolling’ refers to rotation around a front-back direction axis (i.e., x-axis) which is caused by a linear movement along a left-right direction axis (i.e., y-axis) of a coordinate system. With regard to the pitch angle, ‘pitching’ refers to rotation around the left-right direction axis (i.e., y-axis) caused by a linear movement along the x-axis of the coordinate system. With regard to the yaw angle, ‘yawing’ refers to rotation around a vertical direction axis (i.e., z-axis) of the coordinate system.
FIG. 5D
L
L
L
Referring to , the origins of the two coordinate systems are the same. Based on the right-hand rule, when a right hand surrounds the Zaxis, a direction from the palm toward the fingers is a positive direction which may determine the sign of the yaw angle, and a rotation amount may determine a size of the yaw angle. In this case, the yaw angle may be 0° because the local frame is not transformed into the body frame by rotation about the z-axis. Same as the yaw angle, the pitch angle and the roll angle may be determined by using the right-hand rule, respectively based on the Yaxis and the Xaxis. Determining an order of transformation may be valuable when transforming the local frame into the body frame. In the present disclosure, the local frame is transformed in the order of yaw, pitch, and roll. This is because, when transforming the body frame into the local frame, the order of transformation is determined as −1*roll angle, −1*pitch angle, and 0*(−1*yaw angle). The order of transformation may vary depending on the definition of coordinate transformation. Although the definition may vary, a transformation result of the body frame and the local frame (i.e., a position in each of the coordinate systems) does not change.
It should be noted that the body frame and the local frame are merely related to selecting a direction as a positive direction, in an identical space. Since coordinate systems are equivalent when all physical laws may be identically applied, coordinate systems may be transformed into one another. Also, in a coordinate transformation method, transformation processes and formulas may vary depending on how a coordinate system is defined and how a roll angle, a pitch angle, and a yaw angle are defined. However, this is merely a different in terms of expression, and the meaning of coordinate transformation is the same.
FIG. 6
FIG. 6
is a diagram for describing coordinate transformation, according to an exemplary embodiment. In , coordinate transformation is performed with regard to only gravitational acceleration when a device is not moving.
FIG. 6
Referring to , acceleration expressed in a body frame may also be expressed in a local frame. Likewise, information expressed in a local frame may be transformed and expressed in the body frame. Transformation between coordinate systems may vary depending on gravitational acceleration that is sensed in the body frame.
B
B
B
B
B
x
y
z
B
With regard to the body frame, gravitational acceleration Gis sensed via orthogonal projection for each of the three axes, i.e., X, Y, and Zaxes, wherein the subscript ‘B’ refers to ‘body frame.’ Therefore, the gravitational acceleration Gmay be distinguished into g, g, and gwith respect to the three axes. That is, the gravitational acceleration Gis shown as an acceleration component for each of the three axes as shown below in EQN. (1).
G
=[g
,g
,g
B
x
y
z
T
Gravitational acceleration in body frame ] EQN. (1)
B
B
B
B
L
With regard to G, the superscript ‘T’ refers to ‘transpose’ of a vector. Gis a 3×1 vector. Acceleration components may vary depending on a determined coordinate system. The present disclosure mainly describes a transformation of the gravitational acceleration Ginto a local frame that may be distinguished as an acceleration component at a gravitational acceleration axis (transformation of Ginto G).
A transformation matrix may be used to transform information between coordinate systems. Performing coordinate transformation by using a transformation matrix C is shown as below in EQN. (2).
G
=C
*G
L
Coordinate Transformation Matrix
B
EQN. (2)
FIG. 6
B
L
Referring to and EQN. (2), a coordinate system of Gis the body frame, and a coordinate system of Gis the local frame. There may be various reasons for transforming the body frame into the local frame. One of the reasons for performing coordinate transformation is to easily recognize and estimate the user's location. The body frame is usually a piece of information that is obtained by a sensor in a device such as a smartphone, and the local frame is the same as a navigation frame that is frequently used in navigation technology except for a difference in the yaw angle.
B
L
L
L
The body frame may include all components of the gravitational acceleration Gwith respect to the x-axis, y-axis, and z-axis. With regard to acceleration that is generated as the user moves, a gravitational acceleration component and a component other than the gravitational acceleration component cannot be clearly distinguished in the body frame. Accordingly, the inclination angle of the device may not be accurately calculated. However, in the local frame, only the gravitational acceleration component is distinguished, the gravitational acceleration appears only on a vertical axis (Z) of the local frame, and an acceleration component in a proceeding direction of the user with respect to the Xaxis and the Yaxis may be easily shown on a horizontal plane that is perpendicular to the gravitational acceleration. Thus, the inclination angle of the device with respect to the proceeding direction of the user may be accurately calculated.
B
L
EQN. (3) shows coordinate transformation performed by having the coordinate system of Gas the body frame and the coordinate system of the Gas the local frame.
G
=C
*G
L
Coordinate Transformation Matrix
B
EQN. (3)
The coordinate transformation matrix of EQN. (3) is shown in detail in EQN. (4),
<math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mrow><mo>[</mo><mtable><mtr><mtd><msub><mi>g</mi><mi>x</mi></msub></mtd></mtr><mtr><mtd><msub><mi>g</mi><mi>y</mi></msub></mtd></mtr><mtr><mtd><msub><mi>g</mi><mi>z</mi></msub></mtd></mtr></mtable><mo>]</mo></mrow><mi>local</mi></msub><mo>=</mo><mrow><mrow><mo>[</mo><mtable><mtr><mtd><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow></mtd><mtd><mrow><mrow><mrow><mo>-</mo><mi>cos</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φsin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow></mrow></mtd><mtd><mrow><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φsinψ</mi></mrow><mo>-</mo><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow></mtd><mtd><mrow><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φcosψ</mi></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow></mrow></mtd><mtd><mrow><mrow><mrow><mo>-</mo><mi>sin</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φcosψ</mi></mrow><mo>-</mo><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ψ</mi></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mo>-</mo><mi>sin</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mtd><mtd><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φcos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mtd><mtd><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>φcos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mtd></mtr></mtable><mo></mo><mstyle><mspace width="0.em" height="0.ex" /></mstyle><mo>]</mo></mrow><mo></mo><mrow><mo> </mo><msub><mrow><mo>[</mo><mtable><mtr><mtd><msub><mi>g</mi><mi>x</mi></msub></mtd></mtr><mtr><mtd><msub><mi>g</mi><mi>y</mi></msub></mtd></mtr><mtr><mtd><msub><mi>g</mi><mi>z</mi></msub></mtd></mtr></mtable><mo>]</mo></mrow><mi>body</mi></msub></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
wherein φ denotes a roll angle, θ denotes a pitch angle, and ψ denotes a yaw angle.
FIG. 6
The roll angle and the pitch angle of the body frame of may be derived by using EQN. (5) and EQN. (6) below. In EQN. (4), the yaw angle is 0° because the local frame is not transformed into the body frame by rotation about the z-axis.
<math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>Roll</mi><mo></mo><mrow><mo>(</mo><mi>φ</mi><mo>)</mo></mrow></mrow><mo>=</mo><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo></mo><mrow><mo>(</mo><mfrac><mrow><mo>-</mo><msub><mi>g</mi><mi>y</mi></msub></mrow><mrow><mo>-</mo><msub><mi>g</mi><mi>z</mi></msub></mrow></mfrac><mo>)</mo></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
wherein g is the gravitational acceleration.
<math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>Pitch</mi><mo></mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mo>=</mo><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo></mo><mrow><mo>(</mo><mfrac><msub><mi>g</mi><mi>x</mi></msub><msqrt><mrow><msup><mrow><mo>(</mo><msub><mi>g</mi><mi>y</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo>(</mo><msub><mi>g</mi><mi>z</mi></msub><mo>)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mfrac><mo>)</mo></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
wherein g is the gravitational acceleration.
When coordinates are transformed according to EQN. (4), roll, pitch, and yaw angles may be accurately calculated when the acceleration component to be calculated only includes the gravitational acceleration component. However, the acceleration component is not likely to include only the gravitational acceleration component but also include a vertical acceleration component and a horizontal acceleration component, which thus may lead to an error in the coordinate transformation. Therefore, it may be valuable to provide a method of accurately distinguishing a gravitational acceleration component from acceleration information that is sensed by the device.
FIG. 7
is a flowchart of a process of determining a rotation angle of the device, according to an exemplary embodiment.
710
In operation S, a device may receive acceleration information related to a movement of the device, from an accelerometer. The accelerometer may be included in the device and sense the acceleration information that may include a gravitational acceleration component, a vertical acceleration component, and a horizontal acceleration component.
In the present disclosure, the vertical acceleration component refers to an acceleration component that is generated by a height difference that occurs as a user moves, and a horizontal acceleration component refers to an acceleration component related to a proceeding direction of the user (or the device).
720
In operation S, the device may transform coordinates of the device by only using gravitational acceleration information from the acceleration information. The acceleration information may include not only the gravitational acceleration component, but also the vertical and horizontal acceleration components. However, it is possible to only distinguish and use the gravitational acceleration component. When the acceleration component received by the device is expressed in a body frame, the acceleration component may be expressed in the body frame by performing coordinate transformation.
730
In operation S, the device may remove sensor noise by filtering acceleration information expressed in the local frame. Since the vertical and horizontal acceleration components of the acceleration component sensed by the accelerometer based on the movements of the user may change according to a uniform cycle, frequencies of the vertical and horizontal acceleration components may be calculated and filtered by a band pass filter (BPF). The device may calculate the frequencies by deriving a frequency of a magnitude of acceleration. When the user moves forward, due to dynamics, the frequencies of the vertical and horizontal acceleration may be the same as the frequency of the magnitude of acceleration.
The horizontal acceleration information may be acceleration information related to a proceeding direction of the device, and the vertical acceleration information may be acceleration information between the device and a horizontal plane.
Hereinafter, the present disclosure describes a method of determining an inclination angle (rotation angle) of the device by analyzing changes in components of acceleration toward each axis of the device with respect to a proceeding direction of the user.
FIG. 8
is a diagram for describing a change in a vertical height with respect to a proceeding direction of a user, according to an exemplary embodiment.
FIG. 8
7
8
As shown in , the user may move in a constant direction (horizontal direction). Since the user walks with a left leg and a right leg , the center of the user changes according to crossing of the legs. As the center of the user changes, a center of a device that is gripped by the user or moves with the user is also changed. Therefore, an acceleration component of the device changes according to movements of the user.
In order to analyze an acceleration component change according to a proceeding direction of the user, time points of a walking pattern of the user is described as below. First, a height change of the waist of the user is described to analyze a vertical acceleration component.
1
8
8
7
6
7
8
At a time point , the user takes a step by using a right leg in the proceeding direction. When the user takes a step forward by using the right leg , a left leg is located relatively behind, and thus, a height of a waist of the user is the lowest due to a distance between the left leg and the right leg .
2
8
7
8
7
8
6
6
1
At a time point , when the user takes a step by using the right leg in the proceeding direction, the left leg and the right leg cross each other. Since the left leg and the right leg are crossing each other in this case, the height of the waist is greater than the height of the waist of the time point and gradually increases until the maximum value.
3
7
8
7
8
1
6
7
8
At a time point , after the left leg and the right leg cross each other, the left leg is placed at the front and the right leg is located relatively at the back. In this case, as in the time point , the height of the waist decreases due to the distance between the left leg and the right leg and has a minimum value.
4
7
8
7
8
6
3
2
At a time point , the left leg and the right leg cross each other. In this case, since the left leg and the right leg are crossing each other, the height of the waist gradually increases compared to that of the time point until the height is the same as that of the time point .
5
1
8
8
7
6
7
8
A time point is the same as the above-described time point . The user takes a step by using the right leg in the proceeding direction. When the user places the right leg forward, the left leg is placed relatively at the back, and the height of the waist is the lowest according to the distance between the left leg and the right leg .
1
3
5
1
3
5
1
4
6
6
2
4
7
8
1
3
5
7
8
With regard to the height change of the user in the time points , , and , identical patterns are shown in the time points , , and . As a single cycle through the time points to , the height of the waist changes over time in a pattern similar to the sine wave or the cosine wave. The height of the waist has the maximum value at the time points and when the left leg and the right leg cross each other, and has the minimum value at the time points , , and when a distance between the left leg and the right leg is the greatest.
FIG. 9
is a diagram for describing a change in vertical velocity in with respect to proceeding direction of a user, according to an exemplary embodiment.
FIG. 8
FIG. 9
Since velocity may be calculated by differentiating distance with respect to time, a vertical velocity component may be acquired by differentiating a change in a waist height of the user in with respect to time. Accordingly, a change in a vertical velocity with respect to time will be analyzed with reference to .
1
2
First, the waist height of the user increases in between time points and , and vertical velocity has a positive value based on 0 (based on starting to move from a still state). A maximum value of the vertical velocity is at the middle of the two time points, and the vertical velocity decreases after the maximum value.
2
3
The waist height of the user decreases from the maximum value to a minimum in value between time points and , and the vertical velocity has a negative value. The minimum value of the vertical velocity is at the middle of the two time points, and the vertical velocity increases after the minimum value.
3
4
The waist height of the user increases again from the minimum value to the maximum value in between time points and , and the vertical velocity has a positive value. The maximum value of the vertical velocity is at the middle of the two time points, and the vertical velocity decreases again after the maximum value.
4
5
The waist height of the user decreases again from the maximum value to the minimum value in between time points and , and the vertical velocity has a negative value. The minimum value of the vertical velocity is at the middle of the two time points, and the vertical velocity increases again after the minimum value.
1
5
1
2
3
4
2
3
4
5
In between the time points to , the vertical velocity changes over time in a pattern similar to the sine wave or the cosine wave. The vertical velocity has the maximum value at the middle of the time points and and the middle of the time points and , and has the minimum value at the middle of the time points and and the middle of time points and .
FIG. 10
is a diagram for describing a change in vertical acceleration with respect to a proceeding direction of a user, according to an exemplary embodiment.
FIG. 9
FIG. 10
Since velocity may be calculated by differentiating distance with respect to time and acceleration may be calculated by differentiating velocity with respect to time, a vertical acceleration component may be acquired by differentiating a change in vertical velocity of the center of the user of with respect to time. A change in the vertical acceleration with respect to time will be analyzed with reference to .
1
2
2
3
First, a value of acceleration, which is a derivative of velocity with respect to time, decreases from a positive value to a negative value in between time points and . The value of acceleration increases from a negative value to a positive value in between time points and .
3
4
1
2
A pattern between time points and is the same as a pattern between time points and , and thus, a description thereof will be omitted.
4
5
2
3
A pattern between time points and is the same as a pattern between the time points and , and thus, a description thereof will be omitted.
1
5
1
3
5
2
4
1
3
In between the time points to , vertical acceleration changes over time in a pattern similar to the sine wave or the cosine wave. The vertical acceleration has a maximum value at the time points , , and , and a minimum value at the time points and . Also, a change in a waist height of the user has a phase difference of 180° to a change in vertical acceleration. The height, velocity, and acceleration of the user with respect to a vertical axis periodically repeats the pattern in between the time points to , similarly to the sine wave or the cosine wave which repeatedly shows a maximum and a minimum.
FIGS. 8 to 10
As described above with regard to the change in the vertical acceleration with reference to , a change in horizontal acceleration according to a proceeding direction of the user will be described below.
FIG. 11
is a diagram for describing a change in horizontal acceleration with respect to a proceeding direction of a user, according to an exemplary embodiment. Since a horizontal axis is the same as a moving direction of the user, an analysis on a distance and velocity will be omitted.
1
2
7
7
8
In between the time points and , a horizontal acceleration component has a negative value. That is, velocity toward the proceeding direction of the user gradually decreases. The velocity decreases because the left leg is pulled until the left leg and the right leg stepping forward are crossing each other.
2
3
8
8
1
2
8
7
8
2
3
In between the time points and , since the user's weight is added to the right leg and the user moves in the proceeding direction, a value of acceleration is a positive value. This is when the weight of the user starts to be located at the front of the right leg . The value of acceleration is positive because in the case that the user pushes his/her body by applying the same amount of force to legs touching a ground, greater momentum may be created along the horizontal axis when the weight of the user is at the front rather than at the back. In the previous section (between the time points and ), the weight of the user is behind the right leg that is touching the ground, and the left leg is floating in mid-air. If momentum needs to be created in this section, force needs to be horizontally as well as vertically applied to the right leg that is touching the ground in order to raise the weight of the user upward against gravity. That is, additional force against gravity may be valuable. Therefore, in this section, it is more convenient for the user to use the inertia of the body trying to move forward rather than force to move forward. In between the time points and , a vertical proceeding direction of the weight of the user is the same as the direction of gravity. Therefore, in this section, horizontal acceleration created as the user proceeds horizontally is added to vertical acceleration created as the weight free falls, and thus, a greater movement effect may be obtained with a smaller amount of force compared to the previous section.
3
4
1
2
4
5
2
3
A pattern between the time points and is the same as a pattern between the time points and , and a pattern between the time points and is the same as a pattern between the time points and , and thus, descriptions thereof will be omitted.
As the vertical acceleration component, a horizontal acceleration component also has a constant cycle with respect to time, and changes over time in a pattern similar to the sine wave or the cosine wave. Accordingly, the horizontal acceleration is perpendicular to the vertical acceleration in phase.
FIG. 11
In , a maximum value of a positive horizontal acceleration component is greater than an absolute minimum value of a negative horizontal acceleration component, which indicates that the user has increased velocity while moving forward.
FIG. 12
26
32
is a diagram for describing an example in which a user moves with constant velocity and an example in which moves with decreasing velocity, according to an exemplary embodiment;
26
2
3
1
2
26
3
5
1
3
In the example , an absolute value of acceleration in between the time points and is the same as an absolute value of acceleration in between the time points and because acceleration in the proceeding direction of the user is similar to acceleration in an opposite of the proceeding direction. That is, the user moves with constant velocity in the example . A pattern between the time points and is the same as a pattern between the time points and , and thus, a description thereof will be omitted.
32
1
2
2
3
3
5
1
3
In the example , an absolute value of acceleration in between the time points and is greater than an absolute value of acceleration in between time points and because the user decreases velocity and thus acceleration in the opposite of the proceeding direction of the user is greater than acceleration in the proceeding direction. A pattern between the time points and is the same as a pattern between the time points and , and thus, a description thereof will be omitted.
FIGS. 8 to 12
Heretofore, the vertical acceleration component and the horizontal acceleration component have been analyzed with reference to . Since an accelerometer of a device senses not only vertical and horizontal acceleration components but also an acceleration component including a gravitational acceleration component, it may be valuable to clearly distinguish the gravitational acceleration component from the vertical/horizontal acceleration component.
In order to analyze a rotation angle (i.e., roll, pitch, and yaw angles) of the device, gravitational acceleration has to be used on the local frame as in EQN. (4) through (6). Therefore, the roll, pitch, and yaw angles may be accurately calculated by distinguishing the gravitational acceleration component from acceleration information that is sensed by the accelerometer of the device.
FIG. 11
In the present disclosure, a method of distinguishing the gravitational acceleration component from an acceleration component sensed by the accelerometer of the device will be mainly described with reference to .
FIG. 11
1
3
2
1
3
Referring to , the vertical acceleration component and the horizontal acceleration component has a phase difference of 90° and may be shown in the form of sine waves that have maximum and minimum values. When the vertical acceleration component has the maximum value, the horizontal acceleration component is 0. That is, as shown in the drawing, the vertical acceleration component has the maximum value in between the time points and . Since the time points are evenly divided, the vertical acceleration component has the minimum value at the time point , which is in the middle of the time points and .
1
2
1
2
A controller of the device may acquire a gravitational acceleration component by merging the vertical acceleration component and the horizontal acceleration component of the time points and . That is, the horizontal acceleration is 0 at the time point when the vertical acceleration has the maximum value and at the time point when the vertical acceleration has the minimum value, and thus, according to an average acceleration value of the acceleration component of the two time points, the vertical acceleration component also is 0. Therefore, the gravitational acceleration component may be separated from the average of two time points. The roll angle and the pitch angle of the device may be derived by using the gravitational acceleration component.
A time point when the vertical acceleration component has the maximum value is the same as a time point when a magnitude of acceleration sensed by the accelerometer of the device has the maximum value. Hereinafter, it will be proved that a time point when the vertical acceleration component has the maximum value according to the local frame is the same as a time point when the magnitude of acceleration has the maximum value according to the local frame.
Let f(t) be a magnitude of acceleration with respect to time t. Then, the square F(t) of the magnitude of acceleration in the local frame may be calculated as below by using EQN. (7).
F
t
f
t
=AccX
+AccY
+AccZ
2
2
2
2
()=() EQN. (7)
2
2
2
By substituting AccX+AccY+AccZin EQN. (7), EQN. (7) may be shown as EQN. (8).
FIG. 13A
FIG. 13B
FIGS. 8 to 12
FIG. 11
FIG. 13A
1
5
1
11
12
and show two coordinate systems and a local frame used in . Referring to as an example, with regard to a time period between an initial position of the user to a final position of the user, when the initial position of the user is set as an origin, a vertical acceleration is [g+b cos(2πft)], and a horizontal acceleration is −a sin(2πft). Therefore, the square of the magnitude of acceleration expressed by using the coordinate system of may be shown as below in EQN. (8).
F
t
a
ft
+[g+b
ft
2
2
()=[−sin(2π)]cos(2π)] EQN. (8)
In EQN. (8), f denotes step frequency of the user, π denotes the ratio of a circle's circumference to its diameter, t denotes time, g denotes gravitational acceleration and is greater than 0, a denotes a maximum acceleration value with respect to a proceeding direction of the user and is greater than 0, and b denotes a maximum acceleration value excluding gravitational acceleration when the user is moving.
FIG. 13A
FIG. 13B
By using the local frame, EQN. (8) may be expressed as EQN. (9), which is the same as EQN. (8) except for the sign of the vertical acceleration component. It should be noticed that the magnitude of acceleration is the same in two coordinate systems of and , but the sign of the vertical acceleration component is the opposite.
100
In the present disclosure, acceleration information is acquired and calculated based on the proceeding direction of the user (or the device ), but the present disclosure is not limited thereto. The acceleration information may be calculated based on the opposite direction of the proceeding direction, and a rotation angle may be determined by appropriately transforming a positive or negative value according to the direction of acceleration. According to the present disclosure, it is possible to appropriately modify acceleration information and equations used in the method of determining a rotation angle with respect to the proceeding direction, based on the method of determining the rotation angle with respect to the opposite direction of the proceeding direction.
FIG. 14
shows a graph of z-axis acceleration that is acquired by removing acceleration in an x-axis proceeding direction and the gravitational acceleration in a local frame, in the case that the user is matching a position of the device, i.e., a body frame, with the local frame and walking while matching a proceeding direction of the user with an x-axis of the local frame.
FIG. 14
FIG. 11
FIG. 13
FIG. 14
FIG. 14
As shown in , although sensor noise is partially included, two accelerations are perpendicular to each other. The vertical acceleration of is symmetrical with respect to a time axis because a vertical axis direction of the local frame is opposite to a vertical axis direction of the drawing, as described with reference to . In , a horizontal magnitude of acceleration refers to a maximum absolute value of acceleration when the user increases velocity, maintains constant velocity, or decreases velocity. In , the vertical acceleration is greater than the horizontal acceleration. This has been recognized though various experiments, and is used as a valuable feature when proving the above-described processes via EQN. (9) below.
<math overflow="scroll"><mtable><mtr><mtd><mtable><mtr><mtd><mrow><mrow><mi>F</mi><mo></mo><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><msup><mi>a</mi><mi>w</mi></msup><mo></mo><mrow><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><msup><mrow><mo>[</mo><mrow><mrow><mo>-</mo><mi>g</mi></mrow><mo>-</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow><mn>2</mn></msup></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><msup><mi>a</mi><mi>w</mi></msup><mo></mo><mrow><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><msup><mrow><mo>[</mo><mrow><mi>g</mi><mo>+</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow><mn>2</mn></msup></mrow></mrow></mtd></mtr></mtable></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
EQN. (10) shows differentiating EQN. (9) with respect to time to acquire maximum and minimum values of F(t) of EQN. (9).
<math overflow="scroll"><mtable><mtr><mtd><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mtable><mtr><mtd><mrow><mfrac><mrow><mo></mo><mrow><mi>F</mi><mo></mo><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mi /><mo></mo><mrow><mrow><mn>4</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>f</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>a</mi><mn>2</mn></msup><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mn>4</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>fb</mi><mo></mo><mrow><mo>(</mo><mrow><mi>g</mi><mo>+</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mo>-</mo><mn>4</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>f</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>b</mi><mo></mo><mrow><mo>(</mo><mrow><mi>g</mi><mo>+</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mo>-</mo><mn>4</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>f</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>[</mo><mrow><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>+</mo><mrow><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow></mrow></mrow></mtd></mtr></mtable></mtd><mtd><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle></mtd></mtr></mtable></math>
2
2
In order to find a maximum value and a minimum value, sin(2πft)=0 or bg+(b−a)cos(2πft)=0 has to be satisfied for the derivative to be equal to 0.
2
2
First, in order to satisfy bg+(b−a)cos(2πft)=0, cos(2πft) may be either 0, positive, or negative.
2
2
i) When cos(2πft) is 0, i.e., cos(2πft)=0, bg is greater than 0 and bg+(b−a)cos(2πft)>0. Thus, none of the conditions above is satisfied.
2
2
ii) When cos(2πft) is positive, i.e., cos(2πft)>0, bg+(b−a)cos(2πft)=0 has to be satisfied, as shown below in EQN. (11).
a
ft
bg+b
ft
2
2
cos(2π)=cos(2π) EQN. (11)
EQN. (11) rearranged with respect to ‘a’ is shown below as in EQN. (12).
a
bg+b
ft
ft
2
=√{square root over (cos(2π))/cos(2π))} EQN. (12)
2
2
2
2
2
If a is less than √{square root over (bg+bcos(2πft))/cos(2πft))}, bg+(b−a)cos(2πft)>0. √{square root over ((bg+bcos(2πft))/cos(2πft))} has the minimum value is when t=0, i.e., the denominator is the greatest, and thus, a<√{square root over (b−bg)}.
2
2
2
2
According to experiments for comparing maximum horizontal acceleration and maximum vertical acceleration, the maximum horizontal acceleration ‘a’ is smaller than the maximum vertical acceleration ‘b,’ and thus, bg+(b−a)cos(2πft)>0 is satisfied. That is, since bg+(b−a)cos(2πft)=0, the condition above is not satisfied.
2
2
2
2
2
2
iii) When cos(2πft) is smaller than 0 (i.e., cos(2πft)<0), (b−a)cos(2πft)≧0, bg+(b−a)cos(2πft)>0, or bg+(b−a)cos(2πft)=0.
2
2
Based on experiments, in order to satisfy bg+(b−a)cos(2πft)=0 when a<b, EQN. (13) has to be satisfied.
<math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mfrac><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac></mrow></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>13</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
wherein a<b and cos(2πft)<0.
2
2
Since EQN. (13) may satisfy bg+(b−a)cos(2πft)=0 based on the values of ‘a’ and ‘b,’ EQN. (13) may have an extremum.
As a result, the magnitude of acceleration may have an extremum, i.e., a maximum value/minimum value, when both sin(2πft)=0 and EQN. (13) are satisfied, which is shown as below.
<math overflow="scroll"><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mrow><mn>1</mn><mo>)</mo></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>=</mo><mn>0</mn></mrow><mo>,</mo><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mrow><mo>-</mo><mn>1</mn></mrow></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mn>2</mn></mrow><mo>)</mo></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>=</mo><mn>0</mn></mrow><mo>,</mo><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mn>1</mn></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mn>3</mn></mrow><mo>)</mo></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>=</mo><mfrac><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac></mrow><mo>,</mo><mrow><mrow><mi>wherein</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>a</mi></mrow><mo><</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>and</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo><</mo><mn>0</mn></mrow></mrow><mo>)</mo></mrow></math>
The extremum of F(t) is obtained with respect to t that satisfies the condition 1), 2), or 3). Extrema under the conditions may be compared as below. First, the extremum of 1) compared with the extremum of 3) is as below in EQN. (14).
<math overflow="scroll"><mtable><mtr><mtd><mtable><mtr><mtd><mrow><mrow><msup><mrow><mo>(</mo><mrow><mi>g</mi><mo>-</mo><mi>b</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mrow><mo>[</mo><mtable><mtr><mtd><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mrow><msup><mi>a</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo></mrow></mtd></mtr><mtr><mtd><mrow><msup><mi>g</mi><mn>2</mn></msup><mo>+</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>g</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>+</mo><msup><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></mtd></mtr></mtable><mo>]</mo></mrow></mrow><mo>=</mo><mi /><mo></mo><mrow><msup><mrow><mo>(</mo><mrow><mi>g</mi><mo>-</mo><mi>b</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mrow><mo>(</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>g</mi><mn>2</mn></msup><mo>+</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>g</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><msup><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow><mn>2</mn></msup></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><msup><mrow><mo>(</mo><mrow><mi>g</mi><mo>-</mo><mi>b</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mrow><mo>(</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>g</mi><mn>2</mn></msup><mo>+</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>g</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mo>(</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><msup><mrow><mo>(</mo><mrow><mi>g</mi><mo>-</mo><mi>b</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mrow><mo>(</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>g</mi><mn>2</mn></msup><mo>-</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mfrac><mrow><mrow><mrow><mo>(</mo><mrow><msup><mi>g</mi><mn>2</mn></msup><mo>-</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mrow><mrow><mo>(</mo><mrow><mrow><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>-</mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mo>+</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow></mrow><mo>)</mo></mrow></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mfrac><mtable><mtr><mtd><mrow><mrow><mo>(</mo><mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mo>-</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>b</mi><mn>3</mn></msup><mo></mo><mi>g</mi></mrow><mo>+</mo><msup><mi>b</mi><mn>4</mn></msup><mo>-</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>a</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>-</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo></mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mrow><mo>)</mo></mrow><mo>+</mo></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo></mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mo>+</mo><msup><mi>a</mi><mn>4</mn></msup><mo>-</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow></mrow><mo>)</mo></mrow><mo>+</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow></mrow></mtd></mtr></mtable><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mfrac><mrow><mo>(</mo><mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow><mo>-</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>b</mi><mn>3</mn></msup><mo></mo><mi>g</mi></mrow><mo>+</mo><msup><mi>b</mi><mn>4</mn></msup><mo>+</mo><mrow><mn>2</mn><mo></mo><msup><mi>a</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>-</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>a</mi><mn>2</mn></msup><mo></mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mo>+</mo><msup><mi>a</mi><mn>4</mn></msup></mrow><mo>)</mo></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mfrac><mrow><mo>(</mo><mrow><msup><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>g</mi><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow></mrow><mo>)</mo></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow></mtd></mtr></mtable></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>14</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
2
2
2
2
2
When (b−a)=X in EQN. (14), G(X)=X−2bgX+bg.
With respect to a random value of ‘a’ and ‘b,’ a discriminant of
<math overflow="scroll"><mrow><mrow><mi>G</mi><mo></mo><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow><mo>=</mo><mrow><mfrac><mi>D</mi><mn>4</mn></mfrac><mo>=</mo><mrow><mrow><msup><mrow><mo>(</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><msup><mi>g</mi><mn>2</mn></msup></mrow></mrow><mo>=</mo><mn>0.</mn></mrow></mrow></mrow></math>
Therefore, G(X) has an equal root, and X is as below in EQN. (15).
<math overflow="scroll"><mtable><mtr><mtd><mrow><mi>X</mi><mo>=</mo><mrow><mfrac><mrow><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>±</mo><msqrt><mn>0</mn></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>15</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
Therefore, when X=bg, G(X) has a minimum value of 0 as below.
G
bg
bg
bgbg++b
g
2
2
2
()=()−2=0
Thus, a comparison of the three extrema is as below.
<math overflow="scroll"><mrow><mo>∴</mo><mrow><msup><mrow><mo>(</mo><mrow><mi>g</mi><mo>+</mo><mi>b</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>></mo><msup><mrow><mo>(</mo><mrow><mi>g</mi><mo>-</mo><mi>b</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>≥</mo><mrow><mo>(</mo><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mrow><msup><mi>a</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>g</mi><mn>2</mn></msup><mo>+</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>g</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>+</mo><msup><mrow><msup><mi>b</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mfrac><mrow><mrow><mo>-</mo><mi>b</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow></math>
The comparison above corresponds to a comparison of acceleration (F(t)) under the conditions 1), 2), and 3) of EQN. (13).
That is, an extremum of sin(2πft)=0, cos(2πft)=1, is greater than an extremum of sin(2πft)=0, cos(2πft)=−1, and an extremum of sin(2πft)=0, cos(2πft)=−1 is the same as or greater than
<math overflow="scroll"><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mrow><mfrac><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac><mo>.</mo></mrow></mrow></math>
2
Here, (a+b)is an extremum as well as a maximum value of F(t), and may be proved as below.
F
t
a
ft
g+b
ft
2
2
2
()=sin(2π)+(cos(2π))
EQN. (16) shows a second derivative of F(t) differentiated with respect to t for obtaining a maximum value and a minimum value.
<math overflow="scroll"><mtable><mtr><mtd><mtable><mtr><mtd><mrow><mfrac><mrow><msup><mo></mo><mn>2</mn></msup><mo></mo><mrow><mi>F</mi><mo></mo><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mrow><mrow><mo></mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mi /><mo></mo><mfrac><mrow><mo></mo><mrow><mo>(</mo><mrow><mrow><mo>-</mo><mn>4</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>f</mi><mo></mo><mstyle><mspace width="0.6em" height="0.6ex" /></mstyle><mo></mo><mrow><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mo>[</mo><mrow><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>+</mo><mrow><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mrow><mo>-</mo><mn>8</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>[</mo><mrow><mrow><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>+</mo><mrow><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow></mrow><mo>+</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mrow><mo>-</mo><mn>8</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><msup><mi>cos</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mrow><mo>-</mo><mn>8</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo></mo><mrow><msup><mi>cos</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mrow><msup><mi>cos</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mrow><mo>-</mo><mn>16</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><msup><mi>cos</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ft</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd></mtr></mtable></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
2
Therefore, when sin(2πft)=0, cos(2πft)=1 is satisfied, F(t)=(g+b). Equation below shows a second derivative of F(t):
<math overflow="scroll"><mtable><mtr><mtd><mrow><mfrac><mrow><msup><mo></mo><mn>2</mn></msup><mo></mo><mrow><mi>F</mi><mo></mo><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mrow><mrow><mo></mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mi /><mo></mo><mrow><mrow><mrow><mo>-</mo><mn>16</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>+</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mrow><mrow><mrow><mo>-</mo><mn>8</mn></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mi>b</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>g</mi></mrow><mo>-</mo><mrow><mn>8</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mi>π</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>f</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo><</mo><mn>0</mn></mrow></mrow></mtd></mtr></mtable></math>
Thus, F(t) has the maximum value when the condition above is satisfied.
FIG. 10
FIG. 10
F(t) in this case is the square of the magnitude of acceleration in EQN. (7). A time point when the square of the magnitude of acceleration reaches the maximum is the same as a time point when the magnitude of acceleration reaches the maximum. A vertical axis in the local frame is toward a direction from the head of the user to the legs of the user, which is opposite to the vertical axis direction defined with reference to . Therefore, the formulas that have been proved so far have also been proved with regard to the local frame, and sin(2πft)=0, cos(2πft)=1 in the local frame indicates a point where sin(2πft)=0, cos(2πft)=−1 because the vertical axis direction is opposite to that of . That is, it is proved that the vertical acceleration reaches the maximum when the legs of the user cross each other (when a waist height of the user reaches the maximum), and at the same time, acceleration of three axes (2 norm value of acceleration vector) F(t) has the maximum value.
According to the calculation process above, the maximum value of acceleration sensed by the accelerometer of the device is the same as the maximum value of vertical acceleration that is expressed by using gravitational acceleration and cos(2πft). However, the minimum value of vertical acceleration may be different from the minimum value of acceleration. Therefore, a time point when the acceleration reaches the minimum value may be obtained by calculating an average of two time points when acceleration has the maximum value and is near the minimum value.
2
2
2
The theoretical calculation process may be understood through simulation. The maximum acceleration in a vertical direction is changed from 0.1 m/sto 30 m/swith an interval of 0.1 m/s, the horizontal acceleration is changed with an interval of 0.1 from 0.1 times to 0.9 times the acceleration. This reflects the experiment result in which the maximum value of the vertical acceleration is greater than the maximum value of the horizontal acceleration. Also, vertical and horizontal triangular pulses are simulated with an interval of 0.01° with respect to one cycle.
All simulation results show a time point when the vertical acceleration reaches the maximum is the same as a time point when the acceleration reaches the maximum. However, in some cases, a time point when the vertical acceleration reaches the minimum is different from a time point when the acceleration reaches the maximum.
FIG. 15
is a graph showing that, according to a simulation, a time point when vertical acceleration reaches a minimum value may be different from a time point when acceleration reaches a minimum value in a local frame.
Although all analyses have been performed in the local frame, the acceleration from the accelerometer is all expressed in the body frame. In this case, a time point when vertical acceleration reaches a maximum value in the local frame being the same as a time point when acceleration reaches a maximum value in the local frame indicates that a time point when vertical acceleration reaches a maximum value in the body frame is the same as a time point when acceleration reaches a maximum value in the body frame. This is because a time point when acceleration sensed by three-axes accelerometers reaches the maximum value is the same as a time point when the acceleration reaches the minimum value whether the magnitude of acceleration is expressed in the local frame, in the body frame, or in any other coordinate systems with three perpendicular axes. Therefore, a roll angle and a pitch angle of the device may be obtained by only extracting gravitational acceleration from the maximum value of three-axes magnitude of acceleration (2 norm value of 3×1 acceleration vector) sensed by the accelerometer in the body frame.
The device may obtain information about a time point of a maximum value and a time point of a minimum value. The controller of the device may calculate a sum of averages of acceleration values according to axes with respect to the two time points, and obtain acceleration information in which only a gravitational acceleration component is only included in an acceleration component by removing a vertical acceleration component and a horizontal acceleration component.
Consequently, based on dynamics according to movements of the user, a roll angle and a pitch angle may be accurately calculated by using EQN. (5) and EQN. (6) to separate the gravitational acceleration component from acceleration components of the axes of the accelerometer of the device. A coordinate transformation matrix may be derived by substituting the calculated roll angle and the calculated pitch angle into EQN. (4). Then, three-axis acceleration in the local frame may be obtained by coordinate transforming three-axis acceleration in the body frame. Next, horizontal acceleration expressed in the x-axis and y-axis of the local frame may be calculated. Thus, an inclination angle on a horizontal plane of the device with respect to the proceeding direction of the user may be obtained.
FIG. 16
is a diagram for describing a method of filtering acceleration components to reduce error due to noise when calculating a maximum value of a magnitude of acceleration in a body frame, according to an exemplary embodiment.
Rotation angle information of the device, which is obtained by the accelerometer of the device based on a gravitational acceleration component, may include noise. Therefore, error of the rotation angle of the device may be reduced by filtering obtained acceleration information.
It has been described above that acceleration changes according to a certain cycle over time as the user moves. Therefore, vertical acceleration and horizontal acceleration may each have a frequency, which will be referred to as “step frequency” for convenience. When moving, the user may cross left and right legs according to a certain cycle. However, this cycle may not be constant. Therefore, an average cycle may be estimated for a certain period so that a step frequency of the user may be adaptively estimated even when the step frequency changes.
FIG. 16
29
30
29
30
On a graph showing vertical acceleration of , gravitational acceleration may be extracted by calculating an average of acceleration of a time point when a vertical magnitude of acceleration has a maximum value and an average of acceleration of a time point when the vertical magnitude of acceleration has a minimum value. However, error may be caused by sensor noise. Therefore, the average of acceleration of each of the two time points may be obtained based on previous and following time points of each of the time points and . In the average of acceleration obtained in the body frame based on such filtering process, an average of vertical acceleration is a sum of a maximum value and a minimum value that offset one another, and horizontal acceleration is 0. Therefore, only the gravitational acceleration with less error caused by noise remains. If a magnitude of positive horizontal acceleration is similar to a magnitude of negative horizontal acceleration, T′ may be increased by half cycles and a total cycle may be averaged to thus remove the gravitational acceleration. If the magnitude of the positive horizontal acceleration is similar to a magnitude of the negative acceleration, T′ may be extended by N/2, wherein N is a natural number N, averaging N cycle, and thus removing the gravitational acceleration.
FIG. 17
is a diagram showing a magnitude of three-axis acceleration, a magnitude of three-axis acceleration when the gravitational acceleration is removed, and a true value of gravitational acceleration in a body frame.
The magnitude of three-axis acceleration may have a great error similar to the sine wave based on the true value of gravitational acceleration because of vertical acceleration and horizontal acceleration that are generated as the user moves. However, the proposed method effectively removes the vertical acceleration and the horizontal acceleration with respect to a proceeding direction of the user, and thus extracts a value that is almost the same as the true value of gravitational acceleration. This corresponds to a theoretical conclusion that the method proposed in the exemplary embodiments provides an optimum solution via mathematical proof. When a roll angle and a pitch angle are used without removing acceleration in which vertical and horizontal acceleration of the user in the body frame, large position error may be generated. This position error may cause a large coordinate transformation error, and thus lead to errors in x-axis acceleration and y-axis acceleration in the local frame, which thus generates error in the inclination angle of the device with respect to the proceeding direction of the user.
T
The x-axis and y-axis acceleration in the local frame may be obtained by extracting gravitational acceleration from the acceleration component of the body frame according to the above-described process, calculating a roll angle and a pitch angle of the device, substituting the calculated roll angle and the pitch angle to the coordinate transformation matrix of EQN. (4), and performing coordinate transformation. The method of obtaining x-axis and y-axis acceleration in the local frame indicates that acceleration of the local frame is a 3×1 acceleration vector that is calculated by multiplying a 3×1 acceleration vector ‘[x-axis acceleration, y-axis acceleration, z-axis acceleration]’ of the body frame at a right side of the 3×3 coordinate transformation matrix C of EQN. (4). Therefore, first two rows of the 3×1 acceleration vector of the local frame is the x-axis and y-axis acceleration of the local frame.
The inclination angle of the device on a horizontal axis with respect to the proceeding direction of the user may be obtained based the x-axis and y-axis acceleration of the local frame. However, angle error may be generated due to sensor noise. The present disclosure suggests band-pass filtering to remove the noise.
FIG. 18
is a diagram of removing noise of x-axis and y-axis acceleration in the local frame.
FIG. 18
50
51
52
53
53
54
In , time points , , and show processes of adaptively estimating, over time, a frequency of a magnitude of acceleration obtained from the body frame. The frequency may be estimated by using one cycle of steps or N cycles of steps. The frequency is used as a central frequency of a band-pass filter, and the central frequency may be configured to change according to step frequency of the user along a time axis. A bandwidth of the band-pass filter is also a valuable parameter and may be determined by tuning. By performing band-pass filtering on the x-axis and y-axis acceleration in the local frame, acceleration with reduced sensor noise may be obtained.
FIG. 19
is a diagram of an inclination angle of a device, according to an exemplary embodiment.
FIG. 19
The device may not be located in the same direction as a moving (proceeding) direction of the user, and may be located with an inclination (rotation) angle. As shown in , the proceeding direction of the according to an exemplary embodiment may form an angle with an x-axis and a y-axis of the local frame. Ax denotes acceleration with respect to the x-axis that is band-pass filtered, and Ay denotes acceleration with respect to the y-axis that is band-pass filtered. In this case, the inclination angle of the device with respect to the proceeding direction of the user on the x-axis and the y-axis horizontal planes of the local frame is as shown below in EQN. (17).
<math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>Inclination</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>angle</mi></mrow><mo>=</mo><mrow><mi>Ψ</mi><mo>=</mo><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>A</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>y</mi></mrow><mrow><mi>A</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>x</mi></mrow></mfrac><mo>)</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQN</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></mtd></mtr></mtable></math>
As in EQN. (17), the estimated inclination angle of the device may be applied to various applications in the device.
FIG. 20A
FIG. 20B
and show graphs of large to small estimation errors in the inclination angle of the device with respect to the proceeding direction of the user on a horizontal plane perpendicular to the gravitational acceleration formed by the x-axis and the y-axis of the of the local frame, obtained by performing experiments.
FIG. 20A
FIG. 20B
FIG. 20A
FIG. 20A
shows the inclination angle of the device with respect to the proceeding direction of the user estimated by extracting the gravitational acceleration according to the above-described method, and an estimation result obtained by using the acceleration that includes the gravitational acceleration and the vertical and horizontal acceleration. is an enlarged graph of an estimation error range of . When the acceleration component other than the gravitational acceleration has not been properly removed as in , position error of the device may be generated, and components of the horizontal acceleration may be distorted through inaccurate coordinate transformation, and thus, estimation error may increase. The estimation error is derived by using data obtained by performing experiments, not by simulations.
FIGS. 20A and 20B
As shown in , eight angle differences from 0° to 315° with an interval of 45° has been tested 26 times. 1,354 steps were made during the tests, and error related to each step is shown in the order of smallest to greatest. The angle differences have an average of 1.2° and a standard deviation of 9.3°. This result is regarded as an actual test result of the theory on obtaining the inclination angle of the device with respect to the proceeding direction of the user by using only the accelerometer.
FIG. 21
100
is a schematic block diagram of the device , according to an exemplary embodiment.
100
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The device according to an exemplary embodiment may include a controller , a sensor , an input/output (I/O) unit , and a storage unit . In addition, a display unit (not shown) displaying information of the device and a communicator (not shown) performing communication with another device.
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The sensor may obtain various types of information from sources outside the device . The sensor may include an accelerometer that obtains acceleration of the device and environment information such as temperature, humidity, position, and pressure.
130
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100
The I/O unit may include an input unit receiving information and commands from the sources outside the device , and an output unit transmitting information and commands processed in the device to external sources.
140
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100
The storage unit may store the information processed in the device and the information received from the sources outside the device .
100
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The device according to an exemplary embodiment may be a smartphone that includes an operating system (OS), and capable of performing Internet connection and executing various programs. The smartphone may be a digital mobile device including an OS and communication functions so that content may be used in a convenient user environment (user interface/user experience). Alternatively, the device may include a multimedia player or a personal computer.
110
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The controller according to an exemplary embodiment may process acceleration information sensed by the device by using EQNS. (1) through (17). The controller may process information that is input to the device according to preset operations.
110
100
100
The controller may transform coordinates of the obtained acceleration information, filter the acceleration information on the converted coordinates, and determine a rotation angle with respect to a proceeding direction of the device by using gravitational acceleration information on the converted coordinates. In this case, the gravitational acceleration information may be derived by using information about time points when vertical and horizontal acceleration components with respect to the proceeding direction of the device have maximum values, from among the acceleration information.
110
100
The controller may transform the obtained acceleration information from coordinates on a coordinate system based on the device into coordinates on a coordinate system based on the direction of gravity.
110
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100
The controller may filter the acceleration information after transforming the acceleration information into a frequency range. In this case, the filtering process may be band-pass filtering. For example, the controller may band-pass filter on the acceleration information that is transformed into a frequency range based on a central frequency that is determined by using dynamics of the device .
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The controller may encode or decode data that is input via the I/O unit . The controller provides a user interface based on the OS of the device . The user interface may correspond to user's usage patterns.
100
100
The display unit may display data that is processed by the device in the user interface. Also, when an instruction for the device is needed from the user, the display unit may display information on a screen to guide the user to input various instructions.
The communicator may transmit and receive data and commands from other devices. The communicator may include any type of well-known communication modules, such as an infrared communication module, a radio communication module, or an optical communication module. For example, an infrared communication module that supports the Infrared Data Association (IrDA) protocol may be used as the communicator. As another example, a communication module utilizing the 2.4 GHz frequency band or a communication module utilizing Bluetooth may be used as the communicator.
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The sensor according to an exemplary embodiment may sense features that may be measured in or outside the device . The sensor may include the accelerometer that may obtain movements of the device in a 3D space as acceleration information.
130
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The I/O unit according to an exemplary embodiment may receive a command from an external source and output processed information. For example, when the device is a smartphone, the I/O unit may receive a key input or a touch input, and output processed information on a screen or via sound.
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100
The input unit of the I/O unit may include at least one of Universal Serial Bus (USB), Parallel Advanced Technology Attachment (PATA), Serial Advanced Technology Attachment (SATA), flash media, Ethernet, Wi-Fi, and Bluetooth as an interface for receiving data such as content displayed on the display unit. In some cases, the device may receive data via an information storage unit (not shown) such as an optical disk drive or a hard disk drive.
100
The device according to an exemplary embodiment may also include a camera unit (not shown) that includes an optical image sensor. Images that are received via the camera unit may be processed as a single piece of data.
100
100
The input unit may further include a temperature or humidity sensor. The input unit may not only include a temperature sensor for measuring temperature inside the device , but also a temperature sensor for measuring temperature outside the device . The humidity sensor for measuring humidity may also be included in the input unit.
Also, the input unit may be a touch screen having a layered structure of a touch panel and an image display panel. The touch panel may be, for example, a capacitive touch panel, a resistive touch panel, or an infrared touch panel. The image display panel may be, for example, a liquid crystal display panel or an organic light-emitting display panel. Since such touch panels are well-known in the art, detailed description of a structure of the touch panel will be omitted. The image display panel may display graphics of the user interface.
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The storage unit according to an exemplary embodiment may store information that is processed by the controller . Also, the storage unit may store information sensed by the sensor and information received from other devices. The storage unit may classify such information as databases and store therein.
The exemplary embodiments can be written as computer programs and can be implemented in general-use digital computers that execute the programs using a computer-readable recording medium. Examples of the computer-readable recording medium include magnetic storage media (e.g., read-only memory (ROM), floppy disks, hard disks, etc.), optical recording media (e.g., CD-ROMs, or DVDs), etc.
It should be understood that exemplary embodiments described herein should be considered in a descriptive sense only and not for purposes of limitation. Descriptions of features or aspects within each exemplary embodiment should typically be considered as available for other similar features or aspects in other exemplary embodiments.
While one or more exemplary embodiments have been described with reference to the figures, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope as defined by the following claims.
BRIEF DESCRIPTION OF THE DRAWINGS
These and/or other aspects will become apparent and more readily appreciated from the following description of the exemplary embodiments, taken in conjunction with the accompanying drawings in which:
FIG. 1
is a diagram of a rotation axis of a device, according to an exemplary embodiment;
FIGS. 2 to 4
are diagrams of an inclined state of a device with respect to a proceeding direction of the device, according to an exemplary embodiment;
FIGS. 5A to 5D
are diagrams of a coordinate system that may be applied to an exemplary embodiment;
FIG. 6
is a diagram for describing coordinate transformation, according to an exemplary embodiment;
FIG. 7
is a flowchart of a process of calculating an angle of a device, according to an exemplary embodiment;
FIG. 8
is a diagram for describing a change in a vertical height with respect to a proceeding direction of a user, according to an exemplary embodiment;
FIG. 9
is a diagram for describing a change in vertical velocity with respect to a proceeding direction of a user, according to an exemplary embodiment;
FIG. 10
is a diagram for describing a change in vertical acceleration with respect to a proceeding direction of a user, according to an exemplary embodiment;
FIG. 11
is a diagram for describing a change in horizontal acceleration with respect to a proceeding direction of a user, according to an exemplary embodiment;
FIG. 12
is a diagram for describing examples in which a user moves with constant velocity and moves with decreasing velocity, according to an exemplary embodiment;
FIGS. 13A and 13B
are diagrams of a coordinate system before and after coordinate transformation, according to an exemplary embodiment;
FIG. 14
is a graph showing z-axis acceleration in a transformed coordinate system, according to an exemplary embodiment;
FIG. 15
is a graph showing that, according to a simulation, a time point when vertical acceleration has a minimum value in a local frame may be different from a time point when a magnitude of acceleration has a minimum value;
FIG. 16
is a diagram for describing a method of filtering acceleration components according to a proceeding direction of a user, according to an exemplary embodiment;
FIG. 17
is a graph showing gravitational acceleration in a coordinate system before coordinate transformation, according to an exemplary embodiment;
FIG. 18
is a diagram for describing a method of removing noise via filtering, according to an exemplary embodiment;
FIG. 19
is a diagram of an inclination angle of a device, according to an exemplary embodiment;
FIG. 20A
FIG. 20B
and show graphs of inclination angle estimation errors of a device, according to an exemplary embodiment; and
FIG. 21
is a schematic block diagram of a device, according to an exemplary embodiment. | |
The budget deficit is the difference between the money federal government takes in, called receipts, and what it spends, called outlays each year. The U.S. government has run a multibillion-dollar deficit almost every year in modern history, spending much more than it takes in.
The opposite of a budget deficit, a budget surplus occurs when the government’s revenue exceeds current expenditures resulting in an excess of money that can be used as needed.
In fact, the government has recorded budget surpluses in only five years since 1969, most of them under Democratic President Bill Clinton.
Running a budget deficit adds to the national debt and, in the past, has forced Congress to increase the debt ceiling under numerous presidential administrations, both Republican and Democrat, to allow the government to meet its statutory obligations.
Although federal deficits have shrunk markedly in recent years, the CBO projects that under current law increased spending for Social Security and major health care programs, like Medicare, along with increasing interest costs will cause the national debt to rise steadily over the long term.
The larger deficits would cause federal debt to grow faster than the economy. By 2040, CBO projects, the national debt will be more than 100% of the nation’s Gross Domestic Product (GDP) and continue on an upward path – “a trend that cannot be sustained indefinitely,” notes the CBO.
Notice particularly the sudden jump in the deficit from $162 billion in 2007, to $1.4 trillion in 2009. This increase was due primarily to spending for special, temporary government programs intended to re-stimulate the economy during the "great recession" of that period.
Here is the actual and projected budget deficit or surplus by fiscal year, according to Congressional Budget Office data for modern history.
In order to put the federal deficit into proper perspective, it must be viewed in terms of the government’s ability to pay it back. Economists do this by comparing the deficit to Gross Domestic Product (GDP)—the measure of the overall size and strength of the U.S. economy.
This “debt-to-GDP ratio” is a ratio between the cumulative government debt and the GDP over time. A low debt-to-GDP ratio indicates that the nation’s economy is producing and selling enough goods and services to pay back the federal deficit without incurring further debt. In simple terms, a larger economy can sustain a larger budget, and thus a larger budget deficit.
According to the Senate Budget Committee, in the fiscal year 2017, the federal deficit was 3.4% of GDP. For the fiscal year 2018, when the U.S. government operated under its largest budget in history, the deficit was estimated to be 4.2% of GDP. Remember, the lower the debt-to-GDP percentage, the better. Clearly, the more you spend, the harder it is to pay back your debts. | https://www.thoughtco.com/history-of-us-federal-budget-deficit-3321439 |
Hello and welcome! I am an associate professor specializing in philosophy of science and interdisciplinary collaboration in the Department of Knowledge Integration.
Knowledge Integration, or 'KI' as it is affectionately known, is an interdisciplinary honors program that teaches students how to collaborate across disciplines and in diverse teams. I am honored to be part of this amazing program and the incredible community that we have built!
My research focuses on ways to increase engagement between those in my own discipline, philosophy of science, and the rest of the world, including scientists, policymakers, and diverse publics. In short, I want to help philosophers use their skills to make the world a better place. I regularly collaborate with students and faculty from a variety of disciplines, such as philosophy, sociology, psychology, and engineering. Please visit my Research and Publications pages for more information.
I love working with students, and I'm fortunate to get to teach a variety of courses, such as INTEG 220: Nature of Scientific Knowledge, INTEG 221: The Social Nature of Knowledge, INTEG 210: Making Collaboration Work, and INTEG 410: Interdisciplinary Collaboration. Most of my courses are open to all students, so if you're interested, you can check out my course descriptions.
I'm originally from Minnesota, though I've lived in several places throughout North America, as well as Australia and Germany. In 2009, I moved to Ontario and am proud to call Canada my home. I currently live in Waterloo with my partner and my adorable little dog named Scrappy. | https://uwaterloo.ca/scholar/kplaisan |
If cultural property protection is not identified as an issue either before an armed conflict, or when prioritising activity following an environmental disaster, no resources will be allocated to it. No preparations will be made for its protection (such as practicing emergency evacuation in museums), and no military unit will be allocated any responsibility for it. This may well lead to a situation where cultural property is ignored, damaged, destroyed, and/or looted.
Mitigation: It is essential for the heritage sector to try to ensure that cultural property protection is fully integrated and embedded into planning by both politicians and the armed forces – and that resources and responsibilities are allocated to it. At the same time it is essential for the heritage sector to do everything in its own power to plan for disaster risk reduction through, for example: making sure catalogues and inventories are up-to-date and digitised; carrying out regular risk assessments; having, and regularly testing, clear disaster and evacuation plans (including safeguarding the heritage from possible post-disaster damage – for example, from secondary environmental disaster or looting); having good relations and effective communications with emergency organisations and the military; and ensuring all heritage staff are well-trained regarding disaster risk reduction.
Photo: Map showing areas to be spared destruction during World War II: Tubingen. NARA M1944, Records of the American Commission for the Protection and Salvage of Artistic and Historic Monuments in War Areas, 1943-46, via the National Archives and Fold 3.
See key documents on CPP and the military in our Document Library, or see recent reports and documents by armed forces in our Document Library. | https://theblueshield.org/lack-of-planning/ |
-Essential to cardiovascular function Potassium activates many enzymatic reactions and is essential to a number of physiologic processes including transmission of nerve impulses; contraction of cardiac smooth and skeletal muscles, gastric secretion, renal function; tissue synthesis; and carbohydrate metabolism. Potassium is the major cation of intracellular fluid and is essential for maintenance of acid-alkaline balance isotonicity and electrodynamic characteristics of the cell. In addition it works with sodium to regulate water balance heart rhythm and normal nerve and muscle function. Potassium is an essential mineral that offers a wide range of nutritional support to ensure proper physiological functioning of diverse organ systems.
Ingredients;
Potassium 99mg (3%)
—(as Potassium Amino Acid Complex)
Other Ingredients: vegetable cellulose capsule, rice flour, citric acid, magnesium stearate, parsley, chamomile, and watercress. | https://vervehealthshop.com/product/potassium-once-daily-99mg-200ct-veggie-capsule/ |
Penticton City Council has agreed to immediately move ahead with a crime deterrent pilot project brought forward by the Downtown Penticton Association (DPA) and presented to Council on October 5, 2021 by Councillor Watt as a 2022 budget ‘Notice of Motion’.
Supporting the strategic priority of Community Safety, Council has directed staff to provide the DPA with a $40,000 grant to fund the project costs associated with installing downtown surveillance cameras on commercial properties. Located in three to five high-crime locations, and featuring signage, two-way voice notifications and strobe lights, each camera will be monitored from 9pm to 9am with the operator, if needed, advising those trespassing or acting irresponsibly to move on or, if needed, dispatching a response from either Bylaw or the RCMP.
“By way of this pilot project, businesses and residents in the downtown will gain a better sense of security knowing that our Bylaw and RCMP are responding to issues that are happening, versus issues that have happened,” said Penticton Mayor, John Vassilaki. “Overall, the situation downtown is challenging, and while there’s no single solution for addressing the deliberate disorder we witness, I’m pleased to see proactive organizations like the DPA helping the situation by coming forward to Council with ideas that we can introduce now to deter poor behavior and respond to crime.”
“In keeping with City Council’s focus on security, we created this program to fit within the scope of the Community Safety Strategic Priority. With crime and disorder affecting our business community and residents, one solution we brought forward to pilot is the Remote Guard Service,” said Executive Director of the Downtown Penticton Association, Lynn Allin. “Our intent is to reduce unwanted activity in our downtown with a security program to deter unacceptable behaviour that is negatively impacting our members and their customers.”
Through this partnership with the DPA, the DPA will work with a local electrical and security company to implement the pilot program and, on a monthly basis, provide the City with information on the results of the monitoring and the program’s overall performance. | https://www.penticton.ca/city-hall/news-alerts/city-partners-dpa-enhance-downtown-safety |
The recent case of Alfie Evans, a 23-month old who sadly passed away, has drawn huge attention in the media and has highlighted numerous ethical and legal issues at play within medical decisions.
Alife Evans was diagnosed with an unidentifiable degenerative neurological condition, and spent more than a year in a semi-vegetative state. His parents wanted Alfie to be flown to Italy to receive treatment in a hospital, however the hospital he was being treated at in the UK blocked this move, arguing it was not in his best interests. They argued due to the degradation of his brain tissue, further treatment would be “futile” and “unkind and inhumane”.
The key legal issue at play in the case was whether doctors have the ultimate right to decide whether withdrawing life-support treatment is in the best interests of a terminally ill child. However, the law in the UK does not offer a definitive answer to this question. The 1989 Children’s Act states that the state can intervene when a child is at risk of harm. This leads to a legal grey area, whereby the state can challenge the rights of the parents, where they believe they are not acting in the best interests of the child.
The case also highlights the complex interplay of the different medical ethical principles to be considered when deciding how best to treat a patient. The ethical principle of beneficence states that doctors should always act in the best interests of the patient and need to balance the benefits of treatment against the costs. However, patients also have autonomy and have the right to make decisions regarding their own treatment. In the case of a child, this decision falls to the parent, and this leads back to the crux of the case as to whether it is the doctors or parents who can decide this.
Law students could look at the complex legal issues involved in this case, and consider how these laws may differ between different countries. Both Philosophy and Medicine students should consider the ethical implications in the case and how these impact upon the decisions that were taken.
Our Oxbridge-graduate consultants are available between 9.00 am – 5.00 pm from Monday to Friday, with additional evening availability when requested. | https://oxbridgeapplications.com/kyc/life-death-law/ |
- Top left: Salad greens, washed and ready to eat, and some fresh raspberries.
- Top right: My FIDO jar of homemade sauerkraut, and a whole batch of breakfast soup.
- Upper crisper drawer: lemons, ginger, and herbs.
- 2nd shelf: Eggs (AIP reintroduction), a leek, bowls of leftovers, a jar of chopped onions, and 4 mason jars of homemade kombucha.
- 3rd shelf: Fresh vegetables, all chopped and ready to eat or cook. And a pack of AIP-friendly bacon.
- Lower left: Duck breasts for dinner tonight, and a roast I’ll be cooking tomorrow.
- Lower right: Carrots and celery (soup staples).
- Door: Filtered water, bone broth, duck fat, reserved bacon fat, Red Boat fish sauce, coconut aminos, and Primal Kitchen Mayo (AIP reintroduction).
How I Meal Plan
- The day before we go grocery shopping, I sit down and plan out all of our meals for the week.
- Breakfast is easy, because we always make Breakfast Soup which feeds both my husband and I for the workweek. Then on the weekends, we make some type of skillet breakfast. If you’re not sure what to cook for breakfast, check out our cookbook: 85 Amazing AIP Breakfasts.
- For lunches, I depend on food that is already prepared. I don’t have time to cook at lunchtime. I eat a lot of [email protected] salads (as Mark Sisson lovingly calls them), and I do some batch cooking on the weekend so that I have some meat and veggies that I can grab and reheat. This week I made a big batch of roasted butternut squash and Perfect Breakfast Sausage (which tastes good at any time of day.) For other ideas for lunch, check out the e-book AIP Snacks and Quick Lunches.
- For dinner entrees, I do a combination of quick meals and meals that produce a lot of leftovers. When we’re following a healing diet, we spend enough time in the kitchen without making every meal a chore. Here’s this week’s dinner meal plan: Monday – Easy Crispy Duck Breast, Tuesday – Simple Tender Pot Roast with Holy Grail Gravy, Wednesday – Leftovers, Thursday – Leftovers, Friday – Salmon Primavera, Saturday – Simple Marinated Chicken Hearts, Sunday – Carrot Ginger Halibut Soup (which will give me leftovers for Monday)
- Vegetables are the foundation of the AIP Food Pyramid. So, I buy a wide variety every week. We chop them all up when we get home from grocery shopping and put them in Tupperware Fridgesmart containers, because they keep produce fresh a really long time. Then they’re ready to grab for lunch salads and quick dinner side dishes. Looking for inspiration? Here’s an A-Z Vegetable Recipe Roundup.
- Snacks – I actually don’t snack any more. I find my digestion works best when I eat 3 large meals daily and give my body a break between meals. That said, my blood sugar is well-controlled and I don’t suffer from adrenal fatigue. If you have blood sugar or adrenal fatigue issues, you’ll need to eat snacks between meals. The key is to choose satiating snacks. That means you don’t want to grab an AIP dessert; instead, make your snacks mini-meals that have fat, protein and carbs. This is how you will heal over time and eventually be able to widen the times between meals. An ideal snack would be Liver Pate with Apples. For a satiating snack on-the-go, I recommend Wild Zora’s AIP-Friendly Meat and Vegetable Bars or Epic Bar’s AIP-Friendly Varieties.
- Healing Foods – I also check on my stock of healing foods like bone broth, sauerkraut and kombucha, to see if I need to buy the ingredients to make new batches this week.
- Grocery List Staples – Once I’ve written all of my recipe ingredients on my grocery list, along with a good list of vegetables, I look around my kitchen to see if I’m running low on any staple foods. I use an AIP grocery list as a reference.
- Last Tips – (1) When you write down your meal plan, also note which meat/seafood needs to be defrosted each day for the next day’s meal. (2) Plan batch cooking and veggie prep. on your days off, so you can pull dinner together quickly on a worknight. (3) Choose a variety of foods for your weekly menu. The more diverse our choices, the better our nutrition. We all end up having favorite recipes, but it’s also good to try something new once in a while to keep us from getting into food ruts. Check out the weekly AIP Recipe Roundtable for inspiration. (5) Has your food seemed bland lately? Spice up your meals with this Condiment Recipe Roundup. (6) Are you a new cook and feeling a little intimidated, or just finding the transition to the AIP challenging? Listen to my recent podcast: Cooking and Baking Tips from the Paleo Masters.
- Printable PDFs – If you bought my book, A Simple Guide to the Paleo Autoimmune Protocol, just send me your receipt for some free bonuses – a printable PDF of the AIP Food Pyramid, AIP Foods to Avoid, and AIP Grocery List.
Brain Fog? Too Busy? There are Meal Plan Resources Available
When you look at my process above, it may seem overwhelming. Brain fog is a common symptom of autoimmune disease. At its worst, it’s hard to carry on a conversation, never mind organize a week’s worth of meals. The good news is that this is one of the first symptoms that improves on the Paleo Autoimmune Protocol (AIP). However, if you’re just starting, or simply very busy, you might want someone else to do the meal planning for you. There are now lots of great resources available:
- Meal Plan E-Book Series: Christina Feindel is a meal plan master. Check out my review of her first one: 28 Days of AIP. She has since created three more: 28 Days of One-Pot AIP – Less dishes makes us all very happy! 28 Days of No-Cook AIP, designed for preparing healthy meals while traveling. And her most recent one is designed to help people with histamine intolerance: 28 Days of Low-Histamine AIP.
- Meal Plans in Printed Cookbooks: Two of your favorite AIP cookbooks contain meal plans that incorporate those cookbook’s recipes. The Autoimmune Paleo Cookbook has 8 weeks of meal plans and The Healing Kitchen Cookbook has 12 weeks of meal plans.
- Low-FODMAP AIP Meal Plans: If you have SIBO, you might be on a Low-FODMAP diet in addition to the AIP, making meal planning especially challenging. Here are some meal plans available to help: the FODMAP-Free Paleo Breakthrough and 28 Days of Low-FODMAP AIP.
- 30 Day Autoimmune Makeover Guide: This is the newest meal plan on the AIP block, but it includes much more. My favorite section is the weekly Lifestyle plan, that allows you to focus on one healthy habit each day (sleep, journaling, gratitude, self-care, etc.) It’s a great reminder that healing is about more than just food. However, the food plan is complete as well. It incorporates batch cooking and leftovers, and the majority of the recipes are fast and easy (35 minutes or less).
- Online Meal Plan Subscription: Real plans is a meal planning app that can be used on your computer or smartphone. It’s very cool! You choose the meals, and it generates shopping lists, defrost reminders, and how much time is needed to prepare and cook each recipe. They have hundreds of paleo AIP recipes available, and you can also personalize your meal plan according to your unique food needs, filtering for extra restrictions or adding foods back in with successful reintroductions. They also let you sort by budget, season, and preparation time. Do you live outside the USA? In your settings, you can choose metric measurements. They’ve thought of everything! They even offer a 30-day money-back guarantee for a no-risk trial.
The Genius of Batch Cooking
What is batch cooking? It’s spending an hour (or a few hours) in the kitchen, preparing a lot of food at once so you can eat quick meals the rest of the week. There are some great AIP Batch Cooking tutorials online:
- The Batch Cooking Guru in the AIP Community is Mickey Trescott, the author of The Autoimmune Paleo Cookbook. She created a video tutorial which includes recipes and meal plans to cook an entire week’s meals in just 2 two-hour sessions. It’s called AIP Batch Cook.
- A Batch Cooking Cookbook: The Autoimmune Protocol Meal Prep Cookbook gives you 10 weeks of batch cooking meal plans with a wide variety of themes and flavors.
- Phoenix Helix Podcast: In Episode 55, batch cooking masters share their tips.
- Adventures in Partaking put together a Batch Cooking Recipe Roundup, which also includes some tips for batch cooking success.
- AIP Sisterhood shares a batch cooking routine in this post: How To Spend Less Time in the Kitchen.
- EarthyMamacado loves batch cooking with her grill: Batch Cooking a Healing Diet in the Summer.
Ready? Set? Cook!
When I started the AIP, none of these resources were available. We’ve come a long way, baby! That’s because the AIP community is now full of thousands of people reclaiming their health. We’re a movement, and it’s both empowering and inspiring to see! What are your best meal planning tips? Please share in the comments below.
AIP Series
I’ve written a series of articles to guide you through the autoimmune protocol, step by step. It includes FAQ, mistakes to avoid, book reviews, and more. Click here to see the whole list. | https://www.phoenixhelix.com/2016/01/09/meal-planning-a-paleo-aip-survival-tool/ |
Rouen is a city on the River Seine in the north of France. It is the capital of the region of Normandy. Formerly one of the largest and most prosperous cities of medieval Europe, Rouen was the seat of the Exchequer of Normandy during the Middle Ages.
We made a short stop in this city to have lunch and spread our legs from the long ride as coming back to Brussels. Bad for me, I soon realized this city deserves much more attention. So I promised to come back – event though I do not re-visit. Life is to short! World is to wide!
The first stop was Le gros horloge (The Big Clock) recently restored, located in the middle of the Rue du Gros Horloge.
It is a 14th century astronomical clock.
The clock is installed in a Renaissance arch. The mechanism is one of the oldest in France. The Renaissance facade represents a golden sun with 24 rays on a starry blue background. The dial measures 2.5 metres in diameter. The phases of the moon are shown in the oculus of the upper part of the dial. It completes a full rotation in 29 days. The week days are shown in an opening at the base of the dial with allegorical subjects for each day of the week.
Already in love? Me too…
The little cobbled pedestrianised streets will accompany your weekends, holidays… These incomparable charming streets are decked on both sides with timber-framed houses dating from the Middle Ages were so cozy to my traveller heart…
Then the 16th century glory of the Palais de Justice… no it is not a cathedral, yet…
Now, this is the Cathedral… Ready?
It started on the site of the 4th century local church. Then, all the buildings perished during a Viking raid in the 9th century. The Viking leader, Rollo, founder of the Duchy of Normandy, was baptised here in 10th century and buried as well. The next generations of his sons were re-constructing the building to become greater and greater.
The gothic church became the Cathedral in 15th century . In the late 16th century the cathedral was badly damaged during the French Wars of Religion: the Calvinists damaged much of the furniture, tombs, stained-glass windows and statuary.
Time for lunch. We went typical Norman: the neck of the beef… yuck! But apparently the favourite dish of the former French president Jacques Chirac.
The last rushy thing we did was the Place du Vieux Marché – famous again for the timer houses but also for being the burning site of Joan of Arc. Yes, I am a total fan of this discussible icon so the feeling was weird. Ebven more, when I realised that the marking place was some badly recognized statue and modern church… Not enough for this French saint who ran the battles against English to free the nothern France.
However, there is still a lot to see and space to update this post… Gustave Flaubert, Claude Monet…
Until next time, Rouen!
Great and informative post
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The cathedral and the gothis church are just awesome 🌸🌸
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Brave world
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Does that big clock work?
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Like!! Thank you for publishing this awesome article.
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My brother recommended I would possibly like this blog. He was entirely right.
This put up truly made my day. You cann’t imagine simply how a lot time I had spent for this info!
Thank you! | https://redridinghood.blog/2019/05/05/rouen-france-steps-of-jeanne-darc-%F0%9F%97%A1/ |
Some economists are warning that Ghana’s economic outlook, following revisions made to the fiscal targets for 2022 will make things difficult for the business community.
The government in the 2022 mid-year budget review, reduced the country’s Gross Domestic Product (GDP) – growth in income earned from production for the year from 5.8 per cent to 3.7 per cent.
It also announced that there would be a shortfall in revenue, with spending going up.
The government aims at mobilising GH¢100.5 billion in revenues and grants, with a total expenditure of GH¢137.5 billion.
Meanwhile, inflation (the rate of increase in the prices of goods and services), which was set to end the year at eight per cent, is now expected to increase to 28.5 per cent.
Speaking with the Ghana News Agency, the economists explained that the implication of the revised fiscal targets was that there would be slow growth in the economy.
They noted that with the government’s flagship economic programmes – the Planting for Food and Jobs (PFJ), and One District-One Factory – not yielding the expected gains amidst uncertainty in microeconomic stability, and high cost of capital, businesses would continue to face hardships.
Dr Patrick Asuming, a Development Economist with the University of Ghana Business School (UGBS), said that: “Things are going to be significantly worse than was projected at the reading of the original budget in November 2021.”
“The economy is now projected not to grow fast. The growth rate will be lower, and inflation will be more than three times what we had initially projected. The exchange rate depreciation will also be higher. So, overall, businesses are looking at a less prosperous economy and a more unstable economy,” he said.
Dr Asuming asked the government to prioritise the country’s productive sectors, particularly, agriculture and streamline its flagship programmes by ensuring sustainable financing schemes for such projects.
The programmes should also be integrated into other sectors of the economy, like manufacturing, and products be enhanced and made export ready to bring some respite to businesses.
Mr Courage Boti, an Economist and Financial Analyst with GCB Capital, noted that the inflationary pressures were likely to reduce by end of the year, but businesses would suffer.
He said: “Inflationary pressures are likely to slow down by the end of the year, but financial prudence is more critical, so, the government should be prudent by further cutting down expenditure to help the country meet its fiscal targets and provide some respite to businesses.”
Figures provided in the 2022 budget review showed that growth stood at 3.3 per cent for the first quarter of 2022 compared to the 3.6 per cent recorded in the same period in 2021.
The moderation in growth in the first quarter of 2022 as showed by the Bank of Ghana’s updated Composite Index of Economic Activity (CIEA), was 15.8 per cent in March 2022 compared to 26.3 per cent in the corresponding periods of 2021.
Meanwhile, the average cost of inputs received by domestic producers for the production of their goods and services (Producer Price Inflation) for the month of June increased to 38 per cent from 33.3 per cent in May.
Mr Ken Ofori-Atta, the Finance Minister, admitted that the Ghanaian economy was going through challenging times, which had effects on both businesses and individuals.
He said that: “We know things are tough now. But we have a plan and the will to drive it,” and called on the citizens to eschew pessimism, which took invaluable energy away from the forward march to transformation.
He was confident that the Enhanced Domestic Programme with the International Monetary Fund (IMF), expected to take effect from next year would bring the stability the economy needed and confidence to go to the international capital market. | https://www.ghanabusinessnews.com/2022/07/30/businesses-to-face-more-hardships-for-the-rest-of-the-year-economists/ |
Highly invasive plant discovered in wild for first time in Wisconsin
MADISON, Wis. — The Wisconsin DNR today announced that European frogbit – a prohibited invasive plant with the potential to invade shallow or slow-moving water areas – was found for the first time in the state of Wisconsin.
European frogbit, known for its petite lily pad-like leaves and elusive white flower, originally inhabited Europe and parts of Asia and Africa. Wisconsin’s invasive species rule, Wis. Admin. Code NR 40, prohibits European frogbit across the state. Prohibited species are illegal to transfer, sell, possess, transport, or introduce into the state.
The only other finding of European frogbit in Wisconsin was in 2018 at a nursery in southern Wisconsin. The nearest known wild population is in Michigan’s Upper Peninsula near Sault Ste. Marie.
In late July 2021, a botanist conducting surveys for the Great Lakes Coastal Wetland Monitoring Program funded by the Great Lakes Restoration Initiative (GLRI) observed European frogbit growing in an unnamed stream and throughout the adjacent drainage ditches just north of the City of Oconto. After it was reported to the DNR, staff visited the site to verify the species and collect specimens and photographs.
European frogbit is a plant that can form large colonies of dense floating mats that can dramatically affect native aquatic life and recreational activities.
“The streams, wetlands and drainages along the west shore of Green Bay are highly valued ecosystems for many fish species including Northern Pike, Yellow Perch, and many forage fish along with many species of birds, amphibians, and native plants,” said Ken Dolata, Department Head for the Oconto County Land Conservation Department.
Large mats of European frogbit can become dense enough to reduce light that native plants need and prohibit movement of large fish and diving ducks.
“There are numerous ways that plants such as this get introduced,” said Amanda Smith, a DNR Invasive Species Specialist. “For this population in particular, movement by boats is likely as there is a nearby boat launch that is heavily used by boaters from throughout the Midwest who travel long distances to experience the Green Bay fishery. It is also possible that it was released from a water garden or aquarium since European frogbit was once a popular ornamental plant. Once introduced, natural dispersal is also possible given its ability to overwinter and spread rapidly.”
Initial monitoring efforts revealed European frogbit is in numerous marshes and tributaries of Green Bay that are connected by drainage ditches. Removal efforts will begin in the coming days and will continue throughout the summer and subsequent years.
Extensive monitoring of the site and nearby waterbodies will also be necessary to identify other populations given the likelihood of spread. DNR staff and partners are beginning outreach to sportsmen, local garden clubs, bait shops, and at public events. The response effort is in partnership with Oconto and Marinette Counties, Timberland Invasives Partnership, Wild Rivers Invasive Species Coalition, and the Forest Langlade Oconto Waterways Program.
European frogbit, also known as Common frogbit, is not to be confused with common native look alikes such as white waterlily and water-shield. It is usually floating and resembles tiny water lilies with kidney-shaped leaves 0.5-2.25” in diameter with long stems. The leaves also have a tissue containing air pockets located mostly along the midvein. The small white flower is short lived and rarely seen. This species readily reproduces by seed, turions, and plant fragments. | |
Exploring the Potential of Technology as a Professional Learning Tool
Twenty-first century education is radically different as social media and new technologies are now part of life and learning. In order for educators to see technology not as a substitute for play or hands-on experience, but as a way to expand children’s play, options, ideas and problem-solving strategies, they must themselves play with technology. Overcoming resistance and reluctance is critical for the benefits of technology integration to be realized (Dietze, Kashin, 2013).
This hands-on workshop focussed on using technology for professional learning, giving participants opportunities to increase their comfort level with technology integration in early childhood education practice. This was a BYOD (bring your own device) workshop that explored the possibilities and potential of using technology as a professional learning tool. Diane curates multiple professional learning topics across multiple social media platforms including Pinterest, Facebook and Twitter. She is excited about the potential of social media to bring together likeminded individuals in a professional learning network (PLN) as well as its capacity to connect with families and inspire a whole new generation of children on the benefits of technology. | https://supporting-technology.eccdc.org/past_training/exploring-the-potential-of-technology-as-a-professional-learning-tool/ |
An incisor plaque model in rats.
An in vivo model for studying plaque accumulation in rats has been described. This model investigates plaque formation on the mandibular incisors in animals which have been found to be rapid plaque-formers during a pre-test period. The accessibility of these tooth surfaces permits the removal of plaque prior to initiation of tests, the use of test groups balanced on the basis of plaque-forming potential, and interim assessments of plaque formation throughout the test period. In addition, baseline plaque scores of near zero can be attained, thereby permitting investigations of the impact of experimental measures on plaque formation. Moreover, the model permits intermittent plaque assessments throughout the test period. This model was found to have adequate sensitivity to distinguish effects between antimicrobial agents known to differ in their clinical activity and to detect differences between varying concentrations of the same agent.
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Single-layer Perceptron in Pharo
Object-oriented approach to neural networks
In this post I will describe my implementation of a single-layer perceptron in Pharo. It will support multiclass classification (one or many neurons). Each neuron will be implemented as an object. The code of this project can be acquired from Smalltalkhub using this Metacello script (Do It in a Playground of your Pharo image):
I will start by illustrating the design issues and different approaches to the implementation of every single part of this project. It will be quite long, so here is my final design:
What is Perceptron?
First of all, we need to define a perceptron. It is the most basic form of an artificial neural network, still, most people fail to clearly define what it actually is.
For now I will refer to a perceptron as an artificial neural network that follows the perceptron learning procedure.
This definition implies some restrictions to what perceptrons are and what can they do.
Restrictions of Perceptrons
They can only converge on a linearly-separable input (see XOR problem, Minski & Pappet). But if the input is linearly-separable, the perceptron is guaranteed to converge on it, regardless of the initial weights and learning rate (see Perceptron Convergence Theorem, proven in 1962 by Block and Novikoff)
Perceptrons (as defined above) can have only one layer of neurons. The thing is (week 3 of the Neural Networks for Machine Learning course by Geoffrey Hinton), the perceptron learning procedure can only be applied to a single layer of neurons. Neurons in hidden layers would need some sort of feedback in order to calculate their errors and update the weights. That’s why we need a different learning algorithm (e. g. backpropagation, which will be implemented on the next stage).
Perceptrons can only learn online (one example at a time). That’s because the perceptron learning is based on adding (or subtracting) the input vector to the weights based on the error of a binary classifier (this error can be -1, 0, or 1).
Design Issues
How to Represent Weights
When it comes to the object-oriented implementation of neural networks, this is probably the most important question that has to be answered. Should weights belong to the neuron? If yes, should it be the sending or the receiving neuron? Or maybe they should belong to a layer? Or maybe to the whole network? Maybe we should even implement them as separate objects?
Being a feedforward network with only one layer, and therefore having no weights that connect two neurons, single-layer perceptron simplifies this problem. Basically, we have three options:
Input weights of each neuron are stored as a vector inside that neuron. The matrix of all input weights is stored in the network. The weights are implemented as objects and connected to neurons.
Second option is the most efficient (vector-matrix multiplication), but not very object-oriented. What is neuron in this implementation? Clearly, the network is just a matrix of weights + some learning rules. Should the neuron be an activation function with a learning rate? But then again, storing them in the network would be even more efficient. So basically, we don’t need a Neuron class. All we need is a matrix and several functions for manipulating it. That doesn’t sound object-oriented to me.
Third option in this case would be an over-engineering. It would just make the whole thing way more complicated. Implementing weights as objects would probably make some sense in a multi-layer neural network, where each weight is a connection between two neurons (we can think of inputs as of fake neurons). It connects two neurons, sends a signal between them and has a “strength” which can be updated. As a result, neurons would not know about other neurons. They would just receive, process, and emit the signals. I assume that such implementation would not be very fast, but it could be used for modeling purposes. I will write more about this idea in a post dedicated to multi-layer networks.
First option looks like most appropriate for single-layer perceptrons. And it’s very easy to implement, so I’ll stick to it.
Activation Functions
There are two ways of representing activation functions in this project:
Implement them as methods Implement them as classes
The first approach will be faster and consume less memory. We create a base class Neuron with abstract methods activation and activationDerivative . Each subclass will be a special type of neuron, such as BinaryThresholdNeuron , SigmoidNeuron , that implements a corresponding activation function.
Another way of implementing activations is to create a base class ActivationFunction with two abstract methods, value: and derivative: . This approach is more flexible, because if someone wants to use a new activation function, he will be able to implement it as a subclass, only defining what it is and what is its derivative. Then he will be able to pass an object of this class to an existing neuron. It doesn’t seem logical to reimplement the whole neuron every time we need to create a function.
So the real question can sound like this (of course, it could sound better):
Are neurons defined by their activations? Does having a different activation means being a completely different type of neuron?
Shared or Separate Activation and Learning Rate?
Both activation and learning rate can be either shared by all neurons of a perceptron or be stored separately in each neuron.The question is: do we need to have neurons with different activations and different learning rates?
Let’s assume that we don’t. Indeed, in most cases all neurons of a network (or a layer) share the same learning rate and have the same activation. If the network has many neurons (and most networks do), then we will be storing the same number just as many times. And if the activation function is implemented as a class, then we will be creating a separate instance of that class for each neuron.
However, if we wanted to parallelize the computations done by neurons, it would be better to have a separate learning rate and separate activation for each neuron (or each block of neurons). Otherwise they will just block each other trying to access the shared memory on every single step. And besides, the total memory occupied by this “heavy” neuron would still be rather small. I think, such neuron (or a group of them) would easily fit in the local memory of a single core of GPU.
But single-layer perceptrons do not usually perform heavy computations. They are more useful for the modeling purposes. That’s why we should probably take the “separate” approach and allow the user to build a network out of completely different neurons (like building blocks).
By the way, for multi-layer network the nice idea would be to share the same activation and learning rate inside one layer, but allow user to have completely different layers. In the end, he should be able to build some complicated network like the convolutional network on the picture. But that’s not the topic of this post.
Data Shuffling
Online perceptrons are sensitive to the order in which training examples are received. Weight updates are made after each training example, that’s why the training vectors #(#(0 1) #(1 1)) and #(#(1 1) #(0 1)) will result in different weight vectors. Depending on the order of examples, the perceptron may need a different number of iterations to converge.
That’s why, to test the complexity of such learning, the perceptron has to be trained by examples randomly selected from a training set.
Implementation
Putting it all together, here is my design of a single-layer peceptron:
Neuron class
Object subclass: #Neuron
instanceVariableNames: 'weights activation learningRate'
classVariableNames: ''
package: 'NeuralNetwork'
The weights are initialized with random numbers in range [0, 1]. I’m not sure if this is a good range, but on simple examples it works just fine.
BinaryThreshold is a default activation function and the default learning rate is 0.1. These parameters can be changed using the accessors activation: and learningRate: .
initialize: inputSize
"Creates a weight vector and initializes it with random values. Assigns default values to activation and learning rate" activation := BinaryThreshold new.
learningRate := 0.1.
weights := DhbVector new: (inputSize + 1).
1 to: (inputSize + 1) do: [ :i |
weights at: i put: (1 / (10 atRandom))].
^ self
We will also need to prepend 1 as a bias unit to every input vector.
prependBiasToInput: inputVector
“this method prepends 1 to input vector for a bias unit”
^ (#(1), inputVector) asDhbVector.
According to “Numerical Methods” book, each function should implement the value: method. I want to emphasize that from the mathematical point of view neuron is a function.
Though the inner representation uses DhbVector, I want a user to write something like perceptron value: #(1 0). instead of perceptron value: #(1 0) asDhbVector.
value: inputVector
"Takes a vector of inputs and returns the output value"
| inputDhbVector |
inputDhbVector := self prependBiasToInput: inputVector.
^ activation value: (weights * inputDhbVector).
We need accessors for setting the learning rate an activation. I also added a simple accessor for weights for debugging purposes. All these accessors are trivial, so I will not put the code here.
And of course, the perceptron learning rule.
learn: inputVector target: target
"Applies the perceptron learning rule after looking at one training example"
| input output error delta |
output := self value: inputVector.
error := target - output.
input := self prependBiasToInput: inputVector.
delta := learningRate * error * input *
(activation derivative: weights * input).
SLPerceptron class
Single-layer perceptron (according to my design) is a container of neurons. The only instance variable it has is the neurons array.
Object subclass: #SLPerceptron
instanceVariableNames: ‘neurons’
classVariableNames: ‘’
package: ‘NeuralNetwork’
To create an instance of SLPerceptron we need to specify the size of the input vector and the number of classes which equals to the number of neurons in our perceptron (multiclass classification).
initialize: inputSize classes: outputSize
“Creates an array of neurons”
neurons := Array new: outputSize.
1 to: outputSize do: [ :i |
neurons at: i put: (Neuron new initialize: inputSize). ]
The output of a single-layer perceptron is a vector of scalar outputs from each neuron in the layer.
value: input
“Returns the vector of outputs from each neuron”
| outputVector |
outputVector := Array new: (neurons size).
1 to: (neurons size) do: [ :i |
outputVector at: i put: ((neurons at: i) value: input) ].
^ outputVector
If we ask SLPerceptron to learn, he will pass that request to all his neurons (basically, SLPerceptron is just a container of neurons that provides an interface for manipulating them).
learn: input target: output
"Trains the network (perceptron) on one (in case of online learning) or multiple (in case of batch learning) input/output pairs" 1 to: (neurons size) do: [ :i |
(neurons at: i) learn: input target: (output at: i) ].
Testing
I test my SLPerceptron with BinaryThreshold activation function on 4 linearly-separable logical functions: AND, OR, NAND, and NOR, and it converges on all of them.
Here is the test for AND function. Other 3 look exactly the same (only the expected output values are different).
testANDConvergence
"tests if perceptron is able to classify linearly-separable data"
"AND function" | perceptron inputs outputs k |
perceptron := SLPerceptron new initialize: 2 classes: 1.
perceptron activation: (BinaryThreshold new).
"logical AND function"
inputs := #(#(0 0) #(0 1) #(1 0) #(1 1)).
outputs := #(#(0) #(0) #(0) #(1)).
1 to: 100 do: [ :i |
k := 4 atRandom.
perceptron learn: (inputs at: k) target: (outputs at: k) ].
1 to: 4 do: [ :i |
self assert: (perceptron value: (inputs at: i)) equals: (outputs at: i) ].
And this test (or rather a demonstration) shows that single-layer perceptron can not learn the XOR function (not linearly-separable).
testXORDivergence
"single-layer perceptron should not be uneble to classify data that is not linearly-separable"
"XOR function"
| perceptron inputs outputs k notEqual |
perceptron := SLPerceptron new initialize: 2 classes: 1.
perceptron activation: (BinaryThreshold new).
"logical XOR function"
inputs := #(#(0 0) #(0 1) #(1 0) #(1 1)).
outputs := #(#(0) #(1) #(1) #(0)).
1 to: 100 do: [ :i |
k := 4 atRandom.
perceptron learn: (inputs at: k) target: (outputs at: k) ].
notEqual := false.
1 to: 4 do: [ :i |
notEqual := notEqual or:
((perceptron value: (inputs at: i)) ~= (outputs at: i)) ].
self assert: notEqual.
I was also trying to test the Sigmoid function, but that test failed. This means that either perceptrons (as defined at the beginning of this post) can not have sigmoid as their activation, or that I don’t have a good enough understanding of how to implement a perceptron with sigmoid.
What’s Next?
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Meet Lalit Pagaria, who is on a mission to stir up the customer analytics market.
In 2021, Lalit won second prize in the first global hackathon organized by RBI- “HARBINGER – Innovation for Transformation,” for his open-source project Obsei. Soon after, he started building Oraika, a customer feedback tool. His long-term vision is to create an ETL Platform for Unstructured Data.
In an exclusive conversation with the Yellow Chapter, Lalit opens up about his life, professional journey and the challenges of building from scratch.
YC- Welcome to the Yellow Chapter. This interview aims to understand you, your life choices, your professional road map, and finally, Obsei and Oraika. Can we start from the very beginning? Like, where were you born? I want to take you back to your early childhood days.
Lalit: I was born and raised in Begun, a small town in Chittorgarh district, Rajasthan. I belong to the Marwari community, and everyone thinks business. I am the only member of my family with an engineering degree and a tech background.
My father was in a semi-government job. My mother is a very simple woman. She was in constant touch with my teachers and kept track of my progress in school. This made me accountable for my studies.
Both my parents were unable to complete their studies. They were super supportive and stood by me the entire time. I really want to thank my parents for where I am today. Despite coming from a modest upbringing, they were always supportive of me.
@ Family
YC – How was college? What are some suggestions you have for engineering students? How can they get the most out of college life?
Lalit: College was good; I kept exploring and learning. I did a Polytechnic Diploma in Electronics Engineering @BTTI Pilani. I’d never used a computer before my diploma, but I found it fascinating once I did. I decided to major in computer science for graduation and joined the Computer Science Engineering programme at MBM Engineering College, Jodhpur.
I wanted to pursue further studies in computer science engineering. I cleared GATE and joined MS Computer Science and Engineering @IIT Madras 🎓🎓🎓-2007-10.
Suggestion for Engineering Students on Campus 📖:
Just one – Take up more practice-oriented projects/internships. Now, there are so many opportunities around. Theoretical knowledge will help you somewhat, but practical knowledge will take you far. Building real projects matters more than anything else.
Suggestions for Engineering Students on How to Pick a Job:
- Early on in your career, prioritize learning over the package.
- You’ll be spending a lot of time at work. So, please find out about the company’s work culture and ensure you are comfortable with it.
- Till you join, keep the communication channels open with the HR team.
- Try to join younger teams. Young engineers usually struggle to get quality work in a team with many seniors. Also, the adaptability of younger groups is faster. Fresh out of college, I joined a team where everyone had 10+ years of experience. I had to struggle for their attention. Ask for opportunities, and build trust.
- Improve communication skills and learn networking.
- Ask probing questions to HR before joining, like –
- Option to change teams. Sometimes, you are in a group you dislike and might want to leave. It would help if you tried team migration instead of switching jobs in such a situation. Team migrations are easier than company migrations.
- Watch out for frequency and tone of communication. The company should make you feel like a future employee, not a mere resource.
YC – Can we discuss the professional roadmap and learnings along the way?
Lalit- I participated in campus placements and was lucky enough to get two offers from Nvidia and Brocade. I majored in computer networks and joined Brocade (acquired by Broadcom).
2010-2015: Software Engineer @Brocade – It is a global technology leader that designs, develops and supplies a broad range of semiconductor and infrastructure software solutions.
Learnings from Brocade 💻
- Create opportunities for yourself: Look out for tasks that your seniors or managers cannot complete due to other priorities. Try and automate small tasks to make their work easier and faster. I did the same.
- Step outside of your comfort zone: Mingle with colleagues in your team and other teams. Discuss and observe.
- Keep an eye on where the company is headed: Closely following the leadership team will help determine the company’s next major step.
- Visibility is critical: After doing the work, you also have to highlight. Visibility = Opportunities.
@ Team Brocade
2015 – 2018: Software Development Engineer @Olacabs
Why did you switch – Brocade is a corporate company. A typical process-oriented company. Everything was fixed—goals, quarterly objectives, and yearly goals. Though there was predictability, it was becoming monotonous. This was around 2015, when the country was experiencing a start-up boom, so I decided to quit Brocade to join a start-up.
I didn’t want to take too many risks. I didn’t want to join a very early stage start-up. I interviewed with Ola. My interview experience at Ola was very nice. I visited their campus, and during the break, I freely explored the space and got a chance to interact with employees. I concluded that it is a pleasant place to work.
I could also relate to the concept; hence, I accepted when they made me an offer.
Learnings from Ola 🚗🚗🚗
The environment at Ola was very different compared to my previous company. It took me some time to settle. At Ola, execution and speed were our main focus areas. They had a superb team, and I learned a lot from them. I would like to especially mention Nilesh Hiray (my manager) and Pranav Tiwari (my skip manager). The things they taught me are invaluable. At Ola, I learnt –
- How to manoeuvre amid the chaos? The direction might be very hazy, but you have to navigate. I wouldn’t have had that experience anywhere else.
- How to communicate with stakeholders? In my day-to-day work, I had to communicate with various stakeholders ranging from product managers to strategic to the business team.
- How are business decisions made? I learnt about the company framework, which covers everything from decision-making to implementation to final feedback.
2018-2021: Software Engineer @Careem (Acquired by Uber) 🚘🚘🚘
Why did you switch – At this point, Ola started becoming more process-oriented. I was constantly thinking, “What next?” I decided to try an early-stage start-up in India or explore a new geography. That was when Careem reached out. They had given me the option of working in either Dubai or Germany. I chose Germany.
The primary reason for me to choose Careem was the location. I was curious how the geographical shift would affect me, though the job was in the same mobility vertical. Many ex-Ola employees had joined Careem and spoke highly of the organization.
Learnings from Careem 🚗🚗🚗
At Careem, I learnt the following –
- How to work with a diverse team? My team had people from five continents, and one needed to be careful while working with people from diverse backgrounds.
- How to efficiently do time management? In Germany, where every meeting starts and ends at a predefined time, one needs to be kind and considerate about others’ time.
2020 – Open Source Developer (https://github.com/lalitpagaria) I enjoyed my work at Careem. But I like exploring and keeping up with current trends in tech. I am a firm believer in working on side hustles.
I found out about the NLP (Natural language processing) boom. I began exploring how I could contribute to this field. I searched for businesses in AI and NLP while also attending interviews.
I interviewed with Deepset – Bringing cutting-edge Natural Language Processing to the industry via open source. During one of these interviews, I was assigned to add Milvus integration with Haystack.
Though I did not receive an offer, I was thrilled with how the assignment turned out. I approached DeepSet’s team and asked if I could contribute to their repository. They agreed. I used to work after office hours and began contributing big time. At one point, I was contributing more than their staff. So, they made me a part of their community maintainers team.
I’ve never done the same thing twice in any of my jobs. My role at Brocade was system development. I was part of the founding team that built the allocation and discovery engine at Ola. At Careem, I was part of the Site Reliability (SRE) and Identity team while working on access management and cloud cost optimization without compromising reliability. Now I focus on entrepreneurship while building an AI start-up.
YC- How did Obsei happen?
Lalit: I decided to quit Careem and move back to India. By June 2021, I had started exploring opportunities for a start-up. Meanwhile, I was in regular touch with founders I met through my open-source contributions.
These founders assisted me in gaining further insights into the NLP domain. Being an angel investor, I could see common issues in a few of my friend’s and relatives’ start-ups:
- No single source of truth about customer feedback between various stakeholders in an organization like Product, Customer Success and Strategic teams.
- Manual customer feedback analysis often misses out on data from important feedback channels.
- Missing voice of the non-English customer while taking strategic decisions
Problem – Customer Feedback Automation.
Solution – The plan was to search Twitter for customer feedback and use NLP analysis to determine if it was a complaint. If it is, notify the team.
I started working on it. That is how the open-source project Obsei – A low-code AI-powered automation tool for understanding customer feedback, began to take shape.
Obsei- A Cognitive Automation Tool for Customer Feedback— Stands for Observe, Analyze and Inform.
- Observe– Collect customer feedback in text, audio or video mode from various channels like social media, emails, chatbots, support tickets, surveys, interviews etc.
- Analyze– Contextually understand the feedback and extract required features like sentiment, topic, language, and keywords.
- Inform– Provide actionable data in a consumable form, be it reports, dashboards or notifications over various channels like Slack messages, Jira, Zendesk, email etc.
@ RBI Hackathon award from Dy. Governer RBI
YC- How did Oraika happen?
Lalit: Earlier in 2021, I considered turning Obsei into a product. So I started looking into other start-ups in the same industry.
I discovered that the Reserve Bank of India (RBI) had launched a global hackathon— “Harbinger 2021“. It was related to social listening. I felt Obsei fit the theme. By then, I had also got on board Girish Patel as a co-founder, and we applied for it.
We won second place in the hackathon. Overall, 377 companies participated, of which 23 were foreign companies. Following this, we built a SaaS solution on top of Obsei. We launched it as Oraika – A tool to collect feedback across channels and extract actionable insights to make better-informed business decisions.
YC- Can we talk about some numbers of Obsei & Oraika? And Suggestions for fellow founders?
Lalit: Business Vertical and Market Size: We are in the customer analytics market. In 2020, the TAM was $3.74 billion, and it is expected to reach $10.2 billion by 2026. The CAGR is 18.2% as per the report – CUSTOMER ANALYTICS MARKET – GROWTH, TRENDS, COVID-19 IMPACT, AND FORECASTS (2022 – 2027)
Current Numbers:
Six enterprises currently use Obsei. Based on their feedback, we are improving the product. Globally, there is no open-source project like Obsei, though many closed-source products exist.
Oraika remains in closed beta. We currently have three paid customers from India and outside. A few are in the pipeline. As we are running in bootstrapped mode, we don’t onboard free customers. We are profitable at this stage. Our technical architecture is built for scalability and flexibility. The present infrastructure, which three customers use, will serve 100 customers. So we are managing our infrastructure costs quite well.
Ideal Customer:
Obsei: – Product managers and customer experience team. Obsei requires developer assistance for use. It is perfect for businesses that have an engineering and data science team.
Oraika is a finished product. We are currently focusing on B2C start-ups that fall below Series A and have adverse business impacts due to customer opinions. We are particularly interested in the hospitality industry.
The target for 2023 – We aim to get 100 customers on board with a plan to achieve $10K MRR while keeping unit economics under control.
We gather data, analyze it, and provide a dashboard to the potential customer before onboarding them. So, research is being done to make it self-serve, and there currently needs to be a product in the market that onboards customers on a self-serve basis.
Competition –
The market for customer feedback analytics is not new. We have a few competitors, most of which are US-based, like: https://getthematic.com/ and https://www.sentisum.com/, along with recent entrant https://enterpret.com.
Competitive edge – Oraika can analyze feedback in non-English languages. As a result, we are focusing on businesses that get user feedback in their native language.
Careem, for example, receives 50% of its user feedback in Arabic and Urdu. However, the solution that they are using can only analyze English content. Similarly, 20% of SBI reviews are in non-English languages, and we were able to review that 20% as well during the RBI hackathon. We provide 100% analysis of your data.
We conduct our analysis using core NLP and deep learning models. In addition, our target customers will need help to afford the SaaS solutions these large US corporations offer.
@ With Girish
Suggestions for fellow founders:
Lalit:
- Every day is a new learning experience.
- Communication is critical. As tech founders, Girish and I, at times, struggle to balance: development + communication
- Get on board a co-founder with complementary skills.
- A mental break is a must – Spend time with family and friends.
- Hard Work is non-negotiable – There is no quick fix for success; it takes time.
- Impulsive decisions are not good. Often, founders work on their hunch but back it up with data for better output.
- Focus on data and external feedback to ensure you’re on the right track. Make informed choices.
YC- How did you get beta customers on board?
Lalit: Both of us (Girish and me) are technical founders. It took a lot of work for us to connect with customers and sell products. So, we use social media, primarily Twitter and LinkedIn. We posted regular updates about our products on these platforms and built an audience by sharing and helping people within our domain of expertise.
For Oraika, we depended mainly on our network. We approached people, told them about the concept, and asked if they wanted to try and buy. Next, we plan to work on SEO.
YC- How are you marketing Oraika?
Lalit:
- Reaching out and targeting customers via outbound channels and networks.
- Open source – We communicate with customers through Obsei, a distribution channel.
- Doubling down on SEO by publishing high-quality content on our website.
- Channel partners with combo packages. For example, if you purchase Freshdesk, you can also purchase Oraika. Oraika would then analyze the tickets generated or data collected by Freshdesk. As a result, you have a complete solution.
- Being a part of many start-up communities like 1000 Founders, SaaS Community, DataTalks.Club, Indie Hackers and SaaS Boomi.
YC- Let’s get philosophical. What is your investment philosophy as an angel investor + What keeps you going?
Lalit: Investment philosophy -I invest in the start-ups of my relatives| friends| and friends’ friends. The first filter is the person, and then the domain. I also consider my hunch.
What Motivates Me – That is a difficult question to answer. I enjoy what I do. I am self-motivated. I give my 100%. I know the potential of Oraika. The idea that what we’re creating has the potential to be big
Our vision is to be an “ETL Platform for Unstructured Data.” We started with text but will eventually incorporate audio + images + video into it. We know it will take time, so we are taking baby steps. | https://yellowchapter.com/p/lalit-pagaria-co-founder-oraika-interview-on-building-a-notification-infrastructure-tool-for-developers |
The Resistible Rise of Arturo Ui. Stella Adler Studio. John Gould Rubin.
Coriolanus: From Man to Dragon. Combative Theater Company.
Over There. Harold Clurman LAB Productions. Bill Bowers & Scott Illingworth.
Two Gentlemen of Verona. Shakespeare in the Square. Dan Hasse.
Coriolanus. Stella Adler Studio. | http://www.olivercpalmer.com/portfolio/ |
Initially it was the US-China trade war, then domestic political adjustments and now the COVID-19 pandemic – these crises have caused continuous challenges to the businesses in Malaysia. The COVID-19 pandemic that led to movement control order (MCO) in the country added pains and difficulties to the economic situation, particularly the SMEs.
The SME sector, being fragile supported by limited capital and reserves, has been struggling since the commencement of the MCO.
Based on a recent survey on the SMEs, only about one-third of the respondents maintained sufficient cashflow for month of March with another one-third to sustain for another month. This situation is critical because if the situation is prolonged, more than half of the existing SMEs will have to close down their businesses soon.
Stimulus Packages
The government has, through both the Economic Stimulus Package and Prihatin Rakyat Economic Stimulus Package totalling RM250 billion, will introduce various measures to ease the financial burden faced by individuals and businesses due to COVID-19 pandemic.
Despite the government’s effort to do whatever it can within its capability in providing support to the SMEs, the business community, particularly the SMEs have been screaming for more direct and effective financial assistance from the government. There is a need to strike a balance between what should be done and what can be carried out by the government.
While the businesses would like to fulfil the SME’s wish-lists, the government has its limitation due to limited resources. The government needs to ensure it has the means to provide what is deemed essential to the business community.
Having said this, there are still possibilities where the existing stimulus packages can be further enhanced with new measures to be introduced in assisting the SMEs, in particular.
Tactical Plans
In addition to the enhancement of measures that were already announced by the government, there are potential initiatives that could be considered. This tactical plan will be discussed across three broad stakeholders, namely the government, business corporations and SMEs themselves as follows:
- Government
The recently announced economic stimulus packages by the government were initiated at the federal level. These are respectable initiatives but with rooms for enhancements, particularly for the SMEs. The federal government, through various government agencies, can provide further reliefs to the SMEs.
For instance, instead of offering tiered discount on electricity usage for the businesses, it would be more sensible and effective if this discount can cover a wider range of usage. A broad discount of 50% over total usage of electricity by the SMEs until end-2020 will be meaningful and helpful to the SMEs.
On the wage subsidy initiative, the condition of 50% drop in business revenue should be removed. With exception to tourism and travel related sector, many businesses only started to face significant impact when they have to stop operating due to the MCO.
As a result, many SMEs are struggling due to tight cash flow. It may be difficult for many SMEs to show such significant drop of revenue between now and pre-MCO.
Furthermore, the validation of such condition will take time for pay-out of the subsidy. Therefore, subsidy on wages should be applicable to all SMEs without condition.
On the deferment of monthly loan repayment, this is indeed a good initiative for the SMEs. It will help SMEs to save their cash for other business purposes. It would be better if banks can further reduce existing interest charge for the existing loans, say by 1% to 2% per annum for the next six months.
Banks may choose to offer discount of interest rates only to SMEs that have maintained well conducted accounts with them for over the last three years. The banks would have made some profits from these SMEs in the past, hence be able to “re-pay” part of the profits to the SMEs.
Furthermore, the government guarantee fees charged on SMEs by Credit Guarantee Corporation (CGC) and Syarikat Jaminan Pembiayaan Pinjaman (SJPP) for both existing and new credit facilities from banks, should be waived for at least 6 months. This will provide additional relief to the SMEs that require bank financing to support their business operations.
Additional Measures by Federal Government:
The federal government needs dwell deeper into critical requirements of the SMEs in terms of cash flow to fund their basic operating expenses such as staff salary, rental, bank interest that continue to accumulate despite deferment of repayment of instalments, etc. Rental subsidy for business premises used by the SMEs should be considered for the next six months.
Even with the upliftment of MCO, businesses are expected to take few more months to pick-up but operating expenses remain consistent. The recent cut of Statutory Reserve Requirement for banks from 3% to 2% by Bank Negara Malaysia is commendable as it released approximately RM30 billion worth of liquidity into the banking system.
In addition to this, BNM had also reduced the overnight policy rate (OPR) twice this year to 2.5%. The banking system can tolerate lower OPR during this time. As such, BNM can consider to further reduce bank’s OPR by another 0.5% in easing interest expenses for businesses during this trying period.
The government should also consider allowing SMEs to suspend the employer’s portion of EPF contribution for a six months period. The staff would not be impacted by such suspension as the contributions are meant for the staff’s retirement accounts. And the loss to the staff will be minimal which is 12% of monthly salary – a small sacrifice in saving the employers from collapsing.
The additional funding for these additional initiatives can be partly sourced from existing funds currently owned and managed by various government agencies like HRDF and SOCSO. These funds, added up to billions of ringgit are sitting idle at this moment. The government can make full use of these funds for immediate application for SME relief purposes.
The government can choose to repay them when the country economy improved in the future. The initiative to suspend the employer’s portion of EPF contributions does not require any funding from the government.
At the state government level, a few state governments have taken a proactive stance in allocating special relief funds for businesses that are operating in the respective states. These are commendable moves and SMEs will benefit from such initiatives.
Other states that have not allocated any relief funds should start to consider implementing similar relief funds to assist businesses in their respective states. These businesses are key providers of employments in the states.
Additional Measures by State Government:
Waiver of property assessment and quit rents for commercial and industrial property would provide additional relief to the SMEs. The landlords who rent their properties to SMEs can in turn transfer the savings to their tenants.
Waiver of business license fees for SMEs in 2020 would reduce operating cost for the businesses.
- Corporations
In this context, corporations refer to government linked companies (GLC), multi-national companies (MNC) and all other large corporations operating in Malaysia. Many of these companies have since contributed to various funds that were set up for the purchase of medical and personal protective equipment, and health care workers support, etc.
GLCs that operate profitably in the past and currently maintain large cash reserves should declare cash dividend to the government. This cash dividend will be a good source of cash for the government to implement additional initiatives for the businesses, particularly the SMEs.
MNCs and other large corporations can also play a meaningful role in assisting the government to lighten its financial burden by contributing more generously, either in kind or cash, to various funds during this trying period.
These large companies can also assist the SMEs, in particular, by settling whatever payments due to the SMEs in advance, without requesting for any early settlement rebates. This will help the SMEs to improve their cash flow that is critical to bridge over this challenging time.
After all, the SMEs have been part of MNC’s key supply chains, without which, the MNCs would also be struggling in their business operations. Helping the SMEs is equivalent to helping themselves too.
- SMEs
Sitting at the receiving end of various stimulus packages, the SMEs need to also take proactive measures in addressing some of the challenges faced by them. This is crucial to ensure that they can make the best of the situation and be able to overcome this difficult time with minimal losses.
What are the interim measures that SMEs can take to better manage their cash flow and overall businesses? SMEs can opt for temporary reduction of staff salary for three to six months with agreement to reinstate total deducted salary over a period of time when the business environment improved in the near future. Bear in mind that the SMEs that choose to do this must obtain the staff’s consent to participate in this programme.
On the extreme situation where the SMEs may have to retrench part of the staff to remain operational, they can consider pay reduction for all staff in order to keep every employee’s job.
Ideally this reduction of pay serves as a temporary measure with firm commitment to revise the pay upward when the business performances recovered in the future. This should be considered as the last resort, otherwise every staff would lose their jobs if the business is closed down. Again, the staff’s agreement to take on this temporary measure must be obtained before execution.
Way Forward
SMEs need to stay flexible, responsive, resourceful and innovative in making the best of this pandemic. The ability to quickly modify the mode of business operations to suit the current situation could be a success factor. Likely, business operating hours must also be adjusted.
For instance, SMEs that are engaged in essential goods should embrace delivery services in order to capture more business. With most people staying at home, the ability to reach out and connect with them, coupled with readiness to deliver goods ordered by the people would help the business during this trying time.
Whilst this pandemic situation has brought ample challenges to many businesses, it has also unearthed various weaknesses among the SMEs. These weaknesses include business operating model, management of financial resources that cover both cash flow and reserves, people management, among other areas.
However, this is not the right time to work on these issues.
When this pandemic situation is over, SMEs should relook at their respective business models with the aim of improving business resilience and intensifying the financial position of the businesses.
SMEs should also relook into new ways and approaches in conducting their business in the future. These realignment in business models and operations is important and essential in ensuring business sustainability in the long run. | https://moneycompass.com.my/2020/04/17/how-smes-can-survive-the-covid-19-pandemic/ |
The MSF website may undergo scheduled maintenance every Tues, Fri and Sun, from 12am to 9am. Click here for the latest Safe Management Measures for weddings. Click here for other COVID-19 advisories. Click here for COVID-19 FAQs (for support schemes, etc).
6 FEBRUARY 2017
Question
Mr Ang Hin Kee
MP for Ang Mo Kio GRC
To ask the Minister for Social and Family Development
(a) what is the current status of the hand, foot and mouth disease (HFMD) in childcare centres and pre-schools;
(b) whether more support can be given to parents who have to make alternative arrangements when their children are unable to attend school; and
(c) how effective has the Ministry been in tackling challenges faced by parents who have insufficient childcare leave, whose children contracted HFMD more than once in a year, or who are unable to seek childcare support from family members.
Answer
Hand, Foot & Mouth Disease (HFMD) is a generally mild disease which is endemic in Singapore. Preventive measures are in place to minimise the transmission of HFMD in pre-schools. It is a regulatory requirement for pre-schools to conform to the Ministry of Health’s guidelines for the prevention and control of infectious diseases. This includes conducting daily health and temperature checks upon arrival, ensuring appropriate hand-washing by staff and children, and having an unwell child rest at the designated sick-bay while waiting for the parent or an authorised person to bring the child home.
Centres with two or more suspected or confirmed HFMD cases are required to report the cases to the Early Childhood Development Agency (ECDA) and to the Ministry of Health (MOH). Centres are also required to implement enhanced measures to manage the outbreak of HFMD and are encouraged to conduct self-assessment on health and hygiene.
Centres that experience a high number of sustained cases over a period of time may be required to close. We understand that this would cause inconvenience to parents, however it is a useful step to break the cycle of transmission of the disease. Over the past 3 years, there have not been more than 5 centre closures every year. Additionally, there have not been local cases in pre-schools with severe complications due to HFMD.
To support working parents in caring for their young children, the Government has enhanced child and infant care leave provisions over the years. Each working parent with children below the age of seven has six days of child care leave per year, or a total of 12 days of child care leave for every couple. Each parent is also entitled to six days of unpaid infant care leave per year during the child’s first two years. These child care and infant care leave provisions are in addition to the parents’ annual leave provisions. We also recognise that grandparents and relatives too play an important role in supporting working parents by providing alternative care for their young children.
Companies too have an important role to play in supporting their employees to manage their work and family responsibilities. The proportion of firms providing ad-hoc flexible work arrangements rose from 70% in 2015 to 77% in 2016. These firms employ 82% of all employees, up from 76% in 2015. Employers who wish to implement flexible work arrangements can tap on various resources such as the WorkPro Work-Life Grant. The tripartite partners also published the Tripartite Advisory on Flexible Work Arrangements to help employers, supervisors and employees implement flexible work arrangements.
We urge parents to tap on these flexible work arrangements and enhanced leave provisions to better manage their work and parenthood responsibilities in caring for their children.
MSF's response to a parliamentary question by Assoc Prof Jamus Jerome Lim on whether there are plans to implement the use of clear masks in preschool settings.
MSF's response to a parliamentary question by Mr Edward Chia Bing Hui regarding the number of infant care applications and the successful placement rates from January to December 2021. | https://www.msf.gov.sg/media-room/Pages/Management-of-HFMD-in-child-care-centres.aspx |
- Dit evenement is voorbij.
AI Regulatory Sandbox
31 maart - 13:00 - 17:30
Which rules and regulations apply to AI systems? How do you test the compliance of an AI system? Which rules and regulations apply to AI systems? How do you test the compliance of an AI system? Can you temporarily ignore certain rules in order to test the consequences of an AI system?
In the proposal of the AI Act by the
European Commission, the Commission included the possibility for Member States to launch Regulatory Sandboxes. These are projects where AI systems can be developed and tested in a regulated and controlled environment, while temporarily suspending certain requirements on the systems which are being tested. These projects are executed under the supervision of the supervisory authorities of the Member State and they have the ability to stop the project if needed. Organisations which want to participate to a sandbox do need to come with a plan for their system, which includes an exit-plan for the system and a proposal for the project. They also need explain how they will respect the privacy of the data subjects whose personal data will be used in the project.
The value of a Regulatory Sandbox is primarily the fact that the developer of an
AI-system does not immediately need to comply with all legal requirements for AI systems, which will be introduced in the AI Act. This allows the developer to experiment with how to comply later and see how they can respect the idea behind the requirements. During this process, the supervisory authorities present can give input and also detect possible compliance problems due to (outdated) wording of the law.
- What could be a legal framework for an AI Regulatory Sandbox?
- How can we construct this such that SMEs can also use it?
- How do the supervisory authorities see these initiatives?
In the Netherlands, there is no experience with this yet. However, Norway and the UK have already organised successful Sandboxes.
On the
31rd of March 2022, there will be a hybrid event in which we want to exchange (international) experiences and insights. We aim for this to be the start for the design of the legal framework for Dutch AI Regulatory Sandboxes.
Meeting
Date: Thursday March 31st 2022
Location: AI Innovation Center Eindhoven and online
Language: English
Start: 13:00
End: 17:30
Speakers
- Martijn van Grieken; Gimix, Developer of AI systems
- Sofia Ranchordas; University of Groningen
- Florina Pop; European Institute of Public Administration (EIPA)
- Eirik Gulbrandsen; Norwegian Data Protection Authority
- Huub Janssen; Planner Supervision on Artificial Intelligence, Dutch Telecom Supervisory Authority
Organisation
This meeting is organised by the Netherlands AI Coalition, the Dutch Association for AI and Robot Law and AI knowledge platform LegalAIR. | https://bg.legal/event/ai-regulatory-sandbox |
Successful alumni are ready to share valuable information about their careers. In addition, alumni contacts may lend insight or advice regarding the cities where they live and work and may be able to refer you to other industry contacts.
The Alumni Directory is a database of University of Chicago alumni across all the schools and divisions. It’s a great way to find and reconnect with friends from UChicago or grow your professional network by 150,000 people, give or take.
Frequently Asked Questions
Why use the Alumni Directory?
Use the Alumni Directory to find University of Chicago alumni you want to connect with on professional topics. You can use the directory to network at any point in your career—when you’re just starting out, growing in your field, or considering a career change. You can also use the system to simply expand your existing network. It’s a resource for all UChicago alumni.
How do I use it?
First, consider what criteria you would like to use to search for alumni. We recommend identifying one or more organizations you think would be helpful to you in your job search before searching the Alumni Directory. Use your preferred email address to log in to the directory and be sure to update your profile with the most accurate and up-to-date information while you’re there.
What’s the best way to search for alumni?
We recommend you do a keyword search in the Organization Name field first, then narrow your results from there, if necessary. This is the most effective way to find someone at a particular company or organization you are looking to network with.
What about when I’m ready to reach out to alumni?
When you’re ready to reach out to alumni, take a moment to develop a plan. Think about what it is you would like to ask this alumna or alumnus and then prepare to introduce yourself. Please follow these steps to ensure a successful outreach attempt:
- Prepare an introduction for yourself: Formally mention who you are, how you found their contact information, and why you’re contacting them.
- Identify specific goals for the conversation: What is it that you would like to know from this person? What insights do you hope to gain?
- Offer an action item: Ask to schedule a 20- to 30-minute informational interview, either in person or on the telephone. Or maybe an email response is all you need.
How should I reach out?
Use the person’s preferred method of contact, if noted. Otherwise feel free to use the listed email address. If the individual doesn’t respond within two weeks, you may attempt reaching out a second time; however, it’s not recommended to make more than two attempts.
Should I follow up?
It’s important to take a few minutes to either send an email or note thanking the person for their time. Mention what you learned from your meeting and how his or her advice or time will help you.
What if I have technical questions?
If you experience any technical issues using the Alumni Directory, please contact [email protected].
What if I need help networking?
If you need assistance, feel free to contact [email protected]. | https://alumniandfriends.uchicago.edu/career-resources/alumni-directory |
Prosopis invasion and management scenarios for Baringo County, KenyaRené Eschen, Ketema Bekele, Purity Rima Mbaabu, Charles Kilawe & Sandra Eckert
Climate change, land degradation and invasive alien species (IAS) threaten grassland ecosystems worldwide. IAS clearing and grassland restoration would help to reduce the negative effects of IAS, restore the original vegetation cover, and sustain livelihoods while contributing to climate change mitigation, but uncertain financial benefits to local stakeholders hamper such efforts. This study assessed where and when net financial benefit could be realised from Prosopis juliflora management and subsequent grassland restoration by combining ecological, social...
1 citation reported since publication in 2021.
1 view reported since publication in 2021.
These counts follow the COUNTER Code of Practice, meaning that Internet robots and repeats within a certain time frame are excluded. What does this mean? | https://search.datacite.org/works/10.5061/dryad.4xgxd258c |
The present invention relates to a data transmission apparatus for transmitting data and a method of the same, more particularly relates to a data transmission apparatus which suitably manages an encoding key and a decoding key used where a large amount of data is encoded and transferred and a method of the same.
Conventionally, in a TV broadcast or other data distribution service using a communications satellite, the flow of data was made in only one direction, that is, from the data distributor to the user. In recent years, since the transmission of digital data using communications satellite has becomes possible, transmission using the communications satellites has started for not only analog video and audio data such as TVS and movies, but also the text utilized in computers and digital video and audio data.
Here, conventional data distribution services using communications satellites such as TV broadcasting has been of the form with data distributed by a data distributor being simultaneously received and used by a large number of users. Contrary to this, where the digital data used in computers is distributed via a communications satellite, a function for distributing the data from the data distributor to a single or a plurality of users is required.
In the conventional transmission system using a communications satellite, however, there is a problem in that since the distribution is performed for analog data and since the data distribution is performed in only one direction from the data distributor to the user. Since no function for checking the errors in transmission is provided, the reliability of the data transmission is low. In the distribution of digital data, if even one bit of error is caused in the data due by the transmission, the received data no longer has any meaning.
In order to distribute such digital computer data by a wireless system with a high quality, it is necessary to secure a communication path for not only the distribution of data in one direction from the data distributor to the user, but also a communication path from the user to the data distributor. The conventional transmission system is not provided with such a function.
Also, in the conventional simultaneous communication or broadcast system from a data distributor to many users, all users always receive, use, or view the same information. There is no personal identification information of the system users, therefore it is not possible to distribute data from the data distributor to only specific users.
Further, where data is transmitted or a conversation is conducted by using a public telephone line, dedicated line, etc., in order to prevent the leakage of the transmitted information or maintain the reliability of the information against attack (interference) with respect to the transmitted information, plain text data is encoded (scrambled) and then transmitted, and the encoded data is decoded (descrambled) at the destination of reception. As a typical encoding system, a common key encoding system and a public key system have been known.
The common key encoding system is also referred to as the symmetrical encoding system. An algorithm private type and an algorithm public type have been known. As a typical algorithm public type, the DES (data encryption standard) has been known.
In the public key system, since an enormous amount of calculation is necessary for deriving the generated key from an inspection key, the generated key is not substantially decoded, therefore it is an encoding system wherein the encoding key can be made public and is referred to also as the asymmetrical key encoding system.
The encoding system is determined in accordance with the type of the line system through which the transmission data is transmitted, the degree of secrecy (secret) of the transmitted data, the amount of transmitted data, etc.
In data transmission using a dedicated line, the degree of leakage of the information and the attack of the transmitted data is low. But when data is transmitted by using a public telephone line, the degree of the leakage of information and the degree of attack becomes high. Further, the transmission of data using a satellite broadcasting line can be received by many unspecified apparatuses, therefore the degree of leakage of information becomes even higher.
FIG. 1 is a schematic structural view of an example of an encoded data transmitting apparatus for encoding the data on the transmission line by a common key encoding system.
In the encoded data transmitting apparatus of FIG. 1, reference numeral 101 denotes a transmitting apparatus (transmitter), reference numeral 102 denotes a receiving apparatus (receiver), 103 denotes a tapping apparatus (tapper), reference numeral 104 denotes a data transmission line, reference numeral 105 denotes data which should be transmitted, reference numeral 106 denotes an encoding unit provided in the transmitting apparatus 101, reference numeral 107 denotes an encoding key (encoding session key) used for the encoding in the encoding unit 106, reference numeral 108 denotes a decoding key (decoding session key), reference numeral 109 denotes a decoder for decoding the encoded data received from the data transmission line 104 using the decoding key, and reference numeral 110 denotes the data after decoding.
The transmitting apparatus 101, when transmitting the data 105 onto the transmission line 104, has the encoding unit 106 encode the data 105 by using the encoding key 107 and transmits the encoded data to the receiving apparatus 102 via the transmission line 104.
The receiving apparatus 102, when receiving the encoded data from the transmission line 104 (encoded data), has the decoder 109 decode the received encoded data by using the decoding key 108 corresponding to the encoding key 107 so as to obtain an intended decoded (deciphered) data 110.
In this example, even if the tapping apparatus 103 receives the encoded data from the transmission line 104 in the same way as the receiving apparatus 102, there is no decoding key 108, so it is difficult to correctly decode this. Namely, the tapping apparatus 108 ends up handling encoded (scrambled) data as is, therefore, in actuality, the information is prevented from being leaked to the tapping apparatus 103 side.
In a principal encoding system of the common key encoding system in this example, generally the encoding key 107 and the decoding key 108 have the same bit train.
Recently, broadcasters have been making satellite broadcasts for providing TV programs to only specific contractors. The transmission system used for the satellite broadcast can transmit a large amount of data (information) such as a video and audio in a short time. Further, a transmission system using a satellite can transmit a large amount of information in a short time and therefore is not limited to broadcastsxe2x80x94it has been widely utilized for the transmission of data such as computer data.
In transmission using a satellite, however, unlike a one-to-one communication system such as a telephone line and dedicated line, many unspecified receivers can easily receive the data (by receiving apparatuses), so it is easy to be tapped by nature. As a result, there is a high possibility that for example a pay satellite broadcast will be tapped. Therefore, it has been proposed too to also encode the video data and audio data of a TV broadcast for transmission.
In actual transmission, the encoding is not carried out for all data, but the data which should be encoded is encoded and transmitted onto the transmission line in accordance with the content of the data to be transmitted in the transmitting apparatus (for example, whether it is pay data or not). The receiver decodes all or part of the encoded data to determine whether or not the all or partially decoded data is necessary for it at the present by the information obtained as a result of this.
In the encoded data transmitting apparatus for transmitting encoded data in this way, it is necessary for the transmission side and reception side to hold the encoding key and decoding key in advance in secret so as not to be known to third parties.
As in the conventional method where the transmission side holds the encoding key and the reception side holds the decoding key, for example, when encoding and transmitting video data etc. by using for example a satellite transmission line, consideration may be made of the method of the transmitter sending the receiver a piece of paper, an IC card, etc. on which the decoding key is recorded by the mail or another method, the method of transmitting the encoding key and the decoding key through the same transmission line as the satellite transmission line for sending the video data (satellite transmission line), and further a method combining them.
In the conventional method of management of an encoding key and decoding key, there are the following problems.
A first problem is related to how the transmitter gets to hold the encoding key or how the receiver gets to hold the decoding key or.
As explained above, as the method for having the encoding key held by the transmitter and having the decoding key held by the receiver, the method for sending an object such as the paper and IC card on which the decoding key is recorded from the transmitter to the receiver by the method of mail, etc., the method of sending the same by the satellite transmission line, and further the method combining them, are general.
(1) In the method of sending an object on which the decoding key is recorded through the mail etc., due to the trouble of the procedure thereof, it is not easy to change the encoding key and the decoding key. This means that a large amount of data encoded using the same key will be transmitted onto the transmission line and that, since a large amount of information will be given to the tapper, the safety with respect to the deciphering will be low.
(2) In the method of sending the decoding key by using a satellite transmission line, the data on the satellite transmission line will be received by many unspecified persons having the antennas and other equipment irrespective of whether or not the transmitter desires these persons as the receivers. Thus, there is a possibility that the decoding key will be learned by persons other than the receivers expected by the transmitter and therefore there is problem that the safety of the transmission cannot be held.
(3) In the method combining the above two methods, that is, the method of preparing the decoding key from information recorded on an object sent by mail etc. and information transmitted through a satellite transmission line, the drawbacks of the two methods are compensated and the safeness of the transmission method becomes higher to a certain extent. However, the problem that information for a decoding key sent through the mail etc. cannot be easily changed due to the troublesomeness of the procedures and the problem that the information for a decoding key transmitted through a satellite transmission line ends up being received by a large number of unspecified persons not desired by the transmitter remain.
A second problem relates to how to decide whether or not the transmitter has encoded the data or how the receiver should decode the received data.
As mentioned above, in the methods which are used in general at the present, the transmitting apparatus views the contents of the data, encodes the data which must be encoded, and transmits it onto the transmission line. The receiving apparatus decides whether or not this data is necessary for it by the information obtained by decoding all or part of the encoded data received from the transmission line. In this method, however, the transmitting apparatus has to perform processing for learning the contents of the data for determining whether or not the data must be encoded. Further, the receiving apparatus has to determine whether the received encoded data is required by it or not, that is, it has to perform processing for decoding all or part of the encoded data for deciding whether or not the data is addressed to it. For this reason, while it is necessary to perform the transmission at a higher speed and perform the processing in the apparatuses, with the hardware configuration heretofore, such a demand could not be satisfied.
An object of the present invention is to enable effective encoding of transmitted data at the transmitting side and effective decoding of the encoded data transmitted at the receiving side.
Another object of the present invention is to enable transmission of digital data by a wireless method without causing errors in transmission.
Still another object of the present invention is to enable transmission of digital data by a wireless method from a transmitting apparatus to just specific clients.
According to the present invention, there is provided a data transmitting apparatus connected to a first transmission system and a second transmission system, the data transmitting apparatus having a key transmitting means for transmitting through the second transmission system decoding key information for decoding encoded data sent through the first transmission system, generating means for adding first transmission control information to the data to be encoded and transmitted so as to generate transmitted data, encoding means for generating encoded data from the transmitted data based on encoding key information corresponding to the decoding key information, and data transmitting means for transmitting to the first transmission system the encoded data generated by the encoding means.
Preferably, the communication capacity per unit time of the first transmission system is larger than the communication capacity per unit time of the second transmission system. Specifically, the first transmission system includes a satellite transmission line and the second transmission system includes a cable transmission line.
Preferably, the key transmitting means transmits destination information of the transmitted data along with the decoding key information through the second transmission system.
More preferably, the key transmitting means transmits the same decoding key information and destination information to a plurality of receiving apparatuses connected to the first transmission line and the second transmission line.
Still more preferably, the encoding means generates encoded data from the transmitted data based on the encoding key information and the destination information of the transmitted data.
Preferably, further provision is made of a key encoding means for encoding the work key information to generate decoding key information.
Preferably, the encoding means generates encoded data from the transmitted data based on the work key information and the destination information of the transmitted data.
Preferably, the first transmission control information includes the destination information of the transmitted data.
Preferably, the first transmission control information includes an address defined by an Internet protocol as the destination information.
Preferably, the encoding means encodes the transmitted data including the first transmission control information.
Preferably, the encoding means adds to the transmitted data second transmission control information including the same destination information as the destination information included in the first transmission control information to generate the encoded data.
Preferably, the encoding means adds a CRC check bit to generate the encoded data.
Preferably, the second transmission control information includes information indicating the presence of coding of the data to be transmitted.
Preferably, the second transmission control information includes information for distinguishing whether the data to be transmitted is information responding to a request from a receiving apparatus or whether it is control information for operating the communications system including the data transmitting apparatus.
Further, according to the present invention, there is provided a data transmitting apparatus connected to a first transmission system and a second transmission system, the data transmitting apparatus provided with a key receiving means for receiving from the second transmission system encoding key information for encoding encoded data transmitted through the first transmission system, data generating means for adding control information to the data to be encoded and transmitted to generate transmitted data, encoding means for generating encoded data from the transmitted data based on the encoding key information, and data transmitting means for transmitting through the first transmission system the encoded data generated by the encoding means.
Preferably, the encoding means is provided with key decoding means for decoding the encoding key information to generate work key information and uses the work key information decoded by the key decoding means to generate encoded data.
More preferably, the encoding means generates encoded data based on the work key information and the destination information of the encoded data.
Further, according to the present invention, there is provided a data transmission method for transmitting data using a first transmission system and a second transmission system, the data transmission method comprising a key transmitting step for transmitting through the second transmission system decoding key information for decoding encoded data transmitted through the first transmission system, a data generating step for adding first transmission control information to the data to be encoded and transmitted to generate transmitted data, an encoding step for generating encoded data from the generate transmitted data based on encoding key information corresponding to the decoding key information, and a data transmitting step for transmitting the encoded data generated by the encoding step through the first transmission system.
Preferably, the key transmitting step transmits destination information of the transmitted data along with the decoding key information through the second transmission system.
More preferably, the key transmitting step transmits the same decoding key information and destination information to a plurality of receiving apparatuses connected to the first transmission line and the second transmission line.
Still more preferably, the encoding step generates encoded data from the transmitted data based on the encoding key information and the destination information of the transmitted data.
Preferably, further provision is made of a key encoding step for encoding the work key information to generate decoding key information.
Preferably the encoding step generates encoded data from the transmitted data based on the work key information and the destination information of the transmitted data.
Preferably, the first transmission control information includes the destination information of the transmitted data.
Preferably, the first transmission control information includes an address defined by an Internet protocol as the destination information.
Preferably, the encoding step encodes the transmitted data including the first transmission control information.
Preferably, the encoding step adds to the transmitted data second transmission control information including the same destination information as the destination information included in the first transmission control information to generate the encoded data.
Preferably, the encoding step adds a CRC check bit to generate the encoded data.
Preferably, the second transmission control information includes information indicating the presence of coding of the data to be transmitted.
Preferably, the second transmission control information includes information for distinguishing whether the data to be transmitted is information responding to a request from a receiving apparatus or whether it is control information for operating the communications system including the data transmitting apparatus.
Further, according to the present invention, there is provided a data transmission method in a transmitting apparatus connected to a first transmission system and a second transmission system, the data transmission method comprising a key receiving step for receiving from the second transmission system encoding key information for encoding encoded data transmitted through the first transmission system, data generating step for adding control information to the data to be encoded and transmitted to generate transmitted data, an encoding step for generating encoded data from the transmitted data based on the encoding key information, and a data transmitting step for transmitting through the first transmission system the encoded data generated by the encoding step.
Preferably, the encoding step is provided with a key decoding step for decoding the encoding key information to generate work key information and uses the work key information decoded by the key decoding step to generate encoded data.
More preferably, the encoding step generates encoded data based on the work key information and the destination information of the encoded data.
Further, according to the present invention, there is provided a data receiving apparatus connected to a first transmission system over which encoded data is transmitted and a second transmission system over which key information is transmitted, the data receiving apparatus provided with key receiving means for receiving from the second transmission system decoding key information for decoding encoded data received from the first transmission system, a data receiving means for receiving the decoded data from the first transmission system, a data restoring means for deleting first transmission control information from the encoded data, and a decoding means for decoding the encoded data from which the first transmission control information was deleted based on the decoding key information to generate decoded data.
Preferably, the communication capacity per unit time of the first transmission system is larger than the communication capacity per unit time of the second transmission system. Specifically, the first transmission system includes a satellite transmission line and the second transmission system includes a cable transmission line.
Preferably, the key receiving means receives destination information of the encoded data along with the decoding key information from the second transmission system.
More preferably, a plurality of receiving apparatuses are connected to the first transmission system, and the key receiving means receives the same decoding key information and destination information as other receiving apparatuses connected to the first transmission line and the second transmission line.
Preferably, the decoding means generates decoded data from the received data based on the decoding key information and the destination information of the encoded data.
Preferably, the decoding means is provided with key decoding means for decoding the decoding key information to generate work key information and uses the work key information generated by the key decoding means to decode the encoded data.
Preferably, the decoding means decodes the encoded data based on the work key information and the destination information of the encoded data.
More preferably, the first transmission control information includes the destination information of the encoded data.
Still more preferably, the first transmission control information includes an address defined by an Internet protocol as the destination information.
Specifically, the decoding means decodes the encoded data which was encoded including the first transmission control information.
Preferably, further provision is made of a judgement means for judging if the encoded data is directed to itself based on the second transmission control information including the same destination information as the destination information included in the first transmission control information of the encoded data.
Preferably, the judgement means judges if the encoded data is directed to itself and checks to the CRC check bit added to the encoded data to check for errors.
More preferably, the judgement means judges if the encoded data is directed to itself and decides whether to decode or not based on the information indicating the presence of encoding included in the second transmission control information.
Preferably, the second transmission control information includes information for distinguishing whether the received data is information responding to a request from its own receiving apparatus or whether it is control information for operating the communications system including the receiving apparatus.
Further, according to the present invention, there is provided a data receiving apparatus connected to a first transmission system and a second transmission system, the data receiving apparatus provided with a key transmitting means for transmitting through the second transmission system encoding key information for preparing encoded data received from the first transmission system, data receiving means for receiving the encoded data encoded based on the encoding key information from the first transmission system, data restoring means for deleting the first transmission control information from the encoded data, and a decoding means for decoding the encoded data based on decoding key information corresponding to the encoding key information.
Preferably, further provision is made of a key encoding means for encoding work key information to generate encoding key information.
More preferably, the decoding means is provided with a decoding key generating means for generating a decoding key based on the work key information and the destination information of the encoded data and decodes the encoded data based on the decoding key generated by the decoding key generating means.
Further, according to the present invention, there is provided a data receiving method in a receiving apparatus connected to a first transmission system and a second transmission system, the data receiving method comprising a key receiving step for receiving from the second transmission system decoding key information for decoding encoded data received from the first transmission system, a data receiving step for receiving the decoded data from the first transmission system, a data restoring step for deleting first transmission control information from the encoded data, and a decoding step for decoding the encoded data from which the first transmission control information was deleted based on the decoding key information to generate decoded data.
Preferably, the key receiving step receives the same decoding key information and destination information as other receiving apparatuses connected to the first transmission system and the second transmission system.
More preferably, the decoding step generates decoded data from the encoded data based on the decoding key information and the destination information of the encoded data.
More preferably, the decoding step is provided with key decoding step for decoding the decoding key information to generate work key information and uses the work key information generated by the key decoding step to decode the encoded data.
Preferably, the decoding step decodes the encoded data based on the work key information and the destination information of the encoded data.
Preferably, the first transmission control information includes the destination information of the encoded data.
More preferably, the first transmission control information includes an address defined by an Internet protocol as the destination information.
Preferably, the decoding step decodes the encoded data which was encoded including the first transmission control information.
Preferably, further provision is made of a judgement step for judging if the encoded data is directed to itself based on the second transmission control information including the same destination information as the destination information included in the first transmission control information of the encoded data.
Preferably, the judgement step judges if the encoded data is directed to itself and checks to the CRC check bit added to the encoded data to check for errors.
More preferably, the judgement step judges if the encoded data is directed to itself and decides whether to decode or not based on the information indicating the presence of encoding included in the second transmission control information.
Preferably, the second transmission control information includes information for distinguishing whether the received data is information responding to a request from its own receiving apparatus or whether it is control information for operating the communications system including the receiving apparatus.
Further, according to the present invention, there is provided a data receiving method in a receiving apparatus connected to a first transmission system and a second transmission system, the data receiving method comprising a key transmitting step for transmitting through the second transmission system encoding key information for preparing encoded data received from the first transmission system, a data receiving step for receiving the encoded data encoded based on the encoding key information from the first transmission system, a data restoring step for deleting the first transmission control information from the encoded data, and a decoding step for decoding the encoded data based on decoding key information corresponding to the encoding key information.
Preferably, further provision is made of a key encoding step for encoding work key information to generate encoding key information.
Preferably, the decoding step is provided with a decoding key generating step for generating decoding key information based on the work key information and the destination information of the encoded data and decodes the encoded data based on the decoding key generated by the decoding key generating step.
Further, according to the present invention, there is provided a data transmission apparatus having a first transmission system and a second transmission system, the data transmission apparatus provided with:
a transmitting apparatus having a key transmitting means for transmitting through the second transmission system decoding key information for decoding the encoded data transmitted through the first transmission system, data generating means for generating transmitted data added with first transmission control information from the data to be encoded and transmitted, encoding means for generating encoded data from the transmitted data based on encoding key information corresponding to the decoding key information, and data transmitting means for transmitting through the first transmission system the encoded data generated by the encoding means and
a receiving apparatus having a key receiving means for receiving from the second transmission system decoding key information for decoding the encoded data received from the first transmission system, data receiving means for receiving the encoded data from the first transmission system, data restoring means for deleting first transmission control information from the encoded data, and decoding means for decoding the encoded data based on the decoding key information.
Further, according to the present invention, there is provided a data transmission apparatus having a first transmission system and a second transmission system, the data transmission apparatus provided with:
a transmitting apparatus having a key receiving means for receiving from the second transmission system encoding key information for encoding the encoded data transmitted through the first transmission system, data generating means for generating transmitted data added with control information from the data to be encoded and transmitted, encoding means for generating encoded data from the transmitted data based on encoding key information, and data transmitting means for transmitting through the first transmission system the encoded data generated by the encoding means and
a receiving apparatus having a key transmitting means for transmitting through the second transmission system encoding key information for preparing the encoded data received from the first transmission system, data receiving means for receiving the encoded data encoded based on the encoding key information from the first transmission system, data restoring means for deleting first transmission control information from the encoded data, and decoding means for decoding the encoded data based on decoding key information corresponding to the encoding key information.
Further, according to the present invention there is provided
a data transmission method using a transmission apparatus having a first transmission system and a second transmission system, the data transmission method comprising:
a transmitting processing step having a key transmitting step for transmitting through the second transmission system decoding key information for decoding the encoded data transmitted through the first transmission system, a data generating step for generating transmitted data added with first transmission control information from the data to be encoded and transmitted, an encoding step for generating encoded data from the transmitted data based on encoding key information corresponding to the decoding key information, and a data transmitting step for transmitting through the first transmission system the encoded data generated by the encoding step and
a receiving processing step having a key receiving step for receiving from the second transmission system decoding key information for decoding the encoded data received from the first transmission system, a data receiving step for receiving the encoded data from the first transmission system, a data restoring step for deleting first transmission control information from the encoded data, and a decoding step for decoding the encoded data based on the decoding key information.
Further, according to the present invention, there is provided a data transmission method for transmission of data using a transmission apparatus having a first transmission system and a second transmission system, the data transmission method comprising:
a transmitting processing step having a key receiving step for receiving from the second transmission system encoding key information for encoding the encoded data transmitted through the first transmission system, a data generating step for generating transmitted data added with control information from the data to be encoded and transmitted, an encoding step for generating encoded data from the transmitted data based on encoding key information, and a data transmitting step for transmitting through the first transmission system the encoded data generated by the encoding step and
a receiving processing step having a key transmitting step for transmitting through the second transmission system encoding key information for preparing the encoded data received from the first transmission system, a data receiving step for receiving the encoded data encoded based on the encoding key information from the first transmission system, a data restoring step for deleting first transmission control information from the encoded data, and a decoding step for decoding the encoded data based on decoding key information corresponding to the encoding key information.
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The City of Cape Town has deployed fieldworkers to conduct its regional household travel survey within various areas across Cape Town.
The survey aims to gather data on the travel behaviour of households in Cape Town. Residents are urged to participate in the survey, which will assist in updating future transport plans.
“Our objective with this survey is to retrieve an updated demographic of the City’s residents and to collect accurate information on their travel behaviour.
“This data will equip the City to review and update its transport network plans and the travel demand model,” says the City’s mayoral committee member for transport, Felicity Purchase.
This city-wide survey will target households in Cape Town and surrounding areas such as Stellenbosch, Franschhoek, Malmesbury, Darling, Paarl and Wellington.
Information on all of the adults and school-going children per household will
be required. Individual households have been randomly selected in a systematic sampling process.
“I urge residents who are approached to participate in these interviews as we seek to obtain insight and a good grasp on the travel needs and patterns of commuters.
“We would be grateful if community leaders and associations could assist the City in informing residents of the survey on their various platforms,” said Ms Purchase.
The City is aiming to collect information such as how many employed persons there are per household; how many household members travel regularly to work and places of education; the average transport budget per household; the various modes of transport used throughout the week and the duration of their travels.
Umtha Consultancy has been contracted by the City of Cape Town to conduct and manage the roll out of this city-wide survey. Residents to note that all fieldworkers will be identifiable by their Umtha name tags.
Residents can be assured that the findings will not be made public as the only purpose of the survey is to collect information that will inform future planning decisions and City processes.
All of the fieldworkers conducting this survey will be monitored and supervised as the City has recruited supervisors as part of the team.
These supervisors, aside from monitoring supervising the surveyors, will also assist with queries on site.
Residents can be assured that all information collected will be treated anonymously, and the location of their home will by no means be revealed.
The survey will only focus on households and will exclude inhabitants of:
Military and police barracks;
Prison quarters;
Student residences;
Old age homes;
Religious institutions;
Shelters;
Non-residential hostels, school and student residences;
Industrial areas. | https://www.bolanderlifestyle.co.za/news/household-travel-survey-to-inform-citys-transport-plans |
I have started my Master’s studies in Computer Science at the University of Manitoba in 2021 at the HCI lab. In my thesis, I am interested in the impacts of collaborative learning on software learnability for older adult users.
I am holding two BSc degrees in Computer Engineering (IT- 2018) and Industrial Engineering (2020) from Amirkabir University of Technology, Tehran, Iran.
Current project
Recently, older adults are becoming target users of different types of feature-rich software for both non-work and work-related applications. Although older adults’ tendency to learn these applications has altered lately, and they are more open to adopt independent methods such as exploration, their experience is still more negative and frustrating than pleasant. Collaborative learning has not been explored in the context of feature-rich software for older adult users. In my project, I examine the impact of collaboration on older adults’ learning behavior of feature-rich software. I want to observe mixed-age and same-age dyadic interactions to have the opportunity to make a comparison.
If you are interested in participating in my research and for more information, please visit: | https://www.af-baghestani.com/ |
As portable electronic devices become more compact, and the number of functions performed by a given device increase, it has become a significant challenge to design a user interface that allows users to easily interact with a multifunction device. This challenge is particular significant for handheld portable devices, which have much smaller screens than desktop or laptop computers. This situation is unfortunate because the user interface is the gateway through which users receive not only content but also responses to user actions or behaviors, including user attempts to access a device's features, tools, and functions. Some portable communication devices (e.g., mobile telephones, sometimes called mobile phones, cell phones, cellular telephones, and the like) have resorted to adding more pushbuttons, increasing the density of push buttons, overloading the functions of pushbuttons, or using complex menu systems to allow a user to access, store and manipulate data. These conventional user interfaces often result in complicated key sequences and menu hierarchies that must be memorized by the user.
Many conventional user interfaces, such as those that include physical pushbuttons, are also inflexible. This may prevent a user interface from being configured and/or adapted by either an application running on the portable device or by users. When coupled with the time consuming requirement to memorize multiple key sequences and menu hierarchies, and the difficulty in activating a desired pushbutton, such inflexibility is frustrating to most users.
As used herein, widgets (or widget modules) are mini-applications that may be downloaded and used by a user or created by the user. In some embodiments, a widget includes an HTML (Hypertext Markup Language) file, a CSS (Cascading Style Sheets) file, and a JavaScript file. In some embodiments, a widget includes an XML (Extensible Markup Language) file and a JavaScript file (e.g., Yahoo! Widgets). In some embodiments, a widget is a mini-application written in a compiled language (e.g., C, C++, or Objective-C). At present, each widget typically includes its own configuration mode and screen. As more widgets are added to a device, the processes for configuring and displaying widgets become more cumbersome.
Accordingly, there is a need for portable multifunction devices with more efficient user interfaces for configuring and displaying widgets. Such interfaces increase the effectiveness, efficiency and user satisfaction with widgets on portable multifunction devices.
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London: The capture of the most wanted sub-atomic particle in physics - Higgs boson - has topped the chart of the year`s ten biggest scientific breakthroughs.
Scientists had been chasing the Higgs boson, nicknamed the `God particle` for more than four decades.
In July the team from the European nuclear research facility at CERN in Geneva announced the detection of a particle that fitted the description of the elusive Higgs.
The boson is believed to give matter mass via an associated `Higgs field` that permeates space. Without the property of mass, the universe we live in could not exist.
Scientists used the world`s biggest atom smashing machine, the Large Hadron Collider on the Swiss-French border, to track down the missing particle.
Finding the Higgs topped the list of most important discoveries of 2012 released by Science, a prestigious scientific journal, the `Daily Mail` reported.
"Mass must somehow emerge from interactions of the otherwise mass-less particles themselves. That`s where the Higgs comes in," Science news journalist Adrian Cho, who wrote about the discovery in the journal`s latest issue, said.
Nine other pioneering achievements from 2012 which made it to the list included sequencing of the DNA blueprint of the Denisovans, an extinct species of human that lived alongside Neanderthals and the ancestors of people living today.
Japanese researchers showing that embryonic stem cells from mice could be coaxed into becoming viable egg cells was hailed as another breakthrough.
Curiosity rover`s Landing System was also an achievement for the scientific world as mission engineers at the American space agency NASA safely and precisely placed the Curiosity rover on the surface of Mars.
In another advance, researchers used an X-ray laser, which shines a billion times brighter than traditional synchrotron sources, to determine the structure of an enzyme required by the parasite that causes African sleeping sickness.
In 2012, scientists using a tool known as TALENs, which stands for `transcription activator-like effector nucleases`, altered or inactivated specific genes in animals such as zebra fish and toads, and cells from patients with disease.
A team from Netherlands gave solid evidence of the existence of Majorana fermions, particles that act as their own antimatter and annihilate themselves.
A decade-long study reported this year revealed that the human genetic code is more functional than researchers had believed while another team showed that paralysed human patients could move a mechanical arm with their minds and perform complex movements in three dimensions.
Researchers working on the Daya Bay Reactor Neutrino Experiment in China found the last part of the jigsaw describing how particles known as neutrinos morph from one strain or `flavour` to another travelling at near-light speed. | http://zeenews.india.com/news/space/higgs-boson-discovery-biggest-scientific-breakthrough-of-2012_818051.html |
Q:
Many-to-Many relationship in Django
I have the following 3 models:
class Platform(models.Model):
title = models.CharField(max_length=100, unique=True)
class Profile(models.Model):
title = models.CharField(max_length=110, unique=True)
platform = models.ManyToManyField(Platform)
class Register(models.Model):
...
profile = models.ManyToManyField(Profile)
...
My views.py
def info(request):
...
registers=Register.objects.all()
...
for register in registers:
profile= register.profile....???
I need to know the profile or profiles from a query of the Register model
is possible?
A:
You can obtain all the Profiles related to one or more registers with:
Profile.objects.filter(register__in=registers)
or you can obtain the Profiles of a Register object:
def info(request):
# …
registers=Register.objects.all()
# …
for register in registers:
profiles = register.profile.all()
but here you will hit the database per register, which might not scale very well.
You can, like @IainShelvington says, use .prefetch_related(…) [Django-doc] to fetch all these related Profiles in memory with one extra query and do the JOIN at the Django/Python level:
def info(request):
# …
registers=Register.objects.prefetch_related('profile')
# …
for register in registers:
profiles = register.profile.all()
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We have a deep love for science in the fifth grade and we do tons of it! The Science Fusion curriculum has an interactive textbook component where the students will be writing, highlighting, making annotations, underlining, marking, boxing, bracketing, drawing arrows, numbering, writing comments…yes right on their textbooks! Also, students will be able participate in hands-on activities and labs, observe virtual labs, digital interactions, leveled readers, and observe video-based projects.
Units of Study:
· The Scientific Method
· Physical Science: Matter, Forces and Motion, Simple Machines.
· Life Science: Cells to Body Systems, Living Things Grow and Reproduce, Ecosystems/Biomes, Energy and Ecosystems
· Earth Science: Natural Resources, Changes to Earth’s Surface, Earth’s Oceans, Water on Earth, Weather Patterns, The Solar System and the Universe
In the fifth grade, students:
- Study the steps in the Scientific Method
· Study matter (atoms, elements, molecules) and its chemical and physical properties; mixtures and solutions; states of matter (solid, liquid, gas)
· Learn about the basic functions of cells; human body systems
· Gain more in-depth knowledge about plants and animals and the roles and cycles of plants and animals; ecosystems and the role of organisms within an ecosystem
· Study natural resources, renewable and nonrenewable resources
· Study weathering, erosion and deposition
· Study the planet Earth, including its structure, layers, and plate tectonics; earthquakes, volcanoes, and glaciers
· Study weather patterns and causes; Earth’s Oceans
· Study the Solar System
Project 1: Science Fair
Project 2: Simple Machines
Fifth Grade Science
Grade Level Expectations at a Glance
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Standard
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Grade Level Expectation
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1. Physical Science
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1. Mixtures of matter can be separated regardless of how they were created; all weight and mass of the mixtures are the same as the sum of weight and mass of its parts
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2. Life Science
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1. All organisms have structures and systems with separate
functions
2. Human body systems have basic structures, functions, and needs
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3. Earth Science
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1. Earth and sun provide a diversity of renewable and nonrenewable resources
2. Earth’s surface changes constantly through a variety of processes and forces
3. Weather conditions change because of the uneven heating of Earth’s surface by the Sun’s energy. Weather changes are measured by differences in temperature, air pressure, wind and water in the atmosphere and type of precipitation
II. Reading: Reading Street, Scott Foresman
We will cover the five components of reading: phonics, phonemic awareness, vocabulary, comprehension, and fluency; we have read stories from different genres. Students are expected to read aloud to an adult for 20 minutes or more every day at home. The Reading Street series has a spelling component. Every Thursday, students will have their spelling test as well as receive their new spelling words to study for the following week. Students are expected to do a daily oral practice with an adult at home.
The Great Books Foundation, Junior Great Books
This program involves students and the instructor as partners in reading, discussing, and writing about the essential questions raised by outstanding works of literature. The main skill learned is Shared Inquiry. In Shared Inquiry, students discuss interpretive questions and higher-level questioning methods which deal with critical thinking.
In the fifth grade, students:
· Are working toward reading fluency of 150 words per minute
· Read chapter books (fiction and nonfiction), informational texts, and poetry
· Can more easily analyze and interpret poetry
· Use prior knowledge, comprehension strategies, and inference to understand text
· Understand prefixes, suffixes, and use context clues to derive meaning
· Use additional aspects of text (including diagrams, tables, and charts) to assist in understanding what they are reading
· Understanding reading targets such as main idea, key concepts, cause and effect relationships, comparisons, and intention of the author of a selected reading
· Engage in rich discussions
III. Writing: Every Child a Writer
Students in the fifth grade write with an awareness of their audience and purpose. They will also use resources to gather information to support their main ideas and use technology to create documents. The Every Child a Writer curriculum focuses on a genre based writing approach (i.e. descriptive, narrative, instruction, explanation, persuasion); students do differentiated writing according to their writing stage, not their age.
In the fifth grade, students:
· Use the writing process to write narratives, research reports, persuasive letters and compositions, and responses to literature that are several paragraphs in length and have a clear focus and intention
· Use purposeful writing to describe, inform, entertain, and explain
· Use correct grammar, spelling, sentence structure, punctuation, and voice in writing
· Use a dictionary, thesaurus, encyclopedia, library databases, books, textbooks and the Internet to research, gather, and clarify information
IV. English: English, Houghton Mifflin
Units of Study: Sentences, nouns, verbs, adjectives, capitalization and punctuation, pronouns, adverbs and prepositions.
DLI, Daily Language Instruction: The focus of DLI is to provide proofreading and editing tasks to reinforce the skills taught in English.
Fifth Grade Reading, Writing, and Communicating
Grade Level Expectations at a Glance
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Standard
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Grade Level Expectation
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1. Oral Expression and Listening
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1. Effective communication requires speakers to express an opinion, provide information, describe a process, and persuade an audience
2. Listening strategies are techniques that contribute to understanding different situations and serving different purposes
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2. Reading for All Purposes
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1. Literary texts are understood and interpreted using a range of strategies
2. Ideas found in a variety of informational texts need to be compared and understood
3. Knowledge of morphology and word relationships matters when reading
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3. Writing and Composition
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1. The recursive writing process contributes to the creative and unique literary genres for a variety of audiences and purposes
2. The recursive writing process creates stronger informational and persuasive texts for a variety of audiences and purposes
3. Conventions apply consistently when evaluating written texts
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4. Research and Reasoning
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1. High-quality research requires information that is organized and presented with documentation
2. Identifying and evaluating concepts and ideas have implications and consequences
3. Quality reasoning requires asking questions and analyzing and evaluating viewpoints
V. Social Studies/Geography: The United States, Macmillan/McGraw-Hill
Units of Study:
· Our Nation’s Geography: regions and landforms on the United States.
· Unit 2: Exploration and Civilization (Expeditions of early explorers, i.e. Marco Polo, Christopher Columbus, Prince Henry of Portugal, Spanish explorers); French Colonies and English Colonies.
· Unit 3: Colonial America: New England, Middle Colonies, Southern Colonies, Colonial Economies and their Governments.
· Unit 4: The Struggle for North America: The French in Louisiana, The French and Indian War, Colonists Protesting British Rule, Revolutionary War, and the Declaration of Independence.
· Unit 5: The New Nation: The United States Constitution, the Louisiana Purchase, the War of 1812.
· Geography: Central America, Middle East, Europe, and Russia.
· Native People of North America: Native Americans of the Pacific Northwest, Southwest, Plains, and Eastern Woodlands. | http://www.prairieschool.org/node/74 |
Off to the library 1,2,3.....
We have a well resourced library that is full of quality fiction and non-fiction books. The children visit the library once a week with their class. They enjoy a story, learn about a library as well as book knowledge such as author and illustrator.
The children then choose a book to take home for the week.
There is great value in reading to your child each day and our library books can introduce your child to a wide variety of literature.
When reading to your child, encourage them to look at the pictures and tell you what they see.
Ask them questions, get them to predict what's going to happen or just sit and enjoy the story together. | https://johnbrotch-p.schools.nsw.gov.au/our-curriculum/educational-program/library.html |
INTRODUCTION
============
Approximately 15% to 26% of patients with prostate cancer (PC) will present with high-risk disease despite prostate-specific antigen (PSA) screening \[[@B1],[@B2]\]. High-risk disease is understood to be a significant predictor of progressive, symptomatic disease or death from PC \[[@B3]\]. The widely accepted definition of high-risk PC was first proposed by D\'Amico on the basis of a pretreatment Gleason score of 8, a clinical stage of at least T2c, or a presenting PSA level of 20 ng/mL \[[@B4]\].
The optimal management of patients with high-risk PC remains controversial \[[@B5],[@B6],[@B7]\]. Available therapeutic options include monotherapy by radical prostatectomy (RP) or combined modality approaches that include local treatments such as radiotherapy (RT) along with androgen deprivation therapy (ADT) or chemotherapy. High-risk PC patients are at increased risk of locally advanced or micrometastatic disease; therefore, it is reasonable to employ a more aggressive treatment plan targeting the local as well as the systemic components of the disease \[[@B8],[@B9]\]. Considerations for surgical management were often discarded in such individuals owing to the increased risk of biochemical recurrence (BCR), systemic progression, and worse oncologic outcomes \[[@B10],[@B11]\].
Currently, several studies have shown comparable oncologic outcomes for RP relative to RT or ADT in the context of high-risk disease \[[@B12],[@B13],[@B14],[@B15]\]. Zelefsky et al. \[[@B16]\] showed that RP was associated with a nearly 10% lower risk of progression to metastasis and a lower cancer-specific mortality (CSM) compared with high-dose RT in patients with high-risk PC. The 10-year outcomes from the Cancer of the Prostate Strategic Urological Research Endeavor (CaPSURE) database for men with high-risk PC treated with RP showed 90% local recurrence-free survival, 89% systemic progression-free survival (PFS), 95% cancer-specific survival (CSS), and 80% overall survival (OS) \[[@B17]\]. Even in the very-high-risk category using the Cancer of the Prostate Risk Assessment (CAPRA) score, approximately 20% of men will be cured with RP alone \[[@B2],[@B18]\].
High-risk PC patients treated with RP have variable survival outcomes, according to different high-risk definitions. Nevertheless, independent of the definition, highly convincing, long-term CSS rates have been described. Frequent downgrading and downstaging, and a possible therapeutic role of local tumor debulking, support RP and extended pelvic lymph node dissection (e-PLND) as primary management strategies during multimodality treatment \[[@B19]\]. However, many guidelines are reluctant to endorse RP as an equivalent treatment to RT and ADT \[[@B18]\].
The aim of this review was to define high-risk PC and to elaborate on the emerging evidence to support the role of RP as both a monotherapy and as part of a collaborative, multimodal approach in high-risk localized PC. The role of robot-assisted RP (RARP), which is increasingly being utilized in Korea for the surgical treatment of PC in this clinical scenario, is discussed.
WHAT IS HIGH-RISK PROSTATE CANCER?
==================================
[Table 1](#T1){ref-type="table"} summarizes the contemporary and most widely used definitions of high-risk PC. The exact definition of high-risk PC is unclear, and a consensus has not yet been reached. This lack of consensus on a definition of high-risk disease represents a critical barrier for patient counseling, comparative assessment of treatment outcomes, and the design of randomized trials. High-risk, clinically localized disease was classically defined by D\'Amico et al. \[[@B4]\] as any combination of the following factors: a PSA greater than 20 ng/mL, a Gleason score of 8 to 10, or a clinical stage of T2C or higher. The American Urological Association (AUA) has endorsed these D\'Amico high-risk criteria \[[@B20]\]. More recently, the National Comprehensive Cancer Network (NCCN) and the European Association of Urology (EAU) modified this definition to include any combination of a clinical T3 stage, a PSA score greater than 20 ng/mL, or a Gleason score of 8 to 10 \[[@B21],[@B22]\]. The Radiation Therapy Oncology Group also described a classification system to predict overall and cause-specific survival \[[@B23]\]. However, an estimation of patients\' risk of progression with this definition is far from perfect, because these criteria encompass a heterogeneous group of patients.
Clinical stage is often inaccurate in localized PC. Digital rectal exams fail to detect extracapsular extension in 30% to 50% of patients. The role of clinical stage remains controversial, because it does not necessarily add information and displays interobserver variability \[[@B5],[@B24],[@B25]\]. In a recent review of the CaPSURE database, an inaccurate clinical stage was assigned to 35.4% of patients \[[@B24],[@B26]\]. Pretreatment PSA can reflect not only cancer, but benign prostatic hyperplasia or chronic inflammation \[[@B27]\]. Finally, biopsy downgrading after the final pathological assessment is a common phenomenon, occurring in up to 45% of cases \[[@B28],[@B29]\].
Because of these limitations, several multivariate risk assessment tools have been developed. The Kattan preoperative nomogram uses a multivariate model that combines stage, PSA, and additional prostate biopsy information to generate an estimate of the risk of treatment failure following RP \[[@B30]\]. Recently, Cooperberg et al. \[[@B31]\] developed another high-risk PC definition: the CAPRA score. They added secondary parameters, including prostate biopsy profiles (biopsy Gleason score and percentage of positive biopsy cores) and patient age to the existing basic parameters. The CAPRA score ranges from 0 to 10, and a CAPRA score of 6 to 10 represents high-risk PC. This tool was recently updated, because both the CAPRA postsurgical score (CAPSA-S) and postoperative pathologic results can be used to predict BCR after RP on a continuous scale. Additional variables such as extent of cancer in needle biopsy, pretreatment PSA velocity, PSA doubling time, or the presence of a tertiary Gleason pattern have been suggested to optimize risk stratification \[[@B32]\].
To be clinically useful, criteria defining high-risk PC should reliably distinguish patients whose cancer is amenable to cure with local therapy alone from those who may require additional systemic therapy. Novel molecular markers that can both significantly enhance the prediction of relapse following therapy and identify locally advanced and occult metastatic disease are needed. Incorporating several known risk factors together with endorectal magnetic resonance imaging findings, pretreatment PSA velocity, and additional data from prostate biopsies may produce a more precise, high-risk disease definition.
RATIONALE FOR SURGERY FOR HIGH-RISK PROSTATE CANCER
===================================================
Traditionally, RP was not considered a viable treatment option for high-risk PC cases \[[@B33]\]. However, several recent studies of high-risk PC have presented another view ([Table 2](#T2){ref-type="table"}). In some high-risk PC patients, RP is a one-step modality for a cure, with excellent oncological prognosis. One of the most important benefits of RP compared with nonsurgical therapy is pathologic staging of both the primary cancer and regional lymph nodes. Although preoperative risk group stratification and nomograms may identify patients with adverse features, studies have established that pathologic variables, such as pathologic Gleason pattern and stage, more accurately predict who may benefit from additional therapy. In favorable situations, pathologic downgrading and downstaging at RP may potentially spare patients from receiving adjuvant therapy. In a review of the CaPSURE database, an inaccurate clinical stage was assigned to 35.4% of patients \[[@B24]\]. About one-third of high-grade (8-10) biopsy Gleason scores were subsequently downgraded at RP and 26% to 31% were shown to have organ- or specimen-confined disease \[[@B34],[@B35]\]. A study by Abern et al. \[[@B36]\] on this issue of PC adds significantly to the literature by demonstrating that pathologic downstaging occurs more frequently than previously reported and that patients who were downstaged had survival outcomes that were similar to those of patients with intermediate- and low-risk PC.
Lymphadenectomy at the time of RP confers information about the level and extent of nodal involvement and may guide the initiation of earlier adjuvant ADT \[[@B37]\]. Multiple series suggest an approximately 10% to 20% 10-year disease-free recurrence without adjuvant therapy following lymph node dissection for men with lymph node metastases \[[@B38]\]. Another potential benefit of RP for high-risk disease is the possible posttreatment avoidance of additional therapy.
Approximately one-half of men with high-risk disease will be cured with RP monotherapy and thus avoid any further treatment \[[@B9],[@B39],[@B40]\]. In one study, Yossepowitch et al. \[[@B41]\] found that 35% to 76% of high-risk patients avoided secondary therapy altogether 10 years after surgery. Joniau et al. \[[@B42]\] reported on a cohort of 51 men with very high-risk PC (cT3b-T4), in which 31.4% avoided ADT, and after a median follow-up of 9 years, the 10-year biochemical PFS (BPFS) rate was 45.8%. Using CaPSURE data, Meng et al. \[[@B17]\] showed that men receiving RT for high-risk PC are 3.5 times as likely to receive ADT as are patients treated with RP. Even if men ultimately require salvage ADT for disease control after RP, they may delay the time to initiation of ADT. In a study by the Mayo Clinic on patients with cT3 disease, the average duration of freedom from ADT after RP monotherapy was 4.0 years \[[@B43]\].
Another advantage of RP is the expectation and significance of nondetectable PSA. After RP in completely excised patients, serum PSA should decline to a nondetectable level. The sensitivity of post-RP PSA provides a prompt assessment of disease cure and control, allowing early recognition of recurrent disease and delivery of salvage RT if necessary. Primary treatment with RP allows for salvage RT with curative intent in the setting of a promptly recognized local recurrence. Even in patients with poorly differentiated disease and positive margins, recurrence after RP can be effectively treated with salvage radiation that may prevent metastatic progression. Adjuvant or salvage RT cures another 50% of recurrences, representing a three-fold reduction of death from PC after surgery with minimal additional morbidity \[[@B44]\].
ROLE OF SURGERY IN THE TREATMENT OF LOCALLY ADVANCED PROSTATE CANCER
====================================================================
Until recently, surgical treatment had not been used in locally advanced PC. The role of RP in patients with locally advanced PC has been debated, because the combination of RT and hormone therapy is coming to be used more frequently for locally advanced PC. Today, according to the EAU and AUA guidelines, RP is a reasonable treatment option for selected PC patients with cT3a disease, a Gleason score of 8 to 10, or PSA\>20 \[[@B21]\]. Moreover, surgery is considered by the NCCN to be an acceptable primary treatment option for selected patients with low-volume, high-risk PC and a limited number of adverse prognostic factors \[[@B45]\]. In a series from the Memorial Sloan-Kettering Center, of 176 men with cT3 over a 20-year period, the role and effectiveness of RP were reviewed. Within this cohort, only 64 men received neoadjuvant hormone therapy. Fifty-three patients were downstaged to organ-confined disease after pathological evaluation, and more than one-half (52%) of patients remained free of disease recurrence following RP \[[@B46]\]. In a Mayo Clinic study of men undergoing RP, cT3 was found in 841 of the 5,662 patients (15%) studied. Of these 841, 661 men (79%) did not receive neoadjuvant hormone therapy. After a pathological review of these patients, 223 (27%) were found to be overstaged, and in fact had organ-confined disease \[[@B35]\]. It is important to note that surgery can identify a substantial subset of men with favorable features in whom additional therapy is not indicated. Another feature to attribute a very high-risk stratification is the presence of positive regional lymph nodes \[[@B19]\]. Recently, Engel et al. \[[@B47]\] found a doubled risk of overall mortality when RP was abandoned compared with completed RP for patients in whom positive lymph nodes were found at the time of surgery. They concluded that RP may have a survival benefit, and the abandonment of RP in node-positive cases may not be justified. A systematic review by Verhagen et al. \[[@B48]\] concluded that there was a clinically important survival benefit in men with node-positive disease who received ADT when local control of the primary tumor is achieved.
ROBOTIC PROSTATECTOMY FOR HIGH-RISK PROSTATE CANCER
===================================================
Traditionally, RP in high-risk PC is performed by use of an open approach. During the last several years, however, an increasing number of publications have discussed the use of minimally invasive techniques, particularly RARP \[[@B42]\]. The increasing availability of robotic technology to urologists has expanded the roles and indications for RARP, including recent reports of this approach in a high-risk setting. A recent retrospective analysis studied 913 patients with high-risk PC treated with open RP or minimally invasive RP with e-PLND and aimed to compare the pathological and short-term BCR-free survival outcomes for different therapeutic approaches. Of all patients, 81.4% underwent open RP, 11.5% underwent RARP, and 7.1% underwent laparoscopic RP (LRP). The authors demonstrated BCR-free survival rates of 56.3%, 67.8%, and 41.1%, respectively, and positive surgical margin (PSM) rates of 29.4%, 34.3%, and 27.7% for open retropubic RP, RARP, and LRP, respectively. An e-PLND was performed, and 10.8% of positive nodes were found in the open retropubic RP group compared with 3.5% in the minimally invasive RP group. The authors concluded that equivalent rates of PSM and short-term BPFS between open RP and minimally invasive RP were observed \[[@B49]\]. However, major limitations were differences in the cumulative number of high-risk factors, short follow-up, nonstandardized e-PLND, and nerve-sparing indications.
Punnen et al. \[[@B50]\] compared outcomes of 233 high-risk RARP cases with 177 high-risk RRP cases from a single institution. RARP patients had less blood loss and similar pathological outcomes compared to RRP patients. Overall PSM rates were 29% and 23%, respectively, and RFS rates at 4 years were 66% and 79% for RARP and RRP, respectively. Similarly, Busch et al. \[[@B51]\] noted that RARP demonstrated similar oncologic outcomes compared to RRP and LRP in a propensity-score-matched cohort of patients with high-risk PC.
Strong debate surrounds the feasibility and role of robotic surgery in performing e-PLND. A recent series of 143 robotic e-PLND patients with intermediate or high-risk PC according to the D\'Amico classification showed a median number of 20 (range, 9-65) excised nodes with positive node rates of 13% and without Clavien-Dindo complications in 82% of cases, thus confirming the technical feasibility of the procedure with minimally invasive surgery \[[@B52]\]. These promising results must be confirmed by randomized clinical trials, which will be vital to achieve optimal oncological, functional, and sexual outcomes, bearing in mind the high risk of cancer progression in this group of patients.
THE SURGICAL APPROACH AS PART OF MULTIMODAL THERAPY
===================================================
With respect to the treatment of high- and very-high-risk PC in general, the failure of RRP or RT alone (monotherapy) is well recognized, and multimodal therapy may be needed. In well-selected patients, RP combined with adjuvant or salvage treatment when needed may result in better outcomes than RT alone, similar to the combination of RT plus hormone therapy \[[@B9]\]. Definitive therapy for high-risk PC, often requiring a multimodal approach, appears to provide the greatest long-term survival benefit. According to the recent EAU guidelines, patients must be informed about the possible need for a multimodal approach because neoadjuvant hormone therapy has not been shown to increase BPFS and OS and is not recommended in these guidelines \[[@B6],[@B53],[@B54]\].
Although hormone therapy may decrease the size of the tumor and prostate overall, hormone therapy can induce a mild-to-moderate desmoplastic reaction around the prostate, obscuring tissue planes around the periprostatic fascia. In a minority of patients, dissection of the prerectal planes is difficult, and the rectum can be adherent to the posterior prostate. In addition, RP in an extremely small prostate after hormone therapy can be slightly more challenging. This added challenge is mostly due to the desmoplastic reaction as well as to difficulty in identifying the contours of the prostate and the normal tissue planes for neurovascular preservation \[[@B25]\].
Adjuvant hormone therapy has a definite role in the management of high-risk patients after RP. Adjuvant hormone therapy has its most relevant clinical utility after RP in node-positive patients. However, the effect of adjuvant ADT on OS remains unclear, and it appears to be influenced by the individual risk profile. The classic study of Messing et al. \[[@B37],[@B55]\] demonstrated improvement in PSA- and cancer-free survival and OS for hormone therapy immediately following RP for node-positive PC. More recently, Boorjian et al. \[[@B56]\] analyzed data for 507 patients with node-positive PC following RP. In this trial, patients with immediate ADT had a statistically significantly decreased risk of biochemical and local recurrence. There was no statistically significant difference, however, in the rate of systemic progression or CSS between the two groups. Therefore, the advantages of adjuvant hormone therapy after RP are debatable.
Recently, Lee et al. \[[@B57]\] evaluated the competing risks of CSM after initial therapy with RP versus RT in men with clinically localized high-risk PC. Their study had several differences compared with previous reports: (1) relatively long follow-up periods; (2) RP performed by a single surgeon; and (3) the first data in an Asian population. They demonstrated that 5-year estimates of CSS rates for men treated with RP and RT were 96.5% (95% confidence interval \[CI\], 94.2-98.9) and 88.3% (95% CI, 82.8-94.3), respectively. Cumulative incidence estimates for CSM using competing risks were statistically lower in men receiving RP versus RT (p=0.002). They summarized that initial treatment with RP versus RT was associated with a decreased risk of CSM in men with clinically localized high-risk PC.
Definitive results from a large randomized trial are warranted to define the role of adjuvant hormone therapy in high-risk PC. Hormone therapy has also been investigated as an adjuvant therapy to RP in high-risk PC patients, even though few randomized trials are available. Postoperative adjuvant RT after RP for high-risk PC also remains controversial. The results of three randomized trials of postoperative adjuvant RT in high-risk patients, typically categorized by adverse pathology, such as pathologic stage T3-4N0 with PSM, extracapsular extension of disease, or seminal vesicle invasion, have been reported. All detected improvements in BPFS were in association with acceptable rates of toxicity \[[@B58],[@B59],[@B60]\]. However, only one trial, a secondary analysis of the Southwest Oncology Group 8794 trial, noted marked improvement in OS following postoperative adjuvant RT \[[@B61]\].
CONCLUSIONS
===========
Currently, surgery for high-risk PC is applied frequently. Nevertheless, this approach is still controversial. Because there is no standard definition of high-risk PC, outcome comparisons between series and treatment approaches are hampered. However, RP can provide durable local control, long-term CSS, and accurate pathologic staging and may guide further individualized treatment. RP with extended pelvic lymphadenectomy delivers very good cancer-related outcomes in high- and very-high-risk PC, often within a multimodal approach. Definitive results from a large randomized trial are warranted to define the role of adjuvant hormone therapy and RT in high-risk PC. Minimally invasive surgery is showing promising results, but further studies are needed to support its role compared to open RP and e-PLND as the gold standard.
This study was supported by a grant from the Korean Foundation for Cancer Research (CB-2011-04-02), Republic of Korea.
The authors have nothing to disclose.
######
Definition of high-risk prostate cancer
PSA, prostate-specific antigen; GS, Gleason score.
######
Outcomes of radical prostatectomy as monotherapy in high-risk prostate cancer
OCD, organ-confined disease; BCR, biochemical recurrence; CSS, cancer-specific survival; MFS, metastasis-free survival; OS, overall survival.
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29 October 2014
The Science and Technology Committee of the UK Parliament’s House of Commons has released a new report on National Health Screening - antenatal, newborn and adult screening programmes delivered free of charge by the NHS.
Screening is the offer of testing for the presence or risk of a serious disease or condition to a defined group of healthy, non-symptomatic people, based on the principle that early detection of disease can improve health outcomes. The report is the result of an inquiry launched last year; responses were received from over fifty individuals and organisations, including the PHG Foundation.
The new report, National Health Screening, notes that public perception of health screening is generally positive and expectations of screening programmes high; this was said to make it more challenging to convey the potential harms from screening. The report concludes that ‘much more’ needed to be done to ensure that risks as well as benefits were clearly communicated in a balanced fashion by both the NHS and private providers. The Committee calls for a standardised process for the production of screening information and better communications training for health professionals.
With respect to the evidence base for screening (including costs), the importance of careful review by the National Screening Committee (NSC) is emphasised. The report is critical of some screening programmes that were said to have been introduced ‘without a rigorous evidence base’ or NSC review.
Besides calling for use of a more robust and transparent evidence review process by the NSC, the report also recommends development of improved horizon-scanning capacity for relevant new technological developments; many genomic tests fall into this category. NSC Director of Programmes Dr Anne Mackie cited the example of non-invasive prenatal diagnosis as an example of previous responsiveness to emerging science by the NSC; the potential impact of this new technology on health services including antenatal screening was first highlighted by the PHG Foundation’s 2009 report, Cell-free fetal nucleic acids for non-invasive prenatal diagnosis.
The Committee also recognised the particular impact of genomic technologies and screening for rare inherited diseases, which require a special consideration with respect to evidence requirements and may raise distinct ethical, legal and social issues (ELSI). In particular, a review of the criteria for decision-making on potential genetic screening programmes is recommended.
Looking ahead, Committee chair Andrew Miller MP said: “Developments in genetic science mean that it should soon become possible to target screening programmes directly at those most of risk of certain diseases. It is imperative that the UK National Screening Committee develops its capacity for horizon scanning and ensures that proven developments in screening are supported and implemented across the NHS”.
PHG Foundation Director Dr Hilary Burton, who gave evidence to the inquiry on screening, said that she was pleased by the attention paid to the Foundation’s work on stratified screening for cancer and how this would impact on health systems, adding: “We were very clear, as were other witnesses, that risk stratification would become a reality in screening programmes and so we welcome the Committee’s strong recommendation that the NSC and the NHS should look at how such developments would be supported and a wider commitment to achieving some formal mechanism for horizon scanning for the Committee”. | http://www.phgfoundation.org/news/review-of-uk-health-screening-impending-impact-of-genomics |
The scientific concept of entropy, or the tendency of physical systems to evolve toward equilibrium and inactivity, has a well-established central place in the history of the natural sciences. It figures prominently in accounts of the nature of time and its direction from past to future, of order and disorder, of the fundamental processes on which life depends, and of the eventual fate of the cosmos itself. Thermodynamics, the discipline which addresses this concept, has undergone dramatic shifts in perspective over the last few decades, with the arrival of the new fields of Chaos and Complexity Theory, revising the terms in which we are to understand this universal march to equilibrium. In his natural philosophy, Gilles Deleuze engages in depth with the questions bearing on entropy, and indeed has been widely acknowledged as a philosophical influence on the redrafting of its associated conceptual apparatus. Nevertheless, his standpoint is profoundly ambivalent; while readily adopting the key tenets of thermodynamics, which contribute decisively to his account of events in the physical world, he resists the apparently inevitable corollary that the cosmos is fated as a long-term rule to descend into disorder and stasis. Entropy, he claims, is a ‘transcendental illusion’, applicable in principle only to those processes we may observe in the Actual, but an illegitimate notion with respect to the realm of potential events he calls the Virtual.
This one-day workshop will address the contributions and connections of Deleuze’s work to scientific paradigms of physical action, and investigate both the tensions arising between his philosophy of difference and scientific theory, and those installed within his own philosophy as a result of this singular viewpoint.
All welcome. There is no registration charge.
Contact: Bill Ross, [email protected]
10.00 – 10.30 Welcome & coffee
Bill Ross (Staffordshire University), Entropy, Retardation and Delay in the Work of Deleuze
Ashley Woodward (Dundee University), Entropy as Philosophical Problematic
Henry Somers-Hall (Royal Holloway), Entropy, Intensity, and Transcendental Illusion
James Williams (Deakin University), Entropy and the Problem of the New in Deleuze’s Metaphysics
You can download the programme with abstracts here: Deleuze, Entropy, and Thermodynamics Programme. | http://blogs.staffs.ac.uk/philosophy/2016/05/08/deleuze-entropy-and-thermodynamics/ |
Light-induced activity in the activity box is not aversively motivated and does not show between-trial habituation.
The induction of behaviour by sensory stimuli, i.e. sensorimotor stimulation, is a fundamental aspect of behaviour. Recently, it was found that the presentation of white-light stimuli to a rat in an activity box reliably induces locomotor activity, and, thus, may be able to serve as a paradigm to measure basal, non-aversively motivated sensorimotor processing. However, light can be an aversive stimulus to a rat. In order to test if there is a stressful component in light-induced activity, a retreat-box was introduced into the test-apparatus in experiment 1, so that the animals had the opportunity to escape the light stimuli. It was found, that light-induced activity was also shown, when a retreat-box was available in the activity box, and that light-stimulation did not lead to an increase of entries into or the time spent in the retreat box. Experiment 2 examines the stability of the response to light over trials. Three light-induced activity test-trials were conducted with one day between each test. There was no effect of repeated testing on light-induced activity, which was evident during each of the three test-sessions. It is concluded that stress/anxiety does not significantly contribute to the increase of locomotor behaviour induced by light stimulation under the present conditions. Thus, the paradigm appears to involve a non-aversively motivated behavioural response. Furthermore, light-induced activity did not habituate over at least three test trials, and may, therefore, serve for repeated testing.
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“Last month, because of my active resistance, the U.S. government came for me. I will continue my struggle so that tomorrow they don’t come for you.” – Maru Mora Villalpando
Jean. Ravi. Maru. These are the names of immigrant activists targeted by federal immigration forces within the last few weeks.
Jean has been deported to Haiti. Ravi is locked up in a detention center. Maru has been placed in deportation proceedings.
It seems that Immigration and Customs Enforcement (ICE) targeted them solely because of their role in immigration activism fighting against detention, deportation, and supporting community members in their quest for sanctuary.
These are not individuals who are simply advocates or activists; they live their activism because they are directly impacted by their own work.
I know Ravi and Maru through their incredible work on behalf of their communities, and had the privilege of learning from them.
I learned about the practice of accompaniment from Ravi; accompaniment is when immigrants go to their ICE check-ins with swaths of community members by their side for emotional support and to build pressure against ICE’s intent to detain someone out of the public eye.
I learned about detention organizing from Maru, who is a mastermind in how to organize people in detention centers, shining a light on the injustices that happen inside.
The news of ICE targeting immigration activists coincided with my travels to scout organizations for Global Fund for Children’s new Adolescent Girls and Migration initiative.
There I was, traveling in the US and Mexico to find organizations to take part in a transnational protection network for adolescent migrant girls with a particular focus on movement building and advocacy. At the same time, I was hearing news from back home about how immigrant rights leaders, including an amazing immigrant woman, were being targeted for doing movement building and advocacy within their own communities.
Above: a wall juts out into the ocean dividing Tijuana, Mexico, and San Diego, California.
The news hit me hard. Not only was I heartbroken about what was happening to these activists I admire, I also began to question my mission.
Was I putting adolescent migrant girls at a greater risk by working to expand and support opportunities for them to fight back against the systems that deny them of basic rights and justice? Is it responsible to set up young people to risk retaliation for speaking out?
In this political environment should we, as allies, work to shelter marginalized, vulnerable populations because activism is just too risky?
And then, on the last night of my trip, the government shut down.
The shutdown, regardless of your political affiliation, could be viewed as a political mess. But it was not about any political party, it was neither party’s shame nor victory. The shutdown was a show of force by undocumented youth who had descended upon Washington, DC, to force Congress to take action.
At Chaparral Port of Entry in Tijuana, Mexico, children and young women come to seek asylum only to face armed US and Mexican guards and private security forces. Many are turned away, a violation of US law.
Every single day 122 DACA recipients lose their protections. But these young people are not running scared. They keep on fighting, screaming at the top of their lungs, “UNDOCUMENTED UNAFRAID, SIN PAPELES SIN MIEDO.”
Jean, Ravi, and Maru are not backing down from their fights either—they are unafraid of the retaliation, unafraid of the forces that are trying to shut them up.
For GFC, this is a new space to inhabit. The Adolescent Girls and Migration initiative is the first initiative where we are strategically participating in advocacy and movement building. And it’s happening at a time when, more than ever before, migrant girls are at risk and activists are being targeted.
But if the events of the last few days teach us anything, it’s that communities cannot trust politicians to protect them or do what’s right.
For communities impacted by hateful, harmful policies, these are not just political issues. These are their lives.
We are proud to stand by and support those who fight for issues that directly impact them. Our commitment to the grassroots is apolitical, but we are living in a time when people’s lives are politicized. We stand with the people and we know we’re standing on the right side of history.
We will continue to give voice to those whose voices are suppressed. They deserve to be heard.
To support Maru sign her petition here.
Learn how to fight for Ravi’s freedom here.
Global Fund for Children (GFC) UK Trust, created in 2006, is a UK registered charity (UK charity number 1119544). We work to generate vital income, create new fundraising opportunities, and raise awareness of the invaluable work of GFC’s grassroots grantees. Our aim is to extend the reach of GFC in the United Kingdom, Europe, and beyond. | https://globalfundforchildren.org/story/facing-retaliation-immigrant-activists-bravely-fight-for-their-lives/ |
This 1990 IPCC graph shows that current temperatures are much lower than in the recent past and thus was not alarming.
Later, the IPCC picked up Mann’s :hockey stick” (below) and suddenly the world had a climate problem. The only problem was that the “hockey stick” had a number of serious flaws and was quietly de-emphasized in the next IPCC report. These flaws, found by McIntyre & McKitrick and verified by the National Academy of Sciences are outlined below.
The rise in temperature started just after 1900, perhaps 1910, but man’s CO2 emissions were very small before 1950.
The “tree rings, corals and historical records” end at about 1980, while the report was published in 2001. Where is the later data? Some critics observed that tree rings started diverging from temperature during that time period.
The well proven, “little ice age” is missing.
The above graph first appeared in Nature 392: 779-787 . It was criticized by Steve McIntyre etal in several papers: mcintyre 2005 , the criticism was mentioned in several papers WSJ and explained by Ross Mckitrick. Finally a congressional hearing which requested the National Academy of sciences to study the claims and counter claims. Two reports resulted, the North Report and the Wegman Report.
* The instrumentally measured warming of about 0.6?C during the 20th century is also reflected in borehole temperature measurements, the retreat of glaciers, and other observational evidence, and can be simulated with climate models.
* Large_scale surface temperature reconstructions yield a generally consistent picture of temperature trends during the preceding millennium, including relatively warm conditions centered around A.D. 1000 (identified by some as the “Medieval Warm Period”) and a relatively cold period (or “Little Ice Age”) centered around 1700. The existence and extent of a Little Ice Age from roughly 1500 to 1850 is supported by a wide variety of evidence including ice cores, tree rings, borehole temperatures, glacier length records, and historical documents.
Evidence for regional warmth during medieval times can be found in a diverse but more limited set of records including ice cores, tree rings, marine sediments, and historical sources from Europe and Asia, but the exact timing and duration of warm periods may have varied from region to region, and the magnitude and geographic extent of the warmth are uncertain.
* It can be said with a high level of confidence that global mean surface temperature was higher during the last few decades of the 20th century than during any comparable period during the preceding four centuries. This statement is justified by the consistency of the evidence from a wide variety of geographically diverse proxies.
* Less confidence can be placed in large_scale surface temperature reconstructions for the period from A.D. 900 to 1600. Presently available proxy evidence indicates that temperatures at many, but not all, individual locations were higher during the past 25 years than during any period of comparable length since A.D. 900. The uncertainties associated with reconstructing hemispheric mean or global mean temperatures from these data increase substantially backward in time through this period and are not yet fully quantified.
* Very little confidence can be assigned to statements concerning the hemispheric mean or global mean surface temperature prior to about A.D. 900 because of sparse data coverage and because the uncertainties associated with proxy data and the methods used to analyze and combine them are larger than during more recent time periods.
Based on the analyses presented in the original papers by Mann et al. and this newer supporting evidence, the committee finds it plausible that the Northern Hemisphere was warmer during the last few decades of the 20th century than during any comparable period over the preceding millennium.
The substantial uncertainties currently present in the quantitative assessment of large_scale surface temperature changes prior to about A.D. 1600 lower our confidence in this conclusion compared to the high level of confidence we place in the Little Ice Age cooling and 20th century warming. Even less confidence can be placed in the original conclusions by Mann et al. (1999) that “the 1990s are likely the warmest decade, and 1998 the warmest year, in at least a millennium” because the uncertainties inherent in temperature reconstructions for individual years and decades are larger than those for longer time periods, and because not all of the available proxies record temperature information on such short timescales.
We believe that the two most gripping claims about global warming have been shown to be wrong. The other major claim, that we are the warmest in 400 years is essentially a statement that we are warming after the “little ice age.” Is that bad?
Dr. Wegman served in national office in the Institute of Mathematical Statistics, the American Statistical Association and the American Association for the Advancement of Science. He served as President of the International Association for Statistical Computing. He has published more than 160 papers and eight books. His professional stature has been recognized by his election as Fellow of the American Statistical Association, the American Association for the Advancement of Science, the Washington Academy of Science and the Institute of Mathematical Statistics.
Wegman Report, item 7, page 49 (MBH is the hockey stick paper): Our committee believes that the assessments that the decade of the 1990s was the hottest decade in a millennium and that 1998 was the hottest year in a millennium cannot be supported by the MBH98/99 analysis.
Wegman Report, item 7, page 49: The cycle of Medieval Warm Period and Little Ice Age that was widely recognized in 1990 has disappeared from the MBH98/99 analyses, thus making possible the hottest decade/hottest year claim. However, the methodology of MBH98/99 suppresses this low frequency information. The paucity of data in the more remote past makes the hottest-in-a-millennium claims essentially unverifiable.
Wegman Report, item 6, page 49: Generally speaking, the paleoclimatology community has not recognized the validity of the MM05 papers and has tended dismiss their results as being developed by biased amateurs.
Wegman Report, page 52: Conclusion 4. While the paleoclimate reconstruction has gathered much publicity because it reinforces a policy agenda, it does not provide insight and understanding of the physical mechanisms of climate change except to the extent that tree ring, ice cores and such give physical evidence such as the prevalence of green-house gases. What is needed is deeper understanding of the physical mechanisms of climate change.
Wegman Report, page 49: 1. In general we found the writing of MBH98 somewhat obscure and incomplete. The fact that MBH98 issued a further clarification in the form of a corrigendum published in Nature (Mann et al. 2004) suggests that these authors made errors and incomplete disclosures in the original version of the paper. This also suggests that the refereeing process was not as thorough as it could have been. . .
offer both theoretical explanations (Appendix A) and simulations to verify that their observations were correct. . .
Wegman Report, page 49, item 3: . . Because the temperature profile in the 1902-1995 is not similar, because of increasing trend, to the millennium temperature profile, it is not fully appropriate for the calibration and, in fact, leads to the misuse of the principal components analysis. However, the narrative in MBH98 on the surface sounds entirely reasonable on this calibration point, and could easily be missed by someone who is not extensively trained in statistical methodology. Dr. Mann has close ties to both Yale University and Pennsylvania State University. We note in passing that both Yale University and Pennsylvania State University have Departments of Statistics with excellent reputations9. Even though their work has a very significant statistical component, based on their literature citations, there is no evidence that Dr. Mann or any of the other authors in paleoclimatology studies have significant interactions with mainstream statisticians.
Wegman Report, page 49: Although we have not addressed the Bristlecone Pines issue extensively in this report except as one element of the proxy data, there is one point worth mentioning. Graybill and Idso (1993) specifically sought to show that Bristlecone Pines were CO2 fertilized. Bondi et al. (1999) suggest [Bristlecones] “are not a reliable temperature proxy for the last 150 years. . .
Wegman: page 4: In our further exploration of the social network of authorships in temperature reconstruction, we found that at least 43 authors have direct ties to Dr. Mann by virtue of coauthored papers with him. Our findings from this analysis suggest that authors in the area of paleoclimate studies are closely connected and thus “independent studies” may not be as independent as they might appear on the surface.
As mentioned above, McIntyre & McKitrick(2003) found errors in the hockey stick. They also published a corrected version shown above.
A very readable account of the intrigue and deceit trying to keep the hockey stick alive. | http://www.sustainableoregon.com/hockeystick.html |
NASA names new Moon landing program Artemis after Apollo's sister
Half a century after NASA sent men to the moon under project "Apollo," the space agency is now working to land men — and women — on the lunar surface as part of its "Artemis" program.
NASA Administrator Jim Bridenstine revealed the new moniker on Monday (May 13) during a call with reporters that was primarily focused on the budget for the newly named moon program.
"It turns out that Apollo had a twin sister, Artemis. She happens to be the goddess of the moon," said Bridenstine, referring to Greek mythology. "Our astronaut office is very diverse and highly qualified. I think it is very beautiful that 50 years after Apollo, the Artemis program will carry the next man — and the first woman — to the moon."
Related: Can NASA Really Put Astronauts on the Moon in 2024?
The Artemis program, which was previously only referred to by its component names — including the Space Launch System heavy-lift rocket, Orion crew vehicle and Gateway lunar outpost — began when President Donald Trump signed Space Policy Directive 1 in 2017, directing NASA to return astronauts to the moon.
Two years later, in March 2019, Vice President Mike Pence further defined the program by announcing a five-year deadline for the first crewed lunar landing. The 2024 mission, he said, should land at the south pole with the "first woman and the next man on the moon."
On Monday, Trump amended his Fiscal Year 2020 budget request to account for the accelerated schedule and new mission objectives.
"As you know, the President has given our agency the bold charge to land the next man and the first woman on the lunar south pole by 2024, and now President Trump has extended his vote of confidence in our work with an amended budget request for fiscal year 2020," said Bridenstine in a video address to employees. "It includes $1.6 billion in additional funding."
"Among other things, it will allow us to accelerate our development of the Space Launch System and Orion, it will support the development of a human lunar landing system and it will support precursor capabilities on the lunar surface, including increased robotic exploration of the moon's polar region," he said.
To achieve the 2024 goal, NASA intends to scale back its plans for a crew-tended, multi-module Gateway to include only the basic parts needed to support an initial landing. Support for a long-term, sustainable lunar presence, as had been NASA's priority, has been deferred to 2028.
In Greek mythology, Apollo and Artemis were the twin children of Zeus and Leto. In addition to being the goddess of the moon, Artemis was also the goddess of the hunt, with Orion her hunting companion.
The name "Apollo" was first proposed for the 1960s moon landing program by Abe Silverstein, NASA's then-director for spaceflight development. He chose the name because of its connection to Greek mythology and its "attractive connotations," per the space agency.
Before being assigned to the current moon landing program, NASA used Artemis to refer to a pair of lunar probes studying the moon's interactions with the sun. The ARTEMIS — or "Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun" — spacecraft were reassigned from NASA's THEMIS mission in 2010.
Artemis was also selected by a team competing for NASA's Commercial Lunar Payload Services (CLPS) contract. The team, led by Draper, named their proposed lunar lander Artemis-7 in honor of the Greek goddess. (The number 7 signified Draper's seventh lunar landing, having a heritage in Apollo.)
The name has also been used for a European communications satellite (retired in 2017) and was the fictional title given to the first city on the moon in author Andy Weir's ("The Martian") 2017 science fiction novel "Artemis." There is also a small crater with the name in Mare Imbrium, or the Sea of Showers, on the moon.
Bridenstine said the name Artemis represents the program's goal of inclusion.
"I have a daughter who is 11 years old, and I want her to be able to see herself in the same role as the next women [who] go to the moon see themselves in today," he said. "This is really a beautiful moment in American history, and I am very proud to be a part of it."
- NASA Plans to Build a Moon-Orbiting Space Station: Here's What You Should Know
- In Photos: President Trump Aims for the Moon with Space Policy Directive 1
- Home On the Moon: How to Build a Lunar Colony (Infographic)
Original article on Space.com. | https://www.foxnews.com/science/nasa-names-new-moon-landing-program-artemis-after-apollos-sister |
M.A.
Degree Name
Master of Arts (M.A.)
Degree Granting Department
Anthropology
Major Professor
David A. Himmelgreen, Ph.D.
Committee Member
Elizabeth Miller, Ph.D.
Committee Member
Nancy Romero-Daza, Ph.D.
Keywords
adolescence, diet, food insecurity, menarche, nutrition, puberty, life history theory
Abstract
Using life-history theory within a biocultural perspective, this research explores whether household food insecurity correlates with early or delayed menarche among adolescent females in Tampa Bay, Florida. Early onset of puberty and menstruation is connected with numerous health consequences including growth stunting, obesity, type-2 diabetes, adult-onset asthma, reproductive cancers, increased risk for depression, behavioral problems, and early sexual activity which increases the risk for STIs and ovarian cancer. Early menarche also seems to disproportionally impact disadvantaged and minority groups. While there are many known factors that influence age at menarche (e.g.: genetics, diet), little is understood regarding the effect of food insecurity on menstrual timing. When considering food insecurity as an environmental adversity, long-term exposure may result in biological trade-offs within growth and development.
Using a mixed-methods approach, 40 girls and 36 parents or guardians from Pinellas, Hillsborough, and Manatee counties participated in household dyadic interviews that included the assessment of household food security, girls’ dietary analysis, and anthropometry. Using quantitative analyses, the associations of diet, food security, and body size/composition to menarche were evaluated. A Cox hazards model and regression further analyzed the association of food insecurity and the timing of menarche.
The research concludes that adolescents and their families are vulnerable to food insecurity for both biological and social reasons. Qualitative results examine the prevalence, experiences, and perpetrators of food insecurity, as well as strategies used by families to mitigate food insecurity. Food insecurity in this study refers to the inconsistent or limited access to adequate amounts of safe and nutritious foods to sustain health and wellbeing. Food insecurity does not necessarily result in hunger. Once can have access to enough calories and not feel hungry but may still be food insecure if their access does not include enough high-quality, nutritious foods.
Quantitative analyses showed that iliac height, waist-hip ratio, snack consumption, and household food insecurity is associated with age at menarche among this sample. Spearman’s Rho confirms that height, leg length (p = 0.032, rs = 0.407), and snack consumption (p = 0.042, rs = 0.464) significantly positively correlate with age at menarche. Waist-hip ratio significantly negatively correlates with age at menarche (p = 0.032, rs = -0.518). Cox Hazard Regression analysis interprets that for every one unit increase in household food security survey score, the risk of experiencing menarche increases by 25% (p = 0.023, OR = 1.25). However, when adding leg length, waist-hip ratio, and snack consumption to the Cox Hazard Regression equation, no variables significantly predict menarche.
These findings provide a better understanding of the biocultural influences within the timing of menarche. The research provides new insights and further stresses the importance of improving food assistance programs for adolescents and families with older children.
Scholar Commons Citation
Burris, Mecca, "Food Insecurity and Age of Menarche: Using a Biocultural Approach and Life History Theory to Assess Risks of Food Insecurity among Girls in Tampa Bay, FL" (2018). Graduate Theses and Dissertations. | https://digitalcommons.usf.edu/etd/7130/ |
Learner support focuses on forms of assistance to learners beyond the delivery of content, skills development, or formal assessment. Learner support covers a wide range of functions, and is discussed throughout the book, but particularly in:
Brindley et al. (2004) provide an extensive overview of the full range of activities in providing learner support for online and distance education learners. Here though my focus is limited to indicating why it is an essential element of an effective learning environment, and to describe briefly some of the main sub-components of learner support.
6.6.2 Scaffolding
I use the term scaffolding to cover the many functions in diagnosing and responding to learners’ difficulties, including:
- helping students when they struggle with new concepts or ideas;
- helping students to gain a deeper understanding of a topic or subject;
- helping students to evaluate a range of different ideas or practices;
- helping students to understand the limits of knowledge;
- above all challenging students to go beyond their current level of thinking or practice to acquire deeper understanding or a higher level of competency.
These activities normally take the form of personal interventions and communication between an instructor and an individual or a group of students, in face-to-face contexts or online. These activities tend not to be pre-planned, requiring a good deal of spontaneity and responsiveness on the part of the teacher or instructor.
However, more recently there have been examples of automated learner support, such as virtual assistants or chatbots (for a review of research on chatbots in education, see Winkler and Söllner, 2018). Also learning analytics have been used to determine a student’s performance and where necessary to direct them to further readings or work (see for instance, Vesin et al., 2018).
Scaffolding is usually a means of individualising the learning, enabling student differences in learning to be better accommodated as they occur.
6.6.3 Feedback
This could be seen as a sub-category of scaffolding, but it covers the role of providing feedback on student performance of activities such as writing assignments, project work, creative activities, and other student activities beyond the current and perhaps future scope of automated computer feedback. Again, the instructor’s role here is to provide more individualisation of feedback to deal with more qualitatively assessed student activities, and may or may not be associated with formal assessment or grading.
6.6.4 Counselling
As well as direct support within their academic studying, learners often need help and guidance on administrative or personal issues, such as financial difficulties, or whether to repeat a course, delay an assignment because of sickness in the family, or cancel enrollment in a course and postpone it to another date. Although such services may be available outside the provision of a particular course, this potential source of help needs to be considered in the design of an effective learning environment, with the aim of doing all that can be done to ensure that students can manage external pressures while meeting the academic standards of a program.
6.6.5 Other students
Other students can be a great support for learners. Much of this will happen informally, through students talking after class, through social media, or helping each other with assignments. However, instructors can make more formal use of other students by designing collaborative learning activities, group work, and designing online discussions so that students need to work together rather than individually.
6.6.6 Why learner support is so important
We shall see in Chapter 12 that good design can substantially reduce demand for learner support, by ensuring clarity and by building in appropriate learning activities. Students also vary enormously in their need for support in learning. Many lifelong learners, who have already been through a post-secondary education, have families, careers and a great deal of life experience, can be self-managed, autonomous learners, identifying what they need to learn and how best to do this. At the other extreme, there are students for whom the formal school system was a disaster, who lack basic learning skills or foundations, such as reading, writing and mathematical skills, and therefore lack confidence in learning. These will need a lot of support to succeed.
However the vast majority of learners are somewhere in the middle of the spectrum, occasionally running into problems, unsure what standards are expected, and needing to know how they are doing in their studying. Indeed, there is a good deal of research that indicates that ‘instructor presence’ is associated with student success or failure in a course, at least in online learning (see, for instance, Shea et al., 2010). Where students feel the instructor is not present, both learner performance and completion rates decline. For such students, good, timely learner support is the difference between success and failure.
It should be noted that the need for good learner support, and the ability to provide it, is not dependent on the medium of instruction. The kind of credit online courses that have been designed and delivered long before MOOCs came along often provided high levels of learner support, through having a strong instructor presence and careful design to ensure students were supported.
At the same time, although computer programs can go some way to providing learner support, many of the most important functions of learner support associated with high-level conceptual learning and skills development still need to be provided by an expert teacher or instructor, whether present or at a distance. Furthermore, this kind of learner support is difficult to scale up, as it tends to be relatively labour intensive and requires instructors with a deep level of knowledge within the subject area. Thus, the need to provide adequate levels of learner support cannot just be wished away, if we are to achieve successful learning on a large scale.
This may seem obvious to teachers, but the importance of learner support for student success is not always recognised or appreciated, as can be seen from the design of many MOOCs, and the reaction of politicians and the media to the cost savings promised by the kind of MOOCs that focus on eliminating learner support. There are also different attitudes from instructors and institutions towards the need for learner support. Some faculty may believe that ‘It’s my job to instruct and yours to learn’; in other words, once students are presented with the necessary content through lectures or reading, the rest is up to them.
Nevertheless, the reality is that in any system with a wide diversity of students, as is so common today, effective learner support is essential for student success.
References
Brindley, J., Walti, C. and Zawacki-Richter, O. (eds.) (2004) Learner Support in Open, Distance and Online Learning Environments Oldenburg, Germany: Biblioteks- und informationssystem der Universität Oldenburg
Shea, P. et al. (2010) Online Instructional Effort Measured through the Lens of Teaching Presence in the Community of Inquiry Framework: A Re-Examination of Measures and Approach International Review of Research in Open and Distributed Learning, Vol. 11, No. 3
Vesin, B. at al. (2018) Learning in smart environments: user-centered design and analytics of an adaptive learning system Smart Learning Environments, Vol. 5, No. 24
Winkler, R. & Söllner, M. (2018): Unleashing the Potential of Chatbots in Education: A State-Of-The-Art Analysis. Academy of Management Annual Meeting (AOM) Chicago: Illinois
Activity 6.6 Building learner support
- Do you think it is possible to design an effective course or program without the need for high levels of learner support? If so, what would it look like? A development of MOOCs or something completely different?
- Do you share my views about the limitations of computers for providing the kind of high-level learner support needed for conceptual learning in a digital age? What do computers or AI do well in terms of supporting learners?
- Is ‘scaffolding’ the best term to describe the kind of learning support I described in that section? If not is there a better term for this?
For my feedback on these questions click on the podcast below: | https://pressbooks.bccampus.ca/teachinginadigitalagev2/chapter/5-6-learner-support/ |
Click on image for entire issue or scroll down for individual articles.
Download entire issue here
Winfried Eckel
Fragmentation of Text, Fragmentation of Time: Evental Aesthetics in Friedrich Schlegel and Roland Barthes (pp. 7-38)
Friedrich Schlegel and Roland Barthes’s shared preference for the fragment as a form of writing is closely related to their diverging interests in the category of the whole. While Schlegel uses fragmentary forms to evoke the idea of a comprehensive wholeness, which contrasts the contemporary experience of differentiating discourses of knowledge and a growing gap between the culture of experts and the world we live in, Barthes regards such an all-integrating wholeness only as monstrous. Writing under different historical conditions, the French poststructuralist is interested in using the form of the fragment to break up the idea of supposedly homogeneous wholes, such as the bourgeois subject, history, or the work of art. In this context, it has not yet been recognized enough how much both authors understand their writing as a vivid communication and dynamic interaction with the reader: by means of the fragment, both aim at creating evental reading effects that interrupt the continuum of time and involve the recipient in a surprising way. The result of the sudden perception of unexpected connections, according to Schlegel, is “Witz”; of the sudden perception of breaks, colliding codes or the new, according to Barthes, it is “jouissance.” The present essay links Schlegel and Barthes’s theories of the fragment with their aesthetics of eventality, and shows how the fragmentation of the text is connected with a fragmentation of time.
Download here.
Prudence Gibson and Shelley James
Collision. Lantana at Gloaming: Invasive Plants in the Anthropocene (pp. 39-54)
This paper explores a collaborative humanities and science response to the invasive weed lantana. It explores how the weed has been represented in the arts, via a film and an artwork. The lantana is a much-maligned weed. However, the two authors reflect on the lantana through the arts as well as through government papers and reports to establish its place in the Anthropocene’s loss of biodiversity and species extinction. What kind of lantana story emerges from art, science and government documents? The authors investigate whether this process presents new narratorial possibilities for writing the non-human during the sixth extinction.
Download here.
SPECIAL SECTION:
AI and Computation
Peter Polack
AI Discourse in Policing Criticisms of Algorithms (pp. 57-92)
This article addresses the function of the term Artificial Intelligence (AI) in policymaking discourse and how it serves to establish normative conventions for apprehending the consequences of algorithmic technologies. These normative conventions, reflected in the discourses of algorithmic bias and transparency, privilege certain means of evaluating the significance of algorithms for human experience over others. In this way, the use of the term AI involves what Jacques Rancière identifies as a capacity to “indistinguish phenomena,” or to attribute a common cause to diverse events, circumstances, and social concerns. By doing so, AI policy discourse associates disparate social phenomena with the notion of AI, while also selectively associating the term with particular approaches to criticism and intervention. Such selective AI discourse effectively operates to police which criticisms of algorithmic technologies are viewed as legitimate for legal interventions or technical reforms. Against this tendency, this article proposes an approach to disputing the partiality of AI policy discourse by devising alternative designs and uses for algorithmic technologies. In particular, following Arturo Escobar’s notion of autonomous design, this approach uses the identification of interests and concerns derived from personal or communal experiences as a point of departure for questioning whether the standing meaning of AI adequately addresses these concerns. Rather than denouncing the generous meaning of the term AI, we examine how AI policy discourse deploys certain approaches to algorithm criticism and reveal how it might account for or delegitimize other approaches to criticism derived from particular community interests.
Download here.
Alice C. Helliwell
Can AI Mind Be Extended? (pp. 93-120)
Andy Clark and David Chalmers’s theory of extended mind can be reevaluated in today’s world to include computational and Artificial Intelligence (AI) technology. This paper argues that AI can be an extension of human mind, and that if we agree that AI can have mind, it too can be extended. It goes on to explore the example of Ganbreeder, an image-making AI which utilizes human input to direct behavior. Ganbreeder represents one way in which AI extended mind could be achieved. The argument of this paper is that AI can utilize human input as a social extension of mind, allowing AI to access the external world that it would not otherwise be able to access.
Download here.
Ted Kafala
Collision. Ryoji Ikeda Meets Whitehead at CERN: Interdisciplinary Experimentation and Evental Aesthetics (pp. 121-138)
Intermedia artist Ryoji Ikeda’s 2014–15 residency at CERN, the European Organization for Nuclear Research, and its Large Hadron Collider (LHC) facility raises important issues for evental aesthetics, process thought, and the speculative traversing of the boundaries between art and microphysics. Ikeda has been interested in the sonification and visualization of data and mathematics for two decades, and his observation of the CERN LHC and the ATLAS detector, and his engagement with detector data inspired the creation of his large-scale micro | macro (The Planck Universe) video and sound installation in 2015. This Collision briefly explains some of Ikeda’s motivations behind The Planck Universe while engaging with some of A. N. Whitehead’s ideas about events as well as event-particles in the context of process thought. Does Ikeda use microparticle physics outcomes as part of his artistic and creative palette, or, conversely, does he engage with microphysics processes in his intermedial work only on the level of abstraction and through analogy and inspiration? Ikeda does both. Sound “grains,” pulses, wavelets, sound quanta, the data visualization of particle clouds, and other evidence of dynamic microparticle interaction from detection data are part of Ikeda’s intermedial palette in The Planck Universe. The detection data validate that event-particles do have microphysical form and a vital materiality.
Download here. | https://eventalaesthetics.net/ea-vol8-2019-ai-and-computation/ |
---
abstract: |
We initiate the study of a class of real plane algebraic curves which we call *expressive*. These are the curves whose defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of a curve. This concept can be viewed as a global version of the notion of a real morsification of an isolated plane curve singularity.
We prove that a plane curve $C$ is expressive if (a) each irreducible component of $C$ can be parametrized by real polynomials (either ordinary or trigonometric), (b) all singular points of $C$ in the affine plane are ordinary hyperbolic nodes, and (c) the set of real points of $C$ in the affine plane is connected. Conversely, an expressive curve with real irreducible components must satisfy conditions (a)–(c), unless it exhibits some exotic behaviour at infinity.
We describe several constructions that produce expressive curves, and discuss a large number of examples, including: arrangements of lines, parabolas, and circles; Chebyshev and Lissajous curves; hypotrochoids and epitrochoids; and much more.
address:
- 'Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA'
- 'School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel'
author:
- Sergey Fomin
- Eugenii Shustin
title: Expressive curves
---
[^1]
[^2]
Introduction {#introduction .unnumbered}
============
Let $g(x)\in\RR[x]$ be a polynomial of degree $n$ whose $n$ roots are real and distinct. Then $g$ has exactly $n-1$ critical points, all of them real, interlacing the roots of $g$.
In this paper, we study the two-dimensional version of this phenomenon. We call a bivariate real polynomial $G(x,y)\in\RR[x,y]$ (or the corresponding affine plane curve $C$) *expressive* if all critical points of $G$ are real, and their number and locations are determined by the set $C_\RR=\{(x,y)\in\RR^2\mid G(x,y)=0\}$, as follows:
- there is a saddle at each hyperbolic node of $C$ (i.e., a double point of $C_\RR$),
- there is precisely one extremum inside each bounded region of $\RR^2\setminus{C_{\RR}}$, and
- there are no other critical points.
An example is shown in Figure \[fig:3-circles\]. For a non-example, see Figure \[fig:isolines\].
Our main result (Theorem \[th:reg-expressive\]) gives an explicit characterization of expressive curves, subject to a mild requirement of “$L^\infty$-regularity.” (This requirement forbids some exotic behaviour of $C$ at infinity.) We prove that a plane algebraic curve $C$ with real irreducible components is expressive and $L^\infty$-regular if and only if
- each component of $C$ has a trigonometric or polynomial parametrization,
- all singular points of $C$ in the affine plane are real hyperbolic nodes, and
- the set of real points of $C$ in the affine plane is connected.
To illustrate, a union of circles is an expressive curve provided any two of them intersect at two real points, as in Figure \[fig:3-circles\]. On the other hand, the circle and the ellipse in Figure \[fig:isolines\] intersect at four points, two of which are complex conjugate. (In the case of a pair of circles, those two points escape to infinity.)
The above characterization allows us to construct numerous examples of expressive plane curves, including arrangements of lines, parabolas, circles, and singular cubics; Chebyshev and Lissajous curves; hypotrochoids and epitrochoids; and much more. See Figures \[fig:5-irr-expressive\]–\[fig:3-arrangements\] for an assortment of examples; many more are scattered throughout the paper.
\
(a) (b) (c) (d) (e)\
\[fig:5-irr-expressive\]
\
\[fig:3-arrangements\]
On the face of it, expressivity is an analytic property of a function $G:\RR^2\to\RR^2$. This is however an illusion: just like in the univariate case, in order to rule out incidental critical points, we need $G$ to be a polynomial of a certain kind. Thus, expressivity is essentially an algebraic phenomenon. Accordingly, its study requires tools of algebraic geometry and singularity theory.
For a real plane algebraic curve $C$ to be expressive, one needs $$\begin{aligned}
\notag
&\#\{\text{critical points of~$C$ in the complex affine plane}\} \\[-.05in]
\tag{$*$}
=\,&\#\{\text{double points in~${C_{\RR}}$}\} +
\#\{\text{bounded components of $\RR^2\setminus{C_{\RR}}$}\} . \end{aligned}$$ Since a generic plane curve of degree $d$ has $(d-1)^2$ critical points, whereas expression ($*$) is typically smaller than $(d-1)^2$, we need all the remaining critical points to escape to infinity. Our analysis shows that this can only happen if each (real) irreducible component of $C$ either has a unique point at infinity, or a pair of complex conjugate points; moreover the components must intersect each other in the affine plane at real points, specifically at hyperbolic nodes. The requirement of having one or two points at infinity translates into the condition of having a polynomial or trigonometric parametrization, yielding the expressivity criterion formulated above.
As mentioned earlier, these results are established under the assumption of *$L^\infty$-regularity*, which concerns the behaviour of the projective closure of $C$ at the line at infinity $L^\infty$. This assumption ensures that the number of critical points accumulated at each point $p\in C\cap L^\infty$ is determined in the expected way by the topology of $C$ in the vicinity of $p$ together with the intersection multiplicity $(C\cdot L^\infty)_p$. All polynomial and trigonometric curves are $L^\infty$-regular, as are all expressive curves of degrees $\le4$.
**Section-by-section overview.** Sections \[sec:plane-curves\]–\[sec:poly-trig\] are devoted to algebraic geometry groundwork. Section \[sec:plane-curves\] reviews basic background on plane algebraic curves, intersection numbers, and topological invariants of isolated singularities. The number of critical points escaping to infinity is determined by the intersection multiplicities of polar curves at infinity, which are studied in Section \[sec:polar-curves-at-infinity\]. Its main result is Proposition \[prop:milnor-infinity\], which gives a lower bound for such a multiplicity in terms of the Milnor number and the order of tangency between the curve and the line at infinity. When this bound becomes an equality, a plane curve $C$ is called $L^\infty$-regular.
In Section \[sec:L-regular-curves\], we provide several criteria for $L^\infty$-regularity. We also show (see Proposition \[pr:hironaka-milnor\]) that for an $L^\infty$-regular curve $C\!=\!\{G(x,y)\!=\!0\}$ all of whose singular points in the affine plane are ordinary nodes, the number of critical points of $G$ is completely determined by the number of those nodes, the geometric genus of $C$, and the number of local branches of $C$ at infinity. This statement relies on classical formulas due to H. Hironaka [@Hir] and J. Milnor [@Milnor].
Section \[sec:poly-trig\] introduces polynomial and trigonometric curves, the plane curves possessing a parametrization $t\mapsto (X(t),Y(t))$ in which both $X$ and $Y$ are polynomials, resp. trigonometric polynomials. We review a number of examples of such curves, recall the classical result of S. Abhyankar [@Abhyankar-1988] characterizing polynomial curves as those with a single place at infinity, and provide an analogous characterization for trigonometric curves.
Expressive curves are introduced in Section \[sec:expressive\]. We formulate their basic properties and discuss a large number of examples, which include an inventory of expressive curves of degrees $\le 4$.
In Section \[sec:divides\], we introduce A’Campo’s divides and relate them to the notion of expressivity.
Section \[sec:regular+expressive\] contains our main results. Using the aforementioned bounds and criteria, we show (see Theorem \[th:reg-expressive-irreducible\]) that an irreducible real plane algebraic curve is expressive and $L^\infty$-regular if and only if it is either trigonometric or polynomial, and moreover all its singular points in the complex affine plane are (real) hyperbolic nodes. This criterion is then extended (see Theorem \[th:reg-expressive\]) to general plane curves with real irreducible components. Additional expressivity criteria are given in Section \[sec:more-expressivity-criteria\].
As a byproduct, we obtain the following elementary statement (see Corollary \[cor:all-crit-pts-are-real\]): if $C=\{G(x,y)=0\}$ is a real polynomial or trigonometric affine plane curve that intersects itself solely at hyperbolic nodes, then all critical points of $G$ are real.
Multiple explicit constructions of expressive curves are presented in , demonstrating the richness and wide applicability of the theory. In Section \[sec:constructions-irr\], we describe the procedures of bending, doubling, and unfolding. Each of them can be used to create new (more “complicated”) expressive curves from existing ones. Arrangements of lines, parabolas, and circles, discussed in Section \[sec:overlays\], provide another set of examples. These examples are generalized in Section \[sec:shifts+dilations\] to arrangements consisting of shifts, dilations and/or rotations of a given expressive curve. Explicit versions of these constructions for polynomial (resp., trigonometric) curves are presented in Section \[sec:arrangements-poly\] (resp., Section \[sec:arrangements-trig\]).
All expressive curves known to us can be obtained using the constructions described in Sections \[sec:constructions-irr\]–\[sec:arrangements-trig\].
In Section \[sec:alternative-expressivity\], we briefly discuss alternative notions of expressivity: a “topological” notion that treats real algebraic curves set-theoretically, and an “analytic” notion that does not require the defining equation of a curve to be algebraic.
**Motivations and outlook.** This work grew out of the desire to develop a global version of the A’Campo–Guseĭn-Zade theory [@acampo-1975; @acampo-1999; @GZ1974; @gusein-zade-2] of morsifications of isolated singularities of plane curves. The defining feature of such morsifications is a *local* expressivity property, which prescribes the locations (up to real isotopy) of the critical points of a morsified curve in the vicinity of the original singularity. In this paper, expressivity is a *global* property of a real plane algebraic curve, prescribing the locations of its critical points (again, up to real isotopy) on the entire affine plane.
In a forthcoming follow-up paper, we are going to develop a global analogue—in the setting of expressive curves—of A’Campo’s theory of divides and their links. As shown in [@FPST], this theory has intimate connections to the combinatorics of quivers, cluster mutations, and plabic graphs.
It would be interesting to explore the phenomenon of expressivity in higher dimensions, and in particular find out which results of this paper generalize.
The concept of an expressive curve/hypersurface can be viewed as a generalization of the notion of a line/hyperplane arrangement. (Expressivity of such arrangements in arbitrary dimension can be established by a log-concavity argument.) This opens the possibility of extending the classical theory of hyperplane arrangements [@Aguiar-Mahajan; @Dimca; @Stanley-arrangements] to arrangements of expressive curves/surfaces.
**Acknowledgments.** We are grateful to Pavlo Pylyavskyy and Dylan Thurston for the collaboration [@FPST] which prompted our work on this project.
Graphs of curves were drawn with the `Desmos` online graphing tool. We used `Sage` to compute resultants.
While cataloguing expressive curves of degrees $\le 4$, we made use of the classifications produced by A. Korchagin and D. Weinberg [@Korchagin-Weinberg-2005].
Plane curves and their singularities {#sec:plane-curves}
====================================
Let $\PP^2$ denote the complex projective plane. We fix homogeneous coordinates $x,y,z$ in $\PP^2$. Any homogeneous polynomial $F\in\CC[x,y,z]$ defines a *plane algebraic curve* $C=Z(F)$ in $\PP^2$ given by $$C=Z(F)=\{F(x,y,z)=0\}.$$ We understand the notion of a curve (and the notation $Z(F)$) scheme-theoretically: if the polynomial $F$ splits into factors, we count each component of the curve $C=Z(F)$ with the multiplicity of the corresponding factor.
For two distinct points $p,q\in\PP^2$, we denote by $L_{pq}$ the line passing through $p$ and $q$. The *line at infinity* $L^\infty\subset\PP^2$ is defined by $L^\infty=Z(z)$.
For $F$ a smooth function in $x,y,z$, we use the shorthand $$F_x=\tfrac{\partial F}{\partial x}\,\quad
F_y=\tfrac{\partial F}{\partial y}\,,\quad
F_z=\tfrac{\partial F}{\partial z}$$ for the partial derivatives of $F$. The following elementary statement is well known, and easy to check.
Let $F=F(x,y,z)$ be a homogeneous polynomial of degree $d$. Then $$\label{eq:Euler}
d\cdot F=xF_x+yF_y+zF_z\,.$$
Let $F\in\CC[x,y,z]$ be a homogeneous polynomial in $x,y,z$. For a point $q=(q_x,q_y,q_z)\in\PP^2$, we denote $$F_{(q)}=q_xF_x+q_yF_y+q_zF_z\,.$$ The *polar curve* $C_{(q)}$ associated with a curve $C=Z(F)$ and a point $q\in\PP^2$ is defined by $C_{(q)}=Z(F_{(q)})$. In particular, for $q=(1,0,0)\in L^\infty$ (resp., $q=(0,1,0)\in L^\infty$), we get the polar curve $Z(F_x)$ (resp., $Z(F_y)$).
For a point $p$ lying on two plane curves $C$ and $\tilde C$, we denote by $(C\cdot \tilde C)_p$ the *intersection number* of these curves at $p$. We will also use this notation for analytic curves, i.e., curves defined by analytic equations in a neighborhood of $p$.
\[def:top-invariants\] Let $C=Z(F)$ be a plane algebraic curve, and $p$ an isolated singular point of $C$. Let us recall the following topological invariants of the singularity $(C,p)$:
- the *multiplicity* $\operatorname{mult}(C,p)=(C\cdot L)_p$, where $L$ is any line passing through $p$ which is not tangent to the germ $(C,p)$;
- the *$\varkappa$-invariant* $\varkappa(C,p)=(C\cdot C_{(q)})_p$, where $q\in \PP^2\setminus\{p\}$ is such that the line $L_{pq}$ is not tangent to $(C,p)$;
- the *number $\operatorname{Br}(C,p)$ of local branches* (irreducible components) of the germ $(C,p)$;
- the *$\delta$-invariant* $\delta(C,p)$, which can be determined from $$\varkappa(C,p)=2\delta(C,p)+\operatorname{mult}(C,p)-\operatorname{Br}(C,p);$$
- the *Milnor number* $\mu(C,p)=(C_{(q')}\cdot C_{(q'')})_p$, where the points $q', q''\in\PP^2$ are chosen so that $p,q',q''$ are not collinear.
More generally, for any point $p\in C_{(q')}\cap C_{(q'')}$, not necessarily lying on the curve $C$, we can define the Milnor number $$\mu(C,p)=(C_{(q')}\cdot C_{(q'')})_p$$ (provided $p,q',q''$ are not collinear). Note that for $p\notin L^\infty$, we can simply define $$\label{eq:mu-x-y}
\mu(C,p)=(Z(F_x)\cdot Z(F_y))_p\,.$$
See [@Milnor §5 and §10] and [@GLS Sections I.3.2 and I.3.4] for additional details as well as basic properties of these invariants. See also Remark \[rem:invariants-informal\] and Proposition \[pr:invariants-identities\] below.
\[rem:invariants-informal\] All invariants listed in Definition \[def:top-invariants\] depend only on the topological type of the singularity at hand. The Milnor number $\mu(C,p)$ measures the complexity of the singular point $p$ viewed as a critical point of $F$. It is equal to the maximal number of critical points that a small deformation of $F$ may have in the vicinity of $p$. The $\delta$-invariant is the maximal number of critical points lying on the deformed curve in a small deformation of the germ $(C,p)$. The $\varkappa$-invariant is the number of ramification points of a generic projection onto a line of a generic deformation of the germ $(C,p)$.
\[pr:invariants-identities\] Let $(C,p)$ be an isolated plane curve singularity as above. Then we have: $$\begin{aligned}
\label{eq:milnor-formula}
\mu(C,p)&=2\delta(C,p)-\operatorname{Br}(C,p)+1 \quad \text{(Milnor's formula)}; \\
\label{eq:C*Cq}
(C\cdot C_{(q)})_p&=\varkappa(C,p)+(C\cdot L_{pq})_p-\operatorname{mult}(C,p)
\quad \text{for any $q\in\PP^2\setminus\{p\}$;}\\
\label{eq:kappa=mu+mult-1}
\varkappa(C,p)&=\mu(C,p)+\operatorname{mult}(C,p)-1.\end{aligned}$$
\[ex:(x\^2+z\^2)(yz\^2-x\^3+x\^2y)\] Consider the quintic curve $C=Z(F)$ defined by the polynomial $$F(x,y,z)=(x^2+z^2)(yx^2+yz^2-x^3)=(x+iz)(x-iz)(yx^2+yz^2-x^3).$$ It has two points on the line at infinity $L^\infty$, namely $p_1=(0,1,0)$ and $p_2=(1,1,0)$. At $p_1$, the cubical component has an elliptic node, and the two line components are the two tangents to the cubic at $p_1$. At $p_2$, we have a smooth real local branch of the cubical component. Direct computations show that $$\begin{aligned}
{3}
\operatorname{mult}(C,p_1)&=4 &\qquad \operatorname{mult}(C,p_2)&=1\\
\varkappa(C,p_1)&=16&\qquad \varkappa(C,p_2)&=0 \\
\operatorname{Br}(C,p_1)&=4 &\qquad \operatorname{Br}(C,p_2)&=1 \\
\delta(C,p_1)&=8&\qquad \delta(C,p_2)&=0 \\
\mu(C,p_1)&=13&\qquad \mu(C,p_2)&=0 \\
(C\cdot L^\infty)_{p_1}&=4 &\qquad (C\cdot L^\infty)_{p_2}&=1\\
(Z(F_x)\cdot Z(F_y))_{p_1}&=16 &\qquad (Z(F_x)\cdot Z(F_y))_{p_2}&=0 \\
(C\cdot F_x)_{p_1}&=16 &\qquad (C\cdot F_x)_{p_2}&=0
$$ Note that does not hold for $p=p_1$; this is not a contradiction since $p_1\in L^\infty$.
Intersections of polar curves at infinity {#sec:polar-curves-at-infinity}
=========================================
In this section, we study the properties of intersection numbers of polar curves at their common points located at the line at infinity.
\[d1\] Let $F(x,y,z)\in\CC[x,y,z]$ be a non-constant homogeneous polynomial.
- The set $Z(F_{(q')})\cap Z(F_{(q'')})\cap L^\infty$ does not depend on the choice of a pair of distinct points $q',q''\in L^\infty$. Moreover this set is contained in $C$.
- For a point $p\in C\cap L^\infty$, the intersection multiplicity $(Z(F_{(q')})\cdot Z(F_{(q'')}))_p$ does not depend on the choice of a pair of distinct points $q',q''\in L^\infty$.
Any other pair $\hat q',\hat q''$ of distinct points in $L^\infty$ satisfies $$\label{eq:hat-q}
\begin{array}{r}
\hat q'=a_{11}q'+a_{12}q'',\\
\hat q''=a_{21}q'+a_{22}q'',
\end{array}
\text{\quad with\quad}
\left| \begin{matrix} a_{11} & a_{12}\\
a_{21} & a_{22}
\end{matrix}\right|
\ne 0.$$ Consequently $$\begin{aligned}
F_{(\hat q')}&=a_{11}F_{(q')}+a_{12}F_{(q'')},\\
F_{(\hat q'')}&=a_{21}F_{(q')}+a_{22}F_{(q'')}\end{aligned}$$ and the first claim in (i) follows. To establish the second claim, set $q'=(1,0,0)$ and $q''=(0,1,0)$ (i.e., take the polar curves $Z(F_x)$ and $Z(F_y)$), and note that by Euler’s formula , $F$ vanishes as long as $F_z$, $F_y$ and $z$ vanish.
To prove (ii), factor the nonsingular $2\times2$ matrix in into the product of an upper triangular and a lower triangular matrix; then use that, for $bc\ne0$, $$\label{e4e}
(Z(aG_1+bG_2)\cdot Z(cG_1))_p=(Z(G_2)\cdot Z(G_1))_p\,. \qedhere$$
For a plane projective curve $C$ and a point $p\in L^\infty$, we denote $$\muinf \eqdef (Z(F_x)\cdot Z(F_y))_p\,.$$ As pointed out above, if $p$ lies on both $Z(F_x)$ and $Z(F_y)$, then it necessarily lies on $C$, so $\muinf$ can only be nonzero at points $p\in C\cap L^\infty$.
\[r5\] For $p\in C\cap L^\infty$, the number $\muinf$ may differ from the Milnor number $\mu(C,p)$ (cf. ), since the points $p,q',q''$ lie on the same line $L^\infty$. Moreover, $\muinf$ is not determined by the topological type of the singularity $(C,p)$, as it also depends on its “relative position” with respect to the line $L^\infty$. The following example illustrates this phenomenon. Consider the curves $Z(x^2y-z^3-xz^2)$ and $Z(x^2y^2-yz^3)$. Each of them has an ordinary cusp (type $A_2$) at the point $p=(0,1,0)$. On the other hand, we have $\muinf=4$ in the former case versus $\muinf=3$ in the latter. Additional examples can be produced using Proposition \[prop:milnor-infinity\] below.
\[rem:Milnor-number-at-infinity\] The intersection number $\muinf$ is also different from “the Milnor number at infinity” (as defined, for instance, in [@ABLMH; @Siersma-Tibar]) since $\muinf$ depends on the choice of a point $p\in L^\infty$. Moreover, $\muinf$ is not determined by the local topology of the configuration consisting of the germ $(C,p)$ and the line $L^\infty$.
\[prop:milnor-infinity\] Let $C=Z(F)$ be an algebraic curve in $\PP^2$. Let $p\in C\cap L^\infty$. Then $$\label{eq:e2}
\muinf
\ge \mu(C,p)+(C\cdot L^\infty)_p-1.$$
The proof of Proposition \[prop:milnor-infinity\] will rely on two lemmas, one of them very simple.
\[lem:F\*Fq\] For any $q\in L^\infty\setminus\{p\}$, we have $$(C\cdot Z(F_{(q)}))_p=\mu(C,p)+(C\cdot L^\infty)_p-1.$$
Using and , we obtain: $$\begin{aligned}
(C\cdot Z(F_{(q)}))_p&=\varkappa(C,p)+(C\cdot L^\infty)_p-\operatorname{mult}(C,p) =\mu(C,p)+(C\cdot L^\infty)_p-1. \qedhere\end{aligned}$$
\[lem:e1\] Let $Q$ be a local branch (i.e., a reduced, irreducible component) of the germ of the curve $Z(F_y)$ at $p$. Then $$\label{eq:e1}
(Z(zF_z)\cdot Q)_p\ge(Z(F)\cdot Q)_p\ .$$
We will prove the inequality inductively, by blowing up the point $p$. As a preparation step, we will apply a coordinate change intended to reduce the general case to a particular one, in which the blowing up procedure is easier to describe.
Without loss of generality, we assume that $p=(1,0,0)$. In a neighborhood of $p$, we can set $x=1$ and then work in the affine coordinates $y,z$. Abusing notation, for a homogeneous polynomial $G(x,y,z)$, we will write $G(y,z)$ instead of $G(1,y,z)$.
For any curve $Z(G)$, the intersection multiplicity $(G\cdot Q)_p$ can be computed as follows. Write $Q=\{f(y,z)=0\}$, where $f(y,z)$ is an irreducible element of the ring $\CC\{y,z\}$ of germs at $p$ of holomorphic functions in the variables $y$ and $z$. By [@GLS Proposition I.3.4], we have $$f(y,z)=u(y,z)\prod_{1\le i\le k}(y-\xi_i(z^{1/k})), \quad u(y,z)\in\CC\{y,z\},\quad u(0,0)\ne0,$$ where each $\xi_i$ is a germ at zero of a holomorphic function vanishing at the origin. Then [@GLS Propostion I.3.10 (Halphen’s formula)] yields $$(G\cdot Q)_p=\sum_{1\le i\le k}\operatorname{ord}_0G(\xi_i(z),z).
\label{e17}$$ It follows that the variable change $(y,z)=\tau(y_1,z_1)\stackrel{\rm def}{=}(y_1,z_1^k)$ multiplies both sides of by $k$. For $g\in\CC\{y,z\}$, let us denote $\tau^*g(y_1,z_1)=g\circ\tau(y_1,z_1))$. Then $\tau^*Q$ splits into $k$ smooth branches $$Q_i=\{y_1-\xi_i(z_1)=0\}, \quad i=1,...,k,$$ and it suffices to prove the inequality with $Q$ replaced by each of the $Q_i$’s. Moreover, with respect to $Q_i$, the desired inequality is of the same type. Namely, $\tau^*(F_y)=(\tau^*F)_{y_1}$, and hence $Q_i$ is a local branch of the polar curve $Z((\tau^*F)_{y_1})$ of the curve $\tau^*C=Z(\tau^*F)$. Furthermore, $$\begin{aligned}
z_1(\tau^*F)_{z_1}(y_1,z_1)&=z_1\tfrac{\partial}{\partial z_1}[F(y_1,z_1^k)]\\
&=z_1F_y(y_1,z_1^k)+kz_1^kF_z(y_1,z_1^k)\\
&=z_1(\tau^*F_y)(y_1,z_1)+k\cdot(\tau^*(zF_z))(y_1,z_1),\end{aligned}$$ which implies $$(Z(z_1(\tau^*F)_{z_1})\cdot Q_i)_p=(Z(\tau_*(zF_z))\cdot Q_i)_p,\quad i=1,...,k.$$
We have thus reduced the proof of to the case where $Q$ is a smooth curve germ transversal to the line $L^\infty$. To simplify notation, we henceforth write $C,F,y,z$ instead of $\varphi^*C,\varphi^*F,y_1,z_1$, respectively.
We proceed by induction on $\mu(C,p)$. If $\mu(C,p)=0$, then $(C,p)$ is a smooth germ. If $C$ intersects $L^\infty$ transversally, then $(C,p)$ is given by $$F(y,z)=ay+bz+\text{h.o.t.}, \quad a\ne0$$ (hereinafter h.o.t. is a shorthand for “higher order terms”), implying . Thus the polar curve $Z(F_y)$ does not pass through $p$; consequently both sides of vanish. If $C$ is tangent to $L^\infty$ at $p$, then it is transversal to $Q$ at $p$, so we have $$(C\cdot Q)_p=1=(Z(z)\cdot Q)_p\le(Z(zF_z)\cdot Q)_p\,.$$
Suppose that $\mu(C,p)>0$. Then $m\stackrel{\rm def}{=}\operatorname{mult}(C,p)\ge2$. If $C$ and $Q$ intersect transversally at $p$ (i.e., have no tangent in common), then $$(C\cdot Q)_p=\operatorname{mult}(C,p)\cdot\operatorname{mult}(Q,p)=m\cdot 1=m.$$ On the other hand, $\operatorname{mult}(Z(F_z),p)\ge m-1$, and therefore $$(Z(zF_z)\cdot Q)\ge\operatorname{mult}(Z(zF_z),p)\cdot \operatorname{mult}(Q,p)\ge m\cdot 1=m=(C\cdot Q).$$ If $C$ and $Q$ have a common tangent at $p$, we apply the blowing-up $\pi:\widetilde\PP^2\to\PP^2$ of the plane at the point $p$. For a curve $D$ passing through $p$, let $D^*$ denote its *strict transform*, i.e., the closure of the preimage $\pi^{-1}(D\setminus\{p\})$ in $\widetilde\PP^2$. (For more details, see [@GLS Section I.3.3, p. 185].). Since $Q$ is smooth, the strict transform $Q^*$ is smooth too, and intersects transversally the exceptional divisor $E$ at some point $p^*$. More precisely, if $Q=Z(y-\eta z-\text{h.o.t.})$, then in the coordinates $(y_*,z_*)$ given by $y=y_*z_*$, $z=z_*$, we have $E=Z(z_*)$ and $p^*=(\eta,0)$. Since $C$ and its polar curve $Z(F_y)$ are tangent to the line $Z(y-\eta z)$, the lowest homogeneous form of $F(y,z)$ is divisible by $(y-\eta z)^2$, while the lowest homogeneous form of $F_y$ is divisible by $y-\eta z$ and, moreover, $\operatorname{mult}(Z(F_y),p)=m-1$.
We now recall some properties of the blowing-up. For a curve $D\!=\!Z(G(y,z))$ passing through $p$, we have [@GLS Prop. I.3.21 and I.3.34, and computations on p. 186]: $$\begin{aligned}
(D^*\cdot Q^*)_{p^*}&=(D\cdot Q)_p-\operatorname{mult}(D,p)\cdot\operatorname{mult}(Q,p)=(D\cdot Q)_p-\operatorname{mult}(D,p); \\
\textstyle\sum_{q\in D^*\cap E}\delta(D^*,q)&=\delta(D,p)-\tfrac12 \operatorname{mult}(D,p)(\operatorname{mult}(D,p)-1); \\
D^*&=Z(z_*^{-\operatorname{mult}(D,p)}G(y_*z_*,z_*)).\end{aligned}$$ We see that $$\begin{aligned}
F^*(y_*,z_*)&=z_*{-m}F(y_*z_*,z_*),\\
(F^*)_{y_*}(y_*,z_*)&=
z_*^{1-m}F_y(y_*z_*,z_*)=(F_y)^*(y_*,z_*).\end{aligned}$$ Thus $Q^*$ is a local branch of the polar curve $(F^*)_{y_*}\!=\!0$ of the strict transform $C^*$. Hence after the blowing-up we come to the original setting. Furthermore, $$\begin{aligned}
\mu(C^*,p^*)&=2\delta(C^*,p^*)-\operatorname{Br}(C^*,p^*)+1\\
&\le2\delta(C^*,p^*)\\
&\le2\textstyle\sum_{q\in C^*\cap E}\delta(C^*,q)\\
&=2\delta(C,p)-m(m-1)\\
&=\mu(C,p)+\operatorname{Br}(C,p)-1-m(m-1)\\
&\le\mu(C,p)+m-1-m(m-1)\\
&<\mu(C,p).\end{aligned}$$ So we can apply the induction assumption. Observe that $\operatorname{mult}(F_z,p)=m-1+r$ for some $r\ge0$. It follows that $$\begin{aligned}
(Z(F)\cdot Q)_p&=(Z(F^*)\cdot Q^*)_{p^*}+m,\\
(Z(zF_z)\cdot Q)_p&=1+(Z(F_z)\cdot Q)_p=(Z(F_z)^*)\cdot Q^*)_{p^*}+m+r.
\end{aligned}
\label{eq:e3}$$ Now $$\begin{aligned}
z_*(F^*)_{z_*}&=-mz_*^{-m}F(y_*z_*,z_*)+y_*z_*^{1-m}F_y(y_*z_*,z_*)+z_*^{1-m}F_z(y_*z_*,z_*)\\
&=-mF^*(y_*,z_*)+y_*(F^*)_{y_*}(y_*,z_*)+z_*^r(F_z)^*(y_*,z_*).\end{aligned}$$ Finally, the latter formula, the induction assumption, and (\[eq:e3\]) imply $$\begin{aligned}
(Z(zF_z)\cdot Q)_p&=(Z((F_z)^*)\cdot Q^*)_{p^*}+m+r\\
&=(Z(z_*^r(F_z)^*)\cdot Q^*)_{p^*}+m\\
&\ge\min\{Z(z_*(F^*)_{z_*})\cdot Q^*)_{p^*},\ (Z(F^*)\cdot Q^*)_{p^*}\}+m\\
&\ge (Z(F^*)\cdot Q^*)_{p^*}\}+m\\
&=(Z(F)\cdot Q)_p\,. \qedhere\end{aligned}$$
We again assume $p=(1,0,0)$. Set $d=\deg(F)$. In the local affine coordinates $y, z$ (with $x=1$), Euler’s formula becomes $$d F(1,y,z)=F_x(1,y,z)+yF_y(1,y,z)+zF_z(1,y,z).$$ Consequently $\muinf=(Z(F_x)\cdot Z(F_y))_p=(Z(d F-zF_z)\cdot Z(F_y))_p$.
Let ${\mathcal B}$ denote the set of local branches of the polar curve $F_y=0$ at $p$. Then $$\begin{aligned}
\muinf&=(Z(d F-zF_z)\cdot Z(F_y))_p\\
&=\textstyle\sum_{Q\in{\mathcal B}}
(Z(dF-zF_z)\cdot Q)_p\\
&\ge\textstyle\sum_{Q\in{\mathcal B}}\min\{(Z(F)\cdot Q)_p\,,(Z(zF_z)\cdot Q)_p\}\\
&=\textstyle\sum_{Q\in{\mathcal B}}(Z(F)\cdot Q)_p \qquad \text{(by \eqref{eq:e1})}\\
&=(Z(F)\cdot Z(F_y))_p \\
&=\mu(C,p)+(C\cdot L^\infty)_p-1 \quad \text{(by Lemma~{\hyperref}{lem:F*Fq}).}
\qedhere\end{aligned}$$
L-regular curves {#sec:L-regular-curves}
================
\[def:c-regular\] Let $C=Z(F(x,y,z))\subset\PP^2$ be a reduced plane algebraic curve which does not contain the line at infinity $L^\infty$ as a component. The curve $C$ (or the polynomial $F$) is called *$L^\infty$-regular* if at each point $p\in C\cap L^\infty$, the formula becomes an equality: $$\label{eq:c-regularity}
\muinf = \mu(C,p)+(C\cdot L^\infty)_p-1.$$
In the rest of this section, we provide $L^\infty$-regularity criteria for large classes of plane curves.
\[pr:regularity-via-milnor\] Let $C\!=\!Z(F(x,y,z))\!\subset\!\PP^2$ be a reduced algebraic curve of degree $d$ which does not contain $L^\infty$ as a component. Assume that the polynomial $F(x,y,1)$ has $\xi<\infty$ critical points, counted with multiplicities. Then we have $$\label{eq:xi-d-mu}
\xi \le d^2-3d+1-\sum_{p\in C\cap L^\infty} (\mu(C,p)-1),$$ with equality if and only if $C$ is $L^\infty$-regular.
In view of Proposition \[prop:milnor-infinity\], we have $$\label{eq:L-inequality}
\sum_{p\in C\cap L^\infty} \muinf
\ge d+\sum_{p\in C\cap L^\infty} (\mu(C,p)-1),$$ with equality if and only if $C$ is $L^\infty$-regular. Since $F$ has finitely many critical points, Bézout’s theorem for the polar curves $Z(F_x)$ and $Z(F_y)$ applies, yielding $$\sum_{p\in C\cap L^\infty}\muinf = (d-1)^2 -\xi.$$ The claim follows.
\[ex:(x\^2+z\^2)(yz\^2-x\^3+yx\^2)-regular\] As in Example \[ex:(x\^2+z\^2)(yz\^2-x\^3+x\^2y)\], consider the quintic curve $C=Z(F)$ defined by the polynomial $$F(x,y,z)=(x^2+z^2)(yx^2+yz^2-x^3)=(x+iz)(x-iz)(yx^2+yz^2-x^3).$$ Set $G(x,y)=F(x,y,1)=(x^2+1)(yx^2+y-x^3)$. Then $$\begin{aligned}
G_x&= 2x(yx^2+y-x^3)+(x^2+1)(2xy-3x^2) =(x^2+1)(4xy-3x^2)-2x^4, \\
G_y&=(x^2+1)^2,\end{aligned}$$ and we see that $G$ has no critical points in the complex $(x,y)$-plane; thus $\xi=0$. Using the values of Milnor numbers computed in Example \[ex:(x\^2+z\^2)(yz\^2-x\^3+x\^2y)\], we obtain: $$d^2-3d+1-\sum_{p\in C\cap L^\infty} (\mu(C,p)-1)
=25-15+1-(13-1)-(0-1)
=0.$$ It follows by Proposition \[pr:regularity-via-milnor\] that $C$ is $L^\infty$-regular. Alternatively, one can check directly that the equality holds at $p_1$ and $p_2$.
Recall that the *geometric genus* of a plane curve $C$ is defined by $$\label{eq:g(C)}
g(C)=\sum_{C'\in\operatorname{\mathbf{Comp}}(C)} (g(C')-1)+1,$$ where $\operatorname{\mathbf{Comp}}(C)$ is the set of irreducible components of $C$, and $g(C')$ denotes the genus of the normalization of a component $C'$.
\[pr:hironaka-milnor\] Let $C\!=\!Z(F(x,y,z))\!\subset\!\PP^2$ be a reduced algebraic curve of degree $d$. Suppose that
- $C$ does not contain the line at infinity $L^\infty$ as a component;
- all singular points of $C$ in the affine $(x,y)$-plane $\PP\setminus L^\infty$ are ordinary nodes;
- the polynomial $F(x,y,1)\in\CC[x,y]$ has finitely many critical points.
Let $\nu$ denote the number of nodes of $C$ in the $(x,y)$-plane, and let $\xi$ denote the number of critical points of the polynomial $F(x,y,1)$, counted with multiplicities. Then we have $$\label{eq:xi-le}
\xi \le 2g(C)-1+2\nu+\sum_{p\in C\cap L^\infty}\operatorname{Br}(C,p),$$ with equality if and only if $C$ is $L^\infty$-regular.
By Hironaka’s genus formula [@Hir] (cf. also [@GLS1 Chapter II, (2.1.4.6)]), we have $$\label{eq:Hironaka}
g(C)=\tfrac{(d-1)(d-2)}{2}-\sum_{p\in\operatorname{\mathbf{Sing}}(C)}\delta(C,p),$$ where $\operatorname{\mathbf{Sing}}(C)$ denotes the set of singular points of $C$. Combining this with Milnor’s formula , we obtain: $$\begin{aligned}
\sum_{p\in C\cap L^\infty} (\mu(C,p)-1)
&=\sum_{p\in \operatorname{\mathbf{Sing}}(C)} (\mu(C,p)-1) \\
&= \sum_{p\in \operatorname{\mathbf{Sing}}(C)} (2\delta(C,p)-\operatorname{Br}(C,p)) \\
&=(d-1)(d-2)-2g(C)-2\nu-\sum_{p\in C\cap L^\infty}\operatorname{Br}(C,p).\end{aligned}$$ Therefore $$d^2-3d+1-\sum_{p\in C\cap L^\infty} (\mu(C,p)-1)
=2g(C)-1+2\nu+\sum_{p\in C\cap L^\infty}\operatorname{Br}(C,p),$$ and the claim follows from Proposition \[pr:regularity-via-milnor\].
Our next result (Proposition \[pr:nonmax-tangency\] below) shows that equation holds under certain rather mild local conditions, To state these conditions, we will need to recall some terminology and notation.
\[def:Newton-diagram\] We denote by $\Gamma(G)$ the *Newton diagram* of a bivariate polynomial $G$, i.e., the union of the edges of the Newton polygon of $G$ which are visible from the origin. The *truncation* of $G$ along an edge $e$ of $\Gamma(G)$ is the sum of all monomials in $G$ corresponding to the integer points in $e$.
An isolated singularity of an affine plane curve $\{G(y,z)=0\}$ at the origin is called *Newton nondegenerate* (with respect to the local affine coordinates $(y,z)$) if the Newton diagram $\Gamma(G)$ intersects each of the coordinate axes, and the truncation of $G$ along any edge of the Newton diagram is a quasihomogeneous polynomial without critical points in $(\CC^*)^2$.
\[pr:nonmax-tangency\] Let $C=Z(F(x,y,z))\subset\PP^2$ be a reduced curve not containing the line at infinity $L^\infty=Z(z)$ as a component. Let $p=(1,0,0)\in C\cap L^\infty$ be either a smooth point of $C$, or a singular point of $C$ such that $$\begin{aligned}
\label{eq:newton-nondeg}
&\!\!\text{the singularity $(C,p)$ is Newton nondegenerate, in the local coordinates~$y,z$;}\\
\label{eqeq}
&\!\!(Z(y)\cdot C)_p<\deg C=\deg F.\end{aligned}$$ Then $$\label{eq:local-regularity}
\muinf = \mu(C,p)+(C\cdot L^\infty)_p-1.$$ Thus, if conditions – hold at every point $p\in C\cap L^\infty$, then $C$ is $L^\infty$-regular.
Although we did not find Proposition \[pr:nonmax-tangency\] in the literature, similar results—proved using similar tools—appeared before, see for example [@ABLMH].
If $p$ is a smooth point of $C$ with the tangent $L\ne L^\infty$, then $$F(1,y,z)=ay+bz+\text{h.o.t.} \quad (a\ne0),$$ implying that $p\not\in Z(F_y)$. The $L^\infty$-regularity follows: $$(Z(F_x)\cdot Z(F_y))_p=0=\mu(C,p)+(C\cdot L^\infty)_p-1.$$ If $C$ is smooth at $p$ with the tangent line $L^\infty$, then $$F(1,y,z)=ay^n+bz+\text{h.o.t.} \quad (ab\ne0,\ n>1),$$ which implies the Newton nondegeneracy as well as condition : $$(Z(y)\cdot C)_p=1<n\le\deg C\ .$$ Thus, this situation can be viewed as a particular case of the general setting where we have a singular point $p$ satisfying conditions –. We next turn to the treatment of this setting.
We proceed in two steps. We first consider semi-quasihomogeneous singular points, and then move to the general case. We set $x=1$ in a neighborhood of $p$ and write $F(y,z)$ as a shorthand for $F(1,y,z)$.
\(1) Assume that $\Gamma(F)$ is a segment with endpoints $(m,0)$ and $(0,n)$. By the assumptions of the lemma, $m\le d=\deg F$ and $n<d$. The Newton nondegeneracy condition means that the truncation $F^{\Gamma(F)}$ of $F$ on $\Gamma(F)$ is a square-free quasihomogeneous polynomial.
Assuming that $s=\gcd\{m,n\}$, $m=m_1s$, $n=n_1s$, we can write $$F^{\Gamma(F)}(y,z)=\sum_{k=0}^sa_ky^{m_1k}z^{n_1(s-k)},\quad\text{where}\ a_0a_s\ne0\ .$$ Consider the family of polynomials $$F_t(y,z)=t^{-mn}F(yt^n,zt^m)=F^{\Gamma(F)}(y,z)+\sum_{in+jm>mn}c_{ij}t^{in+jm-mn}x^iy^j, \quad t\in[0,1].$$ Note that $F_0=F^{\Gamma(F)}$ and that the polynomials $F$ and $F_t$, $0<t<1$, differ by a linear change of the variables. This together with the lower semicontinuity of the intersection multiplicity implies $$\muinf=(Z(F_y)\cdot Z(dF-zF_z))_p\le(Z(F^{\Gamma(F)}_y)\cdot Z(dF^{\Gamma(F)}-zF^{\Gamma(F)}_z))_p\ .\label{e10}$$ Here $$\begin{aligned}
F^{\Gamma(F)}_y&=\sum_{k=1}^sm_1ka_ky^{m_1k-1}z^{n_1(s-k)},\nonumber\\
dF^{\Gamma(F)}-zF^{\Gamma(F)}_z&=
\sum_{k=0}^s(d-n_1(s-k))a_ky^{m_1k}z^{n_1(s-k)}.
\label{e12}\end{aligned}$$ Since $a_s\ne0$ and $n_1s=n<d$, these are nonzero polynomials, and moreover $F^{\Gamma(F)}_y$ splits into $l_1\ge0$ factors of type $z^{n_1}+\alpha y^{m_1}$, $\alpha\ne0$ and the factor $y^{m-1-l_1m_1}$, while $zF^{\Gamma(F)}_z-dF^{\Gamma(F)}$ splits into $l_2\ge0$ factors of type $z^{n_1}+\beta y^{m_1}$, $\beta\ne0$, and the factor $z^{n-l_2n_1}$. Observe that the polynomials $F^{\Gamma(F)}_y$ and $zF^{\Gamma(F)}_z-F^{\Gamma(F)}$ are coprime. Indeed, otherwise, they would have a common factor $z^{n_1}+\gamma y^{m_1}$ with $\gamma\ne0$, which also would be a divisor of the polynomial $$n_1yF^{\Gamma(F)}+m_1(zF^{\Gamma(F)}_z-dF^{\Gamma(F)})=m_1(n-d)F^{\Gamma(F)}$$ contrary to the square-freeness of $F^{\Gamma(F)}$. Since $$\begin{aligned}
(Z(y)\cdot Z(z))_p&=1, \\
(Z(y)\cdot Z(z^{n_1}+\beta y^{m_1}))_p&=n_1, \\
(Z(z)\cdot Z(z^{n_1}+\alpha y^{m_1}))_p&=m_1\quad \text{as}\quad \alpha\ne0, \\
(Z(z^{n_1}+\alpha y^{m_1})\cdot Z(z^{n_1}+\beta y^{m_1}))_p&=m_1n_1\quad\text{as}\quad\alpha\ne\beta,\end{aligned}$$ the right-hand side of (\[e10\]) equals $$\begin{aligned}
&l_1l_2\cdot(Z(z^{n_1}+\alpha y^{m_1})\cdot Z(z^{n_1}+\beta y^{m_1}))_p+
l_1(n-l_2n_1)\cdot(Z(z)\cdot Z(z^{n_1}+\alpha y^{m_1}))_p \\
&\quad +(m-1-l_1m_1)l_2\cdot(Z(y)\cdot Z(z^{n_1}+\beta y^{m_1}))_p
+(m-1-l_1m_1)\cdot(Z(y)\cdot Z(z))_p \\
=&(m-1)n\\
=&(m-1)(n-1)+m-1\\
=&\mu(C,p)+(C\cdot L^\infty)_p-1\ ,\end{aligned}$$ which together with (\[eq:e2\]) yields the desired equality.
\(2) Suppose that $\Gamma(F)$ consists of $r\ge2$ edges $\sigma^{(1)},...,\sigma^{(r)}$ successively ordered so that $\sigma^{(1)}$ touches the axis of exponents of $y$ at the point $(m,0)$, where $m=(C\cdot L^\infty)_p$, and $\sigma^{(r)}$ touches the axis of exponents of $z$ at the point $(0,n)$, where $n=(C\cdot Z(y))_p<d=\deg F$. By the hypotheses of the lemma, for any edge $\sigma=\sigma^{(i)}$, the truncation $F^\sigma(y,z)$ is the product of $y^az^b$, $a,b\ge0$, and of a quasihomogeneous, square-free polynomial $F_0^\sigma$, whose Newton polygon $\Delta(F_0^\sigma)$ is the segment $\sigma_0$ with endpoints on the coordinate axes, obtained from $\sigma$ by translation along the vector $(-a,-b)$.
Note that the minimal exponent of $z$ in the polynomial $dF(0,z)-zF_z(0,z)$ is $n$, and hence $$(Z(F_y)\cdot Z(dF-zF_z))_p=(Z(yF_y)\cdot Z(dF-zF_z))_p-n\ .\label{e11}$$ Next, we note that the Newton diagram $\Gamma(yF_y)$ contains entire edges $\sigma^{(1)},...,\sigma^{(r-1)}$ and some part of the edge $\sigma^{(r)}$, while $\Gamma(dF-zF_z)=\Gamma(F)$, since the monomials of $dF-zF_z$ and of $F$ on the Newton diagram $\Gamma(F)$ are in bijective correspondence, and the corresponding monomials differ by a nonzero constant factor, cf. (\[e12\]).
By [@GLS Proposition I.3.4], we can split the polynomial $F$ inside the ring $\CC\{y,z\}$ into the product $$F=\varphi_1...\varphi_r,\quad\Gamma(\varphi_i)=\sigma^{(i)}_0,\ \varphi_i^{\sigma^{(i)}_0}=
F_0^{\sigma^{(i)}},\ i=1,...,r,$$ and similarly $$dF-zF_z=\psi_1...\psi_r,\quad\Gamma(\psi_i)=\sigma^{(i)}_0,\ \psi_i^{\sigma^{(i)}_0}=
(dF-zF_z)_0^{\sigma^{(i)}},\ i=1,...,r,$$ $$yF^y=\theta_1...\psi_r,\quad \Gamma(\theta_i)=\sigma^{(i)}_0,\ \theta_i^{\sigma^{(i)}_0}=
(yF_y)_0^{\sigma^{(i)}},\ i=1,...,r-1,$$ while $$\theta_r^{\sigma_0^{(r)}}=(yF_y)^{\sigma^{(r)}}\cdot z^{-c}$$ for $c$ the minimal exponent of $z$ in $(yF_y)^{\sigma^{(r)}}$. Thus, $$(Z(yF_y)\cdot Z(dF-zF_z))_p=\sum_{1\le i,j\le r}(Z(\psi_i)\cdot Z(\theta_j))_p\ .\label{e14}$$ We claim that $$(Z(\psi_i)\cdot Z(\theta_j))_p=(Z(\varphi_i)\cdot Z(\theta_j))_p\quad \text{for all}\ 1\le i,j\le r\ .\label{e15}$$ Having this claim proven, we derive from (\[e14\]) that $$\begin{aligned}
(Z(yF_y)\cdot Z(dF-zF_z))_p&=\sum_{1\le i,j\le r}(Z(\varphi_i)\cdot Z(\theta_j))_p\\
&=(Z(yF_y)\cdot Z(F))_p=(Z(y)\cdot Z(F))_p+(Z(F_y)\cdot Z(F))_p\\
&=n+\varkappa(C,p)+(C\cdot L^\infty)_p-\operatorname{mult}(C,p)\\
&=n+(\mu(C,p)+\operatorname{mult}(C,p)-1)+(C\cdot L^\infty)_p-\operatorname{mult}(C,p)\\
&=n+\mu(C,p)+(C\cdot L^\infty)_p-1\ ,\end{aligned}$$ which completes the proof in view of (\[e11\]).
The equality (\[e15\]) follows from the fact that both sides of the relation depend only on the geometry of the segments $\sigma_0^{(i)}$ and $\sigma_0^{(j)}$. Suppose that $1\le i<j\le r$. We have $\sigma^{(i)}=[(m',0),(0,n')]$, $\sigma^{(j)}=[(m'',0),(0,n'')]$ with $\frac{m'}{n'}>\frac{m''}{n''}$. By the Newton-Puiseux algorithm [@GLS pp. 165–170], the function $\varphi_i(y,z)$ (or $\psi_i(y,z)$) splits into the product of $u(y,z)\in\CC\{y,z\}$, $u(0,0)\ne0$, and $n'$ factors of the form $$z-\alpha y^{m'/n'}+\text{h.o.t.},\quad \alpha\ne0,$$ and then by (\[e17\]) we get $$(Z(\varphi_i)\cdot Z(\theta_j))_p=(Z(\psi_i)\cdot Z(\theta_i))_p=m''n'.$$ This holds even for $j=r$ since the only monomial of $\theta_r(y,z)$ that comes into play is $\beta y^{m''}$, $\beta\ne0$. The case $1\le j<i\le r$ is settled analogously. Now suppose . As we observed in the first part of the proof, the pairs of quasihomogeneous polynomials $\varphi_i^{\sigma^{(i)}_0}$ and $\theta_i^{\sigma^{(i)}_0}$, $\psi_i^{\sigma^{(i)}_o}$ and $\theta_i^{\sigma^{(i)}_0}$ are coprime (even for $i=r$!). Then the above computation yields $$(Z(\varphi_i)\cdot Z(\theta_i))_p=(Z(\psi_i)\cdot Z(\theta_i))_p=m'n'\ ,$$ where $\sigma^{(i)}_0=[(m',0),(0,n')]$.
The following example shows that condition in Proposition \[pr:nonmax-tangency\] cannot be removed.
Consider the cubic $C=Z(xy^2-z^3-yz^2)$ (cf. Remark \[r5\]). It has a Newton nondegenerate singular point $p=(1,0,0)\in L^\infty$, an ordinary cusp with the tangent line $L=Z(y)\ne L^\infty$. Thus $(C\cdot L)=3=\deg(C)$, so fails. Also, $$\begin{aligned}
\muinf=(Z(y^2) \cdot Z(2xy-z^2))_p&=4, \\
\mu(C,p)+(C\cdot L^\infty)_p-1=2+2-1&=3.\end{aligned}$$ so fails as well.
For another (more complicated) instance of this phenomenon, see Example \[example:expressive-non-reg\].
Let $C=Z(F(x,y,z))\subset\PP^2$ be a reduced curve not containing the line at infinity $L^\infty=Z(z)$ as a component. Let $G(x,y)=F(x,y,1)$. Assume that the Newton polygon $\Delta(G)$ intersects each of the coordinate axes in points different from the origin, and the truncation of $G$ along any edge of the boundary $\partial\Delta(G)$ not visible from the origin is a square-free polynomial, except possibly for factors of the form $x^i$ or $y^j$. Then $C$ is $L^\infty$-regular.
The intersection $C\cap L^\infty$ is determined by the top degree form of $G(x,y)$, which has the form $x^iy^jf(x,y)$, with $f(x,y)$ a square-free homogeneous polynomial. Hence $C\cap L^\infty$ consists of the points $(0,1,0)$ (if $i>0$), $(1,0,0)$ (if $j>0$), and $\deg(f)$ other points, at which $C$ is smooth and $L^\infty$-regular (see Proposition \[pr:nonmax-tangency\]). The Newton diagram of each of the points $(0,1,0)$ and $(1,0,0)$ consists of some edges of $\partial\Delta(G)$ mentioned in the lemma, and therefore these points (if they lie on $C$) satisfy the requirements of Proposition \[pr:nonmax-tangency\].
\[rem:Linf-reducible\] A reducible plane curve $C=Z(F)$ with $L^\infty$-regular components does not have to be $L^\infty$-regular. For example, take $F=(xy-1)(xy-2)$: each factor is $L^\infty$-regular, but the product is not, since $F_x$ and $F_y$ have a common divisor $2xy-3$.
Conversely, a curve may be $L^\infty$-regular even when one of its components is not. For example, take $F=(x-y)(x^2y+x^3+x^2z+xz^2+z^3)$: the product is $L^\infty$-regular by Proposition \[pr:nonmax-tangency\]; however, $Z(x^2y+x^3+x^2z+xz^2+z^3)$ is not.
Polynomial and trigonometric curves {#sec:poly-trig}
===================================
In Sections \[sec:poly-trig\] and \[sec:expressive\], we introduce several classes of affine (rather than projective) plane curves. Before we begin, let us clarify what we mean by a real affine plane curve. There are two different notions here: an algebraic and a topological one:
\[def:curves\] As usual, a reduced real *algebraic curve* $C$ in the complex affine plane $\AA^2\cong\CC^2$ is the vanishing set $$C=V(G)=\{(x,y)\in\CC^2\mid G(x,y)=0\}$$ of a squarefree bivariate polynomial $G(x,y)\in\RR[x,y]\subset\CC[x,y]$. We view $C$ as a subset of $\AA^2$, and implicitly identify it with the polynomial $G(x,y)$ (viewed up to a constant nonzero factor), or with the principal ideal generated by it, the ideal of polynomials vanishing on $C$.
Alternatively, one can consider a “topological curve” ${C_{\RR}}$ in the real affine $(x,y)$-plane $\RR^2$, defined as the set of real points of an algebraic curve $C$ as above: $${C_{\RR}}={V_{\RR}}(G)=\{(x,y)\in\RR^2\mid G(x,y)=0\}.$$ In contrast to the real algebraic curve $V(G)\subset\CC^2$, the real algebraic set ${V_{\RR}}(G)$—even when it is one-dimensional—does not determine the polynomial $G(x,y)$ up to a scalar factor. In other words, an algebraic curve $C$ is not determined by the set of its real points ${C_{\RR}}$, even when ${C_{\RR}}$ “looks like” an algebraic curve. (Roughly speaking, this is because $C$ can have “invisible” components which either have no real points at all, or all such points are isolated in $\RR^2$.) There is however a canonical choice, provided ${C_{\RR}}$ is nonempty and without isolated points: we can let $C$ be the Zariski closure of ${C_{\RR}}$, or equivalently let $G(x,y)$ be the *minimal polynomial* of ${C_{\RR}}$, a real polynomial of the smallest possible degree satisfying . (The minimal polynomial is defined up to a nonzero real factor.)
Throughout this paper, we switch back and forth between a projective curve $Z(F(x,y,z))$ and its affine counterpart $V(G(x,y))$, where $G(x,y)=F(x,y,1)$. (Remember that the line at infinity $L^\infty=Z(z)=\PP^2\setminus\AA^2$ is fixed throughout.) For example, we say that $V(G)$ is $L^\infty$-regular if and only if $Z(F)$ is $L^\infty$-regular, cf. Definition \[def:c-regular\].
\[def:poly-curve\] Let $C$ be a complex curve in the affine $(x,y)$-plane. We say that $C$ is a *polynomial curve* if it has a polynomial parametrization, i.e., if there exist polynomials $X(t), Y(t)\in\CC[t]$ such that the map $t\mapsto (X(t),Y(t))$ is a (birational, i.e., generically one-to-one) parametrization of $C$.
A projective algebraic curve $C=\{F(x,y,z)=0\}\subset\PP^2$ is called *polynomial* if $C$ does not contain the line at infinity $L^\infty=\{z=0\}$, and the portion of $C$ contained in the affine $(x,y)$-plane (i.e., the curve $\{F(x,y,1)=0\}$) is an affine polynomial curve.
Not every polynomial map defines a polynomial parametrization. For example, $t\mapsto (t^2-t,t^4-2t^3+t)$ is not a polynomial (or birational) parametrization, since it is not generically one-to-one: $(X(t),Y(t))=(X(1-t),Y(1-t))$.
\[ex:poly-with-elliptic-node\] The cubic $y^2=x^2(x-1)$ is a real polynomial curve, with a polynomial parametrization $t\mapsto (t^2+1,t(t^2+1))$. Note that this curve has an elliptic node $(0,0)$, attained for imaginary parameter values $t=\pm\sqrt{-1}$.
The “witch of Agnesi” cubic $x^2y+y-1$ is rational but not polynomial. Indeed, if $X(t)$ is a positive-degree polynomial in $t$, then $Y(t)=\frac{1}{(X(t))^2+1}$ is not.
Recall that the *Chebyshev polynomials* of the first kind are the univariate polynomials $T_a(x)$ (here $a\in\ZZ_{>0}$) defined by $$\label{eq:chebyshev-poly}
T_a(\cos\varphi)=\cos(a\varphi).$$ The polynomial $T_a(x)$ has integer coefficients, and is an even (resp., odd) function of $x$ when $a$ is even (resp., odd). We note that $T_a(T_b(t))=T_b(T_a(t))=T_{ab}(t)$.
Let $a$ and $b$ be coprime positive integers. The *Chebyshev curve* with parameters $(a,b)$ is given by the equation $$\label{eq:Chebyshev-curve}
T_a(x)+T_b(y)=0.$$ It is not hard to see that this curve is polynomial; let us briefly sketch why. (For a detailed exposition, see [@Fischer Section 3.9].) Without loss of generality, let us assume that $a$ is odd. Then the $(a,b)$-Chebyshev curve has a polynomial parametrization $t\mapsto (-T_b(t), T_a(t))$. Indeed, $T_a(-T_b(t))+T_b(T_a(t))=-T_{ab}(t)+T_{ab}(t)=0$.
To illustrate, consider the Chebyshev curves with parameters $(3,2)$ and $(3,4)$ shown in Figure \[fig:chebyshev-34-32\]. The $(3,2)$-Chebyshev curve is a nodal Weierstrass cubic $$\label{eq:32-Chebyshev}
4x^{3}-3x+2y^{2}-1=0,$$ or parametrically $t\mapsto (-2t^2+1,4t^3-3t)$. The $(3,4)$-Chebyshev curve (see Figure \[fig:chebyshev-34-32\]) is a sextic given by the equation $$\label{eq:34-Chebyshev}
4x^{3}-3x+8y^{4}-8y^{2}+1=0,$$ or by the polynomial parametrization $t\mapsto (-8t^4+8t^2-1, 4t^3-3t)$.
\[fig:chebyshev-34-32\]
\[lem:poly-curve\] For a real plane algebraic curve $C$, the following are equivalent:
- $C$ is polynomial;
- $C$ has a parametrization $t\mapsto (X(t),Y(t))$ with $X(t),Y(t)\in\RR[t]$;
- $C$ is rational, with a unique local branch at infinity.
The equivalence (1)$\Leftrightarrow$(3) (for complex curves) is well known; see, e.g., [@Abhyankar-1988]. The implication (2)$\Rightarrow$(1) is obvious. It remains to show that (3)$\Rightarrow$(2). The local branch of $C$ at infinity must by real, since otherwise complex conjugation would yield another such branch. Consequently, the set of real points of $C$ has a one-dimensional connected component which contains the unique point $p\in C\cap L^\infty$. It follows that the normalization map ${\boldsymbol{n}}:\PP^1\to C\hookrightarrow\PP^2$ (which is nothing but a rational parametrization of $C$) pulls back the complex conjugation on $C$ to the antiholomorphic involution $c:\PP^1\to\PP^1$ which is a reflection with a fixed point set $\operatorname{Fix}(c)\simeq S^1$, and $p$ lifts to a point in $\operatorname{Fix}(c)$. (There is another possible antiholomorphic involution on $\PP^1$, the antipodal one, corresponding to real plane curves with a finite real point set.) Thus, we can choose coordinates $(t_0,t_1)$ on $\PP^1$ so that $c(t_0,t_1)=(\overline t_0,\overline t_1)$ and the preimage of $p$ is $(0,1)$. Hence the map ${\boldsymbol{n}}$ can be expressed as $$x=X(t_0,t_1),\quad y=Y(t_0,t_1),\quad z=t_0^d\,,$$ where $(t_0,t_1)\in\PP^1$, $X$ and $Y$ are bivariate homogeneous polynomials of degree $d=\deg C$, and by construction $$\overline x=X(\overline t_0,\overline t_1),\quad \overline y=Y(\overline t_0,\overline t_1),$$ which means that $X$ and $Y$ have real coefficients.
Recall that a *trigonometric polynomial* is a finite linear combination of functions of the form $t\mapsto \sin(kt)$ and/or $t\mapsto \cos(kt)$, with $k\in\ZZ_{\ge 0}$.
\[def:trig-curve\] We say that a real curve $C$ in the affine $(x,y)$-plane is a *trigonometric curve* if there exist real trigonometric polynomials $X(t)$ and $Y(t)$ such that $t\mapsto (X(t),Y(t))$ is a parametrization of ${C_{\RR}}$, the set of real points of $C$, generically one-to-one for $t\in [0,2\pi)$.
A projective real algebraic curve $C=\{F(x,y,z)=0\}\subset\PP^2$ is called *trigonometric* if $C$ does not contain the line at infinity $L^\infty=\{z=0\}$, and the portion of $C$ contained in the affine $(x,y)$-plane is an affine trigonometric curve.
Not every trigonometric map gives a trigonometric parametrization. For example, $t\mapsto (\cos(t),\cos(2t))$ is not a trigonometric parametrization of its image (a segment of the parabola $y\!=\!2x^2\!-\!1$), since it is not generically one-to-one on $[0,2\pi)$.
The most basic example of a trigonometric curve is the circle $t\mapsto (\cos(t),\sin(t))$, or more generally an ellipse $$t\mapsto (A\cos(t),B\sin(t)) \quad (A, B\in\RR_{>0}).$$
\[ex:Lissajous\] Let $k$ and $\ell$ be coprime positive integers, with $\ell$ odd. The *Lissajous curve* with parameters $(k,\ell)$ is a trigonometric curve defined by the parametrization $$t\mapsto(\cos(\ell t),\sin(kt)).$$ The algebraic equation for this curve is $$\label{eq:Lissajous-algebraic}
T_{2k}(x)+T_{2\ell }(y)=0,$$ cf. . (Indeed, $T_{2k}(\cos(\ell t))+T_{2\ell}(\cos(\frac{\pi}{2}-kt))=\cos(2k\ell t)+\cos(\ell\pi-2k\ell t)=0$.) Note that looks exactly like , except that now the indices $2k$ and $2\ell$ are not coprime (although $k$ and $\ell$ are).
To illustrate, the $(2,3)$-Lissajous curve is given by the equation $$\label{eq:32-Lissajous}
8x^4-8x^2+1+32y^6-48y^4+18y^2-1=0,$$ or by the trigonometric parametrization $$\label{eq:32-Lissajous-parametric}
t\mapsto (\cos(3t),\sin(2t)).$$ Several Lissajous curves, including this one, are shown in Figure \[fig:lissajous-12-13-32-34\].
\[fig:lissajous-12-13-32-34\]
\[ex:rose-curves\] A *rose curve* with parameter $q=\frac{a}{b}\in\QQ_{>0}$ is defined in polar coordinates by $r=\cos(q\theta)$, $\,\theta\in [0,2\pi b)$. While a general rose curve has a complicated singularity at the origin, it becomes nodal when $q\!=\!\frac{1}{2k+1}$, with $k\!\in\!\ZZ_{>0}$. In that case, we get a “multi-limaçon,” defined in polar coordinates by $r=\cos\bigl(\tfrac{\theta}{2k+1}\bigr)$, or equivalently by $$\label{eq:multi-limacon}
r T_{2k+1}(r)-x=0.$$ Note that the left-hand side of is a polynomial in $r^2=x^2+y^2$, so it is an algebraic equation in $x$ and $y$. This is a trigonometric curve, with a trigonometric parametrization given by $$t\mapsto \Bigl(\frac{\cos(kt)+\cos((k+1)t)}{2}, \frac{\sin(kt)+\sin((k+1)t)}{2}\Bigr).$$ The cases $k=1,2,3$ are shown in Figure \[fig:multi-limacons\].
In the special case $k=1$, we get $rT_3(r)=4r^4-3r^2$, and the equation becomes $$\label{eq:limacon}
4(x^2+y^2)^2-3(x^2+y^2)-x=0.$$ This quartic curve is one of the incarnations of the *limaçon* of Étienne Pascal.
![The rose curves $r=\cos\bigl(\tfrac{\theta}{3}\bigr)$ (cf. ), $r=\cos\bigl(\tfrac{\theta}{5}\bigr)$, and $r=\cos\bigl(\tfrac{\theta}{7}\bigr)$.[]{data-label="fig:multi-limacons"}](multi-limacons.png)
\[lem:trig-curve\] For a real plane algebraic curve $C$, the following are equivalent:
- $C$ is trigonometric;
- there exist polynomials $P(\varphi),Q(\varphi)\in\CC[\varphi]$ such that the map $\CC^*\to\AA^2$ given by $$\label{eq:param-PQ}
\varphi\longmapsto (P(\varphi)+\overline P(\varphi^{-1}),Q(\varphi)+\overline Q(\varphi^{-1}))$$ is a birational parametrization of $C$.
- $C$ is rational, with two complex conjugate local branches at infinity and with an infinite real point set.
$\boxed{(1)\Rightarrow(2)}$ The correspondence $t\leftrightarrow \varphi=\exp(t\sqrt{-1})$ establishes a bianalytic isomorphism between $(0,2\pi)$ and $S^1\setminus\{1\}$. (Here $S^1=\{|\varphi|=1\}\subset\CC$.) Under this correspondence, we have $$\label{e4.5}
a\cos(kt)+b\sin(kt)=\tfrac{a-b\sqrt{-1}}{2}\varphi^k+\tfrac{a+b\sqrt{-1}}{2}\varphi^{-k}
\quad (a,b\in\RR),$$ so any trigonometric polynomial in $t$ transforms into a Laurent polynomial in $\varphi$ of the form $P(\varphi)+\overline P(\varphi^{-1})$. Thus a trigonometric parametrization of a curve $C$ yields its parametrization of the form ; this parametrization is generically one-to-one along $S^1$ and therefore extends to a birational map $\PP^1\to C$.
$\boxed{(2)\Rightarrow(1)}$ A parametrization of a curve $C$ sends the circle $S^1$ generically one-to-one to ${C_{\RR}}$, the real point set of $C$, see the formulas . The same formulas convert the parametrization restricted to the circle $S^1$ into a trigonometric parametrization $t\in[0,2\pi)\mapsto(X(t),Y(t))$ of ${C_{\RR}}$.
$\boxed{(2)\Rightarrow(3)}$ A parametrization (\[eq:param-PQ\]) intertwines the standard real structure in $\PP^2$ and the real structure defined by the involution $c(\varphi)=\overline\varphi^{-1}$ on $\CC\setminus\{0\}$. Thus, it takes the set $S^1=\operatorname{Fix}(c)$ to the set ${C_{\RR}}$ of real points of $C$, while the conjugate points $\varphi=0$ and $\varphi=\infty$ of $\PP^1$ go to the points of $C$ at infinity determining two complex conjugate local branches at infinity.
$\boxed{(3)\Rightarrow(2)}$ Assuming (3), the normalization map ${\boldsymbol{n}}:\PP^1\to C$ pulls back the standard complex conjugation in $\PP^2$ to the standard complex conjugation on $\PP^1$, while the circle $\RR\PP^1$ maps to the one-dimensional connected component of ${C_{\RR}}$, and some complex conjugate points $\alpha,\overline\alpha\in\PP^1$ go to infinity. The automorphism of $\PP^1$ defined by $$\varphi=\frac{s-\alpha}{s-\overline\alpha}$$ takes the points $s=\alpha$ and $s=\overline\alpha$ to $0$ and $\infty$, respectively, the circle $\RR\PP^1$ to the circle $S^1$, and the standard complex conjugation to the involution $c$, see above. Hence the parametrization ${\boldsymbol{n}}:\PP^1\to C$ goes to a parametrization (\[eq:param-PQ\]).
\[lem:real-points\] Let $C$ be a real polynomial (resp., trigonometric) nodal plane curve, with a parametrization $\{(X(t),Y(t))\}$ as in Definition \[def:poly-curve\] (resp., Definition \[def:trig-curve\]). Assume that $C$ has no elliptic nodes. Then ${C_{\RR}}=\{(X(t),Y(t))\mid t\in\RR\}$.
This lemma follows from the well known fact (see, e.g., [@IMR Proposition 1.9]) that the real point set of a real nodal rational curve $C$ in $\RR\PP^2$ is the disjoint union of a circle $\RR\PP^1$ generically immersed in $\RR\PP^2$ and a finite set of elliptic nodes.
If we allow elliptic nodes, the conclusion of Lemma \[lem:real-points\] can fail, cf. Example \[ex:poly-with-elliptic-node\].
Recall that an irreducible nodal plane curve of degree $d$ has at most $\frac{(d-1)(d-2)}{2}$ nodes, with the upper bound only attained for rational curves.
\[pr:trig-no-flex\] Let $C$ be a trigonometric curve of degree $d$ with $\frac{(d-1)(d-2)}{2}$ real hyperbolic nodes. Then $C$ has no inflection points.
\[pr:poly-no-flex\] Let $C$ be a real polynomial curve of degree $d$ with $\frac{(d-1)(d-2)}{2}$ real hyperbolic nodes. Then $C$ has no inflection points.
By Hironaka’s genus formula (\[eq:Hironaka\]), the projective closure $\hat C$ of $C$ has a single smooth point $p$ on $L^\infty$, with $(\hat C\cdot L^\infty)_p=d$. We then determine the number of inflection points of $C$ (in the affine plane) using Plücker’s formula (see, e.g., [@Walker Chapter IV, Sections 6.2–6.3]): $$2d(d-2)-(d-2)-6\cdot\tfrac{(d-1)(d-2)}{2}=0. \qedhere$$
\[ex:hypotrochoids\] The curve $$\label{eq:hypotrochoid}
t\mapsto (\cos((k-1)t)+a\cos(kt), \sin((k-1)t)-a\sin(kt))$$ is a trigonometric curve of degree $d=2k$. (It is a special kind of a *hypotrochoid*, cf. Definition \[def:hypotrochoids\] below.) For appropriately chosen real values of $a$, this curve has $\frac{(d-1)(d-2)}{2}=(k-1)(2k-1)$ real hyperbolic nodes, as in Proposition \[pr:trig-no-flex\]. See Figures \[fig:3-petal\] and \[fig:5-petal\].
In the special case $k=1$ illustrated in Figure \[fig:3-petal\], we get a three-petal hypotrochoid, a quartic trigonometric curve with 3 nodes given by the parametrization $$\label{eq:3-petal-param}
t\mapsto (\cos(t)+a\cos(2t),\sin(t)-a\sin(2t)),$$ or by the algebraic equation $$\label{eq:3-petal-alg}
a^2(x^2+y^2)^2+(-2a^4+a^2+1)(x^2+y^2)+(a^2-1)^3-2ax^3+6axy^2=0.
$$
![Three-petal hypotrochoids , with $a=\frac34$ (left) and $a=2$ (right). []{data-label="fig:3-petal"}](3-petal.png)
![Five-petal hypotrochoids $\{(\cos(2t)+a\cos(3t),\sin(2t)-a\sin(3t))\}$, with $a=\frac56$ (left) and $a=2$ (right). Each is a trigonometric curve of degree , with $\frac{(d-1)(d-2)}{2}=
10$ nodes.[]{data-label="fig:5-petal"}](5-petal.png)
Expressive curves and polynomials {#sec:expressive}
=================================
\[def:expressive-poly\] Let $G(x,y)\!\in\!\RR[x,y]\!\subset\!\CC[x,y]$ be a polynomial with real coefficients. Let $C=V(G)$ be the corresponding affine algebraic curve, and let ${C_{\RR}}={V_{\RR}}(G)$ be the set of its real points, see Definition \[def:curves\]. We say that $G(x,y)$ is an *expressive polynomial* (resp., $C$ is an *expressive curve*) if
- all critical points of $G$ (viewed as a polynomial in $\CC[x,y]$) are real;
- all critical points of $G$ are Morse (i.e., have nondegenerate Hessians);
- each bounded component of $\RR^2\setminus {C_{\RR}}$ contains exactly one critical point of $G$;
- each unbounded component of $\RR^2\setminus {C_{\RR}}$ contains no critical points;
- ${C_{\RR}}$ is connected, and contains at least two (hence infinitely many) points.
Let $G(x,y)$ be a real polynomial with real Morse critical points. Then each double point of ${V_{\RR}}(G)$ must be a critical point of $G$ (a saddle). Also, each bounded connected component of $\RR^2\setminus {V_{\RR}}(G)$ must contain at least one critical point (an extremum). Thus, for $G$ to be expressive, it must have the smallest possible number of complex critical points that is allowed by the topology of ${V_{\RR}}(G)$: a saddle at each double point, one extremum within each bounded component of $\RR^2\setminus {V_{\RR}}(G)$, and nothing else.
\[ex:quadratic\] The following quadratic polynomials are expressive:
- $G(x,y)=x^2-y$ has no critical points;
- $G(x,y)=x^2+y^2-1$ has one critical point $(0,0)$ (a minimum) lying inside the unique bounded component of $\RR^2\setminus {V_{\RR}}(G)$;
- $G(x,y)=x^2-y^2$ has one critical point $(0,0)$ (a saddle), a hyperbolic node.
The following quadratic polynomials are not expressive:
- $G(x,y)=x^2-y^2-1$ has a critical point $(0,0)$ in an unbounded component of $\RR^2\setminus {V_{\RR}}(G)$; besides, ${V_{\RR}}(G)$ is not connected;
- $G(x,y)=x^2+y^2$ has ${V_{\RR}}(G)$ consisting of a single point;
- $G(x,y)=x^2+y^2+1$ has ${V_{\RR}}(G)=\varnothing$;
- $G(x,y)=x^2-1$ and $G(x,y)=x^2$ have non-Morse critical points.
\[lem:expressive-poly\] Let $G(x,y)$ be an expressive polynomial. Then:
- $G$ is squarefree (i.e, not divisible by a square of a non-scalar polynomial);
- $G$ has finitely many critical points;
- each critical point of $G$ is either a saddle or an extremal point;
- all saddle points of $G$ lie on ${V_{\RR}}(G)$; they are precisely the singular points of $V(G)$;
- each bounded connected component of $\RR^2\setminus {V_{\RR}}(G)$ is simply connected.
As the critical points of $G$ are real and Morse, each of them is either a saddle or a local (strict) extremum of $G$, viewed as a function $\RR\to\RR$. The extrema must be located outside ${C_{\RR}}$, one per bounded connected component of $\RR^{2}\setminus{C_{\RR}}$. The saddles must lie on ${C_{\RR}}$, so they are precisely the double points of it. We conclude that $G$ has finitely many critical points. Consequently $G$ is squarefree. Finally, since ${C_{\RR}}$ is connected, each bounded component of $\RR^{2}\setminus{C_{\RR}}$ must be simply connected.
Definition \[def:expressive-poly\] naturally extends to homogeneous polynomials in three variables, and to algebraic curves in the projective plane:
\[def:expressive-xyz\] Let $F(x,y,z)\!\in\!\RR[x,y,z]\!\subset\!\CC[x,y,z]$ be a homogeneous polynomial with real coefficients, and $C\!=\!Z(F)$ the corresponding projective algebraic curve. Assume that $F(x,y,z)$ is not divisible by $z$. (In other words, $C$ does not contain the line at infinity $L^\infty$.) We call $F$ and $C$ *expressive* if the bivariate polynomial $F(x,y,1)$ is expressive in the sense of Definition \[def:expressive-poly\], or equivalently the affine curve $C\setminus L^\infty\subset\AA^2=\PP^2\setminus L^\infty$ is expressive.
In the rest of this section, we examine examples of expressive and non-expressive curves and polynomials.
Among real conics (cf. Example \[ex:quadratic\]), a parabola, an ellipse, and a pair of crossing real lines are expressive, whereas a hyperbola, a pair of parallel (or identical) lines, and a pair of complex conjugate lines (an elliptic node) are not.
\[ex:two-graphs\] Let $f_1(x),f_2(x)\in\RR[x]$ be two distinct real univariate polynomials of degrees $\le d$ such that $f_1-f_2$ has $d$ distinct real roots. (Thus, at least one of $f_1,f_2$ has degree $d$.) We claim that the polynomial $$G(x,y)=(f_1(x)-y)(f_2(x)-y)$$ is expressive. To prove this, we first introduce some notation. Let $x_1,\dots,x_d$ be the roots of $f_1-f_2$, and let $z_1,\dots,z_{d-1}$ be the roots of its derivative $f_1'-f_2'$; they are also real and distinct, by Rolle’s theorem. The critical points of $G$ satisfy $$\begin{aligned}
G_x(x,y)&=f'_1(x)(f_2(x)-y) + (f_1(x)-y)f'_2(x)=0, \\
G_y(x,y)&=-f_1(x)-f_2(x)+2y=0.\end{aligned}$$ It is straightforward to see that these equations have $2d-1$ solutions: $d$ hyperbolic nodes $(x_k,f_1(x_k))=(x_k,f_2(x_k))$, for $k=1,\dots,d$, as well as $d-1$ extrema at the points $(z_k,\frac12(f_1(z_k)+f_2(z_k))$, for $k=1,\dots,d-1$. The conditions of Definition \[def:expressive-poly\] are now easily verified. (Alternatively, use the coordinate change $(x,\tilde y)=(x,y-f_1(x))$ to reduce the problem to the easy case when one of the two polynomials is $0$.)
\[ex:lemniscates\] The *lemniscate of Huygens* (or Gerono) is given by the equation $y^2+4x^4-4x^2=0$, or by the parametrization $t\mapsto (\cos(t),\sin(2t))$. This curve, shown in Figure \[fig:lissajous-12-13-32-34\] on the far left, is a Lissajous curve with parameters $(2,1)$, cf. Example \[ex:Lissajous\]. The polynomial $G(x,y)=y^2+4x^4-4x^2$ has three real critical points: a saddle at the hyperbolic node $(0,0)$, plus two extrema $(\pm \frac{1}{\sqrt{2}},0)$ inside the two bounded connected components of $\RR^2\setminus {V_{\RR}}(G)$. Thus, this lemniscate is expressive.
By contrast, another quartic curve with a similar name (and a similar-looking set of real points), the *lemniscate of Bernoulli* $$\label{eq:lemniscate-Bernoulli}
(x^2+y^2)^2-2x^2+2y^2=0,$$ is not expressive, as the polynomial $G(x,y)=(x^2+y^2)^2-2x^2+2y^2$ has critical points $(0,\pm i)$ outside $\RR^2$.
Many more examples of expressive and non-expressive polynomials (or curves) are given in Tables \[table:conics+cubics\] and \[table:conics+cubics+quartics\], and later in the paper.
[|p[1.2in]{}|p[2.1in]{}|p[2.2in]{}|]{}\
$G(x,y)$ & real curve ${V_{\RR}}(G)$ & critical points\
$x^2-y$ & parabola & none\
$x^2-y^2$ & two lines & saddle\
$x^2+y^2-1$ & ellipse & extremum\
\
$G(x,y)$ & real point set ${V_{\RR}}(G)$ & why not expressive?\
$x^2-y^2-1$ & hyperbola & saddle in an unbounded region\
$x^2+y^2+1$ & imaginary ellipse & ${V_{\RR}}(G)$ is empty\
$x^2+y^2$ & elliptic node & ${V_{\RR}}(G)$ is a single point\
$x^2+a$ ($a\in\RR$) & two parallel lines & critical points are not Morse\
\
$G(x,y)$ & real point set ${V_{\RR}}(G)$ & critical points\
$x^3-y$ & cubic parabola & none\
$(x^2-y)x$ & parabola and its axis & single saddle\
$x^3-3x+2-y^2$ & nodal Weierstrass cubic & one saddle, one extremum\
$(x-1)xy$ & two parallel lines + line & two saddles\
$(x^2-y)(y-1)$ & parabola + line & two saddles, one extremum\
$(x+y-1)xy$ & three lines & three saddles, one extremum\
$(x^2+y^2-1)x$ & ellipse + line & two saddles, two extrema\
\
$G(x,y)$ & real point set ${V_{\RR}}(G)$ & why not expressive?\
$x^3-y^2$ & semicubic parabola & critical point is not Morse\
$x^3-3x-y^2$ & two-component elliptic curve & saddle in an unbounded region\
$x^3-3x+3-y^2$ & one-component elliptic curve & saddle in an unbounded region\
$x^3+3x-y^2$ & one-component elliptic curve & two non-real critical points\
$x^3+xy^2+4xy+y^2$ & oblique strophoid & two non-real critical points\
$x^2y-x^2+2y^2$ & Newton’s species \#54 & two non-real critical points\
$yx^2-y^2-xy+x^2$ & Newton’s species \#51 & two non-real critical points\
$x^3+y^3+1$ & Fermat cubic & critical point is not Morse\
$x^3+y^3-3xy$ & folium of Descartes & two non-real critical points\
$x^2y+y-x$ & serpentine curve & two non-real critical points\
$x^2y+y-1$ & witch of Agnesi & two non-real critical points\
$x^2y$ & double line + line & critical points are not Morse\
$x(x^2-y^2)$ & three concurrent lines & critical point is not Morse\
$(x^2-y^2-1)y$ & hyperbola + line & two non-real critical points\
$(xy-1)x$ & hyperbola + asymptote & ${V_{\RR}}(G)$ is not connected\
[|c|c|p[1.9in]{}|p[3.3in]{}|c|]{} $d$ & $\xi$ & $G(x,y)$ & real point set ${V_{\RR}}(G)$\
\
$1$ & 0 & $x$ & line\
$2$ & 0 & $x^2-y$ & parabola\
$2$ & 1 & $x^2-y^2$ & two crossing lines\
$2$ & 1 & $x^2+y^2-1$ & ellipse\
$3$ & 0 & $x^3-y$ & cubic parabola\
$3$ & 1 & $(x^2-y)x$ & parabola and its axis\
$3$ & 2 & $x^3-3x+2-y^2$ & nodal Weierstrass cubic\
$3$ & 2 & $(x-1)xy$ & three lines, two of them parallel\
$3$ & 3 & $(x^2-y)(y-1)$ & parabola crossed by a line\
$3$ & 4 & $(x+y-1)xy$ & three generic lines\
$3$ & 4 & $(x^2+y^2-1)x$ & ellipse crossed by a line\
$4$ & 0 & $y-x^4$ & quartic parabola\
$4$ & 0 & $(y-x^2)^2-x$ &\
$4$ & 1 & $(y-x^2)^2-x^2$ & two aligned parabolas\
$4$ & 1 & $(y-x^2)^2+x^2-1$ &\
$4$ & 1 & $(y-x^3)x$ & cubic parabola and its axis\
$4$ & 2 & $(y-x^2)^2-xy$&\
$4$ & 2 & $(y-x^2)x(x-1)$& parabola + two lines parallel to its axis\
$4$ & 3 & $y^2-(x^2-1)^2$ & co-oriented parabolas crossing at two points\
$4$ & 3 & $y^2+4x^4-4x^2$ & lemniscate of Huygens\
$4$ & 3 & $x(x-1)(x+1)y$ & three parallel lines crossed by a fourth\
$4$ & 3 & $4(x^2+y^2)^2-3(x^2+y^2)-x$ & lima[ç]{}on\
$4$ & 5 & $x(x-1)y(y-1)$ & two pairs of parallel lines\
$4$ & 5 & $(x^2+y^2-1)(x^2-2x+y^2)$ & two circles crossing at two points\
$4$ & 5 & $(y-x^3+x)y$ & cubic parabola + line\
$4$ & 5 & $(x^3-3x+2-y^2)(x-a)$ & nodal Weierstrass cubic + line crossing it at $\infty$\
$4$ & 6 & $4x^3-3x+8y^4-8y^2+1$ & $(3,4)$-Chebyshev curve\
$4$ & 6 & $(y-x^2)(x-a)(y-1) $ & parabola + line + line parallel to the axis\
$4$ & 6 & $(y-x^2)(y-1)(y-2) $ & parabola + two parallel lines\
$4$ & 7 & $(y-x^2+1)(x-y^2+1) $ & two parabolas crossing at four points\
$4$ & 7 & see & three-petal hypotrochoid\
$4$ & 7 & $(x^{3}-3x+2-y^{2})(x+y-a)$& nodal Weierstrass cubic + line\
$4$ & 7 & $(x+y)(x-y)(x-1)(x-a)$ & line + line + two parallel lines\
$4$ & 7 & $(x^2+y^2-1)x(x-a)$ & ellipse + two parallel lines\
$4$ & 8 & $(4y-x^2)(x+y)(ax+y+1) $& parabola + two lines\
$4$ & 8 & $(x^2+y^2-1)(y-4x^2+2)$ & ellipse and parabola crossing at four points\
$4$ & 9 & $x(y+1)(x-y)(x+y-1)$ & four lines\
$4$ & 9 & $(x^2+y^2-1)x(x+y-a)$& ellipse + two lines\
$4$ & 9 & $(x^2 + 4y^2)(4x^2 + y^2)$ & two ellipses crossing at four points\
Definition \[def:expressive-poly\] can be generalized to allow arbitrary “hyperbolic” singular points, i.e., isolated real singular points all of whose local branches are real.
In can be verified by an exhaustive case-by-case analysis that every expressive curve of degree $d\le 4$ is $L^\infty$-regular. Starting with $d\ge 5$, this is no longer the case, cf. Example \[example:expressive-non-reg\] below: an expressive curve $C$ need not be $L^\infty$-regular, even when $C$ is rational. Still, examples like this one are rare.
\[example:expressive-non-reg\] Consider the real rational quintic curve $C$ parametrized by $$x=t^2, \ y=t^{-1}+t^{-2}-t^{-3}.$$ The set of its real points in the $(x,y)$-plane consists of two interval components corresponding to the negative and positive values of $t$, respectively. These components intersect at the point $(1,1)$, attained for $t=1$ and $t=-1$. The algebraic equation of $C$ is obtained as follows: $$\begin{aligned}
&y-x^{-1}=t^{-1}-t^{-3} ,\\
&(y-x^{-1})^2=t^{-2}-2t^{-4}+t^{-6}=x^{-1}-2x^{-2}+x^{-3}, \\
&x^3y^2-2x^2y-x^2+3x-1=0.\end{aligned}$$ The Newton triangle of $C$ is $\operatorname{conv}\{(0,0),(3,2),(2,0)\}$, which means that
- at the point $p_1=(1,0,0)$, the curve $C$ has a type $A_2$ (ordinary cusp) singularity, tangent to the axis $y=0$;
- at the point $p_2=(0,1,0)$, the curve $C$ has a type $E_8$ singularity, tangent to the axis $x=0$.
In projective coordinates, we have $C=Z(F)$ where $$\begin{aligned}
F&=x^3y^2-2x^2yz^2-x^2z^3+3xz^4-z^5,\\
F_x&=3x^2y^2-4xyz^2-2xz^3+3z^4,\\
F_y&=2x^3y-2x^2z^2.\end{aligned}$$ It is now easy to check that the only critical point of $F(x,y,1)$ is the hyperbolic node $(1,1)$ discussed above. It follows that the curve $C$ is expressive.
We next examine the behavior of the polar curves at infinity. In a neighborhood of the point $p_2=(0,1,0)$, we set $y=1$ and obtain $$\begin{aligned}
F_x&=3x^2-4xz^2-2xz^3+3z^4,\\
F_y&=2x^3-2x^2z^2.\end{aligned}$$ The curve $Z(F_x)$ has two smooth local branches at $p_2$, quadratically tangent to the axis $Z(x)$; the curve $Z(F_y)$ has the double component $Z(x)$ and a smooth local branch quadratically tangent to $Z(x)$. Thus the intersection multiplicity is $$(Z(F_x)\cdot Z(F_y))_{p_2}=12>\mu(C,p_2)+(C\cdot L^\infty)_{p_2}-1
=8+3-1=10,$$ so $L^\infty$-regularity fails at $p_2$. (The intersection at $p_1$ is regular by Proposition \[pr:nonmax-tangency\].)
\[ex:lissajous-chebyshev\] Let $a$ and $b$ be positive integers. The *Lissajous-Chebyshev curve* with parameters $(a,b)$ is given by the equation $$\label{eq:Ta+Tb}
T_a(x)+T_b(y)=0.$$ When $a$ and $b$ are coprime, with $a$ odd, we recover the polynomial Chebyshev curve with parameters $(a,b)$, see . When both $a$ and $b$ are even, with $\frac{a}{2}$ and $\frac{b}{2}$ coprime, we recover the trigonometric Lissajous curve with parameters $(\frac{a}{2},\frac{b}{2})$, see . This explains our use of the term “Lissajous-Chebyshev curve.” The general construction appears in the work of S. Guse[ĭ]{}n-Zade [@GZ1974], who observed (without using this terminology) that the Lissajous-Chebyshev curve with parameters $(a,b)$ provides a morsification of an isolated quasihomogeneous singularity of type $(a,b)$.
There is also a variant of the Lissajous-Chebyshev curve defined by $$\label{eq:Ta-Tb}
T_a(x)-T_b(y)=0.$$ When $a$ (resp., $b$) is odd, this curve is a mirror image of the Lissajous-Chebyshev curve , under the substitution $x:=-x$ (resp., $y:=-y$). However, when both $a$ and $b$ are even, the two curves differ. For example, for $(a,b)=(4,2)$, the curve defined by is the lemniscate of Huygens (see Example \[ex:lemniscates\]), whereas the curve defined by is a union of two parabolas.
It is not hard to verify that every Lissajous-Chebyshev curve (and every curve $V(T_a(x)-T_b(y))$) is expressive. The critical points of $T_a(x)\pm T_b(y)$ are found from the equations $$T_a'(x)=T_b'(y)=0,$$ so they are of the form $(x_i,y_j)$ where $x_1,\dots,x_{a-1}$ (resp., $y_1,\dots,y_{b-1}$) are the (distinct) roots of $T_a$ (resp., $T_b$). Since the total number of nodes and bounded components of $\RR^2\setminus{C_{\RR}}$ is easily seen to be exactly $(a-1)(b-1)$, the claim follows.
\[fig:lissajous-chebyshev\]
\[ex:multi-limacons\] Recall that the multi-limaçon with parameter $k$ is a trigonometric curve $C$ of degree $2k+2$ given by the equation . It is straightforward to verify that the corresponding polynomial has $2k+1$ critical points, all of them located on the $x$ axis. Comparing this to the shape of the curve $C_\RR$, we conclude that $C$ is expressive.
Divides {#sec:divides}
=======
The notion of a divide was first introduced and studied by N. A’Campo [@acampo-ihes; @ishikawa]. The version of this notion that we use in this paper differs slightly from A’Campo’s, and from the version used in [@FPST].
\[def:divide\] Let ${{\mathbf{D}}}$ be a disk in the real plane $\RR^2$. A *divide* $D$ in ${{\mathbf{D}}}$ is the image of a generic relative immersion of a finite set of intervals and circles into ${{\mathbf{D}}}$ satisfying the conditions listed below. The images of these immersed intervals and circles are called the *branches* of $D$. They must satisfy the following conditions:
- the immersed circles do not intersect the boundary $\partial{{\mathbf{D}}}$;
- the endpoints of the immersed intervals lie on $\partial{{\mathbf{D}}}$, and are pairwise distinct;
- these immersed intervals intersect $\partial D$ transversally;
- all intersections and self-intersections of the branches are transversal.
We view divides as topological objects, i.e., we do not distinguish between divides related by a diffeomorphism between their respective ambient disks.
A divide is called *connected* if the union of its branches is connected.
The connected components of the complement ${{\mathbf{D}}}\setminus D$ which are disjoint from $\partial{{\mathbf{D}}}$ are the *regions* of $D$. If $D$ is connected, then each region of $D$ is simply connected. We refer to the singular points of $D$ as its *nodes*.
Although all divides of interest to us are connected, we forego any connectivity requirements in the above definition of a divide, which therefore is slightly more general than [@FPST Definition 2.1].
The main focus of [@FPST] was on the class of *algebraic* divides coming from real *morsifications* of isolated plane curve singularities, see [@FPST Definition 2.3]. Here we study a different (albeit related) class of divides which arise from real algebraic curves:
\[def:divide-polynomial\] Let $G(x,y)\in\RR[x,y]$ be a real polynomial such that each singular point of the real algebraic set ${V_{\RR}}(G)=\{G(x,y)=0\}\subset\RR^2$ is a *hyperbolic node* (an intersection of two smooth real local branches). Then the portion of ${V_{\RR}}(G)$ contained in a sufficiently large disk ${{\mathbf{D}}}_R=\{(x,y)\in\RR^2\mid x^2+y^2\le R^2\}$ gives a divide in ${{\mathbf{D}}}_R$. Moreover this divide does not depend (up to homeomorphism) on the choice of $R$. We denote this divide by $D_G$.
\[def:expr-divide\] If $G(x,y)$ is an expressive polynomial, then all singular points of ${V_{\RR}}(G)$ are ordinary hyperbolic nodes, so the divide $D_G$ is well defined. Divides arising via this construction are called *expressive*. Any expressive divide is connected.
Numerous examples of expressive divides are scattered throughout this paper.
A non-example is shown in Figure \[fig:nonexpressive-divide\].
(30,31)(0,0) (0,10)[(1,0)[30]{}]{} (10,20)[(1,0)[10]{}]{} (10,0)[(0,1)[20]{}]{} (20,0)[(0,1)[20]{}]{} (10,20)(0,20)(0,25) (5,30)(0,30)(0,25) (5,30)(10,30)(10,20) (20,20)(30,20)(30,25) (25,30)(30,30)(30,25) (25,30)(20,30)(20,20)
The following problem appears to be very difficult.
Find a criterion for deciding whether a given divide is expressive, cf. Definition \[def:expr-divide\].
(10,10)\[bl\][ (5,5)(7,10)(10,10) (5,5)(3,0)(0,0) (5,5)(3,10)(0,10) (5,5)(7,0)(10,0) ]{}
(10,10)\[bl\][ (0,0)(-5,0)(-5,5) (0,10)(-5,10)(-5,5) ]{}
(10,10)\[bl\][ (0,0)(5,0)(5,5) (0,10)(5,10)(5,5) ]{}
It is even harder to determine whether a divide can be realized by an expressive curve of a given degree. For example, the divide
(26,10)(-5,-5) (0,0)[(0,0)]{} (0,0)[(0,0)]{} (10,0)[(0,0)]{} (20,0)[(0,0)]{}
can be realized by an expressive sextic (the $(2,6)$-Lissajous curve, see Figure \[fig:lissajous-chebyshev\]) but not by an expressive quadric—even though there exists a (non-expressive) quadric realizing this divide.
\[pr:expressivity-criterion\] Let $G(x,y)\in\RR[x,y]$ be a real polynomial with $\xi<\infty$ critical points. Assume that the real algebraic set ${V_{\RR}}(G)=\{G=0\}\subset\RR^2$ is nonempty, and each singular point of ${V_{\RR}}(G)$ is a hyperbolic node. Let $\nu$ be the number of such nodes, and let $\iota$ be the number of interval branches of the divide $D_G$. Then $$\label{eq:expressivity-xi}
\xi \ge 2\nu-\iota+1,$$ with equality if and only if the polynomial $G$ is expressive.
Let $K$ denote the union of the divide $D_G$ and all its regions, viewed as a closed subset of $\RR^2$. Let $\sigma$ be the number of connected components of $K$. Since all these components are simply connected, the Euler characteristic of $K$ is equal to $\sigma$. On the other hand, $K$ can be split into 0-dimensional cells (the nodes, plus the ends of interval branches), 1-dimensional cells (curve segments of $D$ connecting nodes), ovals (smooth closed components of $D_G$), and regions. The number $\beta$ of 1-dimensional cells satisfies $2\beta\!=\!2\iota+4\nu$ (by counting endpoints), implying $\beta\!=\!\iota+2\nu$. We thus have $$\sigma = \chi(K)=(\nu+2\iota)-(\iota+2\nu)+\rho-h = \iota-\nu+\rho-h,$$ where $\rho$ is the number of regions in $D_G$, and $h$ denotes the total number of holes (the sum of first Betti numbers) over all regions.
Denote $u=\xi-\nu-\rho$. The set of critical points of $G$ contains all of the nodes, plus at least one extremum per region. Thus $u=0$ if $G$ has no other critical points, and $u>0$ otherwise.
Putting everything together, we obtain: $$\begin{aligned}
\xi=\nu+\rho+u
=\nu+\sigma-\iota+\nu+h+u
=2\nu-\iota+\sigma+h+u.\end{aligned}$$ Since $\sigma\ge 1$ and $h,u\ge 0$, we get . Moreover $\xi = 2\nu-\iota+1$ if and only if $K$ is connected, all regions are simply connected, and $G$ has exactly $\nu+\rho$ critical points. All these conditions are satisfied if $G$ is expressive. Conversely, they guarantee expressivity. (The curve ${V_{\RR}}(G)$ is connected if $K$ is connected and every region is simply connected.)
Notice that Table \[table:conics+cubics+quartics\] does not list any expressive quartic with $\xi=4$. We can now explain why. By Proposition \[pr:expressivity-criterion\], $\xi=4$ and $d=4$ would imply that either $\nu=2$, $\iota=1$, or $\nu=3$, $\iota=3$. The latter option assumes three real irreducible components of the quartic, i.e., a conic (necessarily a parabola) and two lines crossing it, with three hyperbolic nodes total; such a configuration is impossible. In the former case, it should be an irreducible quartic with $\mu(C,p,L^\infty)=5$, which means that $\mu(C,p)=2$. Then $p$ must be a cusp $A_2$, but the local cuspidal branch intersects its tangent line with multiplicity $3$, not $4$ as required.
L-regular expressive curves {#sec:regular+expressive}
===========================
\[pr:expressive+regular\] Let $C=Z(F)\subset\PP^2$ be a reduced algebraic curve defined by a real homogeneous polynomial $F(x,y,z)\in\RR[x,y,z]$. Assume that
- all irreducible components of $C$ are real;
- $C$ does not contain the line at infinity $L^\infty$ as a component;
- all singular points of $C$ in the affine $(x,y)$-plane are real hyperbolic nodes;
- the polynomial $F(x,y,1)\in\CC[x,y]$ has finitely many critical points;
- the set of real points $\{F(x,y,1)=0\}\subset\RR^2$ is nonempty.
Then the following are equivalent:
- the curve $C$ is expressive and $L^\infty$-regular;
- each irreducible component of $C$ is rational, with a set of local branches at infinity consisting of either a unique (necessarily real) local branch, or a pair of complex conjugate local branches, possibly based at the same real point.
The proof is based on Propositions \[pr:hironaka-milnor\] and \[pr:expressivity-criterion\]. Let us recall the relevant notation, and introduce additional one: $$\begin{aligned}
d&=\deg(C),\\
\iota&=\text{number of interval branches of~$D_G$}\\
s&=|\operatorname{\mathbf{Comp}}(C)|=\text{number of irreducible components of~$C$},\\
s_1&= \text{number of components of $C$ with a real local branch at infinity}, \\
s_2&= \text{number of components of $C$ with a pair of complex conjugate}\\
&\hspace{.225in} \text{local branches at infinity}.\end{aligned}$$ Combining Propositions \[pr:hironaka-milnor\] and \[pr:expressivity-criterion\], we conclude that $$2g(C)-2+\iota+\sum_{p\in C\cap L^\infty}\operatorname{Br}(C,p)
\ge 0,$$ or equivalently (see ) $$\label{eq:restated-reg-expressive}
2\sum_{C'\in\operatorname{\mathbf{Comp}}(C)} g(C')+\iota+\sum_{p\in C\cap L^\infty}\operatorname{Br}(C,p)
\ge 2s,$$ with equality if and only if $C$ is both expressive and $L^\infty$-regular.
On the other hand, we have the inequalities $$\begin{aligned}
\label{eq:sum-g(C')}
\sum_{C'\in\operatorname{\mathbf{Comp}}(C)} g(C')&\ge 0, \\[-.05in]
\iota &\ge s_1\,, \\
\sum_{p\in C\cap L^\infty}\operatorname{Br}(C,p) &\ge s_1+2s_2\,, \\
\label{eq:s+s}
2s_1 + 2s_2 &\ge 2s,\end{aligned}$$ whose sum yields . Therefore we have equality in if and only if each of – is an equality. This is precisely statement (ii).
The curve $C$ from Example \[example:expressive-non-reg\] satisfies requirements (a)–(e) of Proposition \[pr:expressive+regular\]. Since $C$ is not $L^\infty$-regular, condition (ii) must fail. Indeed, while $C$ is rational, it has two real local branches at infinity, centered at the points $p_1$ and $p_2$.
\[prop:nonempty\] Let $C$ be an expressive $L^\infty$-regular plane curve whose irreducible components are all real. Then each component of $C$ is either trigonometric or polynomial.
Since $C$ is $L^\infty$-regular and expressive, with real components, the requirements (a)–(e) of Proposition \[pr:expressive+regular\] are automatically satisfied, cf. Lemma \[lem:expressive-poly\]. Consequently the statement (ii) of Proposition \[pr:expressive+regular\] holds. By Lemmas \[lem:poly-curve\] and \[lem:trig-curve\], this would imply that each component of $C$ is either trigonometric or polynomial, provided the real point set of each component is infinite. It thus suffices to show is that each component $B$ of $C$ has an infinite real point set in $\AA^2$. In fact, it is enough to show that this set is nonempty, for if it were finite and nonempty, then $B$—hence $C$—would have an elliptic node, contradicting the expressivity of $C$ (cf. Lemma \[lem:expressive-poly\]).
It remains to prove that each component of $C$ has a nonempty real point set in $\AA^2$.
We argue by contradiction. Let $C\!=\!Z(F)$. Suppose that $B\!=\!Z(G)$ is a component of $C$ without real points in $\AA^2$. We claim that the rest of $C$ is given by a polynomial of the form $H(G,z)$, where $H\in\RR[u,v]$ is a bivariate polynomial. Once we establish this claim, it will follow that the polynomials $F_x$ and $F_y$ have a non-trivial common factor $\frac{\partial}{\partial u}(uH(u,v))\big|_{u=G,v=z}$, contradicting the finiteness of the intersection $Z(F_x)\cap Z(F_y)$.
Let us make a few preliminary observations. First, the degree $d=\deg G=\deg B$ must be even. Second, by Proposition \[pr:expressive+regular\], $B$ has two complex conjugate branches centered on $L^\infty$. Third, in view of the expressivity of $C$, the affine curve $B\cap\AA^2$ is disjoint from any other component $B'$ of $C$, implying that $$B\cap B'\subset L^\infty.
\label{el1}$$
Consider two possibilities.
**Case 1**: $B\cap L^\infty$ consists of two complex conjugate points $p$ and $\overline p$. Let $Q$ and $\overline Q$ be the local branches of $B$ centered at $p$ and $\overline p$, respectively.
Let $B'=Z(G')$ be some other component of $C$, of degree $d'=\deg B'=\deg G'$. Since $B'$ is real and satisfies statement (ii) of Proposition \[pr:expressive+regular\] as well as , we get $$B'\cap B=B'\cap L^\infty=B\cap L^\infty=\{p,\overline p\};$$ moreover $B'$ has a unique local branch $R$ (resp., $\overline R$) at the point $p$ (resp. $\overline p$). We have $$\begin{aligned}
(R\cdot Q)_p=(\overline R\cdot\overline Q)_{\overline p}=\tfrac{d'd}{2},\qquad
((L^\infty)^{d'}\cdot Q)_p=((L^\infty)^{d'}\cdot\overline Q)_{\overline p}&=\tfrac{d'd}{2}.\end{aligned}$$ It follows that any curve $\hat B$ in the pencil $\operatorname{Span}\{B',(L^\infty)^{d'}\}$ satisfies $$(\hat B\cdot Q)_p\ge\tfrac{d'd}{2},\quad (B'\cdot \overline Q)_{\overline p}\ge\tfrac{d'd}{2}.
\label{el2}$$ Pick a point $q\in B\cap\AA^2$. Since $q\not\in B'\cup L^\infty$, there exists a curve $\tilde B\in\operatorname{Span}\{B',(L^\infty)^{d'}\}$ containing $q$. It then follows by Bézout and by that $\tilde B$ must contain $B$ as a component. In particular, $d'\ge d$. By symmetry, the same argument yields $d\ge d'$. Hence $d'=d$, $B\in\operatorname{Span}\{B',(L^\infty)^d\}$, and the polynomial $G'$ defining the curve $B'$ satisfies $G'=\alpha G+\beta z^d$ for some $\alpha,\beta\in\CC\setminus\{0\}$. The desired claim follows.
**Case 2**: $B\cap L^\infty$ consists of one (real) point $p$. Then $B$ has two complex conjugate branches $Q$ and $\overline Q$ centered at $p$.
Let $B'=Z(G')$ be a component of $C$ different from $B$, and let $B'$ have a unique (real) local branch $R$, necessarily centered at $p$. Denote $d'=\deg B'=\deg G'$. Then $$(R\cdot Q)_p=(R\cdot \overline Q)_p=\tfrac{d'd}{2}, \qquad
((L^\infty)^{d'}\cdot Q)_p=((L^\infty)^{d'}\cdot\overline Q)_p=\tfrac{d'd}{2},$$ which implies (cf. Case 1) that any curve $\hat B'\in\operatorname{Span}\{B',(L^\infty)^{d'}\}$ satisfies $$(\hat B'\cdot q)_p\ge\tfrac{d'd}{2},\quad (\hat B'\cdot \overline Q)_p\ge\tfrac{d'd}{2},$$ and then we conclude—as above—that there exists a curve $\tilde B'\in\operatorname{Span}\{B',(L^\infty)^{d'}\}$ containing $B$ as a component. On the other hand, $$(B\cdot R)_p=d'd,\quad ((L^\infty)^d\cdot R)_p=d'd,$$ which in a similar manner implies that there exists a curve $\tilde B\in\operatorname{Span}\{B,(L^\infty)^d\}$ containing $B'$ as a component. We conclude that $d'=d$, $B\in\operatorname{Span}\{B',(L^\infty)^d\}$, and finally, $G'=\alpha G+\beta z^d$ for $\alpha,\beta\in\CC\setminus\{0\}$, as desired.
Now let $B'=Z(G')$ be a component of $C$ different from $B$, and let it have a couple of complex conjugate local branches $R$ and $\overline R$ centered at $p$. Since $B'$ is real, we have $$(B'\cdot Q)_p=(B'\cdot \overline Q)_p=\tfrac{d'd}{2},\qquad
((L^\infty)^{d'}\cdot Q)_p=((L^\infty)^{d'}\cdot\overline Q)_p=\tfrac{d}{2},$$ and since $B$ is real, we have $$(B\cdot R)_p=(B\cdot\overline R)_p=\tfrac{d'd}{2},\qquad ((L^\infty)^d\cdot R)_p=((L^\infty)^d\cdot\overline R)_p=\tfrac{d'd}{2}.$$ Thus the above reasoning applies again, yielding $d'=d$ and $B'\in\operatorname{Span}\{B,(L^\infty)^d\}$. Hence $G'=\alpha G+\beta z^d$ for $\alpha,\beta\in\CC\setminus\{0\}$, and we are done.
The following example shows that in Proposition \[prop:nonempty\], the requirement that all components are real cannot be dropped.
\[ex:reducible-quintic\] The quintic curve $C=Z(F)$ defined by the polynomial $$F(x,y,z)=(x^2+z^2)(yx^2+yz^2-x^3)$$ has two non-real components $Z(x\pm z\sqrt{-1})$. In Example \[ex:(x\^2+z\^2)(yz\^2-x\^3+yx\^2)-regular\], we verified that this curve is $L^\infty$-regular. It is also expressive, because the polynomial $G(x,y)=F(x,y,1)$ has no critical points in the complex affine plane (see Example \[ex:(x\^2+z\^2)(yz\^2-x\^3+yx\^2)-regular\]) and the set of real points $$\label{eq:y=x^3/...}
{V_{\RR}}(G)=\{(x,y)\in\RR^2\mid y=\tfrac{x^3}{x^2+1}\}$$ is connected. On the other hand, the real irreducible component $$\widetilde C=Z(yx^2+yz^2-x^3)$$ is neither trigonometric nor polynomial because it has two real points at infinity, see Example \[ex:(x\^2+z\^2)(yz\^2-x\^3+x\^2y)\]. Furthermore, $\widetilde C$ is not expressive, since the polynomial $yx^2+y-x^3$ has two critical points $(\pm \sqrt{-1}, \pm \frac32 \sqrt{-1})$ outside $\RR^2$.
Proposition \[prop:nonempty\] immediately implies the following statement.
\[cor:reg-expressive-irreducible\] An irreducible $L^\infty$-regular expressive curve is either trigonometric or polynomial.
We note that such a curve also needs to be immersed, meeting itself transversally at real hyperbolic nodes (thus, no cusps, tacnodes, or triple points).
We next provide a partial converse to Corollary \[cor:reg-expressive-irreducible\].
\[pr:irr-expressive\] Let $C$ be a real polynomial or trigonometric curve whose singular set in the affine plane $\AA^2=\PP^2\setminus L^\infty$ consists solely of hyperbolic nodes. Then $C$ is expressive and $L^\infty$-regular.
By Lemmas \[lem:poly-curve\] and \[lem:trig-curve\], a real polynomial or trigonometric curve $C=Z(F)$ is a real rational curve with one real or two complex conjugate local branches at infinity, and with a nonempty set of real points in $\AA^2$. Thus, conditions (ii), (a), (b), (c), and (e) of Proposition \[pr:expressive+regular\] are satisfied, so in order to obtain (i), we only need to establish (d). That is, we need to show that the polynomial $F$ has finitely many critical points in the affine plane $\AA^2$. We will prove this by contradiction.
Denote $d=\deg C=\deg F$. Suppose that $Z(F_x)\cap Z(F_y)$ contains a (real, possibly reducible) curve $B$ of a positive degree $d'<d$.
We first observe that $B\cap C\cap\AA^2=\emptyset$. Assume not. If $q\in B\cap C\cap \AA^2$, then $q\in\operatorname{\mathbf{Sing}}(C)\cap\AA^2$, so $q$ must be a hyperbolic node of $C$, implying $(Z(F_x)\cdot Z(F_y))_q=\mu(C,q)=1$; but since $q$ lies on a common component of $Z(F_x)$ and $Z(F_y)$, we must have $(Z(F_x)\cdot Z(F_y))_q=\infty$.
Since $B$ is real, and $C$ has either one real or two complex conjugate local branches at infinity, it follows that $B\cap C=L^\infty\cap C$.
**Case 1**: $C$ has a unique (real) branch $Q$ at a point $p\in L^\infty$. Then $(B\cdot Q)_p=d'd$. On the other hand, $((L^\infty)^{d'}\cdot Q)_p=d'd$. Hence any curve $\hat B\in\operatorname{Span}\{B,(L^\infty)^{d'}\}$ satisfies $(\hat B\cdot Q)_p\ge d'd$. For any point $q\in C\setminus\{p\}$ there is a curve $\tilde B\in\operatorname{Span}\{B,(L^\infty)^{d'}\}$ passing through $q$. Hence $C$ is a component of $\tilde B$, in contradiction with $d'<d$.
**Case 2**: $C$ has two complex conjugate branches $Q$ and $\overline Q$ centered at (possibly coinciding) points $p$ and $\overline p$ on $L^\infty$, respectively. Since $B$ is real, we have $$(B\cdot Q)_p=(B\cdot\overline Q)_{\overline p}=((L^\infty)^{d'}\cdot Q)_p=((L^\infty)^{d'}\cdot\overline Q)_{\overline p}=\tfrac{d'd}{2}.$$ This implies that any curve $\hat B\in\operatorname{Span}\{B,(L^\infty)^{d'}\}$ satisfies both $(\hat B\cdot Q)_p\ge\tfrac{d'd}{2}$ and $(\hat Q\cdot\overline Q)_{\overline p}\ge\tfrac{d'd}{2}$, resulting in a contradiction as in Case 1.
In Proposition \[pr:irr-expressive\], the requirement concerning the singular set cannot be dropped: a real polynomial curve $C$ may have elliptic nodes (see Example \[ex:poly-with-elliptic-node\]) or cusps (consider the cubic $(t^2,t^3)$), preventing $C$ from being expressive.
\[rem:poly-trig-expr=>reg\] Proposition \[pr:irr-expressive\] implies that if a real curve $C$ is polynomial or trigonometric, and also expressive, then it is necessarily $L^\infty$-regular. Indeed, expressivity in particular means that all singular points of $C$ are hyperbolic nodes.
\[ex:hypotrochoid-expressive\] Recall from Example \[ex:hypotrochoids\] that for appropriately chosen values of the real parameter $a$, the hypotrochoid $C$ given by the equation is a nodal trigonometric curve of degree $d=2k$ with the maximal possible number of real hyperbolic nodes, namely $\frac{(d-1)(d-2)}{2}=(k-1)(2k-1)$. Thus $C$ has no other singular points in the affine plane, and consequently is expressive by Proposition \[pr:irr-expressive\].
Combining Corollary \[cor:reg-expressive-irreducible\] and Proposition \[pr:irr-expressive\], we obtain:
\[th:reg-expressive-irreducible\] For a real plane algebraic curve $C$, the following are equivalent:
- $C$ is irreducible, expressive and $L^\infty$-regular;
- $C$ is either trigonometric or polynomial, and all its singular points in the affine plane $\AA^2$ are hyperbolic nodes.
Theorem \[th:reg-expressive-irreducible\] is illustrated in Table \[table:irreducible-expressive\]. Each real curve in this table is either polynomial or trigonometric. We briefly explain why all these curves are expressive (hence $L^\infty$-regular, see Remark \[rem:poly-trig-expr=>reg\]).
Expressivity of Chebyshev and Lissajous curves was established in Example \[ex:lissajous-chebyshev\]. The limaçon of Pascal was discussed in Example \[ex:multi-limacons\]. In Example \[ex:hypotrochoid-expressive\], we saw that a hypotrochoid is expressive for appropriately chosen values of $a$. For a more general statement, see Proposition \[pr:epi-hypo\] below.
Regarding the remaining curves in Table \[table:irreducible-expressive\], all we need to check is that each of their singular points in the affine plane is a hyperbolic node. The curves $V(x^d-y)$ are smooth, so there is nothing to prove. Same goes for the ellipse, as well as the curves $V((y-x^2)^2-x)$ and $V((y-x^2)^2+x^2-1)$. Finally, the curve $V((y-x^2)^2-xy)$ has a single singular point in $\AA^2$, a hyperbolic node at the origin.
[|c|c|p[1.7in]{}|p[1.9in]{}|p[1.33in]{}|]{} $d$ & $\xi$ & $G(x,y)$ & $(X(t), Y(t))$ & $V(G)$\
\
$1$ & 0 & $x-y$ & $(t, t)$ & line\
$2$ & 0 & $x^2-y$ & $(t, t^2)$ & parabola\
$2$ & 1 & $x^2+y^2-1$ & $(\cos(t),\sin(t))$ & ellipse\
$3$ & 0 & $x^3-y$ & $(t,t^3)$ & cubic parabola\
$3$ & 2 & $4x^{3}-3x+2y^{2}-1$ & $(-2t^2+1,4t^3-3t)$ & $(3,2)$-Chebyshev\
$4$ & 0 & $x^4-y$ & $(t,t^4)$ & quartic parabola\
$4$ & 0 & $(y-x^2)^2-x$ & $(t^2,t^4+t)$ &\
$4$ & 1 & $(y-x^2)^2+x^2-1$ & $(\cos(t), \sin(t)\!+\!\cos^2(t))$ &\
$4$ & 2 & $(y-x^2)^2-xy$ & $(t^2-t,t^4-t^3)$ &\
$4$ & 3 & $y^2+4x^4-4x^2$ & $(\cos(t), \sin(2t))$ & (1,2)-Lissajous\
$4$ & 3 & $4(x^2+y^2)^2\!-\!3(x^2+y^2)\!-\!x$ & $(\cos(t)\!\cos(3t),\cos(t)\!\sin(3t)$ & lima[ç]{}on\
$4$ & 6 & $4x^3-3x+8y^4-8y^2+1$ & $(-8t^4+8t^2-1, 4t^3-3t)$ & $(3,4)$-Chebyshev\
$4$ & 7 & see & see & (2,1)-hypotrochoid\
Another rich source of examples of expressive curves is provided by the following construction.
\[def:hypotrochoids\] Let $b$ and $c$ be coprime nonzero integers, with $b>|c|$. Let $u$ and $v$ be nonzero reals. The trigonometric curve $$\begin{aligned}
\label{def:epi-hypo1}
x&=u\cos bt+v\cos ct, \\
\label{def:epi-hypo2}
y&=u\sin bt-v\sin ct.\end{aligned}$$ is called a *hypotrochoid* if $c>0$, and an *epitrochoid* if $c<0$. This is a rational curve of degree $2b$.
\[ex:hypotrochoids-again\] A hypotrochoid with (coprime) parameters $b$ and $c$ has $b+c$ “petals.” When $b=c+1$, we recover Example \[ex:hypotrochoids\]. Figure \[fig:3-petal\] shows the case $(b,c)=(2,1)$, Figure \[fig:5-petal\] shows the case $(b,c)\!=\!(3,2)$, and Figure \[fig:double-reflection\] (left) shows the case $(b,c)\!=\!(3,1)$.
An epitrochoid with (coprime) parameters $b$ and $c$ (here $b>-c>0$) has $b+c$ inward-pointing “petals.” When $b=-c+1$, we recover the “multi-limaçons” of Example \[ex:rose-curves\]. Figure \[fig:multi-limacons\] shows the cases $(b,c)=(2,-1)$, $(b,c)=(3,-2)$, and $(b,c)=(4,-3)$. Figure \[fig:double-reflection\] (right) shows the case $(b,c)=(3,-1)$.
\[pr:epi-hypo\] Let $C$ be an epitrochoid or hypotrochoid given by – (As in Definition \[def:hypotrochoids\], $b$ and $c$ are coprime integers, with $b>|c|$; and .) Then $C$ is expressive and $L^\infty$-regular if it has $(b+c)(b-1)$ hyperbolic nodes in $\AA^2$. In particular, this holds if $\frac{|v|}{|u|}$ is sufficiently small.
Setting $\tau=e^{it}$, we convert the trigonometric parametrization – of $C$ into a rational one: $$\begin{aligned}
x&=\ \ \,\tfrac{1}{2}(u\tau^{2b}+v\tau^{b+c}+v\tau^{b-c}+u), \\
y&=-\tfrac{i}{2}(u\tau^{2b}-v\tau^{b+c}+v\tau^{b-c}-u), \\
z&=\tau^b.\end{aligned}$$ This curve has two points at infinity, namely $(1,i,0)$ and $(1,-i,0)$, corresponding to $\tau=0$ and $\tau=\infty$, respectively. Noting that the line $x+iy=0$ passes through $(1,i,0)$, we change the coordinates by replacing $y$ by $$\begin{aligned}
x+iy&=u\tau^{2b}+v\tau^{b-c}.
$$ In a neighborhood of $(1,i,0)$, this yields the following parametrization: $$x=1,\quad x+iy=\tfrac{2v}{u}\tau^{b-c}+\text{h.o.t.},\quad z=\tfrac{2}{u}\tau^b+\text{h.o.t.}$$ Thus, at the point $(1,i,0)$ we have a semi-quasihomogeneous singularity of weight $(b-c,b)$, and similarly at $(1,-i,0)$. The $\delta$-invariant at each of the two points is equal to $\frac{1}{2}(b-c-1)(b-1)$. Hence in the affine plane $\AA^2$, there remain $$\tfrac{1}{2}(2b-1)(2b-2)-(b-c-1)(b-1)=(b+c)(b-1)$$ nodes. So if all these nodes are real hyperbolic (and distinct), then $C$ is expressive and $L^\infty$-regular by Proposition \[pr:irr-expressive\] (or Theorem \[th:reg-expressive-irreducible\]).
It remains to show that $C$ has $(b+c)(b-1)$ hyperbolic nodes as long as $u,v\in\RR^*$ are chosen appropriately (in particular, if $\frac{|v|}{|u|}$ is sufficiently small). Consider the rational parametrization of $C$ given by $$\begin{aligned}
x+iy&=u\tau^b+v\tau^{-c},\\
x-iy&=u\tau^{-b}+v\tau^c, \\
z&=1.\end{aligned}$$ We need to show that all solutions $(\tau,\sigma)\in(\CC^*)^2$ of $$\begin{aligned}
\label{eq:u(tau-theta1)}
&u\tau^b+v\tau^{-c}=u\sigma^b+v\sigma^{-c},\\
\label{eq:u(tau-theta2)}
&u\tau^{-b}+v\tau^c=u\sigma^{-b}+v\sigma^c,\\
\label{eq:tau-neq-sigma}
&\tau\neq\sigma\end{aligned}$$ satisfy $|\tau|=|\sigma|=1$. Let us rewrite – as $$\begin{aligned}
u(\tau^b-\sigma^b)-v(\tau\sigma)^{-c}(\tau^c-\sigma^c)&=0,\\
-u(\tau\sigma)^{-b}(\tau^b-\sigma^b)+v(\tau^c-\sigma^c)&=0.\end{aligned}$$ The condition $\gcd(b,c)=1$ implies that at least one of $\tau^b-\sigma^b$ and $\tau^c-\sigma^c$ is nonzero (or else $\tau=\sigma$). Consequently $$\det\left(\begin{matrix} u & -v(\tau\sigma)^{-c} \\
-u(\tau\sigma)^{-b} & v\end{matrix}\right)
=uv(1-(\tau\sigma)^{-b-c})
=0,$$ meaning that $\omega=\tau\sigma$ must be a root of unity: $\omega^{b+c}=1$. With respect to $\tau$ and $\omega$, the conditions – become: $$\begin{aligned}
\label{eq:omega}
&\omega^{b+c}=1, \\
\label{eq:tau-eps}
&u(\tau^b-\omega^b\tau^{-b})+v(\tau^{-c}-\omega^{-c}\tau^c)=0, \\
&
\label{eq:tau^2}
\tau^2\neq\omega.\end{aligned}$$ Let $\lambda$ be a square root of $\omega$, i.e., $\lambda^2=\omega$. Then states that $\tau\notin\{\lambda,-\lambda\}$.
For each of the $b+c$ possible roots of unity $\omega$, is an algebraic equation of degree $2b$ in $\tau$. We claim that if $u,v\in\RR^*$ are suitably chosen, then all $2b$ solutions of this equation lie on $S^1=\{|\tau|=1\}$. It is easy to see that this set of solutions contains the two values $\tau=\pm\lambda$ which we need to exclude, leaving us with $2(b-1)$ solutions for each $\omega$ satisfying . We also claim that all these $2(b+c)(b-1)$ solutions are distinct, thereby yielding $(b+c)(b-1)$ hyperbolic nodes of the curve, as desired.
Let us establish these claims. Denote ${{\varepsilon}}=\lambda^{b+c}\in\{-1,1\}$. Replacing $\tau$ by $\rho=\tau\lambda^{-1}$ (thus $\tau=\lambda\rho$), we transform into $$u{{\varepsilon}}(\rho^b-\rho^{-b})=v(\rho^c-\rho^{-c}).$$ Making the substitution $\rho=e^{i\alpha}$, we translate this into $$\label{eq:two-sinusoids}
u{{\varepsilon}}\sin(b\alpha)=v\sin(c\alpha).$$ If $|\frac{v}{u}|$ is sufficiently small, then the equation clearly has $2b$ distinct real solutions in the interval $[0,2\pi)$, as claimed. Finally, it is not hard to see that all resulting $2(b+c)(b-1)$ values of $\tau$ are distinct.
We return to the general treatment of (potentially reducible) expressive $L^\infty$-regular curves. First, a generalization of Proposition \[pr:irr-expressive\]:
\[pr:sufficient-expressive\] Let $C$ be a reduced real plane curve such that
- each component of $C$ is real, and either polynomial or trigonometric;
- the singular set of $C$ in the affine plane $\AA^2$ consists solely of hyperbolic nodes;
- the set of real points of $C$ in the affine plane is connected.
Then $C$ is expressive and $L^\infty$-regular.
The proof utilizes the approach used in the proof of Proposition \[pr:irr-expressive\]. Arguing exactly as at the beginning of the latter proof, we conclude that all we need to show is that the polynomial $F$ defining $C$ has finitely many critical points in the affine plane $\AA^2$. Once again, we argue by contradiction. Assuming that $Z(F_x)\cap Z(F_y)$ contains a real curve $B$ of a positive degree $d'<d=\deg(C)$, and reasoning as in the earlier proof, we conclude that for any component $C'$ of $C$, there exists a curve $\hat B_{C'}\in\operatorname{Span}\{B,(L^\infty)^{d'}\}$ containing $C'$ as a component. In view of the connectedness of ${C_{\RR}}$ and the fact that different members of the pencil $\operatorname{Span}\{B,(L^\infty)^{d'}\}$ are disjoint from each other in the affine plane $\AA^2$, we establish that there is just one curve $\hat B\in\operatorname{Span}\{B,(L^\infty)^{d'}\}$ that contains all the components of $C$—but this contradicts the inequality $d'<d$.
\[th:reg-expressive\] Let $C$ be a reduced real plane algebraic curve, with all irreducible components real. The following are equivalent:
- $C$ is expressive and $L^\infty$-regular;
- each irreducible component of $C$ is either trigonometric or polynomial,\
all singular points of $C$ in the affine plane $\AA^2$ are hyperbolic nodes, and\
the set of real points of $C$ in the affine plane is connected.
Follows from Propositions \[prop:nonempty\] and \[pr:sufficient-expressive\].
Let $C$ be an $L^\infty$-regular expressive plane curve whose irreducible components are all real. Let $C'$ be a subcurve of $C$, i.e., a union of a subset of irreducible components. If the set of real points of $C'$ in the affine plane is connected, then $C'$ is also $L^\infty$-regular and expressive.
Follows from Theorem \[th:reg-expressive\].
We conclude this section by a corollary whose statement is entirely elementary, and in particular does not involve the notion of expressivity.
\[cor:all-crit-pts-are-real\] Let $C=V(G(x,y))$ be a real polynomial or trigonometric affine plane curve which intersects itself solely at hyperbolic nodes. Then all critical points of the polynomial $G(x,y)$ are real.
Immediate from Proposition \[pr:irr-expressive\] (or Theorem \[th:reg-expressive-irreducible\]).
More expressivity criteria {#sec:more-expressivity-criteria}
==========================
We first discuss the irreducible case. By Theorem \[th:reg-expressive-irreducible\], an irreducible plane curve is expressive and $L^\infty$-regular if and only if it is is either trigonometric or polynomial, and all its singular points outside $L^\infty$ are real hyperbolic nodes. The last condition is the usually the trickiest to verify.
One simple case is when the number of hyperbolic nodes attains its maximum:
\[cor:max-number-of-nodes\] Let $C$ be a real polynomial or trigonometric curve of degree $d$ with $\frac{(d-1)(d-2)}{2}$ hyperbolic nodes. Then $C$ is expressive and $L^\infty$-regular.
In view of Hironaka’s formula , the curve $C$ has no other singular points besides the given hyperbolic nodes. The claim follows by Proposition \[pr:irr-expressive\].
Examples illustrating Corollary \[cor:max-number-of-nodes\] include Lissajous-Chebyshev curves with parameters $(d,d-1)$ as well as hypotrochoids with parameters (cf. ).
In Corollary \[cor:max-number-of-nodes\], the requirement that the curve $C$ is polynomial or trigonometric cannot be dropped. For example, there exists an irreducible real quadric with three hyperbolic nodes which is not expressive.
Corollary \[cor:max-number-of-nodes\] can be generalized as follows.
\[cor:nodes-Newton\] Let $C=V(G(x,y))$ be a real polynomial or trigonometric curve with $\nu$ hyperbolic nodes. Suppose that the Newton polygon of $G(x,y)$ has $\nu$ interior integer points. Then $C$ is expressive and $L^\infty$-regular.
It is well known (see [@Baker1893] or [@Fulton Section 4.4]) that the maximal possible number of nodes of an irreducible plane curve with a given Newton polygon (equivalently, the arithmetic genus of a curve in the linear system spanned by the monomials in the Newton polygon, on the associated toric surface) equals the number of interior integer points in the Newton polygon. The claim then follows by Proposition \[pr:irr-expressive\].
Applications of Corollary \[cor:nodes-Newton\] include arbitrary irreducible Lissajous-Chebyshev curves .
It is natural to seek an algorithm for verifying whether a given immersed real polynomial or trigonometric curve $C$, say one given by an explicit parametrization, is expressive. By Theorem \[th:reg-expressive-irreducible\], this amounts to checking that each points of self-intersection of $C$ in the affine plane $\AA^2$ corresponds to two real values of the parameter. In the case of a polynomial curve $$t\mapsto (P(t),Q(t)),$$ this translates into the requirement that the resultant (with respect to either variable $s$ or $t$) of the polynomials $$\widehat P(t,s)=\frac{P(t)-P(s)}{t-s} \quad \text{and}\quad
\widehat Q(t,s)=\frac{Q(t)-Q(s)}{t-s}$$ has distinct real roots.
Consider the sextic curve $$t\mapsto (-8t^{6}+24t^{4}+4t^{3}-18t^{2}-6t+1,-2t^{4}+4t^{2}-1).$$ In this case, $$\begin{aligned}
\widehat P(t,s)&=-2 (2s^2 + 2st + 2t^2 - 3) (2s^3 + 2t^3 - 3s - 3t - 1),\\
\widehat Q(t,s)&=-2(s+t)(s^2+t^2-2).\end{aligned}$$ The resultant of $\widehat P$ and $\widehat Q$ (which we computed using `Sage`) is equal to $$-256 (2s^2 - 3)(2s^2 - 2s - 1)(2s^2 + 2s - 1)(8s^6 - 24s^4 - 4s^3 + 18s^2 + 6s - 1).$$ All its 12 roots are real, so the curve is expressive, with 6 nodes. See Figure \[fig:newton-degenerate\].
\[fig:newton-degenerate\]
The case of a trigonometric curve can be treated in a similar way. Let $C$ be a trigonometric curve with a Laurent parametrization $$t\mapsto (x(t),y(t))=(P(t)+\overline P(t^{-1}),Q(t)+\overline Q(t^{-1}))$$ (cf. ), with $P(t)=\sum_k \alpha_k t^k$, $Q(t)=\sum_k \beta_k t^k$. We write down the differences $$\begin{aligned}
\frac{x(t)-x(s)}{t-s}
=\sum_k(t^{k-1}+t^{k-2}s+...+s^{k-1})\Bigl(\alpha_k-\frac{\overline\alpha_k}{t^k s^k}\Bigr),\\[-.05in]
\frac{y(t)-y(s)}{t-s}=\sum_k(t^{k-1}+t^{k-2}s+...+s^{k-1})\Bigl(\beta_k-\frac{\overline\beta_k}{t^k s^k}\Bigr),\end{aligned}$$ clear the denominators by multiplying by an appropriate power of $ts$, and require that all values of $t$ and $s$ for which the resulting polynomials vanish (equivalently, all roots of their resultants) lie on the unit circle.
Let $C\!=\!V(G)$ be an $L^\infty$-regular curve, with $G(x,y)\in\RR[x,y]$. Assume that ${C_{\RR}}$ is connected, and each singular point of it is a hyperbolic node, as in Definition \[def:divide-polynomial\]. Let $\nu$ denote the number of such nodes, and let $\rho$ be the number of regions of the divide $D_G$. Then $C$ is expressive if and only if $$\label{eq:nu+rho}
\nu+\rho=(d-1)^2-\sum_{p\in C\cap L^\infty} \mu(C,p,L^\infty).$$
By Bézout’s theorem, the right-hand side of is the number of critical points of $G$ in the affine plane, counted with multiplicities. Since each region of $D_G$ contains at least one (real) critical point, and each node of ${C_{\RR}}$ is a critical point, the only way for to hold is for $C$ to be expressive.
Bending, doubling, and unfolding {#sec:constructions-irr}
================================
In this section, we describe several transformations which can be used to construct new examples of expressive curves from existing ones. The simplest transformation of this kind is the “bending” procedure based on the following observation:
\[pr:bending\] Let $f(x,y),g(x,y)\in\RR[x,y]$ be such that the map $$\label{eq:real-biregular}
(x,y)\mapsto (f(x,y),g(x,y))$$ is a biregular automorphism of $\AA^2$. If the curve $C=V(G(x,y))$ is expressive, then so is the curve $$\widetilde C=V(G(f(x,y),g(x,y))).$$ If, in addition, $C$ is $L^\infty$-regular, with real components, then so is $\widetilde C$.
Proposition \[pr:bending\] is illustrated in Figure \[fig:bending\].
\[fig:bending\]
The automorphism is an invertible change of variables that restricts to a diffeomorphism of the real plane $\RR^2$. As such, it sends (real) critical points to (real) critical points, does not change the divide of the curve, and preserves expressivity.
Let us now assume that $C$ is expressive and $L^\infty$-regular, with real components. In view of Theorem 7.16, all we need to show is that all components of $\widetilde C$ are polynomial or trigonometric. Geometrically, a polynomial (resp., trigonometric) component is a Riemann sphere punctured at one real point (resp., two complex conjugate points) and equivariantly immersed into the plane. This property is preserved under real biregular automorphisms of $\AA^2$.
It is well known [@vanderKulk] that the group of automorphisms of the affine plane is generated by affine transformations together with the transformations of the form $(x,y)\mapsto (x,y+P(x))$, for $P$ a polynomial. This holds over any field of characteristic zero, in particular over the reals.
Several examples of bending can be extracted from Table \[table:irreducible-expressive\]. Applying the automorphism $(x,y)\mapsto (x,y+x-x^m)$ to the line $V(x-y)$, we get $V(x^m-y)$. The automorphism $(x,y)\mapsto (x,y-x^2)$ transforms the parabola $V(y^2-x)$ into $V((y-x^2)^2-x)$, the ellipse $V(x^2+y^2-1)$ into $V(x^2+(y-x^2)^2-1)$, and the nodal cubic $V(y^2-xy-x^3)$ into $V((y-x^2)^2-xy)$. (In turn, $V(y^2-xy-x^3)$ and $V(4x^{3}-3x+2y^{2}-1)$ are related to each other by an affine transformation.)
The polynomial expressive curves shown in Figure \[fig:doubling-to-limacon-and-hypotrochoid\] (in red) are obtained by bending a parabola and a nodal cubic.
![A curve $C=V(G(x,y))$ and the “doubled” curve $\widetilde C=V(G(x,y^2))$. On the left: $G(x,y^2)$ is the left-hand side of the equation . Cf. Figure \[fig:multi-limacons\]. On the right: $G(x,y^2)$ is the left-hand side of , with $a=2$. Cf. Figure \[fig:3-petal\].[]{data-label="fig:doubling-to-limacon-and-hypotrochoid"}](doubling-to-limacon.png "fig:") ![A curve $C=V(G(x,y))$ and the “doubled” curve $\widetilde C=V(G(x,y^2))$. On the left: $G(x,y^2)$ is the left-hand side of the equation . Cf. Figure \[fig:multi-limacons\]. On the right: $G(x,y^2)$ is the left-hand side of , with $a=2$. Cf. Figure \[fig:3-petal\].[]{data-label="fig:doubling-to-limacon-and-hypotrochoid"}](doubling-to-hypotrochoid.png "fig:")
We next discuss the “doubling” construction which transforms a plane curve into a new curve $\widetilde C=V(G(x,y^2))$. Proposition \[pr:doubling\] below shows that, under certain conditions, this procedure preserves expressivity. See Figure \[fig:doubling-to-limacon-and-hypotrochoid\].
\[pr:doubling\] Let $C$ be an expressive $L^\infty$-regular curve whose components are all real (hence polynomial or trigonometric, see Proposition \[prop:nonempty\]). Suppose that
- each component $B=V(G(x,y))$ of $C$, say with $\deg_x(G)=d$, intersects $Z(y)$ in $d$ real points (counting multiplicities), all of which are smooth points of $C$; moreover, these intersections occur in one of the following ways:
- $\frac{d}{2}$ points of quadratic tangency (this must be the case if $B$ is trigonometric); or
- $\frac{d-1}{2}$ points of quadratic tangency and one point of transverse intersection; or
- $\frac{d-2}{2}$ points of quadratic tangency and 2 points of transverse intersection;
- all nodes of $C$ lie in the real half-plane $\{y>0\}$;
- at each point of quadratic tangency between $C$ and $Z(y)$, the local real branch of $C$ lies in the upper half-plane $\{y>0\}$.
Then the curve $\widetilde C=V(G(x,y^2))$ is expressive and $L^\infty$-regular.
The curve $\widetilde C$ is nodal by construction. It is not hard to see that the set $\widetilde C_\RR$ is connected, and all the nodes of $\widetilde C$ are hyperbolic. (See the proof of Proposition \[pr:accordion\] for a more involved version of the argument.) In view of Theorem \[th:reg-expressive\], it remains to show that all components of $\widetilde C$ are real polynomial or trigonometric.
We only treat the trigonometric case, since the argument in the polynomial case is similar. (Cf. also the proof of Lemma \[lem:accordion2-poly\], utilizing such an argument in a more complicated context.) The natural map $\widetilde C\!\to \!C$ lifts to a two-sheeted ramified covering $\rho:\widetilde C^{\vee}\!\to\! C^\vee$ between respective normalizations. The restriction of $\rho$ to $\widetilde C^{\vee}\!\setminus\!\rho^{-1}(Z(y))$ is an unramified two-sheeted covering, and each component of $\widetilde C$ contains a one-dimensional fragment of the real point set, hence is real. In fact, $\rho$ is not ramified at all, since each point in $C\cap Z(y)$ lifts to a node, and hence to two preimages in $\widetilde C^{\vee}$. Since $C^\vee=\CC^*$, it follows that $\widetilde C^{\vee}$ is a union of at most two disjoint copies of $\CC^*$. We conclude that $\widetilde C$ consists of one or two trigonometric components.
If a curve $C=V(G(x,y))$ satisfies the conditions in Proposition \[pr:doubling\] with respect to each of the coordinate axes $Z(x)$ and $Z(y)$, with all points in $C\cap Z(x)$ (resp., $C\cap Z(y)$) located on the positive ray $\{x=0, y>0\}$ (resp., $\{y=0, x>0\}$), the one can apply the doubling transformation twice, obtaining an expressive curve $\widetilde C=V(G(x^2,y^2))$. A couple of examples are shown in Figure \[fig:double-reflection\].
![A curve $C=V(G(x,y))$ and its “double-double” $C'=V(G(x^2,y^2))$. Left: $C$ is a nodal cubic tangent to both axes, $\widetilde C$ is a 4-petal hypotrochoid, cf. Definition \[def:hypotrochoids\], with $b=3$, $c=1$. Right: $C$ is a cubic parabola tangent to both axes, $\widetilde C$ is an epitrochoid with $b=3$, $c=-1$. ](double-reflection.png "fig:") ![A curve $C=V(G(x,y))$ and its “double-double” $C'=V(G(x^2,y^2))$. Left: $C$ is a nodal cubic tangent to both axes, $\widetilde C$ is a 4-petal hypotrochoid, cf. Definition \[def:hypotrochoids\], with $b=3$, $c=1$. Right: $C$ is a cubic parabola tangent to both axes, $\widetilde C$ is an epitrochoid with $b=3$, $c=-1$. ](double-double-to-epitrochoid.png "fig:")
\[fig:double-reflection\]
The remainder of this section is devoted to the discussion of “unfolding.” This is a transformation of algebraic curves that utilizes the coordinate change $$(x,y)=(x,T_m(u)).
\label{eq:accordion}$$ (As before, $T_m$ denotes the $m$th Chebyshev polynomial of the first kind, see .) A precise description of unfolding is given in Proposition \[pr:accordion\] below. To get a general idea of how this construction works, take a look at the examples in Figures \[fig:ellipse-infolding\]–\[fig:accordion-exotic\]. As these examples illustrate, the bulk of the unfolded curve (viewed up to an isotopy of the real plane) is obtained by stitching together $m$ copies of the input curve $C$, or more precisely the portion of $C$ contained in the strip $\{-1\le y\le 1\}$.
\[fig:ellipse-infolding\]
![A curve $C=V(G(x,y))$ and its triple unfolding $C=V(G(x,T_3(y)))$. Here $G(x,y)=8x^{3}-12x^{2}+(2y+(x-1)^{2})^{2}$. The green dashed lines are given by the equations $y=\pm 1$ (on the left) and $T_3(y)=4y^3-3y=\pm1$. Cf. Figure \[fig:newton-degenerate\]. ](accordion-exotic.png)
\[fig:accordion-exotic\]
\[lem:accordion1\] Let $C=V(F(x,y))$ be a trigonometric curve. Suppose that
- the strip $\{-1<y<1\}$ contains a one-dimensional fragment of ${C_{\RR}}$;
- $d=\deg_x F$ is even;
- $C$ intersects each of the lines $y=\pm 1$ in $d/2$ points;
- all of these points are smooth points of quadratic tangency between $C$ and $Z(y^2-1)$.
Then for any $m\in\ZZ_{>0}\,$, the curve ${C_{(m)}}$ defined by $$\label{eq:Cm}
{C_{(m)}}=V(F(x,T_m(u)))$$ is a union of trigonometric curves.
The natural map ${C_{(m)}}\to C$ given by lifts to the $m$-sheeted ramified covering map $\rho:{C_{(m)}}^{\vee}\to C^\vee$ between the normalizations. The restriction $$\rho:{C_{(m)}}^{\vee}\setminus\rho^{-1}(Z(y^2-1))\to C^\vee\setminus Z(y^2-1)$$ is an unramified $m$-sheeted covering, and each of the components of ${C_{(m)}}$ contains a one-dimensional fragment of the real point set, hence is real. Let us show that $\rho$ is not ramified at all. If $p\in C\cap Z(y-1)$ and $T_m^{-1}(1)$ consists of $a$ simple roots and $b$ double roots, then $p$ lifts to $a$ smooth points (where ${C_{(m)}}$ is quadratically tangent to the lines $u=\lambda$ with $\lambda$ running over all these simple roots) and $b$ nodes, totaling $a+2b=m$ preimages in ${C_{(m)}}^{\vee}$.
As $C$ is trigonometric, $C^\vee\!=\!\CC^*$. Since a cylinder can only be covered by a cylinder, ${C_{(m)}}^{\vee}$ is a union of disjoint copies of $\CC^*$ (not necessarily $m$ of them), so ${C_{(m)}}$ is a union of trigonometric components.
\[lem:accordion2-poly\] Let $C=V(F(x,y))$ be a real polynomial curve. Let $d=\deg_x F(x,y)$. Suppose that
- the strip $\{-1<y<1\}$ contains a one-dimensional fragment of ${C_{\RR}}$;
- $C$ intersects $Z(y^2-1)$ in $2d$ points (counting multiplicities), all of which are smooth points of $C$;
- these points include $d-1$ quadratic tangencies and two transverse intersections.
Then for any $m\in\RR_{>0}\,$, the curve ${C_{(m)}}$ defined by is a union of polynomial or trigonometric components.
It is not hard to see that $C$ has a polynomial parametrization $t\mapsto (P(t),Q(t))$ with . This follows from “Chebyshev’s equioscillation theorem” of approximation theory (due to E. Borel and A. Markov, see, e.g., [@Sodin-Yuditskii Section 1.1] or [@Mason-Handscomb Theorem 3.4]. In the rest of the proof, we assume that $Q(t)=T_d(t)$, as the case $Q(t)=-T_d(t)$ is completely similar.
We note that one can slightly vary the coefficients of $P$ while keeping the intersection properties of $C$ with $Z(y^2-1)$ (and maintaining expressivity if $C$ has this property). Thus, we can assume that $P(t)$ is a generic polynomial (in particular, with respect to $Q(t)=T_d(t)$).
**Case 1**: $\gcd(d,m)=1$. Observe that $$\label{eq:Cm-param-coprime}
\tau\mapsto (x,u)=(P(T_m(\tau)),T_d(\tau))$$ is a parametrization of a polynomial curve lying inside ${C_{(m)}}$. Indeed, $$F(P(T_m(\tau)),T_m(T_d(\tau)))=F(P(T_m(\tau)),T_d(T_m(\tau)))=0$$ because $F(P(t),Q(t))=0$.
Since $\frac{dx}{d\tau}$ and $\frac{du}{d\tau}$ never vanish simultaneously (thanks to the genericity of $P$ and the coprimeness of $d$ and $m$), the map is an immersion of $\CC$ into the affine plane. Since $u=0$ at $d$ points, while $\deg_x F(x,T_m(u))=d$, the image of this immersion is the entire curve ${C_{(m)}}$, which is therefore polynomial.
**Case 2**: $c=\gcd(m,d)>1$. Let $m=cr$, $d=cs$. The curve ${C_{(m)}}$ is given in the affine $(x,u)$-plane by the equations $$x=P(t),\quad T_m(u)=T_d(t)
\label{eq:Cm-parametric}$$ involving an implicit parameter $t$. Setting $t=T_r(\tau)$ we rewrite this as $$x=P(T_r(\tau)),\quad T_m(u)=T_m(T_s(\tau))$$ (since $T_d(T_r(\tau))=T_m(T_s(\tau))$). The equation $T_m(u)=T_m(u')$ has solutions $u=u'$, $u=-u'$ (for $m$ even) as well as $$\arccos u=\pm \arccos u'+2\pi\tfrac{k}{m},\quad k=0,\dots,m-1, \quad u,u'\in[-1,1].$$ From this, we obtain the following components of ${C_{(m)}}$, all of which turn out to be either polynomial or trigonometric. The polynomial components are: $$\begin{aligned}
&x=P(T_r(\tau)),\quad u=T_s(\tau), \\
&x=P(T_r(\tau)),\quad u=-T_s(\tau) \quad (m\in 2\ZZ).\end{aligned}$$ The trigonometric components are (here we set $\tau=\cos\theta$): $$x=P(\cos(r\theta)),\quad
u=\cos(s\theta\pm2\pi\tfrac{k}{m}),
\quad 0<k<\tfrac{m}{2}.$$ One can sort out which of these components are distinct by taking into account that $x$ is invariant with respect to the substitutions $\theta\mapsto-\theta$ and $\theta\mapsto\theta+2\pi\frac{j}{r}$.
\[pr:accordion\] Let $C=V(G(x,y))$ be an expressive $L^\infty$-regular curve all of whose components are real (hence polynomial or trigonometric, cf. Proposition \[prop:nonempty\]). Suppose that
- each component $V(F(x,y))$ of $C$, say with $\deg_x(F)=d$, intersects $Z(y^2-1)$ in $2d$ real points (counting multiplicities), all of which are smooth points of $C$;
- moreover, these intersections occur in one of the following two ways:
- $d$ points of quadratic tangency, or
- $d-1$ points of quadratic tangency and two points of transverse intersection;
- all nodes of $C$ lie in the strip $\{-1<y<1\}$;
- at each point of quadratic tangency between $C$ and $Z(y^2-1)$, the local real branch of $C$ lies in the strip $\{-1\le y\le 1\}$.
Then the curve ${C_{(m)}}=V(G(x,T_m(y)))$ is expressive and $L^\infty$-regular.
By construction, the curve ${C_{(m)}}$ is nodal. By Lemmas \[lem:accordion1\] and \[lem:accordion2-poly\], the components of ${C_{(m)}}$ are real polynomial or trigonometric. In view of Theorem \[th:reg-expressive\], it remains to show that the set $C_{(m),\RR}$ is connected, and that all the nodes of ${C_{(m)}}$ are hyperbolic.
The set of real points $C_\RR$ is connected by Definition \[def:expressive-poly\]. Since all the nodes of $C$ lie inside the strip $\{-1<y<1\}$, it follows that the set $C_\RR\cap\{-1\le y\le1\}$ is connected.
Let $\{a_1<\cdots<a_{m+1}\}$ be the set of roots of the equation $T_m^2(a)=1$. Then each set $$\label{eq:substips}
C_{(m),\RR}\cap\{a_j\le y\le a_{j+1}\}, \quad
j=1,...,m,$$ is an image of $C_\RR\cap\{-1\le y\le1\}$ under a homeomorphism of the strip $\{-1\le y\le1\}$ onto the strip $\{a_j\le y\le a_{j+1}\}$. Furthermore, for each $j=2,...,m$, the pair of sets $$C_{(m),\RR}\cap\{a_{j-1}\le y\le a_j\}
\quad \text{and}\quad
C_{(m),\RR}\cap\{a_j\le y\le a_{j+1}\}$$ are attached to each other at their common points along the line $Z(y-a_j)$. (This set of common points is nonempty since it includes the images of the intersection of $C_\RR$ with one of the two lines $Z(y\pm 1)$.) To obtain the entire set $C_{(m),\RR}\,$, we attach to the (connected) union of the $m$ sets the diffeomorphic images of the intervals forming the set $C_\RR\setminus\{-1\le y\le 1\}$ (if any). We conclude that $C_{(m),\RR}$ is connected.
Regarding the nodes of ${C_{(m)}}$, we observe that they come in two flavours. First, as one of the $m$ preimages of a node of $C$ contained in the strip $\{-1<y<1\}$; all these preimages are real, hence hyperbolic. Second, as a preimage of a tangency point between $C$ and $Z(y^2-1)$; this again yields a hyperbolic node.
Arrangements of lines, parabolas, and circles {#sec:overlays}
=============================================
We next discuss ways of putting together several expressive curves to create a new (reducible) expressive curve. Our key tool is the following corollary.
\[cor:overlays\] Let $C_1,\dots,C_k$ be expressive and $L^\infty$-regular plane curves such that
- each pair $C_i$ and $C_j$ intersect each other in $\AA^2$ at (distinct) hyperbolic nodes, and
- the set $C_\RR$ of real points of the curve $C=C_1\cup \cdots C_k$ is connected.
Then $C$ is expressive and $L^\infty$-regular.
Follows from Theorem \[th:reg-expressive\].
One easy consequence of Corollary \[cor:overlays\] is the following construction.
\[cor:overlays-graphs\] Let $f_1(x),\dots,f_k(x)\in\RR[x]$. Assume that each polynomial $f_i(x)-f_j(x)$ has real roots, and all such roots (over all pairs $\{i,j\}$) are pairwise distinct. Then the curve $V(\prod_i (y-f_i(x)))$ is expressive and $L^\infty$-regular.
\[ex:line-arrangements\] An arrangement of distinct real lines in the plane forms an expressive and $L^\infty$-regular curve, as long as no three lines intersect at a point. Parallel lines are allowed. See Figure \[fig:six-lines\].
\[fig:six-lines\]
\[ex:arrangements-of-parabolas\] Let $C$ be a union of distinct real parabolas in the affine plane. Then $C$ is an expressive and $L^\infty$-regular curve provided
- the set of real points of $C$ is connected;
- no three parabolas intersect at a point;
- all intersections between parabolas are transverse;
- for each pair of parabolas $P_1$ and $P_2$, one of the following options holds:
- $P_1$ and $P_2$ differ by a shift of the plane, or
- $P_1$ and $P_2$ have parallel (or identical) axes, and intersect at 2 points, or
- $P_1$ and $P_2$ intersect at 4 points.
See Figures \[fig:four-parabolas\] and \[fig:two-4-parabolas\].
![An arrangement of four co-oriented parabolas. Each pair of parabolas intersect transversally at two points. []{data-label="fig:four-parabolas"}](four-parabolas.png)
![Two arrangements of four parabolas. Each pair of parabolas intersect transversally at one, two, or four points, all of them real. []{data-label="fig:two-4-parabolas"}](two-arrangements-4-parabolas.png)
Examples \[ex:line-arrangements\] and \[ex:arrangements-of-parabolas\] have a common generalization:
\[ex:lines+parabolas\] Let $C$ be a union of distinct real lines and parabolas in the affine plane. Then $C$ is an expressive and $L^\infty$-regular curve provided
- the set of real points of $C$ is connected;
- no three of these curves intersect at a point;
- all intersections between these lines and parabolas are transverse;
- each line intersects every parabola at one or two points;
- each pair of parabolas intersect in one of the ways listed in Example \[ex:arrangements-of-parabolas\].
Another elegant application of Corollary \[cor:overlays\] involves arrangements of circles:
\[ex:circle-arrangements\] Let $\{C_i\}$ be a collection of circles on the real affine plane such that each pair of circles intersect transversally at two real points, with no triple intersections. Then the curve $\bigcup C_i$ is expressive and $L^\infty$-regular. See Figure \[fig:five-circles\].
\[fig:five-circles\]
Here is a common generalization of Examples \[ex:line-arrangements\] and \[ex:circle-arrangements\]:
Let $\{C_i\}$ be a collection of lines and circles on the real affine plane such that each circle intersects every line (resp., every other circle) transversally at two points, with no triple intersections. Then the curve $\bigcup C_i$ is expressive and $L^\infty$-regular. See Figure \[fig:five-circles+three-lines\].
\[fig:five-circles+three-lines\]
Shifts and dilations {#sec:shifts+dilations}
====================
In this section, we obtain lower bounds for an intersection multiplicity (at a point $p\in L^\infty$) between a plane curve $C$ and another curve obtained from $C$ by a shift or dilation. In Sections \[sec:arrangements-poly\]–\[sec:arrangements-trig\], we will use these estimates to derive expressivity criteria for unions of polynomial or trigonometric curves. Without loss of generality, we assume that $p=(1,0,0)$ throughout this section.
To state our bounds, we will need some notation involving Newton diagrams:
\[def:Newton-Gamma\] Let $C=Z(F(x,y,z))$ be a plane projective curve that contains neither of the lines $Z(z)=L^\infty$ and $Z(y)$ as a component. Furthermore assume that $p=(1,0,0)\in C\cap L^\infty$. We denote by $\Gamma(C,p)$ the Newton diagram of the polynomial $$\label{eq:F1}
F_1(y,z)=F(1,y,z)\in\CC[y,z]$$ at the point $(0,0)$, see Definition \[def:Newton-diagram\]. Since $F_1$ is not divisible by $y$ or $z$, the Newton diagram $\Gamma(C,p)$ touches both coordinate axes. We denote by $S^-(\Gamma(C,p))$ the area of the domain bounded by $\Gamma(C,p)$ and these axes.
\[pr:gen-dilation\] Let $C=Z(F(x,y,z))$ be a projective curve that contains neither $Z(z)=L^\infty$ nor $Z(y)$ as a component. Let $c\in\CC^*$, and let $C_c$ denote the dilated curve $$\label{eq:dilX}
C_c=Z(F(cx,cy,z)).$$ Assume that $p=(1,0,0)\in C\cap L^\infty$. Then $$(C\cdot C_c)_p\ge2S^-(\Gamma(C,p)).
\label{est-dilation}$$
In the coordinates $(y,z)$, the dilation $C\leadsto C_c$ can be regarded as a transition from the polynomial $F_1$ (see ) to the polynomial $F_c(y,z)=F(c,cy,z)$. The polynomials $F_1$ and $F_c$ have the same Newton diagram at $p$ (resp., Newton polygon). Furthermore, let $G(y,z)$ be a polynomial with the same Newton polygon and with generic coefficients. By the lower semicontinuity of the intersection number, we have $$(C\cdot C_c)_p\ge(C\cdot Z(G(y,z)))_p.$$ By Kouchnirenko’s theorem [@Kouchnirenko 1.18, Théorème III${}'$], the total intersection multiplicity of the curves $C$ and $Z(G)$ in the torus $(\CC^*)^2$ equals $2S(P)$, twice the area of the Newton polygon $P$ of $F_1$. Let us now deform $F_1$ and $G$ by adding all monomials underneath the Newton diagram $\Gamma(C,p)$, with sufficiently small generic coefficients. Again by Kouchnirenko’s theorem, the total intersection multiplicity of the deformed curves in $(\CC^*)^2$ equals $2S(P)+2S^-(\Gamma(C,p))$. To establish the bound (\[est-dilation\]), it remains to notice that the extra term $2S^-(\Gamma(C,p))$ occurring in the latter intersection multiplicity geometrically comes from simple intersection points in a neighborhood of $p$, obtained by breaking up the (complicated) intersection of $C$ and $Z(G)$ at $p$.
To state the analogue of Proposition \[pr:gen-dilation\] for shifted curves, we need to recall some basic facts about the *Newton-Puiseux algorithm* [@GLS Algorithm I.3.6]. This algorithm assigns each local branch $Q$ of a curve $C$ at the point $p=(1,0,0)\in C\cap L^\infty$ to an edge $E\!=\!E(Q)$ of the Newton diagram $\Gamma(C,p)$, cf. Definition \[def:Newton-Gamma\]. We denote by $${\mathbf{n}(E)}=(n_y,n_z)\in\ZZ_{>0}^2$$ the primitive integral normal vector to $E$, with positive coordinates.
\[l:wzwy\] Let $Q$ be a local branch of $C$ at . Assume that $Q$ is is tangent to $L^\infty$. Let $E=E(Q)$. Then $$\label{eq:nE=}
{\mathbf{n}(E)}=(n_y,n_z)=\tfrac{1}{r} (m,d)$$ where $$\begin{aligned}
\label{eq:d(Q)}
d=d(Q)&=(Q\cdot L^\infty)_p\,,\\
\label{eq:m(Q)}
m=m(Q)&=\operatorname{mult}(Q)<d,\\
\label{eq:r(Q)}
r=r(Q)&=\gcd(m,d).\end{aligned}$$
We denote by $F^E(y,z)=F^{E(Q)}(y,z)$ the truncation of $F_1$ (see \[eq:F1\]) along the edge $E=E(Q)$. The polynomial $F^E$ is quasihomogeneous with respect to the weighting of $y$ and $z$ by $n_y$ and $n_z$, respectively. We denote $$\begin{aligned}
\label{eq:rho(Q)}
\rho=\rho(Q)&=\lim_{\substack{q=(1,y,z)\in Q\\ q\to p}} \frac{z^{n_y}}{y^{n_z}}\in\CC^*,\\
\label{eq:eta(Q)}
\eta(Q)&=\text{multiplicity of $(z^{n_y}-\rho y^{n_z})$ as a factor of $F^E(y,z)$.}\end{aligned}$$ It is not hard to see that $\rho(Q)$ is well defined, and that $\eta(Q)\ge 1$.
\[pr:gen-shift\] Let $C=Z(F(x,y,z))$ be a projective curve not containing the line $Z(z)=L^\infty$ as a component. Assume that $p=(1,0,0)\in C\cap L^\infty$, and that $C$ is not tangent to the line $Z(y)$ at $p$. Let $a,b\in\CC$, and let ${C_{a,b}}$ denote the shifted curve $$\label{eq:shiftX}
{C_{a,b}}=Z(F(x+az,y+bz,z)).$$ Then $$\begin{aligned}
\label{est-shift}
(C\cdot C_{a,b})_p\ge 2S^-(\Gamma(C,p))&-\operatorname{mult}(C,p)+(C\cdot L^\infty)_p +\sum_Q \min(r(Q), \eta(Q)-1),\end{aligned}$$ where the sum is over all local branches $Q$ of $C$ at $p$ which are tangent to $L^\infty$.
(For the definitions of $S^-(\Gamma(C,p))$, $r(Q)$ and $\eta(Q)$, see Definition \[def:Newton-Gamma\], – and –, respectively.)
Since the intersection multiplicity is lower semicontinuous, we may assume that $a$ and $b$ are generic complex numbers.
Let us denote $$\begin{aligned}
\mathcal{Q}(C,p) &= \text{the set of local branches of $C$ at $p$;}\\
\mathcal{Q}_0(C,p)&= \text{the set of local branches tangent to~$L^\infty$;}\\
\mathcal{Q}_1(C,p)&= \text{the set of local branches transversal to~$L^\infty$.}\end{aligned}$$ The local branches in $\mathcal{Q}_0(C,p)$ correspond to the edges of $\Gamma(C,p)$ such that , cf. Lemma \[l:wzwy\]. Let $\Gamma_0(C,p)$ denote the union of these edges. The local branches in $\mathcal{Q}_1(C,p)$, if any, correspond to the unique edge $E_{(1,1)}\!\subset\!\Gamma(C,p)$ with . Figure \[fig:Gamma(C,p)\] illustrates the case where the edge $E_{(1,1)}$ is present; equivalently, some local branches are transversal to $L^\infty$.
(150,77)(0,0) (0,10)[(1,0)[150]{}]{} (10,0)[(0,1)[73]{}]{} (10,60)[[[ (1,-1)[20]{}]{}]{}]{} (30,40)[[[ (2,-1)[40]{}]{}]{}]{} (70,20)[[[ (6,-1)[60]{}]{}]{}]{} (-10,76)[powers of $z$]{} (135,2)[powers of $y$]{} (29,54)[(0,0)[[[ $E_{(1,1)}$]{}]{}]{}]{} (76,28)[(0,0)[[[ $\Gamma_0(C,p)$]{}]{}]{}]{}
(10,60) (20,50) (30,40) (50,30) (70,20) (130,10)
\[fig:Gamma(C,p)\]
Let us consider the family of curves $\{C_{\lambda a,\lambda b}\}_{0\le\lambda\le1}$ interpolating between and $C_{a,b}\,$. Being equisingular at the point $p$, this deformation preserves the number of local branches at $p$ as well as their topological characteristics. It therefore descends to families of individual local branches at $p$, yielding an equisingular bijection $$\begin{aligned}
\mathcal{Q}(C,p)&\longrightarrow\mathcal{Q}(C_{a,b},p)\\
Q&\longmapsto Q_{a,b}\,.\end{aligned}$$ Since the fixed point set of the shift $(x,y,z)\mapsto(x+az,y+bz,z)$ is the line $L^\infty$, this bijection restricts to bijections $\mathcal{Q}_0(C,p)\to\mathcal{Q}_0(C_{a,b},p)$ and $\mathcal{Q}_1(C,p)\to\mathcal{Q}_1(C_{a,b},p)$.
To obtain the desired lower bound on $(C\cdot C_{a,b})_p\,$, we will exploit the decomposition $$(C\cdot C_{a,b})_p=\sum_{Q,Q'\in\mathcal{Q}(C,p)}(Q\cdot Q'_{a,b})_p
= \Sigma_{00}+\Sigma_{01}+\Sigma_{10}+\Sigma_{11}\,,
\label{eq-branch}$$ where we use the notation $$\Sigma_{\varepsilon\delta}=\sum_{\substack{
Q\in\mathcal{Q}_\varepsilon(C,p)\\
Q'\in\mathcal{Q}_\delta(C,p)
}}
(Q\cdot Q'_{a,b})_p\,, \quad \text{for $\varepsilon,\delta\in\{0,1\}$.}$$
\[lem:sum-QQ\] Suppose $\mathcal{Q}_1(C,p)\neq\varnothing$. Then $$\label{eq:three-sigmas}
\Sigma_{01}+\Sigma_{10}+\Sigma_{11}=2S^-(E_{(1,1)}),$$ where $S^-(E_{(1,1)})$ denotes the area of the trapezoid bounded by the edge $E_{(1,1)}$, the coordinate axes, and the vertical line through the rightmost endpoint of $E_{(1,1)}$.
For $Q\in\mathcal{Q}_1(C,p)$, the tangent lines to $Q$ and $Q_{a,b}$ differ from each other. The foregoing discussion implies that, for any $Q\in\mathcal{Q}_1(C,p)$ and $Q'\in\mathcal{Q}(C,p)$, we have $$(Q\cdot Q'_{a,b})_p=(Q_{a,b}\cdot Q')_p=\operatorname{mult}Q\cdot \operatorname{mult}Q'. $$ We then observe that $$\begin{aligned}
\sum_{Q\in{\mathcal Q}_0(C,p)} \operatorname{mult}Q=\ell_0 &\,\eqdef\, \text{length of the projection of $\Gamma_0(C,p)$ to the vertical axis}, \\
\sum_{Q\in{\mathcal Q}_1(C,p)} \operatorname{mult}Q=\ell_1 &\,\eqdef\, \text{length of the projection of $E_{(1,1)}$ to either of the axes},\end{aligned}$$ implying $$\Sigma_{01}+\Sigma_{10}+\Sigma_{11}=\ell_0\ell_1+\ell_1\ell_0+\ell_1^2=2S^-(E_{(1,1)}).
\qedhere$$
In light of and , it remains to obtain the desired lower bound for the summand $\Sigma_{00}\,$. To simplify notation, we will pretend, for the time being, that all local branches are tangent to $L^\infty$, so that $\mathcal{Q}(C,p)=\mathcal{Q}_0(C,p)$ and $\Gamma(C,p)=\Gamma_0(C,p)$.
Let $\mathcal{Q}(E)$ denote the set of local branches of $C$ at $p$ associated with an edge $E$ of $\Gamma(C,p)$. Equivalently, $\mathcal{Q}(E)=\{Q\in\mathcal{Q}(C,p)\mid E(Q)=E\}$.
\[lem:E1E2\] Let $E_1$ and $E_2$ be two distinct edges of the Newton diagram $\Gamma(C,p)$. Assume that $E_2$ is located above and to the left of $E_1$, so that $$E_1\!=\![(i_1,j_1),(i'_1,j'_1)], \quad
E_2\!=\![(i_2,j_2),(i'_2,j'_2)], \quad
i_2'\!<\!i_2\!\le\! i_1'\!<\!i_1\,,\quad
j_1\!<\!j_1'\!\le\! j_2\!<\!j_2'\,.$$ Then $$\sum_{Q\in\mathcal{Q}(E_1)}\sum_{Q'\in\mathcal{Q}(E_2)}(Q\cdot Q'_{a,b})_p=
\sum_{Q\in\mathcal{Q}(E_1)}\sum_{Q'\in\mathcal{Q}(E_2)}(Q_{a,b}\cdot Q')_p
=(j'_1-j_1)(i_2-i'_2).$$
Note that $(j'_1-j_1)(i_2-i'_2)$ is the area of the rectangle formed by the intersections of the horizontal lines passing through $E_1$ with the vertical lines passing through $E_2$. See Figure \[fig:E1E2\].
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(30,40) (30,20) (30,10) (70,10) (50,30) (70,20) (130,10)
\[fig:E1E2\]
In the coordinates $(1,y,z)$, the shift transformation $$(1,y,z)\mapsto(1+az,y+bz,z)$$ converts the polynomial $F_1(y,z)=F(1,y,z)$ defining the affine curve $C\setminus Z(x)$ into the polynomial $F_{a,b}(y,z)=F(1+az,y+bz,z)$ defining $C_{a,b}\setminus Z(x)$. Under this transformation, each monomial $y^iz^j$ of $F_1$ becomes $$y^iz^j+\sum_{\renewcommand{\arraystretch}{0.6}
\begin{array}{c}
\scriptstyle{i',j'\ge0}\\
\scriptstyle{i'+j'>0}\end{array}}c_{i'j'}y^{i-i'}z^{j+i'+j'}.
\label{eq3}$$ In view of the assumption $\mathcal{Q}(C,p)=\mathcal{Q}_0(C,p)$, the monomials appearing in the sum above correspond to integer points lying strictly above the Newton diagram $\Gamma(C,p)$ of $F_1$. In particular, $F_{a,b}$ has the same Newton diagram $\Gamma(C,p)$, and the same truncations to its edges. Furthermore, each local branch $Q\in\mathcal{Q}(C,p)$ and its counterpart $Q_{a,b}\in\mathcal{Q}(C_{a,b},p)$ are associated with the same edge of $\Gamma(C,p)$. The union of the local branches of $C_{a,b}$ associated with the edge $E_1$ can be defined by an analytic equation $f(y,z)=0$ whose Newton diagram at the origin is the line segment $[(i_1-i'_1,0),(0,j'_1-j_1)]$ (cf. the Newton-Puiseux algorithm [@GLS Algorithm I.3.6]). For the same reason, a local branch $Q$ of $C$ at $p$ associated with the edge $E_2$ has a parametrization $$\begin{array}{l}
y=\varphi(t)=t^m,\\[.03in]
z=\psi(t)=\alpha t^d+O(t^{d+1}),
\end{array}
\quad
\alpha\!\ne\!0,\quad
|t| \! \ll \!1,\quad
d\!=\!(Q\cdot L^\infty)_p\,,\quad
m\!=\!\operatorname{mult}(Q)$$ (cf. –) where $\frac{d}{m}=\frac{j'_2-j_2}{i_2-i'_2}$. Since $\frac{j'_2-j_2}{i_2-i'_2}>\frac{j'_1-j_1}{i_1-i'_1}$, we obtain $$f(\varphi(t),\psi(t))=t^{m(i_1-i_1')}(\beta+O(t)),\quad\beta\ne0.$$ The statement of the lemma now follows from the fact that the total multiplicity of the local branches of $C$ at $p$ associated with the edge $E_2$ equals $j_2'-j_2\,$.
We are now left with the task of computing $$\sum_E \sum_{Q,Q'\in\mathcal{Q}(E)}(Q\cdot Q'_{a,b})_p\,,
\label{eq:last-sum}$$ where the first sum runs over the edges $E$ of the Newton diagram. In this part of the proof, we continue to assume, for the sake of simplifying the exposition, that all local branches are tangent to $L^\infty$. Since the shift $(a,y,z)\mapsto(1+az,y+bz,z)$ acts independently on the analytic factors of $F_1(y,z)$, we furthermore assume, in our computation of $\sum_{Q,Q'\in\mathcal{Q}(E)}(Q\cdot Q'_{a,b})_p$ (see ), that the Newton diagram $\Gamma(C,p)$ consists of a single edge $E=[(0,M),(D,0)]$, with $M<D$ and ${\mathbf{n}(E)}=(n_y,n_z)$.
Pick a local branch $Q\in\mathcal{Q}(E)$. It admits an analytic parametrization of the form $$x=1, \quad y=\varphi(t)=t^m,\quad z=\psi(t)=\alpha t^d+O(t^{d+1}),
\label{eq2}$$ where $t$ ranges over a small disk in $\CC$ centered at zero, $m=r(Q)\cdot n_y$, $d=r(Q)\cdot n_z$, and $r(Q)=\gcd(d,m)$, cf. and .
\[lem:Step3\] We have $$\label{eq:sum-Q'}
\sum_{Q'\in\mathcal{Q}(E)}(Q\cdot Q'_{a,b})_p=dM-m+d+\min(r(Q),\eta(Q)-1).$$
The left-hand side of is the minimal exponent of $t$ appearing in the expansion of $F_{a,b}(\varphi(t),\psi(t))$ into a power series in $t$. Since $F_1(\varphi(t),\psi(t))=0$, we may instead substitute into the difference $F_{a,b}(y,z)-F_1(y,z)$, or equivalently into the monomials of the second summand in (corresponding to individual monomials $y^iz^j$ of $F_1(y,z)$). Evaluating $y^{i-i'}z^{j+i'+j'}$ at $y=\varphi(t)$, $z=\psi(t)$, we obtain $$(t^m)^{i-i'}(t^d(\alpha+O(t)))^{j+i'+j'}=t^{mi+dj+(d-m)i'+dj'}(\alpha^{j+i'+j'}+O(t)).$$ To get the minimal value of the exponent $mi+dj+(d-m)i'+dj'$, we need to minimize $mi+dj$ (which is achieved for $(i,j)\in E$), and take $i'=1$ and $j'=0$. Developing $F_{a,b}(y,z)=F(1+az,y+bz,z)$ into a power series in $a$ and $b$, we see that the corresponding monomials $y^{i-i'}z^{j+i'+j'}=y^{i-1}z^{j+1}$ in $F_{a,b}(y,z)-F(1,y,z)$ add up to $bzF_y(1,y,z)$. We conclude that the desired minimal exponent of $t$ occurs when we substitute $(y,z)=(\varphi(t),\psi(t))$ either into $bzF^E_y(y,z)$ or into a monomial $y^{i-1}z^{j+1}$ such that $(i,j)$ is one of the integral points closest to the edge $E$ and lying above $E$. The latter condition reads $n_yi+n_zj=n_zM+1$.
The truncation $F^E(y,z)$ of $F_1(y,z)$ has the form $$F^E(y,z)=\prod_{k=1}^n(z^{n_y}-\beta_ky^{n_z})^{r_k},
\label{eq:trun}$$ where $\beta_1,\dots,\beta_n\in\CC$ are distinct, and $r_1,\dots,r_n\in\ZZ_{>0}$. Developing $F^E(y,z)$ into a power series in $t$, we see that the monomials of $F^E$ yield the minimal exponent of $t$. Since $F_1(\varphi(t),\psi(t))=0$, these minimal powers of $t$ must cancel out, implying that, for some $k_0\in\{1,\dots,n\}$, we have (cf. , ): $$\begin{aligned}
\rho=\rho(Q)&=\lim_{t\to 0}\frac{(\alpha t^d)^{n_y}}{(t^m)^{n_z}}=\alpha^{n_y}=\beta_{k_0}\,,\\
\eta=\eta(Q)&=r_{k_0}\,.\end{aligned}$$
The factorization formula implies that $$bzF^E_y(y,z)=bn_zy^{n_z-1}z\sum_{k=1}^n\Bigl((-\beta_k)^{r_k}(z^{n_y}-\beta_ky^{n_z})^{r_k-1}\prod_{l\ne k}(z^{n_y}-\beta_ly^{n_z})^{r_l}\Bigr).$$ We then compute the minimal exponent for $bzF^E_y(y,z)$: $$\begin{aligned}
bn_zy^{n_z-1}z\big|_{y=\varphi(t),z=\psi(t)}&=O(t^{mn_z-m+d}),\\
(z^{n_y}-\beta_ky^{n_z})^{r_k-1}\big|_{y=\varphi(t),z=\psi(t)}&=O(t^{dn_y(r_k-1)}),\quad k\ne k_0,\\
(z^{n_y}-\rho y^{n_z})^{\eta-1}\big|_{y=\varphi(t),z=\psi(t)}&=O(t^{(dn_y+1)(\eta-1)}),\\
(z^{n_y}-\beta_ly^{n_z})^{r_l}\big|_{y=\varphi(t),z=\psi(t)}&=O(t^{dn_yr_l}),\quad l\ne k_0,\\
(z^{n_y}-\rho y^{n_z})^{\eta}\big|_{y=\varphi(t),z=\psi(t)}&=O(t^{(dn_y+1)\eta}), \\
bzF^E_y(y,z)\big|_{y=\varphi(t),z=\psi(t)}&=O(t^{dM-m+d+\eta-1}).\end{aligned}$$ Also, for $n_yi+n_zj=n_zM+1$, we have $$y^{i-1}z^{j+1}\big|_{y=\varphi(t),z=\psi(t)}=O(t^{dM-m+d+r(Q)}).$$ Consequently $$\begin{aligned}
\sum_{Q'\in\mathcal{Q}(E)}(Q\cdot Q'_{a,b})_p
&=\min(dM-m+d+\eta-1,dM-m+d+r(Q)), $$ as desired.
We are now ready to complete the proof of Proposition \[pr:gen-shift\]. We first note that in Lemma \[lem:Step3\], $$m=\operatorname{mult}Q,\quad d=(Q\cdot L^\infty)_p\,,$$ and moreover $$\label{eq:M,D}
\sum_{Q\in\mathcal{Q}(E)}\operatorname{mult}Q=M,\quad \sum_{Q\in\mathcal{Q}(E)}(Q\cdot L^\infty)_p=D.$$ Therefore $$\begin{aligned}
\notag
\sum_{Q,Q'\in\mathcal{Q}(E)}(Q\cdot Q'_{a,b})_p
&=\sum_Q (dM-m+d+\min(r(Q),\eta(Q)-1)) \\
\label{eq:DM-M+D...}
&=DM-M+D+\sum_Q \min(r(Q),\eta(Q)-1).\end{aligned}$$ Note that $DM$ is twice the area of the right triangle with hypotenuse $E$.
As illustrated in Figure \[fig:2\*area\], adding up the contributions $DM$ from all edges $E$ of $\Gamma_0(C,p)$, together with the contributions coming from Lemmas \[lem:sum-QQ\] and \[lem:E1E2\], we obtain $2S^-(\Gamma(C,p))$, cf. Definition \[def:Newton-Gamma\].
Finally, in view of , we have $$\begin{aligned}
\sum_{E\subset \Gamma_0(C,p)} (-M+D)
&=\sum_{Q\in \mathcal{Q}_0(C,p)} (-\operatorname{mult}(Q)+(Q\cdot L^\infty)_p)\\
&=\sum_{Q\in \mathcal{Q}(C,p)} (-\operatorname{mult}(Q)+(Q\cdot L^\infty)_p)\\
&=-\operatorname{mult}(C,p)+(C\cdot L^\infty)_p\,.\end{aligned}$$ Putting everything together, we obtain .
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Arrangements of polynomial curves {#sec:arrangements-poly}
=================================
In this section, we generalize Example \[ex:lines+parabolas\] to arrangements of polynomial curves obtained from a given curve by shifts, dilations, and/or rotations. We start by obtaining upper bounds on the number of intersection points of two polynomial curves related by one of these transformations. These bounds lead to expressivity criteria for arrangements consisting of such curves.
Recall that for $a,b\in\CC$ and $c\in\CC^*$, we denote by $$\begin{aligned}
\label{eq:Cab}
{C_{a,b}}&=Z(F(x+az,y+bz,z)), \\
C_c&=Z(F(cx,cy,z))\end{aligned}$$ the curves obtained from a plane curve $C=Z(F(x,y,z))$ by a shift and a dilation, respectively. We will also use the notation $$\label{eq:shift+dilation}
{C_{a,b,c}}=Z(F(cx+az,cy+bz,z))$$ for a curve obtained from $C$ by a combination of a shift and a dilation.
As before, we identify a projective curve $C=Z(F(x,y,z))$ with its restriction to the affine plane $\AA^2=\PP^2\setminus L^\infty$ given by $C=V(G(x,y))$, where $G(x,y)=F(x,y,1)$. Under this identification, we have $$\begin{aligned}
{C_{a,b}}&=V(G(x+a,y+b)), \\
C_c&=V(G(cx,cy)),\\
\label{eq:Cabs=V(G)}
{C_{a,b,c}}&=V(G(cx+a,cy+b)).\end{aligned}$$
\[rem:shift+dilation\] Unless $c=1$ (the case of a pure shift), the transformation $C\leadsto {C_{a,b,c}}$ can be viewed as a pure dilation centered at some point $o\in\CC$ (where $o$ may be different from $0$).
\[cor:shift-poly\] Let $C$ be a real polynomial curve of degree $d$. Let $C\cap L^\infty=\{p\}$ and $m=\operatorname{mult}(C,p)$. Then we have, for $a,b\in\CC$ and $c\in\CC^*$: $$\begin{aligned}
\label{eq:dilation-poly}
(C\cdot {C_{a,b,c}})_p &\ge dm ;\\
\label{eq:shift-poly}
(C\cdot {C_{a,b}})_p &\ge (d-1)(m+1)+\gcd(d,m).\end{aligned}$$
In view of Remark \[rem:shift+dilation\] and the inequality $$(d-1)(m+1)+\gcd(d,m)\ge dm,$$ it suffices to establish in the case $a=b=0$, i.e., with ${C_{a,b,c}}$ replaced by $C_c$.
The bounds – are obtained by applying Propositions \[pr:gen-dilation\] and \[pr:gen-shift\] to the case of a polynomial curve $C$, while noting that in this case, $$\begin{aligned}
S^-(\Gamma(C,p))&=\tfrac12 md,\\
\operatorname{mult}(C,p)&=m,\\
(C\cdot L^\infty)_p&=d,\\
r(Q)=\eta(Q)&=\gcd(d,m). \qedhere \end{aligned}$$
\[pr:dilations-poly\] Let $C$ be a real polynomial curve with a parametrization $$t\mapsto (P(t),Q(t)), \quad \deg(P)=d, \quad \deg(Q)=d'\neq d.$$ Let $a,b,c\in\CC$, $c\neq 0$, and let ${C_{a,b,c}}$ be the shifted and dilated curve given by . Assume that $C$ and ${C_{a,b,c}}$ have $N$ intersection points in $\AA^2=\PP^2\setminus L^\infty$. Then $N\le dd'$.
Without loss of generality, assume that $d>d'$. By Bézout’s theorem, the intersection multiplicity $(C\cdot{C_{a,b,c}})_p$ at the point $p=(1,0,0)\in L^\infty$ is at most . Applying , with $m=d-d'$, we obtain $d^2-N\ge d(d-d')$. The claim follows.
Proposition \[pr:dilations-poly\] and Theorem \[th:reg-expressive\] imply that if $C$ and ${C_{a,b,c}}$ intersect at $dd'$ hyperbolic nodes in the real affine plane, then the union $C\cup{C_{a,b,c}}$ is expressive.
\[ex:23-dilation\] Let $C$ be the $(2,3)$-Chebyshev curve, the singular cubic given by $$\label{eq:23-Chebyshev}
2x^2-1+4y^3-3y=0$$ or parametrically by $$t\mapsto (4t^3-3t, -2t^2+1),$$ cf. . Applying Proposition \[pr:dilations-poly\] (with $d=3$ and $d'=2$), we see that the curve $C$ and its dilation ${C_{a,b,c}}$ ($c\neq 1$) can intersect in the real affine plane in at most 6 points. When this bound is attained, the union $C\cup{C_{a,b,c}}$ is expressive. Figure \[fig:chebyshev23-dilation\] shows one such example, with $a=b=0$ and $c=-1$ (so ${C_{a,b,c}}$ is a reflection of $C$). Cf. also Figure \[fig:three-dilations\].
\[fig:chebyshev23-dilation\]
\[pr:shifts-poly\] Let $C$ be a real polynomial curve with a parametrization $$t\mapsto (P(t),Q(t)), \quad \deg(P)=d, \quad \deg(Q)=d'<d.$$ Let $a,b\in\CC$, and let ${C_{a,b}}$ be the shifted curve given by . Assume that $C$ and ${C_{a,b}}$ have $N$ intersection points in $\AA^2=\PP^2\setminus L^\infty$. Then $$\label{eq:N-shift}
N\le dd'-d'-\gcd(d,d')+1.$$
We use the same arguments as in the proof of Proposition \[pr:dilations-poly\] above, with the lower bound replaced by : $$\begin{aligned}
N\le d^2-(C\cdot {C_{a,b}})_p &\le d^2-(d-1)(m+1)-\gcd(d,m) \\
&=d^2-(d-1)(d-d'+1)-\gcd(d,d') \\
&=dd'-d'+1-\gcd(d,d'). \qedhere\end{aligned}$$
For special choices of shifts, the bound can be strengthened. Here is one example, involving the Lissajous-Chebyshev curves, see Example \[ex:lissajous-chebyshev\]. (Note that such a curve does not have to be polynomial: it could be trigonometric or reducible.)
\[pr:shifts-lissajous\] Let $C$ be a Lissajous-Chebyshev curve given by $$\label{eq:lissajous-kl}
T_k(x)+T_\ell(y)=0.$$ Let $a\!\in\!\CC$, and let $C_{a,0}$ (resp., $C_{0,a}$) be the shift of $C$ in the $x$ (resp., $y$) direction. Assume that $C$ and $C_{a,0}$ (resp., $C_{0,a}$) intersect at $N_x$ (resp., $N_y$) points in $\AA^2$. Then $$\begin{aligned}
\label{eq:x-shift-lissajous}
N_x &\le (k-1)\ell, \\
\label{eq:y-shift-lissajous}
N_y &\le k(\ell-1).\end{aligned}$$
We note that in the case when $\gcd(k,\ell)=1$ and $k<\ell$, the bound matches , with $d=k$ and $d'=\ell$, whereas gives a stronger bound.
Due to symmetry, it suffices to prove . The intersection of the curves $C$ and $C_{0,a}$ is given by $$\begin{aligned}
\begin{cases}
T_k(x)+T_\ell(y)=0 \\
T_k(x)+T_\ell(y+a)=0
\end{cases}
\Longleftrightarrow{\ }
\begin{cases}
T_k(x)+T_\ell(y)=0 \\
T_\ell(y+a)-T_\ell(y)=0.
\end{cases}\end{aligned}$$ The equation $T_\ell(y+a)-T_\ell(y)=0$ has at most $\ell-1$ roots; each of these values of $y$ then gives at most $k$ possible values of $x$.
\[ex:23-shifts\] As in Example \[ex:23-dilation\], let $C$ be the $(2,3)$-Chebyshev curve . Applying Proposition \[pr:shifts-lissajous\] (with $k=2$ and $\ell=3$), we see that the curve $C$ and its vertical shift $C_{0,b}$ ($b\neq 0$) can intersect in the affine plane in at most 4 points. More generally, Proposition \[pr:shifts-poly\] (with $d=3$ and $d'=2$) gives the upper bound of 4 for the number of intersection points between $C$ and its nontrivial shift ${C_{a,b}}$. On the other hand, in the case of a horizontal shift, we get at most $3$ points of intersection. When these bounds are attained, with all intersection points real, the union $C\cup{C_{a,b}}$ is expressive. See Figure \[fig:chebyshev23-shifts\].
\[fig:chebyshev23-shifts\]
In addition to shifts and dilations, we can consider other linear changes of variables that can be used to construct new expressive curves. Let us illustrate one such construction using the example of Lissajous-Chebyshev curves:
\[pr:rescale-lissajous\] Let $C$ be the $(k,\ell)$-Lissajous-Chebyshev curve given by , with $\ell>k\ge 2$. For $q\in\CC^*$, $q\neq 1$, let $C_{[q]}$ denote the curve defined by $$\label{eq:lissajous-kl-q}
T_k(\tfrac{x}{q^\ell})+T_\ell(\tfrac{y}{q^k})=0.$$ Assume that $C$ and $C_{[q]}$ intersect at $N$ points in $\AA^2$. Then $$\label{eq:x-rescale-lissajous}
N \le k(\ell-2).$$
Since $T_k(x)=2^{k-1}x^k+O(x^{k-1})$ and $T_\ell(y)=2^{\ell-1}y^\ell+O(y^{\ell-1})$, the equations defining $C$ and $C_{[q]}$ can be written as $$\begin{aligned}
\label{eq:leading-lissajous}
2^{k-1}x^k+O(x^{k-2})+2^{\ell-1}y^\ell+O(y^{\ell-2})&=0, \\
\label{eq:leading-lissajous-q}
2^{k-1}q^{-k\ell}x^k+O(x^{k-2})+2^{\ell-1}q^{-k\ell}y^\ell+O(y^{\ell-2})&=0.\end{aligned}$$ Multiplying by $q^{k\ell}$ and subtracting , we get an equation of the form $$\label{eq:leading-lissajous-q-1}
O(x^{k-2})+O(y^{\ell-2})=0.$$ We thus obtain a system of two algebraic equations of the form and . Their Newton polygons are contained in the triangles with vertices $(0,0), (k,0), (0,\ell)$ and $(0,0), (k-2,0), (0,\ell-2)$, respectively. The mixed area of these two triangles is equal to $k(\ell-2)$ (here we use that $\ell>k\ge 2$ and therefore $\frac{\ell-2}{k-2}>\frac{\ell}{k}$). By Bernstein’s theorem [@DBernstein], this system of equations has at most $k(\ell-2)$ solutions.
\[ex:23-q\] As in Examples \[ex:23-dilation\] and \[ex:23-shifts\], let $C$ be the $(2,3)$-Chebyshev curve . Applying Proposition \[pr:rescale-lissajous\] (with $k=2$ and $\ell=3$), we see that the curve $C$ and the rescaled curve $C_{[q]}$ defined by can intersect in the affine plane in at most 2 points. When they do intersect at 2 real points, the union $C\cup{C_{a,b}}$ is expressive. See Figure \[fig:chebyshev23-q\].
\[fig:chebyshev23-q\]
\[rem:generic-crossings\] Let $C'$ be a curve obtained from a plane curve $C=V(G(x,y))$ of degree $d$ by an arbitrary affine change of variables: $$C'=V(G(c_{11}x + c_{12}y+a,c_{21}x+c_{22}y+b)).$$ Then $C$ and $C'$ intersect in $\AA^2$ in at most $d^2$ points. Thus, if they intersect at $d^2$ hyperbolic nodes, then $C\cup C'$ is expressive. See Figure \[fig:chebyshev23-x\].
\[fig:chebyshev23-x\]
\[ex:5-chebyshevs\] Figures \[fig:chebyshev23-5\]–\[fig:chebyshev34-5\] show five different ways to arrange two Chebyshev curves (the $(2,3)$-Chebyshev cubic and the $(3,4)$-Chebyshev quartic, respectively) related to each other by an affine transformation of the plane $\AA^2$ so that the resulting two-component curve is expressive. These pictures illustrate:
- Proposition \[pr:rescale-lissajous\], cf. Example \[ex:23-q\];
- Proposition \[pr:shifts-lissajous\], cf. Example \[ex:23-shifts\];
- Proposition \[pr:dilations-poly\], cf. Example \[ex:23-dilation\]; and
- Remark \[rem:generic-crossings\].
\
(a) (b) (c) (d) (e)\
\[fig:chebyshev23-5\]
\
(a) (b) (c) (d) (e)\
\[fig:chebyshev34-5\]
\[rem:arrangements-poly\] More generally, consider a collection of expressive polynomial curves related to each other by affine changes of variables (equivalently, affine transformations of the plane $\AA^2$). Suppose that for every pair of curves in this collection, the number of hyperbolic nodes in their intersection attains the upper bound for an appropriate version of Proposition \[pr:dilations-poly\], \[pr:shifts-poly\], \[pr:shifts-lissajous\], \[pr:rescale-lissajous\], or Remark \[rem:generic-crossings\]. Then the union of the curves in the given collection is an expressive curve. See Figures \[fig:three-nodal-cubics\]–\[fig:four-cubics\].
\[fig:three-nodal-cubics\]
\[fig:four-cubics\]
\[fig:three-dilations\]
Arrangements of trigonometric curves {#sec:arrangements-trig}
====================================
In this section, we generalize Example \[ex:circle-arrangements\] to arrangements of curves obtained from a given trigonometric curve by shifts, dilations, and/or rotations.
We continue to use the notation – for the shifted and dilated curves.
\[cor:shift-dilate-trig-2pts-transversal\] Let $C$ be a trigonometric curve of degree $2d$, with two local branches at infinity centered at distinct points $p,\overline{p}\in C\cap L^\infty$. Suppose that $\operatorname{mult}(C,p)=d$, i.e., these branches are transversal to $L^\infty$. Then we have, for $a,b\in\CC$ and $c\in\CC^*$: $$\label{eq:dilate-trig-transversal}
(C\cdot {C_{a,b,c}})_p \ge d^2.$$ If $C$ and ${C_{a,b,c}}$ intersect in $N$ points in the affine plane $\AA^2$, then $N\le 2d^2$.
We apply Proposition \[pr:gen-dilation\], with $S^-(\Gamma(C,p))=\frac12 d^2$, to obtain . It follows that $N\le (2d)^2-2\cdot \frac12 d^2=2d^2$.
\[ex:limacon-shifts\] Let $C$ be an epitrochoid with parameters $(2,-1)$, i.e., a limaçon. It has two conjugate points at infinity, each an ordinary cusp transversal to $L^\infty$. This is a quartic trigonometric curve, so by Corollary \[cor:shift-dilate-trig-2pts-transversal\] (with $d=2$), any two shifts/dilations of $C$ intersect in at most 8 points in the affine plane. Thus, if they intersect at 8 hyperbolic nodes, then $C\cup {C_{a,b,c}}$ is expressive by Theorem \[th:reg-expressive\]. More generally, an arrangement of limaçons related to each other by shifts and dilations gives an expressive curve if any two of these limaçons intersect at 8 hyperbolic nodes. See Figure \[fig:two-limacons-3\].
\[fig:two-limacons-3\]
\[cor:shift-dilate-trig-2pts-tangent\] Let $C$ be a trigonometric curve of degree $2d$, with two local branches at infinity centered at distinct points $p,\overline{p}\in C\cap L^\infty$. Suppose that $m=\operatorname{mult}(C,p)<d$, i.e., $C$ is tangent to $L^\infty$. Then we have, for $a,b\in\CC$ and $c\in\CC^*$: $$\begin{aligned}
\label{eq:dilate-trig}
(C\cdot {C_{a,b,c}})_p &\ge dm, \\
\label{eq:shift-trig}
(C\cdot {C_{a,b}})_p &\ge (d-1)(m+1)+\gcd(d,m).\end{aligned}$$ If $C$ and ${C_{a,b,c}}$ (resp., ${C_{a,b}}$) intersect in $N$ (resp., $M$) points in the affine plane $\AA^2$, then $$\begin{aligned}
\label{eq:}
N &\le 4d^2-2dm; \\
M &\le 4d^2-2(d-1)(m+1)-2\gcd(d,m).\end{aligned}$$
The proof is analogous to the proof of Corollary \[cor:shift-poly\]. We apply Propositions \[pr:gen-dilation\] and \[pr:gen-shift\] to the case under consideration, taking into account that $$\begin{aligned}
S^-(\Gamma(C,p))&=\tfrac12 dm, \\
(C\cdot L^\infty)_p&=d,\\
r(Q)=\eta(Q)&=\gcd(d,m).
\qedhere\end{aligned}$$
\[ex:hypotrochoid-shifts\] Let $C$ be a hypotrochoid with parameters $(2,1)$, cf. Examples \[ex:hypotrochoids\] and \[ex:hypotrochoids-again\]. It has two conjugate points at infinity; at each of them, $C$ is smooth and has a simple (order 2) tangency to $L^\infty$. By (with $d=2$ and $m=1$), any dilation of $C$ intersects $C$ in the affine plane $\AA^2$ in at most 12 points. Similarly, by , any shift of $C$ intersects $C$ in $\AA^2$ in at most 10 points. When these bounds are attained, and all intersections are hyperbolic nodes, the union of the two curves is expressive. See Figure \[fig:two-hypotrochoids\].
\[fig:two-hypotrochoids\]
\[cor:shift-dilate-trig-1pt\] Let $C=Z(F)$ be a trigonometric projective curve of degree $2d$, with two local complex conjugate branches $Q,\overline Q$ centered at the same point $p\in C\cap L^\infty$. Denote $\operatorname{mult}(C,p)=2\operatorname{mult}Q=2m$. Then we have, for $a,b\in\CC$ and $c\in\CC^*$: $$\begin{aligned}
\label{eq:4dm}
(C\cdot {C_{a,b,c}})_p &\ge 4dm, \\
\label{eq:shift-trig-1pt}
(C\cdot {C_{a,b}})_p &\ge
\begin{cases}
4dm-2m+2d+2\gcd(d,m)-2 &\text{if}\ (Q\cdot\overline Q)_p=dm,\\
4dm-2m+2d+2\gcd(d,m) &\text{if}\ (Q\cdot\overline Q)_p>dm.
\end{cases}\end{aligned}$$
Once again, we apply Propositions \[pr:gen-dilation\] and \[pr:gen-shift\], with $$\begin{aligned}
S^-(\Gamma(C,p))&=2dm, \\
(C\cdot L^\infty)_p&=2d,\\
r(Q)&=\gcd(d,m), \\
\eta(Q)&=\begin{cases}\gcd(d,m),\ &\text{if}\ (Q\cdot\overline Q)_p=dm,\\
2\gcd(d,m),\ &\text{if}\ (Q\cdot\overline Q)_p>dm.\end{cases} \end{aligned}$$ and similarly for $\overline Q$.
\[ex:shifts-of-lemniscates\] Let $C$ be a lemniscate of Huygens $$\label{eq:huygens-again}
y^2+4x^4-4x^2=0,$$ see Example \[ex:lemniscates\]. It has a single point $p=(0,1,0)$ at infinity, with two conjugate local branches $Q$ and $\overline Q$. These branches are tangent to each other and to $L^\infty$; all these tangencies are of order 2. Thus Corollary \[cor:shift-dilate-trig-1pt\] applies, with $d=2$, $m=1$, and $(Q\cdot \overline Q)=2=dm$. The bound yields $(C\cdot {C_{a,b}})_p\ge 10$, implying that $C$ and a shifted curve ${C_{a,b}}$ intersect in $\AA^2$ in at most 6 points. Thus, any arrangement of shifts of $C$ which intersect pairwise transversally in 6 real points produces an expressive curve (assuming all these double points are distinct). See Figure \[fig:three-lemniscates\].
![Left: an expressive curve whose three components are translations of the same lemniscate. Each pair of components intersect at six hyperbolic nodes. Right: two lemniscates differing by a vertical shift, see Example \[ex:lemniscate-vertical\].](three-lemniscates.png)
\[fig:three-lemniscates\]
For special choices of shifts and dilations, the bounds in the corollaries above can be strengthened, leading to examples of expressive curves whose components intersect in fewer real points than one would ordinarily expect. Here are two examples:
\[ex:lemniscate-vertical\] Let $C$ be the lemniscate . Since $C$ is a Lissajous-Chebyshev curve with parameters $(4,2)$, by Proposition \[pr:shifts-lissajous\], its vertical shift $C_{0,b}$ intersects $C$ in $\AA^2$ in at most 4 points. Hence $C \cup C_{0,b}$ is expressive for $b\in(-2,2)$. See Figure \[fig:three-lemniscates\].
\[ex:two-exotic-lemniscates\] Let $C=V(G(x,y))$ be the trigonometric curve defined by the polynomial $$\label{eq:exotic-lemniscate}
G(x,y)=x^2+y^4-11y^2+18y-8=x^2+(y+4)(y-1)^2(y-2).$$ It is easy to see that $C$ is expressive, and that $C$ intersects its dilation/reflection $C_{-1}=V(G(-x,-y))$ in two points in $\AA^2$, both of which are real hyperbolic nodes. Hence the union $C\cup C_{-1}$ is expressive. See Figure \[fig:two-exotic-lemniscates\].
\[fig:two-exotic-lemniscates\]
Alternative notions of expressivity {#sec:alternative-expressivity}
===================================
In this section, we discuss two alternative notions of expressivity. For the first notion, algebraic curves are treated as subsets of $\RR^2$, instead of the scheme-theoretic point of view that we adopted above. For the second notion, bivariate polynomials are replaced by arbitrary smooth functions of two real variables.
Viewing real algebraic curves set-theoretically, as “topological curves” in the real affine plane, we arrive at the following definition:
\[def:expressive-curve\] Let $\mathcal{C}\subset\RR^2$ be the set of real points of a real affine algebraic curve, see Definition \[def:curves\]. Assume that $\mathcal{C }$ is nonempty, with no isolated points. We say that $\mathcal{C }$ is *expressive* if its (complex) Zariski closure $C=\overline{\mathcal{C}}$ is an expressive plane algebraic curve. Thus, a subset $\mathcal{C }\subset\RR^2$ is expressive if
- $\mathcal{C }$ is the set of real points of a real affine plane algebraic curve,
- $\mathcal{C }$ is nonempty, with no isolated points, and
- the minimal polynomial of $\mathcal{C }$ is expressive, see Definition \[def:expressive-poly\].
As always, one should be careful when passing from a real algebraic set to an algebraic curve, or the associated polynomial. A polynomial $G(x,y)\!\in\!\RR[x,y]$ can be expressive while the real algebraic set ${V_{\RR}}(G)$ is not; see Example \[example1\] below. Conversely, ${V_{\RR}}(G)$ can be expressive while $G(x,y)$ is not, see Example \[ex:xy(x\^2+y\^2+1)\]. That’s because $G$ may not be the minimal polynomial for ${V_{\RR}}(G)$.
\[example1\] The real polynomials $$\begin{aligned}
G(x,y)&=(x^2+1)(x^2y-x^3+y), \\
\widetilde G(x,y)&=x^2y-x^3+y,\end{aligned}$$ define the same (connected) real algebraic set $\mathcal{C }= {V_{\RR}}(G)={V_{\RR}}(\widetilde G)\subset\RR^2$, cf. . As we saw in Example \[ex:reducible-quintic\], $G$ is expressive while $\widetilde G$ is not. Consequently, the affine algebraic curve $V(G)$ is expressive while its real point set, the real topological curve $\mathcal{C }$ is not—because $\widetilde G$, rather than $G$, is the minimal polynomial of $\mathcal{C }$.
\[ex:xy(x\^2+y\^2+1)\] The real polynomials $G(x,y)$ and $\tilde G(x,y)$ given by $$\begin{aligned}
G(x,y)&=xy(x^2+y^2+1), \\
\widetilde G(x,y)&=xy,\end{aligned}$$ define the same real algebraic set $\mathcal{C }\!=\! {V_{\RR}}(G)\!=\!{V_{\RR}}(\widetilde G)$. Clearly, $\widetilde G$ is expressive, and so is the affine curve $V(\widetilde G)$, or the projective curve $Z(xy)$. Since $\widetilde G$ is the minimal polynomial of $\mathcal{C }$, this real algebraic set is expressive as well. On the other hand, $$\begin{aligned}
G_x&= 3x^2y+y^3+y=y(3x^2+y^2+1), \\
G_y&=x^3+3xy^2+x=x(x^2+3y^2+1),\end{aligned}$$ and we see that $G$ has 9 critical points: $(0,0)$, $(0,\pm i)$, $(\pm i,0)$, $(\tfrac12 i, \pm\tfrac12 i)$, $(-\tfrac12 i, \pm\tfrac12 i)$. Since 8 of these points are not real, the polynomial $G$ is not expressive; nor are the curves $V(G)$ and $Z(xy(x^2+y^2+z^2))$.
The following criterion is a direct consequence of Theorem \[th:reg-expressive\].
Let $\mathcal{C }\subset\RR^2$ be the set of real points of a real affine algebraic curve. Assume that $\mathcal{C }$ is connected, and contains at least two (hence infinitely many) points. Then the following are equivalent:
- the minimal polynomial of $\mathcal{C }$ is expressive and $L^\infty$-regular;
- each component of $C=\overline{\mathcal{C}}$ is trigonometric or polynomial, and all singular points of $C$ in the complex affine plane $\AA^2$ are real hyperbolic nodes.
We conclude this section by discussing the challenges involved in extending the notion of expressivity to arbitrary smooth real functions of two real arguments.
\[rem:expressive-analytic\] Let $G:\RR^2\to\RR$ be a smooth function. Suppose that
- the set ${V_{\RR}}(G)=\{G(x,y)=0\}\subset\RR^2$ is connected;
- ${V_{\RR}}(G)$ is a union of finitely many immersed circles and open intervals which intersect each other and themselves transversally, in a finite number of points;
- the complement $\RR^2\setminus{V_{\RR}}(G)$ is a union of a finite number of disjoint open sets;
- all bounded connected components of this complement are simply connected;
- all critical points of $G$ in $\RR$ have a nondegenerate Hessian;
- these critical points are located as follows:
- one critical point inside each bounded connected component of $\RR^2\setminus{V_{\RR}}(G)$;
- no critical points inside each unbounded connected component of $\RR^2\setminus{V_{\RR}}(G)$;
- a saddle at each double point of ${V_{\RR}}(G)$.
One may be tempted to call such a (topological, not necessarily algebraic) curve ${V_{\RR}}(G)$ expressive. Unfortunately, this definition turns out to be problematic, as one and the same curve $\mathcal{C}=\RR^2$ can be defined by two different smooth functions one of which satisfies the above-listed conditions whereas the other does not. An example is shown in Figure \[fig:isolines\], with the polynomial $G$ given by $$G(x,y)=(\tfrac{x^{2}}{16}+y^{2}-1)((x-1)^{2}+(y-1)^{2}-1).$$ As the picture shows, the function $G$ is not expressive (in any reasonable sense). At the same time, $\mathcal{C}$ can be transformed into an expressive curve (a union of two circles) by a diffeomorphism of $\RR^2$, and consequently can be represented as the vanishing set of a smooth function satisfying the conditions listed above.
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M. L. Sodin and P. M. Yuditskiĭ, Functions that deviate least from zero on closed subsets of the real axis, *Algebra i Analiz* **4** (1992), 1–61; translation in *St. Petersburg Math. J.* **4** (1993), 201–249.
R. P. Stanley, An introduction to hyperplane arrangements, *Geometric combinatorics*, 389–496, IAS/Park City Math. Ser., 13, AMS, 2007.
W. van der Kulk, On polynomial rings in two variables, *Nieuw Arch. Wisk. (3)* **1** (1953), 33–41.
R. J. Walker, *Algebraic curves*, Springer, NY, 1978.
[^1]: *2020 Mathematics Subject Classification*: Primary 14H50. Secondary 05E14, 14H20, 14H45, 14P05, 14Q05, 51N10.
[^2]: Partially supported by NSF grant DMS-1664722 (S. F.), a Simons Fellowship (S. F.), the ISF grant 501/18, and the Bauer-Neuman Chair in Real and Complex Geometry (E. S.).
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D. Baking powder is used in baking to make cake batter and bread dough rise. The big advantage of baking powder over yeast is that it works instantly.
What does baking powder do to dough?
Baking powder is a two-in-one chemical leavening that combines a powdered alkali (sodium bicarbonate) with a powdered acid (originally, tartaric acid). When moistened in a dough or batter, a chemical reaction takes place that produces carbon dioxide gas, inflating cookies, cakes, and pancakes.
How long does it take for dough to rise with baking powder?
The reason why people often prefer baking powder to yeast is because yeast takes so long — usually two to three hours — to produce its bubbles. Baking powder is instant, so you can mix up a batch of biscuits and eat them 15 minutes later.
Can you add baking powder to bread dough?
When making bread without yeast, baking powder is an effective alternative since it also produces gas. If you’re making bread that contains yeast, you won’t get much benefit from adding baking powder, so it’s needless. Instead, you should use yeast alone and leave the baking powder for recipes that don’t include yeast.
Does baking powder ferment?
Baking powder does not ferment a dough. It is a chemical leavening agent. It’s action ends when the chemical reaction ceases, or falls below a level where it can be considered active.
What happens if I put too much baking powder?
Too much baking powder can cause the batter to be bitter tasting. It can also cause the batter to rise rapidly and then collapse. (i.e. The air bubbles in the batter grow too large and break causing the batter to fall.) Cakes will have a coarse, fragile crumb with a fallen center.
How much baking powder is needed per cup of flour?
Typically, a recipe with one cup of all purpose flour should include about 1 to 1 1/4 teaspoons of baking powder.
Can I leave dough to rise overnight?
Can I leave my bread to rise overnight? Yes, you can let your bread rise overnight in the fridge. Keep in mind, though, you’ll want the dough to come back up to room temperature before baking.
How do you tell if dough has risen enough?
If the indentation disappears, the dough needs more rising time. Make the same test when you have the shaped dough rising in the pan just before baking. When you think it has risen enough, use your finger to make a SMALL dent in the dough near the side of the pan. If the dent remains, the bread is ready to bake.
Can dough rise in the fridge?
Yes, risen dough CAN be placed in a refrigerator. Putting risen dough in the fridge is a common practice of home and professional bakers alike. Since yeast is more active when it’s warm, putting yeasted dough in a refrigerator or chilling it slows the yeast’s activity, which causes dough to rise at a slower rate.
What happens if you put too much baking soda in bread?
Using too much baking soda or baking powder can really mess up a recipe, causing it to rise uncontrollably and taste terrible.
What happens if you add yeast to self rising flour?
If you were to use both self-rising flour and yeast, your bread would likely rise too much, which can cause the top to crack and even cave in. It will also affect the flavor.
What happens if you use yeast and baking powder?
Yeast and baking powder leaven bread by creating carbon dioxide gas, which creates air pockets that get caught in a gluten structure. Yeast acts much more slowly than baking powder, so much of the leavening action of baking powder would be spent by the time the bread is put in the oven.
What’s the difference between yeast and baking powder?
Yeast: What’s the Difference? Although both baking powder and yeast are ingredients often used in baking, they aren’t the same. Baking powder is a chemical leavening agent, whereas yeast is a live, single-celled organism, Tracy Wilk, lead chef at the Institute of Culinary Education, explains.
Can I make bread with baking powder instead of yeast?
In baked goods, you can replace yeast with an equal amount of baking powder. Just keep in mind that the leavening effects of baking powder will not be as distinct as those of yeast. Baking powder causes baked goods to rise rapidly, but not to the same extent as yeast.
Which is healthier baking powder or yeast?
Baking powder is most commonly used in recipes that do not contain an additional acid, therefore, solely water and heat are required. Yeast differs from both baking soda and baking powder, mainly because it is a live organism and takes substantially longer to leaven dough. | https://solefoodkitchen.com/baking/will-baking-powder-make-dough-rise.html |
In the process of laminating or molding structures made from plastic composite materials such as fiber-reinforced resins, care must be taken to eliminate internal voids resulting from the entrapment in the material of air pockets or of gas bubbles formed by the vaporization of moisture, solvents and other residual volatile components.
Air pockets can be formed during the mixing and pouring of the material. Gas bubbles occur mainly during heating and curing phases of the processes.
Until now the most common and practical method for eliminating internal voids has been to enclose the mass of material being molded or laminated into a fluid-tight envelope, typically a bag of plastic sheet material connected to a vacuum pump. Air pockets and gas bubbles which may form in the plastic material are sucked out by the vacuum pump during exposure to internal pressure of an autoclave, and during the pressing, molding and curing cycles. The envelope also acts as a barrier against reentry of air or other ambient gas after the vacuum pull is interrupted or terminated during handling of the material between cycles.
The plastic bag or other fluid-tight envelope is a cumbersome element that, not only impairs the convenient manipulation of the material throughout the various manufacturing cycles, but can also result in the formation of flaws over the surface of the manufactured articles due to folds and creases in the envelope material.
The instant invention results from attempts to palliate the above-described inconvenience and problems by avoiding the need of any vacuum bag or other fluid-tight barrier between the composite material and the surfaces of the laminating or molding implements.
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Salt stimulation of growth and photosynthesis in an extreme halophyte, Arthrocnemum macrostachyum
S. Redondo-Gómez, Dpto. Biología Vegetal y Ecología, Facultad de Biología, Universidad de Sevilla, Av Reina Mercedes s/n, 41012 Sevilla, Spain.
E-mail: [email protected]
Editor
T. Elzenga
Abstract
Halophytes that are capable of tolerating a wide range of salinity may grow best at intermediate salinities, but the physiological mechanisms underlying positive growth responses to salinity are not clear. This work investigated the growth of Arthrocnemum macrostachyum (Moric) C. Koch (a halophytic C3 shrub) over a wide range of salinities, and the extent to which its responses can be explained by photosynthetic physiology. Growth, gas exchange and chlorophyll fluorescence characteristics of plants were examined in a glasshouse experiment; tissue concentrations of photosynthetic pigments, ash, sodium, potassium, calcium and nitrogen were also determined. Plants showed marked stimulation of growth by salt, with a broad optimum of 171–510 mm NaCl for relative growth rate (RGR). Stimulation of RGR appeared to depend mainly on an increase in specific shoot area, whereas reduced RGR at high salinity (1030 mm) could be attributed to a combination of lower unit shoot (leaf) rate and lower shoot mass fraction. The non-saline treatment plants had the greatest fraction of non-photosynthetic, atrophied surface area. However, net photosynthesis (A) was also stimulated by NaCl, with an optimum of c. 510 mm NaCl. The responses of A to salinity could be accounted for largely by limitation by stomatal conductance (Gs) and intercellular CO2 concentration (Ci). Even the most hypersaline treatment apparently had no effect on photosystem II (PSII) function, and this resistance could be an important strategy for this halophyte in saline soils. In contrast, Fv/Fm indicated that absence of salt represents an environmental stress for A. macrostachyum and this could be a contributory factor to salt stimulation of A. Notwithstanding the importance of the ability to develop and maintain assimilatory surface area under saline conditions, stimulatory effects on A also appear to be part of a suite of halophytic adaptations in this plant. | http://onlinelibrary.wiley.com/doi/10.1111/j.1438-8677.2009.00207.x/abstract |
World-famous astrophysicist and media personality recognized for his promotion of science in America.
World-famous astrophysicist and media personality Dr. Neil deGrasse Tyson has been named by ARCS® Foundation as its 2018 inductee into the ARCS Alumni Hall of Fame. It is a rare honor, bestowed on ARCS Scholar Alumni who have made outstanding contributions to the advancement of science and to increase our nation’s scientific competitiveness.
Dr. Tyson, who was an ARCS Scholar in 1991 while pursuing his PhD in the Department of Astronomy at Columbia University in New York City, is currently Director of the Hayden Planetarium and a research associate in the department of astrophysics at the American Museum of Natural History. He has hosted educational science radio programs, podcasts and television including NOVA Science Now, Star Talk, and Cosmos: A Spacetime Odyssey, which is an update to Carl Sagan's Cosmos television series. He is a prolific science writer and sought-after speaker.
Selection to the ARCS Alumni Hall of Fame is done is by a panel appointed by the national president and is based on alumni contributions in the areas of scientific innovation, discovery, economic impact, development of future scientists, and communications that increase awareness of the importance of US scientific superiority. Previous inductees can be found here.
Dr. Tyson discusses the significance being an ARCS Scholar. | https://arcsfoundation.org/news/arcs-alumni-hall-fame-welcomes-dr-neil-degrasse-tyson |
Have you witnessed one of those cringe-worthy interactions in which someone is trying to get an idea across to someone else who does not speak the language? “Can you please tell me where this bus goes?” the lost tourist asks the local at the bus stop. When meet with a shrug and a bewildered look, the tourist repeats the question, this time slower. And then again, louder and even slower. While we, as witnesses, may understand the tourist’s frustration – we also can see that the repeated attempts to communicate are not going to be effective. It is not the well-meaning local’s fault that he cannot understand the tourist. Instead, the onus is on the tourist to find other ways to make herself understood.
“How many times do I need to tell you…?” “If I’ve told you once, I’ve told you a thousand times …” These are phrases that often escape the lips of adults, who like the exasperated tourist, are just trying to make themselves understood. But, like the tourist, just using the same words over and over are not likely to result in a change in a child’s behavior. Once born, we spend the rest of our lives trying to make sense of this crazy world. Ideas that make a lot of sense to adults (like the fact that hitting is not an acceptable behavior) is as foreign to a child as someone speaking an unfamiliar language. Expecting a child to automatically comprehend and integrate this norm into their behavior is not a reasonable expectation. Instead, it is up to teachers to find a way to communicate so that a child understands; both what they did wrong and expectations for appropriate behavior.
Proactively, we need to make sure that we are clear with our expectations so that children know what they need to do and if they are being successful in meeting them. “Sit still” may mean something very different to a teacher than it does for a child. So, as obvious as it may seem, a teacher can make it more likely that a child will meet expectations by clearly explaining and modeling the desired behavior. At school, lunch means sitting at a table and eating the food that is on the plate in front of you. At home, a meal might be eaten in a car seat on the way to a ball game, on a couch with my family surrounding me as we watch a favorite show, or on someone’s lap as we share food from a community dish. By defining expectations, a teacher can also help children exhibit desired behaviors at nap, meals, and during transitions.
These particular times of day can be confusing for young children, especially if classroom expectations are different from those as home. Teachers can lessen these behaviors by proactively making sure that children and teachers are all speaking the same language.
The same strategy can be used when correcting children’s behaviors. “Nice hands” may be a very clear instruction from a teacher’s perspective; but equally confusing from a child’s point of view. Children are much more likely to comply with directions that are simple and tell them exactly what to do. As an alternative to “nice hands”, “hands down” provides a clear directive as to what a teacher wants a child to do. Think about other common phrases teachers might use in the classroom; “no thank you”, “crisscross applesauce”, or “we are nice to our friends”. Consider how these might be rephrased to provide concise directions that are easy for children to understand.
In the scenario presented at the start of this post, it is not the local’s responsibility to learn the language the tourist wants to use. When they are both on the same page, the tourist and local are much more likely to have a positive interaction. In the same way, when a teacher strives to find ways to communicate that children understand; the result is often more positive behaviors in the classroom.
What do you think? Engage with me and others in the ECE community on my social media outlets. You can also find more information about my book and available training sessions, on any of the following: | http://michellesalcedo.com/wp/2018/05/29/understandable-expectations/ |
Abstract art could be seen as having lost its way. With the invention of the internet these shapes that were once sparingly used have been mimicked to the point of little meaning, sometimes even ruining the aesthetic sense. This is why it’s rare to see abstract work that’s full of pure expression. Just through the brush strokes alone we are able to see movement and a playfulness that’s quite unique considering the probability of this diminishing the older we get.
New York-based Chicago born Matt Connors’ on the other hand has been able to keep his child-like powers, producing these abstract artworks that have a strong focus on colour and shape. His works rely heavily on brush technique and share obvious parallels with minimalism and abstraction. Reading his bio and hearing that his work is also influenced by all the fields, such as design, music, poetry, and writing, it made me think deeply about the different references needed to create truly individual works of art. It’s important to look at all these fields and take elements that inspire you so that you can bring them forward in to your own creations. The most abstract subjects might offer the most fruitful results.
You may notice links in Matt’s work and this is not coincidental by any means. There is usually a dialogue going on and one canvas often informs another, on the spot development of sorts. Although a lot of this is about having a good eye and working like an architect in a structural sense, with Matt’s fluid strokes and sometimes erratic movements it elevates this work to a new level and gives an emotion I rarely see in this kind of work. Here are a selection of my favourite pictures from his portfolio, I recommend you view more on the webpage below and also research the various galleries that hold exhibits of his work. He is a true talent and one that’s definitely inspiring. | https://the189.com/art/playful-movement-a-selection-of-abstract-art-by-american-creative-matt-connors/ |
Please check back for more events.
Past Events
Buses on-demand
How flexible, on-demand bus services can help Scotland build back fairer
24 March 2021
This webinar was aimed at local authorities, policy makers and all who are interested in learning more about the opportunities for Scotland from moving to flexible on-demand transport. We heard from a range of on-demand transport operators about the range of services they offer and hear about some examples of successful schemes happening across the UK and Europe.
Building Better Places: 10 March 2021
This webinar focussed on the future of planning in Scotland and how shared transport can help deliver the key outcomes of the NPF4: net zero emissions, resilient communities, a wellbeing economy and greener, better places. We took an in-depth look at the role of shared transport and mobility hubs and their positive contribution to the Scottish Government’s 20-minute neighbourhoods strategy and looked at some of the cutting edge plans being developed here in Scotland.
The event was aimed at planners, developers, architects, landscape architects, academics and related practitioners and organisations. This was reflected in our speakers, representing planning, urban design. Watch the event using the link below.
Shared Mobility Rocks: 3/4 March 2021
We took part in the third edition of this global shared mobility event over 24 hours from 3-4 March. CoMoUK ran the 3:00-4:30pm GMT session on the first day, discussing “the latest evidence for the impacts of shared mobility”. For more details and to see replays visit the event website below.
Future Rural Mobility: 4 February 2021
We held a session on future rural mobility, in light of the Government call for evidence on this, which closed 16th February 2021.
Mobility Hub Forum Business Models : 28 January 2021
Held with our partners at WSP, we heard the latest findings on thoughts around successful business models for mobility hubs and discussed the application of them in workshop groups.
Setting up a Scottish Bike Share Scheme: 8 December 2020
Our third webinar in the Scotland Co-mobility series where we tried to answer key questions around setting up a bike share scheme in Scotland.
Are you a community group in Scotland keen to share a fleet of bikes for the use of your community? Do you have a thousand questions about how to do this, for example how to get started? How to share the bikes? How to promote the scheme? What does success look like?
Collaborative Mobility Virtual Conference: 17-20 November 2020
CoMoUK would like to thank all the speakers and sponsors who made this year’s annual conference a success.
Each day during the 4 day event we had two 90 minute sessions where we took a look back over an extraordinary year of innovations and adaptions, as well as looking forward to how we can share and apply new learning.
For more details please visit the conference page:
CONFERENCE 2020 View all conference session recordings
Pedalling a Green Recovery: Scotland’s Bike Share and a Greener Future: 29 September 2020
Our second webinar in the Scotland Co-mobility series ‘Pedalling a Green Recovery’ where we will explored how we can unlock the potential of bike share in Scotland and gave a snap shot of the different types of schemes providing healthy, affordable and low carbon forms of travel in communities across the country.
Implementing Mobility Hubs in a Rural Area: 21 July 2020
Our series of webinars continues with speakers from Scotland and The Netherlands discussing setting up Mobility Hubs in rural areas of Scotland.
Mobility Hubs: 14th May 2020
Session 1 – Introduction, benefits, EU experience inc. Bremen Mobility Hub Development
Recording Slides Bremen Slides
Session 2 – UK activity and opportunities for collaboration inc. Gascoyne Estates
Recording SLIDES GASCOYNE SLIDES
If you are interested in joining a network to collaborate on certain aspects of mobility hub development please complete this very short survey:
Shared mobility: key to tackling the climate crisis, 19th March 2020
In the ongoing debate about how we can tackle the climate crisis and build a sustainable future, shared transport will have an important role to play in helping achieve Scotland’s ambitious net zero targets. CoMoUK is bringing together some of the country’s top shared mobility experts, operators, policy makers and influencers to discuss and debate how we can reshape Scotland’s transport future to deliver this net zero ambition.
We will be showcasing our new research on the potential for shared mobility in Scotland and the associated environmental, economic, health and social benefits.
In our webinar we launched CoMoUK’s latest annual car club and bike share surveys looking at their impact on cutting carbon, reducing dependency on the private car and improving air quality and congestion.
Scottish Co-Mobility Forum, Small to Medium Employers and Liftshare, 29th January 2020
Aimed at small to medium sized employers – this 45 minute webinar will focus on the more informal lift share shared ride/shared bike options that are available to SMEs, with signposting to regional options across Scotland.
Scottish Co-Mobility Forum, Large Employers and Liftshare, 22nd January 2020
Aimed at Large Employers – this 45 minute webinar will focus on the lift share schemes and formalised shared ride options such as car clubs that are available to larger employers, with signposting to regional options across Scotland.
Scottish Co-Mobility Forum, Bikes for All, 27th November 2019
Learn how Bikes for All, a Glasgow-based cycling inclusion project, helps to reduce inequalities in access to cycling through the provision of low-cost bike hire, building cycling confidence and reducing barriers to cycling for first-time or lapsed cyclists.
Collaborative Mobility Conference, 12th – 13th November 2019
All of the presentations and information from the day are still available to view.
Scottish Co-Mobility Forum, MobiHubs and Opportunity for Scotland, 30th September 2019
Hear from experts from the shared mobility and Mobihub sector. Learn what Mobihubs are, how they promote sustainable travel, and the benefits they can bring to local communities.
Co-Mobility Forum, 19th June 2019 – Car Clubs out of Urban Centres
This session explored the strategies and opportunities to create successful car clubs away from dense city environments. It was a chance to hear from those working actively in the field to develop partnerships and operating models to address the challenges of viability in our suburbs, towns and rural areas.
The representatives we heard from were;
- Keith Kelly, Enterprise Car Club
- Martin Higgitt, Martin Higgitt Associates
- Robert Schopen, Co-Wheels
- Jeffrey Matthijs, Autodelen, Belgium
After the presentations, there was a short question and answer session led by CoMoUK’s new Chief Executive Richard Dilks.
Shared Transport Masterclass
CoMoUK partnered with Landor Links to deliver a masterclass for local authorities planning or working with shared transport schemes – from bike share to car clubs, demand responsive transport to micro mobility. Shared transport innovations offer a host of new opportunities, if you were unable to attend the event we are delighted to be able to share the slides with you.
Collaborative Mobility; Good Mobility 2018
The Collaborative Mobility Conference 2018 was held in September at the Crystal, Docklands in London. All of the presentations and information from the day are still available to view. | https://como.org.uk/events/ |
All users (i.e. students, staff, administration, parents, school board members, community members and others) must sign the Acceptable Use of Electronic Networks and Technology form before using the district's electronic network and information services. For the 2022-23 school year, all parents/guardians will co-sign the student form at the time of registration. Beginning with the 2023-24 school year, this form will only be signed once with any new enrollment in the school district.
All use of the District’s electronic networks shall be consistent with the District’s goal of promoting educational excellence by facilitating resource sharing, innovation, and communication. These procedures do not attempt to state all required or prohibited behavior by users. However, some specific examples are provided. The failure of any user to follow these procedures will result in the loss of privileges, disciplinary action, and/or legal action.
The term electronic networks includes all of the District’s technology resources, including, but not limited to:
- The District’s local-area and wide-area networks, including wireless networks (Wi-Fi), District-provided Wi-Fi hotspots, and any District servers or other networking infrastructure;
- Access to the Internet or other online resources via the District’s networking infrastructure or to any District-issued online account from any computer or device, regardless of location;
- District-owned and District-issued computers, laptops, tablets, phones, or similar devices.
Acceptable Use
Access to the District’s electronic networks must be: (a) for the purpose of education or research, and be consistent with the District’s educational objectives, or (b) for legitimate business use.
Privileges
Use of the District’s electronic networks is a privilege, not a right, and inappropriate use will result in a cancellation of those privileges. The system administrator or Building Principal will make all decisions regarding whether or not a user has violated these procedures and may deny, revoke, or suspend access at any time. His or her decision is final.
Unacceptable Use
The user is responsible for his or her actions and activities involving the networks. Some examples of unacceptable uses are:
- Using the networks for any illegal activity, including violation of copyright or other intellectual property rights or contracts, or transmitting any material in violation of any State or federal law;
- Using the electronic networks to engage in conduct prohibited by board policy;
- Unauthorized downloading of software or other files, regardless of whether it is copyrighted or scanned for malware;
- Unauthorized use of personal removable media devices (such as flash or thumb drives);
- Downloading of copyrighted material for other than personal use;
- Using the electronic networks for private financial or commercial gain;
- Wastefully using resources, such as file space;
- Hacking or attempting to hack or gain unauthorized access to files, accounts, resources, or entities by any means;
- Invading the privacy of individuals, including the unauthorized disclosure, dissemination, and use of information about anyone that is of a personal nature, such as a photograph or video;
- Using another user’s account or password;
- Disclosing any network or account password (including your own) to any other person, unless requested by the system administrator;
- Posting or sending material authored or created by another without his/her consent;
- Posting or sending anonymous messages;
- Creating or forwarding chain letters, spam, or other unsolicited messages;
- Using the electronic networks for commercial or private advertising;
- Accessing, sending, posting, publishing, or displaying any abusive, obscene, profane, sexual, threatening, harassing, illegal, or knowingly false material;
- Misrepresenting the user’s identity or the identity of others; and
- Using the electronic networks while access privileges are suspended or revoked.
Network Etiquette
The user is expected to abide by the generally accepted rules of network etiquette. These include, but are not limited to, the following:
- Be polite. Do not become abusive in messages to others.
- Use appropriate language. Do not swear, or use vulgarities or any other inappropriate language.
- Do not reveal personal information, including the addresses or telephone numbers, of students or colleagues.
- Recognize that email is not private. People who operate the system have access to all email. Messages relating to or in support of illegal activities may be reported to the authorities.
- Do not use the networks in any way that would disrupt its use by other users.
- Consider all communications and information accessible via the networks to be private property.
No Warranties
The District makes no warranties of any kind, whether expressed or implied, for the service it is providing. The District will not be responsible for any damages the user suffers. This includes loss of data resulting from delays, non-deliveries, missed-deliveries, or service interruptions caused by its negligence or the user’s errors or omissions. Use of any information obtained via the Internet is at the user’s own risk. The District specifically denies any responsibility for the accuracy or quality of information obtained through its services.
Indemnification
The user agrees to indemnify the School District for any losses, costs, or damages, including reasonable attorney fees, incurred by the District relating to, or arising out of, any violation of these procedures.
Security
Network security is a high priority. If the user can identify a security problem on the Network, the user must notify the system administrator or Building Principal. Do not demonstrate the problem to other users. Keep your account and password confidential. Do not use another individual’s account without written permission from that individual. Attempts to log-on to the Network as a system administrator will result in cancellation of user privileges. Any user identified as a security risk may be denied access to the networks.
Vandalism
Vandalism will result in cancellation of privileges and other disciplinary action. Vandalism is defined as any malicious attempt to harm or destroy data of another user, the Internet, or any other network. This includes, but is not limited to, the uploading or creation of computer viruses.
Telephone Charges
The District assumes no responsibility for any unauthorized charges or fees, including telephone charges, long-distance charges, per-minute surcharges, and/or equipment or line costs.
Copyright Web Publishing Rules
Copyright law and District policy prohibit the re-publishing of text or graphics found on the web or on District websites or file servers without explicit written permission.
- For each re-publication (on a website or file server) of a graphic or a text file that was produced externally, there must be a notice at the bottom of the page crediting the original producer and noting how and when permission was granted. If possible, the notice should also include the web address of the original source.
- Students and staff engaged in producing web pages must provide library media specialists with email or hard copy permissions before the web pages are published. Printed evidence of the status of “public domain” documents must be provided.
- The absence of a copyright notice may not be interpreted as permission to copy the materials. Only the copyright owner may provide the permission. The manager of the website displaying the material may not be considered a source of permission.
- The fair use rules governing student reports in classrooms are less stringent and permit limited use of graphics and text.
- Student work may only be published if there is written permission from both the parent/guardian and student.
Use of Email
The District’s email system, and its constituent software, hardware, and data files, are owned and controlled by the School District. The School District provides email to aid students and staff members in fulfilling their duties and responsibilities, and as an education tool.
- The District reserves the right to access and disclose the contents of any account on its system, without prior notice or permission from the account’s user. Unauthorized access by any student or staff member to an email account is strictly prohibited.
- Each person should use the same degree of care in drafting an email message as would be put into a written memorandum or document. Nothing should be transmitted in an email message that would be inappropriate in a letter or memorandum.
- Electronic messages transmitted via the School District’s Internet gateway carry with them an identification of the user’s Internet domain. This domain is a registered name and identifies the author as being with the School District. Great care should be taken, therefore, in the composition of such messages and how such messages might reflect on the name and reputation of the School District. Users will be held personally responsible for the content of any and all email messages transmitted to external recipients.
- Any message received from an unknown sender via the Internet should either be immediately deleted or forwarded to the system administrator. Downloading any file attached to any Internet-based message is prohibited unless the user is certain of that message’s authenticity and the nature of the file so transmitted.
- Use of the School District’s email system constitutes consent to these regulations.
Software Regulations and Procedures
The schools and district offices of Woodridge 68 license the use of computer software from a variety of third parties. The software developer normally copyrights such software. Unless expressly authorized to do so, Woodridge 68 has no right to make copies of the software except for backup or archival purposes. The purposes of the regulation are to prevent copyright infringement and to protect the integrity of District 68’s computer environment.
Guidelines
It is the position of the District to respect all computer software copyrights and to adhere to the terms of all software licenses to which the district is a party. The Director of Technology is the district’s software manager, and is charged with the responsibility for enforcing these guidelines.
District employees may not duplicate any licensed software or related documentation for use either on the District premises or elsewhere unless the District is authorized to do so by the agreement with the licenser. Unauthorized duplication of software may subject employees and/or the District to both civil and criminal penalties under the United States Copyright Act. Employees may not give standalone software to any other employee or any software to non-employees including students, parents, and others. District employees may use software on local area networks or on multiple machines only in accordance with applicable license agreements.
Acquisition of Software
All software acquired by the District must be purchased using the school or district accounts. Software acquisition procedures are restricted to ensure that the District has a complete record of all software that has been purchased and can register, support, track and upgrade such software accordingly.
Registration of Software
The schools and district must register every software package. Software must be registered in the name of the district or school/department in which it is used. Because of personnel turnover, software should never be registered in the name of the individual user. IT will keep a record of all district-purchased licenses.
These records shall include the following information:
- Title and publisher of all software including freeware and public domain
- Date and source of the software acquisition
- Location of each installation as well as the serial number of the hardware on which each copy of the software is installed
- Name of the authorized user(s) – as applicable
- Existence and location of backup copies
- The software product’s serial number.
Non-District Owned Software
Only software purchased through the District may be used on District computers. Employees are not permitted to install non-district owned software on district computers. Generally, district-owned software cannot be installed on non-district owned computers. However, if an employee requests to use software on a non-district owned computer, after appropriate approval, the District may purchase a separate package and record it in the software catalog.
Some software companies provide in their license agreements that home use is permitted under certain circumstances. Before installing any software, the license must be reviewed.
Software Audits
The IT team reserves the right to conduct an audit at any time. Any non-licensed or unapproved software found on district/school computers will be uninstalled or the computer will be ghosted and returned to stand settings and programs.
Consequences of Inappropriate Use
All students, staff, and other users of the district computers will be subject to the penalties and reprimands as defined in Board Policy if they are found to be in violation of the Acceptable Use Standards or any law or statute under which the district operates.
Internet Safety
Internet access is limited to only those acceptable uses as detailed in these procedures. Internet safety is almost assured if users will not engage in unacceptable uses, as detailed in these procedures, and otherwise follow these procedures.
Staff members shall supervise students while students are using District Internet access to ensure that the students abide by the Terms and Conditions for Internet access contained in these procedures.
Each District computer with Internet access has a filtering device that blocks entry to visual depictions that are: (1) obscene, (2) pornographic, or (3) harmful or inappropriate for students, as defined by the Children’s Internet Protection Act and as determined by the Superintendent or designee.
The system administrator and Building Principals shall monitor student Internet Access.
6420R2 Administration
Adopted: January 28, 2002
Amended: January 24, 2022
All users (i.e. students, staff, administration, parents, school board members, community members and others) must sign the Google Workspaces Permission form before being issued a district-owned Google account. For the 2022-23 school year, all parents/guardians will co-sign the student form at the time of registration. Beginning with the 2023-24 school year, this form will only be signed once with any new enrollment in the school district.
Woodridge School District 68 supports the use of Google Workspace accounts for students and teachers. The use of Google Workspaces supports our desire to have students create, collaborate, communicate, and use critical thinking skills in the learning process. The most important aspect of Google Workspaces for our current work with students is access to Google Docs. Google Docs allows students to create and share word processing, presentation, and spreadsheet documents online, and to collaborate with both peers and teachers on projects. Students are able to log into their Woodridge Google Workspaces account at home, the library, or anywhere where Internet access is available. Teachers are able to log into their accounts to provide feedback to students at anytime and anywhere an Internet connection is available.
Included Services
The following services are included but not limited to each student and hosted by Google as part of Woodridge School District 68’s online presence in Google Workspaces:
- Email - an individual email account for students in grades 2-8 for school use managed by Woodridge School District 68. Students only have the ability to send/receive email to/from their teachers.
- Calendar - an individual calendar providing the ability to organize schedules, daily activities, and assignments
- Docs/Drive - a word processing, spreadsheet, drawing, and presentation toolset that is very similar to Microsoft Office
- Sites - an individual and collaborative website creation tool
Using these tools, students collaboratively create, edit and share files and websites for school related projects. School staff will monitor student use of Apps when students are at school. Parents are responsible for monitoring their child’s use of Apps when accessing programs outside of school. Students are responsible for their own behavior at all times. Examples of student use include; showcasing class projects, building an electronic portfolio of school learning experiences, and working in small groups on presentations to share with others.
Technology use in Woodridge School District 68 is governed by federal laws including the Children's Online Privacy Protection Act (COPPA). COPPA applies to commercial companies and limits their ability to collect personal information from children under 13. By default, advertising is turned off for Woodridge School District 68’s presence in Google Workspaces. No personal student information is collected for commercial purposes. This permission form allows the school to act as an agent for parents in the collection of information within the school context. The school's use of student information is solely for education purposes. https://www.ftc.gov/tips-advice/business-center/guidance/complying-coppa-frequently-asked-questions
Guidelines for the responsible use of Google Workspaces by students
- Official Email/Google User Account. All students will be assigned a [email protected] user account.
- Conduct. Students are responsible for good behavior just as they are in a traditional school building. Students are not permitted to use obscene, profane, threatening, or disrespectful language. Communication with others should always be school related. Students should notify the teacher of anything inappropriate or that makes them uncomfortable. Bullying will not be tolerated, and the privacy of others should be respected at all times. All provisions of the Parent/Student Handbook, including the Authorization for Electronic Network Access Form, apply to student use of Google Workspaces, whether access through the District or outside of school.
- Access Restriction. Access to, and use of, student account is considered a privilege accorded at the discretion of Woodridge School District 68. The District maintains the right to immediately withdraw the access and use of these services when there is reason to believe that violations of the law or District policies have occurred. In such cases, the alleged violation will be referred to a building administrator for further investigation and adjudication. All use of the Google Workspaces Account must be limited to legitimate educational purposes consistent with the District’s curriculum.
- Security. Students should never share their login information with anyone.
- Privacy. Woodridge School District 68 and all electronic users should treat electronically stored information in individuals' files as confidential and private. Users of student accounts are strictly prohibited from accessing files and information other than their own. The District reserves the right to access the user’s Google account, including current and archival files of user data, at will of when deemed appropriate by administrators. | https://www.woodridge68.org/site/default.aspx?PageType=3&ModuleInstanceID=6388&ViewID=7b97f7ed-8e5e-4120-848f-a8b4987d588f&RenderLoc=0&FlexDataID=9965&PageID=2310&Comments=true |
*subject to validation
The study of History helps you to understand how individuals, communities and societies have lived in the past and how those past experiences have helped to shape the present world. History helps us make sense of our world and understand what may lie ahead because the future is shaped by its history in so many ways. Our History degree gives you the opportunity to study a wide-range of historical periods and topics with elements in British, Irish, European and International History from the late medieval age to the twentieth century.
By studying with us, you can study a range of topics from the Twentieth Century to the Early Modern period. You will engage with a wide variety of historical evidence throughout the whole of your degree programme. History at Liverpool Hope is part of the supportive and friendly environment of the Department of History and Politics. You will benefit from being taught by a team of recognised scholars and experts in their fields who are dedicated and experienced teachers and researchers and regular publishers of their research.
Throughout your degree, you will be able to take advantage of the rich library, archival, museum and heritage resources available in Liverpool and further afield, as well as benefit from our partnership with National Museums Liverpool. Working with the staff and resources of the World Museum, the new Museum of Liverpool and the Maritime Museum and its associated International Slavery Museum forms an important part of your learning experiences. The department runs a range of fieldwork activities every year in the local area and beyond, and offers the opportunity for study visits to major European cities each year.
For more details and information about this course visit:
Contemporary society is becoming ever more complex and the need to understand how it works is increasingly important. Sociology is the study of how society is organised, how this influences the attitudes and behaviour of individuals and the impact this has on social relationships both within and between societies. Accordingly, sociology is now commonly regarded as an essential discipline for understanding the development of all modern societies. The Sociology degree at Liverpool Hope will help you to think critically and constructively about the key questions relating to modern society.
Our sociology degree is based around a core that provides inputs from social theory and from the comparison of different forms of society. The degree will help you to examine ‘common-sense’ assumptions about the world by exploring the issues that confront society nationally and globally and studying the theories and methods that help to explain and understand these issues. It also examines and evaluates the methods of research which make the study of society possible. The degree enables you to study a range of additional topics which cover the whole spectrum of sociological inquiry.
Staff are enthusiastic and dedicated and will help you to get the most out of your degree. In line with Liverpool Hope’s commitment to social justice both nationally and internationally, Sociology attempts to understand social issues and problems that confront the modern world and, in so doing challenges received wisdom.For more details and information about this course visit: | https://www.hope.ac.uk/undergraduate/undergraduatecourses/history/historyandsociology/ |
Desertification, deforestation and environmental degradation have exacerbated resource conflicts between the Beni Halba and Gimir communities. Clashes over land between both communities in 2013 killed more than 160 people.
Land has become an increasingly scarce resource in Western Sudan due to mounting desertification and environmental degradation.
Competition over arable and grazing land is one of the major factors leading to clashes between Beni Halba and Gimir pastoralist communities in South Darfur.
Fighting over contested land between the two communities in 2013 left more than 160 people dead.
Beni Halba and Gimir are pastoralist communities with Arab identity inhabiting South Darfur. Disputes between the communities, primarily over land, have occurred in the past but could often be solved by ways of traditional mediation. In 2013, however, the two communities fought each other fiercely over contested land. The fighting started in early March and the two communities clashed several times throughout the year, leaving more than 160 people dead (UCDP, 2015). Armed forces, which had been sent to the area by the central government to create a buffer zone between the two communities, had retreated, thereby making the outbreak of violence possible. Sources reported that attacks by Beni Halba were supported by the “Central Reserve Forces”, also known as “Abu Tira”, a pro-government militia. After the clashes, both sides accused each other of breaking a recent peace treaty, of which several had been signed and broken in the years prior to the incident in 2013 (Radio Dabanga, 2013; CORI, 2013; UCDP, 2015).
Land is an increasingly scarce resource in western Sudan due to a variety of factors such as desertification, deforestation and environmental degradation. Ensuing competition over arable and grazing land, in turn, is one of the major factors leading to (often violent) conflict between local communities. In the present case, the Gimir accused the Beni Halba of trying to oust them from areas they had lived on for centuries, while the latter claimed the area for themselves. The disputed land is of particular importance for both animal husbandry and the production of gum arabic (Pantuliano, 2007; UN News Centre, 2007; Reeves, 2013; der Standard, 2013).
In addition, representatives of the Gimir community accused the central government of supporting the Beni Halba, of which Sudan's Second Vice President at the time- al-Haj Adam Youssef - originates from. Sources reported that on several occasions, government security forces that were supposed to protect the Gimir either did not intervene during the attacks by Beni Halba or retreated shortly before the attacks started. Furthermore, it has been reported that border guards and Central Reserve Forces were involved in the attacks (CORI, 2013; UCDP, 2015).
Numerous peace treaties have been signed between the two communities throughout their conflictual history. However, the truces were usually broken after a short period of time. In 2014, after a year of negotiations between the leaders of the two communities, a reconciliation agreement was signed on March 17, in Nyala, South Darfur, in the presence of Sudan’s second Vice-President, Hassabu Mohamed Abdalrahman. Both delegations confirmed their full commitment to implement the terms of the agreement (Radio Dabanga, 2014). Since then no more violent clashes have been reported.
3 Treaty/agreement A reconciliation agreement was signed between the leaders of both communities in 2014.
Country of origin research and information (2013). CORI Research Analysis, Fighting between Beni Halba and Gimir in and around Katayla locality.
Pantuliano, S. (2007). The land question: Sudan’s peace nemesis.
UN News Centre (2007). UN report says environmental degradation triggering tensions in Sudan. | https://factbook.ecc-platform.org/conflicts/natural-resource-competition-darfur-beni-halba-vs-gimir |
Luke Sumpter, a senior at Papillion La Vista South High School, has won the prestigious Legion of Valor Bronze Cross Award for 2019.
The honor is only awarded to 22 Navy JROTC across the country. The award recognizes both scholastic achievements in military and academic subjects. Sumpter is only one of two Navy students in the region that Nebraska is in (which includes 12 upper midwestern states) to win the award.
ROTC instructor Lt. Col Carl Lewandowski released the following information about Sumpter:
"At 17, Cadet Sumpter is a very accomplished student, with a standard GPA of 4.0. While he has maintained good grades, he also has a significant involvement with the community. He is a member of the Papillion Mayor’s Youth Council, and Health Academy, which trains students as Certified Nursing Assistants, He is also Vice President of the Midlands Hospital Health Occupations Students Association. Cadet Sumpter is involved in the martial arts training 45 students in Tae Kwon Do and has attained the rank of Eagle Scout. In addition to these accomplishments, Cadet Sumpter volunteers at a local nursing home and church (108 volunteer hours throughout high school), is involved in all the JROTC armed and unarmed drill teams, as well as numerous other JROTC activities such as color guard, Navy ball committee, athletic team and academic team. Cadet Sumpter aspires to become a Surface Warfare Officer in the United States Navy in the future."
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402-829-4600
Fax: | https://www.plcschools.org/site/default.aspx?PageType=3&DomainID=1249&ModuleInstanceID=200&ViewID=6446EE88-D30C-497E-9316-3F8874B3E108&RenderLoc=0&FlexDataID=5764&PageID=2622&Comments=true |
Alessi has recorded nine albums of original compositions which draw on everything from post-bop to neo classical music. He currently records for the ECM record label including his 2016 release Quiver. In 2018, he will release a new This Against That record on the label. As an educator, Ralph is an Assistant Professor of Jazz Studies at University of Nevada-Reno as well as the director of the School for Improvisational Music.
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March 05, 2020
Jazz Musician of the Day: Ralph Alessi
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Jazz Musician of the Day: Ralph Alessi
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Peter Epstein Joins With Ralph Alessi, Sam Minaie And Mark Ferber For...
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Trumpetman Ralph Alessi Fields Powerful Quintet for "Wiry Strong"
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Ralph Alessi in a Quartet at the Jazz Standard
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An Educational Conversation With Jazz Trumpeter and Teacher Ralph Alessi
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Ralph Alessi at Firehouse 12 This Friday 5/16
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Alessi's tone conveys a rounded luminescence, like the moon in full phase... —NY Times
Alessi has drop-dead trumpet chops and his music is as clean and airy and sophisticated and disciplined as post-modern progressive jazz gets... —Jazz Times
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Monash Sessions:... | https://musicians.allaboutjazz.com/ralphalessi |
Reps Speaker tasks lawyers on dysfunction in legal profession
Speaker, House of Representatives, Femi Gbajabiamila, has urged Nigerian lawyers to fix the dysfunction marring the legal profession and undermining its prestige.
He gave the admonition, yesterday, in his keynote address at the 2021 Nigerian Bar Association-Section on Legal Practice (NBA-SLP) conference, held at Ibom Icon Hotel and Golf Resort Uyo, Akwa Ibom State.
Gbajabiamila, who was represented by the Chairman House Committee on Judiciary and Member Representing Etinan/Nsit Ibom/Nsit Ubium Federal Constituency, Mr. Onofiok Luke, stressed that as lawyers and citizens, they must put in more effort at doing things differently for the profession and the country.
According to him, the nation desperately needs honest brokers to mediate a national dialogue, resolve key issues, and give the country a new lease of life.
He said: “The work of fixing our country must begin in our own house, within our profession. Before we can begin to play our full and proper role as lawyers in the difficult, yet necessary task of nation-building, we have to fix the evident dysfunction that corrupts the Nigerian legal profession and undermine its prestige. “
In his remarks, Guest of Honour and Akwa Ibom State Governor Mr. Udom Emmanuel wondered if the current challenges with the Nigerian project were a consequence of the justice lawyers failed to dispense in the past.
The governor who was represented by his deputy, Mr. Moses Ekpo, said the theme of the conference, ‘Law, Lawyer and the Next Generation’ harped on the cross-generational impact of what lawyers do or fail to do in their capacity as ministers in the temple of justice.
“As you take the law practice, this time around, through the crucible of this conference, I urge that you do so within the context of the larger concerns about our country. I hope that you will find a way of reshaping our sense of nationhood towards building land of peace, justice and unity,” he said.
Declaring the four-day conference open, Chief Justice of Nigeria, Mohammed Tanko, who was represented by Justice Abdul Aboki, said women and men of good conscience and leaders of thought must not stand aloof and watch the country degenerate further.
“Our country is officially weak and the leaders of the population have a virtual role to play as the conscience of the society, to secure equity, fairness and justice,” he said.
Earlier, NBA President Mr. Olumide Akpata identified globalisation and technological advancement as factors changing global industries at a rate never before imagined. | https://guardian.ng/news/reps-speaker-tasks-lawyers-on-dysfunction-in-legal-profession/ |
There are “FOUR” dimensions for the abode of spirits awaiting the judgement: TARTARUS”, “GEHENNA”, “HADES”, and “SHEOL”
Each has a different meaning in scriptures and is identified according to the context or the nature of the text. Yet, they are all rendered “Hell” in most English translations of the Bible.
HADES
Hades is called “The Underworld”, yet the Greeks identify Hades as the god of the underworld and the oldest male child of Cronus and Rhea. It is said that the brothers split their rule with Zeus becoming a god of the skies, Poseidon a god of the sea and Hades becoming a god of the underworld.
However, whether there be a demon-god over the domain of the dead or not, the term Under world let us know that it is indeed an actual “world”; a place, a Domain, a Sphere, a Realm where beings dwell.
It’s a place that was divided into two parts; “Gehenna” and “Paradise” (which is called Abraham’s bosom) and was the abode of the souls of both the righteous and unrighteous. It designates not the place of dead carcasses but the state of death or disembodied existence. In this sense even the soul of Jesus was in Hades according’ to Peter’s statement (Acts 2:27, Acts 2:31 – which was a fulfilment of Psalms 16:10).
KJV uses one word Hell to apply to every part of the underworld and does not distinguish between the grave for the dead bodies (Sheol) in Hebrew: and the place of the fallen angels that are bound in darkness (Tartarus), and Hades the abode of spirits.
- GEHENNA – a place where unrighteous souls suffer damnation with eternal fire. The original concept came from a place outside the South-western wall of Jerusalem, where the Children of Israel would burn garbage and build sacrificial fiery altars to offer their children to Molech. (2Kings 23:10, Joshua 15:8, Jeremiah 7:31). Because of the constant throwing of garbage, the fire would continuously burn day and night. This is the valley (or “ravine”) of Hinnom (Nehemiah.11:30) in the land of the Jebusites (Jerusalem) and is called (“the ravine of the son of Hinnom,” or the valley of the sons of Hinnom. The Hebrew phrase Gê (“ravine of”) Hinnom became Ge-hinnon or Gehenna in Greek. The torment in this section is based on the sin of the person. Each sin has its own torment and punishment. Also, once in this place there is no way out. In hell, there is no rest, neither day nor night. Upon arrival, you will see hell. . you will smell hell. . you will breathe hell . . you will hear hell . . you will feel hell. . you will taste hell. . you will be hell. There is a perfect and precise example in Ezekiel 26:20, “I will send you down to the world of the dead to join the people who lived in ancient times. I will make you stay in that underground world among eternal ruins, keeping company with the dead. As a result you will never again be inhabited and take your place in the land of the living”. The place where the rich man went after he died (Luke 16:22-23), is Gehenna; a place of unquenchable fire where worms does not die.
- SHEOL is the Hebrew equivalent of Hades, but donates a place of the dead, without consciousness – (the grave). It is for the dwelling of carcasses not a place of spirits and punishment; therefore, Sheol is on surface as a physical place.
- PARADISE- Before the resurrection of Jesus, the souls of the righteous went to Paradise, which was located in a certain part of Hades, as confirmed by scriptures. Luke 23:43, “And Jesus said unto him, Verily I say unto thee, today shalt thou be with me in paradise.” Yet, the scriptures say that Jesus was in Hell for three days and three nights. Presently, the place of the Righteous (Paradise/Abraham’s Bosom) is no more in the underworld; but has been relocated to the 3rd Heavens in the presence of God. Jesus went to Paradise, yet, the scriptures are saying that he also descended down into hell; Eph. 4:9-10, “…..he also descended first into the lower parts of the earth…..he that descended is the same also that ascended…..” It is confirmed again that Jesus went to hell; Acts 2:31, “….spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.”
TARTARUS (Greek) – This dimension is located in the 5th Heavens, and is separate from Hades, Gehenna or Sheol, and is a place reserved only for Fallen Angels. The word occurs only once in the Bible in 2 Peter 2:4 where it says, “For if God did not spare sinning angels, but thrust them down into Tartarus, and delivered them into chains of darkness, being reserved to judgment”. There are no Biblical references to people going there.
Many people say that God is too loving to send people to Hell fire. We must remember that God is all loving and merciful; but God is also a consuming fire, just and holy and rewards everyone based on their choice. God DOES NOT tolerate sin and rebellion. 1Samuel 15:23, “For rebellion is as the sin of witchcraft, and stubbornness is as iniquity and idolatry.”
Galatians 5:19-21 made it clear, “Now the works of the flesh are clearly revealed, which are: adultery, fornication, uncleanness, lustfulness,
V.s 20, idolatry, sorcery, hatreds, fightings, jealousies, angers, rivalries, divisions, heresies,
V.s 21, envyings, murders, drunkennesses, revelings, and things like these; of which I tell you before, as I also said before, that they who do such things SHALL NOT INHERIT THE KINGDOM OF GOD.
When he says repent and serve Him and have eternal life, He means it; but when He says the reward of living in sin is eternal damnation, He means what he says. Therefore, “We” are responsible for choosing Heaven or Hell, not God!
Jehovah witnesses and many other Christian churches say that the word “Hell” in the Bible means the Grave or Tomb. But according to Psalm 9:17 “Hell” CANNOT mean simply the grave, why?
Book of enoch 41:2 said, “And there I saw the mansions of the elect and the mansions of the holy (John 14:2), and mine eyes saw there all the sinners being driven from thence which deny the name of the Lord of Spirits, and being dragged off: and they could not abide because of the punishment which proceeds from the Lord of Spirits”.
Don’t the righteous people also go to the grave? If the word ‘Hell” means the just the grave as the Jehovah Witnesses say, then it makes Jesus a liar and deceiver.
But we all agree that the righteous in Christ and the wicked (unsaved people) are going to the same place- the Grave.
However, Hell is MORE than the Grave. If we are careful to search the scriptures, we will see that both the prophets of the O.T and the Messiah have made mention to “everlasting fire”, “lake of fire”, “flames”, “fire”, “hell” etc. | https://divinerevelations.com.ng/reality-of-hell/ |
James, the half brother of our Lord, taught that the body without the spirit is dead (James 2:26), but the opposite cannot be said to be true, for the spirit without to body is not dead! Though the body “returns to the dust” (Genesis 3:19), “the spirit shall return to the God who gave it” (Ecclesiastes 12:7). Jesus more than demonstrated this when referring to God as being the God of Abraham, Isaac and Jacob, uttering, “God is not the God of the dead [though dead physically, ENM], but of the living” (Matthew 22:29-32). Clearly implied within His astonishing words is a glimpse into the afterlife. Though these great patriarchs had been physically dead for many years, they lived on. Perhaps the most revealing section of Scripture as to the state of the dead is found in Jesus’ teaching about the Rich man and Lazarus (Luke 16:19-31). Even a cursory reading of this great text reveals a great deal of information regarding life after death (Please turn and read Luke 16:19-31).
The following relevant observations can be drawn from the facts of this text: (1) both the righteous and the wicked are conscious after death; (2) after death, some men are comforted, and other men are tormented; (3) this comfort and torment occur while life is still being lived upon the earth and therefore previous to the judgment. (4) The Hadean world, in which these departed spirits find themselves, is divided by a great gulf; (5) one, the Lord stated, is in Hades, and (6) the other is in the bosom of Abraham.
In this great section of Scripture, Jesus employs the use of the word “Hades” (23). Vine states that this word signifies “all-receiving” (Vine, W. E., Expository Dictionary of New Testament Words, 187). Thayer defines this unseen or invisible world as “the realm of the dead, or the common receptacle of disembodied spirits” (Thayer, Thayer’s Greek-English Lexicon of the New Testament, 86). Every person’s spirit, upon physical death, goes into Hades, but the righteous go into one division and the wicked into another. Sometimes the word Hades is used only in reference to the place of torment (cf. Luke 16:23) and in other instances it is used to refer to the Hadean realm with its respective divisions (Matthew 16:18; Psalm 16:10, etc.). From the Lord’s words in Luke Sixteen and other New Testament references, God has revealed the existence of Paradise (Luke 23:43) or so-called by the Master, “Abraham’s bosom” (Luke 16:22), and that section of Hades which tormented the rich man. Though the King James Version appears to place the Lord in Hell for three days (Acts 2:27), the New King James and many other more correct renderings translate the word Hades as it is in the original. If the Lord, therefore, was in Hades, was He in the presence of the rich man of Luke sixteen or rather poor Lazarus? This query can easily be answered by the Lord’s answer to the penitent thief: “Assuredly, I say to you, today you will be with Me in Paradise” (Luke 23:43). The “paradise” that the Lord here mentioned seems not to fit the description given of that place of torment and flame that plagued the rich man. Paradise is rather the place of the departed spirits of those men and women who were righteous in their physical lives or who passed away before reaching beyond the age of innocence.
The rich man’s location becomes more clear when compared with the apostle Peter’s statement: “For if God did not spare the angels who sinned, but cast them down to hell and delivered them into chains of darkness, to be reserved for judgment” (2 Peter 2:4). The word here translated “hell” is the word tartarus. M. R. Vincent says that this word “represents the Greek hell, though treated here not as equivalent to Gehenna [The Greek word properly translated hell, but not employed here, ENM], but as the place of detention until the judgment” (Vincent, Word Studies in the New Testament, 691). If the proper translation of this word is “hell,” one wonders what, if any reason, there would be for a judgment, if they are already in their eternal place of punishment. Second Peter 2:4 mentions Tartarus as the place where wicked angels are being held until the judgment, and it is reasonable to suppose that Tartarus is that part of Hades reserved for the wicked until their judgment. David Pharr commented:
Unless there are compelling reasons for concluding otherwise, a word in Greek should be understood as meaning what it would have meant to the Greek-speaking world of the New Testament times. We should, therefore, understand Peter’s use of tartarus (translated “hell” in the KJV), to refer to what it ordinarily meant to the Greeks—a place of punishment for disembodied spirits. While the word tartarus itself is not used in the New Testament regarding the spirits of wicked men, the idea of such a place is clearly implied. We find it in Peter’s statement about disobedient men, long since dead, whose spirits were “in prison” at the time Peter wrote (I Pet. 3:19f) (Pharr, The State of the Dead, 25).
One fundamental difference in the punishment of the Hadean realm and that of Hell (Gehenna) is that Tartarus is the punishment of those wicked disembodied spirits, whereas the punishment of Hell consists of both body and spirit. Jesus profoundly stated, “And do not fear those who kill the body but cannot kill the soul. But rather fear Him who is able to destroy both soul and body in hell” (Matthew 10:28).
The disembodied spirits of both the wicked and the righteous will dwell in the Hadean realm until that great call from Him who comes with the clouds (Revelation 1:7) during the resurrection (John 5:28-29). The New Testament gives much emphasis to the resurrection of the body (Romans 8:11; 1 Corinthians 15, etc.), and therefore, implies that something, as far as rewards are concerned is lacking without the resurrection. When the graves burst open, on that Day (John 5:28-29) eternal rewards will be given. Paul taught that the crown of righteousness will be given “on that Day” (2 Timothy 4:8) both to him and “all who have loved His appearing.” We must conclude therefore that Paul has not entered heaven, for claimed he, all will receive their reward on “that day.” It is apparent from many New Testament Scriptures that no one, except Jesus has gone into Heaven. John wrote, “No one has ascended to heaven but He who came down from heaven, that is, the Son of Man who is in heaven” (John 3:13). In fact, after the Lord’s resurrection, He told Mary: “I have not yet ascended to My Father” (John 20:17). Though in the care and keeping of God, Jesus and those other righteous departed spirits had not yet ascended to heaven. Hades will continue until the judgment, at which time it will give up its dead and death and Hades will be cast into the lake of fire (Revelation 20:13-14). | https://www.gospelgazette.com/gazette/2009/jun/page15.html |
The Common Muon and Proton Apparatus for Structure and Spectroscopy (COMPASS) experiment is a multipurpose experiment at CERN’s Super Proton Synchrotron (SPS).
The experiment looks at the complex ways in which the elementary quarks and gluons work together to give the particles we observe, from the humble proton to the huge variety of more exotic particles.
A major aim is to study the internal structure of protons and neutrons and to discover more about how the property called spin arises in them, in particular how much is contributed by the motion of quarks or by the gluons that bind the quarks together. To do this the COMPASS team fires muons (particles that are like heavy electrons) and particles called pions at a polarized target.
Another important aim is to investigate the hierarchy or spectrum of particles that quarks and gluons can form. In these studies, the researchers also look for "glueballs" – exotic particles made only of gluons.
About 220 physicists from 13 countries and 25 institutions work on the COMPASS experiment. The results will help physicists to gain a better understanding of the complex world inside protons and neutrons.
AMBER, or Apparatus for Meson and Baryon Experimental Research, will be the next-generation successor of COMPASS after the experiment’s last run in 2021–2022. | https://press.cern/science/experiments/compass |
For the majority of children and young adults, school is easily one of the main causes of stress; so much so that the pressure and anxiety attached to school is perceived as an almost normal phenomenon. The stress fluctuates throughout the year depending on the workload students are assigned and understandably so, but there are certain times when it all becomes too much. Stories of students lugging themselves around school hallways nursing headaches and dark circles and breaking down in exam rooms speak volumes about the dangers of burnout, a term used to describe a state of chronic stress that leads to complete physical, mental, and emotional exhaustion.
The most obvious symptoms of burnout include feeling constantly tired, a lowered immune response, the loss of motivation and joy once found in work, and procrastination but it can bring about even more troubling outcomes such as feelings of failure and self-doubt, self-isolation, and taking out pent-up frustration on others. While it may seem that burnout is stress taken to its extremes, the two differ in a number of ways. Burnout is closely associated with stress but stress is characterized by hyperactivity and restlessness whereas burnout is the empty sluggishness one feels even in the face of overwhelming pressure.
Burnout is most likely to affect perfectionists and high achievers who are thoroughly and on occasion, excessively engaged with their work but it can also impact any student who is subjected to significant stress over a prolonged period of time. This may be compounded when a student takes a large number of courses, extracurricular activities, and/or sits too many exams for a variety of classes or college applications. As a result, it is possible to reduce the risk of burnout by refraining from taking on too many obligations. However, there are also other ways to accomplish this same goal without sacrificing the desire to learn and do well.
Bouncing back from burnout takes time and effort but the most basic step to take in the direction of recovery is to practice self-care by eating well, staying hydrated, engaging in physical activity, and getting enough sleep— the essential keys to health that, with hectic schedules, long hours, and late nights, tend to be forgotten. In dire circumstances, that is, if the burnout is significantly and negatively impacting an individual’s work and wellbeing, it would be helpful to take time off from work. For students, this can mean resting more on the weekends or taking advantage of school holidays to catch up on hobbies and quality time with friends and family. In the same vein, talking to others is an effective way to combat burnout as it makes your concerns and needs heard and is the opposite reaction to the self-isolating tendencies burnout can induce.
In the meantime, it is important to re-evaluate attitudes towards work and the achievability of personal goals. While hard workers deserve to be applauded for their dedication and the amount of effort they put into meeting their high standards, unhealthy habits can emerge from the pursuit of perfection. It would be wise to establish personal boundaries (for example, working only until a certain time at night instead of pulling an all-nighter and preventing the circumstances that may lead up to said all-nighter) that must not be overstepped and to hold yourself and somebody else accountable if you begin to slip. The pressures of daily living cannot be avoided and will only mount with age but learning to manage stress and knowing oneself will go a long way in staying burnout-free. | https://mygradebooster.com/school-burnout/ |
by Jo Tumbe Mangi
As mentioned above, the bulk of the stone adzes 1 used by the Huli were traded into the study area. Here I briefly discuss the Huli perception and knowledge of stone adzes and how they differentiate the different types of adzes before looking at where these items are actually obtained from. The first point to make is that during the individual interviews my Huli informants offered a lot of information on the different types of stone adzes. Each differentiated between types of adzes and gave the source from which these axes supposedly came. However, when all this information was put together there was little consistency, particularly when they were asked to do it for the demonstration adzes. It appears that the main criterion for determining the type of adze is based not on the shape of the stone adze but on the material that it is made from, that is the type of rock. Even with this, when they were asked to define the differentiating factors, few went on to elaborate further. They just simply said that they knew. I look at a possible explanation of this at the end of this discussion.
The Huli differentiate several types of adzes. The main ones that I came across most often are: Warabia, ayu Mukalo, ayu Kudina, ayu Habina, ayu Pogorali, and Tindi ayu. There was a general consensus amongst the informants that Warabia came in from both the Duna and the Duguba. However when asked in the interview if they ever acquired any adzes from the Duguba, most of the informants said that they never got their adzes from the Duguba.
Therefore it was not possible to work out the values for adzes from the Duguba area. Mukalo is reported to have come from Mt. Mukalo, hari Mukalo, in Muritaka near Laiagam. However when I went into the Muritaka area of the Enga Province the people there denied ever producing these axes. On the other hand, Burton ( 1984:Table 1. 1) does mention the name Mangalo as a stone axe source name from the Enga area. They said that they got theirs from further west. Ayu Kudina, ayu Habina and ayu Pogorali also come in from the Obena.
Tindi literally means, ‘ground adze’. This term is used to refer to all the adzes that the Huli made themselves from stone that they found in the river and creek beds or in other areas where there were large pebble exposures. One of the informants, Kayako Hiwapuk, went on to say something else that further confused the issue. He claimed that when the Tindi ayu was finally ground down in the desired shape they would look at the adze and then decide whether it looked similar to any of the other adzes and name it after them but with the term negane in the end of the name. Negane literally means, ‘jaw’. For example, if it looks similar to ayu Habina, then it would be called~ Habina negane. As I said, this really confuses the issue and I believe there is a lot more work to be done before we get any in-depth knowledge of the issue.
The reason that I think that the Huli are inconsistent in how they differentiate between the different types of adzes may stem from the simple fact that they are so far away from the sources where these adzes are made that by the time they get them the intimate and often rather miniscule knowledge that goes into differentiating the different types is lost. It is equally possible that I did not pursue this whole issue deeply enough to appreciate whatever pattern there may be there. The only thing that really stood in this observation was that when the informants looked at the Medium 1 adze they immediately said that that was the most highly prized of adzes. They claimed that they acquired it from the Obena. John Burton (pers. comm.) says that the stone comes from the Tuman axe quarry in the Western Highlands Province that , it should it equate with kundina, the western corruption of Kunjin, a quarry name. | https://huliculture.com/stone-adzes-a-huli-trade-resource/ |
Sleep deprivation is a medical term to name a series of problems and conditions that cause a lack of a healthy number of sleeping hours. Even though this is not a specific disease, these conditions are affecting most of the adults on our daily basis, which is the reason why you need to know the cause and possible consequences of suffering from sleep deprivation or sleep deficiency.
According to the National Heart, Lung and Blood Institute (NIH) of the United States, sleep deprivation and deficiency are terms for conditions related to sleeping problems that involve symptoms such as:
- Not getting to sleep the adequate time (according to your age, between 7 to 9 hours in adults, children between 9 to 14 hours)
- Sleeping a wrong time of the day (trough daytime or work time mostly)
- You don’t feel rested. You have the sensation of not sleeping well or not getting the type of sleep that your body needs
- You suffer from sleep disorder as the consequence of a mental or physical illness
Sleep deprivation and deficiency are common sufferings in modern society. As this article says, at least one of three individuals suffers from them as a consequence of our modern lifestyle.
Every time, more people are recurring to sacrifice the right amount of sleep every day to “get more things done“. The problem is many of them don’t know the consequences lack of sleep can cause to their overall health, especially while getting older.
Another study named by the Department of Neurology from Columbia University says that at least half of the older adults – people over 65 years – are experiencing sleeping problems and health complications associated with long periods of sleep deprivation and deficiency.
Sleep deprivation probable causes
As mentioned before, a high percentage of people that are not getting their right amount of sleep tend to sacrifice their rest time to pursue their personal goals in entertainment, financial, educational, or working fields, seeing teenagers and young adults the most affected by sleep deprivation.
Family responsibilities as newborns, parents, or partners with illnesses can also cause the appearance of sleep-wake patterns over the night accompanied by insomnia and light sleep.
Medical conditions such as depression, anxiety, and sleep apnea can cause the rise of sleep deficiency as well as other chronic illnesses.
|Read also: How to Improve Your Mental Peace and Performance Through Quality Sleep?|
Symptoms and complications
Sleep deprivation causes minor symptoms until scaling to the next ones:
- Lethargy
- Inability to concentrate
- Partial memory loss
- Reduce physical strength
- More prone to suffer from infections, colds, and flu
The complications of these symptoms may include:
- Increase of the risk of suffering a stroke, heart disease or asthma attacks
- The augment of depression, anxiety, paranoia, and other mental illness as well as suicidal thoughts
- Science has demonstrated that sleep deprivation is the main cause of car accidents and plane crashes
- You can start suffering from hallucinations, cravings and severe mood swings due to sleep deprivation
Treatment and prevention
The treatment for sleep deprivation may vary depending on the level of your symptoms. On the other hand, adjusting your daily sleep routine and dietary regime can make amazing results to minimize the consequences of this condition.
By just going to bed when feeling tired, adjusting your sleep and waking schedule, avoiding eating or heavy meals at least 3 hours before going to bed, having a 20 minutes workout routine, turning off all your electronic devices before getting to the bed and reducing the consumption of caffeine, alcohol or nicotine you will help to set up your body for nights of rest while protecting your overall health.
Sleep Deprivation- Prevention
- Consistent Sleeping schedule
- Avoid short nap during the day
- Follow Bedtime Routine – having the same routine every day will help your brain to prepare for sleeping and slow down all the processes in the organism.
- Avoid Using Devices at least 1 hour before sleeping – electronic devices such as mobile phones, computers, laptops disrupt your biological processes and hormones.
- Clear Your Mind and Relax – try not to think about your daily activities before sleeping, leave your worries. Meditation before sleeping could help you to improve your focus and to feel more balanced.
Remember that, by just sleeping well, you will get slimmer, creative, and productive every day; increase your libido as well as your immune system so, consider all these aspects the next time Netflix tempts you to stay awake.
About The Author:
Maria Matthews is an experienced freelance writer reporting on health, fitness, and travel and covering the latest in food and nutrition. When she’s not writing, you’ll find her drinking tea or running around her hometown of Barcelona. | https://www.safeandhealthylife.com/what-is-sleep-deprivation-and-why-is-bad-for-your-health/ |
We describe here a system designed for behavioral experiments.
The goals of the system are to
- Interact rapidly with the experimental subjects. In other words, the system should respond to the events fast (sub-millisecond level), so as to get reliable time traces of behavior when combining it with electrophysiology.
- Provide a convenient user-interface to study this behavior.
- Regulate the experiments on a daily basis by recording the experimental data and settings used by multiple experimenters on multiple subjects.
The experimental subjects used for explanation purposes in this documentation are rats.
Contents
Interact rapidly with rats
(Goal 1: Real Time Linux State Machine)
The rats reside in a behavior box. The following things can happen in this box.
- The rat gets exposed to certain type of stimulus e.g. sound, light, water, and odor.
- The rat pokes into one of the three pokes, commonly called 'Center', 'Left' and 'Right' pokes.
This is the rat's way of communicating with us about what it feels about the stimulus it received from us. Humans or other animals might communicate differently. We can call this a stimulus-and-response concept; and our job is to study the behavior of the rats with the help of this stimulus-and-response concept.
A state diagram is one of the most convenient ways, to visually summarize how we want to control a rat's behavior with the help of stimulus-and-response concept. We need a system that frequently (meaning in real-time) sends the stimulus to the rats and records the response of the rats to a particular stimulus or a set of stimuli. To facilitate this kind of behavioral experimentation, we associate stimulus/stimuli with a state and say that the rat is in a particular state when it is exposed to a particular set of stimuli or a single stimulus; hence we use state diagrams. Based on the rat's response to the stimulus (or stimuli) when it resides in a state, we may choose to transfer the rat to another state (which may be to subject the rat to a different stimulus or stimuli) or keep it in the same state.
Brain Feed #1: Simple State Diagram comprising states, output actions and events
- A state diagram is composed of states, their output actions, and the events that are responsible for transitions between states.
- The adjacent figure shows a state diagram with three states. Each state is associated with an output action (blue text and a graphic below/beside each state in the adjacent figure) which can be to subject the rat to a single stimulus like light (State_2) or sound (State_3) or multiple stimuli (both light and sound together are outputs of State_4); the events are labeled across the arrows.
- In the adjacent figure, Lin (meaning rat pokes into the left poke) causes a transition from ‘blank state’ to ‘light state’ where the Left Light is turned ON.
- Also, note that some states might not have any output actions (like State_1 in the adjacent figure). This too is a type of stimulus to the rat. It is like subjecting the rat to absolute silence and darkness. We can call it a blank state or empty state.
- The events shown in the adjacent figure are generated by rat pokes and designated with the following names: Cin, Lin, Rin – rat puts its nose into center, left, and right pokes respectively; Cout, Lout, Rout – rat pulls nose out of center, left, and right pokes respectively (e.g. Lin causes transition from State_1 to State_2).
- We call them hard events because they are coming from the subjects (in this case, the rats) and not internally from the software.
The system we designed to run the state diagrams is real-time software which runs on a Linux machine. The job of this software is to send out the different types of stimuli and report the responses of the rats to the real world in real-time based on finite state diagrams designed by us. We call it finite because the number of states is always finite. The machine which runs this software is called Real-Time Linux State Machine (RTLSM) or Finite State Machine (FSM).
Convenient user-interface to study the rat's behavior
(Goal 2: Governing Machine)
Up to this point, we learnt that the RTLSM runs state diagrams. But, who will design those diagrams for the RTLSM? We have custom-software which runs on a separate machine (which we call the Governing Machine) to design state diagrams and dispatch them to the RTLSM. On the Governing Machine, we call the act of designing a single state diagram, a Trial. One might want to run several trials in a particular sequence, for an experiment; which means designing several state diagrams, such that one runs after the other. Sometimes, when a set of trials are completed, the experimenter might choose to mark it as a particular Stage of experiment being completed. For convenience, experimenters design all the trials that are required for an experiment, at once; and they call it a Protocol. When the experiment starts, this Protocol is simply launched. So, we have learnt three new words that are commonly used on the Governing Machine platform: Trial, Stage and Protocol. The adjacent figure shows a pictorial representation of how we design several state diagrams (or Trials) and wrap them in a Protocol.
Now that we have a Protocol design, the next step is to dispatch it to the RTLSM. For this purpose, we have three modules running inside the Governing Machine’s custom-software: Dispatcher, State Machine Assembler/Dissembler, and Transporter.
- Dispatcher is a software module which acts as an interface between the Protocol and the RTLSM. It issues instructions to launch and close a Protocol, and to handle the handshaking between the Governing Machine and RTLSM.
- The job of the State Machine Assembler/Dissembler software module is to act as an interpreter (or translator) between the Governing Machine and the RTLSM. It converts the instructions issued by Dispatcher into an internal language that can be understood only by the RTLSM and vice-versa.
- The Transporter is a module that checks if the communication path between the Governing Machine and the RTLSM is clear; then sends all the interpreted instructions to the RTLSM and receives any information requested by Dispatcher from the RTLSM. It acts as a communication liaison between the Governing Machine and RTLSM, and hence also called a liaison app.
Since multiple experimenters may run multiple experiments on multiple rats, even before the Dispatcher can launch a Protocol, it needs to know some basic information like the names of the experimenter, the rat and the Protocol. This is facilitated by another GUI module on the Governing Machine called Runrats. This module helps us select the Protocol, experimenter and rat and then passes this information to the Dispatcher. There are two ways for Runrats to get this information. One way is for us to feed this information manually to Runrats via its GUI window. The other way is for Runrats to fetch (or retrieve) all this information from a database server via a liaison software module (or app) called Zut. We call it a liaison app because it helps communicate between the Governing Machine and the Server Machine (about which we will talk next in Goal 3)
Regulate experiments on a daily basis
(Goal 3: Server Machine)
- Experimenters build different protocols and run it on different rats at different times of the day. So, we need a scheduler which will decide the experiment to be run based on the following parameters: experimenter, protocol & rat name.
- To automate this whole scheduling process, we built a simple scheduler webpage which collects the above stated parameters and stores them in a database server.
- When requested for information, the database server (which resides on a separate machine called Server Machine) serves these parameters to the Runrats module on Governing Machine, via Zut, which will help Runrats pick the scheduled Protocol for that date & time; and Runrats finally sets that Protocol for the Dispatcher to launch.
Software Architecture
Now that we have an idea of what are the goals, let us look at the Software Architecture of this Behavioral Software Suite and learn how it realizes these three primary goals.
As we can see in the adjacent figure, the entire block diagram is separated into three parts corresponding to the three goals which are realized by three physically separate machines: 1.) State Machine; 2.) Governing Machine; 3.) Server Machine.
The goals are separated using purple lines. We can call them goal separator lines. You will notice that there are two small boxes intercepting purple lines (the goal separators). Although these are Governing Machine’s software modules they intercept the goal separator lines because they act as liaison apps between the Governing Machine and, Server Machine & State Machine.
To better understand the adjacent block diagram, we will see step-by-step what happens starting from the top; when an experimenter, on a typical day, sets the schedule to run a particular protocol on a rat; to the bottom where the rat’s behavior in the behavior box is studied:
- Experimenter opens scheduler webpage and sets the schedule to run a rat (named R0113) using protocol called (say) Light Chasing under his/her name.
- The schedule is transferred to the web server which in turn transfers it to the database server with the names of the experimenter, protocol and rat.
- Technician arrives at the Governing Machine, starts the GUI app Runrats.
- Runrats now communicates with the Database Server via back-end app Zut to retrieve the rat name, experimenter name and the protocol name.
- Zut retrieves the information, requested by Runrats, from Database Server and passes it to Runrats.
- Runrats is ready with the protocol to be run and calls the Dispatcher.
- The Dispatcher reads the Protocol and sends the first state diagram to the State Machine Assembler (SMA) which translates (or interprets) the state diagram into an internal language understandable by the RTLSM and delivers it to the RTLSM using the liaison app Transporter.
- The RTLSM receives the state diagram, and starts running it. As a consequence of running a state diagram, hard events will be generated and state transitions occur.
- The Dispatcher continuously bugs the RTLSM for information like the latest events and state transitions that occurred. At this point, the system takes a reverse path. All this information is transmitted to the Transporter by the RTLSM. This whole process is called handshaking.
- The information held by Transporter is again interpreted into a language (that the Dispatcher can understand) by the State Machine Dissembler (SMD) and subsequently sent to the Dispatcher.
- Dispatcher analyzes the information it received from the RTLSM and checks if the state diagram it just sent has been completed or not.
- If Dispatcher learns that the RTLSM has completed running the current trial, it buckles up and starts bugging the Protocol to build the next state diagram.
- Protocol analyzes the performance results of the current trial and prepares the next trial; in other words builds the next state diagram and delivers it to the Dispatcher.
- Also, once the Protocol knew that a certain number of trials have been completed, it marks it as a stage completion.
- Once the entire Protocol finishes running, the results are saved and sent to the database server. | https://brodylabwiki.princeton.edu/bcontrol/index.php?title=Software_goals |
This is a revised version of a paper presented to the conference 'Defining Merit' held at Macquarie University in September 1985.
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The merit principle, used as a way of removing biases in occupational structures, is flawed. The evaluation of merit is tied to the interests of those in positions of power, so that application of the merit principle is compatible with continued structural inequalities. In practice the concept of merit is used as a resource in organisational power struggles. A deeper problem with the merit principle is its acceptance of occupational hierarchies. A more fundamental equal opportunity requires some form of self-management.
Paradoxically, the concept of merit has become a catchphrase of both supporters and opponents of legislated equal employment opportunity. On the one hand, advocates of women's and other minority rights have supported application of the merit principle, underpinned by affirmative action to remove unfair starting handicaps, to provide real equal employment opportunity. On the other hand, traditional bureaucratic elites have invoked the merit principle to oppose what they allege is reverse discrimination against white middle-class males. In the struggle over equal opportunity, the concept of merit is being used by both sides as a tool. To understand how this comes about, it is necessary to examine the power structures of organisations.
The merit principle is most commonly applied in bureaucratic or semi-bureaucratic organisations. These organisations are constructed most fundamentally on hierarchy and a division of labour. The classical picture sees bureaucracy as an instrument for rational administration, operating on the basis of universalistic principles (Weber 1964). Seniority is commonly used as a basis for advancement in a bureaucracy simply because it is easy to measure and because it supposedly shows commitment to the organisation. But seniority does not seem to be a suitable principle for maximising organisational performance. Merit, an assessment of a person's ability, experience and motivation relevant to performing a job, would seem to be a more suitable principle for measuring and rewarding performance in an ideal bureaucracy.
What is merit in the conventional theory of bureaucracy? 'Ability plus effort' is a typical formula. There are three standard ways of assessing merit: examinations, credentials and work experience and performance. Examinations are often used in recruitment into bureaucracies, but much less commonly in promotion. Credentials are especially important in professions: credentials are a prerequisite for entry to law, medicine, engineering and many other occupations. It is commonly argued that credentials demonstrate one's ability or suitability to undertake a job in bureaucracies as well. Finally, work experience and performance provide indicators of merit, especially in demonstrating whether abilities shown by examinations or credentials are actually utilised on the job.
In practice the measures of examinations, credentials and performance are mixed together in the assessment of merit. Credentials become important, for example, when professional and bureaucratic systems of social organisation are intertwined, as they often are. In hospitals, advancement through the organisational hierarchy usually depends on having a medical degree as well as experience in administration. In many high-technology companies, degrees in engineering or science provide a basis for rising into the management stream. To become head of a school a background as a teacher, implying possession of suitable teaching credentials, is usually a prerequisite. In these and other cases there is commonly a parallel 'administrative stream' for those without professional credentials. This administrative stream may or may not provide access to the highest levels of the organisation, depending on the relationship of the professional system compared to the bureaucratic system.
The standard picture of the role of merit then is as a means of assessing a person's suitability for a job in a bureaucratic and/or professional system. The question which needs to be faced by supporters of equal opportunity is whether merit can indeed be applied in an unbiased manner, or at least a relatively unbiased manner. If this cannot be done in practice, it may not be wise to rely too heavily on merit in pursuing the project of overcoming discrimination in employment. To approach this issue, I will look more closely and critically at the way in which power is exercised in large organisations.
I will begin by arguing that the struggle for advancement within complex organisations is part of a wider power struggle, in which resources provided by white middle-class male culture are crucial. Since work is embedded in the organisational context, evaluation of merit is shot through with the biases of those in positions of power as well as biases in the very definition of merit in a system which imposes unequal life opportunities. The usual definition of merit within organisations may seem fair, and be applied fairly within its own terms, while being entirely compatible with the continuance of structural inequalities such as male dominance. Merit can never be unambiguously assessed, but is rather one tool among others in organisational power struggles.
Going beyond this, a fundamental flaw in the merit principle lies in its acceptance of occupational hierarchies in which the decisions of the few control the work of the many. Rather than trying to equalise opportunity within a hierarchical system - which at most can change the individuals who occupy the slots - a more fundamental 'equal opportunity' would involve redesigned occupational structures in which workers defined the conditions and goals of their work. This would allow women, the disabled and others to be involved in an equal way by restructuring the hitherto distinct and unequal arenas of public and private life.
Traditional views on bureaucracies and professions have been challenged in recent years by scholars who see these as political systems. First consider bureaucracy. The traditional Weberian picture of bureaucracy as a rational system of organisation has strongly influenced much organisational theory, which concentrates on how management can overcome obstacles to efficiency. Nevertheless, it is widely recognised that actual bureaucracies do not behave precisely according to Weber's ideal-typical picture. There is a constant struggle for power within bureaucracies, a process which includes power relations embodied in interpersonal discourse, competition between internal factions, conflicts between bureaucrats and clients, and struggles between bureaucracies.
Rejecting the Weberian assumptions is the political perspective on organisations presented by Deena Weinstein (1977,1979), according to which bureaucracies are best understood as political systems. Individuals and groups within bureaucracies exercise power using the particular social and material resources available, including control over labour power, positions, clients, funding and knowledge. Overt political activity by workers is commonly inhibited by fear of reprisals and by habits of acquiescence, often based on beliefs or fear.
The key role of power is most obvious when oppositions form within bureaucracies, either individual dissidents or whole movements. What usually happens is not a rational assessment of the claims of the dissidents, but rather suppression of the dissidents themselves: corporation executives who speak out critically about their employer's behaviour typically will be sacked; soldiers who rebel will be court-martialed; rank-and-file revolts by trade unionists may be smashed by expulsions (Weinstein 1977, 1979; see also Anderson et al. 1980; Perrucci et al. 1980; Zald & Berger 1978).
Weinstein likens bureaucracies to authoritarian states in their political structure in that control is exercised from the top with few opportunities for popular participation. Democratic structures are token or non-existent, and the elites control the main political and economic resources. The main difference between bureaucracies and authoritarian states is that normally bureaucratic elites cannot use violence to enforce their control. One of the consequences of this power struggle is that the goal of the bureaucracy may be displaced from outer service to inner control (Hummel 1977). This picture does not assume that bureaucracies are monolithic structures, nor that the only political power exercised is strictly according to formal structures. Indeed, it is the existence of oppositions which shows that power is based on a set of practices which do not accord with formal rationality.
A similar analysis of professions has been developed in recent years. Contrary to the traditional picture of professionals using their knowledge and skills purely in the service of society, this analysis sees occupational groups using knowledge and skills as resources to increase their power, wealth and status. Doctors for example use credentialing and licensing systems to keep down numbers in the medical profession and then use their control over the resulting scarce resource of 'legitimate' expertise to push for higher salaries and control over medical decision-making (Freidson 1970; Johnson 1972; Larson 1977; Parkin 1979; Willis 1983; for a critique see Saks 1983). Opposition movements also arise in professions. The medical profession has routinely taken action to deny status and resources to challengers such as practitioners of 'fringe therapies', for example by lobbying to deny their inclusion under medical benefits schedules.
The political picture of bureaucracy and professions provides a useful way to begin to analyse their interactions with systems based on class, gender and ethnicity, which can be treated as power systems which cannot be reduced to each other nor to some other essence (Brittan & Maynard 1984). Class, gender and ethnicity in this picture are resources which can be deployed in bureaucratic and professional struggles, and conversely bureaucratic and professional power are resources which can be deployed in struggles involving class, gender and ethnicity.
For example, there are various ways in which male domination is maintained in bureaucracies and professions. Overt discrimination against women is the most obvious way. This is made possible by control of the top decision-making positions by men. Secondly, external support systems for employees are biased against women. Since women continue to carry most of the burden of housework and child care, most women employees are doing 'double duty' compared to men, especially those who have the support of wives for these tasks. Thirdly, organisational styles usually favour those with personal characteristics which are typically masculine, such as aggressiveness and competitiveness. Women who do not behave this way are not deemed as suitable material for promotion, while women who do behave this way are denigrated as not behaving appropriately for their sex. Finally, the gender division of labour excludes most women from opportunities to rise in organisational or professional hierarchies. Similar mechanisms are used to limit the advancement of members of ethnic minorities, those who maintain links with working class culture, and those who take threatening political stands.
This example of the meshing of bureaucracy and patriarchy is silent about the precise mechanisms of domination and group cohesion within bureaucratic and patriarchal systems. One possible analysis, avoiding the resort to a dominant ideology thesis (Abercrombie et al. 1980), could be based on the material interests of most men in patriarchal systems and of most bureaucratic elites in their positions. These elites, for example, mobilise the support of other men, lower in the job hierarchy, by supporting them against the challenge to jobs or status by women. This can explain management's promotion or at least acceptance of a constantly renegotiated gender division of labour (Game & Pringle 1983) which keeps women in the inferior jobs at the cost of overall efficiency.
How can the conventional application of the merit principle be compatible with the sort of bias consequent on the routine exercise of power to serve group interests? Let me look in turn at examinations, credentials and job performance.
The strengths and limitations of examinations in assessing merit have been studied in some depth. Their advantages include uniformity and anonymity (of those taking an examination to those marking it). But this does not remove the possibility of cultural bias. Examinations usually select out those schooled in the 'cultural mainstream' and also those skilled in taking examinations, which is again an indication of success in the dominant culture within the schooling system.
Studies have shown the class bias in IQ tests (Kamin 1974). The IQ, which is widely believed to signify innate ability, is not able to explain educational and economic inequalities (Bowles & Gintis 1976). A few decades ago, only a relatively small fraction of children completed high school and therefore those who competed for professional and managerial jobs were a select group, mostly from better-off families. As progress through high school became more universal, it seemed that everyone would be able to share in the 'common culture' sufficiently to obtain equal opportunity through examinations. But as schooling has become universalised, its focus has changed from preparation for elite careers to inculcating middle-class culture (Collins 1979) - something which works better for those with the appropriate class background and family support. Working class boys, for example, typically resist this process (Willis 1977). In any case, the outcome is culturally biased: those with the appropriate cultural background will learn most readily and be able to show their skill on ostensibly neutral examinations.
Another problem with examinations is that most of them have limited relevance to the job, since jobs are quite different from answering questions. The only really relevant examination is an 'on-the-job' test, which displaces the assessment of merit to job performance.
Even if these problems with examinations could be overcome, there is the problem of their limited use. Typically, examinations are used as a screening mechanism in recruitment, but once inside a bureaucracy, tenure is reasonably secure. A true merit system would have regular open competitions, in which any person could vie for any post. In only a few occupations, such as competitive sports and the performing arts, is there a continuous and public examination of talent and performance which affects a person's standing and career. Significantly, these occupations are notable for their absence of formal examinations, and for the relative ease with which individuals can establish themselves without credentials.
Credentials are a second major way of measuring merit. Credentials, like examinations, commonly have little relevance to the job. Most of the skills for professional and managerial positions are learned on the job (Collins 1979). The role of formal education in reproducing and legitimating the social class structure has been widely documented (Bowles & Gintis 1976). Credentials are the symbols and currency of competence, but numerous studies have shown that there is little connection between educational performance and job performance. I have talked to many students who comment, 'this course has nothing to do with my job, but I need the degree to get a promotion.'
The use of credentials to judge merit is not just to rely on irrelevant measures. Rather, the cultural and gender biases in educational systems serve as a filter which legitimates unequal outcomes. The social biases inherent in credentialing are most pronounced in poor countries such as Kenya or Sri Lanka in which qualifications are the means by which individuals can join the privileged western sector of government employment. Students desperately cram down irrelevant information in an attempt to snare one of the few high-paying jobs at the end. The result is a massively wasteful educational system, irrelevant to the needs of the bulk of the population, which serves to justify and promote the imposition of an inappropriate western model of development. The problems with credentialing are not so dramatic in richer countries, but many of the same problems exist (Dore 1976).
There are problems with using examinations or credentials to assess merit. What then about job performance? The first point here is that it is very hard to separate out the performance of an individual worker within a bureaucracy (Collins 1979; Emery & Emery 1974). Work is embedded in the organisational context. It is done within overall policies and procedures set from above. It requires cooperation with other people and resources provided by other groups. Above all, performance depends on working as part of an overall system, on making the whole operation go along more smoothly. Who is to say what was a particular individual's contribution?
This question is a key one. The answer of course is that it is those people in the top positions who evaluate performance. This gives them the opportunity to judge on the basis of conformity to the cultural norms of the organisation. The concept of 'political labour' is a valuable one here (Collins 1979). Much of the activity in bureaucracies and professions, especially in the higher echelons, consists of interacting with others through conversations, committee meetings, lunches and so forth. What is happening is a continual process of 'social negotiation' over preferences, policies and alignments. The status of any individual is at stake in this process. Those who play the game poorly, or opt out entirely, are liable to lose out in some reshuffle or power play. Others are able to forge alliances and mobilise resources to promote the interests of themselves and those similar to them (Kanter 1977). The problem here is that political labour, or in other words playing the game within organisations, is something which depends sensitively on possessing the right cultural attributes and resources. Verbal skill, personal attributes and social compatibility are important.
The importance of political labour means that it is difficult for cultural outsiders to get ahead. This mean women, ethnic minorities, nonconformists or indeed anyone falling outside the standard mould in a particular organisation. Of course, organisations vary in their cultural style. In some cases a particular group, such as graduates of a particular university, constitute the in-group. In other cases personal attributes, such as a hard-driving entrepreneurship - which can be closely linked to gender and class background - may be most important. The point is that the cultural milieu of the organisation is not neutral, but rather favours some groups over others.
A further problem is that most assessments of merit are confounded with simultaneous assessments of 'loyalty' and 'fitting in': whether a person gets along with workmates and superiors, is unlikely to rock the boat, associates with the right people, etc. This type of conformity is especially prized by organisational elites, since an uncommitted employee is a potential leader of or trigger for wider opposition. In evaluations of workers, loyalty in this sense is typically a prime consideration, often completely overwhelming the formal merits of a person who is perceived as difficult. Convincing people of one's suitability is of course a crucial part of political labour, and is inextricably linked with gender, class, ethnicity and other ascribed characteristics.
This point about political labour can be made clearer by looking at the performance of academics, who work in a more professionalised and less bureaucratised system in which achievement of individuals can be judged according to teaching and research. Teaching can be ignored here, since it is rarely judged and is not treated as important in career advancement. Research performance on the other hand is supposedly quite important, and can be judged by the public record of publications.
In practice, research productivity is not nearly so important in career advancement as commonly believed. For example, Lionel S. Lewis has shown that a much more significant factor is years of service (Lewis 1975; Lewis & Doyno 1983; Lewis & Gregorio 1984; Lewis et al. 1979). How can the apparently objective record of research be compatible with biases arising from systems of power? There are several factors.
Firstly, in research teams, the supervisor or team leader often takes undue credit for the work of subordinates. This is even more common in bureaucracies. Among public servants I have talked to, it is commonly taken as a fact of life that some superiors will claim or attempt to claim credit for the work of subordinates. Secondly, credit for research work depends on being in the right place at the right time. The same contribution is likely to be given much more attention and credit if the author is at the right university and known by the key people in the field. Those scholars who are too young, too old, women, in minor institutions or in the wrong field will be ignored. Work is judged according to who did it, not solely on the basis of the work itself (Caplow & McGee, 1958).
Thirdly, people look almost solely at research outputs, and not at the inputs to achieve them. Many male academics receive major career support from their wives (Papanek 1973). Young men who have had full support from wives are deemed more successful than somewhat older women with the same record of performance who have devoted significant time to housework and child rearing. Fourthly, appointments and promotions depend only partly on research performance. Also important are fitting in socially, working in a suitable speciality and having credentials from the right places. Finally, dissidents - those who do research or teaching or make public statements that challenge the interests of powerful groups, especially within academia itself - often encounter severe difficulties in their careers (Martin et al. 1986).
What is in operation is a highly biased system in which particularistic practices are justified by the merit principle. The widespread belief that publication is the key to success in academia testifies to the importance that merit has in legitimating academic position and power. This is compatible with system bias through the means noted above: performance is attributed to individuals even when much credit is due to subordinates or spouses, and perceptions of performance are shot through with distortions due to the current distribution of status and power.
There is really little hope of overcoming these biases by a 'true' application of the merit principle, because there are no neutral judges who sit outside the academic system. For example, judgements of academic merit partly depend on how central a contribution is to the recognised core of the discipline. This would not be a problem, except that judgements of what the 'core' is depend on the outcome of continual power struggle between individuals and groups who have their own status and power at stake in the struggle. Performing successfully means adapting to the conception of the discipline which is promulgated by the most powerful figures and groups in the discipline. Of course, these individuals and groups promote a vision which puts them in the prime positions. In other words, the assessment of academic merit within a discipline depends on the outcome of a power struggle in which the criteria of merit itself are a key stake.
All this is quite compatible with continued bias against women, ethnic minorities, members of the working class and so forth. For example, scholars who choose to develop forms of feminist analysis are almost always seen as marginal to an academic discipline. The elites of the discipline define the essence of its study in male terms or simply in terms which they, who happen to be men, also happen to control.
The importance of power struggles in academia, in which merit is a tool rather than an objective assessment, throws light on struggles in more bureaucratised organisations. Performance within bureaucracies is much more embedded in the organisational context than it is in academia. Unlike academia, it is not easy to appeal to experts in other organisations to judge performance by assessing publications. The good graces of supervisors, the cooperation of co-workers and the availability of support systems for non-work life are all vital.
All this means that performance must be judged by a 'merit system' which includes an enlightened evaluation of these factors. But good intentions and enlightened assessments are hardly sufficient to establish a merit system. As long as the organisational resources are available to be used in power struggles, then they will be used to maintain and extend the power of those who are best able to deploy them.
Within bureaucracies, the Weberian model of rational administration is itself a powerful rhetorical and ideological resource for maintaining commitment to the organisation. The belief in bureaucracy as administration is favoured and promoted especially by those who are successful in the system, since it attributes that success to individual performance rather than to being on the winning side of a power struggle reliant on cultural resources.
In summary, individual productivity has a relatively low impact on career performance in large-scale organisations. Advancement depends greatly on jockeying for position, for example by forming alliances, obtaining personal credit for collective work and increasing the evaluation of particular types of contributions. In this struggle for position, resources provided by culture - namely the dominant white middle-class male culture - are vital.
While the reality is that the struggle for advancement is basically part of a wider power struggle, it is no longer acceptable to admit the importance of system biases in an era in which egalitarian sentiments are strong. Hence it is very convenient to justify decisions on the basis of merit - for example academic credentials - because this legitimates inequality. This is the basis of the defence of 'merit' by traditionalists who in practice oppose changes in the gender and ethnic composition of hierarchies. The supporters of legislated equal opportunity on the other hand recognise the biases built into normal selection processes and therefore push for 'true' adherence to the merit principle, in other words merit stripped of its links to gender stereotypes, middle-class culture and so forth. This is the explanation of the paradox of merit: that both opponents and proponents of equal opportunity make appeals to it.
What then should the harried equal opportunity officer or personnel manager do with the merit principle? Is it simply a tool of those already in power? Or is it, as usually thought, a tool of those who are actually achieving valuable things in their work? The answer is that merit is a tool for both groups at the same time.
To recapitulate: under the ideal-typical conception of bureaucracy as a system of rational administration, merit can be used unambiguously as a measure of performance, and affirmative action then can be used to assure true equal opportunity. I have argued that the picture of bureaucracy and professions as political systems is more realistic. In this picture, 'merit' is not something judged in the abstract, but rather is something continually created, debated and negotiated through the social processes of the organisation. Those individuals and groups with the greatest power are in the best position to shape the conception of merit to serve their own ends. But, at the same time, others with less power can argue for a different interpretation of merit which promotes their interests.
In this view, what is called merit is a tool in the power struggles within bureaucracies and professions. Those promoting the interests of disadvantaged groups should not assume that an argument based on merit will be taken on face value. Rather, an argument promoting the interests of disadvantaged individuals or groups, based on claims about merit, is part of a political move to change the distribution of power, in either a minor or major way. It should be expected that some of the merit arguments will be contested, less by direct rejection than by a different interpretation of merit. The change in general definitions of merit over the years (Stanton 1978) - for example from legislation against discrimination to affirmative action, and then to comparable work - is a consequence of the challenges mounted by blacks and women. Interpretations of merit are intrinsically political, just as are bureaucracies and professions, in the sense that power is always involved rather than just rationality and formal procedures.
If merit is a tool or resource used by different groups in struggles within bureaucracies and professions, the question arises, who can most easily use this tool? Tools, whether butter knives, nuclear weapons or ideas, are not equally useful for performing tasks. Butter knives are more suited to cutting butter than are chain saws. The idea of merit in many circumstances is of great value to disadvantaged groups: the most blatant forms of discrimination are harder to sustain. But merit is not a perfect tool for creating equal opportunity: it has a fundamental flaw.
The most massive barrier to application of the merit principle in bureaucracies is the division of labour. It is virtually impossible for a cleaner or a steno-secretary to move into top management - or even to move from her position - no matter how well she does her job. In any situation where there are large differences between jobs, the problem arises that people can't be judged as unsuitable until they have been given a chance in the other job. The incongruities involved in actually putting people into jobs of completely different status forms the basis of the humour in the story of a millionaire and a pauper who change life situations, for example in the film Trading Places.
in some bureaucracies a limited degree of job rotation is practised. This certainly has the advantage of allowing individuals to show their ability in a variety of positions. But usually job rotation is only carried out with tasks on a similar level. Managing directors are not rotated to be gardeners, nor vice versa. In practice, many workers are refused any real chance to move out of dead-end positions.
The main way this is justified is through appeal to the merit principle! For example, typists are refused opportunities to undertake research positions because they have neither the right credentials nor appropriate experience.
The usual pattern then is one in which credentials and experience are used to justify appointments and promotions. The problem is that the credentials usually have little relevance to the job, and previous experience says little about a person's ability to handle a different type of job. One example is teaching. The theoretical, classroom part of teacher training is notorious for being irrelevant to actual teaching. (Apprentice teaching, essentially learning on the job, is literally the exception which proves the rule.) Once on the job, some teachers are promoted to administrative positions. There is no logical reason why excellence in teaching would be a basis for promotion to administration, even if excellence in teaching were taken as the criterion of merit (male ambition seems a more common reason for promotion among teachers).
This brings me to what I believe is a fundamental flaw in the usual conception of the merit principle. The application of 'merit' assumes not only that individual achievement can be measured, but also that the existing occupational slots are suitable for the allocation of meritorious workers to them. In other words, the merit principle assumes that the slots are fixed while people are chosen for them - not vice versa.
The difficulties in this can be illustrated by a not-so-hypothetical example. Assume that there are 10 people working in a section. They are all literate and have an average potential for learning. In a bureaucratic system, the 10 people are ranked 1 to 10: one person administers from the top while those at the bottom do routine work requiring little or no initiative. The person at the top develops a broad view of the operations, hobnobs with corresponding figures in other sections, obtains inside information about the organisation and about the other workers, and gains increasing confidence and self-assurance through the exercise of power and from the deference of subordinates. The point of this is that the initial distribution of workers into slots could almost have been done at random, and the result would have been the same. The power system creates the very differences in information, confidence and performance which are used to justify it.
In practice, the workers are not allocated at random to different slots. White middle-class men hold most of the positions of power, and they use that power to maintain themselves and those like them in the top positions. The merit principle helps to sustain this system by justifying it; the merit principle may be the best justification yet for a highly stratified society (Young 1958).
But to be fair, it is not the merit principle which lies behind stratification. The most important support for system bias is the hierarchy itself. Resources are given to small groups which they can use to maintain their privilege. It is inevitable that groups with more cultural resources - whether this is maleness or ethnic dominance - will use those resources to gain organisational power, and use organisational power to promote group interests. While insisting on the application of a 'true' merit principle has the potential to make inroads into this system, a more far-reaching approach is to restructure the job hierarchy and division of labour.
The standard solution is worker self-management, in which workers collectively decide on how they will organise their work and carry it out. There can still be a division of labour, but it is one that is freely chosen (and it is likely to be a division that changes more or less frequently). Worker self-management needs to be accompanied by job redesign, in which the technology and the organisational decision-making process are set up in a way which fosters equality and participation by all workers (Bolweg 1976; Emery & Thorsrud 1976; Herbst 1976; Hunnius et al. 1973; Roberts 1973; Wilson 1974).
I have claimed that the power systems in bureaucracies and professions generate differentials in information, confidence and performance. What is the evidence for this claim? Actually, the best evidence comes from experiences in worker self-management, in which workers are given the chance to demonstrate their capacity in a supportive environment. Most people are able to learn the complex skills of driving a car or managing a household. Similarly, most people should be able to learn carpentry and learn to manage a carpentry business.
What would merit mean in a workplace in which the workers collectively controlled their work? In such a situation, merit could be recognised even though performance was embedded in the work organisation. For example, some workers might be able to do certain jobs quicker or more elegantly. Indeed, it would be easier to assess merit in many cases since different workers would be regularly doing the same tasks, for example on a rotating basis. It would also be easier to assess merit because many of those doing the assessing would have recently done the same tasks themselves.
Let me now compare the definitions of merit under hierarchy and self-management. The usual definition is built around picking the individual who will perform 'best' in a given job situation. If meritocracy is justified on the basis of its greater productivity, this usual definition is a micro principle: merit considerations apply to each job assignment in isolation from other jobs. A slightly wider picture arises from the aim of maximising productivity from a whole ensemble of jobs. People are assigned to jobs in a way which maximises productivity for the full set of jobs. This macro principle of merit on occasion may violate the micro principle. The macro principle again assumes a fixed distribution of jobs (Daniels 1978).
Under self-management, jobs are not fixed. Rather, the design principles for work are themselves something to be democratically decided. Under the project of socio-technical design (Herbst 1974), merit is just as usefully attached to the organisation of work as to individuals. The most 'meritorious work organisation' is the one which maximises the performance, satisfaction and personal growth of all individuals, within the constraints of current knowledge and resources. (Some might prefer a maximin principle in which the aim is to maximise, relative to feasible targets, the performance, satisfaction and personal growth of the person least advanced in these areas. The maximin principle is designed to avoid a utilitarian maximisation which perpetuates inequalities.) For example, socio-technical design typically implies elimination or automation of jobs which are satisfying to no one, rather than automation on the basis of profits and material productivity.
Although the introduction of self-management is often associated with lowering productivity, actually the converse is often the case (Melman 1958). Self-management can increase conventional productivity - not to mention worker satisfaction - because the capacities and enthusiasm of workers are more effectively used. Another way to look at this is that hierarchical structures carry a burden of inefficiency, namely the managerial and technological expense and organisational rigidity required to keep workers in their place (Braverman 1974). As often as not, the productivity loss required to maintain hierarchies is greater than the loss entailed in self-managerial decision-making processes.
One other point is worth making: there is no reason why merit and a more responsible position should automatically lead to greater rewards for a person (Daniels 1978; Luard 1979, pp. 89-75). Under a meritocracy justified by productivity, the only differentials in rewards would be those necessary to motivate workers, and these would be far less than those in present bureaucracies. According to the political perspective on bureaucracy and professions, the reason why merit and reward are conventionally linked is that those with power use that power to increase their income. Where the medical profession is powerful, as in the United States and Australia, average incomes of doctors are high. Where medical workers are more subordinate to the state, as in the Soviet Union, their average incomes are closer to the average wage.
Under self-management, there would be no reason for meritorious performance to lead to greater formal power to tell other workers what to do, nor to gain disproportionate economic rewards. That would not be compatible with the principle of self-management, and in any case it would not be necessary. Those workers who worked harder or came up with better ideas would be naturally recognised by the others for the value of their contributions. The reward for good performance would be the performance itself, more influence (since others would respect the person's views) and more recognition.
Self-management is not an alternative sitting on the shelf waiting to be applied should the decision be made. Rather, the operation of self-managing systems would depend on the political processes used to establish and maintain them, just as in the case of the operation of bureaucracies and professions. Still to be further studied and developed through practice are the limits of consensus decision-making (Mansbridge 1980), the role of community control (Morris & Hess 1975) and the nature of wider political decision-making (Benello & Roussopoulos 1971). Self-management is part of a particular strategy for social change. For example, whereas many liberal feminists use the merit principle to help the cause of women within bureaucracies, some radical feminists favour self-management as an alternative to bureaucracy itself (Ferguson 1984).
The alternative of worker self-management throws light on the assumptions underlying the usual use of the merit principle. Applied to advancement within a bureaucratic system, merit is inevitably linked to the exercise of power. The evaluation of merit is shaped by the current elites and is also used to justify the hierarchy itself. Those pushing for equal opportunity through application of 'true' merit have an uphill battle because they must accept the hierarchy and division of labour which give power to those groups with the greatest cultural resources. Merit in this situation can never be a neutral principle to judge contenders in the occupational power struggle. Rather, merit is a tool in the power struggle itself.
For those who are pushing for rights for women, ethnic minorities, the handicapped and so forth, it is important to realise that using merit as a lever for the advancement of individuals has important limits. It does nothing for the bulk of workers who are relegated to dead-end jobs and occupations, and it may help to legitimate the whole system of inequality and privilege. Instead of applying the merit principle only to individuals, it should also be applied to work structures. Instead of workers being judged according to how they fulfil fixed job specifications, work structures should be evaluated according to how they allow the greatest use and development of each person's potential contribution. The challenge is to turn this vision into a practical program for organisational change (Williams 1982).
Hester Eisenstein and two anonymous referees provided valuable comments on an earlier version of this paper.
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The influence of brand equity on consumer responses: a replication and extension
Mkhize, Duduzile
URI:
https://hdl.handle.net/10539/27790
Date:
2018
Abstract:
Purpose: The purpose of this paper is to replicate and extend the brand equity model that was developed by Buil, Martínez, and de Chernatony (2013) in South Africa. The paper also seeks to compare the impact of brand equity on consumer goods and in media companies. Design and Methodology: Structural Equation Modelling was used to test the hypotheses. Classic continuous modelling techniques and structural equation path modelling were used. The structural equation models were conducted using the twophase approach: the measurement section is analysed in a confirmatory factor analysis and path models are then constructed as per the Buil et al. (2013) model and analysed for deviations. Findings: The results of the study were quite similar to the original study done by Buil et al. (2013). There was a positive correlation between overall brand equity and the underlying dimensions of brand equity. All hypotheses aside from those for perceived quality were supported. In the inter-category comparison, there is no difference, the consumers of media are also influenced by brand equity and its dimensions. However, overall brand equity seems to be very important for influencing purchase intention for television broadcasters. Limitations: This research was limited to South Africa; thus, it cannot be generalised to other countries. The research was also limited to people with access to smart phones and computers, as it was only available online. There is an opportunity for the study to be replicated in other countries and also in a way that is accessible to people who do not have access to computers. In the findings, there was consistently high and significant positive correlations between all variables that act to support the model; this could be a limitation as some of this strength may arise from common method bias. The survey participants had to answer all questions using the slider; this might have caused the bias. The research produced a high number of incomplete surveys. Future research: The analysis of Lagrange multipliers suggests two paths that could be considered, namely, for direct associations between purchase intention and both brand awareness and brand associations.
Description:
A research article submitted to the Faculty of Commerce, Law and Management, University of the Witwatersrand, in partial fulfillment of the requirements for the degree of Master of Business Administration Johannesburg, 2018
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Lamivudine, a commonly used antiretroviral medication for the treatment of HIV, improves the cognitive capacity of a mouse model of Down's syndrome, according to a new joint study by researchers at the Centre for Genomic Regulation (CRG) and the IrsiCaixa AIDS Research Institute, a centre jointly promoted by the "la Caixa" Foundation and the Catalan Government's Department of Health. The article has been published in the Journal of Cellular and Molecular Medicine.
Although clinical studies are needed to confirm that the drug has a similar effect in humans, the results of this animal study highlight the potential of using pharmacological interventions such as lamivudine - or other drugs capable of blocking the same therapeutic target - as a treatment to improve cognitive impairment in people with Down's syndrome.
Down syndrome is a condition caused by the presence of an extra chromosome in the genome. Normally, the human genome contains 23 pairs of chromosomes, but in the case of Down's syndrome, one of these pairs has three copies instead of two, namely chromosome number 21. This results in an intellectual disability that can range from mild to moderate, affecting general cognitive skills such as memory, attention span and speech. In addition, when they reach adulthood, people with Down's syndrome experience accelerated ageing. This results in the onset of cognitive decline that, in the general population, would be typical of older people.
People with Down's syndrome are also at increased risk of Alzheimer's disease because their chromosome 21, which is triplicated, contains the genes for a protein that is particularly relevant to Alzheimer's disease. This protein, known as amyloid precursor protein (APP), has the ability to accumulate in the brain generating protein aggregates that cause altered brain function. The presentation of these protein aggregates is common in most adult individuals over the age of 40 with Down syndrome.
To support independent living, most people with Down syndrome undergo psychosocial interventions such as cognitive stimulation therapy, one of the only treatment options currently available as there are currently no pharmacological interventions. Now, the results of this study point to a possible drug treatment pathway and position retrotransposons as a potential therapeutic target of great interest for Down syndrome.
Retrotransposons are segments of DNA that change their location within the genome; to do this, they create RNA copies of themselves to move out of the area of the genome where they are located and then convert back into DNA so that they can be inserted back into the genome, but in a different location. These segments can insert themselves into specific areas of the genome and, by chance, position themselves in gene promoter regions associated with neurodegenerative diseases, boosting their activity. The activity of these DNA segments to jump from one site to another in the genome increases with age.
In addition, retrotransposons have some similarities to HIV in that, like HIV, they need to switch from DNA to RNA, and vice versa, to make copies of themselves. Thus, researchers hypothesised that the use of molecules capable of inhibiting HIV replication - such as the enzyme reverse transcriptase - could also work to block retrotransposons.
"Both HIV and retrotransposons need the same molecule to make copies of themselves: the enzyme reverse transcriptase," explains Dr Bonaventura Clotet, director of IrsiCaixa. "The scientific community had shown that lamivudine, an inhibitor of this enzyme already used against HIV, decreased the activation of retrotransposons in aged mice. We therefore thought that the use of lamivudine could also be useful in counteracting the cognitive impairment associated with Down's syndrome," he adds.
To demonstrate this, researchers worked with Ts65Dn mice, the most studied animal model of Down's syndrome to date. For four months, one group of mice was treated with lamivudine, while the other was used as a water-only control. The team then conducted several behavioural experiments designed to test locomotor activity, recognition memory and anxiety. They found that the mice receiving lamivudine showed improved cognitive abilities. The results of the study hypothesise that the observed benefits of lamivudine may be due to its effect on one or more variants of the APP gene.
"Our work aims to support people with Down syndrome and their families by giving them more options for independent living, particularly for individuals affected by early-stage Alzheimer's disease," says Dr Mara Dierssen, CRG researcher and co-author of the study.
"We still need drug treatments that consistently help to improve memory, attention and language functions, or prevent cognitive decline associated with ageing. This study is a step towards changing this situation, as it reveals that retrotransposon activity is an interesting mechanism to study not only in ageing, but also in neurodevelopmental disorders," concludes Dr Dierssen.
Lamivudine is a prescription drug approved by US and EU medical authorities for the treatment of HIV infection in adults and children. The next step for the research team is to start clinical trials with the drug for people with Down's syndrome and Alzheimer's disease. | https://atalayar.com/index.php/en/content/common-antiretroviral-medication-improves-cognitive-ability-mouse-model-downs-syndrome |
Writing essays is thought of as one of the hardest and most difficult task in college. In fact, it’s been called as the author’s responsibility to present his/her viewpoint on the specified subject. Essays are normally a mix of personal experience and academic knowledge. As such, an essay is considered to be a formal sort of record which presents some details and ideas. The main purpose of composing an essay is to put across the idea in an orderly way.
Writing essays requires the author to have a fantastic control on grammar, reading comprehension, and writing styles. In addition, he should be able to investigate and collect enough information about the subject he will be writing about. Moreover, since writing essays is usually on a particular topic, it requires the students to have the capability to analyze, synthesize, and interpret the given information. The writing process of an essay involves essay punctuation checker the author presenting his view or interpretation about a specific subject, or he is required to do some research on the specified subject. It also has to be remembered that since writing essays involves critical evaluation, the writer should be careful not to plagiarize anything from different sources.
After finishing the writing process, the essay usually tests the capability of the pupil to organize, control, and evaluate information. Essays are made on specific topics and also the essay itself is based on the thoughts, perspectives, and opinions of this author. Dependent on the specific subject of the essay, different styles of writing may be used. However, the most usual fashion of writing an essay is written with a personal opinion.
Essays may be written in a prescribed order, which might vary according to the topic of the given assignment. A frequent structure for essays is based on the private thesis statement that is written in the very beginning of the essay. A more structured type of structure is offered by an outline of this essay, which is a part of the composing process.
In composing a persuasive essay, there must be a clear demonstration of a specific argument. But it has to be proven that the topic is correctly known and is relevant to the topic of the essay. The writer must demonstrate their knowledge through proper research. For instance, if the topic is all about public safety, an author must first show that there is a need for public safety.
Writing a knowledge based composition requires one to think critically. The whole essay depends upon the knowledge supplied by the author. There are many skills which are developed when pupils are writing such assignment. One of comma checker these skills is being adept in organizing advice. Thus, correct organization of the information needed while developing a knowledge based argument is a vital skill to learn. | https://www.pagolo.net/2022/11/07/writing-an-essay-requires-critical-and-knowledge-based-opinions/ |
The earliest Russia’s track and field suspension can be lifted is February.
Banned since November 2015, Russia has made progress toward satisfying reinstatement conditions since June, said Norwegian anti-doping expert Rune Andersen, who has headed an independent inspection team to monitor Russia’s progress.
The IAAF, track and field’s international governing body, won’t make a decision regarding lifting Russia’s ban until at least February. Then, the independent inspection team hopes to provide a timeline for Russia’s potential reinstatement.
Andersen outlined three criteria that must be met.
- Russia’s track and field federation complies in full with the World Anti-Doping Agency Code and IAAF anti-doping rules.
- IAAF and Russia’s anti-doping agency (currently non-compliant) are able to conduct their anti-doping programs in Russia and, in particular, drug testing effectively and without interference.
- Reintegration of Russian athletes into international competitions will not jeopardize the integrity of those competitions.
“There is a recognition that it is important that clean athletes are given a system to get back into competition, but as the report says, they do not jeopardize the rights of the clean athletes and certainly don’t jeopardize the integrity of the competitions they come back to,” IAAF president Seb Coe said.
A key date on the road to February is Dec. 9, when independent investigator Richard McLaren is to deliver his final report on doping in Russia.
Russian athletes can still apply to a doping review board to compete individually while Russia is banned, if they have been subject to robust testing.
One Russian track and field athlete, Darya Klishina, competed in the Rio Olympics, finishing ninth in the long jump.
The next major international track and field event for Russians is the European Indoor Championships from March 3-5 in Belgrade, Serbia. | https://olympics.nbcsports.com/2016/12/01/russia-track-and-field-ban-doping/ |
The Newfoundland and Labrador Archaeological Society (NLAS) is keen on engaging with private collectors of archaeological material. Under the Community Collections Archaeological Research Project (CCARP) the NLAS hopes to locate and record these private collections as well as facilitate public education and awareness of heritage and archaeological resources. The attached PDF report and photo gallery showcases artifacts collected by Baxter Andrews on Cape Island in Cape Freels, Newfoundland, between 1953 and 2010. Seventeen artifacts were surfaced collected by Mr. Andrews from eroding sand banks during walks along the beach with his wife Bernice. The artifacts represent six precontact cultures including: Maritime Archaic Indian, Dorset Palaeoeskimo, Cow Head Recent Indian, Beaches Recent Indian, and Little Passage Recent Indian-Beothuk. This is the second collection catalogued under CCARP.
It’s important to note that collecting artifacts is contrary to Newfoundland and Labrador’s Historic Resources Act. With this project, the NLAS does not condone the future collection of artifacts, but rather, it serves as a mechanism which allows existing collections to be shared for educational purposes.
The Community Collections Archaeological Research Project was funded through the Cultural Economic Development Program – Heritage, Department of Business, Tourism, Culture and Rural Development. The work was carried out by John Andrew Campbell, Department of Archaeology, Memorial University of Newfoundland.
Baxter Andrews Collection photo gallery | https://nlarchsociety.ca/2016/03/04/community-collections-archaeological-research-project-baxter-andrews-collection/ |
Langjökull Tours
Iceland is famous for the extraordinary natural beauty of its volcanic-carved landscapes and more than ten per cent of the island is covered with ice. The nearest extensive glacier to the capital city of Reykjavik is Langjökull, which stretches across 367 miles sq (950 km sq) in the mid-western highlands and is the second-largest in the country. The glacier sits at 4,000 ft (1,200 m) above sea level and its melt waters travel through subterranean streams to feed Lake Þingvallavatn 32.25 miles (50 km) to the south. Over many millennia Langjökull’s ice has grown to a thickness of 1,650 ft (500 m), and in 2010 a system of vast manmade ice caves and tunnels were excavated underneath the glacier, big enough to be explored by eight-wheeled trucks, which venture underground to tour a mysterious world of dazzling blue and silver compacted ice.
Visiting Langjökull can be combined with a tour of the Golden Circle, a popular sightseeing route from Reykjavik that encompasses some of Iceland’s most extraordinary geographical phenomena, from geysers and volcanic craters to spectacular waterfalls such as Gullfoss. The snow-swept countryside around the glacier is also popular for snow mobile expeditions, cross-country (Nordic) ski-ing, trekking and mountaineering.
Practical Info
Langjökull is 12.5 miles (20 km) from Husafell down an unmade track, which is open June through September, weather permitting. Thanks to the unpredictability of the ice, it is not possible to make a private visit to the glacier.
| |
The Trappists are Cistercian monks, belonging to the great monastic family of St. Benedict, of which it is a “reformed” branch.
The order had its origin in the twelfth century with the founding of Citeaux, the first monastery of our order established in Bourgogne, whose daughter houses and influence soon extended throughout Europe, thanks to the extraordinary spiritual gifts of St. Bernard (1090-1153).
A group of monks of Ia Trappe, a Cistercian monastery in Normandy, were the sole survives of the French Revolution of 1789. It was they who re-established the Order, and who gave it its popular name of Trappists.
The work of reclaiming and cultivating the land, which is the basis of the livelihood of the monastery, began immediately: olive groves, vineyards grain fields and vegetable gardens in the fertile places, with pine trees and cypresses in the rocky areas.
In 1890 a call came from the Holy Land to found a contemplative monastery there. It was the Abbey of Sept-Fons in the diocese of Moulins in France who sent monks to establish Latroun.
At the beginning of the First World War, the monastery was surprised and its laborious progress came to a halt. Because of the political situation, the monks were expelled, but at the end of the hostilities, they returned. In 1926 they began the construction of the Monastery as you see it today.
The Abbey is situated in the foothills midway between Jerusalem and the coast, with the plain of Sharon to our north-west, and the plain of Esdreion to our south-west. The monastery is built on a hillside. At the top of the hill are the ruins of a crusader castle.
From Latroun there is a beautiful view of many biblical sites: Emmaus, Ayalon. Bethoron, Gezer, Modin, Lydda, Sorec and Jaffa.
An atmosphere of peace and recollection, in silence and solitude, offers an invitation to lift the soul to God. With the monks coming from different countries, the community offers an image of a little “Society of Nations” where a common rule and fraternal charity establishes a unity of hearts. | http://holy-wine.com/home/welcome-to-holy-wine/ |
Gross revenue stood at $12.5 million for the quarter, missing the IPO forecast of $21.5 million by 42.1 per cent.
The lower revenue was mainly attributed to the effect of Singapore's circuit breaker measures and rental waivers granted to tenants at 313 @ somerset, the manager said in a regulatory filing on Tuesday. This was partly offset by higher revenue from Lendlease Global Reit's office asset in Milan, Sky Complex, due to a stronger euro against the Singapore dollar, the manager said.
For Q4, net property income (NPI) of $7.5 million was 53.3 per cent lower than the $16.1 million forecast.
Distributable income came in at $5.7 million for the quarter, 62.2 per cent below the IPO forecast of $15.1 million.
Landlease Global Reit was listed on the Singapore Exchange's mainboard on Oct 2, 2019, with the real estate investment trust (Reit) jumping 6.8 per cent on its trading debut. The Reit's IPO had ended with its public offer tranche 14.5 times subscribed.
For the period from Oct 2 to June 30, DPU was 3.05 cents, 19.7 per cent lower than the IPO forecast of 3.80 cents. A distribution of 1.29 cents per unit was paid on March 16 this year. The remaining DPU of 1.76 cents will be paid out on Sept 15, after books closure on Aug 19.
Gross revenue for the period was $55.5 million, 13.1 per cent below the IPO forecast, while NPI stood at $40.3 million, 15.6 per cent below the forecast.
Kelvin Chow, chief executive officer of the manager, noted that safe distancing measures at 313 @ somerset may "inevitably affect footfall and tenant sales", and that the manager will continue to engage with tenants in meeting their space requirements.
He added that Sky Complex is expected to "remain stable and generate steady revenue" to the Reit, given its long lease term till 2032, assuming that Sky Italia does not exercise its break option in 2026. "Alongside its triple net lease structure, Sky Complex helps to mitigate downside risks during Covid-19," Mr Chow said.
As at 10.55am on Tuesday, units in Lendlease Global Reit were trading at 62.5 cents, down 2.5 cents or 3.9 per cent.
The Straits Times
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As awareness of mental illness and common sources of stress continue to grow, the field of psychology is rapidly expanding. Developmental psychology is one of the main fields of psychology, because it encompasses all individuals. From those with mild stress to those with mental conditions, developmental psychology plays a crucial role in the function of many clients. As a result, developmental psychologists are know found in many different settings, including schools, hospitals, and nonprofit agencies. In these settings, psychology professionals are expected to work with a wide array of patients, including elderly individuals, teens, children, those who are mentally ill, and disabled individuals. Families, victims of abuse, and those who fell victim to drug/alcohol abuse are all common consumers of developmental psychologist services.
Individuals who go into the field of developmental psychology are expected to research and study contextual aspects of life such as gender and culture as well as socioeconomic factors. Since this field encompasses almost any aspect of the human experience, many developmental psychologists choose to narrow their field of study down to a particular stage of life (infancy, childhood, adolescence, adulthood, geriatric, etc.). Many career opportunities within this field require candidates to have at least a Master’s Degree in Psychology. However, internships and social field work allow students to gain work experience before graduating college. Positions that entail duties such as teaching and those that are research-based usually require a Ph.D. Some individuals may even be eligible to participate in student teaching prior to graduation in order to gain more experience.
Since there are so many diverse opportunities within the psychology field, one can expect a variance in salaries. While a behavioral technician may make a median of $25,000 annually, a psychologist can expect to earn around $85,000 annually. Psychology assistants also rank at the lower end with annual earnings of around $40,000, while an educational diagnostician can expect to earn around $68,000. As with any other career, salaries increase with education and experience. Salaries may also vary between different geographic areas and may be dependent on the need of such services in any particular setting.
Depending on the type of facility one is employed at, a developmental psychologist can perform a wide array of duties. From performing psychology-based research to working independently as a counselor, developmental psychologists have many career options. From a typical day as a preschool counselor to one as a rehabilitation assistant as a residential facility, developmental psychologists are needed in various settings to perform a wide array of duties pertaining to the well-being of patients. No matter what setting one is employed within, the ultimate duty of a developmental psychologist is to help individuals deal with stress that is caused by common occurrences. Eliminating or managing stress can lead to better health, less anxiety, and more pleasure from daily life for most clients. In the case of children, simply having another caring individual listen to their concerns can relieve stress and enhance desirable behavior.
American Psychological Association – The world’s largest association of psychologists, consisting of over 137,000 researchers, consultants, researchers, and clinicians.
Social Psychology Network – Features developmental psychology subtopics with links for more information about each field.
Psychology Careers – Obtain details about the career field of developmental psychology, including current trends, pay rates, and duties.
Psychology Field – Explore the Princeton Review pertaining to developmental psychology and essential educational information for success in this field.
Child-Psych – A research blog that explores issues related to child psychology and parenting.
The Mouse Trap – Comprehensive scientific findings featured in a blog that is displayed from methodical and analytical viewpoints.
American Psychological Society – Offers a wide array of developmental psychology research that is education-, research-, and analytically-based. | https://www.bestpsychologydegrees.org/subfields/developmental-psychology/ |
Background
==========
During recent decades, rates of mortality from coronary heart disease (CHD) have steadily declined in Sweden as in many other Western European countries and Northern America \[[@B1],[@B2]\]. A suggested explanation for the decline is that severity of acute myocardial infarction (AMI) has been reduced as a consequence of not only treatment procedures but also by primary prevention efforts \[[@B3]\]. Psychosocial stress in relation to AMI \[[@B4]\] has made it necessary to include the concept of stress as a risk factor that should be targeted in primary prevention programs.
Stress is subjective because it reflects a dynamic relationship between an individual and the environment. Coping strategies are used to modify psychological and physiological reactions of stress and are generally thought to have a buffering effect on stress. The coping process includes behavioral efforts but also cognitive dimensions because action is preceded by an appraisal of both the situation at hand and of available coping resources \[[@B5]\]. Individuals react differently in response to different stimuli depending on situation, nature of the stressor, and predisposition. Different coping responses have different physiological correlates. Active coping has been related to increased catecholamine release and sympathetic activation whereas passive behavior has been related to corticosteroid secretion \[[@B6]\]. If a stress reaction takes place it is assumed that the coping strategy was not sufficiently efficient or that it was maladaptive. Maladaptive coping is a response that elicits or maintains a harmful physiological process and if this occurs repeatedly the probability of mortality and morbidity is assumed to increase \[[@B7]\]. Individual differences in ability to cope with stress could serve as an explanation as to why certain individuals are more vulnerable than others.
We have previously shown that it is possible to assess how an individual cognitively manages and adapts to a stressful situation by the use of the serial Color Word Test (CWT) \[[@B8]\]. The test was included in the cohort study \"Men born in 1914\" in Malmö \[[@B9]\] which was the first time the test was used in an epidemiological context. Our analyses showed that the semi-experimental application of the test could be a significant contributor when analyzing prospective cardiovascular risk. Hypertensive men who many years in advance of a clinical event had difficulties to adapt to the stressful test were exposed to an increased risk of a myocardial infarction (MI) \[[@B10]\] or stroke \[[@B11]\]. Ventricular arrhythmia \[[@B12]\] and asymptomatic atherosclerosis \[[@B13]\] were less important predictors among the men who managed to handle the stressful task in an adaptive manner. Postinfarction mortality within 28 days and within one year could also be explained by behavior in the serial CWT \[[@B14]\]. Men with difficulties in the test were also less likely to benefit from a supportive network and were consequently exposed to an increased risk of a future MI \[[@B15]\].
Personality dimensions have been investigated in the pursuit of links between psychology and vulnerability in association with CHD. Personality can be defined as \"those characteristics of the person that account for consistent patterns of feeling, thinking, and behaving\" (16, p. 4) and could thus be viewed as a factor explaining why certain behaviors are expressed when an individual interacts with the environment. The Type D personality \[[@B17]\] and hostility \[[@B18]\] are examples of personality traits that have been associated with cardiovascular morbidity and mortality. The tendency to show exaggerated cardiovascular responses in association with mental stress has been labeled cardiovascular reactivity and such increased reactivity may act as a risk factor for coronary artery disease (CAD) development \[[@B19]\]. Cardiovascular reactivity has been related to exaggerated blood pressure responses \[[@B20]\], progression of carotid artery atherosclerosis \[[@B21]\], and increased serum lipid concentrations \[[@B22]\]. The phenomenon is not observed in all individuals and it has therefore been proposed that cardiovascular reactivity bears associations with dispositional factors \[[@B23]\]. Differences in cardiovascular reactivity as a response to stress could thus also explain why certain individuals are more vulnerable than others.
Our knowledge of which individuals are exposed to the greatest risks needs to be improved if primary prevention of MI shall be efficient. Popular opinion associates stress with MI in general whereas our assumption is that certain individuals are more vulnerable than others when exposed to stress. Maladaptive behavior as reflected in the serial CWT has previously been identified as a risk for cardiovascular events and one objective of the current study will be to explore whether maladaptive behavior also is associated with severity of MI. The five factor model of personality distinguishes five factors of personality and gives measures on Neuroticism, Extraversion, Openness, Agreeableness, and Conscientiousness \[[@B24],[@B25]\]. Because the personality trait Neuroticism is related to emotional instability, anxiety, and depressiveness this would be the trait most likely to be associated with severity of disease. A second objective will be to consider whether maladaptive behavior in combination with any of these personality dimensions is associated with severity.
Methods
=======
The Secondary Prevention and Compliance following Acute Myocardial Infarction (SECAMI)-study was designed as a patient-based prospective cohort study with an overall aim of identifying the psychosocial factors that increase the risk of mortality and determine compliance with treatment. The serial CWT was included at baseline and at the same time measures on personality were collected.
The chosen indicators of disease severity were the biochemical markers maximum troponin I and creatine kinase-MB maximum levels above medians \[[@B3],[@B26]\]. In addition, we chose Q-wave infarction \[[@B26]\], and a left ventricular ejection fraction (LVEF) ≤ 50% \[[@B17],[@B27]\] to indicate severity.
Patients
--------
The collection of baseline-data in the SECAMI-study started in 2002 and ended in 2005. At the Cardiology Department, Skåne University Hospital, Malmö, approximately 630 cases of acute MI are treated each year and about 240 of these patients are below the age of 71. All patients with a diagnosis of AMI (International Classification of Diseases (ICD) ICD-10 code I21) who had not reached their 71st birthday were invited to take part. The cut-off at 71 years was decided on because we did not want to expose elderly patients to a large collection of examinations in such close proximity to the acute event. Patients below the age of 71 who did nor want to participate or had communication problems were excluded. At times of research staff\'s absence AMI-patients could not be asked to participate which constitutes another exclusion factor. Data from medical charts and socioeconomic circumstances together with cultural background were recorded. Before discharge, each patient met a clinical psychologist who administered the serial CWT and the questionnaire on personality.
Four hundred patients were included in the SECAMI and 180 patients were able to participate in the serial CWT. Thirty-three patients were excluded because of non-participation in all or some of the examinations of interest to this study. The analyses, thus, include 147 patients with a mean age of 58.1 years (range 30-70 years) and 39 (26.5%) were women.
Written consent was obtained from each patient and The Ethical Committee of the Faculty of Medicine, Lund University, Sweden, had approved the study.
Background characteristics
--------------------------
Background characteristics included educational level (less than nine years/nine years or more), whether the individual had immigrated (yes/no), was living alone (yes/no), and whether the individual was professionally active or employed (yes/no).
Clinical characteristics
------------------------
Patients were asked about smoking habits and current smoking was coded as such when smoking was acknowledged (independent of quantity). The artery interventions Percutaneous Coronary Intervention (PCI) and Coronary Artery Bypass Graft (CABG) that the patients had undergone during previous hospitalizations were asked for and were here treated as a single variable called \"previous revascularization\". Registration was also made of previous MI, treatment of hypertension, hyperlipidemia, angina pectoris, diabetes mellitus and level of body mass index (BMI). The Beck Depression Inventory (BDI) \[[@B28]\] was used to measure prevalent depression. A cut-off at 17 points or more was used to indicate moderate to severe levels of depression \[[@B29]\].
Psychological factors
---------------------
### Behavior in the serial Color Word Test
The CWT is a semi-experimental way to measure how individuals adapt in a stressful situation \[[@B8]\]. It is a version of the Stroop test \[[@B30]\], originally designed for the study of interference, and it has in detail, complete with graphic illustrations, been described elsewhere \[[@B8],[@B10],[@B31],[@B32]\]. In short, the test consists of color words printed in an incongruent color where the object is to name the color of the print and disregard the written word. Scoring is done by measuring the time it takes to complete the test. The cognitive adaptation is studied as a process through a series of five identical subtests \[[@B33]\]. The unfolding time-pattern is assumed to reflect how the individual generally adapts when confronted with a challenging and conflicting task \[[@B34]\].
The analysis of test scores is done by considering the temporal aspects in a two-dimensional analysis where linear change of time consumption, from beginning until end, constitutes the Regression-dimension. The Variability-dimension is created by the observations that show a simultaneous variation along the long-term progression but which are not captured by a straight line. Difficulties in adaptation, i.e. failures in finding successful strategies to master the conflict between naming the color and disregarding the printed word, are shown as time consumptions that increase and vary from beginning until end. These difficulties are exhibited as time-patterns with high variability in both the Regression- and the Variability-dimension \[[@B8]\] and this behavior is labeled *maladaptive*. Behaviors categorized as *adaptive*show stable or increasing time consumption throughout the test but do not show recurrent declines and increases in time consumption. The Variability-dimension was chosen for the present study because its associations with increased incidence of MI in men \[[@B10],[@B12],[@B13]\]. All categorization of behavior in this study is based on comparisons of test scores with reference-medians obtained from the 180 patients that were able to participate in the CWT in the SECAMI-study.
Personality
-----------
The abbreviated version of the NEO Personality Inventory was used to measure personality traits \[[@B24],[@B25]\]. This inventory gives measures on five basic dimensions of personality; Neuroticism, Extraversion, Openness, Agreeableness, and Conscientiousness. The results from each dimension were treated as dichotomous variables. In order to construct clear variables of personality we decided on cut-off points at the 67^th^percentile or the 33^rd^percentile instead of dichotomizing at the median value. A high level of neuroticism was scored at levels above the 67^th^percentile. Low levels of extraversion, openness, agreeableness, and conscientiousness were scored at levels below the 33^rd^percentile.
Severity of MI
--------------
All four indicators of severity of MI were chosen to be dichotomized in order to make the results clear.
### Troponin I
Troponin I is a sensitive and specific biochemical marker of myocardial damage measurable within 3-4 hours from the onset of an MI \[[@B26]\]. The peak value during the first 24 hours was obtained from the patient\'s medical record. Measures were obtained with an interval of six hours. Range 0.07-271.00; SD = ± 36.0; Md = 5,87. Levels above median were used to indicate severity \[[@B3]\].
### Creatine kinase
Creatine kinase and its MB isoenzyme CKMB, is also a sensitive and specific biochemical biomarker of myocardial damage, measurable within 4-6 hours after onset of an MI \[[@B26]\]. The peak value during the first 24 hours was obtained from the patient\'s medical record. Measures were obtained with an interval of six hours. Range 1.00-457.00; SD = ± 92.9; Md = 44.0. Levels above median were used to indicate severity \[[@B3]\].
### Pathological Q-wave
A pathological Q wave on the 12 lead ECG signifies abnormal electrical activity seen in several conditions of the heart \[[@B26]\]. The diagnosis was given if a new pathological Q-wave was observed on ECG-recordings during the hospital stay.
### Left ventricular ejection fraction
LVEF is a key measure of the left ventricular systolic function of the heart. It is most commonly determined by a two-dimensional echocardiography. A decreased LVEF can be caused by an infarction and might lead to heart failure with clinical signs and symptoms like edema and dyspnea \[[@B27]\]. Patients with an LVEF ≤ 50% were considered to have a decreased function \[[@B17]\].
Statistical analyses
--------------------
Unadjusted odds ratios were calculated by means of logistic regression analyses for the background and clinical variables in association with the severity indicators maximum troponin I level above median, maximum CKMB level above median, Q-wave infarction, and a left ventricular ejection fraction LVEF ≤ 50%. Differences in mean levels of maximum troponin I and CKMB were compared between patients with adaptive and maladaptive behavior and between patients with different levels in the five personality dimensions by using the one-way ANOVA test. The Pearson chi-square test was used to analyze differences in distribution of adaptive and maladaptive behavior in the CWT and low versus high levels in the five personality dimensions between patients with and without Q-wave infarctions and between patients with and without an LVEF ≤ 50%. Personality dimensions with p ≤ 0.10 were decided to be eligible for the final analyses.
The multivariate analyses of whether behavior in the CWT together with a specific personality dimension was associated with severity of MI were performed by means of logistic regression. In these analyses the odds ratios for a severe infarction were calculated for four strata of patients defined in terms of adaptive/maladaptive behavior in the CWT respectively low/high level in the chosen personality dimension. The following parameters were eligible for inclusion in the multivariate analyses: age, sex, having immigrated to Sweden, educational level less than 9 years, history of MI, previous revascularization, treatment for hypertension, treatment for hyperlipidemia, treatment for angina pectoris, treatment for diabetes mellitus and level of BMI, living alone, current smoking, presently not employed or professionally active, and moderate to severe level of depression. Four different analyses were performed because we had four different indicators of severity and in each analysis only variables associated with the severity-indicator with p \< 0.20 were included.
Results
=======
Background data and clinical characteristics of the included 147 patients are presented in Table [1](#T1){ref-type="table"} (Table [1](#T1){ref-type="table"}). Eighteen (12.2%) patients had a previous experience of an MI, less than half (44.2%) had been prescribed treatment for hypertension, and approximately one fifth had been prescribed drugs to lower lipid levels (21.1%). Fifteen patients were considered to have a moderate to severe level of depression (10.2%).
######
Background and clinical characteristics
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Maximum troponin I;\ Maximum creatine\ Q-wave infarction\ Left ventricular ejection\
Above median\ kinase-MB;\ n = 51 fraction (LVEF) ≤ 50%\
n = 74 Above median\ n = 79
n = 74
--------------------------------------------------- ------------- --------------- ---------------------- ------------------- -------------------- ---------------------------- ------------- ------ -------------- ------
Age 58.1 (mean) ± 8.7 (SD^3^) 0.98\ 0.22 0.98\ 0.18 1.02\ 0.45 1.01\ 0.56
(0.94-1.01) (0.94-1.01) (0.98-1.06) (0.97-1.05)
Female sex 39 26.5 0.69\ 0.33 0.80\ 0.54 1.08\ 0.85 2.42\ 0.03
(0.33-1.45) (0.38-1.66) (0.50-2.31) (1.11-5.27)
Immigrant 17 11.6 2.63\ 0.08 2.63\ 0.08 1.80\ 0.26 0.56\ 0.27
(0.88-7.90) (0.88-7.90) (0.65-4.99) (0.20-1.57)
Educational level less than 9 years 42 28.6 0.50\ 0.06 0.50\ 0.06 1.07\ 0.87 0.71\ 0.35
(0.24-1.04) (0.24-1.04) (0.50-2.25) (0.35-1.45)
History of myocardial infarction 18 12.2 0.76\ 0.59 0.45\ 0.13 0.34\ 0.10 2.48\ 0.10
(0.28-2.06) (0.16-1.27) (0.09-1.23) (0.84-7.36)
Previous revascularization^4^ 17 11.6 0.37\ 0.08 0.18\ 0.01 0.37\ 0.13 1.67\ 0.34
(0.12-1.11) (0.05-0.65) (0.10-1.34) (0.58-4.79)
Treatment for hypertension 65 44.2 1.15\ 0.67 0.92\ 0.81 1.52\ 0.23 1.26\ 0.49
(0.60-2.21) (0.48-1.77) (0.77-3.01) (0.65-2.42)
Treatment for hyperlipidemia 31 21.1 0.91\ 0.81 0.55\ 0.15 1.05\ 0.92 1.48\ 0.34
(0.41-2.00) (0.25-1.24) (0.46-2.40) (0.66-3.32)
Treatment for angina pectoris 29 19.7 0.44\ 0.06 0.37\ 0.02 0.99\ 0.98 2.72\ 0.03
(0.19-1.04) (0.15-0.87) (0.42-2.32) (1.11-6.62)
Treatment for diabetes mellitus 22 15.0 0.51\ 0.16 0.79\ 0.62 0.86\ 0.76 1.62\ 0.32
(0.20-1.30) (0.32-1.97) (0.33-2.27) (0.63-4.12)
BMI 27.5 (mean) ± 4.5 (SD^3^) 1.01\ 0.76 1.02\ 0.68 0.98\ 0.65 1.03\ 0.38
(0.94-1.09) (0.94-1.09) (0.91-1.06) (0.96-1.11)
Living alone 36 24.5 0.63\ 0.23 1.14\ 0.74 1.49\ 0.31 0.82\ 0.61
(0.29-1.35) (0.54-2.42) (0.69-3.22) (0.39-1.74)
Currently smoking 65 44.2 1.44\ 0.28 2.26\ 0.02 1.72\ 0.12 1.13\ 0.72
(0.75-2.76) (1.16-4.39) (0.87-3.41) (0.59-2.16)
Presently not employed or professionally active 74 50.3 0.70\ 0.28 0.78\ 0.46 1.49\ 0.25 1.78\ 0.09
(0.37-1.34) (0.41-1.50) (0.75-2.96) (0.92-3.43)
Moderate to severe level of depression (BDI ≥ 17) 15 10.2 1.14\ 0.81 1.14\ 0.81 0.66\ 0.49 6.50\ 0.02
(0.39-3.33) (0.39-3.33) (0.20-2.18) (1.41-29.94)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Distribution and associations with four different indicators of severity of myocardial infarction (n = 147).
^1^Odds Ratio; ^2^Confidence Interval; ^3^Standard Deviation; ^4^PCI (Percutaneous Coronary Intervention) or CABG (Coronary Artery Bypass Graft)
Univariate analyses
-------------------
Background factors and clinical characteristics were analyzed in association with each indicator of severity. No factor showed statistically significant univariate associations with maximum troponin I levels above median or with a pathological Q-wave infarction. Current smoking was associated with CKMB-levels above median whereas previous revascularization and treatment for angina pectoris showed statistically significant associations with CKMB-levels below median. Female sex, treatment for angina pectoris, and BDI-scores ≥ 17 were associated with a decreased LVEF.
We continued the analyses by investigating whether behavior in a stressful situation as measured by the serial CWT and personality dimensions were related to severity of disease (Table [2](#T2){ref-type="table"}). The behavior in the test and the personality dimensions were each analyzed separately in relation to the four indices of severity. Behavior in the CWT was in these univariate analyses not associated with any severity indicator in a statistically significant manner. The difference in maximum troponin I-levels was statistically significant comparing patients in the extraversion dimension of personality. Patients scoring low on extraversion had higher maximum troponin I-levels than patients scoring high.
######
Behavior in the serial CWT and personality-factors in relation to four indicators of severity of myocardial infarction (n = 147)
------------------------------------------------------------------------------------------------------------------------------------------
Maximum troponin I Maximum creatine\ Q-wave infarction\ Left ventricular\
kinase-MB n = 51 ejection fraction\
(LVEF) ≤ 50%\
n = 79
--------------------- ----- -------------------- ------------------- -------------------- -------------------- ------ ------ ------ ------
Behavior in the CWT
Adaptive 74 18.57 80.22 35.1 51.4
Maladaptive 73 20.78 0.71 85.13 0.75 34.2 0.91 56.2 0.56
Neuroticism
Low level 100 17.16 81.82 36.0 55.0
High level 47 25.01 0.22 84.45 0.87 31.9 0.63 51.1 0.66
Extraversion
Low level 45 29.58 102.58 44.4 57.8
High level 102 15.29 0.03 73.87 0.08 30.4 0.10 52.0 0.51
Openness
Low level 47 23.45 78.96 25.5 51.1
High level 100 17.89 0.39 84.40 0.74 39.0 0.11 55.0 0.66
Agreeableness
Low level 48 18.29 89.24 35.4 52.1
High level 99 20.33 0.75 79.47 0.55 34.3 0.90 54.5 0.78
Conscientiousness
Low level 52 23.57 98.55 34.6 48.1
High level 95 17.53 0.33 73.97 0.13 34.7 0.99 56.8 0.31
------------------------------------------------------------------------------------------------------------------------------------------
^1^One-way ANOVA; ^2^Percentage within each category of behavior in the CWT or within each level of personality dimension; ^3^Pearson Chi-square.
Multivariate analyses
---------------------
Extraversion was chosen as the personality dimension to be analyzed in conjunction with adaptive behavior for the investigation of a possible association with severity of MI. Because we had four indicators of severity there were carried out four separate analyses. A maladaptive behavior in the serial CWT together with a low level in the personality dimension extraversion was associated with maximum levels above median of cardiac troponin I (OR 2.97, CI 1.08-8.20, p = 0.04) (Table [3](#T3){ref-type="table"}). A statistically significant association between maximum CKMB-levels above median and a maladaptive behavior together with low scores on extraversion could also be established (OR 3.33, CI 1.12-9.93, p = 0.03). Current smoking (OR 2.36, CI 1.14-4.88, p = 0.02) and previous revascularization (OR 0.19, CI 0.04-1.00, p = \< 0.05) did also show associations with CKMB-levels above median. No association was found between Q-wave infarctions and the combination maladaptive behavior and low scores on extraversion nor were any of the included background factors or clinical characteristics related to Q-wave infarctions. Female sex was associated with a decreased LVEF but no other associations could be discerned in the multivariate analyses.
######
Results from multivariate analyses: Background, clinical, and psychosocial factors and their associations with four different indicators of severity of myocardial infarction, (n = 147).
Indicator of severity Factor OR^1^ 95% C I^2^ p
------------------------------------------------- ------------------------------------------------------ ------- --------------- ---------
Maximum troponin I-level; above median Behavior in the CWT and level of extraversion
Adaptive behavior and high level of extraversion Reference
Adaptive behavior and low level of extraversion 1.88 0.60-5.90 0.28^3^
Maladaptive behavior and high level of extraversion 1.23 0.53-2.83 0.63^3^
Maladaptive behavior and low level of extraversion 2.97 1.08-8.20 0.04^3^
Formal education of \< 9 years 0.48 0.21-1.08 0.08
Immigrant 2.18 0.70-6.79 0.18
Treatment for angina pectoris 0.52 0.17-1.62 0.26
Previous revascularization^4^ 0.63 0.15-2.72 0.54
Maximum creatine kinase-MB; above median Behavior in the CWT and level of extraversion
Adaptive behavior and high level of extraversion Reference
Adaptive behavior and low level of extraversion 1.26 0.40-4.01 0.70^3^
Maladaptive behavior and high level of extraversion 1.10 0.46-2.61 0.83^3^
Maladaptive behavior and low level of extraversion 3.33 1.12-9.93 0.03^3^
Current smoking 2.36 1.14-4.88 0.02
Previous revascularization^4^ 0.19 0.04- \< 1.00 0.05
Formal education of \< 9 years 0.50 0.21-1.15 0.10
Immigrant 2.27 0.69-7.51 0.18
Treatment for angina pectoris 0.71 0.22-2.33 0.58
Q-wave infarction Behavior in the CWT and level of extraversion
Adaptive behavior and high level of extraversion Reference
Adaptive behavior and low level of extraversion 1.31 0.43-4.02 0.64^3^
Maladaptive behavior and high level of extraversion 0.73 0.31-1.75 0.48^3^
Maladaptive behavior and low level of extraversion 1.65 0.65-4.18 0.30^3^
History of MI 0.37 0.10-1.34 0.37
Left ventricular ejection fraction (LVEF) ≤ 50% Behavior in the CWT and level of extraversion
Adaptive behavior and high level of extraversion Reference
Adaptive behavior and low level of extraversion 1.15 0.35-3.80 0.82^3^
Maladaptive behavior and high level of extraversion 1.14 0.49-2.64 0.76^3^
Maladaptive behavior and low level of extraversion 1.06 0.39-2.91 0.91^3^
Female sex 2.28 \< 1.00-5.21 \< 0.05
Moderate to severe level of depression (BDI ≥ 19) 4.56 0.89-23.26 0.07
Presently not employed or professionally active 1.62 0.81-3.27 0.17
History of MI 2.05 0.55-7.59 0.28
Treatment for angina pectoris 1.45 0.48-4.39 0.51
^1^Odds Ratio
^2^Confidence Interval
^3^In comparison with the reference stratum
^4^PCI (Percutaneous Coronary Intervention) or CABG (Coronary Artery Bypass Graft)
Discussion
==========
The results from this study suggest that patients with a maladaptive behavior in the serial CWT together with low scores on extraversion were the patients where the highest maximum levels of the two cardiac biomarkers troponin I and CKMB were registered in connection with the acute event. These associations were independent of sociodemographic factors, biomedical factors, and even moderate to severe levels of depression. To conclude that an association between severity and psychological factors was found is, however, premature because the relationship was not found when severity was defined as a Q-wave infarction or a decreased LVEF.
Psychosocial stress is both among laymen and professionals generally considered to contribute to adverse effects on the heart. Estimations from the INTERHEART-study including results from 52 different countries showed that psychosocial stressors collectively accounted for approximately 33% of the population attributable risk of AMI \[[@B4]\]. Our focus is on behavior in the stressful situation. Stress is commonly reported as a risk factor in association with CHD but it is a vague concept and is measured in many various manners \[[@B35]\]. When a stressor is identified, activations in the hypothalamic-pituitary-adrenocortical and sympathetic-adrenomedullary systems are heightened and followed by responses of the cardiovascular system \[[@B36]\]. The CWT does not measure cardiovascular reactivity per se but tells us how individuals actually behave when facing challenging tasks. A pathophysiological mechanism that may explain why individuals with a maladaptive behavior are exposed to an increased risk of CVD is that these individuals may be more likely to show elevated blood pressure levels when responding to stress.
The assumption that a maladaptive behavior in the face of challenging situations would be associated with a more severe infarction could, however, not be substantiated when maladaptive behavior was considered by itself. The relationship between maximum troponin I- and CKMB-levels above medians and maladaptive behavior was only found when the maladaptive behavior was present in conjunction with low levels of extraversion. This aspect of personality gives a measure of an individual\'s level of social interaction. Individuals scoring low could be characterized as reserved or introverted. A suggested pathway between disease and this specific personality-type is that individuals with low levels of extraversion have not been able to cultivate their social network and as a consequence lack the social support that could increase resilience to disease \[[@B37]\].
The finding that maladaptive stress-behavior together with low levels of extraversion was associated with higher levels of cardiac biomarkers at the time of the event should be compared with results from Denollet and colleagues \[[@B17],[@B38],[@B39]\] because there are some similarities regarding social interaction. They studied personality as a risk-factor in relation to CHD and found the Type D personality especially vulnerable to chronic distress and thereby to adverse health outcomes. The distinguished features of that personality-type are negative affectivity and social inhibition. The suggested pathogenic effects of social inhibition on disease is that social interaction is experienced as threatening to the socially inhibited individual who in such situations responds with increased sympathetic activity, elevated levels of catecholamines, increased heart rate, and increased blood pressure levels \[[@B39]\].
No association between maladaptive behavior in combination with personality and a decreased LVEF was found. In this aspect our results are not compatible with those from Denollet and Brutsaert \[[@B38]\]. They found that severity, defined as a decreased LVEF, in combination with Type D personality and younger age was associated with an increased risk of a cardiac event during a follow-up time of almost eight years. It should, however, be mentioned that momentary drops of \> 5% in LVEF in response to laboratory stressors have been observed and studied in CAD-patients. Such drops can be prognostically significant because patients exhibiting such drops in response to stress were the ones most likely to experience a cardiac event during a four year follow-up \[[@B35]\].
Another discrepancy that appears when comparing results from our study with results from other studies concerns depression. Moderate to severe levels of depression as measured with the BDI was used as a covariate in our analyses of a possible association between stress-behavior, personality, and severity of MI. A univariate association between moderate to severe levels of depression and a decreased LVEF was observed but the association could not be confirmed in the multivariate analysis. This is noteworthy because depression has increasingly been shown to confer increased risk of negative prognosis following an MI. Psychological factors in association with severity of MI have rarely been studied but in a recent publication with a decreased LVEF as a measure of severity was found that the somatic/affective aspects as opposed to the more cognitive/affective aspects of depression were associated with severity and prognosis \[[@B40]\]. This could possibly serve as an explanation as to why we did not find an association between behavior in the CWT, personality and a decreased LVEF. Behavior in the serial CWT relies on perception which is an act of cognition \[[@B33]\].
Depression has strongly been related to MI and subsequent survival \[[@B41]\] and depression preceding the infarction has been related to worse cardiac failure \[[@B42]\]. Frasure-Smith and co-writers \[[@B43]\] found a prevalence of depression at about 32% in a population of 887 MI-patients that were interviewed concerning depression and social support seven days following the event. The proportion with moderate to severe signs of depression (as measured with the BDI) in our study cohort was 10.2% and consequently considerably smaller. A possible explanation is that our examination occurred with closer proximity to the event, a time when feelings of gratefulness for having been taken care of could be the most prominent emotion.
Neuroticism was perhaps the personality dimension that was expected to be associated with disease severity because its associations with anxiety, emotional instability, and depressiveness \[[@B24]\]. Anxiety as a separate emotion has been associated with an increased risk of incident MI in older men \[[@B44]\] and is estimated to be as high as 70-80% among patients that have experienced an acute cardiac event \[[@B45]\]. Our results did not indicate associations between severity and neuroticism which could be explained by the fact that the study cohort was substantially circumscribed because a majority of the SECAMI-patients were not fit to participate in the serial CWT.
The strength of the present study is the semi-experimental manner in which behavior in a stressful situation was measured which means that the way the situation is managed is not influenced by a retrospective memory bias. Shortcomings should also be mentioned. The first concerns reliability of results which cannot be considered conclusive because maladaptive behavior in conjunction with the personality dimension extraversion was not associated with all four measures of severity. The reasons for the lacking associations between behavior in the CWT and the personality extraversion on the one hand and a decreased LVEF or Q-wave infarction on the other can, of course, be ascribed to nonexistent relationships but can also be referred to the way behavior was categorized. Previous studies have been based on the norms obtained from the study \"Men born in 1914\" which is the only study where the serial CWT has been applied in an epidemiologic context and been validated as a prognostic risk factor in association with CVD. Categorization of behavior was in the present study necessarily based on behavior observed in the 180 patients that completed the serial CWT during their hospital stay which means that the norms can not be generalized to all populations. It is possible that categorization should have been based specifically on women by themselves and men by themselves or on specific age groups. That adjustment would, however, have left us with too small groups for multivariate analyses to become meaningful.
The study cohort was small because not all patients did consent to participate in the CWT and some felt too frail to finish the complete test. Certain selection effects were, thus, at play and could have contributed to the lack of an association between behavior and Q-wave infarctions or a decreased LVEF. However, the 253 patients that were excluded were compared with the included 147 and there could not be discerned any statistically significant differences regarding age or prevalence of maximum troponin I above median, maximum creatine kinase-MB above median, left ventricular ejection fraction (LVEF) ≤ 50% or q-wave infarctions (not in table). It should also be remembered that patients with an unstabilized condition and those above the age of 70 years had been excluded. Another criticism that should be pointed out was that amount of physical exercise was not asked about. Furthermore can be mentioned that approximately 30% of the population with incident MI die before reaching hospital \[[@B46]\].
There is also a need to point at some general methodological issues that entitles very careful interpretation of our results. The present study is by character explorative. We chose to investigate the relationship between maladaptive behavior in combination with five specific personality dimensions in association with four different indicators of severity of MI. These analyses showed that the combination of maladaptive behavior and low levels of extraversion could be associated with severity of disease. By making many comparisons without proper adjustment there is always a risk that the significant finding could be the result of chance alone. The combination of behavior in the serial CWT and level on extraversion was entered into the multivariate analyses together with those traditional cardiovascular risk-factors that had shown an association with the particular severity indicator with a p-level \< 0.20 and were not chosen according to an a priori selected hypothesis. It is possible that this procedure allows too many confounders.
The severity indicators reflect different aspects of pathophysiology and four measures were chosen with the conception of gaining greater credibility if stress behavior and personality factors would have been associated with all four indicators. All indicators are relevant but because they are used as single entities and not combined in a joint measure as e. g. the PREDICT-score \[[@B47]\] they may not reflect true severity. Although biomarkers are specific, sensitive and their circulatory levels agree well with level of necrosis it is the subsequent survival following the acute event that is essential. The follow-up of the SECAMI-cohort aims at providing more definite answers on how psychosocial factors act on subsequent survival following an AMI.
Conclusions
===========
In this cohort of AMI-patients we wanted to investigate whether a maladaptive behavior in a stressful situation in combination with any of the personality dimensions Neuroticism, Extraversion, Openness, Conscientiousness, or Agreeableness would be associated with the severity of an MI. We found that a maladaptive behavior in the serial CWT together with low scores in the Extraversion-dimension was related to severity of disease when severity was defined as maximum levels above median of the cardiac biomarkers troponin I and CKMB. The association was not found when severity was defined as a Q-wave infarction or a decreased LVEF which makes it premature to state that there exist associations between behavior in stressful situations, personality dimensions, and severity of infarction. An implication of the results, however inconclusive, is that individuals with difficulties in adapting to stressful events could be exposed to an increased risk of a more severe disease but above all, these individuals should be identified at an even earlier stage in their disease.
Competing interests
===================
The authors declare that they have no competing interests.
Authors\' contributions
=======================
LAP participated in the design of the study, collected the material, performed the statistical analyses, and drafted the manuscript. MS participated in the design of the study and collected the material. GE, PT, and BH designed the study and revised the manuscript. All authors have read and approved the manuscript.
Authors\' information
=====================
LA-P: Department of Clinical Sciences, Lund University, Skåne University Hospital, Malmö, Sweden, and Department of Neurology, Skåne University Hospital, Malmö, Sweden.
MS: Department of Cardiology, Lund University, Skåne University Hospital, Malmö, Sweden.
GE: Department of Clinical Sciences, Lund University, Skåne University Hospital, Malmö, Sweden.
PT: Department of Cardiology, Lund University, Skåne University Hospital, Malmö, Sweden.
BH: Department of Clinical Sciences, Lund University, Skåne University Hospital, Malmö, Sweden.
Pre-publication history
=======================
The pre-publication history for this paper can be accessed here:
<http://www.biomedcentral.com/1471-2261/11/45/prepub>
Acknowledgements
================
This study was supported by grants from the Swedish Heart and Lung Association, the Swedish Research Council, the Swedish Heart and Lung Foundation, the Medical Faculty at Lund University, the Region of Skåne, and Skåne University Hospital.
| |
The Department of Cauca is located in southwestern Colombia, an area heavily impacted by ongoing armed conflicts in the country. Women, especially in indigenous and Afro-decendant communities were particularly affected and continue to face challenges in access to education, a decent income, land ownership, and decision-making. Communities in the region live primarily in rural areas and work primarily in agriculture and livestock farming.
El proyecto
Fundación CODESPA has been working to empower indigenous women artisans in North Cauca, since 2012, by helping them create and consolidate a social enterprise, so that they can produce and sell handicrafts and textiles in local markets and craft fairs. The project aims to further strengthen the capacities of the artisans by providing with technical and business skills training and improved access to local markets, particularly in the ‘slow fashion’ industry, a growing sector in Colombia.
Fondation CHANEL is supporting CODESPA in scaling-up its program in Colombia and providing 200 indigenous women artisans with training to strengthen their technical and business skills, improve the quality of their products, and increase their access to local markets. Additionally, CODESPA will assist the women in improving the management and efficiency of their social entreprise, and build partnerships with local fashion designers, boutiques and hotels specializing in ‘slow fashion’.
El compañero
Fundación CODESPA is an international non-profit organization that aims to empower the poor by increasing their access to economic and social opportunities, so that they can, through their own work, improve their skills and take charge of their own development. | https://www.fondationchanel.org/es/projet/providing-technical-and-business-training-to-indigenous-women-artisans-2/ |
If Donald Trump is said to fear walking down steps, my phobia was ‘going upstairs’.
You were warned early and often on this page of a grim, unwatchable future for football; of endless delays, of challenges and appeals, of muted celebrations, and of protracted, super-slo-mo searches for ‘contact’.
And yet, a week into the World Cup, VAR has been grand. Put this down as a U-turn. Or, as the politicians prefer these days, the completion of a journey.
Not everyone is satisfied, of course. But when we hear Danish boss Åge Hareide tell us, “it does remove a bit of the charm of football to have such a precise system”, we can instinctively identify these to be words of a man who has just had a penalty rightly awarded against him.
Interestingly, former Premier League referee Mark Halsey insisted it was farcical that Yussuf Poulsen should be penalised for blocking Mathew Leckie’s header with an arm stretched above his head in our old friend the ‘unnatural position’, a decision even Hareide regarded as charmless but “probably correct”.
It was further evidence, for Halsey, that VAR “shouldn’t be at the tournament”.
But maybe his outrage was further evidence as to why there are no Premier League referees at the tournament.
And as I begin a long, penitent period of soul-searching to examine how I got this one so badly wrong, perhaps, in my defence, it can be offered that I was visualising the operation of VAR in the hands of Premier League referees.
Indeed, there was no need to visualise such a terrible thing, since the Premier League referees had last season’s FA Cup to show us just how much damage they’d be capable of given the use of the machines on a permanent basis.
Crippled with indecision, conferring on everything, taking an age to review replays, we were heading for an era when teams would have to organise new warm-ups every time somebody went down in the box.
But then we are dealing with a special breed of referee in the Premier League, a species whose role is less to apply the rules than to ‘manage the game’.
We have heard how Mark Clattenburg went into matches with a ‘gameplan’.
Bobby Madley recently explained how vital his pre-match chat with both captains is so they understand his ‘approach’.
They seem to have a lot on their minds, these guys, getting their tactics right, before they can even begin to consider keeping an eye on handball in the box.
And still they have become an integral part of the show. In an interview with the Daily Telegraph, we learned that Halsey “loved being out there every weekend, playing a part in the world’s most-watched football competition”, his decision-making “as likely to be discussed in Bangkok as Burnley”.
So perhaps the opportunity to get endlessly lost in their decision-making, ensuring there was nothing else to discuss from Bangkok to Burnley, just became too much for them.
Because the lads at the World Cup are making it look straightforward enough. Not much has been missed and the VAR calls have been scarce and swift. Yesterday, VAR saved Bjorn Kuipers from himself when Neymar tumbled under ‘contact’.
It rescued Kiwi ref Matt Conger on a stonewall pen for Iceland. And earlier in the week the penalty awarded to Viktor Claesson against South Korea was a textbook example of why there was such a clamour to allow refs go upstairs.
As we wonder how the VAR officials have been getting all these calls right, yet somehow resisting the temptation to make too many calls, we must consider that it might be because we have no idea who they are, these faceless operatives back in Moscow.
There is no credit in it for these lads, who are not known in Burnley or Bangkok. And while our instincts tell us to worry about the world’s fate being decided in a ‘centralised video operation room’ in Moscow, we are slowly growing to trust them — AVAR, VAR 1, VAR 2 and VAR 3, to give them their official titles.
Alas, the English pundits have taken against it, since Harry wasn’t given his spotter against Tunisia. Unfortunately, grappling in the box figures behind only the waving of imaginary yellow cards, imaginative haircuts, swapping shirts at half-time, and going down too easily, on their list of distastes. So this was always going to be a sore one.
But even in Harry’s distress there were positives for VAR, a sign that common sense has survived a handover to the machines. When they see two or three fouls happening at the same time, the lads in Moscow are capable of saying, ‘fack it, leave ‘em off’.
But it has put these faceless men in the firing line and we know where this is going now.
“Who is Sweden vs South Korea VAR official Mauro Vigliano and how many World Cups has the Argentine refereed in,” demanded The Sun.
Sepp Blatter, never to be found wanting when wrongness is required, has waded in wanting accountability and a VAR figurehead who can be blamed for all mistakes going forward, from Burnley to Bangkok.
Inevitably, we will get to know them all and soon even VAR2 and VAR3 will be writing autobiographies, telling us their gameplan, how they always went for the behind the goal angle first.
And just as we grow to trust what goes on inside the centralised video operation room, we will give them a glimpse of life outside it, a life of credit and blame and headlines from Burnley to Bangkok.
And soon, they will be in the ref’s ear every five minutes and we may well be back where we started. | https://www.irishexaminer.com/sport/columnists/larry-ryan/var-is-working-just-dont-give-anyone-the-credit-472264.html |
1. A tall tale is a type of story that uses exaggeration to solve a real-life problem. As the story progresses, the main character demonstrates superhuman abilities to overcome ordinary obstacles. The story shown below is an example of a tall tale.
It had been raining without a break for four days. The roads were flooded, power outages were common, and dry basements had become a thing of the past. At the same time, a drought on the other side of the country was responsible for dangerously low reservoir levels, thirsty cattle, and parched fields.
Victor, a young man who lived in one of the flooded towns, was very unhappy about the continuing bad weather. Not only had he spent the last two days bailing water from his family’s basement, but he was due to miss out on a camping trip, originally planned for the upcoming weekend, that he and his friends had been excitedly anticipating.
Victor put a small rope in his back pocket and walked outside. As he stood with the rain pelting down on him, he grew until he stood a mile high. Standing up above the rain clouds, he took the rope from his back pocket. The rope was now hundreds of yards long and Victor used it to lasso the rain clouds. Holding the clouds in the rope, he walked across the country taking fifty-mile steps. He untied the clouds over the drought-stricken land and a heavy rain began to fall there. Then he walked back to his house in his town where the sun was now shining, shrunk back down to his regular size, and went inside to pack for the camping trip.
Imagine that you will participate in a “tall-tale writing contest” at your school. Write you own tall tale. You can write about yourself, someone you know, or someone you imagine. Be sure to give your main character whatever superhuman abilities are necessary to save the day.
• Tells a clear story that is consistently well-developed and detailed; details enhance story being told.
• Well organized; integrates narrative events into a smooth telling; effective transitions move the story forward.
• Consistently exhibits variety in sentence structure and precision in word choice.
• Errors in grammar, spelling, and punctuation are few and do not interfere with understanding.
• Tells a clear story that is well-developed and supported with pertinent details in much of the response.
• Well organized with story elements that are connected across most of the response; may have occasional lapses in transitions.
• Exhibits some variety in sentence structure and uses good word choice; occasionally, words may be used inaccurately.
• Errors in grammar, spelling, and punctuation do not interfere with understanding.
• Tells a clear story that is developed with some pertinent details.
• Generally organized, but transitions among parts of the story may be lacking.
• Sentence structure may be simple and unvaried; word choice is mostly accurate.
• Tells a story that may be clear and developed in parts; other parts are unfocused, repetitive, or minimally developed OR is no more than a well-written beginning.
• Organized in parts of the response; other parts are disjointed and/or lack transitions.
• Exhibits uneven control over sentence boundaries and sentence structure; may exhibit some inaccurate word choices.
• Errors in grammar, spelling, and punctuation sometimes interfere with understanding.
• Attempts to tell a story, but is very undeveloped, list-like, or fragmentary.
• Disorganized or unfocused in much of the response OR the response is too brief to detect organization.
• Minimal control over sentence boundaries and sentence structure; word choice may often be inaccurate.
• Errors in grammar, spelling, and punctuation interfere with understanding in much of the response.
• Responds to prompt but provides little or no coherent content OR merely paraphrases the prompt.
• Little or no apparent organization.
• Minimal or no control over sentence boundaries and sentence structure; word choice may be inaccurate in much or all of the response.
• Errors in grammar, spelling, and punctuation severely impede understanding across the response.
2. A novel written in the 1950’s describes a world where people are not allowed to read books. A small group of people who want to save books memorize them, so that the books won’t be forgotten. For example, an old man who has memorized the novel The Call of the Wild helps a young boy memorize it by reciting the story to him. In this way, the book is saved for the future.
If you were told that you could save just one book for future generations, which book would you choose?
Write an essay in which you discuss which book you would choose to save for future generations and what it is about the book that makes it important to save. Be sure to discuss in detail why the book is important to you and why it would be important to future generations.
• Information is presented effectively and consistently supported with well-chosen details.
• Information is focused and well organized, with a sustained controlling idea and effective use of transitions.
• Response consistently exhibits variety in sentence structure and precision in word choice.
• Information is presented clearly and supported with pertinent details in much of the response.
• Response is well organized, but may lack some transitions.
• Response exhibits some variety in sentence structure and uses good word choice; occasionally, words may be used inaccurately.
��� Errors in grammar, spelling, and punctuation do not interfere with understanding.
• Information is presented clearly and supported with some pertinent details.
• Information is generally organized, but has few or no transitions among parts.
• Information is presented clearly in parts; other parts are undeveloped or repetitive OR is no more than a well-written beginning.
• Provides information that is very undeveloped or list-like.
• Much of the response is disorganized or unfocused, OR the response is too brief to detect organization.
• Author has minimal control over sentence boundaries and sentence structure; word choice may often be inaccurate.
• Responds to prompt but may be incoherent OR provides very minimal information OR merely paraphrases the prompt.
3. Who are our heroes? The media attention given to celebrities suggests that these people are today’s heroes. Yet ordinary people perform extraordinary acts of courage every day that go virtually unnoticed. Are these people the real heroes?
Write an essay in which you define heroism and argue who you think our heroes really are—mass-media stars, ordinary people, or maybe both. Be sure to use examples of specific celebrities, other people you have heard or read about, or people from your own community to support your position.
• Takes a clear position and supports it consistently with well-chosen reasons and/or examples; may use persuasive strategy to convey an argument.
• Focused and well organized, with effective use of transitions.
• Takes a clear position and supports it with pertinent reasons and/or examples through much of the response.
• Well organized, but may lack some transitions.
• Takes a clear position and supports it with some pertinent reasons and/or examples; there is some development.
• Generally organized, but has few or no transitions among parts.
• Takes a position and provides uneven support; may lack development in parts or be repetitive OR is no more than a well-written beginning.
• Takes a position but is very undeveloped.
• Disorganized or unfocused in much of the response OR clear but very brief.
• Attempts to take a position (addresses topic) but position is very unclear OR takes a position but provides minimal or no support; may only paraphrase the prompt. | http://written.co/author/admin/ |
PURPOSE: To suppress vibrations of a hydraulic machine with immediate response, by controlling the flow rate of an auxiliary hydraulic oil in response to the pressure of a hydraulic actuator.
CONSTITUTION: An accumulator 7 is jointed with a pipe line 11 connecting the head side of a boom cylinder and a flow control valve 4. And a variable restrictor 8a is arranged in the pipe line connecting the pipe line 11 and the accumulator 7. The pressure before and after the variable restrictor 8a is detected by pressure sensors 10a, 10b and the differencial pressure of the variable ristrictor 8a is obtained from the detected pressures by use of a control unit 9 and the absolute value of multiplied figure of the differencial pressure by the control gain is output the solenoid controller 8c of the variable restrictor 8a as an instructing value of flow rate. In this way, the opening of variable restrictor 8a is controlled in accordance with the variation of pressure and vibration is suppressed with good response.
COPYRIGHT: (C)1994,JPO | |
In the quest for a Health IT ecosystem, the Office of the National Coordinator for health IT has gathered a task force of 11 members that met last week for the first time. The objective was to determine how APIs will be used to share health information, according to a recent article by Molly Bernhart Walker for FierceGovernmentIT.
The ONC is encouraging the use of APIs to allow patients to send health data to the API of a selected third party from any healthcare portal in a capability called View, Download, Transmit. Any API must meet the ONC’s specified certification criteria, which includes the ability to view and download health records, but there are some security and privacy concerns that must be addressed.
The first meeting of this task force outlined its primary objectives;
- Identify perceived and real security risks that prohibit the adoption of APIs
- Identify perceived and real privacy concerns that prohibit the adoption of APIs
- "Identify priority recommendations for ONC that will help enable consumers to leverage API technology to access patient data, while ensuring the appropriate level of privacy and security protection."
The group is anticipating the possibility of hundreds of highly specific questions around these topics once the ONC’s API rules are first implemented. "A lot of this may come down to, in the end, clinical judgment," said Jeremy Maxwell, IT security specialist with ONC's office of the chief privacy officer. However, he added that "Our goal here is security and privacy concerns rather than on how well defined these APIs are". | https://www.programmableweb.com/news/healthcare-api-task-force-launched/elsewhere-web/2015/12/24 |
This role will be based in the Haringey Floating Support team. The floating support team provides sessional support to people across the borough who are living with mental health problems and need housing related support. The team supports people to develop the skills and confidence they need to have a more fulfilling and independent life. The service operates with staff members who work in the locality teams at St Ann’s hospital who provide brief intervention support with people and those who work in the community and provide longer term support with customers.
This role would be based in one of the locality teams at St Ann’s hospital primarily providing Brief Interventions to customers.
The post involves lone working and requires an ability to work under your own initiative with management support.
At Peabody, where possible, we provide flexible working opportunities from day one to our employees, as we recognise the importance of a good work-life balance; and to improve our productivity and performance, we embrace agile working, which means if you are in a desk based role, that will be a hybrid of office and home working. If your role is in a client facing environment, appropriate base location will apply.
Our mission is to help people make the most of their lives and an important part of this is to ensure that our organisation reflects the wider communities we serve. We want to attract recruit and retain a diverse, inclusive and creative workforce to give us the best opportunity to meet the diverse needs of our residents and customers. We actively encourage applications from all groups and communities, as well as from BAME, LGBTQ+ and disabled people. | https://london.jobsgopublic.com/vacancies/291986 |
Every day, Tamarack O’Donnell works with children who span the range of disorders on the autism spectrum. Some children flap their hands and cannot engage even in basic social interactions; others are visibly intelligent and have only mild eccentricities, such as eating only out of a green bowl.
After working with 100 children over eight years, “It’s a real hodgepodge,” says O’Donnell, an autism specialist at the Birth to Three Developmental Center in Federal Way, Washington.
This is a common observation ― sometimes complaint ― as researchers grapple with the diversity of autism cases. But some scientists now say that perhaps there is no single explanation for autism.
Autism is defined by three core symptoms: social problems, communication difficulties and repetitive behaviors. What these researchers are proposing is that each of these cardinal features has an independent origin, rather than being the result of a single primary cause.
“People have been assuming that autism is a unitary genetic construct,” says Angelica Ronald, a lecturer in psychology at Birkbeck College in London. “We’re not finding evidence for that.”
Instead, Ronald and her colleagues say, the symptoms are inherited independently, and autism is at the intersection of these three different causal pathways1. To garner support for her hypothesis, Ronald is trying to discover genes involved in each core symptom of autism, rather than in autism as a whole.
Tracking traits in twins:
Double jeopardy: Twin studies suggest that each of autism’s three core symptoms is inherited separately.
To expedite the search for autism-related genes, other scientists have been trying to identify endophenotypes, which are defined by selected traits found in a subset of autism cases, and which may indicate different causes for those traits.
Ronald is taking this further by asking whether the disparate behavioral traits found in all autism cases might also have separate causes.
Based on observations from 7,000 pairs of twins in the general population, she is investigating what each of the disparate behavioral traits found in autism can reveal about its cause. Her rationale is that if the three traits associated with autism share a similar origin, they should also co-occur in the general population.
Because the severity of autism-like traits varies continuously between unaffected and diagnosed individuals, the traits can be quantified in her twin population.
Using the Childhood Asperger Syndrome Test, she and her colleagues found that among the twins, each of the three features ― social, communication and repetitive, or nonsocial, behaviors ― when considered separately was highly heritable2.
If the three traits originate from the same genes, they should cluster together. But this was not the case, Ronald says. “One identical twin’s social difficulties didn’t correlate very highly with their co-twin’s nonsocial [difficulties],” she says.
This segregation held true even for those who showed significant impairments, at the extreme 5 percent of the range of scores3.
“They would score very highly on social impairments, as high as children with autism did, but they wouldn’t show any of the other two types of symptoms,” says Ronald.
All in the family:
The model of autism as the intersection of three separate genetic pathways is also supported by research into the broad autism phenotype, or BAP.
Researchers look for behavioral features in unaffected relatives of individuals with autism that might reflect “genetic liability to autism,” says Molly Losh, assistant professor of psychiatry at the University of North Carolina at Chapel Hill.
Losh and her colleagues have found that personality traits such as ‘aloof’ or ‘untactful’ are more frequent in the parents of children with autism than in controls4.
These personality traits and other behaviors form the basis of BAP features, which include rigidity, anxiety, language and sociability characteristics that parallel the core symptoms of autism.
Most people who have these features are only mildly affected, however, and have successful marriages and careers. “For example, the social characteristics we observe in relatives involve a social reticence rather than any social problems,” says Losh.
As in the twin studies, the BAP features do not correlate strongly with each other, suggesting that their genetic underpinnings are independent. Many of these unaffected parents have only a single BAP feature.
But this parent study also found that these traits can occur together, which argues against their independence. About a third of parents with one child with autism and 56 percent of those with multiple children with autism have two or more BAP features.
Another family study found a high level of correlation in unaffected relatives between two autism-related traits categorized as social motivation ― which includes qualities such as how comfortable a person is in a social situation ― and range of interests, including how much a person likes routine5.
When two or more of these traits seem to be inherited together, it suggests they share a common genetic cause.
But Annette Estes, assistant professor of psychiatry and behavioral sciences at the University of Washington and one of the authors of the study, cautions against that interpretation.
“It’s suggestive that we need to understand how they are related, but it doesn’t necessarily mean that they are related in the sense of sharing the same genetic etiology,” she says.
Measuring sticks:
The specific results of these studies might depend on how autism-related traits are divvied up and quantified. Genes do not necessarily segregate neatly according to the specific categories of behavior chosen by a researcher.
For example, Estes has unpublished evidence suggesting that traits usually lumped into the repetitive behavior category can be disassociated.
At the International Meeting for Autism Research in London earlier this month, Estes presented evidence from imaging studies suggesting that children with physically repetitive behaviors, such as hand flapping, differ neuro-anatomically from those with higher-order repetitive behaviors such as repetitive speech or interests. These differences could have distinct genetic sources, says Estes.
Tools used to measure autism-like behaviors may also pick up traits not specific to autism, and confound the results, cautions John Constantino, associate professor of psychiatry and of pediatrics at Washington University School of Medicine.
For example, with the CAST test, language impairments or liabilities for obsessive-compulsive disorder “could be contributing to scores for social, language, and repetitive behavior problems, even if they have nothing to do with autistic impairment,” Constantino says.
These impostor traits might then imply a genetic ‘fractionation’ of symptoms in the autism triad where there is none.
In his own studies, Constantino instead relies on the Social Responsiveness Scale (SRS). That tool “is certainly not immune to confounding by other disorders, but may be more specific to autistic impairment,” he says.
Using this tool, Constantino has obtained some of the strongest evidence for a single cause behind autism’s diverse symptoms.
Using a statistical method that can resolve the basic factors contributing to variability, he has shown that much of the range of SRS scores among children with pervasive developmental disorders and controls could be explained by a single factor6.
One vs. many:
A single causal pathway to autism could contribute directly to each different symptom, like spokes emanating from the hub of a wheel.
Alternatively, a single cause could work through a domino effect. Certain genes could initiate symptoms in one symptom domain, which could then trigger deficits in the other domains as the brain tries to cope with the original problem.
“A severe deficit in the fundamental motivation to engage socially could result in social impairment, delay in the development of language, and a tendency to become preoccupied and resort to repetitive behaviors as a primary focus of interest,” says Constantino.
These models for a single primary cause may be appealing in their parsimony, but the reality may lie somewhere between them and Ronald’s theory of multiple, independent pathways, some experts say.
Until they find that middle ground, scientists’ efforts are a bit like the story of the blind men and the elephant, notes Estes. “Any individual research paper is going to be touching one part of the elephant.”
References: | https://www.spectrumnews.org/news/could-autisms-core-features-have-independent-origins/ |
Hurricane Dorian: Who’s Most at Risk?
Natural disasters often impact people who are more socially vulnerable, including those without access to a vehicle, people with a disability, and older adults.
By Noah Smith
Hurricane Dorian is currently over the Bahamas and is projected to head north, sparing Florida the full force of its Category 5 strength, according to the National Weather Service. Serious damage was recorded Sunday in the northern Bahamas, where the storm wreaked havoc with winds of 185 miles per hour and intense storm surges. Florida is still bracing, even though it may not experience a direct hit. Certain populations are among those especially vulnerable to the storm’s impact.
Between Titusville and Port St. Lucie on Florida’s east coast, almost a quarter of the population is over the age of 65 and an estimated 15% of people have a disability of some sort, according to a social vulnerability analysis by Direct Relief’s Research and Analysis team, based on U.S. Census data.
The number of people over 65 in that part of coastal Florida is 8% higher than the U.S. average, though the number of people with a disability is 11% lower, based on CDC data.
“Natural disasters… have a profound destabilizing effect on older adults, who often have multiple medical problems, including functional and cognitive limitations. They often also have medication and nutritional needs that suffer in the days following a storm,” said David Dosa and Kali Thomas, Brown University School of Public Health faculty members, in a Brown University-published article about their NIH-funded research on how hurricanes impact the elderly.
Direct Relief’s latest Esri-hosted Geographic Information Systems map for Florida and The Bahamas displays local demographic information along with other health infrastructure data — including the location of pharmacies, urgent care centers, hospitals, public health departments, and Direct Relief’s Hurricane Prep Packs — with the goal of revealing the social vulnerability characteristics of an area as well as all relevant health data.
For The Bahamas, a high resolution settlement layer has added. This layer was built by combining satellite imagery and household survey from the Bahamian government. Then, AI is able to place settlement populations in very precise ways, with an accuracy to 30 meters, according to Facebook Research.
In Florida, the population mapping is accurate to the county or census block level.
“By combining new data sources on what’s happening to populations during a crisis, with more established sources on what makes people vulnerable before a crisis, we gain a new set of insights into how different and dynamic communities really are when the respond to emergencies,” said Andrew Schroeder, head of research and analysis at Direct Relief.
“For Direct Relief, that gives us a window into what they need, when they need it, and more precisely where that need may be greatest,” he said.
Beyond infrastructure and age, the map also pulls data from CDC on income levels, which can give NGOs, public health officials, and health care professionals more insights regarding how to best position resources in order to serve those who might need it most.
“About 2% of the population in this area has no access to a vehicle, which doesn’t sound like a high percentage, except that it’s a pretty densely populated area so that equates to just over 25,000 people,” said Schroeder, in discussing one of the more granular pieces of data he analyzed.
Deciding whether to evacuate people remains a difficult call to make for state and local officials, though having access to new sources of information helps.
“[Evacuation] Decisions aren’t made lightly. You have make sure you don’t make unnecessary moves, so that people don’t take action next time,” said Mike Steele, Communications Director for the Governor’s Office of Homeland Security and Emergency Preparedness in Louisiana, a state which had to make such decisions ahead of Hurricane Barry earlier this year.
This decision is even more complex in Florida’s coastal regions, given the high percentage of elderly residents.
First shared in The Conversation, research from Lindsay J. Peterson, an instructor at the University of Florida’s School of Aging Studies, and Kathryn Hyer, a USF professor and director of the Florida Policy Exchange Center on Aging, shows that the evacuation of nursing home residents posed a greater risk to their health than staying in place. Their analysis focused on storms that hit between 2005 and 2008, including Hurricanes Katrina, Rita, Gustav and Ike.
The National Emergency Management Agency of The Bahamas and Tallahassee Emergency Operations Center is preparing to use the map as well, with a particular eye towards population movement.
Direct Relief is planning to send an Emergency Hurricane Kit to Florida’s Department of Health and is also coordinating response efforts with The Bahamas’ Ministry of Health, Pacific Disaster Center, Caribbean Disaster Emergency Management Agency, and Organization of Eastern Caribbean States.
Fifteen Direct Relief Emergency Hurricane Kits — each of which has about 150 essential medicines and medical items — are already in Florida, and four additional pallets full of supplies are in transit from Direct Relief’s California warehouse. Staff members are on the ground and ready to respond to requests from partners in The Bahamas, Florida, Georgia, and South Carolina.
In Florida, a Direct Relief representative will be working out of the Emergency Operations Center in Tallahassee.
Direct Relief staff are slated to be arriving Monday, via seaplane, to Grand Bahama and Abaco with sufficient medication for up to 1,000 people. | |
Impostors and impostures featured prominently in the political, social and religious life of early modern England. Who was likely to be perceived as impostor, and why? This book offers a full-scale analysis of this multifaceted phenomenon. Using approaches drawn from historical anthropology and micro-history, it investigates changes and continuities within the impostor phenomenon from 1500 to the late eighteenth century, exploring the variety of representations and perceptions of impostors, and their deeper meanings within the specific contexts of social, political, religious, institutional and cultural change. The book examines a wide range of sources, from judicial archives and other official records to chronicles, newspapers, ballads, pamphlets and autobiographical writings. Given that identity is never fixed, but involves a performative dimension, changing over time and space, it looks at the specific factors which constitute identity in a particular context, and asks why certain characteristics of an allegedly false identity were regarded as fake.
differing agendas, collective and individual. In the following sections I lay out some of the general contours of this historical anthropology project; they in turn will illuminate some of the principal theoretical and methodological concerns and interventions underpinning this body of work. Colonial and postcolonial studies: ‘provincializing’ Portugal One
) of social worlds. These are issues to which I shall return. The point now is that the account ahead explores the elaborations of identities within historical anthropology, including postcolonial perspectives and subaltern approaches. In these domains, identities have been articulated as part of critical considerations, at once theoretical and empirical, not only of colony and community and empire and nation, but also of
conceptual investments of this historical anthropology project: to ‘translate’ saint veneration to a colonial context; to examine the spiritual and the material aspects of colonialization and missionization; to look at the production of a relational triad of church, state, and public at five different historical moments through the lens of ritual; to delve into the space of ritual as a practical and
-modern/trans-modern that have characterized South Asian subaltern studies, Latin American scholarship on coloniality/decoloniality, and postcolonial perspectives at large. The critical concerns extend to the tangible presence yet ambivalent articulations of time/space – turning on “culture” and “tradition” – in formations of history, anthropology, and historical anthropology. On offer are intellectual
This collection explores how concepts of intellectual or learning disability evolved from a range of influences, gradually developing from earlier and decidedly distinct concepts, including ‘idiocy’ and ‘folly’, which were themselves generated by very specific social and intellectual environments. With essays extending across legal, educational, literary, religious, philosophical, and psychiatric histories, this collection maintains a rigorous distinction between historical and contemporary concepts in demonstrating how intellectual disability and related notions were products of the prevailing social, cultural, and intellectual environments in which they took form, and themselves performed important functions within these environments. Focusing on British and European material from the middle ages to the late nineteenth century, this collection asks ‘How and why did these concepts form?’ ‘How did they connect with one another?’ and ‘What historical circumstances contributed to building these connections?’ While the emphasis is on conceptual history or a history of ideas, these essays also address the consequences of these defining forces for the people who found themselves enclosed by the shifting definitional field.
Anthropology after Gluckman places the intimate circle around Max Gluckman, his Manchester School, in the vanguard of modern social anthropology. The book discloses the School’s intense, argument-rich collaborations, developing beyond an original focus in south and central Africa. Where outsiders have seen dominating leadership by Gluckman, a common stock of problems, and much about conflict, Richard Werbner highlights how insiders were drawn to explore many new frontiers in fieldwork and in-depth, reflexive ethnography, because they themselves, in class and gender, ethnicity and national origins, were remarkably inclusive. Characteristically different anthropologists, their careers met the challenges of being a public intellectual, an international celebrity, an institutional good citizen, a social and political activist, an advocate of legal justice. Their living legacies are shown, for the first time, through interlinked social biography and intellectual history to reach broadly across politics, law, ritual, semiotics, development studies, comparative urbanism, social network analysis and mathematical sociology. Innovation – in research methods and techniques, in documenting people’s changing praxis and social relations, in comparative analysis and a destabilizing strategy of re-analysis within ethnography – became the School’s hallmark. Much of this exploration confronted troubling times in Africa, colonial and postcolonial, which put the anthropologists and their anthropological knowledge at risk. The resurgence of debate about decolonization makes the accounts of fierce, End of Empire argument and recent postcolonial anthropology all the more topical. The lessons, even in activism, for social scientists, teachers as well as graduate and undergraduate students are compelling for our own troubled times.
Between 1598 and 1800, an estimated 3, 271 Catholic women left England to enter convents on the Continent. This study focuses more particularly upon those who became Benedictines in the seventeenth century, choosing exile in order to pursue their vocation for an enclosed life. Through the study of a wide variety of original manuscripts, including chronicles, death notices, clerical instructions, texts of spiritual guidance, but also the nuns’ own collections of notes, this book highlights the tensions between the contemplative ideal and the nuns’ personal experiences. Its first four chapters adopt a traditional historical approach to illustrate the tensions between theory and practice in the ideal of being dead to the world. They offer a prosopographical study of Benedictine convents in exile, and show how those houses were both cut-off and enclosed yet very much in touch with the religious and political developments at home. The next fur chapters propose a different point of entry into the history of nuns, with a study of emotions and the senses in the cloister, delving into the textual analysis of the nuns’ personal and communal documents to explore aspect of a lived spirituality, when the body, which so often hindered the spirit, at times enabled spiritual experience.
This book explores the reasons and justifications for the Chinese state’s campaign to erase Uyghur identity, focusing, in particular, on how China’s manipulation of the US-led Global War on Terror (GWOT) has facilitated this cultural genocide. It is the first book to address this issue in depth, and serves as an important rebuttal to Chinese state claims that this campaign is a benign effort to combat an existential extremist threat. While the book suggests that the motivation for this state-led campaign is primarily China’s gradual settler colonization of the Uyghur homeland, the text focuses on the narrative of the Uyghur terrorist threat that has provided international cover and justification for the campaign and has shaped its ‘biopolitical’ nature. It describes how the People’s Republic of China (PRC) was able to successfully implicate Uyghurs in GWOT and, despite a lack of evidence, brand them internationally as a serious terrorist threat within the first year of the war. In recounting these developments, the book offers a critique of existing literature on the Uyghur terrorist threat and questions the extent of this threat to the PRC. Finding no evidence for the existence of such a threat when the Chinese state first declared its existence in 2001, the book argues that a nominal Uyghur militant threat only emerged after over a decade of PRC suppression of Uyghur dissent in the name of counterterrorism, facilitating a ‘self-fulfilling prophecy’ that has served to justify further state repression and ultimately cultural genocide. | https://www.manchesterhive.com/search?q=%22historical+anthropology%22 |
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Showing results for tags 'Duration'.
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Emby Server / Emby Theater - Option to Download (and Display) Duration/Length Metadata for Media Stubs
funwithmedia posted a topic in Feature RequestsIt would be helpful if Media Stubs that have online metadata would automatically download (or there be an option to make set it as automatic) additional metadata that normally would be derived from the video file, particularly Duration / Length / Runtime of the video (and then of course actually display that metadata in Emby Theater). I realize that the online metadata may not always exactly match the true duration (eg, a special edition DVD with extra scenes not in the official theatrical length), but anything would be more useful than nothing here. If I'm trying to decide on something to watch it is unfortunate to have to go dig up the physical DVD/Blu-ray (or switch to the online service provider, if is something I have on Vudu, iTunes, etc.) in order to find out how long it is (particularly since movies can vary in length from ~1.5 hours to 2.5+ hours). Thanks!
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Movie/Episode duration
Noustaa posted a topic in Feature RequestsHello I would like to request to add the possibility to see the duration of a movie or an episode of a TV SHOW please ? i know TVDB & TMDB provide those information. For movies just show the full duration of the movie but for TV show no need to get the duration of each episodes but just the average (for example The big bang theory 25 minutes). Let me know if some peoples are also interested for that feature
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Add Grouping and Filters for Length/Duration (Emby Theater, Windows Desktop)
funwithmedia posted a topic in Feature RequestsIn addtion to things like Unwatched, Collections, Genres, Years, etc. I would find it nifty if there was a grouping for Length/Duration (Length might make the most sense, but I'm open to other words), perhaps by 15 minute increments? And adding in this sort of thing other places (eg, search filters, etc., whenever those types of things get implemented) would be useful. The use case for this is that I often only have a certain amount of time to watch something, and so I'll search (in my old, custom media setup) via time groupings for what I could watch within the time I have available. So I'm interested in any ways to achieve that easily within Emby Theater. Thanks for considering my request! PS-If this is something you might like to see implemented, be sure to "Like" this top/first post (as well as any subsequent posts in this thread that highlight particular aspects of what you are interested in) -- "Liking" the top/first post helps the Devs to know how much interest there is in a given Feature Request. | https://emby.media/community/index.php?/search/&tags=Duration&updated_after=any&sortby=relevancy |
This chapter illustrates how enthusiasm can become both ideological and apolitical. As enthusiasm developed from a religious to a political phenomenon, the result was a bifurcation of its meanings, where enthusiasm was sometimes experienced as an affect that accompanied zealotry, and at others as a more benign swooning. Focusing on the political thought of Hannah Arendt, this chapter pays particular attention to the affective basis of zealotry. It examines the role of the spectator in democratic politics, and the place of the spectator’s enthusiasm in public discourse. While sympathetic to Arendt’s aims, this chapter also presents a critique, noting that she inherits a binary notion of enthusiasm, one that turns political enthusiasm into a depoliticizing affect. Paying attention to this contrasting logic, this chapter shows how Arendt’s reading of enthusiasm fuels an exclusionary and secularized affect, while vacating the concept of its potency. The aim of the chapter is to highlight and push against the binary logic underlying Arendt’s thinking on enthusiasm, and the culmination of that logic in a kind of depoliticization. By delineating varieties of the binaries of enthusiasm, this chapter works to form a new ground for the rethinking of enthusiasm.
Enthusiasm has long been perceived as a fundamental danger to democratic politics. Many have regarded it as a source of threatening instabilities manifest through political irrationalism. Such a view can make enthusiasm appear as a direct threat to the reason and order on which democracy is thought to rely. But such a desire for a sober and moderate democratic politics is perilously misleading, ignoring the emotional basis on which democracy thrives. Enthusiasm in democracy works to help political actors identify and foster progressive changes. We feel enthusiasm at precisely those moments of new beginnings, when politics takes on new shapes and novel structures. Being clear about how we experience enthusiasm, and how we recognize it, is thus crucial for democracy, which depends on progression and the alteration of ruler and the ruled. This book traces the changing ways enthusiasm has been understood politically in modern Western political thought. It explores how political actors use enthusiasm to motivate allegiances, how we have come to think on the dangers of enthusiasm in democratic politics, and how else we might think about enthusiasm today. From its inception, democracy has relied on a constant affective energy of renewal. By tracing the way this crucial emotional energy is made manifest in political actions – from ancient times to the present – this book sheds light on the way enthusiasm has been understood by political scientists, philosophers, and political activists, as well as its implications for contemporary democratic politics.
Chapter 5 offers a refocusing on enthusiasm in democracy and especially the contemporary affective strategies and conditions faced in democratic life. As an entry into the contemporary view of democracy, this chapter explores Rancière’s essay “Hatred for Democracy” as a site to begin to consider these affective dimensions. At the heart of this affective life, according to Rancière, is the condition of hatred. This chapter shows how Rancière deploys a “democratic” rhetoric that does not seek to destroy this logic of hatred, but rather finds a means of existing in a world where hatred(s), including hierarchies and xenophobia, are a profound reality to be resisted – springs to take energy from. This move, from the hatreds that plague democratic life (hatred of democracy), to a political engagement with hatred that acknowledges its reality (hatred for democracy), depends on developing a grammar that begins to reflect these democratic forces between subjectivities. This chapter shows that, at the heart of this grammar of hatred, there lurks a persistent enthusiasm, one that helps make sense of such hatreds and the specific ways they damage democracy.
This chapter explores how to distinguish enthusiasm in political action. Considering Walter Benjamin’s essay Critique of Violence (1921), this chapter explores acts of enthusiasm, and especially the general strike. Benjamin’s discussion of the general strike draws the political imagination to what he named a “pure” politics, beyond mediation. This chapter reads the strike as a principle of political intrusion – one that is a lurking, though sublimated, enthusiasm. This reading productively problematizes the force of the strike. It extends Benjamin’s thesis, beyond any historical imagination of the general strike as the mere force of labor, instead reading the strike as an act of enthusiasm that extends and complicates Kant’s thinking, and in different ways from the Arendtian inheritance. This chapter also moves to more contemporary examples of enthusiastic acts, considering immolations, hunger strikes, and other “suicides” as similarly “general” politics, rupturing the violence of the state according to its own pathways of power.
This chapter begins with a vignette of ‘super Saturday’ in autumn 2019 when the House of Commons held a ‘meaningful vote’ on Brexit but hardly anyone – including MPs – understood what actually happened in the House of Commons. It makes the case that parliamentary procedure is excessively complex and arcane and argues that it is detrimental to democracy if the public does not understand what is going on in parliament.
The chapter explains what parliamentary procedure is and how its uncodified nature makes it difficult for MPs, let alone the public, to understand. It considers why procedure is so complicated and argues that complexity should not be an inherent feature of parliamentary rules. It explores what has been done to try to simplify parliamentary procedure and make it easier to understand, and the barriers to democratising the workings of parliament in this way.
The public’s perception is that the House of Commons is a private club, run according to incomprehensible rules which set MPs apart from their constituents. This is damaging and should be addressed by a continuous process of reviewing and simplifying the rules. But this will only happen with government support.
The conclusion opens by arguing that MPs ought to be more concerned than they are about the spiral of declining public trust and government contempt into which the House of Commons has fallen. It observes that there have been significant efforts in recent years to communicate the work of MPs but argues that the public is more likely to judge parliament by the behaviour of MPs than by the outputs of parliamentary processes.
MPs should make the House of Commons an exemplar of best practice rather than an exception to the rules. The long history of the House of Commons is no guarantor of modern value and the preferences of current MPs should not be allowed to prejudice the future of the institution by preventing reform. MPs should address the inappropriate degree of control over the procedures and processes of the House of Commons which is exercised by whichever party is in government.
The chapter concludes that at present there is neither the will among MPs nor the incentive for the government to undertake the reforms that are needed to reverse the vicious cycle of decline. Ironically, perhaps it is only if the unmodernised palace finally goes up in flames and parliamentarians find themselves forced out of Westminster without notice that they will be forced to reflect on many previously unthinkable questions about the way our politics operates.
This chapter opens with a description of the decrepit nature of the Palace of Westminster. The chapter discusses the problems that have dogged the project to restore the palace and the consequences – actual and potential – of parliamentarians’ refusal to allow it to proceed. It argues that the disinclination of today’s politicians to renovate the palace means that historical choices will continue to condition future behaviours and thinking in intended and unintended ways.
The chapter argues that the problems which have dogged the restoration are symptomatic of wider issues which are undermining public trust in the House of Commons, and that these need to be addressed in order to reverse the spiral of decline in public confidence in parliament. MPs’ failure to make the House of Commons more diverse, comprehensible and modern has created a risk parliament’s credibility and relevance as an institution.
The chapter opens with a vignette from a Commons debate in June 2020 on an independent bullying investigation process. The story illustrates a persistent problem which undermines the reputation of the House of Commons – the tendency of MPs to treat themselves as an exception to the rules which they dictate for the rest of the country.
The chapter explains the ways in which MPs do have an exceptional status – as elected office holders with certain privileges and powers. But it argues that MPs often misinterpret their status and inappropriately exempt themselves from the rules – using the examples of the Cash for Questions and MPs’ expenses scandals.
The chapter argues that self-regulation breeds misbehaviour and that the Palace of Westminster exacerbates MPs’ sense of their exceptional status. It concludes that MPs need to be honest with themselves about the actual purposes for which their powers, privileges and exemptions have been granted and recognise the proper boundaries that these place around their exceptional status.
Held in Contempt argues that Brexit and Covid-19 have reinforced a vicious cycle of decline in Westminster – of executive disregard for parliament, which undermines public trust in its role, and in turn further emboldens ministers to side-line the legislature. This is damaging parliament’s ability to play its part in UK democracy.
The book shows how Brexit and Covid-19 have highlighted and exacerbated existing worrying trends – government’s increasing use of fast-track processes to make laws in ways which minimise the role of parliament and ministers’ disregard for scrutiny and their disinclination to update inadequate parliamentary processes. These trends in government behaviour are contributing to low public trust, which itself is damaged by the exceptionalism and unrepresentativeness of MPs and the arcane nature of parliamentary procedures.
MPs should recognise these problems and look for ways to reverse the cycle of decline into which their institution has fallen – nurturing greater public trust in and government respect for parliament’s role. But this is unlikely to happen because many of the shortcomings of the House of Commons operate in the government’s favour, so it has no incentive to allow reforms to take place.
Potentially only a disaster – such as a major fire in the crumbling Palace of Westminster – will be enough to jolt MPs and the government out of their complacency, compelling them to acknowledge the strength of public unhappiness with the way they are currently ‘doing’ politics and forcing them to identify and act to rectify the shortcomings of the House of Commons.
The introduction uses the 2019 prorogation crisis to introduce the idea of government contempt for parliament and how this has been exacerbated by the twin crises of Brexit and Covid-19. It describes the role of the House of Commons and sets out current data on low levels of public trust in parliament before examining the factors that shape that trust. Finally it briefly describes the structure of the book and the key arguments of the five main chapters. | https://www.manchesterhive.com/browse?access=all&page=10&pageSize=10&sort=datedescending&t_1=POL |
Why is a dialogue important?
Dialogue is a useful tool for developing your characters and moving your plot forward.
Dialogue can help you establish the backstory, and it can reveal important plot details that the reader may not know about yet.
Dialogue is great for ratcheting up the tension between characters.
Dialogue can also establish the mood..
What is another word for dialogue?
In this page you can discover 28 synonyms, antonyms, idiomatic expressions, and related words for dialogue, like: conversation, passage, monologue, talk, exchange, remarks, discussion, composition, converse, jaw and chat.
How do you start a dialogue?
How to Write Natural Dialogue in 11 Steps, With Examples!Enter the conversation late. … Keep dialogue tags simple. … Use descriptive action beats. … Make each character sound distinct. … Develop character relationships. … Show, don’t tell as much as possible. … Bounce quickly back and forth. … Read your dialogue out loud.More items…•
What is a meaning of dialogue?
noun. conversation between two or more persons. the conversation between characters in a novel, drama, etc. an exchange of ideas or opinions on a particular issue, especially a political or religious issue, with a view to reaching an amicable agreement or settlement.
What is dialogue in simple words?
(Entry 1 of 2) 1 : a written composition in which two or more characters are represented as conversing. 2a : a conversation between two or more persons also : a similar exchange between a person and something else (such as a computer)
What are the 4 types of dialogue?
In a competitive conversation, people are more concerned about their own perspective, whereas in a cooperative conversation participants are interested in the perspective of everyone involved. Based on direction and tone, I grouped conversations into four types: debate, dialogue, discourse, and diatribe.
What are the 5 purposes of dialogue?
It makes the story advance. A major feature of dialogue is that it moves the story forward in a more straight-forward way than a narrator’s explanation would. … It develops the characters. Characters can also evolve through dialogue. … It brings dynamics. … It provides realism. … It defines characters. … It provides information.
What is a good dialogue?
Good dialogue has a purpose and builds toward something A good conversation is an escalation. The dialogue is about something and builds toward something. If things stay even and neutral, the dialogue just feels empty. Characters in a novel never just talk.
What is an example of a dialogue?
Dialogue refers to a conversation or discussion or to the act of having a conversation or discussion. … Often, we read outer dialogue, which occurs between two characters as spoken language. Examples of Dialogue: “Lisa,” said Kyle, “I need help moving this box of toys for the garage sale. | https://changes-uk.com/qa/question-what-dialogue-means.html |
Third graders use the scientific method as they separate the colors used in ink. In this chromatography lesson, the teacher introduces students to how chromatography is used in several careers, then students perform an experiment to see...
Chromatography of photosynthetic pigmentsLesson Planet
11th - Higher Ed
Learners explore the technique of chromatography to separate compounds in a mixture. In small groups, they separate by paper chromatography and identify the major and accessory photosynthetic pigments.....................................
Standard One: Lab Design and Appendix A Lab SkillsLesson Planet
9th - 12th
In this lab design and lab skills worksheet, students answer questions about experimental design including finding variables, determining controls, and graphing data. They answer questions about microscopy and label the parts of a...
Cell Structures and Their FunctionsLesson Planet
7th - 12th
Life science learners investigate live cells. They examine wet mount slides of cyanobacteria and Elodea plants. They peer into the dynamic microscopic world of protists. Afterward, they construct a model of a cell, including rudimentary...
Autumn Leaves: Where Does the Color Come From?Lesson Planet
9th - 12th
Students examine and discuss photosynthesis, and how the change of season affects the color of leaves. They perform an experiment that analyzes leaf pigmentation through chromatography, and write an essay describing the results.
Energy and Metabolism - PhotosynthesisLesson Planet
9th - 12th
Although the title slide says that this is a reading check, valuable and applicable information is included in this presentation that you can use in your biology class. Foster an understanding of photosynthesis with the notes, graphs,...
TV Forensics: What Do CSIs Actually Do?Lesson Planet
4 mins 9th - Higher Ed CCSS: Adaptable
TV dramas tend to exaggerate the forensic science components. Learn what true forensic chemistry looks like in an installment of a larger series covering reactions. Viewers see that chromatography, mass spectrography, and methodical...
Forensic Science: Case of the Missing Diamond MakerLesson Planet
5th - 9th CCSS: Adaptable
Someone stole a diamond-making machine. Who done it? Scholars use forensic science at six different stations to determine the culprit. They analyze fingerprints, use their senses, and complete chemistry experiments to determine the...
Forensic Sciences: A Crime Scene Investigation UnitLesson Planet
9th - 12th CCSS: Adaptable
Mr. Bergman has been murdered and we need you to solve the crime! The cross-curricular unit covers 11 different types of forensic science and includes 17 activities. Scholars perform blood type analysis, blood spatter analysis, height... | https://lessonplanet.com/search?keywords=chromatography&page=4 |
I’m exploring ways to avoid generic cookie-cutter improvisations on blues and rhythm tunes. Step 1 is to NOT improvise on the chord changes. Step 2 is to paraphrase the melody until its distinguishing characteristics are thoroughly metabolized by the imaginal ear. Then present those characteristics with the sparsest melody imaginable. This sparse melody can serve as the framework for improvised elaborations when practicing the tune, which is now no longer a “blues” or a “rhythm” tune but regains its singular identify as “Au Privave”, “Straight No Chaser”,”Veird Blues”,etc. I call this melodic framework a “skeletune”. There could of course be several “Skeletunes” derived from any particular tune.
For “Au Privave”, I created a Skeletune by removing what I hear as the embellishing notes while preserving what I feel is the rhythmic thrust of the melody.
Back to Menu
Form
Melody
Over the I Chord
The first two phrases share an identical rhythmic pattern and the same general melodic pattern. The rhythmic pattern spans 3 beats starting with 4 consecutive eighth notes followed by a quarter note rest. The melodic pattern starts on a chord tone, follows with a lower chromatic neighbor tone, goes back to the chord tone, and finishes with a descent to the perfect fifth. Phrase 1 use the tonic as the chord tone and phrase 2 uses the major 3rd. | http://harpscomplete.com/wordpress/?p=1242 |
can get in the way of building a faith community.
Sociologist Robert Bellah, in his frequently cited book
Habits of the Heart (University of California Press, 1985),
provides helpful guidance for our reflections on this
problem. In his analysis, Bellah discerns a "utilitarian
individualism," growing out of the Enlightenment,
which celebrates both the autonomy of the individual
over institutional authority and the triumph of reason
over tradition. American individualism has roots in the
social thought of Thomas Hobbes and John Locke, who
saw society as an association of contracting individuals
all of whom have their own distinct purposes and private goals. It was fueled by the rise of science and the
Industrial Revolution and places great emphasis on
economic self-interest. It led to the "modern manager
type" who specializes in effective means to economic
success, often without consideration for social good or
more personal goals.
Bellah's analysis helps pastoral leaders understand
some of the reluctance they encounter in trying to
achieve a sense of common purpose in their parishes.
Persons accustomed to act in an individualistic way
may, for example, find it difficult to participate wholeheartedly in communally oriented prayer.
Utilitarian individualism has begotten a reaction that
Bellah calls "expressive individualism." This term describes the stance of persons who have turned their attention to self-fulfillment, precisely because they have
sensed the dehumanizing effect of concentrating on
the efficient pursuit of private goals and economic success. Their goal now is self-actualization through developing their latent talents, self-expression through rec-
Reverend James J. Bacik is copastor of Corpus Christi University Parish in Toledo, Ohio.
ognizing and venting their feelings, and self-liberation
through overcoming institutional and societal constraints. This therapeutic approach to life often produces striking personal development, but also reinforces the individualistic tendency to ignore the common good. Bellah claims that the language of community, which we associate with biblical religion and republican virtues, is lost or muted in the midst of all the
voices calling for efficient management and personal
growth.
JL astoral ministers often find hidden beneath the surface of the pursuit of self-interest an intense hunger for
community that includes a longing for close, intimate
relationships, as well as a desire to work in solidarity
on important common tasks. Pastoral leaders have the
responsibility of placing these human desires in a
Christian context, which maintains that authentic fulfillment can come only in solidarity with others and in
pursuit of the common good. As part of their leadership mission they should deal explicitly with the limitations of utilitarian individualism, both unmasking its
implicit claims to be the only road to happiness, and
suggesting the positive values of more communal
experiences. Getting people involved in the various renewal programs or social justice projects often gives
them a taste of the satisfaction and joys accompanying
group activities for common ends.
In this regard, I am reminded of the effectiveness of
the Christian Family Movement that was so popular in
the early stages of the renewal spawned by the Second
Vatican Council. This movement was able to combine a
sense of shared values and close relationships with
group activities designed to benefit the public interest. | http://cdm16999.contentdm.oclc.org/cdm/ref/collection/myfirst/id/7/ |
WayForward Technologies, Inc. (also known as WayForward) is a video game development studio based in Valencia, California. It was founded in 1990 by Voldi Way. WayForward started by developing games for consoles such as the Super Nintendo Entertainment System, Sega Genesis, Game Boy Color and others, before branching out in 1994 to TV games and PC educational software. In 1997 they returned to producing more generalist video games, choosing to be a contractor for other publishers and working on several licensed assets.
Besides these, the company has created a few original games IP, including Shantae and the Mighty! series. Currently, WayForward Technologies works on games for the Nintendo 3DS handheld console, and WiiWare games for Nintendo's Wii U console, as well as a few for the PlayStation Network and Xbox Live Arcade.
Contents
- 1 History
- 2 Games developed
- 3 References
- 4 External links
History
Origins
WayForward Technologies was founded in 1990 by Voldi Way as an independent video game design company, after a previous company of which he was also a co-founder that specialised in software for sheet metal fabrication. He financed WayForward by selling his parts in this company. The name WayForward Technologies may refer to the novel "Dirk Gently's Holistic Detective Agency", by Douglas Adams, where a character named Gordon Way had founded a company by the same name. The company first focused on producing games for the Super Nintendo Entertainment System, Sega Genesis, Sega CD, Game Gear and Game Boy Color. They also began to branch out into educational computer games for PC and Leapster. During these early years, many of the staff were doing other jobs to live, as the pays were not always enough to support their ambition to become game developers. Some were delivering lunches, and Matt Bozon, for instance, was doing sketches in a Six Flags theme park.
As an educational games producer
In 1994, WayForward Technologies concluded a partnership with American Education Publishing in order to focus on developing exclusively educational computer games (working under the name Brighter Child Interactive). The partnership was successful, with the company winning awards for innovation at the 1995 Consumer Electronics Show. During this time, WayForward still focused on licensed assets such as the Muppets for their educational games, but also Godzilla or The Scorpion King for their more traditional games.
Return to traditional video games
WayForward returned exclusively to their video game development business in April 1997, choosing to be a "developer for hire" by providing services to software publishers. John Beck, the current CEO, has said that by providing services on these projects the company managed to create a stable structure.
Creation of Shantae
In mid 2002, WayForward released their first game based on their own intellectual property called Shantae, created by Matt Bozon, with Capcom as publisher. It achieved critical acclaim, but it was released for the Game Boy Color one year after the release of the Game Boy Advance and as a result only enjoyed limited success. It would later develop a small cult following by the era of emulators.
Early plans for a Shantae sequel
Despite this setback, WayForward believed in the franchise's potential and started work on a sequel for the Game Boy Advance. The resulting game, Shantae Advance, was cancelled during production as WayForward did not find a publisher because of the sales of the first game. When Nintendo announced a dual-screen handheld console that became the Nintendo DS in early 2004, WayForward began examining the various possibilities offered by this new engine. Work started on a sequel to Shantae called Shantae: Risky Waters using the two screens. However, they were yet again unsuccessful at securing a deal. As a large number of Shantae related assets were produced, including 3D models, WayForward frequently used them when trying out new technology or development platforms.
From 2004 to 2009
Later in 2004, the company was contracted by THQ to produce a new chat game, Ping Pals, for the Nintendo DS. Despite the tight timescales involved in developing the game, WayForward seized the opportunity to obtain development kits for the platform. The game was panned by most critics and gained only a single positive review. In 2006, the company produced Justice League Heroes: The Flash as the Game Boy Advance was reaching the end of its commercial life cycle, which this time met with largely positive reviews. Since then, WayForward has gone on to develop further titles for the Nintendo DS. One of them, Looney Tunes: Duck Amuck, based on the 1951 Warner Bros. cartoon Duck Amuck was highly anticipated at the E3 trade show but unfortunately received mixed reviews upon release. On the contrary, Contra 4, a game developed for Konami for the popular series of Contra games, was almost universally praised by critics.
On February 19, 2008, John Beck and Matt Bozon were speakers at the Independent Games Summit, during the 2008 Game Developers Conference, discussing a range of issues facing independent games companies. By this time, WayForward was developing titles for Nintendo's Wii console using internally developed intellectual property anew. LIT was announced on March 5, 2008 and was released on February 9, 2009 for the WiiWare online shop platform.
Creation of the Mighty! series
In the Spring 2009 entry of the Shantae Fan Club online newsletter, WayForward introduced a new character named Alta, a pink-haired girl wielding a scepter. She was to represent a brand-new original franchise. This was revealed on March 9, 2009 to be a DSiWare exclusive game called Mighty Flip Champs!. The game spawned an entire Mighty! series, including Mighty Milky Way, another puzzle platformer with a new character named Luna, and its sequel, Mighty Switch Force! which was released on the Nintendo 3DS eShop on December 22, 2011. Another sequel was released two years later called Mighty Switch Force! 2 on the 3DS eShop. | https://shantae.fandom.com/wiki/WayForward |
The Mission Pharmacist shall ensure the overall functioning of the PUI Pharmacies at central, base and project level, securing an adequate and timely supply of quality health consumables, equipment and medicines to the projects.
The Mission Pharmacist will be responsible for giving technical support to the pharmacy teams at field level and building capacity to respect PUI procedures. The Mission Pharmacist must ensure proper pharmaceutical management (procurement, storage, distribution, inventory, consumption, and data management) for the entire mission, both at the coordination level and at operational bases and supported health structures.
The Mission Pharmacist will work closely with the logistics team to ensure the supply chain health consumables, equipment and medicines in a timely, reliable and well documented way at all levels.
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2- RESPONSABILITIES AND TASKS
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Role and Responsibilities
Pharmaceutical Management: The Mission Pharmacist is in charge of monitoring all pharmaceutical matters regarding stock and supply across the Mission, in collaboration with the Central Pharmacists (supervised by the Mission Pharmacist) and the Field Pharmacists (supervised by the Project Managers). The Mission Pharmacist shall ensure that the items in stock are on good standards of humidity, safety and temperature, acting when the indicators are not adequate or when there is shortage or overstock;
Procurement: The Mission Pharmacist is in charge of the Medical Procurement Process from the Programs’ perspective. With the support of the Central Pharmacists, Health Coordinator and Deputy, Project Managers and other field positions, the Mission Pharmacists shall prepare the needs assessment, proposal’s budget, procurements request and choose the items from the market, in collaboration with the logistics and projects;
Training: The Mission Pharmacist shall work towards the development of the mission and his team, by developing presentations and trainings from the scratch or based on available models, prepare a timeline for delivering it and collect feedback for continuous improvement;
specific objective and linked activities
Data Analysis, Collection and Treatment
o Analyze the data to optimize the management of health consumables, equipment and medicines (needs assessment, purchase, control, supply, cold chain, expiry dates, overstock/shortage etc.);
o Contribute technically to the writing of donors’ reports and proposals specifically for information on pharmacy;
o Have technical oversight on data collection (in/out, consumption) of bases and health facilities and ensure accurate data entry into the pharmacy management software (currently tools on excel/SagaStock);
o With the Health Coordinator improve the loan/return policies and donation of drugs and medical items;
o Work in collaboration with the medical department to check, in relation to epidemiological data, the status of stocks and the consumptions and assess the appropriateness of prescriptions;
Mission Strategy
o Conduct regular assessment visits and support Central Pharmacist field visits, in order to ensure proper management of drugs at both base pharmacies as well as health facilities;
Development of policies;
o Provide training and technical support to the pharmacists and staff in charge of pharmacies on: Stock management, rational use of medicines, substitution and therapy options, and analysis of consumption of health facilities;
o Provide technical support to staff in charge of pharmacies in health facilities supported by PUI: implementation tools, ad hoc training;
Reporting and Representation
o Ensure the appropriate filing of documentation and archives;
o Maintain and share an annual PUI pharmacy activity planning;
o Participate in base coordination meetings;
o Participate in external meetings related to pharmacy and PUI projects (Health Cluster, etc.);
o Participate in health team meetings;
o Share monthly copies of all relevant data including AMC, stock reports, with the Health Coordinator HQ pharmacist and HQ health advisor;
o Write a monthly activity report to be transmitted to Situation Report;
Stocks Management
o Conduct pharmacy assessment of the Pharmacies, focusing on: Stock movements both computerized and physical, anticipation and management of expired drugs, organization of the stock for project requirements (according with donors);
o Develop of pharmaceutical SOP and tools for stock management of the base pharmacies and health facilities, in collaboration with project managers, training or implementation, monitoring and evaluation;
o Support the implementation, the understanding and application of procedures and tools used at base level and health facilities supported.
o Supervision of pharmacovigilance including the review of report concerning the quality of a drug in accordance with PUI pharmaceutical management procedures;
o Supervise the stock management of particular pharmacies (first aid kits, etc). Inform the Health Coordinator in case of irrational consumption or any misuse of pharmacy items;
o Technical oversights on adaptation of SOP to meet the national legislation, in particular for narcotic and psychoactive medicines, ensure quality and safety;
Staff Management
o Conduct the appraisal of the Central Pharmacist and support the appraisal of Pharmacy Storekeeper;
o Develop an Annual Planning for the activities of the Central Pharmacist;
o Support the Project Manager/PHCC Manager to conduct technical aspects of Pharmacists appraisals at project level;
Supply Management
o Ensure in collaboration with the logistics department, procedures with the local health and administrative authorities to obtain import licenses and taxes exemption.
o Participate in the technical inspection of local suppliers where appropriate;
o Place orders in collaboration with the Health Coordinator and monitor the purchase orders sent to HQ in collaboration with the Logistics Coordinator;
o Work with logistics and medical departments of Erbil and Headquarters for the purchase of consumables, equipment and medicines, in accordance with PUI and donors procedures;
Technical Support
o Draw up in collaboration with Project Managers the Job Descriptions of the members of the pharmacy team and play an active role in recruitment;
o Strengthen the capacity of health facility teams so that they can assume duties independently and can be critical in terms of consumption;
o Support, in collaboration with Field Coordinator/ Health Coordinator/ Logistic coordinator, the settlement of new warehouse when needed, including settlement of appropriate management tools, human resources and training implementation and follow up;
The tasks and responsibilities defined in this job description are non-exhaustive and can evolve depending on the project’s needs.
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3- PRIORITIES OF THE DEPARTMENT
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Mission Strategy: PUI is a NGO mostly funded by grants from different donors. With the majority of the activities on health, the participation of the Mission Pharmacist on the proposal (Budget and Needs Assessment) is essential even in projects without medicines. With short deadlines and unexpected calls, the Mission Pharmacist must be able to answer to the mission needs;
Procurement: As the main position in charge of initializing and following the procurement process, the Mission Pharmacist must be able to follow up procurements in collaboration with the Coordination, Field and Headquarters, both on Programs (Health) and Support (Logistics) with a critical view on the consumption, needs, quality, quantities, quotes and time for delivery;
Stock and Supply Management: With multiple pharmacies and warehouses, the Mission Pharmacist collects, analyses and share the results and directions for the central and field pharmacists, while communicating with the Headquarters in order to improve and guarantee the best stock and supply conditions in the Mission.
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QUALIFICATIONS
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Mandatory requirements
Language skills
Education degree
Work experience
Knowledge and skills
Computer skills
Other
assets
Interests: Humanitarian and International activities in Iraq, Middle East and nearby countries. Interest in activities of partner organizations;
Transversals skills: Analytical skills, creativity, diplomacy, independency, initiative, pro-activeness, professionalism, reactiveness and take the responsibility.
APPLICATION PROCESS
In order to submit an application, all candidates are invited to fill the following google form by clicking on the link below:
Apply Here - Mission Pharmacist Erbil
Premiere Urgence will proceed to the preselection of candidates on a rolling basis and reserve the right to close the advertisement as soon as a candidate is identified for the position. Therefore, you are kindly invited to submit your application as soon as possible.
Kindly note that all applications received by email or by paper will not be considered. Only those submitted through the application link will be processed.
Premiere Urgence International thank you for your interest in the organization. | https://ncciraqjobs.com/index.php/jobseeker-control-panel/job-detail/job-mission-pharmacist-22815/nav-15 |
The ancient water tanks remain some of the ruined city’s most beautiful architecture.
The ruins of Hampi, once a grand city in the Indian state of Karnataka, were once home to more than 250,000 people in the Vijayanagar Empire, and filled with Hindu temples. The abandoned city is now dotted with hundreds of individual ruins, home to countless architectural wonders.
Among the most beautiful ruins of Hampi are the pushkarnis, ancient water tanks. Like many Hindu temples in India, Hampi’s majestic temples have accompanying stepped tanks or basins used for religious and ceremonial purposes. Though thousands of miles away, water in the pushkarnis was considered part of the Ganges, Hinduism’s most sacred river, and therefore sacred.
The pushkarnis all follow a similar architectural form, designed symmetrically as either rectangles or squares. Each generally has several large tiers which contain multiple steps in semi-pyramidal from, leading down to the next level. Many of the pushkarnis were surrounded by pillars, like those at the Pattabhirama Temple, all of which added to the sense of grandeur.
These sacred tanks were integral parts of each temple complex. The stepped tanks were used for ritual bathing and cleansing before prayers. They also performed important ritualistic functions for festivals. At the end of Ganesh Chaturthi, the festival celebrating Ganesh, the idol of the god must be submerged in water in order to ritualistically dispose of it, a practice known as visarjan.
The steps carved into the sides of each pushkarni allowed for worshippers to easily get in and out of the water. The pushkarnis were fed with the water of the nearby Tungabhadra River through a series of canals and aqueducts. While some, like the tank at the Krishna Temple, are no longer functional, others still receive some water through the ancient water systems.
Visit India with Atlas Obscura Trips
Diwali in Northern India
Visit towering forts and palaces, partake in Diwali festivities, explore local villages, wander centuries-old ruins, learn to cook in a family home, and witness the sunrise over the Taj Mahal on this immersive tour of Delhi, Rajasthan, and Udaipur. | https://assets.atlasobscura.com/places/stepped-tanks-pushkarani-hampi |
The urban planning policy agenda is strongly influenced by sustainability objectives with particular emphasis upon environmental issues. But, the original definition was much broader and included economic well-being and social equality as well as environmental balance. But it is environmental sustainability, as illustrated in this paper with reference to the UK, that has become the ersatz religion and zeitgeist of politicians, urban policy makers and academics (Boot, 2014: 186). However worthy and admirable it might sound to be concerned about ‘saving the Planet’, in reality this agenda provides little space for social policy (Dempsey et al, 2011), or for taking into account the wider value base of the policy makers, or the beliefs and religions of the planned. There is little consideration given to the ways in which particular sustainability policies might impact upon different groups of human beings in society, in terms of their class, gender, lifestyle and religion and so forth. Likewise there is little linkage between sustainability policy and social issues such as poverty, social exclusion, disability, unemployment, and homelessness. A strict application of sustainability policy, which puts environmental concerns above human considerations, may actually exacerbate the situation by creating a people-less approach to planning (Greed, 2011). In the UK, the 2010 Equality Act lists seven protected categories that should be taken into account in all aspects of government policy making, including (in theory at least) urban planning. These are Age; Disability; Gender Reassignment; Pregnancy and Maternity; Race; Sex (gender) and Sexual Orientation; and Religion and Belief. However, overall equality issues tend to be given low priority compared with environmental considerations (Greed, 2005; 2017). Religion is on the list but it does not follow that it will get as much attention as the other categories. Some issues are higher up the pecking order than others, and nowadays sexuality tends to be given primary attention as the factor defining a person’s identity (Habermas and Ratzinger, 2007). Social class (which does not even appear on the list) used to be the primary social factor, arguably because planners could justify their unpopular policies by claiming they were planning for the working class and knew what was best for society. Religion, faith and belief, as will be explained, are very low on the pecking order. | https://uwe-repository.worktribe.com/output/898797/planning-for-diversity-and-sustainable-spatial-planning-religion-space-gender-and-ethnicity |
Q:
Shouldn't Superman Be (Literally) Black?
Supposedly Superman gets his powers from absorbing sunlight. I've read that plants on planets with dim red dwarf suns would likely appear black to our eyes, absorbing across the entire visible wavelength range in order to use as much of the available light as possible. Krypton had a red sun, so if Kryptonians evolved a photosynthetic ability, shouldn't Superman's skin be black?
A:
I don't believe it is ever stated that Kryptonians are photosynthetic; only that the exposure to the radiation of a yellow sun triggers enhanced abilities.
Even if they were photosynthetic, it wouldn't necessarily entail a pigment change to the degree you're discussing. Kryptonians eat and drink as humans do; plants, generally speaking, do not.
Kryptonians therefore would not require special pigmentation to use as much of the available light as possible, because they would not be nearly as dependant upon light as a source of nutrients as plants would be.
A:
Disclaimer: There is no good answer to this question.
Inference: Not likely. Since the nature of how plants and animals derive energy from sunlight is very different, the Kryptonians being animals, would NOT necessarily need to be dark-pigmented since they derive their energy from eating other plants and animals, not from the Kryptonian sun itself.
The Kryptonians are a literary creation. As such, they were created by writers who projected their ideas into a mythical mode in order to tell stories.
There is no indication in canon that the Kryptonians were able to utilize red sun radiation in any way to alter their metabolism. The original stories told a tale of super-humans, whose powers were derived from superior strength and the gravity of the larger than Earth planet Krypton. These were genetically enhanced supermen whose abilities were theorized to one day be possible (in humanity).
Unfortunately due to writing creep, Superman's powers continued to expand and evolve, and eventually the element of the yellow rays of the sun found their way into the legend.
The powers derived by the yellow sun are never fully explained and without an explanation, based somewhat in science, it is impossible to determine how or why the Kryptonian powers function AT ALL.
Given the surface area of a Kryptonian, even if he were able to absorb all the radiation from the sun across his entire body, 24 hours a day, he would not derive enough energy to be able to perform even one of his super-feats. There is still a missing element to the conversion or translation of solar energy once it is metabolized by the Kryptonian.
It is likely this element or capacity will never be discussed due to the intrinsic story-telling problems likely to occur.
Also See: How different is Superman's physiology from a normal human?
Also See: How and/or why did the original comic book Jor-El choose Earth as the target for his son's rocket?
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Like the mythical Greek character Sisyphus, who is forced to roll a boulder up a hill for all eternity only to watch if fall back down, local government has made a Herculean effort to divert half the waste stream through recycling, only to see the amount of garbage sent to their landfills increase.
Twenty years ago, AB 939 put the onus on local government to reduce landfill by 50 percent by 2000 and imposed a fine of $10,000 per day for noncompliance. Cities and counties, at great cost, vigilantly put into place recycling, education and reuse campaigns.
Some of that effort paid off, according to the California Dept. of Resources Recycling and Recovery. Diversion from landfills has increased seven-fold since 1989 when 42.4 million tons of stuff a year was buried. However, despite waste management’s collective 47 percent alternative disposal effort, in 2003, 40,276 tons was still going to waste.
The reason this story doesn’t have a happy ending is that consumption has increased, explained Heidi Sanborn, executive director of the California Product Stewardship Council. She estimated that 75 percent of this “buried treasure” is product and packaging waste that could have been avoided – or planned for easy reincarnation – if it were designed properly during the manufacturing stage.
The solution, according to Sanborn, is to start at the source with extended producer responsibility (EPR) or product stewardship. “EPR places primary responsibility with producers and manufacturers, because only they can change product design and incorporate recycling costs into the price of the products,” Sanborn said.
That holistic approach would allow consumers to make more informed choices about the total impact of their purchases.
Calaveras County Supervisor Steve Wilensky called the precarious financial position of local government between a garbage truck and an overflowing dump “a moment of crisis.”
Calaveras County is struggling with an imminent need for another cell in its landfill that will cost millions of dollars. “We are facing the Faustian choice of whether to put money into safety issues such as plowing the roads or dealing with garbage. There is no right decision,” Wilensky said.
Calaveras supervisors have considered everything from raising taxes and garbage rates to dumping fees. However, when they added a $25 recovery charge to “white garbage” such as dishwashers and ovens, people simply dumped them in a rural spot and then the county spent even more money to retrieve the environmental hazards.
Every time the state bans a material, cities and counties have to scramble to figure out how to isolate and dispose of the material, whether it is mercury or batteries.
Santa Clara County spent $2.9 million in 2008 to manage the hazardous waste collected from just 5 percent of its households, according to Rob D’Arcy, Santa Clara County hazardous materials program manager.
Sanborn would like to stop putting the burden on local government. “No more bans without plans,” she quipped at a recent Sacramento Sustainability Forum.
“It is not a question of the environment or profit, you can have both if you plan correctly,” Sanborn said. “Local government can’t and shouldn’t raise taxes and garbage rates enough to deal with all the disposal needs.”
A total of 75 jurisdictions have passed resolutions supporting product stewardship. Some tried to influence manufacturers with their wallets by establishing preferences for companies with take-back provisions in purchasing contracts. Others, including Central Contra Costa County Solid Waste Authority, called on legislators to require producer responsibility.
The only way to encourage manufacturers to follow the lead set in many other countries who effectively include plans for – and the cost of – recycling into the sales price is to require it by law. “That would create a level playing field,” Sanborn said.
Sanborn also predicts that requiring recycling and cradle-to-cradle planning for reusing materials would create a more competitive and cheaper recycling industry.
The alternative, Sanborn warns, is not viable – higher taxes and higher garbage collection rates.
The League of California Cities and California State Association of Counties have both worked with Assemblyman Wesley Chesbro (D, Glendale) to craft that would require end-of-life planning in production. The bill AB283, died in committee last year, but Chesbro Chief Consultant on the Environmental and Safety Committee said the Assemblyman plans to introduce a new Product Stewardship Act of 2010 that would cover only a few specific products to show that the concept can work.
The former Humboldt County supervisor and Arcata City councilman is no stranger to garbage issues. He served on the California Integrated Waste Management Board and was the founder of the Arcata Community Recycling Center in the early ‘70s.
Today, he chairs the Assembly Environmental Safety and Toxics Committee.
Another component necessary to make product life cycle planning more viable, according to Sanborn, is streamlining siting of recycling centers. In addition to reducing costs of shipping the materials overseas to be recycled in less than environmentally and humane circumstances, it would create local jobs. | https://www.publicceo.com/2010/02/local-governments-turn-to-product-stewardship-to-fill-bottomless-budget-hole/ |
Many people prefer to check reviews on the movie or book before watching or reading it. The summary information and honest point of view on the subject matter are usually included in an evaluation essay. You just need to analyze both sides of the chosen criterion through thorough research, analysis of your thesis, and examination of your own values. To write a good evaluation essay, you should forget about your feelings and create an objective overview of the topic. That way, you will reveal the truth about the real worth of the particular subject matter.
Many people prefer to check reviews on the movie or book before watching or reading it. The summary information and honest point of view on the subject matter are usually included in an evaluation essay. You just need to analyze both sides of the chosen criterion through thorough research, analysis of your thesis, and examination of your own values. To write a good evaluation essay, you should forget about your feelings and create an objective overview of the topic. That way, you will reveal the truth about the real worth of the particular subject matter.
So, what is an evaluation essay? The answer to this question you will find out in this post.
What Is an Evaluation Essay?
An evaluation paper is a kind of essay in which you express your argumentative point of view on various topics. As a form of literary thinking, it is based on much more than just a quick judgment about a person, place, or object. The common standards of evaluation writing, such as clearance, objectivity, and coherence, are to be followed throughout the text. These standards help identify how well a subject meets up or falls short of the ideal. No wonder this kind of essay is widely used for scientific purposes when the comparison of two inventions or technologies is required. In an evaluation essay, all the arguments are delivered objectively, while your personal opinion is stated at the very end as a summary.
On the Internet, you can find lots of reviews with one sentence only: “This essay is fine.” Does it look informative to you? Can you rely on this kind of feedback? Let’s be honest, such a review can hardly provide you with a clear understanding of whether the subject is worth your attention or not. The main feature of an evaluation essay is that it contains details and evidence to support your point of view. Instead of discussing every observation, you just need to underpin your point of view with examples that will make your paper look convincing.
CJE guidelines
How to start an evaluation essay? What needs to be preconsidered? Every evaluation essay consists of three structural elements – criteria, judgement, and evidence. Let’s get deeper into details.
Criteria
The criteria that you choose should evaluate a person or subject through the prism of their ideal version. What can their best features be? For instance, you would expect an interesting plot and professional acting from a movie. Once you have specific benchmarks in mind, they can be used to evaluate these points.
Judgement
The judgement aspect is used to estimate whether or not the benchmarks have been met. For instance, you can start a movie evaluation from judging whether it aligns with the specific benchmark. Does it offer the quality acting you expect? Does it have gaps in the plot? These are only some of the possible options to consider.
Evidence
Remember that you must develop clues to advocate your judgements. For instance, if you make the judgement that the movie quality does not meet your expectations, you should be ready to provide evidence. Without eligible evidence, your evaluation essay won’t look convincing.
When structuring your evaluation essay, it is crucial to address a different criterion in each paragraph. In that paragraph, you should reflect on each criterion, make the relevant judgements and provide supporting proofs.
How to Write an Evaluation Essay?
With this step-by-step guide, you will learn how to write an evaluation essay. Here are the major steps to be taken:
- Choose your topic. Whatever kind of essay you are writing, you will have to take this step. Your topic can be offered by your instructor, as the case may be. But if you have to choose it yourself, you should consider a subject that you are familiar with. Thus, it will be easier for you to take an in-depth look at the subject and make a judgement on its value.
- Create a thesis statement. This is an important element of your essay as it contains the general purpose of the evaluation. In the thesis, you need to reflect on the criteria being used to judge the subject matter and state its value. Your statement should look apparent and to the point. In the process of writing, you may revise it as your essay gets shaped.
- Identify the criteria to be used for accessing the subject matter. Determine the benchmarks in your essay in order to make it interesting and engaging. The criteria you choose will depend on the subject of your evaluation. For instance, a movie will be judged using different points of reference than a book.
- Find supporting evidence. Don’t forget that an essay is not just about your opinion. You will need to find some supporting information from trustworthy sources while making each judgement. Don’t think that stating the movie or book title is enough. Use some questions to find out answers that can help you collect more information. How can you evaluate the subject? What kind of readers are you focused on? Will you focus on good or bad sides of the subject?
- Write a draft of your essay. All you need to do is to continue writing. As soon as you have something written on paper, you will rewrite or restructure it unless you are totally happy with the result.
Review, revise and rewrite. When a draft is completed, you will read over your work and make some changes if needed. You should be ready to rewrite your paper several times to get it just right.
Evaluation Essay Example
Here, you will find a well-written evaluation essay example that you can use for yourself:
- https://academichelp.net/samples/academics/essays/evaluation/standardized-tests.html
- https://www.examples.com/education/evaluation-essay-examples.html
Evaluation Essay VS Review
An evaluation essay is widely associated with a review paper. This is a common mistake many students make. Although the two types of paper have some similarities, there are more differences that set them apart. You can take a look at those differences in the table below.
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Criteria
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Evaluation
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Review
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Analysis
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The topic is examined thoroughly.
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Evaluation of a product or service is provided.
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Depth of analysis
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You get engaged in in-depth analysis.
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You do not need to conduct profound scientific research.
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Evidence
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Adequate supporting evidence aims to increase the quality of the evaluation essay. You should provide only credible and scholarly evidence.
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You don’t need academic evidence throughout the appraisal process.
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Opinion
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You provide an unbiased view on the subject.
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You provide unbiased information by relying on personal consideration that analyzes the subject.
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Benchmarks
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You use predefined criteria that evaluate the subject matter.
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You express opinions that do not follow particular criteria.
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Scope
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You cover a broader scope by evaluating a particular topic and searching for adequate data that can critique the particular subject.
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You cover a narrower scope by providing views focused on the particular subject.
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Thesis statement
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You provide a central claim as the essay’s thesis .
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You do not need a thesis statement.
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Structure
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You follow the standard essay structure splitting the paper into sections.
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You do not have to follow any specific structure in review writing.
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References
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You include the works cited page.
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You do not have to include the works cited page.
Tips on Writing an Evaluation Essay from Our Experts
Following the quick tips below, you will find it easier to write an effective evaluation argument essay:
- Provide the right amount of details: Make sure you explain your thoughts clearly and provide sufficient information to convince the reader in the correctness of your judgment.
- Thesis sentence should reveal your actual opinion. If you want to build up the basis for your body, you can include the main reasons for your evaluation in the thesis sentence.
- Know your target audience. By knowing your reader, you can adjust the plot to their specific needs. Whether you write for college students or professors, you will have to apply a bit different approach in the language choice.
- Make some notes. By using a three-column note-taking method, you can organize your thoughts. The columns of criteria, evidence, and judgment will contain the relevant information which will not let you forget or mix facts.
- Be opinionated. By sounding passionate in your evaluation essay, you will increase your chances of catching readers’ attention. The use of vivid nouns and engaging verbs will strengthen the effect produced by your paper. You should have a strong judgment of how the particular subject is either better or worse than other subjects of the same type.
- Back up every judgement you make. Every time you make a judgment, you should be ready to use specific, interesting, and convincing reasons to make it up. For evidence, you can describe the subject, use funny stories, or compare and contrast some notions with a similar subject.
- Provide counter-arguments. When you disagree with what most people think about the particular subject, it makes sense to provide some counter-arguments. This will make the narration more engaging for readers.
List of 50 Evaluation Topics
Since there are many people and objects you are able to assess, an evaluation essay can be written on a wide range of topics. To evaluate something, you will need to compare it with an example within a subject you have chosen. Some possible evaluation essay topics can be found below:
- Analyze the dissimilarity between seeing a sporting event live and watching it on ITV.
- Create a comparative assessment of watching a sporting event in a cafe and watching it without leaving the comfort of your home.
- Evaluate the experience of watching a sporting event on your own and with other people.
- Evaluate how a recent drama movie portrays the tragedies of real life.
- Evaluate a classic criminal movie and what it states about the real crime rates in the modern society.
- Evaluate your favorite Chinese restaurant.
- Compare two popular Chinese restaurants in your city.
- Appraise football or basketball from the perspective of a contestant or that of a watcher.
- Analyze the way in which football or basketball has advanced over the last decade.
- Discuss the influence of ESPN on sporting events.
- Evaluate the coverage of the latest Eurovision Song Contest.
- Evaluate a fancy restaurant for how it makes the customer feel after having the meal
- Analyze the way in which a popular horror movie depicts people’s fears.
- Assess a classic action movie and talk about its ideas regarding the functions of men and women.
- Explore the change that occurred in recent war movies if compared to classic war movies.
- How do drama books affect readers?
- Evaluate a book about war and analyze whether it addresses current concerns associated with war and peace.
- Evaluate the effects of online educational programs on students’ performance.
- Do historical movies encourage history learning?
- Evaluate an Italian cafe located in your city. What is the difference between the Italian and local food?
- What makes a traditional Italian meal great?
- Can hamburgers be healthy? Mention some details and provide relevant arguments.
- How mental health issues affect students’ academic performance?
- Analyze teachers’ responsibilities in terms of elementary students’ needs.
- Evaluate the power of verbal encouragement as a motivational factor in the educational process.
- Critically reflect on education services provided to children experiencing difficulties in learning.
- Discuss the advantages and disadvantages of German secondary education.
- Evaluate teaching methods used at the American universities.
- Ways in which online libraries affect the students’ academic performance.
- How well the film “BraveHeart” portrays historical events?
- Analyze a movie produced in a foreign country and discuss how it reveals its national characteristics.
- Assess Kate Winslet’s play in “Titanic” and discuss which means this actor applies to adapt to this role.
- Make a comparison between modern and classic drama movies.
- Assess the distinct approaches used to transfer data from a smartphone to a PC.
- Make comparisons between various phone plans and determine which provider has the best deals for travelers.
- Assess current information security methods. Which one is the most efficient?
- Assess the key characteristics of WhatsApp.
- Compare the use of several cloud systems that can be implemented by the movie hub website.
- Estimate the chances of Facebook as a marketing resource.
- Evaluate the effectiveness of online advertising.
- Assess the existing approaches to using the Internet in colleges.
- Analyze the consequences of cultural shock.
- Assess the negative sides of overwhelming cultural diversity in the United States.
- Discuss the development path of rap and hip-hop music.
- What is the impact of Buddhism on Indian culture?
- Compare two popular social media platforms in terms of their users, features, and benefits.
- Evaluate the latest version of your favorite smartphone and estimate the positive or negative changes that will affect the industry.
- Compare an educational approach in the military, Christian, or classical school.
- Evaluate the SAT versus the ACT tests.
- Compare the foreign policies established by a few states in the US.
Note that our company provides academic writing help. You can buy an essay written from scratch by our essay writer.
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The History Lab aims to support and encourage student engagement with online primary and secondary sources.
The History Lab aims:
- To provide access & encourage the use of digital primary sources
- To develop advanced research skills that teach students to read and think about these sources in meaningful ways
- To teach students how to think like a historian i.e how to investigate historical questions by employing reading strategies such as sourcing, contextualizing, corroborating, and close reading using digital documentary evidence
- To encourage inquiry based learning
Over the past twenty-five years, millions of primary sources have been digitised by libraries and archives and made available online. (Malkmus, 2008) From an Irish context, in the lead up to the centenary of the 1916 Rising, there has been a major drive to survey and digitise relevant archival material. These digitisation projects share a common ideal to make Ireland’s heritage widely available to everyone and to enrich the historical narrative. The Decade of Centenaries has contributed archival developments such as the digitisation of the Bureau of Military History Military Service Pensions Collection, and the 1901 and 1911 censuses. Other projects such as the Google virtual tour “Dublin Rising 1916-2016 Virtual Tour” a unique digital primary source project demonstrate scale and scope of online primary sources available to history learners.
History is the study and interpretation of the past, and engaging with primary sources is central to the development of authentic critical historical thinking. (Wineburg, 1999) Since the 1970s, millions of primary sources have been digitised by libraries and archives which has created a wealth of rich content for historians and history students. However the sheer scale of sources material, websites and questions about source quality make it a challenging research environment for history students. (Tally & Goldenberg, 2005)
Our solution to this was to create “The History Lab” Digital Research Skills resource to support and scaffold the learners’ engagement with digital primary sources. | https://www.historians.ie/the-history-lab-new-resource-for-students-seeking-to-use-online-resources/ |
This invention relates to a pneumatic tire, and more particularly to an improvement of a bead portion structure in such a pneumatic tire which facilitates the increase and tuning of rigidity required in the bead portion and hence the tire itself and simultaneously establishes the steering stability and the ride comfort at a high level.
Heretofore, it has widely been conducted to embed an additional reinforcing member such as a wire insert, flipper or the like in the bead portion for the increase and tuning of the rigidity in the bead portion of the pneumatic tire.
However, when the rigidity of the bead portion is increased by such an additional reinforcing member, for example a wire insert wherein the wire extends obliquely in a constant direction crossing with a circumferential line segment viewing at a side face of the tire, the longitudinal rigidity of the bead portion in the tire is increased in addition to the rigidity in front and back directions, so that the steering stability is improved but the ride comfort is largely degraded.
Attention is also drawn to the disclosures of US-A-5660656 and FR-A-2055988.
It is, therefore, an object of the invention to solve the aforementioned problems of the conventional technique and to provide a pneumatic tire capable of simultaneously establishing the steering stability and ride comfort at a higher level by adequately selecting a winding form of a bead wire, which develops to fix an end portion of a carcass ply and adhere the bead portion of the tire to a rim sheet or the like, and to simply and easily increase or decrease the rigidity required in the bead portion as being expected without using the additional reinforcing member such as wire insert, flipper or the like.
According to the present invention, there is provided a pneumatic tire having a bead portion structure such that at least two bead wire structural bodies, each being obtained by spirally winding one or more bead wires so as to continuously extend in a circumferential direction, are disposed in a bead portion so as to sandwich a carcass ply or enclose with the carcass ply, in which an outer end of at least one of the bead wire structural bodies in the radial direction is located at a position corresponding to a rim line or outward therefrom, characterized in that a lateral rigidity of the tire is made larger in the bead wire structural body located at the inside in the widthwise direction of the tire than that in the bead wire structural body located at the outside in the widthwise direction.
According to such a bead portion structure in the tire, the bead wire is spirally wound up to the position corresponding to the rim line or outward therefrom in the radial direction of the tire, whereby the rigidity of the bead portion and hence the tire in front and back directions can be increased to advantageously improve the steering stability.
Furthermore, the spirally wound bead wire continuously extends in the circumferential direction and has no component extending in a direction crossing with a circumferential line segment as in the aforementioned wire insert, so that the increase of longitudinal rigidity can effectively be prevented with the increase of the rigidity in the front and back directions of the tire to ensure an excellent ride comfort.
In a preferable embodiment of the invention, the outer end of at least one of the bead wire structural bodies is positioned between the position corresponding to the rim line and the position of the maximum tire width.
According to this embodiment, the rigidity required in the tire or rigidity in the front and back directions is sufficiently increased and also the increase of the longitudinal rigidity can advantageously be controlled. In other words, if the outer end of the bead wire structural body in the radial direction is located over the maximum tire width position, the rigidity of a sidewall portion is increased and hence the longitudinal rigidity of the tire is also increased to degrade the ride comfort.
According to the invention, the rigidity in the lateral direction of the tire is changed between the mutual bead wire structural bodies located at inside and outside in the widthwise direction of the tire. Thus, the rigidity of the tire in the front and back directions can easily and properly be tuned in accordance with the required performances without excessively reinforcing the bead portion, whereby the reductions of tire weight and cost can be realized.
For instance, when the rigidity to lateral input directing inward in the widthwise direction is made high and the rigidity to lateral input directing outward in the widthwise direction is made low to make stress created in the deformation of the bead portion outward in the widthwise direction of the tire small and inversely make stress created in the deformation inward in the widthwise direction large, longitudinal spring constant in the riding over projections or the like so as to deform both bead portions outward in the widthwise direction can be controlled to a small value to ensure excellent ride comfort.
On the other hand, during cornering or the like so as to deform one of the bead portion inward and the other bead portion outward in the widthwise direction, excellent steering stability can be ensured by the high rigidity of the bead portion to the inward deformation.
On the contrary, when the rigidity to lateral input directing inward in the widthwise direction is made low and the rigidity to lateral input directing outward in the widthwise direction is made high, the lateral rigidity of the tire can advantageously be controlled to more improve the steering stability. In this case, the longitudinal rigidity of the tire is also increased in the riding over projections or the like to deny the degradation of the ride comfort, so that the adoption of this structure allows improvement of the steering stability.
In order to simply provide the required rigidity difference, it is preferable that the change in the rigidity of the bead wire structural body in the lateral direction of the tire is caused by at least one means applied to each bead portion between the mutual bead wire structural bodies located at the inside and outside in the widthwise direction of the tire, which is selected from means for changing a diameter of the bead wire, means for changing an end count of bead wire in the bead wire structural body, means for changing the outer end position of the bead wire structural body in the radial direction and means for changing the construction of the bead wire, for example using a combination of single wire and cable of twisted wires.
In another preferable embodiment of the invention, the rigidity of each bead wire structural body in the longitudinal direction of the tire is changed in the radial direction. More particularly, the rigidity is made smaller in the outer portion of the bead wire structural body in the radial direction.
According to this embodiment, the rigidity of each of two or more bead wire structural bodies is changed together in the radial direction of the tire, whereby the balance between the rigidity in the front and back directions and the longitudinal rigidity in the tire can be controlled at a higher level and hence high steering stability can be ensured while realizing excellent ride comfort under the more effective control of the longitudinal rigidity.
Also, sudden change of the rigidity in each direction ranging from the bead portion to the sidewall portion can advantageously be mitigated.
It is preferable that such a rigidity change is caused by at least one means selected from means for changing a bead wire diameter in the bead wire structural body in the radial direction, means for changing an arranging pitch of the bead wire and means for changing the construction of the bead wire.
Figs. 1 to 9 are diagrammatic section views of various embodiments in the main part of pneumatic tires, wherein Figs. 3 to 6 in particular illustrate tires according to the invention, respectively.
The invention will be further described with reference to the accompanying drawings, wherein:
In Fig. 1 is sectionally shown a first embodiment of a main part in a pneumatic tire, wherein numeral 1 is a bead portion, numeral 2 a carcass ply as a reinforcing member for the tire casing, and numeral 3 a rim line formed on an outer side surface of the bead portion 1.
In the bead portion 1 of the tire, a bead wire structural body 5 is formed by spirally winding one or more bead wires 4, which continuously extend in a circumferential direction, for example, from an inside toward an outside in a radial direction. Also, such two bead wire structural bodies 5 are disposed in the bead portion 1 and are adjacent to each other at the inside and outside in the widthwise direction of the tire. In this case, as shown in Fig. 1, an end portion of the carcass ply 2 is sandwiched between the two bead wire structural bodies 5, or as shown in Fig. 2, these bead wire structural bodies 5 are sandwiched between a main body 2a and a turnup portion 2b of the carcass ply 2.
An outer end of at least one of the bead wire structural bodies 5 in the radial direction, both outer ends of these bead wire structural bodies 5 in the illustrated embodiment, are located in a position corresponding to the rim line 3 or outward therefrom. More preferably, the outer end is located between the position corresponding to the rim line 3 and a position of a maximum tire width.
Moreover, the position in the radial direction of the outer end of the bead wire structural body 5, rim line 3 or the like means a position in the radial direction at a use state of the tire or at a state that the tire assembled onto a rim is inflated under a given air pressure.
According to such a bead portion structure, each of these bead wire structural bodies 5 can sufficiently develop functions inherent thereto such as fixation of the end portion of the carcass ply, adhesion of the bead portion to the rim sheet and the like. In addition, the rigidity of the bead portion and hence the tire in front and back directions can be increased by winding the spirally extended bead wire 4 upward from the position corresponding to the rim line in the radial direction, if necessary, without requiring additional reinforcing members such as wire insert, flipper and the like to effectively improve the steering stability.
On the other hand, the bead wire 4 continuously extending in the circumferential direction of the tire hardly restrains the inward deformation of the tread portion in the radial direction and hence the inward deformation of the bead portion 1 and the sidewall portion in the widthwise direction of the tire, so that the longitudinal rigidity of the tire is maintained at a sufficiently small level to ensure excellent ride comfort.
Figs. 3 to 6 are partial section views of various embodiments of the pneumatic tire according to the invention, respectively, which correspond to various modified embodiments of Fig. 1. In these cases, the rigidity in the lateral direction of the tire is changed between the bead wire structural bodies 5 located at the inside and outside in the widthwise direction of the tire sandwiching the end portion of the carcass ply 2 therebetween.
In order to make the bending rigidity of the bead portion 1 inward in the widthwise direction of the tire and hence the lateral rigidity larger than the bending rigidity outward in the widthwise direction as shown by an arrow A in Fig. 3, the diameter of the bead wire in the inner bead wire structural body 5 is made larger than that in the outer bead wire structural body 5 in Fig. 3, and the end count of bead wire in the inner bead wire structural body is made larger than that in the outer bead wire structural body in Fig. 4, and the position of the outer end of the inner bead wire structural body 5 in the radial direction is located outward from the position of the outer end of the outer bead wire structural body in Fig. 5, and the bead wire constituting the inner bead wire structural body is a single wire and the bead wire constituting the outer bead wire structural body is a cable of twisted wires in Fig. 6.
When the rigidity of each of the bead wire structural bodies 5 in the lateral direction of the tire is changed as mentioned above, the steering stability can advantageously be improved while ensuring excellent ride comfort in riding over projections as previously mentioned without requiring an additional reinforcing member and hence increasing the tire weight, tire cost and the like accompanied therewith.
Moreover, when the relative construction of the bead wire structural bodies 5 located at the inside and outside in the widthwise direction is made opposite to the above case, the rigidity in the front and back directions of the tire can be more effectively increased with somewhat sacrificing the longitudinal rigidity of the tire.
Figs. 7 to 9 are partial section views of other embodiments of pneumatic tires, respectively, which also correspond to various modified embodiments of Fig. 1. In these cases, the outer end of at least one bead wire structural body in the radial direction, both outer ends of the two bead wire structural bodies 5 in these embodiments are located at a position corresponding to the rim line 3 or outward therefrom, while the rigidity of each of the bead wire structural bodies 5 in the longitudinal direction of the tire is changed in the radial direction so that the rigidity in an outer portion in the radial direction is made smaller than that in an inner portion.
This is realized by making the diameter of the bead wire in each bead wire structural body 5 smaller in an outer portion in the radial direction than that in an inner portion in Fig. 7, or by making an arranging pitch of the bead wire 4 larger in an outer portion of the bead wire structural body in the radial direction than in an inner portion thereof in Fig. 8, or by using a single wire 4a in an inner portion of the bead wire structural body in the radial direction and a cable 4b of twisted wires in an outer portion thereof in Fig. 9.
According to such a bead portion structure, the rigidity in the front and back directions of the tire can be enhanced based on the selection of the position of the outer end of each bead wire structural body in the radial direction and the like to advantageously improve the steering stability. Furthermore, further improved ride comfort can be achieved by reducing the longitudinal rigidity of the bead wire structural body, and also any sudden change of the rigidity from the bead portion to the sidewall portion can be mitigated.
As mentioned above, according to the invention, the rigidity in the front and back directions of the tire is increased without using an additional reinforcing member, whereby the tire weight and the cost can be reduced to provide a higher steering stability, while increase of the longitudinal rigidity of the tire can effectively be controlled to ensure excellent ride comfort. |
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