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Karnataka Chief Minister Siddaramaiah used his debit card for the first Time !!!
Karnataka CM Siddaramaiah and Law Minister TB Jayachandra would remove only on May 1st
Mysuru, Feb 13: Chief minister Siddaramaiah on Sunday used his debit card to withdraw cash for the first time.
He withdrew Rs 10,000 from the Hebbal branch of the Mysuru Merchants’ Cooperative Bank ATM after inaugurating it.
Bank president M N Sumana reminded the CM that he has cash deposit of Rs 60,000 as dividend. The CM decided to use a debit card issued to him on the spot and withdrew Rs 10,000. | |
The problem was to determine the extent to which a selected group of professional nurses employed on a part-time basis were satisfied with certain selected factors relative to their employment. It was the purpose of this study to (l) gather data from selected nurses employed on a part-time basis to determine the degree of satisfaction felt by each regarding certain predetermined factors which are representative of the integral parts of their particular employment; (2) analyze the data to determine which of the factors seemed to contribute most to the job satisfaction of the professional nurse employed on a part-time basis; and (3) present data which are of interest to, and can be utilized by, a director of nursing service to aid in planning for, and staffing with, professional nurses employed on a part-time basis. The sample surveyed included 138 nurses employed on a part-time basis in six hospitals of a large metropolitan area of the Rocky Mountain region. The normative survey method of research and the mail questionnaire technique were used to obtain the data. The contents of the questionnaire included opinion-seeking questions concerning factors thought to contribute to job satisfaction of the professional nurse employed on a part-time basis, which might be relative to her particular situation. From the analysis of the data it may be assumed that the factors were contributory to job satisfaction. It was also considered that the areas of greatest satisfaction were those of job content, and the areas of least satisfaction were those of secondary elements which did not involve professional training, skills, or abilities. It was thus found that the professional nurses employed on a part-time basis were satisfied with those factors of their job involving total competency and were least satisfied with the factors that were matters of hospital policy, administration, and working conditions.
Smith, Marion Leigh, "A Study of the Extent of Job Satisfaction of a Group of Professional Nurses with Certain Factors Relative to Their Employment" (1963). University Libraries Digitized Theses 189x-20xx. 113. | https://scholar.colorado.edu/print_theses/113/ |
Field of the invention
The present invention relates to a system for determining positions of a plurality of labels, each label comprising a processor and a transmitting and receiving device which is connected with the processor. Furthermore, the invention relates to a label.
Such systems are used for, among other purposes, the position determination, also: positioning, of objects in a space. In particular, such systems are used, for example, within livestock farming for the positioning of animals in a barn. Multiple beacons hung up at suitable points in the barn receive the signals from one or more labels, and by means of triangulation of transmitted signals the position of each label is determinable. Use is then made of, for example, radio frequency identification (RFID). Triangulation can either take place in the label when the labels include, for example, a processor and memory, or can take place centrally in the system, for example by triangulation of return signals received by the beacons from passive labels. The labels (also called 'tags') are worn by animals, so that with the aid of this system it is known where each animal is.
While the application of such systems within livestock farming brings many advantages with it as regards, for example, automation of the farm processes, the use of the beacons is not ideal. The position of the beacons should be accurately chosen to ensure that the beacon signal can be properly received throughout the space. Due to the beacons needing to hang sufficiently high, installation costs are high, for instance because use has to be made of tower wagons and long cables. Also, the transmitted power needs to be sufficiently high, in consequence of which the supply power is also high and the system hence consumes a relatively great deal of power and is little energy-efficient. For triangulation, at least three beacons are needed, but for obtaining accuracy and/or for complete coverage (by at least three beacons) in a large space, easily a greater number of beacons will be necessary. Also, the beacons themselves are relatively expensive, so that implementing such a system on an average-size stock farm requires a high investment.
It is an object of the present invention to obviate the disadvantages of the prior art and to provide a system for determining positions of a plurality of labels that is relatively simple to implement, is energy-efficient, and also provides sufficient accuracy.
To this end, the invention provides, according to a first aspect thereof, a system for determining positions of a plurality of labels, each label comprising a processor and a transmitting and receiving device which is connected with the processor, characterized in that each label is configured for transmitting with the transmitting and receiving device an electromagnetic first type beacon signal, and that each label is configured for receiving with the transmitting and receiving device an electromagnetic first type beacon signal which has been transmitted by another label, each label is configured to determine with the aid of the processor of the label first type positioning data, and that each label is configured to transmit with the transmitting and receiving device information about the first type positioning data determined by the processor of that label, wherein the system further comprises at least a receiver for receiving the information about the first type positioning data transmitted by the labels and a computer which is communicatively connected with the receiver, wherein at least one of the labels or the computer is configured to identify on the basis of the received first type beacon signal the label from which the received first type beacon signal originates, and wherein the computer is configured to calculate at least on the basis of information about the first type positioning data received with the receiver the relative positions of the labels relative to each other and to export information about the relative positions of the labels, in particular in the form of an electrical information signal.
The present invention makes use of the labels present in the system. The labels are each suitable for generating a beacon signal, each label being identifiable on the basis of the transmitted beacon signal. The beacon signal is to be received by other labels that are in sufficiently close proximity to the respective label. These receiving labels, on the basis of the received beacon signal, generate positioning data and forward this data to a receiver of the system. The receiver receives the transmitted positioning data from all labels, and sends this data to a computer which, on the basis of all received positioning data, determines per label what the exact position of that label is. In the system, each label is configured for generating an identifiable beacon signal and also to receive beacon signals from other labels, to generate positioning data therefrom, and to forward the data to the receiver. Thus the computer can determine the mutual positions of all labels from this received data. For this, it is not necessary to equip the system with powerful beacons as in the systems according to the state of the art.
The identifiability of the labels on the basis of the transmitted first type beacon signals can take place in different ways. As will be further explained in the present disclosure, identification can take place in a preferred embodiment by having each of the labels transmit the first type beacon signal in its own timeslot within a transmission period. During that timeslot, the other labels receive only the transmitted beacon signal and do not themselves transmit anything. The transmitting label is then identifiable on the basis of the assigned timeslot. Of course, in an alternative embodiment, also an identification code may be sent along with the beacon signal. This makes the labels a bit more advanced because in this last embodiment the label has to be suitably designed for this purpose (the labels must store the unique code and be able to incorporate it in the signal and send it along with the signal). Identification via an assigned timeslot may be implemented in different manners, which will be further elucidated hereinafter.
In the system according to the invention, the labels are able, by means of mutual exchange of the signals, to jointly determine the mutual relative positions of all labels. For this, as explained, no fixed beacons are needed. However, to be able to determine not only the relative positions but also the absolute positions of all labels, it is necessary to have knowledge of the absolute positions of at least two of the labels. For this, use can be made of fixed beacons, but this may also be implemented in a different way. When the absolute position data of at least two labels are made known in the system in a different way, the use of fixed beacons for obtaining absolute position data is superfluous. In that case, in effect, the function of the beacons is fulfilled by the at least two labels whose absolute position data are already known. These absolute position data of the at least two labels can be obtained in different manners.
According to an embodiment, the at least two of the labels are, for instance, in a known position, this absolute position then being stored in the system. It is possible, for example, to place two or more labels at a position known in the system, and to make it knowable to the system where each of the at least two labels is. For example, the system may comprise two or more charging points whose absolute positions are known in the system. When a label is placed in one of the charging points, it is directly known that the respective label is in this absolute position. When, accordingly, two or more labels have been placed in respective charging points in this way, for each of these labels the absolute position is known in the system. By combining the data of these known absolute positions of the respective labels with the data of the mutual relative positions as determined in the system, the absolute position of all labels is known in the system.
The above example of a charging point is just an embodiment. Because the labels have their own accumulator or battery, an embodiment as described here is simple to implement. Indeed, the connecting of a label to a charger can be simply automatically reported back to the system, so that the system is directly informed of the absolute current position of this label. In another embodiment, of course, the absolute position of some labels may also be determined in a different way. It is possible, for example, to detect a label with the aid of camera pictures. Also, a user can report the absolute location of a label to the system, for example from a mobile phone, a tablet, a laptop or any other mobile operating unit, or from the label itself. Labels can also establish their own absolute position, for example through detecting an identification signal that can be received exclusively from a particular location. Also, in some embodiments, the absolute position of some labels may for instance be determined when an animal wearing the label is at a known position, for example, when a cow is being milked by a milking robot the label is also close to the milking robot. As described, there are different manners in which establishing of the absolute positions of the at least two labels can be implemented.
The use of labels in the system to fulfill the function of fixed beacons, for providing absolute position data as a reference for determining the absolute positions of all labels, will be further discussed further on in this disclosure.
The mutual relative position of each transmitting label can be determined in the system from the positioning data as generated by three or more receiving labels. It provides advantages, however, to do positioning on the basis of a larger number of receiving labels, and the system according to the present invention makes this simply possible in that all labels present in the system determine their positions mutually. The more labels there are within the transmission range of the transmitting label, the more accurately the positioning of the transmitting label can take place, since the measuring statistics are augmented in this manner. Certainly when there are a great number of labels about within the system, positioning can be carried out with very high accuracy. This accuracy can be used, if so desired, to ease the requirements regarding, for example, the signal strength of the transmitting labels, or to be able to compensate for signal reflection and interference resulting from any obstacles present.
In exceptional situations, for that matter, fewer than three receiving labels may suffice for obtaining a rough estimate of the position of a transmitting label. Positioning is still possible, in principle, on the basis of the positioning data of two receiving labels; in that case, however, it can only be done by compensating for the lacking positioning data by supplementing the data with other data or by making an assumption. One of the assumptions that can be made is that the positions of animals are within a specific height from the floor: the animals may be standing, lying or sitting, and are not all equally tall, so there is a certain range in height from the floor within which all labels must be present. Another assumption may be that the animals must in any case be inside the barn. On the ground of such assumptions the position of each label can be determined on the basis of positioning data of two receiving labels, albeit with some (acceptable) uncertainty. Below, in principle, the assumed starting point will be positioning data of at least three receiving labels for triangulating; however, the invention can also be applied by making use of the positioning data of two receiving labels, supplemented with other data or with assumptions. The invention is therefore not limited to triangulation based on the positioning data of at least three receiving labels.
The sending of the positioning data to the receiver can take place in different manners. In a first embodiment, each label can generate a sufficiently strong transmitted signal that is received by the receiver. Also, it is possible, according to another embodiment, that the transmitted signal with positioning data of each label is forwarded via the other labels until it can reach a receiver (similarly to the forwarding of data in a relay network). In the first embodiment, preferably, the transmitted power of each label is sufficiently great to reach the receiver. In the second embodiment, the transmitted power can remain smaller, but the data rate for transmitting and receiving data of each of the labels should be sufficiently high to be able to receive the signals from all labels and retransmit them. An advantage of the first embodiment is that the transmitting system can be relatively simply operative. An advantage of the second embodiment is that the coverage of the network is better and the chance that all signals reach the receiver is much greater. A label can only be outside the range of the receiver when an animal separates itself from the group sufficiently far.
According to embodiments, the positioning data as determinable by each label with the aid of the processor comprises one or more data from a group comprising: information about the signal strength of a first type beacon signal received with that label, possibly in combination with information about the signal strength with which the first type beacon signal was transmitted and/or information about the time at which the first type beacon signal was received, possibly in combination with the time at which the first type beacon signal was transmitted. This data can be advantageously used for establishing the exact position of a label, if combined with such data received from other labels.
According to some embodiments, the system is configured such that, in use, each first type beacon signal is transmitted with a predetermined signal strength known within the system, while the first type positioning data determined with the processor comprises information about the strength with which the first type beacon signal was received; and/or that each first type beacon signal comprises information about what signal strength the first type beacon signal was transmitted with, while the first type positioning data determined with the processor comprises this information together with information about the signal strength with which the respective first type beacon signal was received. These embodiments make it possible to determine the position of the labels on the basis of signal attenuation of the received beacon signals. Because the beacon signal is transmitted from the source - the transmitting label - omnidirectionally, the transmitted power decreases as the square of the distance from the source. When the initial strength of the signal is known, the signal attenuation can be calculated on the basis of the reception strength, and hence also the distance to the source - the transmitting label - can be determined. By combining the positioning data as determined by three (or more) receiving labels, the distance of the transmitting label to each of the receiving labels is known, and the position of the transmitting label can be determined.
According to some embodiments, the system is configured such that, in use, each first type beacon signal is transmitted at a predetermined time known within the system, while the first type positioning data determined with the processor comprises information about the time at which the first type beacon signal was received and/or that each first type beacon signal comprises information about the time at which the first type beacon signal was transmitted, while the first type positioning data determined with the processor comprises this information together with information about the time at which the respective first type beacon signal was received. These embodiments make it possible to determine the position of the labels on the basis of time of flight of the received beacon signals. When the exact time of transmission of the signal is known, it can be determined from the exact reception time of different receiving labels what the distance of each of those labels to the transmitting label is. In some embodiments, the time-of-flight data as described above can be combined with the signal strength data as described in preceding embodiments, for augmenting the accuracy of positioning.
In some of the above-mentioned embodiments, each label is provided with a clock to determine when a label transmits the first type beacon signal. This data can then be sent along with the beacon signal to be processed by the receiving labels or, in an alternative embodiment, be sent to the receiver directly so that the computer can process this data.
According to some embodiments, the system further comprises a plurality of fixedly disposed beacons, while each beacon is configured to transmit a second type beacon signal, each label is configured to receive the second type beacon signal with the aid of the transmitting and receiving device of the label, and the system is configured to determine for at least two of the labels, at least on the basis of the second type beacon signals received by the at least two labels, a position of the at least two labels relative to the beacons. The second type beacon signals may also be identifiable, for example, based on time of transmission, based on a particular transmission characteristic, or through incorporation of an identification code of the beacon.
While in the above embodiments the mutual distances between the labels and hence their relative positions with respect to each other can be properly determined, information regarding the position of at least two labels is necessary to be able to determine the positions of the other labels in an absolute sense as well. To this end, the system according to these embodiments may yet make use of a few fixed beacons whose absolute position is fixed and is known in the system. However, the fixed beacons do not need to comply with the stringent requirements that beacons in conventional systems have to comply with. In principle, a beacon provided with a transmitter as is also present in the labels suffices. As has already been discussed above, therefore, in some embodiments the beacons can be formed by labels whose position is known in the system.
These labels whose absolute positions are known can in the same way receive and process the transmitted signals from the other labels, to be able to establish the positions of all other labels. That is why the computer, according to some embodiments, is configured for, on the basis of the calculated relative positions of the labels relative to each other and the determined position of the at least two labels relative to the beacons, determining the relative positions of the labels relative to the beacons, while the information about the relative positions of the labels exported by the computer comprises the relative positions of the labels relative to the beacons.
According to some of the above embodiments, each label is configured to determine with the processor, on the basis of second type beacon signals received with the transmitting and receiving device of the respective label, its position relative to the beacons, and to transmit information about the determined position with the transmitting and receiving device to the receiver, while the computer is configured to process received information about the position of at least two labels relative to the beacons in combination with the received information about the first type positioning data of the labels, for determining the positions of the labels relative to the beacons.
Furthermore, according to some specific embodiments, each label is configured to determine with the processor, on the basis of second type beacon signals received with the transmitting and receiving device of the respective label, second type positioning data such as the strengths of the received second type beacon signals, possibly in combination with information about the signal strengths with which the second type beacon signals were transmitted and/or information about the time at which a received second type beacon signal was received, possibly in combination with information about the times at which the second type beacon signals were transmitted, and then transmit this with the transmitting and receiving device to the receiver, while the computer is configured to process this received information in combination with at least the received information about the first type positioning data and/or the determined relative positions of the labels, for determining the positions of the labels relative to the beacons.
This embodiment may be combined with other embodiments for obtaining additional accuracy. For example, in specific ones of the above embodiments, the system is configured such that, in use, each second type beacon signal is transmitted with a predetermined signal strength known within the system, while the second type positioning data determined with the processor comprises information about the strength with which the second type beacon signal was received; and/or that each second type beacon signal comprises information about what signal strength the second type beacon signal was transmitted with, while the second type positioning data determined with the processor comprises this information together with information about the signal strength with which the second type beacon signal was received.
In accordance with yet another example, in some specific ones of the above embodiments, the system is configured such that, in use, each second type beacon signal is transmitted at a predetermined time known within the system, while the second type positioning data determined with the processor comprises information about the time at which the second type beacon signal was received and/or that each second type beacon signal comprises information about the time at which the second type beacon signal was transmitted, while the second type positioning data determined with the processor comprises this information together with information about the time at which the second beacon signal was received.
According to further embodiments, the first type beacon signals and the second type beacon signals are identical, while one or more beacons are formed by fixedly disposed labels. When the first and second type beacon signals are identical, beacons in the system can always be formed by or replaced with a label. This makes the system technically simpler and, moreover, easier to implement.
In accordance with embodiments already described hereinabove, in use of the system, a plurality of the labels are fixedly disposed and thus function as beacons, with the absolute positions of each label of the plurality of fixedly disposed labels being known within the system, while the system is configured to determine for at least two of the labels, on the basis of the first type beacon signals of the fixedly disposed labels received by the at least two labels, a position of each of the at least two labels relative to the fixedly disposed labels.
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In accordance with an embodiment, the system is configured such that the labels respectively, successively, one after another transmit the first type beacon signal. The labels may for instance be numbered or be assigned a serial number, with the labels in sequential order transmitting their beacon signals while the other labels listen. If each label can receive the signals from the other labels, in this way in a system of 100 labels, per positioning round 100 100 = 10,000 measuring points can be obtained and as many as 1,000,000 given a farm of 1,000 cows. The accuracy of positioning is thus obtained in particular from the statistic of measuring points: a great number of measuring points enable a very accurate determination of the position of each label.
According to some embodiments, the system is configured such that the labels respectively, one after another, transmit the first type beacon signal during one or more transmission periods. For example, in accordance with some implementations of the system, each label is provided with an electronic clock, with the clocks of the labels mutually synchronized and with the transmission period divided into timeslots, while each of the labels has been assigned a unique timeslot within the, or each, transmission period for transmitting the first type beacon signal. Each label is then identifiable in the system, for example on the basis of the timeslot in which the label sent the first type beacon signal. According to a specific embodiment, each label is for instance provided with an electronic clock, with the clocks of the labels mutually synchronized and with the labels, on the basis of signals generated by the clocks, transmitting respectively, one after another, the first type beacon signal. The labels, in this way, are independently able to determine the proper timeslot within which the first type beacon signal is to be transmitted.
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Synchronization can take place in various manners. For example, in some systems, the labels can be synchronized once at initialization of a system, or periodically, for example at charging of a label in a charging station. Synchronization can take place, for example, every second or every 10 or 100 milliseconds. In accordance with some embodiments, however, the system is configured for transmitting a synchronization signal, while each label is configured for receiving the synchronization signal and for synchronizing the electronic clock of the label on the basis of the synchronization signal. The synchronization signal may be transmitted with a dedicated transmitter, but it is also possible for one or more of the labels to be configured for generating the synchronization signal. For example, a label may be configured to generate a synchronization signal upon instruction from the system, or, for example, upon request of a neighboring label which has been synchronized less recently. Also, in an embodiment in which one or more labels are used as fixed beacons, these labels may be configured to generate a synchronization signal. Mutual synchronization of the labels may also be effected via the labels themselves, without central control. This may be done, for example, through exchange of synchronization signals between the labels. When, for example, a label at time t sends a synchronization signal which is received by another label at time t (the clocks of the labels having an unknown mutual time deviation relative to each other), and in reply the other label returns a synchronization signal at time t which is received at time t by the one label, it can be determined from the registered times t, t, t and t what the mutual time deviation between the clocks of the labels is (this time deviation in an absolute sense equals (t - t + t - t)/2). When all labels perform a synchronization procedure in this way, the clocks of the labels can be accurately synchronized relative to each other.
Accurate synchronization is of interest to keep the transmission duration of the labels as short as possible and consequently reduce energy consumption. This is not only energy-saving but also prolongs the useful life of the labels that is feasible between two charging moments of the internal battery. This last is of interest to prevent the labels on the animals needing to be replaced unduly often.
According to an embodiment, the system is configured such that, in use, a label only transmits an update of first type positioning data. In that case, no positioning data are transmitted when there has been no change or insufficient change in the positions of other labels. The amount of data can be strongly reduced in this way, without loss of accuracy.
According to some embodiments of the system, the transmitting and receiving device of each label is configured for transmitting and receiving electromagnetic signals with a frequency of between 300 MHz and 3,000 MHz, preferably between 300 MHz and 1,000 MHz, for example with a frequency of 434 MHz, 868 MHz or 922 MHz. Such labels are already widely available and can be made suitable to be operative within a system according to the invention. The system according to the invention is able, despite the inherent erratic nature of the signals in this band, yet to make an accurate position determination based on the transmitted first type beacon signals. This is because the number of labels together provide a measuring statistic that is sufficiently large to compensate for inaccuracies in the signal.
According to some embodiments of the system, the transmitting and receiving device of each label is configured for transmitting and receiving electromagnetic signals with a frequency of less than 500 kHz, for example with a frequency of 400 kHz. At these frequencies, the transmitted signals are hardly if at all hindered by reflections and/or unpredictable damping. Positioning based on this signal can therefore be done relatively accurately, even with a limited measuring statistic. While a disadvantage of these frequencies is the limited transmission range, this is made up for by accurate positioning being possible with a relatively small number of receiving labels. Due to the labels being able to mutually relay the obtained position information until a beacon is reached, the system can yet collect all position information of all labels.
In a specific embodiment, each label is configured for, during at least a part of a duration of the transmission of the electromagnetic first type beacon signal, sending the electromagnetic first type beacon signal such that it comprises merely a carrier wave. By, for instance, sequentially for each of the labels, temporarily leaving out any data in the signal and merely sending a carrier wave as first type beacon signal, it is yet known in the system what label transmits the first type beacon signal, since the transmitting label is the label that is associated with the timeslot. An advantage is further that the signal now merely comprises the carrier wave and, as described earlier, is hardly if at all hindered by reflections and/or unpredictable damping. Positioning is therefore accurately possible, even with a smaller number of labels (for example, three or more labels).
Furthermore, the above-described system may be designed on the basis of ultra-wideband (UWB). While UWB-based systems have a smaller transmission range, this suffices for the system described here. Ultra-wide band is for instance used for interim transfer of information which, in use, is stored in the labels (for example, activity data or health status data of the animal) to a livestock management system by making use of UWB readers. The reader yields not only the actual data, but also a signal strength with which the data was received. The measured UHF signal strengths can thus be used within a system according to the present invention when the labels can receive the UWB signal from other labels and can determine the signal strength therefrom.
Further, as already mentioned before, according to some embodiments, each label may be configured for sending along with the first type beacon signal an identification code for identifying the respective label. In that case, identification takes place directly by reading a received first type beacon signal.
According to a second aspect, the invention provides a label for use in a system as described above. In accordance with some embodiments, the invention provides a label comprising a processor and a transmitting and receiving device which is connected with the processor, characterized in that the label is configured for transmitting with the transmitting and receiving device an electromagnetic first type beacon signal, each label is configured for receiving with the transmitting and receiving device an electromagnetic first type beacon signal which has been transmitted by another label, each label is configured for, with the aid of the processor of the label, determining first type positioning data such as information about the signal strength of a first type beacon signal received with that label, possibly in combination with information about the signal strength with which the first type beacon signal was transmitted and/or information about the time at which the first type beacon signal was received, possibly in combination with the time at which the first type beacon signal was transmitted, and that each label is configured to transmit with the transmitting and receiving device information about the first type positioning data determined by the processor of that label.
Brief description of the figures
Figure 1
is a schematic representation of a system according to an embodiment of the present invention;
Figure 2
is a schematic representation of a system according to a further embodiment of the present invention;
Figures 3a and 3b
represent two timeslots within a positioning round carried out with a system according to an embodiment of the present invention;
Figure 4
shows a data matrix of signal strengths of transmitted and received signals, as stored in a memory of a system according to an embodiment of the invention.
The invention will be discussed below on the basis of specific embodiments thereof not intended as limiting, with reference to the appended figures, in which:
Detailed description
Figure 1
Figure 1
Figure 1
shows a system 1 according to an embodiment of the present invention. In the system 1 is represented with three receivers 3, 4 and 5 which also function as fixed beacons for system 1. The receivers/beacons 3, 4 and 5 are at different places in a space. Furthermore, the system comprises five labels 8-1, 8-2, 8-3, 8-4 and 8-5. The receivers/beacons 3, 4 and 5 are communicatively connected through a wired network to a computer 15 provided with memory 16. In lieu of a wired network, the connections between the receivers/beacons 3-5 and the computer 15 may also be formed by means of wireless connections via, for example, a Wi-Fi network. The receivers 3, 4 and 5 are configured for receiving signals which have been transmitted by the labels 8-1 through 8-5. In system 1 is drawn with just five labels, but this has been done merely to be able to represent the working principle. In reality, the system 1 can include any desired number of labels, ranging from one label to 1,000 or 10,000 or 100,000 labels.
Figure 1
The working of system 1 for determining the positions, also called positioning, of a plurality of labels 8-1 through 8-5 is as follows. Each of the labels 8-1 through 8-5 is configured to generate a beacon signal which can be received by the other labels 8. Preferably, the beacon signals of different labels are not simultaneously transmitted but sequentially. This can be achieved in different manners. Thus, for example, with a certain time frequency a positioning round can be carried out, where the time per round is divided into timeslots, and each label 8-1 through 8-5 is assigned a unique timeslot. For example, label 8-1 may be assigned the first timeslot, so that this label will always start transmitting its beacon signal. In this sequential order for label 8-1 is indicated with ①. The order for labels 8-2 through 8-5 is correspondingly indicated with ②, ③, ④, and ⑤.
Figure 1
Figure 1
In , the situation during the first timeslot is represented. Label 8-1 sends its beacon signal 10 (in the drawing also indicated as Bi). This beacon signal contains data regarding the transmitted power (for example, -50 dBm) with which the beacon signal 10 was transmitted. The beacon signal 10 can be received by each of the other labels 8-2 through 8-5. Upon reception of beacon signal 10, each label 8-2 through 8-5 will determine an RSSI value (remote signal strength indicator (RSSI)) of the signal. Because the beacon signal 10 contains data regarding the original transmitted power, each label 8-2 through 8-5 can determine the signal attenuation with the aid of an internal processor. This information is forwarded as positioning data by way of a positioning signal for label 8-1. In , there are shown the positioning signal 11-3 of label 8-3, the positioning signal 11-4 of label 8-4, and the positioning signal 11-5 of label 8-5. Label 8-2 also transmits a positioning signal for label 8-1. The positioning signals can be received by the receivers 3, 4 and 5. These will forward the positioning data to computer 15 and memory 16 for further processing and storage.
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The labels 8-1 through 8-5 may be provided with an internal clock on the basis of which the assigned timeslot for transmission of the beacon signal 10 can be determined. Synchronization of the clocks of all labels in the system should preferably be as accurate as possible, because this makes the system more energy-efficient. The internal clocks of all labels 8-1 through 8-5 may for example be synchronized once with each other and with the system time of the system 1 (for example as monitored by the computer 15). Also, it is possible to synchronize the internal clocks with the system time periodically, for example when the labels are in a charging station or in the proximity of labels which have been synchronized more recently. In the latter case, the labels 8-1 through 8-5 synchronize their internal clocks relative to each other. Interim mutual synchronization is also possible through exchange of synchronization signals between the labels. When, for example, label 8-1 at time t sends a synchronization signal which is received by label 8-2 at time t (the clock of label 8-2 having an unknown time deviation relative to the clock of 8-1), and in reply the label 8-2 sends a synchronization signal back to 8-1 at time t which is received at time t, it can be determined from the registered times t, t, t and t what the time deviation of the clock of label 8-2 relative to that of label 8-1 is (time deviation = (t - t + t - t)/2).
∗
∗
Optionally, however, the system 1 may also be configured for generating a synchronization signal. With this synchronization signal the transmission of beacon signals in accordance with assigned timeslots can be coordinated. One or more of the beacons 3, 4 and/or 5 may, for example, generate a synchronization signal. This may consist of, for example, a single starting signal, or a continuous or periodical synchronization signal. The synchronization signal can be received by the labels 8-1 through 8-5. On the basis of the synchronization signal, each label is able to determine the timeslot assigned to the respective label for transmitting a beacon signal 10. For example, in the system 1 a predetermined timeslot duration of x milliseconds may be set for the duration of each timeslot. The duration x can have any suitably chosen value, for example a value between 1 and 20. Suppose, for example, that it has been set in the system that x=3 and hence that a timeslot lasts three milliseconds. Label 8-1 has been assigned serial number ① (n=1) and it can hence start sending its beacon signal 10-1 during the first timeslot. Label 8-1 therefore starts directly after reception of the synchronization signal, so after t=(n-1)x milliseconds where n=1 and x=3 and so t=0 milliseconds, to send its beacon signal 10-1. Label 8-5 has serial number n=5, so that the beacon signal 10-5 is transmitted by label 8-5 at time t=(5-1)3=12 milliseconds.
While each label 8 is sending a beacon signal 10 during its assigned timeslot, the other labels 8 listen and determine, for example, the reception strength of the received signal 10. In that case, the beacon signals of the labels 8-1 through 8-5 do not need to comprise any identification code, because it can be determined on the basis of the timeslot what label is currently sending a beacon signal. For example, during the first timeslot, label 8-1 sends its beacon signal 10-1 and labels 8-2 through 8-5 listen with a view to receiving the signal 10-1. The signal 10-1, within the assigned timeslot, identifiably originates from label 8-1 and may contain data regarding the transmitted power. Upon reception, each label 8-2 through 8-5 determines the signal strength of the received signal. This information, possibly together with the payload from the received transmitted signal 10-1, is added to the payload of a return signal to be generated: the positioning signal 11. So, for example, label 8-2 generates positioning signal 11-2, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-2, and optionally the timeslot number (if it is not already known to the system). Further, label 8-3 generates positioning signal 11-3, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-3, and optionally the timeslot number of reception. Furthermore, label 8-4 generates positioning signal 11-4, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-4, and optionally the timeslot number of reception. Also, furthermore, label 8-5 generates positioning signal 11-5, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-5, and optionally the timeslot number of reception. These positioning signals are received by beacons 3, 4 and 5. On the basis of the timeslot in which the beacon signal was sent, this information is assignable to label 8-1.
inter alia
In an alternative embodiment, it is also possible that the signals do comprise identification codes of the labels 8-1 through 8-5. For example, in that case, during the first timeslot, label 8-1 sends its beacon signal 10-1 and labels 8-2 through 8-5 listen with a view to receiving the signal 10-1. The signal 10-1 includes an identification code Y1 of label 8-1 and can contain data regarding the transmitted power. Upon reception, each label 8-2 through 8-5 determines the signal strength of the received signal. This information, together with an identification code for the respective receiving label and the payload from the received transmitted signal 10-1, is added to the payload of a return signal to be generated: the positioning signal 11. So, for example, label 8-2 generates positioning signal 11-2, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-2, the identification code Y2 of label 8-2, and the identification code Y1 of label 8-1. Further, label 8-3 generates positioning signal 11-3, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-3, the identification code Y3 of label 8-3, and the identification code Y1 of label 8-1. Furthermore, label 8-4 generates positioning signal 11-4, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-4, the identification code Y4 of label 8-4, and the identification code Y1 of label 8-1. Also, furthermore, label 8-5 generates positioning signal 11-5, and this positioning signal has as payload the transmitted signal strength from the data of signal 10-1, the received signal strength of the signal 10-1 as received by label 8-5, the identification code Y5 of label 8-5, and the identification code Y1 of label 8-1. These positioning signals are received by beacons 3, 4 and 5.
The signals 11-2 through 11-5, in this last case, may also be sent by the labels 8-2 through 8-5 at the same time. For upon reception, the signals can be separated on the basis of the identification code sent along with them. In a known manner, this can also be done also by assigning the signals their own channel or phase, but also by using a coding of signals. In another embodiment, the signals may also be transmitted in succession, with the duration of the timeslot needing to be sufficiently long to be able to transmit all signals. The time duration of the timeslot may then, for example, be accordingly tuned to this in the system.
Instead of or additionally to being operative on the basis of transmitted power, the present invention may also be operative on the basis of time of flight. This, however, requires an accurately synchronizable system clock that is available in each label.
Figure 2
Figure 1
Figure 1
Figure 2
Figure 1
Figure 2
In , an alternative embodiment of the system 1 according to the invention is shown. The fixed beacons 3, 4 and 5 from , which also do duty as receivers in the system 1 of , are absent here. The function of these beacons is fulfilled in the system 1 of by labels 8-6, 8-7 and 8-8 which have been placed in fixed positions. The absolute position data of these fixed positions are known in the system 1, and may for instance be stored by computer 15 in memory 16. For the rest, the labels 8-6 through 8-8 take part in the mutual communication between the labels 8 in the same way as described above for . In , further, the positioning signals 11-6, 11-7 and 11-8 of labels 8-6, 8-7 and 8-8 respectively are shown. Also, in each of the labels 8-6, 8-7 and 8-8 the respective serial number ⑥, ⑦ and ⑧ for transmitting a beacon signal 10 is represented.
Figure 2
Accordingly, in system 1 in the absolute position of the labels 8-6 through 8-8 is known, and the mutual relative positions of all labels 8-1 through 8-8 can be determined. With this, the system can also determine the absolute positions of the other labels 8-1 through 8-5. For this manner of determining absolute positions of all labels 8, the absolute position of at least two labels should be known.
As described earlier, there are different methods of determining the absolute position data of the beacons 8-6, 8-7 and 8-8. For this purpose, as described hereinabove, use can be made, for instance, of a charging station, of camera pictures, of data inputted by a user, or of data to be detected by the label.
Figure 2
Figure 1
Figure 2
Figure 2
Figure 1
Synchronization of the labels 8-1 through 8-8 in a system 1 as shown in can take place in a same manner as in the system 1 according to . The labels can hence be synchronized, for example, once, or periodically when a label 8 is in a charging station. Also mutual synchronization of the labels 8, for instance, as indicated, on the basis of the most recently synchronized label 8, is a possibility. Also in the embodiment of , the system 1 may include means for generating a synchronization signal. The system 1 may for instance, via computer 15, instruct one or more of the labels 8-6 through 8-8 to generate such synchronization signal which can be received by the other labels 8-1 through 8-8. Alternatively, it is also possible that the system 1 includes one fixed transmitter or transmitting antenna (not shown in ) for transmitting such a synchronization signal. The use of a synchronization signal can take place in the same way as described for the embodiment in .
Figure 1
2
The synchronization signal which, in accordance with some embodiments, can be used in a system 1 according to the invention (for instance as shown in or ), may, as indicated, consist of a starting signal on the basis of which the labels 8 themselves monitor when they are allowed to send their beacon signals 10. It can also be a continuous or periodical synchronization signal on the basis of which the internal clock of each label 8 is synchronized, and which, for instance, can also be used by the labels 8 to determine when the beacon signal 10 is to be sent in conformity with the timeslot assigned to them. A person skilled in the art will understand how such a synchronization signal can be implemented.
In the embodiments of the system 1 in which a synchronization signal is applied, it will preferably be applied exclusively for that function: synchronizing the labels for application of positioning as described. In some embodiments, moreover, additionally to this function, the synchronization signal itself can also be used for positioning. Thus, for instance, the synchronization signal can be transmitted with a transmitted power known in the system, and the labels 8 which receive the synchronization signal can periodically report the reception strength of the synchronization signal back to computer 15. When the synchronization signal is transmitted from a fixed transmitter whose location is known in the system, this will generate an additional fixed position point on the basis of which an absolute position determination can be made. In that case, just at least one other fixed known position point is then needed to be able to find all other absolute positions of the labels 8. So in that case the synchronization signal provides one of the at least two known fixed absolute positions that are needed for absolute position determination.
Figures 3a and 3b
Figure 3a
Figure 3b
show the first two timeslots in a system 1 according to the present invention, which includes one hundred labels. As represented in , in the first timeslot, label 8-1 will generate a beacon signal 10-1. The other labels 8-2 through 8-100 listen out the beacon signal, and process it during this timeslot and transmit a positioning signal 11-2 through 11-100. In the second timeslot, in , it is label 8-2 that sends a beacon signal 10-2 while the other labels send positioning signals 11-1, and 11-3 through 11-100.
Figures 1
2
Figure 4
Figure 4
Figure 4
Figure 1
Figure 4
Figure 4
T,B1
T,B2
T,B3
T,B4
T,B5
R,B1
When in this way in a system 1 according to and a positioning round is carried out, the computer 15 will fill a data matrix as represented in . The matrix in shows the timeslots T1 through T5 in the first column, each timeslot T1-T5 having a row assigned to it. Each of the labels 8-1 through 8-5 present in the system has a column assigned to it, as represented in the header of the matrix. The signal strengths of the transmitted beacon signals for each label 8-1 through 8-5 can be found in the matrix in the cells along the diagonal. For example, the signal strength of the transmitted beacon signal of label 8-1 is indicated in as P where 'P' stands for "power", the subscript T for "transmitted", and the subscript B1 indicates the signal B1 in . The cells along the diagonal further provide P for label 8-2, P for label 8-3, P for label 8-4 and P for label 8-5. The received signal strengths at each receiving label 8-1 through 8-5 are indicated for each timeslot in the cells of the corresponding row. For example, the second left cell in the row for timeslot T1 gives the signal strength of the signal B1 from label 8-1 such as it was received by label 8-2, indicated with P (P for "power", R for "received" and B1 for the signal B1 from label 8-1). The division of a matrix as shown in , of course, can be chosen freely, and the invention is not limited to any particular division. The signal strengths of transmitted signals, for that matter, may also be stored in the memory in a way other than in the matrix of . In that case, the cells along the diagonal are empty.
Figure 1
Figure 2
Figure 2
On the basis of the information in the matrix, the mutual relative position of each label 8-1 through 8-5 can be accurately determined. This information may be supplemented with absolute position information of at least two beacons 3, 4 or 5 as in , or with absolute position information of at least two labels 8-6, 8-7 and 8-8 which are at a fixed location known in the system, as in . With this additional information, also the absolute position of each of the other labels 8-1 through 8-5 can be determined. A label 8, such as labels 8-6, 8-7 and 8-8 in , which is placed at a location known in the system, can do duty as a beacon and at the same time in the same manner receive and process beacon signals from other labels. Thus, labels in a charging station can for instance do duty as beacons when the location of the charging station is known in the system. It is therefore, though possible, not necessary to install special beacons, because, if desired, labels 8 from the system can suffice.
Figure 4
While the beacon signals from the labels 8-1 through 8-5 in the matrix of , for instance as a result of a difference in battery voltage, have each been transmitted with just a bit different transmitted power, positioning is yet possible by normalizing each received signal strength on the basis of the transmitted signal strength. The normalized signal strengths can be mutually compared with each other.
For a system according to the present invention it holds that the greater the number of labels 8, the greater the amount of data and the greater the measuring statistic. This augments the accuracy of the measurement.
The system according to some embodiments can be operative with RFID labels 8 which exchange signals via the UHF band, preferably between 300 MHz and 3,000 MHz, more preferably between 300 and 1,000 MHz, in particular, for example, 434 MHz, 868 MHz or 922 MHz. The advantage is that such labels are already widely available and could be made suitable to be operative within the system 1. A disadvantage is that the signals in this band are known to be erratic, and individual signals may entail an inaccuracy for positioning of a few tens of meters. This is an unduly high inaccuracy. However, the large amount of statistics that is available in a system according to the present invention in this case makes a reliable measurement possible nonetheless.
The system could also, in accordance with some embodiments, be operative in the low-frequency range up to 500 kHz, for example at 400 kHz. At this low frequency, each label could very briefly switch on a carrier only signal. As a result, it can be seen within a radius of about five meters what labels (animals) are in the vicinity. This can be done very accurately because at these frequencies there are no reflections and unpredictable damping. The position is now merely known very locally, but by collecting information about all cows/labels, it is yet known where all labels are.
Furthermore, the above-described system may be designed on an ultra-wide band (UWB) basis. While UWB-based systems have a smaller transmission range, this suffices for the system described here.
The above-described specific embodiments of the invention are intended to illustrate the inventive principle. The invention is only limited by the appended claims. | |
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Strong leadership is crucial for the success of any organisation. The theory for leadership trait helps companies and individuals identify some common personality traits that contribute to successful leadership in various situations. If you want to become a better leader in the workplace, knowing more about the trait theory of leadership can help you identify your strengths and weaknesses as a leader. In this article, we discuss the leadership trait theory, share some of its advantages and outline some common leadership traits.
What Is The Leadership Trait Theory?
The leadership trait theory is a concept based on the practice of discovering specific personality traits and characteristics proven to lead to successful leadership in various contexts. This theory proposes one of the oldest methods of improving workplace effectiveness and derives its foundation from the "great man theory of leadership" introduced by Thomas Carlyle in the 19th century.
According to the leadership trait theory, leaders are born with specific natural characteristics that ensure success in their work duties. This theory also acts as an approach to identify potential leaders by using personality assessments to determine the likelihood of success or failure of a potential leader. Once a person displays traits related to becoming an effective leader, this theory states that they can get trained to maximise their leadership potential.
Related: 7 Leadership Theories For Career Growth
Common Leadership Traits
Several studies have identified vital features and traits that make an effective leader, including several characteristics that can help predict a person's leadership potential with maximum accuracy. The presence of these traits in a person is not a guarantee that the respective person would become a good leader, but is instead a way of identifying individuals with the highest potential for achieving success in leadership. According to most studies, some common leadership traits that show a person's potential for becoming an effective leader include:
Emotional stability
In professional life, challenging situations can appear, and influential leaders benefit from having good emotional stability and regulation in their life. Managing one's emotions effectively in the workplace takes practice, and good leaders know that this is a crucial trait in determining the success of their professional ventures. Influential leaders know how to overcome difficult situations as they are solution-oriented and develop practical solutions to tackle an issue without letting their emotions guide their decisions. Poor emotion management can cause dysregulation in management practices. Having leaders with good emotional stability can encourage employees to trust their leaders.
Related: What Is Skills Leadership Theory? (And Why It Is Important)
Accepting responsibility
Leaders who accept responsibility for their actions are credible and accountable professionals who get respect from employees and colleagues alike. They also take responsibility for the actions of the people they supervise, with no excuses. Influential leaders know that to succeed in a competitive environment, taking responsibility for their actions can position them as trustworthy professionals who are aware of their mistakes and willing to improvise them. This key leadership trait can also help them win more business deals, clients and customers, as they are authentic and employ fair practices.
Action-oriented thinking
Professionals have a lot of decisions to make daily, but influential leaders know that only thinking about taking action does not bring results. They employ action-oriented thinking in their work-life to achieve organisational goals, both individually and collectively. Leaders tend to make decisions and take action with the aim of moving the entire group forward. Efficient leaders have action-oriented thinking as one of their crucial traits because it allows them to seek new ways of improving themselves, their team members and the people under their supervision.
Related: Critical Thinking Skills: Definitions And Examples
Competence
Influential leaders are competent in executing tasks and can inspire action by setting examples of leadership. These professionals are qualified and skilled at performing their specialised duties while constantly showing up at work with their high level of competency and skills. Having competence as a core strength can help these leaders position themselves as successful examples of skilled and talented professionals for their subordinates. They can also set up a performance standard for other employees in the organisation.
Related: Types Of Motivation For Career Advancement (With Examples)
Empathy
Decisive leaders are aware of their employees' problems and think about ways of providing them with sustainable solutions to overcome these issues. Efficiency in corporate leadership results from influential leaders who understand the perspective and challenges of their employees and direct them to the right resources without avoiding the problem. A successful way of ensuring that leaders understand the difficulties faced by their subordinates is through empathising with their situation without judging them for the outcome. Empathy is a crucial trait that can help leaders navigate their professional journeys with ease and purpose.
Communication
Having good communication and interpersonal skills can add to the personality of a leader while ensuring that they convey all ideas and visions with clarity to the relevant parties. Effective communication can enhance leaders' charisma to help them attract the right opportunities and clients for their business. Excellent communication skills can help leaders appear more trustworthy to their immediate team members and other employees. This trait can also help get the attention of the right customers to the business. Speaking and writing with clarity reflects the leader's professional growth to convey complex ideas quickly.
Ambition
Successful leaders have a constant need for achievement and success. They seek personal success but also understand that their successes are derivative of the achievements and successes of their employees and team. While leaders work incredibly hard to achieve their milestones, they also work well with a team and encourage their team members to perform better.
Motivational abilities
A leader's success depends on the people they work with and the organisation they represent. So, being a good leader is as much about motivating themselves as motivating their team to perform better. Efficient leaders know that a large part of their job is encouraging their team members and assigning them tasks according to their strengths. These professionals are receptive and listen to the feedback given to them, which they use to improve the methods of the organisation to ensure that all employees are happy and motivated to work with them. This strategy also enables them to maximise company productivity.
Related: What Is Behavioural Theory Of Leadership? (With Types)
Courage and resilience
One of the essential traits of influential leaders is the courage to take risks and follow unconventional paths and the resilience to sustain in the market when things do not go as per the plan. Having the courage and strength to envision company goals and believing that they can achieve them is essential for leaders. These traits also enable them to move forward with their vision and execute ambitious projects despite the possibilities of setbacks. If leaders know and believe that a particular business project can positively influence their company's growth, these traits can help them achieve those goals.
Related: Top Qualities Of An Outstanding Leader
Perseverance
Perseverance, or the ability to endure challenges and keep moving towards achieving organisational objectives, is crucial for influential leaders. These professionals know that every business faces adversity and unforeseen circumstances, but they equip themselves with the right resources to solve the issue. Having the ability to persevere despite enormous obstacles can ensure organisational success and personal satisfaction. It can also position them as determined and professional leaders who derive strength from their long-term goals.
Moral standing
A leader sticks to their morals, values and principles in every aspect of their professional life. Morally sound leaders have the organisation's and its employees' highest good in mind, and they work towards achieving their end goals that benefit all stakeholders involved. Moral standing also enables these professionals to maintain the highest ethical and moral standards in their work and lead their team by example.
Decision-making
Effective leaders make timely decisions that benefit the organisation and its people. They believe in their vision for the company. Confidently deciding on strategies for improving the workplace and work policies can enhance the organisation's overall employee experience and productivity. Leaders encounter unexpected situations and challenges almost daily, so having the determination and self-belief in their decisions can help them guide their team out of a difficult situation. Working with confident leaders also inspires subordinates to believe in their abilities and encourages them to work hard for achieving organisational goals.
Related: Traits Of A Powerful Personality And How To Build Them
Advantages Of The Trait Theory Of Leadership
Some advantages of the trait theory of leadership include:
Serves as a standard to measure and assess the leadership traits and potential of an individual
Provides helpful insight into leadership and its core elements
Applicable in different companies under various contexts
Related: Big Five Personality Traits (And Ideal Jobs For Each Trait)
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Guest post by Diane Pierre-Louis
The best leaders are nearly always excellent communicators. Clear and productive communication between management and staff is a great stage-setter for a successful and rewarding workplace environment. Whether you feel that you’re already communicating well with your employees or know this is an area that needs polishing, it’s always wise to review some common-sense strategies.
Listen with Intent
The art of meaningful listening requires effort and practice, but it is well worth the effort in the end. Generally, most of us are pretty lousy listeners. Although we might keep our mouths shut, we’re mostly likely just biding our time until the other person is finished and we can have our say. We think we know what our conversation partner will say next, so we plan our responses, which means we are not honestly listening. How can we possibly understand what someone means if our attention is silently focused elsewhere? Pay attention and be an active listener. And whatever you do, don’t interrupt.
Pay Attention to Tone and Body Language
Body language is often more telling than the words that leave our mouth. As you’re listening to your employee, be an active observer as well as an attentive listener. Body language experts assert that 90% of how we communicate is nonverbal, so what we do with our body and facial expressions are as powerful as the words we speak. Practice using open body language that indicates you are receptive and willing to enter into a healthy conversation. This can include leaving your arms by your sides instead of crossing them and leaning slightly toward the speaker.
Tone of voice is also important. Unless we listen to recordings of ourselves regularly, it’s hard for us to relate to how our voice sounds. Be aware that your voice may indicate how tired, stressed, bored or irritated you are – even if your words indicate otherwise.
Follow up on Conversations
Don’t depart from a meeting without restating what you just heard. That will go a long way to eliminating the possibility of misunderstandings. Also, get into the habit of sending a quick email recapping what was discussed in a meeting or other work-related gathering. Often, employees bring up questions or concerns during a meeting, so a prompt follow-up addressing those issues is a valuable communication tool that lets your staff know you were listening and that you care.
Great leaders know that a company’s fortunes will rise and fall on the contributions of its employees. Creating an environment that promotes open communication among all employees and supervisors will foster the trust and collaboration necessary for long-term success.
Diane Pierre-Louis is a writer for Bisk Education and covers a variety of topics related to higher education and the workplace, including effective leadership and conflict management.
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Summary: In The Dividing Line episode Behold the Secular Woman & WLC on Molinism (Once Again) James White argues that if Molinists are anti-realists about abstract objects, then they cannot consistently affirm that middle knowledge demarcates the range of feasible worlds available for God to create. This is because, according to White, counterfactuals of creaturely freedom (hereafter, CCFs) must first exist in order for them to be able to demarcate the range of those feasible worlds available to God. Here, I argue that White’s response begs the question against the anti-realist Molinist. I then entertain and refute a stronger version of White’s objection which turns out to be a variant of The Indispensability Argument for Platonism.
Notice that White presents no justification for the idea that CCFs must exist in order for it to be true that they demarcate the range of feasible worlds available for God to create. White instead merely assumes that Molinists ought to accept this assumption. He therefore begs the question against the anti-realist Molinist. Now, at this point, we’ve sufficiently responded to White’s objection and so may call it a day. However, for the sake of a more substantive discussion, in the proceeding section I shall attempt to formulate a criterion for White which, in the context of an argument I shall give on behalf of him, will attempt to conclude that Molinists who are anti-realists about CCFs cannot consistently affirm that CCFs demarcate the range of worlds God is able to create.
Simple sentence: a sentence with a single clause, with a single subject, and predicate.
Singular term: a word or phrase that serves to denote some particular. Singular terms consist of proper names (e.g., ‘Jesus’, ‘The Eiffel Tower’, ‘Star Wars: Attack of The Clones’, etc.), definite descriptions (e.g., ‘the man with the golden voice’, ‘my best friend’, ‘the first female President’, etc.), and demonstrative terms (e.g., ‘this essay’, ‘that desk’, etc.). With respect to the sentence “CCFs are grounded in counterfactual states of affairs.” the singular terms that appear in that sentence (i.e., ‘CCFs’ and ‘counterfactual states of affairs’) both qualify as definite descriptions.
a: a symbol which we may substitute in for a singular term that appears in the domain of quantification in order to form a simple sentence. So, for example, we can substitute the relevant symbol in the sentence ‘a’s are f’ so that it now states ‘CCFs are f’.
f: a symbol for which we may substitute any property which we might predicate of the individual picked out by the singular term. So, for example, the simple sentence “CCFs are f” could be restated as “CCFs are grounded in counterfactual states of affairs”.
R: any relation in which the object specified by the singular term may be said to stand.
Those who are already familiar with the contemporary philosophical scene concerning abstract objects will recognize (1) to be the so-called neo-Quinean criterion of ontological commitment. I’ve chosen to address this particular criterion because I suspect that White, if pressed, would espouse something roughly similar. Moreover, so far as I can tell, this particular criterion appears to be the most popular among philosophers and so an evaluation of this criterion will be of interest to many.
Now let us now add further clarity to (1). According to this criterion we make ontological commitments by utilizing singular terms and/or existential quantification in literally true simple sentences. The reason why this criterion applies itself only to literally true sentences is to preserve the meaning of non-literally true sentences which we employ in our ordinary, non-formal discourse. For example, when James White asserts a statement like “Kira is dead in sins and trespasses”, White surely does not mean to communicate that Kira is literally dead—soul separated from body in the afterlife—and is such in these curious objects known as “sins” and “trespasses”. Rather, being faithful to his Calvinism, White simply means to convey that Kira is affected by his own sin nature such that he is totally depraved (in the Calvinist sense), has total inability (in the Calvinist sense), or something roughly similar. So although it is true that Kira is dead in trespasses and sins, nevertheless, faithfulness to the intended meaning of White’s statement about Kira requires that we construe it as being metaphorically true rather than as literally true. Thus, as this example illustrates, if one wants to preserve the intended meaning of certain sentences, then one’s criterion of ontological commitment will have to exclude non-literally true sentences as (1) attempts to do.
In sum, (I) expresses a criterion of ontological commitment which attempts to not overreach in its scope in so far as it does not impose itself upon non-literally true sentences as well as intensional contexts. (I), therefore, will be inapplicable to perhaps the majority of human discourse.
(1) If a simple sentence (i.e., a sentence of the form ‘a is F’, or ‘a is R-related to b’, or . . .) is literally true, then the objects which its singular terms denote exist. Likewise, if an existential sentence is literally true, then there exist objects of the relevant kinds; e.g., if ‘There is an F’ is true, then there exist some Fs.
(3) Therefore, abstract objects exist.
The above argument shouldn’t be alien to those already familiar with contemporary philosophical debates concerning abstract objects. For the argument just is a modified version of the so-called Indispensability Argument for Platonism. The only difference here is that I’ve singled out particular sentences in premise (2) rather than generalizing the premise.
Now, prior to evaluating the relevant argument we should first understand its implications so that we can grasp what exactly lies at stake for the Molinist. Most obviously, notice that even if the relevant objection is successful, it does not conclude that Molinism is false. Rather, the conclusion entails that anti-realism is false, thereby implying that Molinists who are anti-realists about abstract objects ought to be committed to the reality of CCFs and feasible worlds. Therefore, the argument’s conclusion is irrelevant to Molinists who are already realists concerning abstract objects. With this in mind, in the proceeding section, we move to evaluating premise (1).
Even further, as we previously noted (1) assumes that reference is to be understood as a relation. But notice that no argument has been given for why we ought to accept this presupposition. What needs to be appreciated here is that there are multiple theories of reference and of these theories are ones that construe reference not as a relation between word and object, or even as a relation between speaker and object, but instead as a property of persons that is relation-like. So, for example, on such a view my engaging in the activity of referring to X (where X stands for any given singular term) just is identical to my having the mental-relational property of thinking-about-X, being-directed-toward-X, or something roughly similar, whether or not X exists.
What is meant by the term “relation-like”? An illustration may help elucidate the concept: Suppose that you were to induce a hallucination in me such that it appears to me that there is a red balloon in front of me. I then form a thought about the balloon so that I bare the property of thinking-about-the-red-balloon-in-front-of-me. In such a scenario, this mental-relational property of my thinking-about-the-red-balloon-in-front-of-me obtains, notwithstanding, the balloon itself doesn’t actually exist. Hence, in this case I possess a mental-relational property about a particular that does not exist in a heavyweight sense. Similarly, for those who take reference to be an intentional property of persons, we can bare mental-relational properties about abstracta such as being-directed-to-X or referring-to-X, even though the abstract object of our intention does not exist in a heavyweight sense.
Now, at this point, one might argue that since anti-realists believe that abstract objects don’t exist, then it follows that when anti-realists claim to think about abstract objects they are really thinking about nothing, and hence, not thinking at all, since there isn’t any existent object to which the intention of our thought corresponds. But, the objector further argues, we obviously are engaged in the act of thought when thinking about abstract objects. Therefore, abstract objects must exists in a heavyweight sense.
This objection fails to appreciate the point we just made about competing views of reference. For the objection stipulates that in order for us to think about something (and hence, refer to it) there must be this relation in so far as there is some existent which corresponds to the intention of our thought. Hence, the objector is assuming without argument that reference should be construed as a relation rather than as a property. The objector has therefore begged the question against non-relational views of reference.
Responding to Premise (1) – Are Singular Terms Devices of Ontological Commitment?
Craig then highlights that since standard logicians take singular terms as being devices of ontological commitment, their way of avoiding making untoward ontological commitments is to treat identity statements involving vacuous singular terms (i.e., singular terms with no corresponding existent(s) denoted by the term(s)) as false. But, this too, Craig argues, is intuitively wrongheaded. For this would imply that a statement such as Vulcan = Vulcan isn’t true, even though the statement is an obviously true tautology irrespective of if Vulcan exists. Craig thus concludes that standard logic can’t distinguish whether statements like Zeus = Zeus or Allah = Zeus are true or not even though the first identity statement seems to be necessarily true while the other necessarily false.
The above argument appears to be formally valid, exhibiting a modus ponens structure. Moreover, in order for the conclusion to be validly derived, one of the premises will have to be identical or else logically equivalent to the premise ‘Lincoln brooded’. Prima facie, this appears to be the case with respect to the above argument. However, if for the sake of argument, we take it to be the case that Lincoln no longer exist implying that ‘Lincoln’ is a vacuous term, then the argument will turn out to be logically invalid. This is because standard logic will prohibit us from inferring whether or not Lincoln = Lincoln. Moreover, neither can the argument’s formal validity be redeemed by substituting the term ‘Lincoln’ in premise (2) for a co-referring term such as ‘The 16th President of the United States’. For if ‘The 16th President of the United States’ is vacuous term, then standard logic will prohibit us from inferring whether The 16th President of the United States = The 16th President of the United States or if The 16th President of the United States = something non-identical or something that doesn’t co-refer to Lincoln.
Because Craig finds standard logic’s treatment of singular terms untenable, he finds himself sympathizing with and defending neutralism, a view which maintains that neither singular terms or existential quantifers in first-order logic are devices of ontological commitment. Such a view, if correct, will obviously force revisions in classical logic since classical logic affirms that singular terms are devices of ontological commitment. Notwithstanding, Craig does think that a thoroughgoing logic that is neutral with respect of ontological commitment does free us from these unwanted ontological commitments and does make for a less bloated ontology.
Responding to Premise (1) – Is Existential Quantification a Device of Ontological Commitment?
Proceeding ahead, the second horn of the neo-Quinean criterion asserts that we make ontological commitments by means of employing existential quantification. In other words, according to this criterion, we make these commitments by employing existentially quantifying phrases or symbols such as “For all”, “For some”, “There exists”, “∃”, etc. Craig has given a number of reasons why he thinks existential quantification shouldn’t be taken as being ontological committing.19 Let us discuss three of these reasons.
First, Craig argues that taking existential quantification as being a device of ontological commitment is ontologically inflationary. That is to say that it commits us to the existence of entities needlessly. To demonstrate the point, consider the notion of ‘months’. Presumably most of us will want to affirm that months are nothing more than a created social convention. Not so, given the neo-Quinean criterion of ontological commitment. For the sentence “There are 12 months in a year” would commit us to the existence of these abstract objects called ‘months’ simply in virtue of our existentially quantifying over them. Similarly, consider the statement “There is a lack of love in the world”. According to the neo-Quinean criterion, since I have asserted that there is a ‘lack’ (thereby quantifying over the term ‘lack), I am thereby ontologically committed to there being ‘lacks’, which, on Craig’s view, is surely wrongheaded.
Second, Craig thinks that taking existential quantification as being ontologically committing prohibits us from accepting the truth of tensed statements given the truth of a certain version of presentism. For example consider the past-tense statement “There have been 6 ice cubes which have melted in this cup”. We commonly accept the truth of such innocuous sounding statements. Furthermore, let us suppose that some version of presentism which asserts that there exist no non-present entities is also true; I shall take it for granted that most of my readers, whether they are Molinists or otherwise, will be sympathetic to such a view. Now, if such a version of presentism is true, and if we take it to be the case that existential quantification is a device of ontological commitment, then that statement involving the 6 ice cubes will turn out to be false. This is because there will be no existent ice cubes which correspond to the objects denoted in that statement. Of course, one could attempt to ground the statement by appealing to the B-theory of time so that the ice cubes bare a tenseless existence, but I take it to be the case that there are good independent reasons for thinking that the B-theory of time is false.20 Therefore, given the truth of these reasons, ontological frameworks which require B-theory should be avoided unless we have some good independent reason(s) for preferring it.
UMC: Necessarily, whenever there are some things, then there are a fusion of those things.
That in mind, it is obviously true that there exists sharks and there exists tornadoes. Thus, given the principle of UMC, there exists a fusion of those objects which we shall call a Sharknado, where by ‘Sharknado’ I am not referring to a tornado with sharks in it, but am instead referring to an object that is composed of, say, a localized tornado in Kansas and a shark in the Pacific Ocean. Moreover, since, I have existentially quantified over that fusion, then, given the truth of the neo-Quinean criterion of ontological commitment, I am thereby ontologically committed to there being Sharknadoes. Craig takes this untoward conclusion to be counter-intuitive and ontologically inflationary, especially in light of the fact that are a potentially infinite number of fusions. Given the truth of mereological universalism and given the falsity of the Neo-Quinean Criterion of ontological commitment, Craig thinks that the obvious solution to this problem will be to adopt neutralism which permits us to freely speak about fusions without being ontologically committed to their existence.
While there are a number of ways in which the anti-realist can respond to this premise (e.g. Fictionalism, Figuralism, Pretence Theory, etc.), we shall restrict ourselves to Craig’s view since it is his view of which White is concerned. Craig’s view is unique in that he takes a combinatorial view which adopts certain elements from both Figuralism and Pretence theory without accepting every aspect of these respective theories. Prior explaining how Craig does this, we should first have an understanding of what each of these respective theories involve.
According to Pretence theory, abstract object talk is merely a fictional discourse that is prescribed to be imagined (or make-believed) as true, similar to how we imagine Santa Claus to live in the North Pole. To be clear, Pretence theory is not identical to the anti-realist view known as Fictionalism. For Fictionalism claims that sentences involving quantification over or reference to abstract objects are untrue while Pretence theory is simply neutral on the matter. Neither should Pretence theory be confused with Figuralism. For Figuralism affirms that, at least, sometimes abstract discourse is figuratively true while Pretence theory, again, is simply neutral on the matter. Simply put, Pretence theory is neutral with respect to whether or not our abstract discourse is true. To avoid further confusion, it’s also worth noting that certain Pretence theorists such as Kendall Walton do not take truth and fictionality to be mutually exclusive.25 For consider the propositions prescribed to be imagined in the historical fiction War and Peace. While the story is itself fictional, nevertheless, some of the propositions in this book are, in fact true. Thus, for Pretence theorists like Walton (and Craig), what is crucial to understanding the notion of fictionality, is not falsehood, but the prescription to be imagined.
So, with respect to Craig’s combinatorial approach, he adopts and defends a thesis according to which abstract discourse sometimes involves our using figurative language, while, at other times, it involves our engaging in pretence.26 That said, since premise (2) supposes that an anti-realist like Craig believes that abstract discourse is to be construed as literally true, the premise therefore fails to accurately characterize Craig’s position. As a result, the Indispensability Argument we’ve formulated on behalf of White not only bares two challengeable premises, but also fails to constitute a successful reductio argument against the anti-realist Molinist position.
In conclusion, White’s initial objection to the anti-realist Molinist position was weak in so far as he presented no justification for why the Molinist ought to accept the assumption that CCFs must exist in order to delimit the range of feasible worlds God is able to create. In light of this shortcoming, I strengthened White’s argument so that it paralleled the Indispensability Argument for Platonism. We saw that both premises of this reformulated argument were challengeable in that the first premise stipulates an unargued and implausible criterion of ontological commitment, while the second premise fails to accurately characterize certain anti-realist perspectives concerning abstract discourse. Of course, it goes without saying that a variety of other anti-realist theories are available to the Molinist. So is realism. Thus, so far as I can tell, anti-realism presents no threat to the Molinist.
6To be clear, I agree that there are at least some contexts where, in order for a sentence of a certain kind to be true, there must exist, in a heavyweight sense, whichever object(s) I refer to in or by that sentence. My gripe instead lies with the notion that this principle universally applies to all contexts.
7Here, it’s important to understand that, throughout this essay, I am not using the word ‘refer’ in a colloquial sense so as to denote the subject or topic of discourse. Rather, I am using the term in a philosophical context. As we shall later see, philosophers understand relevant term in different ways and there are competing views concerning the nature of reference.
8See Mark Balaguer, Platonism in Metaphysics for the original formulation of the Indispensability Argument for Platonism from which I’ve derived my variant of his argument.
9Definition is adapted from William Lane Craig, God Over All: Divine Aseity and the Challenge of Platonism p. 47.
10For an explanation as to how modal and temporal operators supply intentional contexts see Ibid., p. 48 n.6.
11For further discussion on competing theories of reference see Ibid., pp. 132-139.
12On Ibid., pp. 133-134 Craig supports the notion that philosophers sometimes beg the question in favor of relational views of reference by appealing to a standard encyclopedia entry by Timothy Williamson where Williamson defines reference as being relational.
14For a more thorough critique of the view that singular terms are devices of ontological commitment see Ibid., pp. 140-143.
15Karel Lambert, Meinong and the Principle of Independence (Cambridge: CUP, 1983), 98–9.
16I’ve modified Craig’s example. The example Craig originally gives involves the singular terms ‘Lincoln’ and ‘Aristotle’. I’ve withheld using these singular terms because of the following issue which might be raised: Suppose that by ‘Lincoln’ and ‘Aristotle’ Craig means to refer to them as essences. If such is the case, then Craig’s claim that Lincoln and Aristotle no longer exist will be false because the essences of Lincoln and Aristotle never existed (in a metaphysically heavyweight sense) to begin with since, on Craig’s view, essences don’t exist in a heavyweight sense. But let us now suppose that by ‘Lincoln’ and ‘Aristotle’ Craig means to refer to them as concrete particulars. If such is the case, then it will still be false that Lincoln and Aristotle no longer exist since, given Christian theology, they exist as spirits in the afterlife.
Additionally, on June 10, 2018 I had the opportunity to speak personally with Craig about this following his Defenders Class. According to Craig, this criticism is technically correct, notwithstanding, he was speaking in a non-theological context.
17In order to grasp the B-theory of time (also known as the tenseless or static view of time), it may be helpful to first contrast it with the A-theory of time (also known as the tensed or dynamic view of time). As a cursory definition, the A-theory of time asserts only time that exist is the present. In contrast, the B-theory of time asserts that past, present, and future exist on ontological par; that is to say that they are all equally real—they occupy a spatial location, possess causally potent entities, inter alia. On the B-theory of time, one may think of time on the analogy of a yardstick. On a yardstick, the 10th inch exists prior to the 11th inch. Moreover, the 12th inch exists posterior to the 11th inch. Notwithstanding, the 10th and 12th inch aren’t any less real than the 11th inch. Similarly, according to the B-theory of time, although the past and future are respectively prior and to the moment which appears to be present to us, nevertheless, the past and future aren’t any less ontic. So, on the B-theory, for the people who live in 1947, that year will appear to be present to them. Similarly, for the people who live in the year 2300, that year will appear to be present to them. On the B-theory of time, temporal becoming—that is the notion that things really do come into and then go out of existence—is an illusion of human consciousness. For on the B-theory of time all moments in time exist tenselessly.
18I’m assuming the truth of the A-theory of time because I take it to be the case that there are good independent arguments on behalf of this theory. It should be clear that I am not committing the same error that the B-theorist might commit by inferring the truth of some theory of time solely on the basis of some identity statement being true.
19For a fuller analysis of the issues with taking existential quantification as being a device of ontological commitment see William Lane Craig, God Over All: Divine Aseity and the Challenge of Platonism p. 113-124.
20The brevity I seek to preserve throughout this essay will not permit me to defend an argument against the B-theory of time. For this reason I will merely delineate the issues that I think this theory faces without doing anything by way of elaboration. That said, perhaps the most glaring issue which the B-theory faces its approach to the problem of intrinsic change. The problem of intrinsic change asks how something can remain identical to itself if it has different properties at different times. The A-theorist’s solution to this question is to deny that any object is presently such that it possesses different properties at different times. Since, on the A-theory, only the present exist, an object only possesses those properties it presently has. On the A-theory, objects exist wholly at a time and endure through time to later times. This doctrine is known as endurantism.
In contrast, the typical solution offered by B-theorists is what is known as perdurantism. According to perdurantism, no object exists wholly at a time. Instead, the three-dimensional objects that appear to us are really these four-dimensional objects extended in space-time so that the three-dimensional object we see just is a segment of this greater four-dimensional object. It may be helpful to think of this view on the analogy of a flip book animation involving Superman. When one quickly flips through the pages of the flip book there is this illusion of a single, continuous Superman, but, in reality, there are actually these individual drawings—or we can call them segments—of Superman which, when flipped through quickly, create the illusion of a single Superman which endures throughout the animation.
There are at least four issues with the doctrine of perdurantism: (1) Perdurantism’s account of intrinsic change is implausible (2) Perdurantism is incompatible with the phenomenology of personal consciousness (3) Perdurantism is incompatible with moral responsibility, praise, and blame and (4) Perdurantism implies an implausible view of essential properties. Last, it’s worth mentioning that the B-theory of time is itself incompatible with a robust doctrine of creatio ex nihilo. For an in depth discussion of the reasons that I reject perdurantism and the B-theory of time see William Lane Craig, Time and Eternity: Exploring God’s Relationship to Time pp. 200-215.
21Mereology is the study of parts and wholes.
22See William Lane Craig, God Over All: Divine Aseity and the Challenge of Platonism p .122.
25See Kendall L. Walton, Mimesis as Make-Believe: On the Foundations of the Representational Arts (Cambridge, MA: Harvard University Press, 1990).
26Craig’s view involves more nuance than what I’ve stated. For example, Craig acknowledges that our recursion to abstract discourse is often due to its convenience. He even acknowledges that it’s epistemically possible that in some cases our recursion to abstract discourse is unavoidable due to the exigencies of our language so that there may be no other way for us to express certain claims. Moreover, Craig views our recursion to abstract discourse as proceeded by our adopting a certain linguistic framework according to which we can speak without making metaphysically heavyweight ontological commitments. | https://freethinkingministries.com/responding-to-james-whites-anti-molinist-critiques-abstract-objects/ |
Popular Twitch streamer Trainwreckstv was left enraged when his Call of Duty: Warzone match was interrupted by a bizarre glitch that ruined his game.
Warzone is the latest battle royale from the iconic Call of Duty franchise, and has been a major hit since its March debut. However like any game, it can have glitches that show in the most unexpected ways.
This is what happened to popular streamer Trainwrecks, who found his match ruined during a May broadcast. The Twitch personality was furious when the game’s environment turned against him at the worst timing possible.
Related – The Incredible Call of Duty COMEBACKS That Shocked Everyone
Trainwrecks rages at Warzone glitch
The streamer was pushing towards the final circle, when he found himself engaged in an intense battle with the remaining opponents. Suddenly he found himself unable to move, and became stuck in a tree.
“I’m stuck in a tree! I’m stuck in a tree!” he screamed, as he shook his in-game camera around to try to break loose. After being unable to, Trainwrecks stood up and slammed his hand on his desk as his character became engulfed in gas.
Teammate Dimitri ‘Greekgodx’ Antonatos mocked the situation, exclaiming, “We got f**king treetop Andy here, trying to make a treehouse, mate.” The streamer replied, “I can’t even rez because I’m… Oh my.”
Train eventually got knocked down by the gas, but managed to break from the glitched environment. Unfortunately it was too late, as he died trying to crawl to safety. Fortunately, his team was able to secure the victory.
The victory was bittersweet for the Twitch personality, who told his teammates, “That literally shows you it’s actually a bad day. What the f**k! How do I get stuck in a f**king tree!? Shameless.”
This wasn’t the first time the streamer had bad luck in his match. Minutes before, he exploded in anger after squadmates Greekgodx and Mason ‘Symfuhny’ Lanier’s talking muffled his audio, which led to an enemy sneaking up and killing him. “SHUT THE F**K UP!” he screamed.
While his team eventually went on to win, Trainwrecks’ rage was completely understandable. After all, none of the situations were his fault, as the tree glitch was just extremely bad luck.
Despite the Warzone frustrations, the streamer continues to be one of the most watched personalities on Twitch. At the time of writing, he’s amassed over 600k followers to his channel. | https://www.dexerto.com/call-of-duty/trainwrecks-rages-after-shameless-warzone-glitch-ruins-his-match-1361177/ |
Under the scheme’s guidelines, as voted for by the DUP and Sinn Féin, households earning up to £60,000 a year had the right to apply for a one-off £100 fuel hardship payment from the total £1 million set aside by the Council.
The distribution of the £100 funds was decided on a ‘first come, first served’ basis, and was controversially carried out by the same ‘strategic partners’ or community groups that were picked to receive and deliver millions of pounds of ratepayers' money from the start of the COVID-19 pandemic.
Alliance have asked for an update on the progress of this report for this month's Committee and it is due to be completed 'in the New Year', according to a Council response.
“I am pleased that the Audit Office are taking our concerns seriously and want to examine the independent review”, said Belfast City Councillor Sam Nelson, who attended the emergency meeting with the Audit Office.
“When the Partners were first used, they were nominated in the initial emergency around Covid, which meant that we had to act quickly. However, since then the same groups have been continually used to allocate millions of pounds of Council funding with absolutely no review of how effective they have been.
“In addition, there has been no open competition for other organisations to become involved.
“The DUP/SF block have continually pushed through the same groups again and again. The fact that they unilaterally swapped in and out new Partners, with no competition for the Fuel Poverty Hardship Fund, is also of concern and reeks of a carve up.
“Alliance has no issue with any of the Partners, but we have always believed in open and transparent processes. When groups are being used to allocate food parcels or funding on behalf of the Council, we need to be sure that they are the best equipped to do so and that the most vulnerable in our community are receiving the help they need. With that in mind, this independent review must be completed quickly to ensure that this has been the case. | https://www.allianceparty.org/audit_office_requests_copy_of_report_on_funding_awards_after_alliance_raises_concerns_about_roll_out_of_fuel_poverty_hardship_fund |
Based on the fact that some foreign friends don't have adequate understanding about written Chinese, and that some of them claim that Chinese characters are destined to die out, I realized this topic should be brought up, in order to make it known to all that Chinese characters will flourish.
Frankly I'm NOT a student of language majur. I'm 23 and I just graduated with a mechanical engineering bachelor's degree. However, my primary interest is building electronic systems, including those with LCD user interfaces. Sometimes I need to embed a Chinese input method and character display function into my system. So you know,
We all know that our screens are made up of luminescence materials which form tiny pixels. And that characters are a type of special images. Actually alphabetic letters are images too, but relatively simpler. Anyway, the way they are displayed are the same. We draw them on the creen, so they look the way a character appears.
Take the letter "A" and the character "国"(guo/country) for example:
let's put them both in a small 16 pixel height.
A:
00000000 = 0x00
00000000 = 0x00
00010000 = 0x10
00111000 = 0x38
01101100 = 0x6C
11000110 = 0xC6
11000110 = 0xC6
11111110 = 0xFE
11000110 = 0xC6
11000110 = 0xC6
11000110 = 0xC6
11000110 = 0xC6
00000000 = 0x00
00000000 = 0x00
00000000 = 0x00
00000000 = 0x00
国:
0000000000000100 = 0x00, 0x04
0111111111111110 = 0x7F, 0xFE
0100000000100100 = 0x40, 0x24
0101111111110100 = 0x5F, 0xF4
0100000100000100 = 0x41, 0x04
0100000100000100 = 0x41, 0x04
0100000101000100 = 0x41, 0x44
0100111111100100 = 0x4F, 0xE4
0100000100000100 = 0x41, 0x04
0100000101000100 = 0x41, 0x44
0100000100100100 = 0x41, 0x24
0100000100000100 = 0x41, 0x04
0101111111110100 = 0x5F, 0xF4
0100000000000100 = 0x40, 0x04
0111111111111100 = 0x7F, 0xFC
0100000000000100 = 0x40, 0x04
A digital 1 stands for a visible pixel on the screen, and digital 0 stands for the background. and that's how we draw images on the screen. Actually each digit takes up a bit in the memory. And 8 bits, make up a byte. So we can also put the dots into hexdecimal format. That's what those magic 0xxx numbers are. So the letter A takes up 16 bytes while being displayed, and the character 国 takes up 32 bytes.
Where do the images come from? They come from what we call a library, which is actually a file filled with sequential bytes. There are 128 ASCII codes, each displayed same way as illustrated above for letter "A". So an ASCII library takes exactly 128*16=2048 bytes, or 2KB. There are 8192 most frequently used Chinese characters according to the national standard(GBxxxx). These characters are usually arranged together to form a standard library. Given the fact a single 16*16 size Chinese character takes up 32 bytes, the tatal space 8192 characters consume is exactly 8192*32=262144 bytes. Because 262144/1024=256, we can say it takes 256KB to store such a library. How much space have you guys got in your computer? 40GB? 120GB? 400GB? or 2TB? I got 320GB here. so I've got a hell lotta space to save over 1.3 million duplicates of this library. So, you see, a 256KB library isn't big deal nowadays.
What does the computer do when we input Chinese characters? There are different types of IME's or we call input methods. I'm not digging deep into the algorithm they implement. I'm ganna tell you how characters are fetched from this library with a certain index. The 8192 characters are stored inside this library in a certain order. GB has set a table of index to retrieve these characters by giving each of them a unique address code. And in Chinese it is called "区位输入法", which means index by zone code and serial code. This makes the sequence characters form the library.
When we type Chinese characters, they appear as complicated images on the screen, but what's inside, is much simpler. Let's creat a *.txt file and type something into it. For example input Chinese characters "中国"(China) without any space or enter. Save the file, and check its properties, what's its size? 4 bytes right? How come two complex Chinese characters take only four bytes? I'll tell you how this is done inside the computer. (And actually the four specific bytes will be 0xD6,0xD0,0xB9,0xFA if you're curious enough to look into the file with WinHEX or UltraEdit.)
Take 国 for example again. Like I said it is stored as 0xB9,0xFA inside the machine, which we call the "internal code". Its zone code is 0xB9-0xA0=0x19 = 25(decimal), and its serial code is 0xFA-0xA0=0x5A = 90(decimal). 0xA0 or 160(decimal),is the threshould of whether the computer should consider a byte stored is for a Chinese character or an ASCII letter. When it gets 0xB9, it compares the number with 0xA0, and finds out it's greater than 0xA0, so the computer does the math as below:
absolute address of first byte of character in library = 32*[(zone code-161)*94+(serial code-161)]
-- 32 means each character takes 32 bytes.
-- 94 means there 94 zones inside the library
-- serial code-161 is the position this character stands in the zone of the library,or what we call the OFFSET
-- (zone code-161)*94+OFFSET means the sequence number of the character in the whole library. For 国, it is 2345, which means it's the 2345th character in the entire library. Multiply it by 32, and we get the address number 75040. This is where we start to pick up 32 sequential bytes. And they will be 0x00,0x04,0x7F,0xFE......0x40,0x04 just as illustrated above.
On the other hand, an ASCII code takes one byte in a *.txt file. This byte is its address in the ASCII table, i.e, A being 0x41. The computer checks the ASCII library pretty much the same way it does with a Chinese character, but the calculation is much simpler. 0x41-1=0x40 is multiplied by 16, instead of 32 because of the space the image takes.
So we've come all the way to this understanding, that a 8192(count)*16*16(size) characters Chinese library takes up 256KB of memory inside a digital device. And that our texts are stored inside the computer for two bytes per Chinese character and one byte per ASCII code. Most importantly, ONLY ONE LIBRARY IS SUFFICIENT IN A DIGITAL DIVICE TO DISPLAY ALL THE CHARACTERS IT SUPPORTS!! I don't think anyone would mind sparing 256KB extra space to support 8192 Chinese characters' compatibility. Some one said on most U.N confrences, printed documents with the same content come with different thickness, and the one typed in Chinese is always the thinest. The written Chinese language is brief. I've seen so many English articles being translated into Chinese, in less than half the original length. So I say, given the algorithm that one Chinese character takes twice an English letter does, a Chinese digital document can take no more than an English one, at least not much more. Consequently, space isn't an issue which will cause Chinese characters to die out. Neither will input efficiency be one. My cousin used to work as a typist, she could type an article even faster than someone reciting the same thing. So, my point is, Chinese characters will last, won't you agree? | http://www.chinalanguage.com/forums/viewtopic.php?f=11&t=2984 |
- Venue is on west side of Station Road (A862) just south of village centre, connected to library. Car park at venue. Venue has caretaker.
- Built 1903 by Henry Phipps (business partner of Andrew Carnegie).
- Capacity 196 if stage used, approx 130 if performing on floor. Non-interlocking, stacking chairs.
- Mobile reception good.
- Beauly has Banks & cashpoint, general store, hotels, café, Post Office, & petrol. All other services in Inverness (12 miles).
Hall Details
- Hall Dimensions: 11.17M (36’8”) wide x 16.46M (54’) long. Height at side walls 4.75M (15’7”) rising to approx 6.7M (22’) at centre – roof is arched.
- Stage: 7.32M (24’) wide x 4.09M (13’5”) deep. Height above 3.96M (13’), height of stage 1.12M (3’8”). No wings or crossover. Access treads off stage right. Stage has back blacks and legs & borders. FOH tabs are red.
- Décor: floor polished wood with Badminton Court markings; walls dark wood panelling lower, light green upper; roof light green with mouldings & white support arches.
- Get-in: through front entrance, 2 sets double doors & right angle turn, flat. Approx 20M from van loading area to stage. 1.32M (4’4”) wide x 2.08M (6’10”) high.
- Acoustics slightly reverberant.
- Blackout reasonable, all windows have blinds and lined curtains. Only FOH doors have windows & no curtains.
- Heating by radiators.
- Upright piano on stage. No smoke detectors.
- Small extending ladder.
Technical
- Power: 100amp 3-phase incomer. Lighting dimmer on 63amp single-phase supply. 2 x 32amp single-phase sockets in SR wing.
- Small stage lighting rig – Jands 12 channel 2 preset lighting desk, 12 channels Pulsar non-patchable dimmers, 2 FOH side LX bars, 2 stage LX bars, 6 650w CCT profile spots, 6 x 650w CCT fresnels.
- Small PA system – Mynob 16-4-3 mixer, Celestion & EMC amps, mounted Celestion speakers, graphic EQ, 6 mics & stands, CD player. Hard-wired multicore to FOH. Locked rack for sound equipment in SL wing.
- Houselights are up-lighters switched in SR wing or switched sodium’s (switches in main entrance lobby).
Backstage
- Can use small hall upstairs as dressing room.
- Kitchen available. | https://rightlines.net/venue/beauly-phipps-hall/ |
(1) The original Italian text and an English translation of a 20-year-old conscript's diary from the years 1881-1883. There is a brief summary of his journal lower on this page.
- Part I: Pages 1-19.
- Part II: Pages 20-42.
- Part III: Pages 43-60.
- Part IV: Pages 61-78.
- Part V: Pages 79-101.
The pages of the text were numbered by its author ( ) or by the transcriber [ ], so that each page of the author's text has a number at its top. The translation of the text is interlinear (between the lines); the English version is everywhere in CAPITAL LETTERS.
The division of the text into five parts was made by the transcriber in order to reduce Internet page length. These divisions do not exist in the original.
(2) Summary of the 1887 Civil Wedding Banns (pubblicazioni) of Michele Fuschino and Luisa Chiatto, from which can be deduced that Michele Fuschino was 20 years old when he began his national service. Michele's future bride makes an appearance at the very end of his journal.
(3) An English language summary of the Italian Web page Historical Notes from "Vinchiaturo On Line" as it existed in January of 1998. (That text has since been altered, and its title has been changed from Notizie storiche to Informazioni turistiche.) With four photographs of Vinchiaturo, one historical.
(4) Map of the Kingdom of Italy circa 1881, showing most of the cities and towns of Italy referred to by Michele Fuschino.
(5) Map of the Province of Campobasso as it has been since 1970, highlighting the townships of the province referred to by Michele Fuschino in his journal.
(6) Notes about the conventions followed in creating this transcription and translation of Michele Fuschino's journal.
(7) The Italian text of Giambattista Masciotta, Il Molise dalle origini ai nostri giorni, Volume II (Napoli, 1915), la monografia di Vinchiaturo ("Molise - From its Origins to Our Own Day", the chapter about Vinchiaturo).
Summary of Michele Fuschino's Journal
Michele Fuschino was a stone worker born in the village of Vinchiaturo in the Province of Molise, Italy. At the age of twenty in 1881 he was called up for compulsory national service in the corps of engineers of the Italian army. The diary begins with Michele's account of being torn away from his family in Campobasso. From there he is taken to public works projects in the north of Italy (King Umberto I inspects a bridge Michele's engineering unit builds). There is endless guard duty and there is endless telegraph wire to string in and around Verona, but then a tremendous fire destroys the mountain village of Rivai near the old Austrian border. Michele's journal ends with his account of the great 1883 earthquake at Casamicciola on the island of Ischia near Naples.
Copyright © 1998. The copyright to the original document from which this transcription and translation were made is held by Steven C. Petosa, who reserves all rights.
The translation was last modified on 17 October 1998 ; minor changes were made to Part V on 9 May 2001. Send Internet mail to Robert [Wesley] Angelo. Scrivetemi in italiano. También puede escribirme en español. | https://www.roangelo.net/journal/ |
In South Carolina, a person’s Will cannot be filed until after they have died. It is no longer a common practice for an attorney to keep a client’s original Will in their office. This can often lead to a lot of confusion if family members know the decedent had a Will but don’t know where to locate it. It can lead to even more confusion if the Will is located significantly after the estate is opened when the presumption was that one didn’t exist.
It is the client’s responsibility to keep and protect their original Will. There is no perfect solution for storing a Will because everyone’s situation is different. Some people are comfortable with others seeing their intentions, while others may consider this to be a very private document not to be viewed until after death.
You should always keep your original Will in a safe, secure place with your other important documents. Here are some important things to consider:
Fireproof Box or Safe
Placing your documents in a fireproof container in your home may be the best option. If you choose this option, make sure that at least one other person (preferably your personal representative) has the combination or key so that your documents can be accessed after your death.
It is helpful if this person is someone who does not live in the household, as members of the same household can often pass in a simultaneous accident. It is also important that someone who will likely disagree with the contents of your Will (for example a child who may be disinherited) does not have access, as they could potentially destroy the document after your death.
Safe Deposit Box
A safe deposit box is definitely secure, but it is important that you make arrangements for access after your death. For example, the person that is going to serve as your personal representative should be listed as someone with permission to access the box after your death or be provided a key.
It is equally important that others know this is where your Will is located. Without access or knowledge, a Will can be left ignored in a safe deposit box while the estate is probated.
Personal Representative
Some people choose to give the original Will to their personal representatives for safekeeping. If you are not comfortable doing this, consider giving them a copy with written directions describing the location of the original. You should also include any specific instructions they will need to obtain the Will.
Secure Your Will, Don’t Hide It
However you decide to store your original Will, be sure it is secure but not hidden. A Will that cannot be found cannot express your wishes, and your family will need to present your original Will to the Probate Court. There are ways a copy of a Will can be accepted by the Probate Court, but they will add time and expense to the procedure and are best avoided. Keep your original Will safe for the sake of your heirs.
To speak to an experienced estate planning lawyer at PMC Law Firm about your important legal matters, please give us a call today at (800) 914-0620 to set up your consultation. | https://www.pmclawfirm.com/legal-blogs/2020/june/where-to-store-your-last-will/ |
Centuries of mariners have plied the waters off North Carolina’s coast, harvesting its aquatic beasts, protecting or prowling the shore, and skirting or foundering on its dangerous shoals. As beautiful as North Carolina’s lighthouses are, they were built to perform a service of life-and-death importance. Today, the historic lights—some still in operation—are popular destinations for visitors. Most are open for climbing and offer fantastic views. The following are some of North Carolina’s favorites.
- Visitors willing to climb the 214 spiral steps to the top of Currituck Beach Lighthouse are treated to a dazzling view of Currituck Sound.
- Climb to the top of Bodie Island Lighthouse, which overlooks Lighthouse Bay and the Atlantic Ocean. This striking structure has been sending its signal out to sea since 1872, but was closed to the public until 2013.
- Cape Hatteras Lighthouse, the tallest brick lighthouse in the United States, has a black-and-white spiral exterior that makes it visible from miles away. Pay a small admission price to climb all the way to the top.
- Whale oil originally powered the beam of Ocracoke Lighthouse, the second-oldest working lighthouse in the United States. Because it’s still on duty, visitors can’t go inside, but there are lovely places to walk on the grounds.
- The black-and-white diamond-spangled Cape Lookout Lighthouse, one of the most iconic symbols of North Carolina, has stood watch since 1859. The nearby keeper’s quarters give an intriguing glimpse into the isolated and meditative life of the light keeper. While you’re there, explore Cape Lookout’s 56 miles of unspoiled beach, where you may have a close encounter with one of the Outer Banks’ famous wild horses.
- Commissioned by Thomas Jefferson and built in 1817, Old Baldy Lighthouse is North Carolina’s oldest lighthouse. From its strategic point on the southern coast of Bald Head Island, Old Baldy has seen has seen nearly two centuries of commerce, war, and peace.
Excerpted from the Fifth Edition of Moon North Carolina. | http://moon.com/2014/04/historic-lighthouses-of-north-carolina/ |
3 (10)m, Majestic Heaven Lotus is a tall shrub to medium sized evergreen tree from Colombia to Bolivia and adjacent areas with large, slightly glossy leaves and terminal whiite Lotus like flowers with pale rose petal tips. For any humus rich substrate in full sun to partial shade at a minimum of some 20°C throughout the year. Seeds are recalcitrant and will be shipped slightly moist. They have to be sown upon receipt. Sow in any rich, well draining substrate and keep pots at some 25°C in partial shade. Seeds are from plants grown in Europe and scarce. Each seed has a fibrous aril attached and has to be cleaned manually. For the work and time involved we will never offer larger quantities from Gustavia augusta.
|price (plus Shipping Costs)|
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There are currently no reviews of this product. | http://www.rareplants.de/shop/product.asp?P_ID=13543 |
The aftershock occurred at 3:06 p.m. in waters about 40 kilometers off the island's southwestern city of Seogwipo, near the epicenter of Tuesday's quake, according to the interior ministry and the Korea Meteorological Administration (KMA).
The agency said no damage was expected from the aftershock.
So far 15 aftershocks with magnitudes ranging between 1.3 and 1.7 occurred since Tuesday's quake took place at 5:19 p.m.
Tuesday's quake was the 11th strongest ever to strike on or off South Korea in terms of magnitude and the biggest to hit the island in history. The strongest one was a 5.8 magnitude quake that hit the southeastern city of Gyeongju on Sept. 12, 2016.
The interior ministry said it has received 173 reports about the tremor being felt in the country, with 114 from Jeju and 37 from South Jeolla Province. No deaths or injuries have been reported and four cases of minor property damage have been reported in Jeju.
The government was maintaining the disaster response readiness system at Level 1 against more potential aftershocks and damage reports.
Later in the day, another 2.3 magnitude earthquake hit near the southern county of Geochang, 225 kilometers south of Seoul.
The quake was reported at a region 15 kilometers northwest of Geochang, South Gyeongsang Province, at 10:02 p.m. at a depth of 10 kilometers, according to the agency. | |
---
abstract: 'We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. In this work we consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.'
author:
- Marco Tomamichel
- 'Vincent Y. F. Tan'
bibliography:
- 'library.bib'
title: |
Second-Order Asymptotics for the Classical\
Capacity of Image-Additive Quantum Channels
---
Introduction
============
One of the landmark achievements in quantum information theory is the establishing of the coding theorem for sending classical information across a noisy quantum channel by Holevo [@holevo98], and independently by Schumacher-Westmoreland [@schumacher97]—the so-called HSW theorem. The HSW theorem can be formally stated as follows: Let ${\mathcal{W}}^n$ denote the $n$-fold memoryless composition of the channel ${\mathcal{W}}$ and let $M^*({\mathcal{W}}^n,{\varepsilon})$ denote the maximum size of a length-$n$ block code for the channel ${\mathcal{W}}$ with average error probability ${\varepsilon}\in (0,1)$. Then, the HSW theorem, together with the weak converse established by Holevo [@holevo73b] in the 1970s (the Holevo bound), asserts that $$\begin{aligned}
\label{eq:holevo0}
C({\mathcal{W}}) := \lim_{{\varepsilon}\to 0} \liminf_{n\to\infty} \frac{1}{n}\log M^*({\mathcal{W}}^n,{\varepsilon}) = \lim_{n \to \infty} \frac{1}{n} \chi({\mathcal{W}}^{n}) ,\end{aligned}$$ where $\chi({\mathcal{W}})$ is the *Holevo capacity* of the channel. (We define all quantities precisely in the following.) Let us emphasize that the Holevo capacity is generally not additive [@hastings09], and we can thus not simplify the limit on the right hand side of without further assumptions.
However, for discrete classical-quantum (c-q) channels, the converse part of HSW theorem was strengthened significantly by Ogawa-Nagaoka [@ogawa99] and Winter [@winter99; @winterthesis] who proved the [*strong converse*]{} for discrete memoryless c-q channels, namely $$\begin{aligned}
\label{eq:sc-winter}
\lim_{n\to\infty} \frac{1}{n}\log M^*({\mathcal{W}}^n,{\varepsilon}) = \chi({\mathcal{W}}) = C({\mathcal{W}}),\quad\mbox{for all } {\varepsilon}\in (0,1).\end{aligned}$$ In the work by Ogawa-Nagaoka [@ogawa99], the strong converse was proved using ideas from Arimoto’s strong converse proof [@arimoto73] for classical channels, which itself was based on techniques to prove Gallager’s random coding error exponent [@gallager65]. Hence, Ogawa and Nagaoka’s proof [@ogawa99] also applies to c-q channels whose inputs are not necessarily discrete. Winter’s strong converse proof [@winter99], on the other hand, is based on the method of types [@csiszar98] which is a powerful tool developed in classical information theory for discrete memoryless systems. Winter then combines this method with a suitable discretization of the output space to show the strong converse for non-stationary channels [@winterthesis]. We also mention the work by Hayashi-Nagaoka [@hayashi03] in which a necessary and sufficient condition was provided for the strong converse property to hold for general (not only memoryless) c-q channels. More recently, Wilde-Winter-Yang [@wilde13] established that the strong converse, Eq. , also holds if ${\mathcal{W}}$ is an *entanglement-breaking* channel or a Hadamard channel. In particular, this shows that the Holevo capacity is additive for these channels.
In this work we focus our attention on channels ${\mathcal{W}}$ that are (tensor product) *image-additive* [@wolf14], namely quantum channels ${\mathcal{W}}$ that satisfy $$\begin{aligned}
\operatorname{im}({\mathcal{W}}^n) = \operatorname{conv}\big( \operatorname{im}({\mathcal{W}})^{\otimes n} \big) , \label{eq:im-add}
$$ where $\operatorname{im}({\mathcal{W}})$ denotes the image of the channel (i.e. the set of all quantum states that can be output by ${\mathcal{W}}$ if the input is a quantum state) and $\operatorname{conv}$ denotes the convex hull. This class of channels is a proper subset of the entanglement-breaking channels but strictly larger than c-q channels [@wolf14]. Finally, if we restrict the input to an arbitrary quantum channel to product states (or, more generally, separable states), then the respective channel images automatically satisfy .
We are interested in characterizing $M^*({\mathcal{W}}^n, {\varepsilon})$ for these channels beyond the strong converse statement in . This quantity represents the fundamental limit for the size of a codebook that allows transmission of classical information over $n$ uses of the quantum channel ${\mathcal{W}}$ up to an error ${\varepsilon}$. Notably such communication schemes generally require a joint measurement of $n$ quantum systems at the receiver’s terminal, which is technologically challenging even for moderate values of $n$. Thus, an asymptotic characterization for $n \to \infty$ as in seems insufficient. To this end, our goal here is to approximate $M^*({\mathcal{W}}^n, {\varepsilon})$ in terms of efficiently computable quantities for large but finite $n$.
For image-additive channels, the results of Wilde-Winter-Yang in fact imply that [@wilde13] $$\begin{aligned}
\log M^*({\mathcal{W}}^n,{\varepsilon}) = n C({\mathcal{W}})+ O(\sqrt{n}),\quad\mbox{for all } {\varepsilon}\in (0,1).\end{aligned}$$ Our present work refines the $O(\sqrt{n})$ term by identifying the implied constant in this remainder term as a function of ${\varepsilon}$ and a new channel parameter called the *dispersion* of the quantum channel. The resulting second-order approximation generalizes results for classical channels that go back to Strassen’s work in the 1962 [@strassen62]. In this seminal work, he showed for most well-behaved discrete classical channels $W:{\mathscr{X}}\to{\mathscr{Y}}$ that $$\begin{aligned}
\log M^*(W^n,{\varepsilon}) = nC(W) + \sqrt{nV_{\varepsilon}(W)}\,\Phi^{-1}({\varepsilon}) + O(\log n), \label{eqn:strass}\end{aligned}$$ where $C(W)$ is the Shannon capacity, $\Phi$ is the cumulative distribution function of a standard normal random variable, and $V_{\varepsilon}(W)$ is another fundamental property of the channel known as the ${\varepsilon}$-channel dispersion, a term coined by Polyanskiy [*et al.*]{} [@polyanskiy10]. Refinements to and extensions of the expansion of $\log M^*(W^n,{\varepsilon})$ were pursued by Hayashi [@hayashi09], Polyanskiy [*et al.*]{} [@polyanskiy10] and the present authors [@tomamicheltan12].[^1]
Main Contributions
------------------
In Section \[sec:pre\] we introduce the necessary concepts and definition required to formally state our main results, which we detail in Section \[sec:results\]. There are three main contributions in this paper:
1. It is a well-known fact that the capacity of a classical or c-q channel can be represented geometrically as the divergence radius of the channel image. In this paper, in the course of proving our main result, and especially the converse part, we leverage this fact heavily and refine the geometric interpretation of the Holevo capacity in Section \[sec:res-radius\].
2. We develop a one-shot converse bound on $M^*({\mathcal{W}}, {\varepsilon})$ in terms of the geometry of the image of the channel by employing a non-asymptotic quantity known as the [*${\varepsilon}$-hypothesis testing divergence radius*]{}. This is a one-shot analogue of the divergence radius that is commonly used to characterize the channel capacity. We find that such an approach allows to shift our attention from the input to the output space already in the non-asymptotic (one-shot) regime. Indeed, all the necessary calculations to yield the second-order approximation are done in the output space, thus allowing the input space to be arbitrary. This approach of working solely on the output space by employing a one-shot divergence radius to find the converse of the second-order approximation is new and does not have a classical analogue.
3. We then use this technique to refine the asymptotic expansion of $\log M^*({\mathcal{W}}^n,{\varepsilon})$ for c-q channels whose input alphabet is neither discrete nor otherwise structured. In fact our only requirement is that the image of the channel is comprised of quantum states on a finite-dimensional Hilbert space. We prove a quantum analogue of Strassen’s [@strassen62] refinement to the Shannon capacity in . This result is presented as Theorem \[th:main\] and discussed in Section \[sec:res-main\].
Finally, we show how our result for c-q channels with unstructured inputs can be adapted to yield an asymptotic expansion for all image-additive channels as well as the product state capacity of arbitrary quantum channels in Section \[sec:image-add\]
Because of the generality that is being afforded in our setup, several auxiliary technical results have to be developed either by modifying arguments from the literature or proving them from scratch. These results may be of independent interest in other contexts. First, we develop several alternative representations of the divergence radius that turn out to be amenable for computations involved in both the direct part and converse parts of the proof of our main theorem. Second, in the course of proving the direct part, we also show, by appealing to Caratheodory’s theorem, that it suffices to choose a finite input ensemble in order to achieve the second-order approximation. Third, for the converse part, to deal with ensembles of “bad” states that are not close to Holevo capacity-achieving, we construct an appropriate $\gamma$-net whose size can be controlled appropriately and whose elements serve to approximate those ensembles of “bad” states. (Notably, Winter [@winterthesis Thm. II.7] also employed a related idea to get beyond the assumption of discrete input alphabets.) Finally, we also prove several useful continuity properties of quantum information quantities. These allow us to establish that the third-order term in the Strassen-type asymptotic expansion in for c-q channels with discrete support is $O(\log n)$, as in the classical case.
Preliminaries {#sec:pre}
=============
We consider the real vector space of self-adjoint (Hermitian) operators on a finite-dimensional inner product (Hilbert) space. We denote the space of self-adjoint operators by ${\mathscr{H}}$ and keep it fixed throughout to ease notation. For $A, B \in {\mathscr{H}}$, we write $A \geq B$ iff $A - B$ is positive semi-definite. Moreover, we denote by $\{ A > B \}$ and $\{ A \geq B\}$ the projectors onto the positive and non-negative subspaces of $A - B$, respectively. We write $A \gg B$ to denote the fact that the kernel of $A$ is contained in the kernel of $B$. Let $\lambda_{\min}(A)$ denote the minimum eigenvalue of $A$. We equip ${\mathscr{H}}$ with a metric, the trace distance $\delta_{\operatorname{tr}}(A,B) := \frac12 \operatorname{tr}| A - B |$, where $\operatorname{tr}$ denotes the trace. The *identity operator* is denoted by ${\mathrm{id}}$. The set of *quantum states* is given by ${\mathscr{S}}:= \{ \rho \in {\mathscr{H}}\,|\, \rho \geq 0 \land \operatorname{tr}(\rho) = 1 \}$. Clearly, $({\mathscr{S}}, \delta_{\operatorname{tr}})$ is a compact metric space.
For any closed (and thus compact) subset ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$, we denote by ${\mathcal{P}}({{\mathscr{S}}_{\circ}})$ the set of probability measures on $({{\mathscr{S}}_{\circ}}, \Sigma_{\circ})$, where $\Sigma_{\circ}$ is the Borel $\sigma$-algebra on $({{\mathscr{S}}_{\circ}}, \delta_{\operatorname{tr}})$. Since $({{\mathscr{S}}_{\circ}}, \delta_{\operatorname{tr}})$ is a compact metric space, $\big({\mathcal{P}}({{\mathscr{S}}_{\circ}}), \delta_{\textrm{wc}}\big)$ is a compact metric space, where $\delta_{\textrm{wc}}$ denotes the Prohorov metric [@partha67 Sec. 6 and Thm. 6.4]. We will not use $\delta_{\textrm{wc}}$ explicitly but simply note that convergence in $\delta_{\textrm{wc}}$ is equivalent to weak convergence of probability measures. As such, any function of the form $$\begin{aligned}
{\mathcal{P}}({{\mathscr{S}}_{\circ}}) \to \mathbb{R}, \qquad {\mathbb{P}}\mapsto \int_{{{\mathscr{S}}_{\circ}}} {\textnormal{d}}{\mathbb{P}}(\rho) f(\rho) \end{aligned}$$ is continuous if $f$ is bounded and continuous. If ${{\mathscr{S}}_{\circ}}$ is discrete, we abuse notation and also use ${\mathcal{P}}({{\mathscr{S}}_{\circ}})$ to denote the set of probability mass functions on ${{\mathscr{S}}_{\circ}}$. We then use $P \in {\mathcal{P}}({{\mathscr{S}}_{\circ}})$ to denote its elements. We often use the abbreviations $\rho^{({\mathbb{P}})}$ and $\rho^{(P)}$ to denote the averaged states $$\begin{aligned}
\rho^{({\mathbb{P}})} := \int_{{{\mathscr{S}}_{\circ}}} {\textnormal{d}}{\mathbb{P}}(\rho)\rho \qquad \textrm{and} \qquad
\rho^{(P)} := \sum_{\rho \in {{\mathscr{S}}_{\circ}}} P(\rho)\rho .\end{aligned}$$
For any $n \in \mathbb{N}$, we also consider the $n$-fold products of the underlying inner-product space and denote the associated set of self-adjoint operators and states with ${\mathscr{H}}^n$ and ${\mathscr{S}}^n$, respectively. For any ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$, we denote by ${{\mathscr{S}}_{\circ}}^{\otimes n} \subseteq {\mathscr{S}}^n$ the set of $n$-tuples of states in ${{\mathscr{S}}_{\circ}}$, represented as a product state $\bigotimes_{i=1}^n \rho_i$, where $\rho_i \in {{\mathscr{S}}_{\circ}}$. Clearly, ${\mathscr{S}}^{\otimes n} \subseteq {\mathscr{S}}^n$.
We employ the cumulative distribution function of the standard normal distribution $$\begin{aligned}
\Phi(a) := \int_{-\infty}^a \frac{1}{\sqrt{2 \pi}} \exp \Big(-\frac12 x^2\Big) \,\mathrm{d}x\end{aligned}$$ and define its inverse as $\Phi^{-1}({\varepsilon}) := \sup \{ a \in \mathbb{R} \,|\, \Phi(a) \leq {\varepsilon}\}$, which reduces to the usual inverse for $0 < {\varepsilon}< 1$ and extends to take values $\pm \infty$ outside that range.
Codes for Classical-Quantum Channels
------------------------------------
We consider general c-q channels, i.e. arbitrary functions ${\mathcal{W}}: {\mathscr{X}}\to {\mathscr{S}}$, where ${\mathscr{X}}$ is an arbitrary set. A special case of this is a quantum channel, namely a completely positive trace-preserving (CPTP) map ${\mathcal{W}}: {\mathscr{S}}' \to {\mathscr{S}}$, where ${\mathscr{S}}'$ denotes a set of quantum states. We denote the image of the channel by $$\begin{aligned}
\operatorname{im}({\mathcal{W}}) := \{ \rho \in {\mathscr{S}}\,|\, \exists\, x \in {\mathscr{X}}: \rho = {\mathcal{W}}(x) \} ,
\end{aligned}$$ and its closure by $\overline{\operatorname{im}({\mathcal{W}})}$. Without loss of generality, we may assume that $\operatorname{im}({\mathcal{W}})$ has full support on the underlying Hilbert space, i.e. every vector (of the underlying Hilbert space) is supported by at least one element in $\operatorname{im}({\mathcal{W}})$. Thus, we will usually set $d = |\operatorname{supp}(\operatorname{im}({\mathcal{W}}))|$.
A [*code*]{} ${\mathcal{C}}$ for ${\mathcal{W}}$ is defined by the triple $\{{\mathscr{M}}, e, {\mathcal{D}}\}$, where ${\mathscr{M}}$ is a (discrete) set of messages, $e: {\mathscr{M}}\to {\mathscr{X}}$ an encoding function and ${\mathcal{D}}= \{ Q_m \}_{m \in {\mathscr{M}}}$ is a positive operator valued measure (POVM).[^2] We write ${|{\mathcal{C}}|} = {|{\mathscr{M}}|}$ for the cardinality of the message set. We define the *average error probability* of a code ${\mathcal{C}}$ for the channel ${\mathcal{W}}$ as $$\begin{aligned}
{p_{\textrm{err}}}({\mathcal{C}},{\mathcal{W}}):= 1-\frac{1}{ |{\mathscr{M}}|}\sum_{m\in{\mathscr{M}}} \operatorname{tr}\big( {\mathcal{W}}(e(m)) Q_{m} \big)\end{aligned}$$ where the distribution over messages $M$ is assumed to be uniform on ${\mathscr{M}}$. Alternatively, we may write ${p_{\textrm{err}}}({\mathcal{C}},{\mathcal{W}}) = \Pr[M \neq M']$ where $$\begin{aligned}
M \xrightarrow{\ e\ } X \xrightarrow{\ {\mathcal{W}}\ } {\mathcal{W}}(X) \xrightarrow{\ {\mathcal{D}}\ } M'\end{aligned}$$ forms a Markov chain, ${\mathcal{W}}(X)$ denotes the (random) output of the channel, and $M'$ thus denotes the output of the decoder.
To characterize the non-asymptotic fundamental limit of data transmission over a single use of the channel, we define the *maximum size of a codebook for ${\mathcal{W}}$ with average error ${\varepsilon}$* as $$\begin{aligned}
M^*({\mathcal{W}},{\varepsilon}) := \max \big\{ m \in \mathbb{N} \,\big|\, \exists\, {\mathcal{C}}:\ {|{\mathcal{C}}|} = m \ \land\ {p_{\textrm{err}}}({\mathcal{C}}, {\mathcal{W}}) \leq {\varepsilon}\big\} .\end{aligned}$$ We are interested to evaluate this quantity for the composite channel ${\mathcal{W}}^n$, corresponding to $n \geq 1$ uses of a memoryless channel ${\mathcal{W}}$. Formally, the $n$-fold i.i.d. repetition of the channel, ${\mathcal{W}}^n: {\mathscr{X}}^n\to {\mathscr{S}}^{\otimes n}$, takes as input a vector ${\textnormal{\textit{\textbf{x}}}} =( x_1,x_2, \ldots , x_n) \in {\mathscr{X}}^n$ and maps it to ${\mathcal{W}}(x_1) \otimes {\mathcal{W}}(x_2) \otimes \ldots \otimes {\mathcal{W}}(x_n) \in {\mathscr{S}}^{\otimes n}$. In particular, this model does not allow for entangled channel outputs. The non-asymptotic fundamental limit of data transmission over $n$ uses of the channel is consequently given by $M^*({\mathcal{W}}^n,{\varepsilon})$.
Information Quantities
----------------------
The following basic quantities are of interest here. For any $\rho \in {\mathscr{S}}$, we employ the von Neumann entropy $H(\rho) := - \operatorname{tr}(\rho \log \rho)$. Moreover, for positive semi-definite $\sigma$ satisfying $\sigma \gg \rho$, the *relative entropy* [@umegaki62; @hiai91] and the *relative entropy variance* [@tomamichel12; @li12] are respectively defined as $$\begin{aligned}
D(\rho\|\sigma) &:= \operatorname{tr}\Big( \rho \big( \log \rho - \log \sigma \big) \Big) \qquad \textrm{and}\\
V(\rho\|\sigma) &:= \operatorname{tr}\Big( \rho \big( \log \rho - \log \sigma - D(\rho\|\sigma)\cdot {\mathrm{id}}\big)^2 \Big) \,.\end{aligned}$$ As usual, we implicitly use the convention $0 \log^k 0 \equiv 0$ for all $k \in \mathbb{N}$.
Classically, for two probability mass functions $P, Q \in {\mathcal{P}}({\mathscr{X}})$, the relative entropy $D(P\|Q)$ is the expectation value of the log-likelihood ratio $\log \big( P(X)/Q(X)\big)$ where $X \leftarrow P$, and $V(P\|Q)$ is the corresponding variance. The above definition of $V(\rho\|\sigma)$ is thus a natural non-commutative generalization of the classical concept, with its operational meaning firmly established in [@tomamichel12; @li12].
We summarize some properties of the above quantities, which we will employ later.
1. $\rho \mapsto H(\rho)$ is strictly concave (cf., e.g., Lemma \[lm:strict\]) and continuous.
2. $(\rho,\sigma) \mapsto D(\rho\|\sigma)$ is jointly convex and lower semi-continuous. In fact, it is continuous except when it diverges to infinity, i.e. when $\sigma \not\gg \rho$.
3. $D(\rho\|\sigma)$ is positive definite, i.e. $D(\rho\|\sigma) \geq 0$ with equality iff $\rho = \sigma$.
4. $(\rho,\sigma) \mapsto V(\rho\|\sigma)$ is continuous except when $\sigma \not\gg \rho$.
Finally, in order to express the one-shot bounds, we introduce the *${\varepsilon}$-hypothesis-testing divergence* [@wang10]. For any ${\varepsilon}\in (0,1)$ and $\rho, \sigma \in {\mathscr{S}}$, it is defined as $$\begin{aligned}
D_h^{{\varepsilon}}(\rho\|\sigma) := - \log \frac{\beta_{1-{\varepsilon}}(\rho\|\sigma)}{1-{\varepsilon}}, \qquad \textrm{where} \quad \beta_{1-{\varepsilon}}(\rho\|\sigma) := \min_{0 \leq Q \leq {\mathrm{id}}\atop \operatorname{tr}(Q \rho) \geq 1-{\varepsilon}} \operatorname{tr}(Q \sigma) \,. \label{eq:defhypo}\end{aligned}$$ Note that $\beta_{1-{\varepsilon}}$ is the smallest type-II error of a hypothesis test between $\rho$ and $\sigma$ with type-I error at most ${\varepsilon}$. The ${\varepsilon}$-hypothesis testing divergence satisfies the following basic properties, which we summarize here for later reference.
\[lm:hypo-prop\] Let ${\varepsilon}\in (0,1)$, let ${{\mathscr{S}}_{\circ}},{{\mathscr{S}}_{\circ}}' \subseteq {\mathscr{S}}$ be discrete sets, and let $P \in {\mathcal{P}}({{\mathscr{S}}_{\circ}})$, $Q \in{\mathcal{P}}({{\mathscr{S}}_{\circ}}')$. Define $\rho = \sum_{\tau \in {{\mathscr{S}}_{\circ}}} P(\tau) \tau$ and $\sigma = \sum_{\omega \in {{\mathscr{S}}_{\circ}}'} Q(\omega) \omega$. Then $D_h^{{\varepsilon}}(\rho\|\sigma)$ satisfies the following properties:
1. $D_h^{{\varepsilon}}(\rho\|\sigma) \geq 0$ with equality if and only if $\rho = \sigma$. *(cf. [@dupuis12 Prop. 3.2])*
2. For any CPTP map $\mathcal{M}$ we have $D_h^{{\varepsilon}}(\rho\|\sigma) \geq D_h^{{\varepsilon}}\big(\mathcal{M}(\rho) \big\| \mathcal{M}(\sigma) \big)$. *(cf. [@wang10])*
3. $D_h^{{\varepsilon}}(\rho\|\sigma) \leq \min_{\omega \in {{\mathscr{S}}_{\circ}}'} \big\{ D_h^{{\varepsilon}}(\rho\|\omega) + \log \frac{1}{Q(\omega)} \big\}$.
4. $D_h^{{\varepsilon}}(\rho\|\sigma) \leq \max_{\tau \in {{\mathscr{S}}_{\circ}}} D_h^{{\varepsilon}}(\tau\|\sigma)$.
The last inequality shows that $\rho \mapsto D_h^{{\varepsilon}}(\rho \| \sigma)$ is quasi-convex. The last two inequalities can be verified by a close inspection of the definition in and we omit the proof.
Main Results {#sec:results}
============
The Divergence Radius of a Set of Quantum States {#sec:res-radius}
------------------------------------------------
It is well known that the capacity of a classical or classical-quantum channel can be represented geometrically as the divergence radius of the channel image. (For the quantum case, see, e.g. [@ohya97] and [@schumacher01].) Here, we take a complementary approach and investigate the divergence radius of subsets of the set of quantum states. If such a set is the image of a channel, our analysis allows us to construct capacity-achieving ensembles by just looking at the channel image. Furthermore, this viewpoint leads to a natural quantum generalization of the concept of channel dispersion. Thus, somewhat surprisingly, we will see that not only the capacity but also the finite blocklength behavior of channels is governed by the geometry of the channel image.
### Divergence Radius
Let us start by investigating the divergence radius of arbitrary closed subsets of the set of quantum states on a finite-dimensional Hilbert space.
\[def:radius\] Let ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ be closed. The *divergence radius* of ${{\mathscr{S}}_{\circ}}$ (in ${\mathscr{S}}$) is defined as $$\begin{aligned}
\chi({{\mathscr{S}}_{\circ}}) := \inf_{\sigma \in {\mathscr{S}}} \sup_{\rho \in {{\mathscr{S}}_{\circ}}} D(\rho\|\sigma) \,. \label{eq:dr}\end{aligned}$$
We show the following properties of the divergence radius.
\[th:radius\] Let ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ be closed. We find the following:
1. The *divergence center*, defined as $\sigma^*({{\mathscr{S}}_{\circ}}) := \operatorname*{\arg\min}_{\sigma \in {\mathscr{S}}} \big\{ \sup_{\rho \in {{\mathscr{S}}_{\circ}}} D(\rho\|\sigma) \big\}$, exists and is unique. Moreover, $\sigma^*({{\mathscr{S}}_{\circ}}) \gg \rho$ for all $\rho \in {{\mathscr{S}}_{\circ}}$.
2. Define the set of *peripheral points* of ${{\mathscr{S}}_{\circ}}$, i.e. $$\begin{aligned}
\label{eq:gamma}
\Gamma({{\mathscr{S}}_{\circ}}) := \operatorname*{\arg\max}_{\rho \in {{\mathscr{S}}_{\circ}}} D\big(\rho \big\|\sigma^*({{\mathscr{S}}_{\circ}}) \big) .
\end{aligned}$$ Then, $D\big(\rho \big\|\sigma^*({{\mathscr{S}}_{\circ}}) \big) \leq \chi({{\mathscr{S}}_{\circ}})$ for all $\rho \in {{\mathscr{S}}_{\circ}}$ with equality iff $\rho \in \Gamma({{\mathscr{S}}_{\circ}})$.
3. We have $\sigma^*({{\mathscr{S}}_{\circ}}) \in \operatorname{conv}(\Gamma({{\mathscr{S}}_{\circ}}))$.
4. The divergence radius has the following alternative representation: $$\begin{aligned}
\label{eq:holevo}
\chi({{\mathscr{S}}_{\circ}}) = \sup_{{\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}})} \int {\textnormal{d}}{\mathbb{P}}(\rho)\, D\bigg(\rho\,\bigg\|\, \int {\textnormal{d}}{\mathbb{P}}(\rho') \rho' \bigg) .
\end{aligned}$$
5. The set of probability measures that achieve the supremum is given by the *peripheral decompositions of the divergence center*, namely the compact convex set $$\begin{aligned}
\Pi({{\mathscr{S}}_{\circ}}) := \bigg\{ {\mathbb{P}}\in {\mathcal{P}}\big(\Gamma({{\mathscr{S}}_{\circ}})\big) \,\bigg|\, \int {\textnormal{d}}{\mathbb{P}}(\rho) \rho = \sigma^*({{\mathscr{S}}_{\circ}}) \bigg\} . \label{eq:pi}
\end{aligned}$$ Moreover, $\Pi({{\mathscr{S}}_{\circ}})$ contains a discrete probability measure with support on at most $d^2$ points in $\Gamma({{\mathscr{S}}_{\circ}})$.
The proof of this theorem is presented in Section \[sec:radius\] and we illustrate it in Figure \[fig:radius\].
Uniqueness of $\sigma^*({{\mathscr{S}}_{\circ}})$ was also claimed by Ohya, Petz and Watanabe [@ohya97 Lem. 3.4] in a related context. However, they argue that this directly follows from the “fact that the relative entropy functional is strictly convex in the second variable”. We submit that more care has to be taken to establish uniqueness. Notably, the functional $\sigma \mapsto D(\rho\|\sigma)$ is only strictly convex if $\rho > 0$ is positive definite and trivial counterexamples can be constructed otherwise. It is then unclear how to apply this property directly to the situation at hand.
[continuous\_set.pdf]{} (51,43)[$\sigma^*$]{} (30,65)[${{\mathscr{S}}_{\circ}}$]{} (100,24)[$\Gamma$]{} (88,58)[$\Gamma$]{} (2,59)[$\Gamma$]{} (6,21)[$\Gamma$]{} (35,23)[$\operatorname{conv}(\Gamma)$]{}
[discrete\_set.pdf]{} (51,43)[$\sigma^*$]{} (100,24)[$\Gamma$]{} (90,58)[$\Gamma$]{} (2,59)[$\Gamma$]{} (4,21)[$\Gamma$]{} (30,25)[$\operatorname{conv}(\Gamma)$]{}
Property 3 is of particular importance for our argument and has not been shown before. A weaker property, namely $\sigma^*({{\mathscr{S}}_{\circ}}) \in \operatorname{conv}({{\mathscr{S}}_{\circ}})$ was already pointed out in [@ohya97 Lem. 3.4]. However, our stronger Property 3 implies that $\sigma^*({{\mathscr{S}}_{\circ}})$ can be written as a convex combination of states in $\Gamma({{\mathscr{S}}_{\circ}})$, i.e. $\sigma^*({{\mathscr{S}}_{\circ}}) = \rho^{({\mathbb{P}})}$ for some ${\mathbb{P}}\in {\mathcal{P}}(\Gamma({{\mathscr{S}}_{\circ}}))$. If ${{\mathscr{S}}_{\circ}}$ is the image of a quantum channel ${\mathcal{W}}$, we write ${\mathcal{W}}^{-1}(\Gamma({{\mathscr{S}}_{\circ}}))$ to denote any pre-image of $\Gamma({{\mathscr{S}}_{\circ}})$. Then, the tuple $\{{\mathbb{P}}, {\mathcal{W}}^{-1}(\Gamma({{\mathscr{S}}_{\circ}}))\}$ corresponds to an optimal ensemble of input states, i.e. an ensemble that achieves the maximum Holevo information. In particular, $\Pi({{\mathscr{S}}_{\circ}})$ as defined in is non-empty.
It is natural to see as the dual problem (cf. [@boyd04]) to the convex optimization problem in ; in particular, the integral in is concave in ${\mathbb{P}}$. As such implies strong duality.[^3]
### Peripheral Information Variance
The above observations allow us to define the minimal and maximal peripheral information variance of ${{\mathscr{S}}_{\circ}}$ in terms of the information variance of peripheral decompositions of the divergence center. To do so, we consider measures ${\mathbb{P}}\in \Pi({{\mathscr{S}}_{\circ}})$ and optimize $$\begin{aligned}
V({\mathbb{P}}|\sigma^*({{\mathscr{S}}_{\circ}})), \qquad \textrm{where} \quad V({\mathbb{P}}|\sigma) := \int {\textnormal{d}}{\mathbb{P}}(\rho)\, V( \rho \big\| \sigma) \,.\end{aligned}$$ is the *conditional information variance*. This leads to the following definitions.
Let ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ be closed and $\Pi({{\mathscr{S}}_{\circ}})$ defined in . Then, the *minimal and maximal peripheral information variance* of ${{\mathscr{S}}_{\circ}}$ (in ${\mathscr{S}}$) are respectively defined as $$\begin{aligned}
v_{\min}({{\mathscr{S}}_{\circ}}) &:= \inf_{{\mathbb{P}}\in \Pi({{\mathscr{S}}_{\circ}})} V\big({\mathbb{P}}\big|\sigma^*({{\mathscr{S}}_{\circ}})\big) = \inf_{{\mathbb{P}}\in \Pi({{\mathscr{S}}_{\circ}})} \int {\textnormal{d}}{\mathbb{P}}(\rho)\, V\big( \rho \big\| \sigma^*({{\mathscr{S}}_{\circ}}) \big), \qquad \textrm{and} \label{eq:vmin}\\
v_{\max}({{\mathscr{S}}_{\circ}}) &:= \sup_{{\mathbb{P}}\in \Pi({{\mathscr{S}}_{\circ}})} V\big({\mathbb{P}}\big|\sigma^*({{\mathscr{S}}_{\circ}})\big)= \sup_{{\mathbb{P}}\in \Pi({{\mathscr{S}}_{\circ}})}\int {\textnormal{d}}{\mathbb{P}}(\rho)\, V\big( \rho \big\| \sigma^*({{\mathscr{S}}_{\circ}}) \big) .\label{eq:vmax}
\end{aligned}$$
It is evident from the compactness of $\Pi({{\mathscr{S}}_{\circ}})$ that the infimum and supremum are achieved so we may replace $\inf$ and $\sup$ with $\min$ and $\max$, respectively. Moreover, the minimum in Eq. is achieved for a probability measure ${\mathbb{P}}\in {\mathcal{P}}(\Gamma({{\mathscr{S}}_{\circ}}))$ that satisfies the linear constraints $$\begin{aligned}
&\int {\textnormal{d}}{\mathbb{P}}(\rho) \rho = \sigma^*({{\mathscr{S}}_{\circ}}) \quad \textrm{and} \quad \int {\textnormal{d}}{\mathbb{P}}(\rho)\,V\big(\rho\big\|\sigma^*({{\mathscr{S}}_{\circ}})\big) = v_{\min}({{\mathscr{S}}_{\circ}}).\end{aligned}$$ These constitute $d^2-1$ real constraints for the first equality and one additional constraint for the second one. Since $\Gamma({{\mathscr{S}}_{\circ}})$ is not connected in general, Caratheodory’s theorem (see, e.g., [@eggleston58 Thm. 18]) yields the following lemma:
\[lm:cara\] There exist discrete probability measures with support on at most $d^2+1$ points in $\Gamma({{\mathscr{S}}_{\circ}})$ that achieve the infimum and supremum in and , respectively.
Second-Order Approximation for the Classical Capacity {#sec:res-main}
-----------------------------------------------------
### Capacity of Classical-Quantum Channels
Our main result is the evaluation of the second-order asymptotics for the capacity of c-q channels with general input. (Recall that we consider general channels ${\mathcal{W}}: {\mathscr{X}}\to {\mathscr{S}}$, where ${\mathscr{X}}$ is an arbitrary set[^4] and ${\mathscr{S}}$ is the set of quantum states on an arbitrary finite-dimensional Hilbert space.)
\[th:main\] Let ${\varepsilon}\in (0,1)$ and ${\mathcal{W}}$ be a c-q channel. Setting ${{\mathscr{S}}_{\circ}}= \overline{\operatorname{im}({\mathcal{W}})}$, we find $$\begin{aligned}
&\log M^*({\mathcal{W}}^n, {\varepsilon}) = n\, C({\mathcal{W}}) + \sqrt{n\, V_{{\varepsilon}}({\mathcal{W}})}\, \Phi^{-1}({\varepsilon}) + K(n, {{\mathscr{S}}_{\circ}}, {\varepsilon}), \quad \textrm{where} \\
&\qquad \quad C({\mathcal{W}}) = \chi({{\mathscr{S}}_{\circ}}) \quad \textrm{and} \quad V_{{\varepsilon}}({\mathcal{W}}) = v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) := \begin{cases} v_{\min}({{\mathscr{S}}_{\circ}}) & \textrm{if }\ 0 < {\varepsilon}\leq \frac12 \\
v_{\max}({{\mathscr{S}}_{\circ}}) & \textrm{if }\ \frac12 < {\varepsilon}< 1 \end{cases} .
\end{aligned}$$ We have $K(n, {{\mathscr{S}}_{\circ}}, {\varepsilon}) = o(\sqrt{n})$ for all channels. Moreover, if ${{\mathscr{S}}_{\circ}}$ is finite and $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) > 0$, we have $K(n, {{\mathscr{S}}_{\circ}}, {\varepsilon}) = O(\log n)$.
The *${\varepsilon}$-channel dispersion* is an operational quantity defined as [@polyanskiy10 Eq. (221)] $$\begin{aligned}
V_{{\varepsilon}}({\mathcal{W}}) := \limsup_{n\to\infty} \frac{1}{n} \bigg( \frac{n C({\mathcal{W}}) - \log M^*({\mathcal{W}}^n, {\varepsilon})}{\Phi^{-1}({\varepsilon})} \bigg)^2 .
\end{aligned}$$ Our results imply that it equals $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})$, the minimal or maximal peripheral information variance of the channel image, depending on the value of ${\varepsilon}$.
Traditionally, classical-quantum channels are studied for the case when ${\mathscr{X}}$ is discrete. In our framework, this corresponds to a discrete set ${{\mathscr{S}}_{\circ}}= \{ {\mathcal{W}}(x) \,|\, x \in {\mathscr{X}}\}$.
Some restrictions on ${{\mathscr{S}}_{\circ}}$ are necessary in order to show that $K(n, {{\mathscr{S}}_{\circ}},{\varepsilon}) = O(\log n)$. Indeed, there exists a class of classical discrete memoryless channels, so-called exotic channels [@polyanskiy10 p. 2231 and App. H], for which $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) = 0$ and $K(n, {{\mathscr{S}}_{\circ}}, {\varepsilon}) = \Theta(n^{1/3})$ hold [@polyanskiythesis10 Thm. 51].
We sketch the main ideas and outline of our proof in the following.
#### Summary of the Proof of the Direct Part:
The direct part of Theorem \[th:main\], established in Section \[sec:direct\], is derived employing a one-shot bound due to Wang and Renner that relates $M^*({\mathcal{W}}^n, {\varepsilon})$ with the ${\varepsilon}$-hypothesis-testing divergence, $D_h^{{\varepsilon}}(\cdot\|\cdot)$, defined in above. The bound is valid for classical-quantum channels with finite input alphabets and the asymptotics are derived in this setting based upon the second-order asymptotics of the hypothesis testing divergence evaluated on i.i.d. states established in [@li12] and [@tomamichel12]. Finally, a simple application of Caratheodory’s theorem (Lemma \[lm:cara\]) shows that it is possible to achieve the second-order asymptotics with finite alphabets (of size depending on the dimension of the output space).
#### Summary of the Proof of the Converse Part:
The converse part of Theorem \[th:main\] is proved in Sections \[sec:proof/one-shot-converse\]–\[sec:converse\]. The proof employes a one-shot analogue of the divergence radius in Definition \[def:radius\].
Let ${\varepsilon}\in (0,1)$ and ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$. The ${\varepsilon}$-*hypothesis-testing divergence radius* is defined as $$\begin{aligned}
\chi_h^{{\varepsilon}}({{\mathscr{S}}_{\circ}}) := \inf_{\sigma \in {\mathscr{S}}} \sup_{\rho \in {{\mathscr{S}}_{\circ}}} D_h^{{\varepsilon}}(\rho\|\sigma) .\end{aligned}$$
This quantity, evaluated for the channel image, constitutes an upper bound on $M^*({\mathcal{W}}, {\varepsilon})$ for c-q channels with general input. In Section \[sec:proof/one-shot-converse\], we establish the following one-shot converse bound:
\[pr:one-shot-converse\] Let ${\varepsilon}\in (0,1)$ and let ${\mathcal{W}}$ be a c-q channel. For any $\mu \in (0, 1-{\varepsilon})$, we have $$\begin{aligned}
\log M^*({\mathcal{W}},{\varepsilon}) \leq \chi_h^{{\varepsilon}+\mu}\Big(\overline{\operatorname{im}({\mathcal{W}})}\Big) + \log \frac{{\varepsilon}+\mu}{\mu(1-{\varepsilon}-\mu)} . \label{eq:conv}
\end{aligned}$$
This bound should be compared to the bounds by Renner-Wang [@wang10] and Matthews-Wehner [@matthews12]. Both of these works also establish one-shot converse bounds in terms of the ${\varepsilon}$-hypothesis testing divergence (see also [@hayashi03 Remark 15]). However, our result crucially differs in that our bound only depends on the image of the channel, independently of the input alphabet supported by the channel. It thus allows us to treat the remaining evaluation as a problem on the output space.
Applied to the $n$-fold memoryless repetition of the c-q channel ${\mathcal{W}}$, it yields $$\begin{aligned}
\log M^*({\mathcal{W}}^n,{\varepsilon}) \leq \chi_h^{{\varepsilon}+\mu}({{\mathscr{S}}_{\circ}}^{\otimes n}) + O(\log n) . \label{eq:sketch1}\end{aligned}$$ where $\mu$ is chosen inversely polynomial in $n$. Proposition \[pr:thedifficultpart\] in Section \[sec:converse\], then establishes that $$\begin{aligned}
\chi_h^{{\varepsilon}+\mu}\big({{\mathscr{S}}_{\circ}}^{\otimes n}\big) \leq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\, \Phi^{-1}({\varepsilon}) + o(\sqrt{n}) \label{eq:sketch2}\,,\end{aligned}$$ which, combined with , concludes the proof.
This asymptotic expansion in constitutes the technically most challenging part of our derivation. To evaluate these asymptotics for a suitable choice of $\sigma^n$ we extend the second-order approximation of [@tomamichel12] to non-identical product distributions. Moreover, we show that these bounds hold uniformly in all sequences $\rho^n = \bigotimes_{i=1}^n \rho_i \in {{\mathscr{S}}_{\circ}}^{\otimes n}$ that appear in the supremum above. This is particularly challenging because we have to treat separately sequences for which the average relative entropy variance is small, and hence the convergence to the second-order approximation is too slow.[^5] To tackle this, we employ a net on ${{\mathscr{S}}_{\circ}}$ and in particular do not appeal to the use of constant composition codes and type-counting arguments, which are workhorses of the second-order analysis for discrete memoryless channels in the classical setting. Our novel proof thus departs from the usual treatment, which in particular allows us to consider general input alphabets.
### Classical Capacity for Image-Additive Quantum Channels {#sec:image-add}
First, note that the achievability bounds in Theorem \[th:main\] in fact apply for the classical capacity of all quantum channels, and can be achieved using product states. To see this, let ${\mathscr{X}}$ be a set of quantum states (whether the states in ${\mathscr{X}}$ are modeled as density operators on a Hilbert space or states of a C\* algebra is irrelevant here) and ${\mathcal{W}}$ be the quantum channel from ${\mathscr{X}}$ to ${\mathscr{S}}$, as usual. Obviously the channel is now a completely positive trace-preserving map, but we do not need to use this structure here and focus again on its image, ${{\mathscr{S}}_{\circ}}= \operatorname{im}({\mathcal{W}})$, where closure is now unnecessary since the image is compact. Thus, for all quantum channels ${\mathcal{W}}$, we have[^6] $$\begin{aligned}
&\log M^*({\mathcal{W}}^n, {\varepsilon}) \geq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\, \Phi^{-1}({\varepsilon}) + o(\sqrt{n}) \,.\end{aligned}$$
Moreover, the converse part of the proof of Theorem \[th:main\] can be easily adapted to cover general image-additive quantum channels. The logarithm of the maximum codebook size of a quantum channel is certainly also upper bounded by $\chi_h^{{\varepsilon}}({{\mathscr{S}}_{\circ}})$ as in , so in particular we find $$\begin{aligned}
\log M^*({\mathcal{W}}^n,{\varepsilon}) \leq \chi_h^{{\varepsilon}+\mu}({{\mathscr{S}}_{\circ}}^n) + \log \frac{{\varepsilon}+\mu}{\mu(1-{\varepsilon}-\mu)} , \qquad \textrm{where} \quad {{\mathscr{S}}_{\circ}}^n = {\operatorname{im}({\mathcal{W}}^n)} \,.\end{aligned}$$
However, the crucial difference vis-à-vis classical-quantum channels is that here we generally have ${{\mathscr{S}}_{\circ}}^n \neq {{\mathscr{S}}_{\circ}}^{\otimes n}$ as the channel image can be enlarged in the presence of non-product input states. Restricting to image-additive channels ${\mathcal{W}}$, however, we find $$\begin{aligned}
{{\mathscr{S}}_{\circ}}^n = {\operatorname{im}({\mathcal{W}}^n)} = { \operatorname{conv}(\operatorname{im}({\mathcal{W}})^{\otimes n}) } = \operatorname{conv}({{\mathscr{S}}_{\circ}}^{\otimes n})\end{aligned}$$ Now the only missing observation is that $\chi_h^{{\varepsilon}}(\operatorname{conv}({{\mathscr{S}}_{\circ}}^{\otimes n})) = \chi_h^{{\varepsilon}}({{\mathscr{S}}_{\circ}}^{\otimes n})$ for all ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$, which is an immediate consequence of the quasi-convexity of $\rho \mapsto D_h^{{\varepsilon}}(\rho\|\sigma)$, shown in Part 4 of Lemma \[lm:hypo-prop\]. Hence, Proposition \[pr:thedifficultpart\] directly applies to this situation as well and we arrive at the following corollary:
Let ${\varepsilon}\in (0,1)$ and ${\mathcal{W}}$ be an image-additive quantum channel. Then, $$\begin{aligned}
&\log M^*({\mathcal{W}}^n, {\varepsilon}) = n\, C({\mathcal{W}}) + \sqrt{n\, V_{{\varepsilon}}({\mathcal{W}})}\, \Phi^{-1}({\varepsilon}) + o(\sqrt{n}) \end{aligned}$$ with $C({\mathcal{W}})$ and $V_{{\varepsilon}}({\mathcal{W}})$ as defined in Theorem \[th:main\].
Similarly, if the input of the channel is restricted to separable states then clearly the restricted image satisfies $\operatorname{im}_{\textrm{sep}}({\mathcal{W}}^n) = \operatorname{conv}(\operatorname{im}({\mathcal{W}})^{\otimes n})$ and thus Proposition \[pr:thedifficultpart\] again suffices to determine the second-order asymptotics.[^7]
\[cor:qq\] Let ${\varepsilon}\in (0,1)$, let ${\mathcal{W}}$ be any quantum channel. Let $M_{\textrm{sep}}^*({\mathcal{W}}^n, {\varepsilon})$ denote the maximum size of a codebook for classical information transmission over ${\mathcal{W}}$ with average error ${\varepsilon}$ when the channel is restricted to separable input states. Then, $$\begin{aligned}
\log M_{\textrm{sep}}^*({\mathcal{W}}^n, {\varepsilon}) = n\, C({\mathcal{W}}) + \sqrt{n\, V_{{\varepsilon}}({\mathcal{W}})}\, \Phi^{-1}({\varepsilon}) + o(\sqrt{n}) , \label{eq:cor}
\end{aligned}$$ with $C({\mathcal{W}})$ and $V_{{\varepsilon}}({\mathcal{W}})$ as defined in Theorem \[th:main\].
Qubit Pauli channels are symmetric under reflection at the center of the Bloch sphere. As such, $\sigma^*({{\mathscr{S}}_{\circ}}) = \frac12 {\mathrm{id}}$ and it is furthermore easy to verify that any capacity-achieving ensemble (of minimal size) is commutative. Hence, the capacity and dispersion of a Pauli channel equal those of a (classical) binary symmetric channel (see, e.g., [@polyanskiy10 Thm. 52]).
The amplitude damping channel with magnitude $\gamma$ is given as $$\begin{aligned}
{\mathcal{E}}_{\textrm{ad}}^{\gamma}: \rho \mapsto \left( \begin{array}{cc} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{array} \right) \rho \left( \begin{array}{cc} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{array} \right) + \left( \begin{array}{cc} 0 & \sqrt{\gamma} \\ 0 & 0 \end{array} \right) \rho \left( \begin{array}{cc} 0 & 0 \\ \sqrt{\gamma} & 0 \end{array} \right) .\end{aligned}$$ Its channel image, ${{\mathscr{S}}_{\circ}}^{\gamma} = \operatorname{im}({\mathcal{E}}_{\textrm{ad}}^{\gamma})$, is displayed in Figure \[fig:ad1\]. In Fig. \[fig:ad2\], the channel capacity and dispersion are evaluated numerically for different values of $\gamma$. The second-order approximation, i.e. the first two terms on the right-hand side of are plotted as a function of $n$ in Figure \[fig:ad3\].
It was already noted in [@schumacher01 Fig. 1] that it is necessary to consider non-orthogonal input states to achieve $\chi({{\mathscr{S}}_{\circ}}^{\gamma})$—in particular, ${\mathcal{E}}_{\textrm{ad}}^{\gamma}(|0\rangle\!\langle0|) \notin \Gamma({{\mathscr{S}}_{\circ}}^{\gamma})$ for general $\gamma \in (0,1)$.
This naturally leaves many open questions. Most intriguingly, it was recently shown that for entanglement-breaking and Hadamard channels, we have [@wilde13] $$\begin{aligned}
\log M^*({\mathcal{E}}^n, {\varepsilon}) = n\, \chi({{\mathscr{S}}_{\circ}}) + O(\sqrt{n})\end{aligned}$$ Thus, one could reasonably conjecture that a second-order approximation of the form also holds for such channels (and not only image-additive channels). In particular, it would be interesting to see if the second-order term is again given by the peripheral information variance. The proof of the strong converse in [@wilde13] relies on the additivity of a suitable Rényi divergence radius [@lennert13; @wilde13] of the channel image. However, it appears that their techniques are insufficient to derive a second-order expansion of the ${\varepsilon}$-hypothesis testing divergence radius.
Proofs: Quantum Divergence Radius {#sec:radius}
=================================
This section contains various lemmas which, combined, establish Theorem \[th:radius\]. Recall that ${\mathscr{S}}$ denotes the set of quantum states on a Hilbert space of dimension $d$, and ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ is an arbitrary closed subset of ${\mathscr{S}}$, and thus also compact.
We will later show that the divergence center $\sigma^*({{\mathscr{S}}_{\circ}})$, as defined in Theorem \[th:radius\], is indeed a singleton, but at this point we have to be satisfied with the following statement.
\[lm:center\] The set $\sigma^*({{\mathscr{S}}_{\circ}})$ is nonempty, convex and $\sigma \in \sigma^*({{\mathscr{S}}_{\circ}})$ implies $\sigma \gg \rho$ for all $\rho \in {{\mathscr{S}}_{\circ}}$.
Since ${{\mathscr{S}}_{\circ}}$ is compact, $\sup_{\rho \in {{\mathscr{S}}_{\circ}}} D ( \rho \| \sigma )$ is finite if and only if $\sigma \gg \rho$ for all $\rho \in {{\mathscr{S}}_{\circ}}$. Moreover, since ${\mathscr{S}}$ is compact and the function $f: \sigma \mapsto \sup_{\rho \in {{\mathscr{S}}_{\circ}}} D ( \rho \| \sigma )$ convex, the set of minima contains at least one element and is convex.
In analogy to Theorem \[th:radius\], we define the set of extremal points in ${{\mathscr{S}}_{\circ}}$ corresponding to the center $\sigma \in \sigma^*({{\mathscr{S}}_{\circ}})$ as $\Gamma_{\sigma}({{\mathscr{S}}_{\circ}}) := \operatorname*{\arg\max}_{\rho \in {{\mathscr{S}}_{\circ}}} D\big(\rho \big\|\sigma \big)$.
\[pr:contain\] For every $\sigma \in \sigma^*({{\mathscr{S}}_{\circ}})$, we have $\sigma \in \operatorname{conv}(\Gamma_{\sigma}({{\mathscr{S}}_{\circ}}))$.
Let us fix $\sigma \in \sigma^*({{\mathscr{S}}_{\circ}})$ to simplify notation. We define $$\begin{aligned}
\Theta^{\nu} := \big\{ \rho \in {{\mathscr{S}}_{\circ}}\,\big|\, D(\rho\| \sigma) \geq \chi({{\mathscr{S}}_{\circ}}) - \nu \big\} .\end{aligned}$$ and its complement $\bar{\Theta}^{\nu} := {{\mathscr{S}}_{\circ}}\setminus \Theta^{\nu}$ for any $\nu \geq 0$. We first observe that $\Theta^\nu \subseteq {{\mathscr{S}}_{\circ}}$ is closed since $D(\cdot\|\sigma)$ is continuous and ${{\mathscr{S}}_{\circ}}$ is closed itself. Thus, both $\Theta^{\nu}$ and $\operatorname{conv}(\Theta^{\nu})$ are compact. Moreover, we clearly have $\bigcap_{\nu > 0} \Theta^{\nu} = \Theta^0 = \Gamma_{\sigma}({{\mathscr{S}}_{\circ}})$.
For the sake of contradiction, let us now assume that $\sigma \notin \operatorname{conv}(\Theta^{\nu})$ for some fixed $\nu > 0$. We employ the following lemma (also known as the Pythagorean theorem for relative entropy).
[[@ohya97 Lem. 3.3]]{.nodecor} \[lm:closest-point\] Let ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ be compact convex and let $\sigma \in {\mathscr{S}}$. Then, $\tau := \operatorname*{\arg\min}_{\tau \in {{\mathscr{S}}_{\circ}}} D(\tau\|\sigma)$ is unique. Moreover, for all $\rho \in {{\mathscr{S}}_{\circ}}$, we have $$\begin{aligned}
D(\rho\|\sigma) \geq D(\rho\|\tau) + D(\tau\|\sigma) .
\end{aligned}$$
This establishes that there exists a unique state $\tau \in \operatorname{conv}(\Theta^{\nu})$ that minimizes $D(\tau\|\sigma)$. Furthermore, $D(\rho\|\sigma) > D(\rho\|\tau)$ for all $\rho \in \Theta^{\nu}$. Consequently, using the parametrization $\tau^{\lambda} := \lambda \tau + (1-\lambda) \sigma$ and the convexity of $D(\rho\|\cdot)$, we find $$\begin{aligned}
D(\rho\|\tau^{\lambda}) \leq \lambda D(\rho\|\tau) + (1-\lambda) D(\rho\|\sigma) < D(\rho\|\sigma) \qquad \forall \lambda \in (0, 1) .\end{aligned}$$ Hence, $D(\rho\|\tau^{\lambda}) < D(\rho\|\sigma)$ for all $\rho \in \Theta^{\nu}$ and for all $\lambda \in (0,1)$. Furthermore, recall that $D(\rho\|\sigma)$ is bounded away from $\chi({{\mathscr{S}}_{\circ}})$ for all $\rho \in \bar{\Theta^{\nu}}$ by definition. Due to the continuity of $D(\rho\|\cdot)$, we thus find that for sufficiently small $\lambda > 0$, $$\begin{aligned}
D\big(\rho \big\| \tau^{\lambda}\big) < \chi({{\mathscr{S}}_{\circ}}) \qquad \forall \rho \in {{\mathscr{S}}_{\circ}}.\end{aligned}$$ However, this implies that $\sigma \notin \sigma^*({{\mathscr{S}}_{\circ}})$ and thus leads to a contradiction.
Hence, we conclude that $\sigma \in \operatorname{conv}(\Theta^{\nu})$ and since this holds for all $\nu > 0$, we find $\sigma \in \bigcap_{\nu > 0} \operatorname{conv}(\Theta^{\nu})$. The statement then follows by the following lemma proven in Appendix \[app:set-limit\].
\[lm:set-limit\] Let $\Theta_1 \supseteq \Theta_2 \supseteq \ldots$ be a sequence of compact sets in a finite-dimensional vector space. Then, $$\begin{aligned}
\bigcap_{n \in \mathbb{N}} \operatorname{conv}(\Theta_n) = \operatorname{conv}( \Theta_{\infty}) \qquad
\textrm{whenever}\qquad \Theta_{\infty} := \bigcap_{n \in \mathbb{N}} \Theta_n \neq \emptyset .
\end{aligned}$$
This establishes that $\bigcap_{\nu > 0} \operatorname{conv}(\Theta^{\nu}) = \operatorname{conv}(\Theta^0)$ and concludes the proof.
The fact that $\sigma \in \sigma^*({{\mathscr{S}}_{\circ}}) \implies \sigma \in \operatorname{conv}(\Gamma_{\sigma}({{\mathscr{S}}_{\circ}}))$, first established here, is crucial since it allows the following construction:
Due to Caratheodory’s theorem, we may decompose $\sigma$ into a convex combination of (at most $d^2$) peripheral states, namely we may write $$\begin{aligned}
\label{eq:decomp}
\sigma = \sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, \rho, \qquad \textrm{where}\quad {{\mathscr{X}}_{\circ}}\subseteq \Gamma_{\sigma}({{\mathscr{S}}_{\circ}}),\ |{{\mathscr{X}}_{\circ}}| \leq d^2 \quad \textrm{and} \quad P \in {\mathcal{P}}({{\mathscr{X}}_{\circ}}).\end{aligned}$$ Using this decomposition and the fact that $D(\rho\|\sigma) = \chi({{\mathscr{S}}_{\circ}})$ for all $\rho \in {{\mathscr{X}}_{\circ}}$, we find $$\begin{aligned}
\label{eq:r-holevo}
\chi({{\mathscr{S}}_{\circ}}) = \sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, D(\rho \| \sigma) = H(\sigma) - \sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, H(\rho) \,.\end{aligned}$$ The uniqueness of $\sigma^*({{\mathscr{S}}_{\circ}})$ now follows from a standard argument (see, e.g., [@gallager68 Sec. 4.5]) and using the strict concavity of $H$.
\[lm:unique\] The set $\sigma^*({{\mathscr{S}}_{\circ}})$ contains exactly one state.
We have already established that $\sigma^*({{\mathscr{S}}_{\circ}})$ is nonempty and convex in Lemma \[lm:center\]. Assume for the sake of contradiction that $\sigma_0, \sigma_1 \in \sigma^*({{\mathscr{S}}_{\circ}})$ with $\sigma_0 \neq \sigma_1$. Consequently, $\sigma_{\lambda} := \lambda \sigma_1 + (1-\lambda) \sigma_0$ is in $\sigma^*({{\mathscr{S}}_{\circ}})$ for all $\lambda \in [0,1]$. Following , we may write $$\begin{aligned}
\sigma_{\lambda} = \sum_{\rho \in {{\mathscr{X}}_{\circ}}'} P_\lambda(\rho)\, \rho ,
\qquad \textrm{where}\quad {{\mathscr{X}}_{\circ}}' \subseteq \Gamma_{\sigma_0}({{\mathscr{S}}_{\circ}}) \cup \Gamma_{\sigma_1}({{\mathscr{S}}_{\circ}}),\ |{{\mathscr{X}}_{\circ}}'| \leq 2d^2\,.
\end{aligned}$$ and $P_{\lambda}(\rho) = \lambda P_1(\rho) + (1-\lambda) P_0(\rho)$ for $P_{\lambda} \in {\mathcal{P}}({{\mathscr{X}}_{\circ}}')$ . Then, due to , we have $$\begin{aligned}
\chi({{\mathscr{S}}_{\circ}}) &= H(\sigma_0) - \sum_{\rho \in {{\mathscr{X}}_{\circ}}'} P_0(\rho) H(\rho) = H(\sigma_1) - \sum_{\rho \in {{\mathscr{X}}_{\circ}}'} P_1(\rho) H(\rho) .
\end{aligned}$$ Hence, using the strict concavity of $H(\cdot)$, we find $$\begin{aligned}
\chi({{\mathscr{S}}_{\circ}}) &= \lambda H(\sigma_1) + (1-\lambda) H(\sigma_0) - \sum_{\rho \in {{\mathscr{X}}_{\circ}}'} P_{\lambda}(\rho)\, H(\rho) \\
&< H(\sigma_{\lambda}) - \sum_{\rho \in {{\mathscr{X}}_{\circ}}'} P_{\lambda}(\rho)\, H(\rho) \\
&= \sum_{\rho \in {{\mathscr{X}}_{\circ}}'} P_{\lambda}(\rho)\, D(\rho\|\sigma_{\lambda}) .
\end{aligned}$$ Finally, the fact that $D(\rho\|\sigma_{\lambda}) \leq \sup_{\rho \in {{\mathscr{S}}_{\circ}}} D(\rho\|\sigma_{\lambda}) = \chi({{\mathscr{S}}_{\circ}})$ since $\sigma_{\lambda} \in \sigma^*({{\mathscr{S}}_{\circ}})$ yields the desired contradiction.
The previous lemma justifies writing $\Gamma({{\mathscr{S}}_{\circ}})$ in Theorem \[th:radius\], i.e. $\Gamma_{\sigma}({{\mathscr{S}}_{\circ}})$ does not depend on $\sigma$. We will thus drop the subscript $\sigma$ in $\Gamma_{\sigma}$ hereafter.
For any ${\mathbb{P}}\in {\mathcal{P}}({\mathscr{S}})$ and $\sigma \in {\mathscr{S}}$, let us introduce the notation $$\begin{aligned}
I({\mathbb{P}}| \sigma) := \int {\textnormal{d}}{\mathbb{P}}(\rho)\, D(\rho \big\| \sigma) \quad \textrm{and} \quad I({\mathbb{P}}) := I\Big({\mathbb{P}}\Big| \rho^{({\mathbb{P}})} \Big)\end{aligned}$$ in analogy with the conditional mutual information.
\[lm:alt\] We have $\chi({{\mathscr{S}}_{\circ}}) = \sup_{{\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}})} I({\mathbb{P}})$. The supremum is achieved by a discrete probability measure with support on at most $d^2$ points in $\Gamma({{\mathscr{S}}_{\circ}})$.
First, note that for every ${\mathbb{P}}\in {\mathcal{P}}({\mathscr{S}})$ we have $I({\mathbb{P}}) = \min_{\sigma \in {\mathscr{S}}} I({\mathbb{P}}|\sigma)$ due to the positive-definiteness of $D(\cdot\|\cdot)$. Now, Sion’s minimax theorem [@sion58] yields $$\begin{aligned}
\sup_{{\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}})} \min_{\sigma \in {\mathscr{S}}} I({\mathbb{P}}|\sigma) =
\min_{\sigma \in {\mathscr{S}}} \sup_{{\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}})} I({\mathbb{P}}|\sigma) \label{eq:minimax}
\end{aligned}$$ Indeed, it is easy to verify that $I({\mathbb{P}}|\sigma)$ is convex in $\sigma$ and linear in ${\mathbb{P}}$. Moreover, ${\mathscr{S}}$ is compact convex and ${\mathcal{P}}({{\mathscr{S}}_{\circ}})$ is convex, as required. Finally, the supremum over distributions on the right-hand side of can be replaced by a supremum over Dirac measures on ${{\mathscr{S}}_{\circ}}$ without loss of generality. This establishes $$\begin{aligned}
\sup_{{\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}})} \int {\textnormal{d}}{\mathbb{P}}(\rho)\, D(\rho \big\| \rho^{({\mathbb{P}})}) = \min_{\sigma \in {\mathscr{S}}} \sup_{\rho \in {{\mathscr{S}}_{\circ}}} D(\rho\|\sigma) .
\end{aligned}$$
The second statement follows immediately due to the construction given in Eq. and .
We are now ready to summarize the proof of Theorem \[th:radius\].
Property 1 follows from Lemmas \[lm:center\] and \[lm:unique\]. Property 2 is a trivial consequence of Property 1 and the definition of $\Gamma$. Property 3 is implied by Proposition \[pr:contain\] whereas Property 4 is established in Lemma \[lm:alt\]. Finally, Property 5 is established as follows:
Clearly, every ${\mathbb{P}}\in \Pi({{\mathscr{S}}_{\circ}})$ achieves the supremum in , $\chi({{\mathscr{S}}_{\circ}})$, by definition of $\Gamma({{\mathscr{S}}_{\circ}})$. Conversely, let us assume that there exists a distribution ${\mathbb{P}}\in {\mathcal{P}}$ that achieves $\chi({{\mathscr{S}}_{\circ}})$. Then, $\rho^{({\mathbb{P}})} = \sigma^*({{\mathscr{S}}_{\circ}})$ by the argument in Lemmas \[lm:unique\] and \[lm:alt\]. Moreover, ${\mathbb{P}}[\Gamma({{\mathscr{S}}_{\circ}})] = 1$ is necessary due to the definition of $\Gamma$.
Proofs: Second-Order Approximation {#sec:asymp}
==================================
The direct part of the proof of Theorem \[th:main\] is presented in Section \[sec:direct\]. We split the proof of the converse part of Theorem \[th:main\] into several parts. First, Section \[sec:proof/one-shot-converse\] provides a proof of our one-shot converse bound in Proposition \[pr:one-shot-converse\]. Then, Section \[sec:prop\] introduces some non-asymptotic bounds on the ${\varepsilon}$-hypothesis testing divergence for product states that are essential for our asymptotic analysis. As a warm-up, Section \[sec:warm-up\] shows the strong converse property for c-q channels using these techniques. The converse part of Theorem \[th:main\] is then established in Section \[sec:converse\], and an improved third-order bound for discrete classical-quantum channels is given in \[sec:converethird\].
Proof of Direct Part of Thoerem \[th:main\] {#sec:direct}
-------------------------------------------
We base our result on the following straightforward generalization of the one-shot bounds by Hayashi and Nagaoka [@hayashi03] in the form of Wang and Renner [@wang10] (see also [@datta11a; @renes10-2; @dupuisszehr12] for recent one-shot achievability bounds for c-q channels).[^8]
[[@wang10 Thm. 1]]{.nodecor} \[pr:one-shot-direct\] Let ${\varepsilon}\in (0, 1)$, $\eta \in (0, {\varepsilon})$, and let ${{\mathscr{X}}_{\circ}}\subseteq \operatorname{im}({\mathcal{W}})$ be discrete. Then, $$\begin{aligned}
\log M^*({\mathcal{W}}, {\varepsilon}) \geq
&\sup_{P \in {\mathcal{P}}({{\mathscr{X}}_{\circ}})} D_h^{{\varepsilon}-\eta}\Bigg( \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho\, \Bigg\| \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho^{(P)} \Bigg) - \log \frac{4{\varepsilon}(1-{\varepsilon}+\eta)}{\eta^2} .
\end{aligned}$$
We can include the closure of $\operatorname{im}({\mathcal{W}})$ due to the continuity of the above expression when the set ${{\mathscr{X}}_{\circ}}$ is varied by replacing an element with one that is close in $({\mathscr{S}},\delta_{textrm{tr}})$. Thus, our bound reads $$\begin{aligned}
\log M^*({\mathcal{W}}, {\varepsilon}) \geq \sup_{{{\mathscr{X}}_{\circ}}\subseteq \overline{\operatorname{im}({\mathcal{W}})}} \sup_{P \in {\mathcal{P}}({{\mathscr{X}}_{\circ}})} D_h^{{\varepsilon}-\eta}\Big( \omega^{(P)} \Big\| \tau^{(P)} \otimes \rho^{(P)} \Big) - \log \frac{4{\varepsilon}(1-{\varepsilon}+\eta)}{\eta^2} , \label{eq:direct}\end{aligned}$$ where ${{\mathscr{X}}_{\circ}}$ is discrete and we introduced the shorthands $\omega^{(P)} := \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho$ and $\tau^{(P)} := \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)$. The similarity of the above expression with the asymptotic expression in is evident once is specialized to the discrete case as well.
The restriction to finite subsets of ${{\mathscr{S}}_{\circ}}$ is unproblematic in light of Lemma \[lm:cara\]. Let us then proceed to prove the lower bound in Theorem \[th:main\], which we restate in a slightly stronger form here.
Let ${\varepsilon}\in (0, 1)$ and let ${\mathcal{W}}$ be a c-q channel. Set ${{\mathscr{S}}_{\circ}}:= \overline{\operatorname{im}({\mathcal{W}})}$. Then, $$\begin{aligned}
\log M^*({\mathcal{W}}^n, {\varepsilon}) \geq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) + O(\log n) .
\end{aligned}$$
First, let us apply to the $n$-fold repetition of the channel ${\mathcal{W}}$. Fixing any discrete set ${{\mathscr{X}}_{\circ}}\subseteq {{\mathscr{S}}_{\circ}}$ and $P \in {\mathcal{P}}({{\mathscr{X}}_{\circ}})$, we first confirm that $$\begin{aligned}
\log M^*({\mathcal{W}}^n, {\varepsilon}) \geq D_h^{{\varepsilon}-\eta} \Big( \big( \omega^{(P)} \big)^{\otimes n} \Big\| \big( \tau^{(P)} \otimes \rho^{(P)} \big)^{\otimes n} \Big) - \log \frac{4{\varepsilon}(1-{\varepsilon}+\eta)}{\eta^2} \label{eq:direct1}
\end{aligned}$$ Note that we applied using the set ${{\mathscr{X}}_{\circ}}^{\otimes n} \subseteq \overline{\operatorname{im}({\mathcal{W}})}^{\otimes n} = \overline{\operatorname{im}({\mathcal{W}})^{\otimes n}}$ and the $n$-fold product distribution $P^{\times n}$. By Lemma \[lm:cara\] there exists a probability mass function (let it be our choice of $P$) with support on $\Gamma({{\mathscr{S}}_{\circ}})$ (let the support set be our choice of ${{\mathscr{X}}_{\circ}}$) such that $$\begin{aligned}
\rho^{(P)} = \sigma , \quad \sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, D(\rho\|\sigma) = \chi({{\mathscr{S}}_{\circ}}), \quad \textrm{and} \quad \sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, V(\rho\|\sigma) = v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) , \label{eq:direct3}
\end{aligned}$$ where we set $\sigma = \sigma^*({{\mathscr{S}}_{\circ}})$. Now, we can verify that $$\begin{aligned}
\sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, D\big(\rho\big\|\rho^{(P)}\big) = D\Bigg( \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho\, \Bigg\| \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho^{(P)} \Bigg) , \label{eq:direct2}
\end{aligned}$$ and, the following simple generalization of [@polyanskiy10 Lm. 62] proved in Appendix \[app:direct\] holds.
\[lm:v-expand\] For any probability mass function $P \in \Pi({{\mathscr{S}}_{\circ}})$, we have $$\begin{aligned}
\sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)\, V\big(\rho\big\|\rho^{(P)}\big) = V\Bigg( \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho\, \Bigg\| \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \rho^{(P)} \Bigg) .
\end{aligned}$$
As such, we are left to evaluate the asymptotics of $D_h^{{\varepsilon}-\eta}$ for identical product states. Let us set ${\varepsilon}_n := {\varepsilon}- \eta$ with $\eta = 1/{\sqrt{n}}$. First, consider the case where $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) > 0$. The second assertion in Proposition \[pr:asymptotics\] (i.e. the bound in ) specialized to i.i.d. states, establishes that $$\begin{aligned}
&D_h^{{\varepsilon}-\eta} \Big( \big( \omega^{(P)} \big)^{\otimes n} \Big\| \big( \tau^{(P)} \otimes \rho^{(P)} \big)^{\otimes n} \Big) \\
&\qquad \qquad \geq n D\big( \omega^{(P)} \big\| \tau^{(P)} \otimes \rho^{(P)} \big) + \sqrt{n V\big( \omega^{(P)} \big\| \tau^{(P)} \otimes \rho^{(P)} \big) }\, \Phi^{-1}({\varepsilon}) - L_2 \log n \\
&\qquad \qquad = n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) - L_2 \log n \,.
\end{aligned}$$ for all $n \geq N_2$ and some constants $L_2$ and $N_2({\varepsilon},{{\mathscr{S}}_{\circ}})$. In the last step we employed , Lemma \[lm:v-expand\] and . Moreover, the last summand in is of the form $O(\log n)$ and we are done.
The proof for the case $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) = 0$ proceeds similarly but employs the first bound in Eq. in Proposition \[pr:asymptotics\] instead. This yields $$\begin{aligned}
D_h^{{\varepsilon}-\eta} \Big( \big( \omega^{(P)} \big)^{\otimes n} \Big\| \big( \tau^{(P)} \otimes \rho^{(P)} \big)^{\otimes n} \Big) \geq n D\big( \omega^{(P)} \big\| \tau^{(P)} \otimes \rho^{(P)} \big) - L_1 \log n .
\end{aligned}$$ for all $n \geq N_1$ and some constants $L_1$ and $N_1({\varepsilon}-\eta,{{\mathscr{S}}_{\circ}})$. The rest of the proof then proceeds analogously to the discussion above.
Proof of Proposition \[pr:one-shot-converse\] {#sec:proof/one-shot-converse}
---------------------------------------------
Let us recall the statement of Proposition \[pr:one-shot-converse\]. For ${\varepsilon}\in (0,1)$ and $\mu \in (0, 1-{\varepsilon})$, we want that $$\begin{aligned}
\log M^*({\mathcal{W}},{\varepsilon}) \leq \chi_h^{{\varepsilon}+\mu}\Big(\overline{\operatorname{im}({\mathcal{W}})}\Big) + \log \frac{{\varepsilon}+\mu}{\mu(1-{\varepsilon}-\mu)} . \label{eq:conv2}
\end{aligned}$$
Let ${\mathcal{C}}=\{ {\mathscr{M}}, e, {\mathcal{D}}\}$ be a code with $p_{\textrm{err}}({\mathcal{C}}, {\mathcal{W}}) \leq {\varepsilon}$ given by codewords $x_m = e(m) \in {\mathscr{X}}$ and a decoder ${\mathcal{D}}= \{Q_m\}_{m\in{\mathscr{M}}}$. By assumption, we thus have $\frac{1}{|{\mathscr{M}}|} \sum_{m \in {\mathscr{M}}} \operatorname{tr}(Q_m {\mathcal{W}}(x_m) ) \geq 1 - {\varepsilon}$. For an arbitrary but fixed $\sigma \in {\mathscr{S}}$, we define the set $$\begin{aligned}
{\mathcal{K}}:= \big\{ m \in {\mathscr{M}}\,\big| \operatorname{tr}\big( Q_m {\mathcal{W}}(x_m) \big) \geq 1 - {\varepsilon}- \mu \big\}, \quad \textrm{and} \quad m^* := \operatorname*{\arg\min}_{m \in {\mathcal{K}}}\ \operatorname{tr}( Q_m \sigma ).\end{aligned}$$ By definition of this set, we have $$\begin{aligned}
1 - {\varepsilon}\leq \frac{1}{|{\mathscr{M}}|} \sum_{m \in {\mathscr{M}}} \operatorname{tr}( Q_m {\mathcal{W}}(x_m) ) &= \frac{1}{|{\mathscr{M}}|} \sum_{m \in {\mathcal{K}}} \operatorname{tr}( Q_m {\mathcal{W}}(x_m) ) +
\frac{1}{|{\mathscr{M}}|} \sum_{m \in {\mathscr{M}}\setminus {\mathcal{K}}} \operatorname{tr}( Q_m {\mathcal{W}}(x_m) ) \\
&< \frac{|{\mathcal{K}}|}{|{\mathscr{M}}|} + \frac{|{\mathscr{M}}| - |{\mathcal{K}}|}{|{\mathscr{M}}|} (1 - {\varepsilon}- \mu) $$ Hence, $|{\mathcal{K}}| > |{\mathscr{M}}| \frac{\mu}{{\varepsilon}+\mu}$. Moreover, we have $$\begin{aligned}
1 = \operatorname{tr}(\sigma) = \sum_{m \in {\mathscr{M}}} \operatorname{tr}(Q_{m} \sigma) \geq |{\mathcal{K}}| \operatorname{tr}(Q_{{m^*}} \sigma) > |{\mathscr{M}}| \frac{\mu}{{\varepsilon}+\mu} \operatorname{tr}(Q_{{m^*}} \sigma) .
\end{aligned}$$ By definition of the ${\varepsilon}$-hypothesis testing divergence we find $$\begin{aligned}
D_h^{{\varepsilon}+\mu}({\mathcal{W}}(x_{m^*}) \| \sigma) \geq - \log \frac{ \operatorname{tr}(Q_{{m^*}} \sigma)}{1-{\varepsilon}-\mu} > \log |{\mathscr{M}}| - \log \frac{ {\varepsilon}+ \mu }{\mu(1-{\varepsilon}-\mu)} .
\end{aligned}$$ Thus, in particular we have $$\begin{aligned}
\sup_{\rho \in\, \overline{\operatorname{im}({\mathcal{W}})}}\, D_h^{{\varepsilon}+\mu}(\rho \| \sigma) > \log |{\mathscr{M}}| - \log \frac{ {\varepsilon}+ \mu }{\mu(1-{\varepsilon}-\mu)}
\end{aligned}$$ Finally, Eq. follows by observing that the above bound holds for all $\sigma \in {\mathscr{S}}$.
Non-Asymptotic Bounds on the Hypothesis-Testing Divergence {#sec:prop}
----------------------------------------------------------
Some of the main ingredients of our asymptotic analysis in the converse part of the proof of Theorem \[th:main\] are the following non-asymptotic bounds on the ${\varepsilon}$-hypothesis testing divergence evaluated for product states. Before we state the bounds, recall that $I({\mathbb{P}}| \sigma) = \int {\textnormal{d}}{\mathbb{P}}(\rho) \, D(\rho\|\sigma)$ and define $V({\mathbb{P}}| \sigma) := \int {\textnormal{d}}{\mathbb{P}}(\rho) \, V(\rho\|\sigma)$ analogously for any ${\mathbb{P}}\in {\mathcal{P}}({\mathscr{S}})$ and $\sigma \in {\mathscr{S}}$. Moreover, given a sequence of states $\rho^n = \bigotimes_{i=1}^n \rho_i$, we denote by $P_{\rho^n}(\rho) := \frac1{n} \sum_{i=1}^n 1\{\rho = \rho_i\}$ the empirical distribution of $\rho^n$.
\[pr:asymptotics\] Let ${\varepsilon}\in (0,1)$, ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ and $\lambda_0 > 0$. Let $\{{\varepsilon}_n\}_{n=1}^{\infty}$ be any sequence satisfying $|{\varepsilon}_n - {\varepsilon}| \leq 1/\sqrt{n}$ for all $n$ and set ${\varepsilon}^* := \min\{{\varepsilon}, 1-{\varepsilon}\}$. Then, there exist constants $N_1({\varepsilon},{{\mathscr{S}}_{\circ}},\lambda_{0})$ and $K_1({\varepsilon},{{\mathscr{S}}_{\circ}},\lambda_{0})$ and $L_1$ such that the following holds. For every $n \geq N_1$, every $\sigma \in {\mathscr{S}}$ with $\lambda_{\min}(\sigma) \geq \lambda_0$ and every sequence $\rho^n = \bigotimes_{i=1}^n \rho_i$, $\rho_i \in {{\mathscr{S}}_{\circ}}$, we have $$\begin{aligned}
\Big|\, D_h^{{\varepsilon}_n}\big(\rho^n \big\|\, \sigma^{\otimes n} \big) - n I \big( P_{\rho^n} \big| \sigma\big) \Big|
\leq \sqrt{\frac{n V(P_{\rho^n}|\sigma)}{{\varepsilon}^*}} + L_1 \log n
\leq K_1 \sqrt{n}\, . \label{eq:cheby}
\end{aligned}$$
Further let $\xi > 0$ and fix $\sigma \in {\mathscr{S}}$ with $\lambda_{\min}(\sigma) > 0$. Then, there exist constants $N_2({\varepsilon},{{\mathscr{S}}_{\circ}},\sigma,\xi)$ and $L_2$ such that the following holds. For every $n \geq N_2$ and every sequence $\rho^n = \bigotimes_{i=1}^n \rho_i$, $\rho_i \in {{\mathscr{S}}_{\circ}}$ satisfying $V(P_{\rho^n}|\sigma) \geq \xi$, we have $$\begin{aligned}
\Big|\, D_h^{{\varepsilon}_n}\big(\rho^n \big\|\, \sigma^{\otimes n} \big) - n I \big( P_{\rho^n} \big| \sigma\big) - \sqrt{n V\big( P_{\rho^n} \big| \sigma \big)}\,\Phi^{-1}({\varepsilon}) \Big| \leq L_2 \log n . \label{eq:berry}
\end{aligned}$$ Finally, if $\sigma = \rho^{(P_{\rho^n})}$ in , then the statement holds for $n \geq N_3({\varepsilon},{{\mathscr{S}}_{\circ}},\xi)$ independent of $\sigma$.
In the asymptotic limit as $n \to \infty$, all inequalities imply the seminal quantum Stein’s lemma [@hiai91] and its strong converse [@ogawa00] when the sequence is chosen i.i.d. The proof is based on the techniques of [@li12; @tomamichel12] and presented in Appendix \[app:hypo\]. It is crucial for our application that $L_1, L_2, K_1, N_1, N_2$ and $N_3$ are uniform over $\sigma$ and sequences $\rho^n$ satisfying the constraints. This is nontrivial and requires arguments beyond those in [@li12; @tomamichel12] which only treat the i.i.d. case.[^9]
Asymptotics of the ${\varepsilon}$-Hypothesis Testing Divergence Radius: First-Order {#sec:warm-up}
------------------------------------------------------------------------------------
As a warm-up, we use our techniques to provide a simple proof of the strong converse property of general classical-quantum channels. The strong converse is evidently a corollary of Proposition \[pr:one-shot-converse\] and the following result.[^10]
\[pr:strong\] Let ${\varepsilon}\in (0,1)$ and ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ closed. Let $\{{\varepsilon}_n\}_{n=1}^{\infty}$ be any sequence satisfying $|{\varepsilon}_n - {\varepsilon}| \leq 1/\sqrt{n}$ for all $n$. Then, $$\begin{aligned}
\chi_h^{{\varepsilon}_n}\big( {{\mathscr{S}}_{\circ}}^{\otimes n} \big) \leq n\, \chi({{\mathscr{S}}_{\circ}}) + O(\sqrt{n}) .
\end{aligned}$$
Note that Winter [@winterthesis] and Ogawa-Nagaoka [@ogawa99] first showed the strong converse for classical-quantum channels for the generality we consider here.
By definition of the ${\varepsilon}$-hypothesis testing divergence radius, we have $$\begin{aligned}
\chi_h^{{\varepsilon}_n}\big({{\mathscr{S}}_{\circ}}^{\otimes n}\big) \leq \sup_{\rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n}} D_h^{{\varepsilon}_n} \big( \rho^n \,\big\|\, \sigma^{\otimes n} \big) , \label{eq:chiheps-bound}\end{aligned}$$ where we chose an $n$-fold product of the divergence center, $\sigma = \sigma^*({{\mathscr{S}}_{\circ}}) \in {\mathscr{S}}$, as the output state. The states $\rho^n$ are of the form $\rho^n = \bigotimes_{i=1}^n \rho_i$. For a fixed and arbitrary $\rho^n$, we define the set ${{\mathscr{S}}_{\circ}}^n := \{ \rho_i \}_{i=1}^n \subseteq {{\mathscr{S}}_{\circ}}$ and the empirical distribution $P_{\rho^n} \in {\mathcal{P}}\big({{\mathscr{S}}_{\circ}}^n\big)$ given by $P_{\rho^n}(\rho) = \frac1n \sum_{i=1}^n 1\{ \rho = \rho_i \}$.
We then use in Proposition \[pr:asymptotics\] to assert that $$\begin{aligned}
D_h^{{\varepsilon}_n} \big( \rho^n \,\big\|\, \sigma^{\otimes n} \big) \le n I(P_{\rho^n} | \sigma) + K_1 \sqrt{n} \label{eq:sc-1}\end{aligned}$$ for sufficiently large $n \geq N_1$. Here, we used that $\lambda_{\min}(\sigma) > 0$ and recall that $I({\mathbb{P}}|\sigma)$ is defined as $I({\mathbb{P}}|\sigma) = \int {\textnormal{d}}{\mathbb{P}}(\rho)\, D( \rho \| \sigma)$. Therefore, Theorem \[th:radius\] ensures that $D(\rho\|\sigma) \leq \chi({{\mathscr{S}}_{\circ}})$ for all $\rho \in {\mathscr{S}}_o$ and we have established that $$\begin{aligned}
&\chi_h^{{\varepsilon}_n}\big({{\mathscr{S}}_{\circ}}^{\otimes n}\big) \leq \sup_{\rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n}} n I(P_{\rho^n}|\sigma) + K_1 \sqrt{n} \leq n \chi({{\mathscr{S}}_{\circ}}) + K_1 \sqrt{n} . \qedhere\end{aligned}$$
Asymptotics of the ${\varepsilon}$-Hypothesis Testing Divergence Radius: Second-Order {#sec:converse}
-------------------------------------------------------------------------------------
In view of Proposition \[pr:one-shot-converse\] and the discussion in the previous section, we therefore want to find a second-order upper bound on $\chi_h^{{\varepsilon}}\big({{\mathscr{S}}_{\circ}}^{\otimes n}\big) = \min_{\sigma^n \in{\mathscr{S}}^{n}}
\sup_{\rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n}} D_h^{{\varepsilon}}\big( \rho^n \| \sigma^n\big) $. The following results constitute the main technical contribution of this paper.
### An Appropriate Choice of $\sigma^n$
The proof of the strong converse in Propositon \[pr:strong\] hinges on choosing $\sigma^n$ as the $n$-fold product of the divergence center and then taking advantage of the fact that $D(\rho\|\sigma) \leq \chi({{\mathscr{S}}_{\circ}})$ for all $\rho \in {{\mathscr{S}}_{\circ}}$. This will not be sufficient if we want to pin down the exact second-order term proportional to $\sqrt{n}$.[^11]
Before we commence, we thus introduce an appropriate choice of auxiliary state $\sigma^n$. To construct it, we require the following auxiliary result whose proof is provided in Appendix \[app:net\]. This establishes that there exists a $\gamma$-net on ${{\mathscr{S}}_{\circ}}$ whose cardinality can be bounded appropriately.
\[lm:net\] For every $\gamma \in (0,1)$, there exists a set of states ${\mathscr{G}}^{\gamma} \subseteq {\mathscr{S}}$ of size $$\begin{aligned}
|{\mathscr{G}}^\gamma| \leq \left(\frac{5}{\gamma}\right)^{2d^2} \left(\frac{2d}{\gamma}+2\right)^{d-1}
\end{aligned}$$ such that, for every $\rho \in {\mathscr{S}}$, there exists a state $\tau \in {\mathscr{G}}^\gamma$ satisfying the following: $$\begin{aligned}
\frac{1}{2} \| \rho - \tau \|_1 \leq \gamma, \quad
D(\rho\|\tau) \leq \gamma \cdot 4 (2d + 1), \quad \textrm{and} \quad
\lambda_{\min}(\tau) \geq \frac{\gamma}{2d+\gamma} .
\end{aligned}$$
Now, for a $\gamma$ to be specified below, we choose the output state $\sigma^n \in{\mathscr{S}}^{n}$ as follows: $$\begin{aligned}
\sigma^n := \frac12 \sigma^{\otimes n} + \frac1{2 |{\mathscr{G}}^\gamma|} \sum_{\tau \in {\mathscr{G}}^\gamma } \tau^{\otimes n} , \qquad \textrm{where}\quad \sigma = \sigma^*({{\mathscr{S}}_{\circ}}). \label{eq:sigman}\end{aligned}$$ Note that $\sigma^n$ is normalized and is, in fact, a convex combination of the $n$-fold tensor product of the divergence center and the $n$-fold tensor product of the elements of the net, of which there are only finitely many. With this choice of $\sigma^n$ we bound $D_h^{{\varepsilon}}\big( \rho^n \| \sigma^n \big)$ in the following.
### Different Sequences of Inputs
We will also need to treat different types of state sequences separately. We keep ${{\mathscr{S}}_{\circ}}$ fixed for the following to simplify notation. Let us define $\Omega_1^{\nu}, \Omega_2^{\nu} \subseteq {{\mathscr{S}}_{\circ}}^{\otimes n}$ for some $0 < \nu \leq 1$, which describe sets of state sequences of length $n$ that are close to achieving the first-order fundamental limit. (We omit the dependence on $n$ in our notation here.) The first set ensures that the states are close to $\Gamma({{\mathscr{S}}_{\circ}})$, and is defined as $$\begin{aligned}
\Omega_1^{\nu} := \Bigg\{ \rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n} \ \Bigg|\ \frac{1}{n} \sum_{i=1}^n \underbrace{\min_{\tau \in \Gamma({{\mathscr{S}}_{\circ}})} \frac12 \| \rho_i - \tau \|_1}_{ =:\, \Delta(\rho_i, \Gamma({{\mathscr{S}}_{\circ}}))} \leq \nu \Bigg\} .\end{aligned}$$ The second set ensures that the average state is close to the divergence center, and is defined as $$\begin{aligned}
\Omega_2^{\nu} := \Bigg\{ \rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n} \ \Bigg|\ \frac12 \bigg\| \frac1{n} \sum_{i=1}^n \rho_i - \sigma^*({{\mathscr{S}}_{\circ}}) \bigg\|_1 \leq \nu \Bigg\} .\end{aligned}$$ The interesting, close to capacity-achieving sequences are those that are in $\Omega_1^{\nu} \cap \Omega_2^{\nu}$.
### Dealing with Sub-Optimal Input Sequences
We first deal with sequences that are far from optimal in the sense prescribed above.
\[pr:conv-bad\] Let ${\varepsilon}\in (0,1)$, $\nu > 0$ and ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$. Let $\{{\varepsilon}_n\}_{n=1}^{\infty}$ be any sequence satisfying $|{\varepsilon}_n - {\varepsilon}| \leq 1/\sqrt{n}$ for all $n$. Then, there exist constants $N_0({\varepsilon}, {{\mathscr{S}}_{\circ}}, \nu)$ and $\gamma_0({{\mathscr{S}}_{\circ}},\nu)$ such that, for all $n \geq N_0$ and all $\rho^n \notin \Omega_1^{\nu} \cap \Omega_2^{\nu}$, we have $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n \| \sigma^n)
\leq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) ,
\end{aligned}$$ where $\sigma^n$ is defined as in for a fixed $\gamma = \gamma_0$.
The technique for bounding $D_h^{{\varepsilon}_n}\big( \rho^n \| \sigma^n \big)$ differs depending on the state sequence $\rho^n$. We consider two cases: (a) $\rho^n \notin \Omega_1^{\nu}$ and (b) $\rho^n \notin \Omega_2^{\nu}$ in the following subsections.
#### (a) Sequences $\rho^n \notin \Omega_1^{\nu}$: {#a-sequences-rhon-notin-omega_1nu .unnumbered}
Applying Property 3 of Lemma \[lm:hypo-prop\] to $D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n)$ with our choice of $\sigma^n$ in and picking out the divergence center $\sigma^{\otimes n}$ yields an upper bound of the form $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) &\leq D_h^{{\varepsilon}_n} (\rho^n \| \sigma^{\otimes n} \big) + \log 2. \end{aligned}$$ Furthermore, as in the proof of Proposition \[pr:strong\], we employ in Proposition \[pr:asymptotics\] to obtain $$\begin{aligned}
D_h^{{\varepsilon}_n}\big(\rho^n\big\|\sigma^{\otimes n}\big) &\leq \sum_{i=1}^n D( \rho_i \| \sigma) + K_1 \sqrt{n} \, ,\end{aligned}$$ for all $n \geq N_1$. (We absorbed the constant term $\log 2$ into the constant $K_1$ here for convinience.)
Now, we define $\hat{\chi}^{\nu}_1 := \sup_{ \rho \in {{\mathscr{S}}_{\circ}}:\, \Delta(\rho,\Gamma) > \frac{\nu}2 } D ( \rho \| \sigma) < \chi({{\mathscr{S}}_{\circ}})$ and employ the following lemma which is shown in Appendix \[app:selection\].
\[lm:selection\] Let $\rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n}$ be fixed and let $\nu \in (0, 1)$. If $\rho^n \notin \Omega_1^{\nu}$, then there exists a set $\Xi^{\nu} \subseteq [n]$ of cardinality $| \Xi^{\nu} | > n \frac{\nu}{2}$ such that, for all $i \in \Xi^{\nu}$, we have $\Delta(\rho_i, \Gamma) > \frac{\nu}{2}$.
This leads us to bound $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) \leq \sum_{i \in \Xi^{\nu}} \hat{\chi}^{\nu}_1 + \sum_{i \notin \Xi^{\nu}} \chi({{\mathscr{S}}_{\circ}}) + K_1 \sqrt{n}
\leq n \chi({{\mathscr{S}}_{\circ}}) - n(\chi({{\mathscr{S}}_{\circ}}) -\hat{\chi}^{\nu}_1) \frac{\nu}{2} + K_1 \sqrt{n} . \end{aligned}$$ In particular, we have $D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) \le n\,\chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{\varepsilon}({{\mathscr{S}}_{\circ}})} \Phi^{-1}({\varepsilon})$ for sufficiently large $n \geq N$, where $N$ is appropriately chosen.
#### (b) Sequences $\rho^n \notin \Omega_2^{\nu}$: {#b-sequences-rhon-notin-omega_2nu .unnumbered}
For these sequences, we extract the state $\tau^{\otimes n}$ from the convex combination that defines $\sigma^n$ in , where $\tau$ is the state closest (in the relative entropy sense) to the average output state $\bar{\rho} = \rho^{(P_{\rho^n})} = \frac1{n} \sum_{i=1}^n \rho_i$ in ${\mathscr{G}}^{\gamma}$ and the constant $\gamma >0$ is to be chosen later. In other words, $\tau \in\operatorname*{\arg\min}_{\tau\in{\mathscr{G}}^\gamma}D(\bar{\rho}\|\tau)$. Thus, by Property 3 of Lemma \[lm:hypo-prop\], we have $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) \leq D_h^{{\varepsilon}_n}\big(\rho^n\big\|\tau^{\otimes n}\big) + \log |{\mathscr{G}}^{\gamma}| .\end{aligned}$$
Then, by using in Proposition \[pr:asymptotics\] we find for all $\rho^n \notin \Omega_2^{\nu}$ that $$\begin{aligned}
D_h^{{\varepsilon}_n}\big(\rho^n\big\|\tau^{\otimes n}\big) &\leq \sum_{i=1}^n D(\rho_i \| \tau) + K_1' \sqrt{n} . $$ for $n \geq N_1'$. Here, we take advantage of the fact that the minimum eigenvalue of $\tau$ satisfies $\lambda_{\min}(\tau) \geq \frac{\gamma}{2d+\gamma}$ such that the constants $K_1'$ and $N_1'$ can be chosen uniformly for all $\tau \in {\mathscr{G}}^{\gamma}$.
We continue to bound $$\begin{aligned}
D_h^{{\varepsilon}_n}\big(\rho^n\big\|\tau^{\otimes n}\big)
&\leq \sum_{i=1}^n D( \rho_i \| \bar{\rho}) + \sum_{i=1}^n \operatorname{tr}\big( \rho_i (\log \bar{\rho} - \log \tau) \big) + K_1' \sqrt{n}
\\
&= \sum_{i=1}^n D( \rho_i \| \bar{\rho}) + n D(\bar{\rho}\|\tau) + K_1' \sqrt{n} \\
&\leq n\, I\Big(P_{\rho^n} \Big|\, \rho^{(P_{\rho^n})} \Big) +n\cdot 4\gamma (2d + 1)+ K_1' \sqrt{n} ,\end{aligned}$$ where the second inequality follows from the properties of the $\gamma$-net stated in Lemma \[lm:net\] and on the last line we introduced the empirical distribution of $\rho^n$, defined as $P_{\rho^n}(\rho) = \frac1{n} \sum_{i=1}^n 1 \{ \rho = \rho_i \}$.
Then, by Theorem \[th:radius\] and the definition of $\Pi({{\mathscr{S}}_{\circ}})$ and $\nu \in (0,1)$, we know that $$\begin{aligned}
\tilde{\chi}^{\nu}_2 := \sup \bigg\{ I\Big( {\mathbb{P}}\Big| \rho^{({\mathbb{P}})} \Big) \,\bigg|\, {\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}}):\, \frac12 \Big\| \rho^{({\mathbb{P}})} - \sigma^*({{\mathscr{S}}_{\circ}}) \Big\|_1 > \nu \bigg\} < \chi({{\mathscr{S}}_{\circ}}) .
\end{aligned}$$ Summarizing the above, we have $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) \leq n \chi({{\mathscr{S}}_{\circ}}) - n \big( \chi({{\mathscr{S}}_{\circ}}) - \tilde{\chi}^{\nu}_2 - 4\gamma (2d + 1) \big)+ K_1' \sqrt{n} + \log |{\mathscr{G}}^{\gamma}| .\end{aligned}$$ By choosing $\gamma = \gamma_0(\nu,{{\mathscr{S}}_{\circ}})$ small enough such that $\chi({{\mathscr{S}}_{\circ}}) -\tilde{\chi}^{\nu}_2
- 4\gamma (2d + 1) > 0$, we find that $D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) \leq n\chi({{\mathscr{S}}_{\circ}}) + \sqrt{n v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})} \Phi^{-1}({\varepsilon})$ for sufficiently large $n \geq N'$, appropriately chosen.
We conclude by observing that the statement of the proposition holds for $n \geq \max\{N, N'\}$.
### Putting Everything Together: Proof of Converse Part of Theorem \[th:main\]
The upper bound in Theorem \[th:main\] is now a corollary of Proposition \[pr:one-shot-converse\] and the following result.
\[pr:thedifficultpart\] Let ${\varepsilon}\in (0,1)$ and ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$. Let $\{{\varepsilon}_n\}_{n=1}^{\infty}$ be any sequence satisfying $|{\varepsilon}_n - {\varepsilon}| \leq 1/\sqrt{n}$ for all $n$. Then, $$\begin{aligned}
\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \leq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\, \Phi^{-1}({\varepsilon}) + o(\sqrt{n}) .
\end{aligned}$$
For any $\nu \in (0, 1)$, we first invoke Proposition \[pr:conv-bad\] to verify that $$\begin{aligned}
\sup_{\rho^n \notin \Omega_1^{\nu} \cap \Omega_2^{\nu}} D_h^{{\varepsilon}_n}(\rho^n \| \sigma^n)
\leq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\,v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) \label{eq:outliers}
\end{aligned}$$ for $n \geq N_0({\varepsilon},\nu,{{\mathscr{S}}_{\circ}})$ sufficiently large. It remains to consider sequences $\rho^n \in \Omega_1^{\nu} \cap \Omega_2^{\nu}$. Define the set of sequences $\rho^n$ with empirical distribution $P_{\rho^n}$ resulting in a $\xi$-positive relative entropy variance as $$\Omega_3^\xi:=\left\{ \rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n } : V( P_{\rho^n} |\sigma) \ge \xi\right\}, \label{eq:xiset}$$ where $\xi>0$ is a constant to be chosen later. For $\rho^n \notin \Omega_3^\xi$, we again pick out $\sigma^{\otimes n}$ from to find $D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) \leq D_h^{{\varepsilon}_n}(\rho^n\|\sigma^{\otimes n}) + \log 2$. Then, we employ in Proposition \[pr:asymptotics\] to obtain $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n \| \sigma^{\otimes n}) \le n I(P_{\rho^n}|\sigma) + \sqrt{\frac{n V(P_{\rho^n}|\sigma)}{{\varepsilon}^*}} + L_1 \log n < n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{\frac{n\xi}{{\varepsilon}^*}} + L_1 \log n . \label{eq:cheby1}\end{aligned}$$ For sequences $\rho^n \in \Omega_3^\xi$, by the Berry-Esseen-type bound in Proposition \[pr:asymptotics\], we have $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n \| \sigma^{\otimes n}) &\le n I(P_{\rho^n}|\sigma) + \sqrt{n V(P_{\rho^n}|\sigma)} \Phi^{-1}({\varepsilon})+ L_2 \log n \nonumber\\
&\leq n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}^{\nu}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) + L_2 \log n \label{eq:berry1} ,\end{aligned}$$ where we define $v_{{\varepsilon}}^{\nu}({{\mathscr{S}}_{\circ}})$ similarly to $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) = v_{{\varepsilon}}^0({{\mathscr{S}}_{\circ}})$ as $$\begin{aligned}
v_{{\varepsilon}}^{\nu}({{\mathscr{S}}_{\circ}}) := \begin{cases} \inf_{{\mathbb{P}}\in \Pi^{\nu}} V({\mathbb{P}}|\sigma) & \textrm{if }\ 0 < {\varepsilon}\leq \frac12 \\
\sup_{{\mathbb{P}}\in \Pi^{\nu}} V({\mathbb{P}}|\sigma) & \textrm{if }\ \frac12 < {\varepsilon}< 1 \end{cases} \end{aligned}$$ where we employed the set $\Pi^{\nu} \subseteq {\mathcal{P}}({{\mathscr{S}}_{\circ}})$ of probability measures close to $\Pi({{\mathscr{S}}_{\circ}})$, given as $$\begin{aligned}
\Pi^{\nu} := \bigg\{ {\mathbb{P}}\in {\mathcal{P}}({{\mathscr{S}}_{\circ}}) \,\bigg|\, \int {\textnormal{d}}{\mathbb{P}}(\rho)\, \Delta(\rho, \Gamma) \leq \nu \ \land \ \frac{1}{2}\Big\| \rho^{({\mathbb{P}})} - \sigma^*({{\mathscr{S}}_{\circ}}) \Big\|_1 \leq \nu \bigg\} .\end{aligned}$$ Clearly, the empirical distribution of a sequence $\rho^n$ is in $\Pi^{\nu}$ if and only if $\rho^n \in \Omega_1^{\nu} \cup \Omega_2^{\nu}$. The sets $\Pi^{\nu}$ are compact. Moreover, we may write $\Pi({{\mathscr{S}}_{\circ}}) = \bigcap_{\nu > 0} \Pi^{\nu}$ to recover the definition in .
Now, we will choose the parameters $\xi$ and $\nu$ differently depending on some properties of ${{\mathscr{S}}_{\circ}}$. Let us first consider two cases for which $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) > 0$.
1. $v_{\min}({{\mathscr{S}}_{\circ}}) >0$. In this case, the constant $\xi >0$ is chosen to be $\xi = \frac{ v_{\min}({{\mathscr{S}}_{\circ}})}2 > 0$. Now, for all $\nu$ sufficiently small we have $\inf_{{\mathbb{P}}\in \Pi^{\nu}} V({\mathbb{P}}|\sigma) > \xi$ so that $\Omega_1^{\nu} \cap \Omega_2^{\nu} \setminus \Omega_3^{\xi}$ is empty. Thus, combining and , we find $$\begin{aligned}
\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \leq \sup_{\rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n}} D_h^{{\varepsilon}_n}(\rho^n \| \sigma^n) \leq n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\,v_{{\varepsilon}}^{\nu}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) + O(\log n) \label{eq:type1}\end{aligned}$$
2. ${\varepsilon}> \frac{1}{2}$ and $v_{\max}({{\mathscr{S}}_{\circ}})>v_{\min}({{\mathscr{S}}_{\circ}})=0$. Here we note that $\Phi^{-1}({\varepsilon}) > 0$ and $v_{\varepsilon}({{\mathscr{S}}_{\circ}})>0$. Thus, we may choose $\xi>0$ sufficiently small so that $$\sqrt{\frac{\xi}{{\varepsilon}^*}}\le \sqrt{v_{\varepsilon}({{\mathscr{S}}_{\circ}})}\Phi^{-1}({\varepsilon}) \leq \sqrt{v_{\varepsilon}^{\nu}({{\mathscr{S}}_{\circ}})}\Phi^{-1}({\varepsilon}) \nonumber$$ for any $\nu > 0$. The bounds , and can then be summarized and holds.
The bounds for cases 1 and 2 can be restated as follows. For all $\nu > 0$ sufficiently small, we have $$\begin{aligned}
\limsup_{n \to \infty} \frac{\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) - n \chi({{\mathscr{S}}_{\circ}}) }{\sqrt{n}} \leq \sqrt{v_{{\varepsilon}}^{\nu}}\,\Phi^{-1}({\varepsilon})\end{aligned}$$ Since $\nu > 0$ is arbitrary small we take $\nu \searrow 0$. Then, it remains to show that $\lim_{\nu \to 0} v_{{\varepsilon}}^{\nu}({{\mathscr{S}}_{\circ}}) = v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})$. This is a consequence of the following lemma (proved in Appendix \[app:v-limit\]).
\[lm:v-limit\] Let $\Theta_1 \supseteq \Theta_2 \supseteq \ldots$ be a sequence of compact sets in a metric space and let $f: \Theta_1 \to \mathbb{R}$ be continuous and bounded. Then, $$\begin{aligned}
\lim_{n \to \infty}\, \inf_{x \in \Theta_n} f(x) = \inf_{x \in \Theta_{\infty}} f(x) \qquad \textrm{whenever}\qquad \Theta_{\infty} := \bigcap_{n \in \mathbb{N}} \Theta_n \neq \emptyset. \label{eq:limitcompact}
\end{aligned}$$
This establishes that $\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \leq n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) + o(\sqrt{n})$, as desired.
Let us now turn our attention to the cases for which $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) = 0$.
1. $v_{\max}({{\mathscr{S}}_{\circ}}) = v_{\min}({{\mathscr{S}}_{\circ}}) = 0$. Here, we note that for any $\xi > 0$ there exists a $\nu > 0$ such that $\sup_{{\mathbb{P}}\in \Pi^{\nu}} V({\mathbb{P}}|\sigma) < \xi$ and, thus, the set $\Omega_1^{\nu} \cap \Omega_2^{\nu} \cap \Omega_3^{\xi}$ is empty. Hence, the bounds and can be combined to yield $$\begin{aligned}
\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \leq \sup_{\rho^n \in {{\mathscr{S}}_{\circ}}^{\otimes n}} D_h^{{\varepsilon}_n}(\rho^n \| \sigma^n) \leq n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{\frac{n \xi}{{\varepsilon}^*}} + O(\log n) \label{eq:type2} .\end{aligned}$$
2. ${\varepsilon}\leq \frac{1}{2}$ and $v_{\max}({{\mathscr{S}}_{\circ}}) > v_{\min}({{\mathscr{S}}_{\circ}}) = 0$. Here, any choice of $\xi>0$ enforces that $$\begin{aligned}
\sqrt{\frac{\xi}{{\varepsilon}^*}} \geq 0 = \sqrt{v_{{\varepsilon}}^{\nu}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) . \end{aligned}$$ Thus, the bounds , and together establish that holds.
Again, let us restate the bounds for cases 3 and 4 as follows. For all $\xi > 0$, we have $$\begin{aligned}
\limsup_{n \to \infty} \frac{\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) - n \chi({{\mathscr{S}}_{\circ}}) }{\sqrt{n}} \leq \sqrt{ \frac{\xi}{{\varepsilon}^*}}.\nonumber\end{aligned}$$ Since $\xi>0$ is arbitrary, we may take $\xi \searrow 0$ and deduce that $$\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \le n\chi({{\mathscr{S}}_{\circ}}) + o\big(\sqrt{n}\big).\nonumber$$ This concurs with the second-order approximation since $v_{\varepsilon}({{\mathscr{S}}_{\circ}})$ is zero and concludes the proof.
Asymptotics of the ${\varepsilon}$-Hypothesis-Testing Divergence Radius: Beyond Second-Order {#sec:converethird}
--------------------------------------------------------------------------------------------
In this section we want to improve the upper bound of $o(\sqrt{n})$ in Theorem \[th:main\] to $O(\log n)$ for the important special case where ${{\mathscr{S}}_{\circ}}$ is a discrete set. To simplify the exposition here, we further assume that $v_{\min}({{\mathscr{S}}_{\circ}}) > 0$. Comparing with the proof of Proposition \[pr:thedifficultpart\], it is however easy to see that this condition can be relaxed to $v_{{\varepsilon}}({{\mathscr{S}}_{\circ}}) > 0$.
Let ${\varepsilon}\in (0,1)$ and ${{\mathscr{S}}_{\circ}}\subseteq {\mathscr{S}}$ be discrete and $v_{\min}({{\mathscr{S}}_{\circ}}) > 0$. Let $\{{\varepsilon}_n\}_{n=1}^{\infty}$ be any sequence satisfying $|{\varepsilon}_n - {\varepsilon}| \leq 1/\sqrt{n}$ for all $n$. Then, $$\begin{aligned}
\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \leq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\, v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\, \Phi^{-1}({\varepsilon}) + O(\log n) .
\end{aligned}$$
For any $n$, consider all sequences $\rho^n = \bigotimes_{i=1}^n \rho_i$ with $\rho_i \in {{\mathscr{S}}_{\circ}}$. The method of types [@csiszar98] reveals that $P_{\rho^n}$ is in a set ${\mathcal{P}}_n({{\mathscr{S}}_{\circ}}) \subseteq {\mathcal{P}}({{\mathscr{S}}_{\circ}})$ with cardinality satisfying $\log |{\mathcal{P}}_n({{\mathscr{S}}_{\circ}})| = O(\log n)$.
We use this for a further refinement of our state $\sigma^n$ (see also [@hayashi09 Sec. X.A]) as follows: $$\begin{aligned}
\sigma^n := \frac13 \sigma^{\otimes n} + \frac1{3 |{\mathscr{G}}^\gamma|} \sum_{\tau \in {\mathscr{G}}^\gamma } \tau^{\otimes n} + \frac{1}{3 |{\mathcal{P}}_n({{\mathscr{S}}_{\circ}})|} \sum_{P \in {\mathcal{P}}_n({{\mathscr{S}}_{\circ}})} \Big( \rho^{(P)} \Big)^{\otimes n} . \label{eq:sigman2}\end{aligned}$$ Clearly, Proposition \[pr:conv-bad\] still applies with this definition, and for any $\nu \in (0, 1)$ we find that $$\begin{aligned}
\sup_{\rho^n \notin \Omega_1^{\nu} \cap \Omega_2^{\nu}} D_h^{{\varepsilon}_n}(\rho^n \| \sigma^n)
\leq n\, \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\,v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon})
\end{aligned}$$ Now, observe that due to our condition on the channel, we have $v_{\min}({{\mathscr{S}}_{\circ}}) > 0$. Thus, $V(P) = \sum P(\rho)\,V\big(\rho\big\|\rho^{(P)}\big)$ evaluated for $P \in \Pi$ is lower bounded by $v_{\min}({{\mathscr{S}}_{\circ}})$. Moreover, by continuity, $\inf_{P \in \Pi^{\nu}} V(P) > v_{\min}({{\mathscr{S}}_{\circ}})/2$ if $\nu$ is chosen sufficiently small. Thus, we in particular have that $V(P_{\rho^n}) > v_{\min}/2$ for all $\rho^n \in \Omega_1^{\nu} \cap \Omega_2^{\nu}$. For such a sequence $\rho^n$, we apply Proposition \[pr:asymptotics\] to find $$\begin{aligned}
D_h^{{\varepsilon}_n}(\rho^n\|\sigma^n) &\leq D_h^{{\varepsilon}}\Big(\rho^n\Big\|\big(\rho^{(P)}\big)^{\otimes n}\Big) + \log |{\mathcal{P}}_n({{\mathscr{S}}_{\circ}})|\\
&\leq n I(P_{\rho^n}) + \sqrt{n\, V(P_{\rho^n})}\,\Phi^{-1}({\varepsilon}) + \log |{\mathcal{P}}_n({{\mathscr{S}}_{\circ}})| + L_3 \log n
\end{aligned}$$ for $n \geq N_3$. Thus, we immediately find $$\begin{aligned}
\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) \leq \sup_{P \in \Pi^{\nu}} \bigg( n I(P) + \sqrt{n\,V(P)}\,\Phi^{-1}({\varepsilon}) \bigg) + O(\log n) \label{eq:takethis1}
\end{aligned}$$ and it only remains to show that the supremum is achieved in $\Pi$, without too much loss. As Polyanskiy, Poor and Verdú discuss in [@polyanskiy10 App. J], we indeed have $$\begin{aligned}
\sup_{P \in \Pi^{\nu}} \bigg( n I(P) + \sqrt{n\,V(P)}\,\Phi^{-1}({\varepsilon}) \bigg) &= \sup_{P \in \Pi} \bigg( n I(P) + \sqrt{n\,V(P)}\,\Phi^{-1}({\varepsilon}) \bigg) + O(1) \label{eq:takethis2}
\end{aligned}$$ if $I(P)$ drops fast enough when we move away from $\Pi$ (but stay in $\Pi^{\nu}$) in the following sense. We require that $\frac{{\textnormal{d}}^2}{{\textnormal{d}}\alpha^2} I(P + \alpha v) \big|_{\alpha=0}$ is strictly negative for all $P \in \Pi$ and for all vectors $v$ satisfying $\sum_{\rho \in {{\mathscr{S}}_{\circ}}} v(\rho) = 0$ such that $P + v \notin \Pi$.[^12] This is equivalent to the condition $$\begin{aligned}
\frac{{\textnormal{d}}^2}{{\textnormal{d}}\alpha^2} H\Big(\rho^{(P)} + \alpha \Delta^{(v)} \Big) \bigg|_{\alpha = 0} < 0, \qquad \textrm{where} \quad \Delta^{(v)} := \sum_{\rho \in {{\mathscr{S}}_{\circ}}} v(\rho) \rho ,
\end{aligned}$$ which is satisfied due to Lemma \[lm:strict\] below.
Thus, combining and , we conclude that $$\begin{aligned}
\chi_h^{{\varepsilon}_n}({{\mathscr{S}}_{\circ}}^{\otimes n}) &\leq \sup_{P \in \Pi} \bigg( n I(P) + \sqrt{n\,V(P)}\,\Phi^{-1}({\varepsilon}) \bigg) + O(\log n) \\
&= n \chi({{\mathscr{S}}_{\circ}}) + \sqrt{n\,v_{{\varepsilon}}({{\mathscr{S}}_{\circ}})}\,\Phi^{-1}({\varepsilon}) + O(\log n) \,.\end{aligned}$$
\[lm:strict\] Let $\rho \in {\mathscr{S}}$ and let $\Delta \in {\mathscr{H}}$ with $\operatorname{tr}(\Delta)=0$, $\Delta \neq 0$ and $\Delta \ll \rho$. Then, we have $\frac{{\textnormal{d}}^2}{{\textnormal{d}}\lambda^2} H(\rho + \lambda \Delta) \big|_{\lambda=0} < 0$. In particular, $\rho \mapsto H(\rho)$ is strictly concave.
Note that strict negativity of the second derivative is a stronger property than strict concavity, which it implies.[^13]
We are grateful to David Reeb for allowing us to present a proof based on his ideas here [@reebpc13].
We define $\rho_{\lambda} := \rho + \lambda \Delta$. First, we note that $\frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} \rho_{\lambda}^{-1} = - \rho_{\lambda}^{-1} \big( \frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} {\rho_{\lambda}} \big) \rho_{\lambda}^{-1} = - \rho_{\lambda}^{-1} \Delta \rho_{\lambda}^{-1}$ by applying the product rule to $\frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} \big( \rho_{\lambda}^{-1} \rho_{\lambda} \big)$. Since $\Delta \ll \rho$, we can restrict to the subspace $\{\rho > 0\}$ without loss of generality. There, for $\lambda$ small enough such that $\rho_{\lambda} > 0$, we use the integral representation $$\begin{aligned}
\log \rho_{\lambda} = \int_0^\infty {\textnormal{d}}s\ (1-s)^{-1} {\mathrm{id}}- (\rho_{\lambda} + s\,{\mathrm{id}})^{-1}
\end{aligned}$$ which directly follows from its scalar analogue. As such, it is easy to compute $$\begin{aligned}
\frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} \log \rho_{\lambda} = \int_0^\infty {\textnormal{d}}s - \frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} (\rho_{\lambda} + s\,{\mathrm{id}})^{-1} = \int_0^\infty {\textnormal{d}}s\, (\rho_{\lambda} + s\,{\mathrm{id}})^{-1} \Delta (\rho_{\lambda} + s\,{\mathrm{id}})^{-1} .\end{aligned}$$ Recalling that $\frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} \operatorname{tr}\big(f(\rho_{\lambda})\big) = \operatorname{tr}\big(f'(\lambda) \frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} \rho_{\lambda} \big)$ for $f: t \mapsto - t \log t$, we find that $$\begin{aligned}
\frac{{\textnormal{d}}}{{\textnormal{d}}\lambda} H(\rho_{\lambda}) &= - \operatorname{tr}(\Delta \log \rho_{\lambda}) \qquad
\qquad \textrm{and}\\
\frac{{\textnormal{d}}^2}{{\textnormal{d}}\lambda^2} H(\rho_{\lambda}) &= - \int_0^\infty {\textnormal{d}}s \operatorname{tr}\Big( \Delta (\rho_{\lambda} + s\,{\mathrm{id}})^{-1} \Delta (\rho_{\lambda} + s\,{\mathrm{id}})^{-1} \Big) \\
&= - \int_0^\infty {\textnormal{d}}s \left\| (\rho_{\lambda} + s\,{\mathrm{id}})^{-\frac12} \Delta (\rho_{\lambda} + s\,{\mathrm{id}})^{-\frac12} \right\|_2^2.
\end{aligned}$$ For all $s > 0$ we thus find that the integrand is positive whenever $(\rho_{\lambda} + s\,{\mathrm{id}})^{-\frac12} \Delta (\rho_{\lambda} + s\,{\mathrm{id}})^{-\frac12} \neq 0$, which is evident since $\Delta \neq 0$ and $\rho_{\lambda} + s\,{\mathrm{id}}$ has full support. Hence, the desired inequality holds.
#### Acknowledgements: {#acknowledgements .unnumbered}
We thank Andreas Winter and Mark Wilde for discussions and comments on a previous version of this manuscript. MT also thanks David Reeb, Milán Mosonyi and especially Corsin Pfister for many insightful discussions, and the Isaac Newton Institute (Cambridge) for its hospitality while part of this work was completed. MT acknowledges funding by the Ministry of Education (MOE) and National Research Foundation Singapore, as well as MOE Tier 3 Grant “Random numbers from quantum processes” (MOE2012-T3-1-009). VT gratefully acknowledges financial support from the National University of Singapore (NUS) under startup grants R-263-000-A98-750/133 and the NUS Young Investigator Award R-263-000-B37-133.
Proof of Lemma \[lm:set-limit\] {#app:set-limit}
===============================
The inclusion $\supseteq$ is obvious because by the monotonicity of the convex hull operator and the fact that $\Theta_n\supseteq \Theta_\infty$ for any $n\in\mathbb{N}$, we have $\operatorname{conv}(\Theta_n) \supseteq \operatorname{conv}(\Theta_\infty )$.
It remains to prove the inclusion $\subseteq$. Let $$\begin{aligned}
\rho \in \bigcap_{n\in\mathbb{N}}\operatorname{conv}( \Theta_n) .\end{aligned}$$ This means that for every $n\in\mathbb{N}$, $\rho$ can be written as $\rho = \sum_{j=1}^{l} \alpha_{jn} \rho_{jn}$ where $\rho_{jn} \in \Theta_n$ for each $j = 1,\ldots, \ell$ and $(\alpha_{1n},\ldots,\alpha_{\ell n} )$ is a probability distribution. Note that $\ell$ is finite and does not depend on $n$ due to Caratheodory’s theorem since $\Theta_n$ for each $n$ are subsets of the same finite-dimensional vector space.
Consider the sequence $\{\rho_{1n}\}_{n\in\mathbb{N}} \subset \Theta_1$, i.e., $j=1$. Since $\Theta_1$ is compact, there must exists a convergent subsequence, say indexed by $n_{k}[1]$, i.e., the sequence $\{\rho_{1n_{k}{[1]} }\}_{k\in\mathbb{N}}$ is convergent and $$\lim_{k\to\infty} \rho_{1n_{k}{[1]}}=\rho_1$$ where $\rho_1 \in \Theta_\infty$ since $\Theta_n$ decrease to $\Theta_\infty$. Now, consider the sequence $\{ \rho_{2 n_k{[1]}}\}_{k\in\mathbb{N}}$. By the same argument, we may extract a subsequence of $n_{k}{[1]}$ indexed by $n_k{[2]}$ for which $$\lim_{k\to\infty} \rho_{2n_{k}{[2]}}=\rho_2, \qquad \textrm{and} \quad \rho_2 \in \Theta_\infty {\nonumber}.$$ Continue extracting subsequences until we reach $\ell$. Now consider the subsequence indexed by $m_k := n_k{[\ell]}$. Clearly, $\rho$ can be written also as $$\rho = \sum_{j=1}^{\ell} \alpha_{j m_k} \rho_{j m_k}. \label{eqn:rep_rho}$$ By construction, each $\rho_{j m_k}$ converges to $\rho_j \in \Theta_\infty$ when we take $k\to\infty$. So by representation of $\rho$ in , and the arbitrariness of $k$, we have that $\rho$ is a convex combination of elements from $\Theta_\infty$, i.e., $\rho\in\operatorname{conv}(\Theta_\infty)$ as desired.
Background and Proof of Proposition \[pr:asymptotics\] {#app:hypo}
======================================================
Nussbaum-Skoła Distributions
----------------------------
For the proof we leverage on a hierarchy of information measures in quantum information that was introduced in [@tomamichel12]. To apply these results, let us first review the following concept. For any two quantum states $\rho, \sigma \in {\mathscr{S}}$, we define their (classical) *Nussbaum-Skoła distributions* $P^{\rho,\sigma},\, Q^{\rho,\sigma} \in {\mathcal{P}}\big([d] \times [d]\big)$ via the relations [@nussbaum09] $$\begin{aligned}
P^{\rho,\sigma}(a,b) = r_a \big| \langle \phi_a | \psi_b \rangle \big|^2 \quad \textrm{and} \quad
Q^{\rho,\sigma}(a,b) = s_b \big| \langle \phi_a | \psi_b \rangle \big|^2\,,\end{aligned}$$ where $\rho = \sum_a r_a {|\phi_a\rangle\!\langle \phi_a|}$ and $\sigma = \sum_b s_b {|\psi_b\rangle\!\langle \psi_b|}$. We summarize some properties of the Nussbaum-Skoła distributions that will turn out to be of great use in the sequel (these were already pointed out in [@tomamichel12]). First, it is easy to verify by substitution that $$\begin{aligned}
\label{eq:nussbaum-moments}
D(\rho\|\sigma) = D(P^{\rho,\sigma} \| Q^{\rho,\sigma} ) \quad \textrm{and} \quad V(\rho\|\sigma) = V(P^{\rho,\sigma} \| Q^{\rho,\sigma} ) \,.\end{aligned}$$ Second, for product states $\rho_1 \otimes \rho_2$ and $\sigma_1 \otimes \sigma_2$, we have $$\begin{aligned}
\label{eq:nussbaum-product}
P^{\rho_1 \otimes \rho_2,\sigma_1 \otimes \sigma_2} = P^{\rho_1,\sigma_1} \otimes P^{\rho_2,\sigma_2}, \quad \textrm{and}
\quad Q^{\rho_1 \otimes \rho_2,\sigma_1 \otimes \sigma_2} = Q^{\rho_1,\sigma_1} \otimes Q^{\rho_2,\sigma_2} \,.\end{aligned}$$ Third, the condition $\sigma \gg \rho$ holds if and only if $Q^{\rho,\sigma} \gg P^{\rho,\sigma}$. Now, let $$\begin{aligned}
\Xi(\sigma) := 2 \Big\lceil \log \frac{\lambda_{\max}(\sigma)}{\tilde{\lambda}_{\min}(\sigma)} \Big\rceil,\end{aligned}$$ where $\lambda_{\max}(\sigma)$ and $\tilde{\lambda}_{\min}(\sigma)$ denote the largest and smallest nonzero eigenvalues of $\sigma$, respectively.
[[[@tomamichel12 Thm. 14]]{}]{.nodecor} \[lm:q-to-cl\] Let $\rho, \sigma \in {\mathscr{S}}$ and $\sigma \gg \rho$. Then, for $0 < \delta < \min\{{\varepsilon},\frac{1-{\varepsilon}}4\}$, $$\begin{aligned}
D_h^{{\varepsilon}}(\rho\|\sigma) &\leq D_s^{{\varepsilon}+4\delta}(P^{\rho,\sigma} \| Q^{\rho,\sigma})
+ \log \Xi(\sigma) + 4\log \frac{1}{\delta} + F_1({\varepsilon},\delta)
\,, \quad \textrm{and} \\
D_h^{{\varepsilon}}(\rho\|\sigma) &\geq D_s^{{\varepsilon}-\delta}(P^{\rho,\sigma} \| Q^{\rho,\sigma})
- \log \Xi(\sigma) - \log \frac{1}{\delta} - F_2({\varepsilon}) \,,
\end{aligned}$$ where $F_1({\varepsilon},\delta) := \log \frac{(1-{\varepsilon}) ({\varepsilon}+3\delta)}{1-({\varepsilon}+3\delta)}$ and $F_2({\varepsilon}) := \log \frac{1}{1-{\varepsilon}}$.
Here, the (classical) *information spectrum divergence* (in the spirit of Verdú and Han [@verdu93; @han02]) for two probability distributions $P, Q \in {\mathcal{P}}(\mathcal{X})$ (where $\mathcal{X}$ is a discrete set) is given by $$\begin{aligned}
D_s^{{\varepsilon}}(P \| Q) := \sup \bigg\{ R \in \mathbb{R} \,\bigg|\, \Pr_{X \leftarrow P} \bigg[ \log \frac{P(X)}{Q(X)} \leq R \bigg] \leq {\varepsilon}\bigg\}
\label{eq:inf-spec} .\end{aligned}$$
In the following, we also need the [*third absolute moment of the log-likelihood ratio*]{} between $P$ and $Q$, given as[^14] $$\begin{aligned}
T(P\|Q) &:= \sum_{x\in{\mathscr{X}}} P(x) \bigg| \log \frac{P(x)}{Q(x)} - D(P\|Q) \bigg|^3 \, \quad \textrm{and} \quad T(\rho\|\sigma) := T\big(P^{\rho,\sigma}\big\|Q^{\rho,\sigma}\big) \,. \end{aligned}$$
Non-Asymptotic Bounds on the ${\varepsilon}$-Hypothesis Testing Divergence
--------------------------------------------------------------------------
It is immediate that the probability appearing in the definition of the information spectrum divergence evaluated for product distributions is subject to the central limit theorem if the variance of $\log \frac{P}{Q}$ is bounded away from zero.
\[lm:asymptotics-2\] Let $ n \geq 1$, $\{ \rho_i \}_{i=1}^n$, for $\rho_i \in {\mathscr{S}}$ a set of states and let $\sigma \in {\mathscr{S}}$ such that $\sigma \gg \rho_i$ for all $i \in [n]$. Moreover, let ${\varepsilon}\in (0,1)$ and $\delta < \min\{{\varepsilon}, \frac{1-{\varepsilon}}{4}\}$. Define $$\begin{aligned}
D_n := \frac{1}{n} \sum_{i=1}^n D(\rho_i \| \sigma), \quad
V_n := \frac{1}{n} \sum_{i=1}^n V(\rho_i \| \sigma), \quad
T_n := \frac{1}{n} \sum_{i=1}^n T(\rho_i \| \sigma).
\end{aligned}$$ Then, the following Chebyshev-type inequalities hold: $$\begin{aligned}
D_h^{{\varepsilon}}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) &\leq n D_n + \sqrt{\frac{n V_n}{1-{\varepsilon}-4\delta}} + \log \big(n \Xi(\sigma)\big) + 4 \log \frac{1}{\delta} + F_{1}({\varepsilon},\delta) \,,\nonumber\\
D_h^{{\varepsilon}}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) &\geq n D_n - \sqrt{\frac{n V_n}{{\varepsilon}- \delta}} - \log \big(n \Xi(\sigma)\big) - \log \frac{1}{\delta} - F_{2}({\varepsilon}) \,. \label{eq:cheby-2}
\end{aligned}$$ Moreover, if $V_n > 0$, then the following Berry-Esseen type bounds holds: $$\begin{aligned}
D_h^{{\varepsilon}}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) &\leq n D_n + \sqrt{n V_n} \Phi^{-1}\bigg( {\varepsilon}+ 4\delta + \frac{6\, T_n}{\sqrt{nV_n^3}} \bigg) + \log \big(n \Xi(\sigma)\big)+ 4 \log \frac{1}{\delta} + F_{1}({\varepsilon},\delta) \,,\nonumber\\
D_h^{{\varepsilon}}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) &\geq n D_n + \sqrt{n V_n} \Phi^{-1}\bigg( {\varepsilon}- \delta - \frac{6\, T_{n}}{\sqrt{nV_n^3} } \bigg) - \log \big(n \Xi(\sigma)\big)- \log \frac{1}{\delta} - F_{2}({\varepsilon}) \,, \label{eq:berry-2}
\end{aligned}$$ where $F_1, F_2$ are given in Lemma \[lm:q-to-cl\].
We first apply Lemma \[lm:q-to-cl\] to replace $D_h^{{\varepsilon}}$ with $D_s^{{\varepsilon}+4\delta}$ (for the upper bounds) and $D_s^{{\varepsilon}-\delta}$ (for the lower bound). For this purpose, we note that $\Xi(\sigma^{\otimes n}) \leq n \Xi(\sigma)$. For the upper bound, this yields $$\begin{aligned}
D_h^{{\varepsilon}}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) \leq
D_s^{{\varepsilon}+4\delta} \Big( \bigotimes_{i=1}^n P^{\rho_i,\sigma} \Big\| \bigotimes_{i=1}^n Q^{\rho_i,\sigma} \Big)
+ \log \big(n \Xi(\sigma)\big)+ 4\log \frac{1}{\delta} + F_1({\varepsilon},\delta) \label{eq:asym-proof1}
\end{aligned}$$ Note that the information spectrum divergence on the right-hand side of is evaluated for classical product distributions $\bigotimes_{i=1}^n P^{\rho_i,\sigma}$ and $\bigotimes_{i=1}^n Q^{\rho_i,\sigma}$. Consider the independent random variables $$\begin{aligned}
Z_i := \log \frac{P^{\rho_i,\sigma}(A_i, B_i)}{Q^{\rho_i,\sigma}(A_i, B_i)}, \qquad (A_i, B_i) \leftarrow P^{\rho_i,\sigma}
\end{aligned}$$ for each $i \in [n]$. Then, the definition of the information spectrum divergence in yields $$\begin{aligned}
D_s^{{\varepsilon}+4\delta} \Big( \bigotimes_{i=1}^n P^{\rho_i,\sigma} \Big\| \bigotimes_{i=1}^n Q^{\rho_i,\sigma} \Big) = \sup \bigg\{ R \in \mathbb{R} \,\bigg|\, \Pr \bigg[ \sum_{i=1}^n Z_i \leq R \bigg] \leq {\varepsilon}+ 4\delta \bigg\} \,. \label{eq:asym-proof2}
\end{aligned}$$ Further, observe that the average mean and variance of $Z_i$ are respectively given by $$\begin{aligned}
\frac{1}{n} \sum_{i=1}^n \operatorname*{E}[Z_i] = \frac{1}{n} \sum_{i=1}^n D(P^{\rho_i,\sigma} \| Q^{\rho_i,\sigma}) &= \frac{1}{n} \sum_{i=1}^n D(\rho_i\|\sigma) = D_n \,, \qquad \textrm{and} \\
\frac{1}{n} \sum_{i=1}^n \operatorname*{Var}[Z_i] = \frac{1}{n} \sum_{i=1}^n V(P^{\rho_i,\sigma} \| Q^{\rho_i,\sigma}) &= \frac{1}{n} \sum_{i=1}^n V(\rho_i\|\sigma) = V_n \, .
\end{aligned}$$ Thus, we apply standard Chebyshev or Berry-Esseen [@feller71 Sec. XVI.5] bounds on the probability in . (See, e.g. [@tomamicheltan12 Lem. 5], for details.) The proof of the lower bounds proceeds analogously.
Uniform Upper Bounds
--------------------
The following two lemmas give uniform upper bounds on $V(\rho\|\sigma)$ and $T(\rho\|\sigma)$.
\[lm:V-uni\] Let ${{\mathscr{S}}_{\circ}}\subset {\mathscr{S}}$ and $\lambda_0 > 0$. Then, there exists a constant $V^+({{\mathscr{S}}_{\circ}},\lambda_0)$ such that $V(\rho\|\sigma) \leq V^+$ for all $\rho \in {{\mathscr{S}}_{\circ}}$ and $\sigma \in {\mathscr{S}}$ such that $\lambda_{\min}(\sigma) \geq \lambda_0$.
First, note that $(\rho, \sigma) \mapsto V(\rho\|\sigma)$ is continuous on the compact set ${\overline{{\mathscr{S}}}_{\circ}}\times \{ \sigma \in {\mathscr{S}}\,|\, \lambda_{\min}(\sigma) \geq \lambda_0 \}$ since $\sigma \gg \rho$ everywhere. Thus, we may simply choose $$\begin{aligned}
V^+ &:= \max \big\{ V(\rho\|\sigma) \,\big|\, \rho \in {\overline{{\mathscr{S}}}_{\circ}},\ \sigma \in {\mathscr{S}},\ \lambda_{\min}(\sigma) \geq \lambda_0 \big\} . \qedhere
\end{aligned}$$
\[lm:T-uni\] Let ${{\mathscr{S}}_{\circ}}\subset {\mathscr{S}}$ and $\sigma \in {\mathscr{S}}$ such that $\lambda_{\min}(\sigma) > 0$. Then, there exists a constant $T^+({{\mathscr{S}}_{\circ}},\sigma)$ such that $T(\rho\|\sigma) \leq T^+$ for all $\rho \in {{\mathscr{S}}_{\circ}}$.
We have $\sigma \gg \rho$ and thus $Q^{\rho,\sigma} \gg P^{\rho,\sigma}$ for all $\rho \in {{\mathscr{S}}_{\circ}}$ since $\sigma$ is strictly positive. Hence, $\rho \mapsto T(\rho\|\sigma) = T(P^{\rho,\sigma}\|Q^{\rho,\sigma})$ is continuous and it suffices to define $T^+ := \max_{\rho \in {\overline{{\mathscr{S}}}_{\circ}}} T(\rho\|\sigma)$.
For the following, let us define $V(P) := V\big(P\big|\rho^{(P)}\big)$ and $T(P) := \sum_{\rho \in {{\mathscr{S}}_{\circ}}} P(\rho)\, T\big(\rho\big\|\rho^{(P)}\big)$ for all $P \in {\mathcal{P}}({{\mathscr{S}}_{\circ}})$ in a discrete set ${{\mathscr{S}}_{\circ}}$. These quantitates have the following uniform upper bounds:
\[lm:VT-uni2\] Let ${{\mathscr{S}}_{\circ}}\subset {\mathscr{S}}$ be discrete. Then, there exist constants $V^{*}({{\mathscr{S}}_{\circ}})$ and $T^{*}({{\mathscr{S}}_{\circ}})$ such that $V(P) \leq V^{*}$ and $T(P) \leq T^{*}$ for all $P \in {\mathcal{P}}({{\mathscr{S}}_{\circ}})$.
To convince ourselves that the functions $P \mapsto V(P)$ and $P \mapsto T(P)$ are continuous, we note that, for all $P \in {\mathcal{P}}({{\mathscr{S}}_{\circ}})$ and all $\rho \in {{\mathscr{S}}_{\circ}}$ at least one of the following conditions holds 1) $P(\rho) = 0$ or 2) $\rho^{(P)} \gg \rho$. The lemma then follows from the fact that ${\mathcal{P}}({{\mathscr{S}}_{\circ}})$ is compact.
Proof of Proposition \[pr:asymptotics\]
---------------------------------------
The first statement relies on the Chebyshev-type inequalities in in Lemma \[lm:asymptotics-2\], which for any $\delta = \frac{1}{\sqrt{n}}$ and for $n$ sufficiently large such that $\frac{2}{\sqrt{n}} < \min \{ {\varepsilon}, \frac{1-{\varepsilon}}{4} \}$ yield $$\begin{aligned}
\bigg| D_h^{{\varepsilon}_n}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) - n D_n \bigg| \leq \sqrt{\frac{n V_n}{\min\big\{ 1-{\varepsilon}_n-\frac{4}{\sqrt{n}}, {\varepsilon}_n - \frac1{\sqrt{n}}\big\}}} + 3 \log n + \log \Xi(\sigma) \\
\qquad \qquad + \max \Big\{ F_1\Big({\varepsilon}_n,\frac{1}{\sqrt{n}}\Big), F_2({\varepsilon}_n) \Big\} .
\end{aligned}$$ Now, we note that $\Xi(\sigma) \leq 2 \log \frac{1}{\lambda_0} + 1 = O(1)$ and note that $$\begin{aligned}
&\sqrt{\frac{n V_n}{\min\big\{ 1-{\varepsilon}_n-\frac{4}{\sqrt{n}}, {\varepsilon}_n - \frac1{\sqrt{n}}\big\}}} \leq \sqrt{\frac{n V_n}{\min\big\{ 1-{\varepsilon}-\frac{5}{\sqrt{n}}, {\varepsilon}- \frac2{\sqrt{n}}\big\}}} = \sqrt{\frac{n V_n}{{\varepsilon}^*}} + O(1) \qquad \textrm{and} \\
&\max \Big\{ F_1\Big({\varepsilon}_n,\frac{1}{\sqrt{n}}\Big), F_2({\varepsilon}_n) \Big\} \leq \max \Big\{ F_1\Big({\varepsilon}+\frac{1}{\sqrt{n}},\frac{1}{\sqrt{n}}\Big), F_2({\varepsilon}-\frac{1}{\sqrt{n}}) \Big\} = O(1) .
\end{aligned}$$ Thus, any choice of $L_1 > 3$ will yield the desired result.
Finally, we have $V_n \leq V^+$ by Lemma \[lm:V-uni\] due to the assumption on $\lambda_{\min}(\sigma)$. We can thus pick the constant $$\begin{aligned}
K_1({\varepsilon},{{\mathscr{S}}_{\circ}},\lambda_0) > \sqrt{\frac{V^+}{{\varepsilon}^*}}
\end{aligned}$$ uniformly in $\{ \rho_i \}_{i=1}^n$. Finally, for any such choices of $L_1$ and $K_1$, we find a number $N_1({\varepsilon},{{\mathscr{S}}_{\circ}},\lambda_0)$ such that the statement holds.
The second statement is based on the Berry-Esseen-type inequalities in in Lemma \[lm:asymptotics-2\]. We prove the upper bound and note that the lower bound follows by an analogous argument. First, we use and set $\delta = \frac{1}{\sqrt{n}}$ to establish that $$\begin{aligned}
D_h^{{\varepsilon}_n}\Big(\bigotimes_{i=1}^n \rho_i \Big\| \sigma^{\otimes n} \Big) &\leq n D_n + \sqrt{n V_n} \Phi^{-1}\bigg( {\varepsilon}_n + \frac{4}{\sqrt{n}} + \frac{6\, T_n}{\sqrt{nV_n^3}} \bigg) + 3 \log n + \log \Xi(\sigma) + F_{1}\Big({\varepsilon}_n,\frac1{\sqrt{n}}\Big) \end{aligned}$$ Now, note that $V_n \geq \xi$ by assumption of the theorem and $T_n \leq T^+({{\mathscr{S}}_{\circ}},\sigma)$ by Lemma \[lm:T-uni\]. Since ${\varepsilon}\mapsto \Phi^{-1}({\varepsilon})$ is monotonically increasing, we find $$\begin{aligned}
\Phi^{-1}\bigg( {\varepsilon}_n + \frac{4}{\sqrt{n}} + \frac{6\, T_n}{\sqrt{nV_n^3}} \bigg) \leq \Phi^{-1}\bigg({\varepsilon}+ \frac{B}{\sqrt{n}} \bigg), \qquad \textrm{where} \quad B = 5 + 6 \frac{T^+({{\mathscr{S}}_{\circ}}, \sigma)}{\xi^{\frac{3}{2}}} .
\end{aligned}$$ Moreover, since $V_n \leq V^+$ and ${\varepsilon}\mapsto \Phi^{-1}({\varepsilon})$ is continuously differentiable we find that $$\begin{aligned}
\sqrt{n V_n} \Phi^{-1}\bigg( {\varepsilon}+ \frac{B}{\sqrt{n}} \bigg) \leq \sqrt{n V_n} \Phi^{-1}({\varepsilon}) + O(1).
\end{aligned}$$ by Taylor’s theorem. Collecting the remaining terms as $3 \log n + O(1)$ and choosing $L_2 > 3$ reveals that there exists a constant $N_2({\varepsilon},{{\mathscr{S}}_{\circ}},\sigma,\xi)$ such that the statement holds.
To confirm the final statement, we need to be a bit more careful because $\lambda_{\min}(P_{\rho^n})$ can be arbitrarily close to zero and thus Lemmas \[lm:V-uni\] and \[lm:T-uni\] do not apply. However, the proof goes through analogously if we instead of these lemmas employ Lemma \[lm:VT-uni2\].
Proof of Lemma \[lm:net\] {#app:net}
=========================
The following construction is likely not optimal in the parameters $\gamma$ and $|{\mathscr{G}}^{\gamma}|$, but it suffices for our purpose and allows us to use previously established results.
First, we employ a construction in [@hayden04b Lem. II.4] to establish that, for every $0 < \gamma < 1$, there exists a set of pure states $\{ \psi_i \}_{i \in [K]} \subseteq {\mathscr{S}}_{\circ}$ with cardinality $K \leq (5/\gamma)^{2d}$ such that the following holds: for every $\phi \in {\mathscr{S}}_{\circ}$, we have $\min_{i \in [K]} \| \phi - \psi_i \|_1 \leq \gamma$.
Second, consider the set ${\mathcal{P}}_m^{>0}$ of $m$-types [@csiszar98] with full support, defined as $$\begin{aligned}
{\mathcal{P}}_m^{>0} := \big\{ P \in {\mathcal{P}}([d]) \,\big|\, m P(i) \in [m] \textrm{ for all } i \in [d] \big\} .
\end{aligned}$$ Setting $m = \lceil 2 d \frac{1}{\gamma} \rceil$, we will now show that, for every $P \in {\mathcal{P}}([d])$, we have $\min_{Q \in {\mathcal{P}}_m^{\setminus 0}} \| P - Q \|_1 \leq \gamma$. To see this, we construct a $Q \in {\mathcal{P}}_m^{> 0}$ for every $P$ as follows. Start by setting $Q(i) = \frac{1}{m}$ for all $i \in [d]$. (Note that $m > d$ so that the total weight is smaller than one.) Then, pick any index $i$ for which $Q(i) < P(i)$ and increase $Q(i)$ by $\frac{1}{m}$. Repeat this until $Q$ is normalized. We observe that $\| P - Q \|_1 = 2 \sum_{i: Q(i) > P(i)} Q(i) - P(i) \leq \frac{2d}{m} \leq \gamma$ since $Q(i) - P(i)$ never exceeds $\frac{1}{m}$ by construction. Note that this choice also ensures that $\min_i Q(i) \geq \frac{1}{m}$. Furthermore, the number of types is bounded as [@csiszar98], $$\begin{aligned}
|{\mathcal{P}}_m^{> 0}| \leq (m+1)^{d-1} \leq ( 2d/\gamma + 2)^{d-1} .
\end{aligned}$$
Now, we are ready to define an $\gamma$-net for mixed states as follows: $$\begin{aligned}
{\mathscr{G}}^{\gamma} := \Big\{ \tau \in {\mathscr{S}}\,\Big|\, \tau = \sum_{i=1}^d Q(i) \psi_{\ell(i)}, \ Q \in {\mathcal{P}}_m^{> 0}, \ \ell: [d] \to [K] \Big\} .
\end{aligned}$$ We have $| {\mathscr{G}}^{\gamma}| = K^d \cdot |{\mathcal{P}}_m^{> 0}| \leq (5/\gamma)^{2d^2} (2d/\gamma+2)^{d-1}$. Moreover, let $\rho \in {\mathscr{S}}(B)$ be an arbitrary state with $\rho = \sum_i P(i)\, \phi_i$ its eigenvalue decomposition, where $\phi_i \in {\mathscr{S}}_{\circ}(B)$ are (mutually orthogonal) pure states and $P \in {\mathcal{P}}(B)$. Now, choose $Q \in {\mathcal{P}}_m^{> 0}$ and $\ell: [d] \to [K]$ such that $$\begin{aligned}
\| P - Q \|_1 \leq \gamma \quad \textrm{and} \quad \forall i \in [d] : \| \psi_{\ell(i)} - \phi_i \|_1 \leq {\varepsilon}.
\end{aligned}$$ For $\tau = \sum_{i=1}^d Q(i) \psi_{\ell(i)} \in {\mathscr{G}}^{\gamma}$, we then have $$\begin{aligned}
\| \rho - \tau \|_1 &\leq \sum_{i=1}^d \Big\| P(i) \phi_i - Q(i) \psi_{\ell(i)} \Big\|_1 \leq \sum_{i=1}^d P(i) \Big\| \phi_i - \psi_{\ell(i)} \Big\|_1 + \big| P(i) - Q(i) \big| \leq 2\gamma ,
\end{aligned}$$ where we used the triangle inequality multiple times.
To get the second statement, we employ a continuity result by Audenaert and Eisert [@audenaert05 Thm. 2], which ensures that $D(\rho\|\tau) \leq 4 \, \kappa^2/\beta$, where $\beta$ is the minimum eigenvalue of $\tau$, and $\kappa := \frac12 \| \rho - \tau \|_1$. By our construction of $\tau$—in particular, recall the construction of $Q \in {\mathcal{P}}_m^{> 0}$—we enforce that $\beta \geq \frac{1}{m}$. Hence, the above can be further bounded as $$\begin{aligned}
D(\rho\|\tau) \leq 4 \kappa\cdot \frac{\kappa}{\beta} \leq 4\gamma (2d + 1) ,
\end{aligned}$$ where we used that $\kappa \leq \gamma$ and $\kappa/\beta \leq \gamma m = \gamma \lceil 2 d \frac{1}{\gamma} \rceil \leq 2d + 1$.
Finally, we note that every $\tau\in{\mathscr{G}}^\gamma$ has minimum eigenvalue bounded from below by $\frac{1}{m}\ge 1/(2d/\gamma + 1)=\gamma/(2d+\gamma)$.
Auxiliary Lemmas for Sections \[sec:direct\] and \[sec:converse\] {#app:selection}
=================================================================
\[app:v-limit\] \[app:direct\]
Proof of Lemma \[lm:v-expand\]
------------------------------
This is a straightforward generalization of the argument in [@polyanskiy10 Lem. 62].
By a simple calculation (or employing the law of total variance), it is easy to verify that $$\begin{aligned}
&V\Bigg( \bigoplus_{\rho \in {{\mathscr{S}}_{\circ}}} P(\rho) \rho\, \Bigg\| \bigoplus_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho)
\rho^{(P)} \Bigg)\\
&\qquad \qquad = \sum_{\rho \in {{\mathscr{S}}_{\circ}}} P(\rho)\, V\big(\rho\big\|\rho^{(P)}\big) +
\sum_{\rho \in {{\mathscr{X}}_{\circ}}} P(\rho) \bigg( D\big(\rho\big\|\rho^{(P)}\big) - \sum_{\rho \in {{\mathscr{S}}_{\circ}}} P(\rho)\, D\big(\rho\big\|\rho^{(P)}\big) \bigg)^2 .
\end{aligned}$$ Thus, if we choose $P \in \Pi({{\mathscr{S}}_{\circ}})$ we clearly have $\rho^{(P)} = \sigma^*({{\mathscr{S}}_{\circ}})$ and the second term vanishes due to Property 2 of Theorem \[th:radius\].
Proof of Lemma \[lm:selection\]
-------------------------------
Let $\Xi^{\nu}$ be the set of indices for which $\Delta(\rho_i, \Gamma) >\frac{\nu}{2}$ holds. Then, we have $$\begin{aligned}
\nu<\frac{1}{n}\sum_{i=1}^n\Delta(\rho_i,\Gamma) \le\frac{1}{n}\sum_{i\in\Xi^\nu}1+\frac{1}{n}\sum_{i\notin\Xi^\nu}\frac{\nu}{2}\le\frac{ | \Xi^\nu|}{n}+\frac{\nu}{2}\end{aligned}$$ from which the condition on the cardinality of $\Xi^{\nu}$ follows.
Proof of Lemma \[lm:v-limit\]
-----------------------------
First note that all infima can be replaced with minima since the optimization is over compact sets. Denote $\min_{x \in \Theta_{\infty}} f(x)$ by $f*$. Clearly, $\limsup_{n \to \infty} \min_{x \in \Theta_n} f(x) \leq f^*$ since the inequality holds for every $n \in \mathbb{N}$ as $\Theta_n \supseteq \Theta_{\infty}$.
Suppose, for the sake of contradiction that $\liminf_{n \to \infty} \min_{x \in \Theta_n} f(x) < f^*$. Then, there exists a subsequence indexed by $\{ n_k \}_{k \in \mathbb{N}}$ with the property that $\min_{x \in \Theta_{n_k}} f(x) < f^*$. For every $k \in \mathbb{N}$, let $x_k \in \operatorname*{\arg\min}_{x \in \Theta_{n_k}} f(x)$ be any minimizer. Since the sets $\Theta_{n_k}$ are compact, there must exist a converging subsequence indexed by $\{ k_l \}_{l \in \mathbb{N}}$ such that $\lim_{l \to \infty} x_{k_l} = x^*$. Clearly, $x^*$ must be in $\Theta_{\infty}$. However, this leads to a contradiction with $f(x^*) < f^* = \min_{x \in \Theta_{\infty}} f(x)$. Hence, $\liminf_{n \to \infty} \min_{x \in \Theta_n} f(x) \geq f^*$.
[^1]: The latter two works establish that the remainder term satisfies $O(\log n) = \frac12 \log n + O(1)$ for most channels, and as such the third-order contribution is independent of the detailed channel description.
[^2]: A POVM in this context is a set of operators $\{ Q_m \}_{m \in {\mathscr{M}}}$ satisfying $Q_m \geq 0$ for all $m \in {\mathscr{M}}$ and $\sum_{m \in {\mathscr{M}}} Q_m = {\mathrm{id}}$.
[^3]: A dual problem to for the discrete case has also been established in [@sutter14], but elementary manipulations reveal that the dual program there is equivalent to the divergence radius optimization in .
[^4]: In particular, this set is not assumed to be countable or have any topological structure.
[^5]: For a classical analogue, recall that the convergence speed in the Berry-Esseen theorem is inversely proportional to $\sigma^{3}$, where $\sigma^2$ is the average variance of a sequence of non-i.i.d. random variables.
[^6]: But note that $\chi({{\mathscr{S}}_{\circ}})$ could generally be smaller than $C({\mathcal{W}})$.
[^7]: The first-order asymptotics (for the case of product state inputs) were discussed in detail in [@fujiwara98].
[^8]: To compare with [@wang10 Thm. 1], simply note that we may restrict our channel to a discrete classical-quantum channel bijectively mapping from an arbitrary index set to element in ${{\mathscr{X}}_{\circ}}$. The direct sum notation reveals the classical quantum structure of the underlying state. Finally, the constant $c$ in [@wang10] can be optimized over.
[^9]: For this reason we also do not rely on the ubiquitous $O(\cdot)$ notation here, which tends to hide such subtleties.
[^10]: To verify this, apply Proposition \[pr:one-shot-converse\] for the $n$-fold repetition of the channel, ${\mathcal{W}}^n$ with image ${{\mathscr{S}}_{\circ}}^{\otimes n}$, and choose $\mu(n) = 1/\sqrt{n}$ such that ${\varepsilon}_n = {\varepsilon}+ \mu$ in Proposition \[pr:strong\].
[^11]: To see why this is so, consider a sequence of states $\rho^n = \bigotimes_{i=1}^n \rho_i$ with $\rho_i \in \Gamma({{\mathscr{S}}_{\circ}})$. Then, following the notation in the proof of Proposition \[pr:strong\], we realize that $D_n = \chi({{\mathscr{S}}_{\circ}})$. However, since $\frac1n \sum_{i=1}^n \rho_i \neq \sigma^*({{\mathscr{S}}_{\circ}})$ in general, the empirical distribution $P_{\rho^n}$ can be arbitrarily far from $\Pi({{\mathscr{S}}_{\circ}})$. Thus, we cannot hope to bound $V_n$ in terms of $v_{{\varepsilon}}$.
[^12]: Note that $\frac{{\textnormal{d}}}{{\textnormal{d}}\alpha} I(P + \alpha v) \big|_{\alpha=0} = 0$ on $\Pi$ by definition as $I(P)$ is maximized on $\Pi$.
[^13]: This is revealed, for example, by the behavior of the function $t \mapsto -t^4$ at $t = 0$.
[^14]: It is not evident how a non-commutative version of this quantity should be defined directly; however, the commutative case is sufficient for our work.
| |
As Christmas arrives the students of Solon High School (SHS) share their Christmas trees and plans for decoration. Some SHS students celebrate Christmas, and some students do not, but those who do have exciting ways of celebrating and involving their Christmas trees in their traditions. Some people decorate their Christmas trees the same but some people have different and intriguing decorations they do each year.
Having interviewed many of the students at SHS there are many students who celebrate Christmas. Seven out of the 11 interviewees have 1-2 Christmas trees in their homes for the holidays. Excitingly, freshmen Ella Nasca and CJ Burney, sophomore Sasha Zahler and junior Kate Rose have three or more Christmas trees in their homes, of varying sizes.
Eight out of the 11 interviewees have a fake Christmas tree in their homes, while the other three have real ones in their homes. Senior Marissa Parfejewiec, though, has both a fake and a real Christmas tree in her house.
One thing that many people don’t realize is a debatable topic is whether or not to use a real or fake Christmas tree and which they like better.
“Real is better because the trees smell good and give a more authentic take to decorations and the Christmas vibe of the house,” Nasca said.
Zahler disagrees.
“I like fake Christmas trees because then I can put up as early as I want without having to worry about it dying,” she said.
As decorating a tree is one of the most exciting parts of the holiday season and Christmas time, some students describe how they decorate their Christmas trees for the holiday’s. Each person has a different family home and life, it is popular to decorate with lights and ornaments, but each house’s Christmas tree brings their own traditions to light.
“My Christmas tree is Mickey Mouse themed, so I use red and black lights along with ornaments,” Beautiful York said.
Student Lindsay Lebowitz even though she is Jewish still participates in Christmas traditions and decorates her tree with lights and ornaments.
Some students have a theme for their trees at home.
“I decorate my tree with lights and shiny ornaments, especially Star Wars themed ones,” Senior Jake Millet said.
Christmas time is a magical time that brings families together, and Christmas trees are a symbol of the holiday and the spirit in the air. All these students have their own unique ways of celebrating Christmas and how they go about the trees they use and their own opinions on these trees. | https://theshscourier.com/6182/feature/christmas-tree-o-christmas-tree/ |
Continuity of Operations Planning (COOP)
Continuity of Operations planning is a federal initiative to encourage people and departments to plan to address how critical operations will continue under a broad range of circumstances. COOP is important as a good business practice and because the planning fosters recovery and survival in and after emergency situations.
A COOP plan addresses emergencies from an all-hazards approach. A continuity of operations plan establishes policy and guidance ensuring that critical functions continue and that personnel and resources are relocated to an alternate facility in case of emergencies. The plan should develop procedures for:
- alerting, notifying, activating and deploying employees
- identify critical business functions
- establish an alternate facility
- roster personnel with authority and knowledge of functions
Create a continuity of operations plan for your department
Creating a continuity of operations plan is a guided process and a team effort which will draw on your understanding of department operations with Emergency Management’s expertise in preparing for contingencies. The University has implemented a new software product, Kuali Ready, that automates the COOP process. Please contact Emergency Management and we will provide training and materials to help you plan.
Guides and templates are available on this site and the Research Support site to facilitate the planning process. However, since this is a guided process, these guides and documents are only part of the planning process.
The COOP Planning Team
- Senior Management
- The department COOP coordinator or point-of-contact
- The COOP planning team
Senior Management ensures that the agency is capable of carrying out each respective function related to COOP. They oversee:
- Planning for continuity of operations
- Activating a COOP plan
- Restarting regular operations
Agency leaders may delegate many of their responsibilities, but overall accountability remains within their leadership.
The COOP Coordinator/POC serves as the agency’s manager for all COOP activities. The Coordinator manages all activities to ensure the agency can perform its critical functions during an emergency.
An effective COOP Planning team requires a mix of organization professionals and includes members from all levels of management and staff. It also consists of members from various divisions of the organization, including those not directly related to the mission, such as human resources. Team members should act as COOP coordinators for their respective functions, elements or divisions.
Emergency Management is not responsible for developing continuity of operations plans for individual schools, colleges, or departments, though it does coordinate COOP activities across the University and provide guidance to organizations. Emergency Management:
- drafts policies, procedures and projects necessary to implement COOP plans
- provides contingency-planning expertise to colleges, schools or departments as needed
- coordinates financial forecasting and reporting for COOP-related funding
- monitors and reports the current state of COOP capability across the University
- coordinates with external organizations
- integrates operation continuity with the overall emergency management program
Things to Consider
- How will plans be implemented, especially when there is no advanced warning?
- What is necessary to sustain and maintain operations for time periods of up to 30 days?
- What types of training, testing, and exercises are necessary for personnel, systems, processes, and procedures to ensure the department is ready?
Each Continuity of Operations Plan should include information about:
- The department’s mission statement
- Critical business functions, prioritized
- Recovery locations
- A department organization chart
- Continuity of authority
- Essential staff, including their contact information
- External resources
- Critical department records
- Computer inventory
- Necessary office supplies and furniture
- Software and IT needs
- Necessary communication tools
Develop the plan
Step One: Contact Emergency Management at [email protected]
Step Two: Select a Department COOP Coordinator/Point of Contact
Step Three: Assemble a Department COOP Planning Team
Step Four: Begin a Plan
This departmental Continuity Planning tool is specifically designed for Higher Education and is flexible enough for all types of departments.
An academic department, research unit, center or institute would typically create a single Continuity Plan for the department. Departments that share administrative staff (sometimes called clustered departments) would typically create a single plan encompassing all departments in the cluster.
If your unit is large and complex, it may be better to create separate plans for your major subunits, rather than a single plan for the entire organization.
Step Five: Collect Department Information
- Staff
- Faculty
- Student Staff
- Buildings
- Evacuation Plans
Step Six: Identify Action Plans
Action Items are the most important part of Continuity Planning. The process of thinking through the steps you need to take to prepare, is critical to developing a culture of preparedness.
Step Seven: Add Important Department Documents
Step Eight: Identify and Manage Critical Functions
We are asking here for the functions you normally perform. (Instruction is covered in another section.) Here are some typical examples:
- research
- non-elective surgery
- purchasing
- paying employees
- inpatient care
- facilities repair
- providing meals for residents of university housing
- pharmacy services
- grant accounting
Step Nine: Identify Information Technology Needs
The Information Technology Section should be completed by someone familiar with the IT applications and equipment used in your department.
Step Ten: Add Information for Academic Departments
Step Eleven: Add Key Resources
Key resources are those staff, equipment, supplies, facilities and skills that you need to effectively continue your operations in a disaster.
Step Twelve: Maintain your plan
- Disseminate the plan to employees. A shared drive or a password-protected web page can be good ways to ensure employees have access to the plan regardless of where they are.
- Review the plan annually and update as needed.
- Practice!
- Keep the plan in an accessible location at work and off site. (Keep in mind you may not have power or access to your office.)
For questions or assistance, contact Emergency Management at [email protected]. | http://www.bu.edu/emd/emergency-planning/coop/ |
The prints were discovered in the cliffs and the foreshore of Folkestone, Kent, after stormy conditions exposed new fossils in the area.
They are believed to have been left behind by ankylosaurs, rugged-looking armoured dinosaurs which were like living tanks; theropods, three-toed flesh-eating dinosaurs like the tyrannosaurus rex; and ornithopods, plant-eating ‘bird-hipped’ dinosaurs so-called because of their pelvic structure being similar to birds.
David Martill, professor of palaeobiology at the University of Portsmouth, said: ‘This is the first time dinosaur footprints have been found in strata known as the ‘Folkestone Formation’ and it’s quite an extraordinary discovery because these dinosaurs would have been the last to roam in this country before becoming extinct.
‘They were walking around close to where the white cliffs of Dover are now – next time you’re on a ferry and you see those magnificent cliffs just imagine that.’
A tridactyl dinosaur footprint (Credits: PA)
The find was made by Philip Hadland, collections and engagement curator at the Hastings Museum and Art Gallery.
He said: ‘Back in 2011, I came across unusual impressions in the rock formation at Folkestone. They seemed to be repeating and all I could think was they might be footprints.
‘This was at odds with what most geologists say about the rocks here, but I went looking for more footprints and as the tides revealed more by erosion, I found even better ones.
‘More work was needed to convince the scientific community of their validity, so I teamed up with experts at the University of Portsmouth to verify what I’d found.’
Phil Hadland, collections and engagement curator at the Hastings Museum and Art Gallery, next to a tridactyl dinosaur footprint (Credits: PA)
Most of the findings are isolated footprints but one discovery comprises six footprints – making a ‘trackway’, which is more than one consecutive print from the same animal.
This trackway of prints is similar in size to an elephant footprint and has been identified as likely to be an ornithopodichnus, of which similar but smaller-sized footprints have been found in China from the same time period.
The largest footprint found – measuring 80cm in width and 65cm in length – has been identified as belonging to an iguanodon-like dinosaur.
Iguanodons were also plant-eaters, grew up to 10 metres long and walked on both two legs or on all fours.
A Theropod footprint found close to the white cliffs of Dover. (Credits: PA)
Prof Martill said: ‘To find such an array of species in one place is fascinating. These dinosaurs probably took advantage of the tidal exposures on coastal foreshores, perhaps foraging for food or taking advantage of clear migration routes.’
Mr Hadland added: ‘Aside from finding that dinosaurs went to the seaside just like their modern relatives the birds, we have also found new evidence that changes the interpretation of the geology of the Folkestone Formation strata.
‘It just goes to show that what has been previously published about the geology of an area isn’t always correct and new insights can be made.
‘There is also the potential for almost anyone to make a discovery that adds to scientific knowledge from publicly accessible geological sites.’
The paper is published in Proceedings Of The Geologists’ Association and some of the footprints are currently on display at Folkestone Museum. | |
1. Introduction {#sec1-sensors-17-00928}
===============
In the age of artificial intelligence, sensors play quite an important role for environment sensing and information acquisition. At the same time, sensors may be affected by the complicated application environment. Thus, multi-sensor modeling and sensor data fusion are important issues in many real applications \[[@B1-sensors-17-00928],[@B2-sensors-17-00928],[@B3-sensors-17-00928],[@B4-sensors-17-00928],[@B5-sensors-17-00928],[@B6-sensors-17-00928],[@B7-sensors-17-00928]\]. Driven by real applications, many methods have been proposed for multi-sensor modeling and sensor data fusion \[[@B8-sensors-17-00928]\], including neural network models \[[@B1-sensors-17-00928],[@B9-sensors-17-00928]\], belief function theory \[[@B10-sensors-17-00928],[@B11-sensors-17-00928]\], Dempster--Shafer evidence theory \[[@B12-sensors-17-00928],[@B13-sensors-17-00928],[@B14-sensors-17-00928]\], fuzzy set theory \[[@B15-sensors-17-00928]\], Z-Numbers \[[@B16-sensors-17-00928]\], and so on \[[@B17-sensors-17-00928]\]. Furthermore, accompanied by multi-sensor data fusion, how to measure the uncertain degree or the reliability of sensor reports with heterogeneous sources is still an open issue. This paper focuses on multi-sensor data fusion by firstly proposing a new uncertainty measure and then designing a new uncertainty measure-based sensor data fusion approach.
Dempster--Shafer evidence theory \[[@B18-sensors-17-00928],[@B19-sensors-17-00928]\] is effective in uncertain information modeling and processing, and it has been widely used in many fields, such as multiple attribute decision making \[[@B20-sensors-17-00928],[@B21-sensors-17-00928],[@B22-sensors-17-00928]\], risk analysis \[[@B23-sensors-17-00928],[@B24-sensors-17-00928],[@B25-sensors-17-00928],[@B26-sensors-17-00928],[@B27-sensors-17-00928],[@B28-sensors-17-00928]\], pattern recognition \[[@B29-sensors-17-00928],[@B30-sensors-17-00928],[@B31-sensors-17-00928],[@B32-sensors-17-00928],[@B33-sensors-17-00928],[@B34-sensors-17-00928]\], fault diagnosis \[[@B11-sensors-17-00928],[@B12-sensors-17-00928],[@B13-sensors-17-00928]\], controller design \[[@B35-sensors-17-00928],[@B36-sensors-17-00928]\] and so on \[[@B37-sensors-17-00928],[@B38-sensors-17-00928],[@B39-sensors-17-00928]\]. Although Dempster--Shafer evidence theory is an effective method for information processing, the classical Dempster's rule of combination can't be used directly for conflict sensor data fusion, especially when there exists highly conflicting data, which may lead to counterintuitive results \[[@B40-sensors-17-00928],[@B41-sensors-17-00928]\]. One way to handle the conflict information in real applications, such as sensor data fusion, is to quantify the uncertainty before applying data fusion \[[@B11-sensors-17-00928],[@B13-sensors-17-00928],[@B42-sensors-17-00928]\]. However, how to measure the uncertainty of uncertain information in the framework of Dempster--Shafer evidence theory is still an open issue \[[@B43-sensors-17-00928],[@B44-sensors-17-00928],[@B45-sensors-17-00928]\].
Shannon entropy is an admitted way for measuring information volume \[[@B46-sensors-17-00928]\], which is a typical way for uncertainty measure in the probabilistic framework. Although Shannon entropy has been generalized to many fields, for example, as a generalization of Shannon entropy, network entropy is an effective measurement for measuring the complexity of networks \[[@B47-sensors-17-00928],[@B48-sensors-17-00928],[@B49-sensors-17-00928],[@B50-sensors-17-00928]\], and Shannon entropy can't be used directly among mass functions in the framework of Dempster--Shafer evidence theory because a mass function is a generalized probability assigned on the power set of the frame of discernment (FOD). To address this issue, many uncertainty measures in Dempster--Shafer framework are proposed, such as Hohle's confusion measure \[[@B51-sensors-17-00928]\], Yager's dissonance measure \[[@B52-sensors-17-00928]\], the weighted Hartley entropy \[[@B53-sensors-17-00928]\], Klir and Ramer's discord measure \[[@B54-sensors-17-00928]\], Klir and Parviz's strife measure \[[@B55-sensors-17-00928]\] and George and Pal's conflict measure \[[@B56-sensors-17-00928]\] and so on \[[@B43-sensors-17-00928],[@B44-sensors-17-00928]\]. However, the existed methods may not be that effective in some cases \[[@B57-sensors-17-00928]\]. Recently, another uncertainty measure named Deng entropy is proposed \[[@B57-sensors-17-00928]\]. Although Deng entropy had been successfully applied in some real applications \[[@B11-sensors-17-00928],[@B12-sensors-17-00928],[@B13-sensors-17-00928],[@B14-sensors-17-00928],[@B16-sensors-17-00928]\], Deng entropy didn't take into consideration of the scale of FOD, which means a loss of available and valuable information in information processing.
In order to overcome this shortage of Deng entropy, a weighted belief entropy based on Deng entropy is proposed in this paper. The weighted belief entropy takes advantage of the relative scale of a proposition with respect to the FOD. In other words, the cardinality of the proposition and the number of element in FOD are used to define the weight factor in the proposed uncertain measure. After that, based on the proposed measure, a new sensor data fusion approach is proposed. In the proposed method, the weighted belief entropy is used to preprocess the conflict data by measuring the uncertain degree of each body of evidence (BOE). Finally, the conflict data can be fused by Dempster's rule of combination.The effectiveness of the weighted belief entropy is verified with the numerical example in \[[@B57-sensors-17-00928]\]. In addition, the new sensor data fusion method is applied on fault diagnosis of a motor rotor to show the capacity of the new method in real application.
The rest of this paper is organized as follows. In [Section 2](#sec2-sensors-17-00928){ref-type="sec"}, the preliminaries on Dempster--Shafer evidence theory, Shannon entropy, Deng entropy and some uncertainty measures in Dempster--Shafer framework are briefly introduced. In [Section 3](#sec3-sensors-17-00928){ref-type="sec"}, the weighted belief entropy is proposed. In [Section 4](#sec4-sensors-17-00928){ref-type="sec"}, a new sensor data fusion approach based on the weighted belief entropy is proposed. In [Section 5](#sec5-sensors-17-00928){ref-type="sec"}, a numerical example for the new method is presented. In [Section 6](#sec6-sensors-17-00928){ref-type="sec"}, the proposed sensor data fusion method is used for fault diagnosis of a motor rotor. The conclusions are given in [Section 7](#sec7-sensors-17-00928){ref-type="sec"}.
2. Preliminaries {#sec2-sensors-17-00928}
================
Some preliminaries are briefly introduced in this section, including Dempster--Shafer evidence theory \[[@B18-sensors-17-00928],[@B19-sensors-17-00928]\], Shannon entropy \[[@B46-sensors-17-00928]\], Deng entropy \[[@B57-sensors-17-00928]\] and some other typical uncertainty measures in Dempster--Shafer framework \[[@B51-sensors-17-00928],[@B52-sensors-17-00928],[@B53-sensors-17-00928],[@B54-sensors-17-00928],[@B55-sensors-17-00928],[@B56-sensors-17-00928]\].
2.1. Dempster--Shafer Evidence Theory {#sec2dot1-sensors-17-00928}
-------------------------------------
Let $\mathsf{\Omega}\mspace{600mu} = \left\{ {\theta_{1},\theta_{2},\ldots,\theta_{i},\ldots,\theta_{N}} \right\}$ be a finite nonempty set of mutually exclusive and exhaustive events, $\mathsf{\Omega}$ is called the *frame of discernment* (FOD). The power set of $\mathsf{\Omega}$, denoted as $2^{\mathsf{\Omega}}$, is composed of $2^{N}$ elements denoted as follows:$$2^{\mathsf{\Omega}} = \left\{ {\mathsf{\varnothing},\left\{ \theta_{1} \right\},\left\{ \theta_{2} \right\},\ldots,\left\{ \theta_{N} \right\},\left\{ {\theta_{1},\theta_{2}} \right\},\ldots,\left\{ {\theta_{1},\theta_{2},\ldots,\theta_{i}} \right\},\ldots,\mathsf{\Omega}} \right\}.$$
A *mass function* *m* is defined as a mapping from the power set $2^{\mathsf{\Omega}}$ to the interval \[0,1\], which satisfies the following conditions \[[@B18-sensors-17-00928],[@B19-sensors-17-00928]\]:$$m\left( \mathsf{\varnothing} \right) = 0,{}\sum\limits_{A \in \mathsf{\Omega}}{m\left( A \right) = 1}.$$ If $m\left( A \right) > 0$, then *A* is called a *focal element*, the mass function $m\left( A \right)$ represents how strongly the evidence supports the proposition *A*.
A *body of evidence* (BOE), also known as a *basic probability assignment* (BPA) or *basic belief assignment* (BBA), is represented by the focal sets and their associated mass value:$$\left( {\Re,m} \right) = \left\{ {\left\langle {A,m\left( A \right)} \right\rangle:A \in 2^{\mathsf{\Omega}},m\left( A \right) > 0} \right\},$$ where *ℜ* is a subset of the power set $2^{\mathsf{\Omega}}$, and each $A \in \Re$ has an associated nonzero mass value $m\left( A \right)$.
A BPA *m* can also be represented by its associate belief function $Bel$ and plausibility function $Pl$ respectively, defined as follows:$$Bel\left( A \right) = \sum\limits_{\phi \neq B \subseteq A}{m\left( B \right)}\text{ }and\text{ }Pl\left( A \right) = \sum\limits_{B \cap A \neq \phi}{m\left( B \right)}.$$
In Dempster--Shafer evidence theory, two independent mass functions, denoted as $m_{1}$ and $m_{2}$, can be combined with Dempster's rule of combination defined as \[[@B18-sensors-17-00928],[@B19-sensors-17-00928]\]:$$m\left( A \right) = \left( {m_{1} \oplus m_{2}} \right)\left( A \right)\mspace{180mu} = \frac{1}{1 - k}\sum\limits_{B \cap C = A}{m_{1}\left( B \right)m_{2}\left( C \right)},$$ where *k* is a normalization constant representing the *degree of conflict* between $m_{1}$ and $m_{2}$, *k* is defined as \[[@B18-sensors-17-00928],[@B19-sensors-17-00928]\]:$$k = \sum\limits_{B \cap C = \mathsf{\varnothing}}{m_{1}\left( B \right)m_{2}\left( C \right)}.$$
2.2. Shannon Entropy {#sec2dot2-sensors-17-00928}
--------------------
As an uncertainty measure of information volume in a system or process, Shannon entropy plays a central role in information theory. Shannon entropy indicates that the information volume of each piece of information is directly connected to its uncertain degree.
Shannon entropy, as the information entropy, is defined as follows \[[@B46-sensors-17-00928]\]:$$H = - \sum\limits_{i = 1}^{N}{p_{i}\log_{b}p_{i}},$$ where *N* is the number of basic states, $p_{i}$ is the probability of state *i*, and $p_{i}$ satisfies $\sum\limits_{i = 1}^{N}p_{i} = 1$. If the unit of information is bits, then $b = 2$.
2.3. Deng Entropy {#sec2dot3-sensors-17-00928}
-----------------
Deng entropy is a generalization of Shannon entropy in Dempster--Shafer framework. If the information is modelled in the framework of a probability theory, Deng entropy can be degenerated to Shannon entropy. Deng entropy, denoted as $E_{d}$, is defined as follows \[[@B57-sensors-17-00928]\]:$$E_{d}\left( m \right) = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}\frac{m\left( A \right)}{2^{|A|} - 1}},$$ where $\left| A \right|$ denotes the cardinality of the proposition *A*, and *X* is the FOD. If and only if the mass value is assigned to single elements, Deng entropy can be degenerated to Shannon entropy, in this case, the form of Deng entropy is as follows:$$E_{d}\left( m \right) = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}\frac{m\left( A \right)}{2^{|A|} - 1}} = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}m\left( A \right)}.$$ For more details about Deng entropy, please refer to \[[@B57-sensors-17-00928]\].
2.4. Uncertainty Measures in Dempster--Shafer Framework {#sec2dot4-sensors-17-00928}
-------------------------------------------------------
In this section, some other typical uncertainty measures in the framework of Dempster--Shafer evidence theory are briefly introduced. Assume that *X* is the FOD, *A* and *B* are focal elements of the mass function, and $\left| A \right|$ denotes the cardinality of *A*. Then, the definitions of different uncertainty measures are shown as follows.
### 2.4.1. Hohle's Confusion Measure {#sec2dot4dot1-sensors-17-00928}
Hohle's confusion measure, denoted as $C_{H}$, is defined as follows \[[@B51-sensors-17-00928]\]:$$C_{H}\left( m \right) = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}Bel\left( A \right)}.$$
### 2.4.2. Yager's Dissonance Measure {#sec2dot4dot2-sensors-17-00928}
Yager's dissonance measure, denoted as $E_{Y}$, is defined as follows \[[@B52-sensors-17-00928]\]:$$E_{Y}\left( m \right) = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}Pl\left( A \right)}.$$
### 2.4.3. Dubois and Prade's Weighted Hartley Entropy {#sec2dot4dot3-sensors-17-00928}
Dubois and Prade's weighted Hartley entropy, denoted as $E_{DP}$, is defined as follows \[[@B53-sensors-17-00928]\]:$$E_{DP}\left( m \right) = \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}\left| A \right|}.$$
### 2.4.4. Klir and Ramer's Discord Measure {#sec2dot4dot4-sensors-17-00928}
Klir and Ramer's discord measure, denoted as $D_{KR}$, is defined as follows \[[@B54-sensors-17-00928]\]:$$D_{KR}\left( m \right) = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}\sum\limits_{B \subseteq X}{m\left( B \right)\frac{\left| {A \cap B} \right|}{\left| B \right|}}}.$$
### 2.4.5. Klir and Parviz's Strife Measure {#sec2dot4dot5-sensors-17-00928}
Klir and Parviz's strife measure, denoted as $S_{KP}$, is defined as follows \[[@B55-sensors-17-00928]\]:$$S_{KP}\left( m \right) = - \sum\limits_{A \subseteq X}{m\left( A \right)\log_{2}\sum\limits_{B \subseteq X}{m\left( B \right)\frac{\left| {A \cap B} \right|}{\left| A \right|}}}.$$
### 2.4.6. George and Pal's Conflict Measure {#sec2dot4dot6-sensors-17-00928}
The total conflict measure proposed by George and Pal, denoted as $TC_{GP}$, is defined as follows \[[@B56-sensors-17-00928]\]:$$TC_{GP}\left( m \right) = \sum\limits_{A \subseteq X}{m\left( A \right)\sum\limits_{B \subseteq X}{m\left( B \right)\left( {1 - \frac{\left| {A \cap B} \right|}{\left| {A \cup B} \right|}} \right)}}.$$
3. The Proposed Uncertainty Measurement {#sec3-sensors-17-00928}
=======================================
In this section, a weighted belief entropy based on Deng entropy is proposed. In the framework of Dempster--Shafer evidence theory, the uncertain information is represented not only by mass functions, the FOD is also a source of uncertainty, for example, the number of elements in a FOD can be changed even if the mass value of each proposition keeps still. However, the existed belief entropy, such as Dubois and Prade's weighted Hartley entropy and Deng entropy, only takes into consideration of mass functions, the cardinality of the proposition and the scale of FOD are ignored. This may lead to information loss in information processing.
3.1. Weighted Belief Entropy {#sec3dot1-sensors-17-00928}
----------------------------
By addressing more available information in the evidence, includes the scale of FOD, denoted as $\left| X \right|$, and the relative scale of a focal element with respect to the FOD, denoted as $\left( \left| A \right|/\left| X \right| \right)$. The new belief entropy named the weighted belief entropy is proposed as follows:$$E_{Wd}\left( m \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m\left( A \right)}{\left| X \right|}\log_{2}\frac{m\left( A \right)}{2^{|A|} - 1}},$$ where *X* is the FOD, *A* is the focal element of the mass function, $\left| A \right|$ denotes the cardinality of the proposition *A* and $\left| X \right|$ is the number of elements in FOD.
Compared with Deng entropy, the weighted belief entropy addresses more uncertain information in BOE, which can contribute to a more accurate information processing procedure in real applications. In the next subsection, a numerical example is used to show the effectiveness of the new measure, as well as making a comparison with some other typical uncertainty measures in Dempster--Shafer framework.
3.2. Numerical Example {#sec3dot2-sensors-17-00928}
----------------------
In order to test the capacity and superiority of the weighted belief entropy, recall the example in \[[@B57-sensors-17-00928]\].
Consider the mass function $m\left( \left\{ 6 \right\} \right) = 0.05$, $m\left( \left\{ {3,4,5} \right\} \right) = 0.05$, $m\left( T \right) = 0.8$ and $m\left( X \right) = 0.1$ in a FOD $X = \left\{ {1,2,...,14,15} \right\}$ with fifteen elements denoted as Element 1, \..., and Element 15. *T* represents a variable subset with its number of element changes from Element 1 to Element 14, as is shown in [Table 1](#sensors-17-00928-t001){ref-type="table"}.
Deng entropy $E_{d}$ in Equation ([8](#FD8-sensors-17-00928){ref-type="disp-formula"}) and the weighted belief entropy $E_{Wd}$ in Equation ([16](#FD16-sensors-17-00928){ref-type="disp-formula"}) are calculated with a changed proposition, and the results are shown in [Table 1](#sensors-17-00928-t001){ref-type="table"}. According to [Table 1](#sensors-17-00928-t001){ref-type="table"}, the values of weighted belief entropy are all smaller than that of Deng entropy. This is reasonable because more information in the BOE is taken into consideration with the weighted belief entropy, which means the weighted belief entropy has less information loss than Deng entropy. By reducing the uncertain degree, the new measure can be more accurate than Deng entropy for uncertainty measure in information processing.
[Figure 1](#sensors-17-00928-f001){ref-type="fig"} shows the comparison results of different uncertainty measures in Dempster--Shafer framework. The uncertain degree measured by Hohle's confusion measure never changes with the variation of the element number in proposition *T*, thus it cannot measure the variance of uncertainty in this case. Similar to the confusion measure, Yager's dissonance measure has a limited capacity of uncertainty measure in this case. The uncertain degree measured by Klir and Ramer's discord measure, Klir and Parviz's strife measure and George and Pal's conflict measure all decreases with the increase of the element number in proposition *T*. Thus, the confusion measure, dissonance measure, discord measure, strife measure and conflict measure can't effectively measure the increase of uncertain degree in BOE in this case. With Dubois and Prade's weighted Hartley entropy, Deng entropy and the weighted belief entropy, the uncertain degree increases significantly with the increase of the element number in proposition *T*. However, the weighted Hartley entropy and Deng entropy have significant information loss compared with the weighted belief entropy because the uncertain information modelled as the scale of FOD ($\left| X \right|$) hasn't been addressed in Equation ([8](#FD8-sensors-17-00928){ref-type="disp-formula"}) and Equation ([12](#FD12-sensors-17-00928){ref-type="disp-formula"}). Above all, the weighted belief entropy is more reasonable than the other uncertain measures in this case.
4. The Weighted Belief Entropy-Based Sensor Data Fusion Approach {#sec4-sensors-17-00928}
================================================================
In order to fuse conflict sensor data properly in real applications, in this section, a multi-sensor data fusion approach is proposed based on the new measure. In the proposed method, the uncertain degree of evidence is measured by the new weighted belief entropy. Five steps are included in the proposed multi-sensor data fusion method, as is shown in [Figure 2](#sensors-17-00928-f002){ref-type="fig"}.
The details of the five steps in [Figure 2](#sensors-17-00928-f002){ref-type="fig"} are presented as follows.
1. Uncertain data modeling with BPA.
In real applications, the information or data can be any style, so the first step of information processing in the frame of the Dempster--Shafer evidence theory mainly focuses on modeling uncertain information with BPAs in BOE.
2. Uncertainty measure of BPA with weighted belief entropy.
The uncertain degree of information modeled by BPAs in the 1st step needs to be measured with a proper uncertainty measure before further processing. In the proposed method, the weighted belief entropy is used to measure the uncertain degree of each BOE.
For the *i*th BOE ($i = 1,2,\cdots,n$), its corresponding uncertain degree with the weighted belief entropy $E_{Wd}$ is calculated as follows: $$E_{Wd}\left( m_{i} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{i}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{i}\left( A \right)}{2^{|A|} - 1}}.$$
3. Calculate the weight of each BOE.
Based on the value of weighted belief entropy, the weight of each BOE can be calculated. Generally, the weight of each BOE has a positive correlation with the uncertainty measure of each BPA \[[@B12-sensors-17-00928]\].
For the *i*th BOE ($i = 1,2,\cdots,n$), its weight based on the uncertain degree measured by the weighted belief entropy is calculated as follows: $$w_{i} = \frac{E_{Wd}\left( m_{i} \right)}{\sum\limits_{i = 1}^{n}{E_{Wd}\left( m_{i} \right)}}.$$
4. Calculate the weighted mass functions.
The weighted mass function of each proposition is calculated for the final data fusion.
For each proposition *A* in the BOE, the weighted mass function can be calculated as follows: $$m_{w}\left( A \right) = \sum\limits_{i = 1}^{n}{w_{i}m_{i}\left( A \right)}.$$
5. Data fusion with Dempster's rule of combination.
In the proposed method, the conflict among different evidence is transformed and measured by the weighted belief entropy, and now data fusion can be completed with Dempster's rule of combination.
For each proposition *A* in the BOE, the combination result can be obtained by calculating Dempster's rule of combination with $\left( n - 1 \right)$ times: $$m\left( A \right) = \left( \left( \left( \left( m_{w} \oplus m_{w} \right)_{1} \oplus m_{w} \right)_{2}... \oplus m_{w} \right)_{(n - 2)} \oplus m_{w} \right)_{(n - 1)}\left( A \right),n \geq 2.$$
5. Experiment with Artificial Data {#sec5-sensors-17-00928}
==================================
In order to verify the rationality and effectiveness of the proposed multi-sensor data fusion method, an experiment is performed in this section. The experiment in \[[@B58-sensors-17-00928]\] is recalled for the convenience of making a comparison with some other methods.
Considering a target recognition problem, three potential targets are denoted as *A*, *B* and *C*, respectively. The evidence reported by five sensors is modeled as BPAs, as is shown in [Table 2](#sensors-17-00928-t002){ref-type="table"}. Intuitively, as is described in \[[@B58-sensors-17-00928]\], the report from the 2nd sensor is contrary to the other four sensors and *A* will be the recognized target with the highest belief.
Execute the method in [Figure 2](#sensors-17-00928-f002){ref-type="fig"} of [Section 4](#sec4-sensors-17-00928){ref-type="sec"}. The result of the 1st step is adopted from \[[@B58-sensors-17-00928]\], and the BPAs are presented in [Table 2](#sensors-17-00928-t002){ref-type="table"}.
For the 2nd step, with Equation ([17](#FD17-sensors-17-00928){ref-type="disp-formula"}), the weighted belief entropy of each sensor report is calculated as follows: $$E_{Wd}\left( m_{1} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{1}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{1}\left( A \right)}{2^{|A|} - 1}} = 0.5221,$$ $$E_{Wd}\left( m_{2} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{2}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{2}\left( A \right)}{2^{|A|} - 1}} = 0.1563,$$ $$E_{Wd}\left( m_{3} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{3}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{3}\left( A \right)}{2^{|A|} - 1}} = 0.9647,$$ $$E_{Wd}\left( m_{4} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{4}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{4}\left( A \right)}{2^{|A|} - 1}} = 0.9921,$$ $$E_{Wd}\left( m_{5} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{5}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{5}\left( A \right)}{2^{|A|} - 1}} = 0.9225.$$
For the 3rd step, the weight of each evidence (BOE) can be calculated with Equation ([18](#FD18-sensors-17-00928){ref-type="disp-formula"}), the calculation results are as follows: $$w_{1} = \frac{E_{Wd}\left( m_{1} \right)}{\sum\limits_{i = 1}^{5}{E_{Wd}\left( m_{i} \right)}} = 0{.1468},$$ $$w_{2} = \frac{E_{Wd}\left( m_{2} \right)}{\sum\limits_{i = 1}^{5}{E_{Wd}\left( m_{i} \right)}} = 0{.0439},$$ $$w_{3} = \frac{E_{Wd}\left( m_{3} \right)}{\sum\limits_{i = 1}^{5}{E_{Wd}\left( m_{i} \right)}} = 0{.2712},$$ $$w_{4} = \frac{E_{Wd}\left( m_{4} \right)}{\sum\limits_{i = 1}^{5}{E_{Wd}\left( m_{i} \right)}} = 0{.2789},$$ $$w_{5} = \frac{E_{Wd}\left( m_{5} \right)}{\sum\limits_{i = 1}^{5}{E_{Wd}\left( m_{i} \right)}} = 0{.2593}.$$
For the 4th step, with Equation ([19](#FD19-sensors-17-00928){ref-type="disp-formula"}), the weighted mass function of each proposition in [Table 2](#sensors-17-00928-t002){ref-type="table"} is calculated as follows: $$m_{w}\left( A \right) = \sum\limits_{i = 1}^{5}{w_{i}m_{i}\left( A \right)} = 0.5264,$$ $$m_{w}\left( B \right) = \sum\limits_{i = 1}^{5}{w_{i}m_{i}\left( B \right)} = 0.1549,$$ $$m_{w}\left( C \right) = \sum\limits_{i = 1}^{5}{w_{i}m_{i}\left( C \right)} = 0.0484,$$ $$m_{w}\left( {A,C} \right) = \sum\limits_{i = 1}^{5}{w_{i}m_{i}\left( {A,C} \right)} = 0.2703.$$
Finally, for the 5th step, with Dempster's rule of combination and Equation ([20](#FD20-sensors-17-00928){ref-type="disp-formula"}), each of the new weighted mass function is fused four times. The fusion results are shown as follows: $$m\left( A \right) = \left( \left( \left( \left( m_{w} \oplus m_{w} \right)_{1} \oplus m_{w} \right)_{2} \oplus m_{w} \right)_{3} \oplus m_{w} \right)_{4}\left( A \right) = 0.9895,$$ $$m\left( B \right) = \left( \left( \left( \left( m_{w} \oplus m_{w} \right)_{1} \oplus m_{w} \right)_{2} \oplus m_{w} \right)_{3} \oplus m_{w} \right)_{4}\left( B \right) = 0.0003,$$ $$m\left( C \right) = \left( \left( \left( \left( m_{w} \oplus m_{w} \right)_{1} \oplus m_{w} \right)_{2} \oplus m_{w} \right)_{3} \oplus m_{w} \right)_{4}\left( C \right) = 0.0057,$$ $$m\left( {A,C} \right) = \left( \left( \left( \left( m_{w} \oplus m_{w} \right)_{1} \oplus m_{w} \right)_{2} \oplus m_{w} \right)_{3} \oplus m_{w} \right)_{4}\left( {A,C} \right) = 0.0045.$$
With the proposed method, it can be concluded that target *A* is the recognized target. The results of this experiment with different methods are shown in [Table 3](#sensors-17-00928-t003){ref-type="table"}. Although the experiment results with the methods in \[[@B11-sensors-17-00928],[@B58-sensors-17-00928],[@B59-sensors-17-00928]\] all get a high belief on target *A*, the proposed method has the highest belief (98.95%) on the recognized target *A*. In addition, in \[[@B11-sensors-17-00928]\], the method for evidence modification is based on evidence distance and Deng entropy simultaneously, which is not convincing, because both evidence distance and Deng entropy are based on mass functions of BOE, thus there exists a coupling relationship among those two indices in \[[@B11-sensors-17-00928]\]. Compared with the methods in \[[@B11-sensors-17-00928],[@B58-sensors-17-00928],[@B59-sensors-17-00928]\], the weighted belief entropy in the new method contributes to a stronger capacity in conflict data fusion by addressing more available uncertain information in BOE.
6. Application in Fault Diagnosis {#sec6-sensors-17-00928}
=================================
In this section, the proposed method is applied to an experiment of fault diagnosis for a motor rotor. The practical data in \[[@B16-sensors-17-00928]\] is adopted for the convenience of making a comparative study with some other methods.
6.1. Problem Description {#sec6dot1-sensors-17-00928}
------------------------
According to \[[@B16-sensors-17-00928]\], suppose there are three types of fault in a motor rotor, denoted as $F_{1} = \left\{ Rotor\mspace{600mu}\mspace{600mu} unbalance \right\}$, $F_{2} = \left\{ Rotor\mspace{600mu}\mspace{600mu} misalignment \right\}$ and $F_{3} = \left\{ Pedestal\mspace{600mu}\mspace{600mu} looseness \right\}$, respectively. Three vibration acceleration sensors are placed in different installation positions to collect the vibration signal. The acceleration vibration frequency amplitudes at the frequencies of $Freq1$, $Freq2$ and $Freq3$ are taken as the fault feature variables. The results of sensor reports modelled as BOEs are presented in [Table 4](#sensors-17-00928-t004){ref-type="table"}, where $m_{s_{1}}\left( \cdot \right)$, $m_{s_{2}}\left( \cdot \right)$ and $m_{s_{3}}\left( \cdot \right)$ denote the BOEs reported from these three vibration acceleration sensors.
6.2. Data Fusion Based on the New Method {#sec6dot2-sensors-17-00928}
----------------------------------------
Execute the method presented in [Section 4](#sec4-sensors-17-00928){ref-type="sec"} to solve the fault diagnosis problem mentioned above.
**Step 1** Uncertain data modeling with BPA.
In this paper, BPAs of sensor reports are directly adopted from \[[@B16-sensors-17-00928]\], as is shown in [Table 4](#sensors-17-00928-t004){ref-type="table"}. In real applications, how to model uncertain information with BPAs is an open issue \[[@B60-sensors-17-00928],[@B61-sensors-17-00928]\], which is not the scope of this paper. For more information about generating BPAs of [Table 4](#sensors-17-00928-t004){ref-type="table"}, please refer to \[[@B16-sensors-17-00928]\].
**Step 2** Uncertainty measure of BPA with weighted belief entropy.
In the proposed method, the uncertainty of sensor reports is measured based on the weighted belief entropy. With Equation ([17](#FD17-sensors-17-00928){ref-type="disp-formula"}), the weighted belief entropy of each BOE under the vibration acceleration frequency of $Freq1$ is calculated as follows: $$E_{Wd}\left( m_{s_{1}} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{s_{1}}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{s_{1}}\left( A \right)}{2^{|A|} - 1}} = 0.5657,$$ $$E_{Wd}\left( m_{s_{2}} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{s_{2}}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{s_{2}}\left( A \right)}{2^{|A|} - 1}} = 0.7096,$$ $$E_{Wd}\left( m_{s_{3}} \right) = - \sum\limits_{A \subseteq X}{\frac{\left| A \right|m_{s_{3}}\left( A \right)}{\left| X \right|}\log_{2}\frac{m_{s_{3}}\left( A \right)}{2^{|A|} - 1}} = 0.7206.$$
Similarly, the weighted belief entropy of sensor reports under $Freq2$ and $Freq3$ can be calculated, and the results are shown in [Table 5](#sensors-17-00928-t005){ref-type="table"}.
**Step 3** Calculate the weight of each BOE.
With Equation ([18](#FD18-sensors-17-00928){ref-type="disp-formula"}), for the vibration acceleration frequency of $Freq1$, the weight of each BOE for evidence modification is calculated as follows: $$w_{S_{1}} = \frac{E_{Wd}\left( m_{s_{1}} \right)}{\sum\limits_{i = 1}^{3}{E_{Wd}\left( m_{s_{i}} \right)}} = \frac{0.5657}{0.5657 + 0.7096 + 0.7206} = 0.2834,$$ $$w_{S_{2}} = \frac{E_{Wd}\left( m_{s_{2}} \right)}{\sum\limits_{i = 1}^{3}{E_{Wd}\left( m_{s_{i}} \right)}} = \frac{0.7096}{0.5657 + 0.7096 + 0.7206} = 0.3555,$$ $$w_{S_{3}} = \frac{E_{Wd}\left( m_{s_{3}} \right)}{\sum\limits_{i = 1}^{3}{E_{Wd}\left( m_{s_{i}} \right)}} = \frac{0.7206}{0.5657 + 0.7096 + 0.7206} = 0.3610.$$
The weight of different sensor reports under $Freq2$ and $Freq3$ is shown in [Table 6](#sensors-17-00928-t006){ref-type="table"}.
**Step 4** Calculate the weighted mass functions.
With Equation ([19](#FD19-sensors-17-00928){ref-type="disp-formula"}), the modified mass function for each judgement on fault types with respect to $Freq1$ can be calculated as follows: $m_{w}\left( \left\{ {F2} \right\} \right) = \sum\limits_{i = 1}^{3}{w_{s_{i}}m_{i}\left( \left\{ {F2} \right\} \right)} = 0.2834 \times 0.8176 + 0.3555 \times 0.5658 + 0.3610 \times 0.2403 = 0.5196,$$m_{w}\left( \left\{ {F3} \right\} \right) = \sum\limits_{i = 1}^{3}{w_{s_{i}}m_{i}\left( \left\{ {F3} \right\} \right)} = 0.2834 \times 0{.0003} + 0.3555 \times 0{.0009} + 0.3610 \times 0{.0004} = 0.0006,$$m_{w}\left( \left\{ {F1,F2} \right\} \right) = \sum\limits_{i = 1}^{3}{w_{s_{i}}m_{i}\left( \left\{ {F1,F2} \right\} \right)} = 0.2834 \times 0{.1553} + 0.3555 \times 0{.0646} + 0.3610 \times 0{.0141} = \mspace{600mu} 0.0721,$$m_{w}\left( \left\{ {F1,F2,F3} \right\} \right) = \sum\limits_{i = 1}^{3}{w_{s_{i}}m_{i}\left( \left\{ {F1,F2,F3} \right\} \right)} = 0.2834 \times 0.0268 + 0.3555 \times 0.3687 + 0.3610 \times 0.7452 = 0.4077.$
The modified mass function for $Freq2$ and $Freq3$ can also be calculated with Equation ([19](#FD19-sensors-17-00928){ref-type="disp-formula"}), and the results are shown in [Table 7](#sensors-17-00928-t007){ref-type="table"}.
**Step 5** Data fusion with Dempster's rule of combination.
With Equation ([20](#FD20-sensors-17-00928){ref-type="disp-formula"}), for the vibration acceleration frequency of $Freq1$, the modified mass function will be fused with Dempster's rule of combination two times, shown as follows: $$m\left( \left\{ {F2} \right\} \right) = \left( {\left( {m_{w} \oplus m_{w}} \right)_{1} \oplus m_{w}} \right)_{2}\left( \left\{ {F2} \right\} \right) = 0.8891,$$ $$m\left( \left\{ {F3} \right\} \right) = \left( {\left( {m_{w} \oplus m_{w}} \right)_{1} \oplus m_{w}} \right)_{2}\left( \left\{ {F3} \right\} \right) = 0.0003,$$ $$m\left( \left\{ {F1,F2} \right\} \right) = \left( {\left( {m_{w} \oplus m_{w}} \right)_{1} \oplus m_{w}} \right)_{2}\left( \left\{ {F1,F2} \right\} \right) = 0.0427,$$ $$m\left( \left\{ {F1,F2,F3} \right\} \right) = \left( {\left( {m_{w} \oplus m_{w}} \right)_{1} \oplus m_{w}} \right)_{2}\left( \left\{ {F1,F2,F3} \right\} \right) = 0.0679.$$
The fusion results for $Freq2$ and $Freq3$ are shown in [Table 8](#sensors-17-00928-t008){ref-type="table"}.
6.3. Discussion {#sec6dot3-sensors-17-00928}
---------------
The result of fault diagnosis, according to [Table 8](#sensors-17-00928-t008){ref-type="table"}, is that $F2$ is the fault type. The conflict of sensor reports in the problem, e.g., under $Freq2$, the belief on $F2$ is 0.8176, 0.5658 and 0.2403, respectively, is overcome with the new method. According to [Table 9](#sensors-17-00928-t009){ref-type="table"}, the fusion result is consistent with the method in \[[@B16-sensors-17-00928]\]. In addition, the fusion result with the proposed method has a higher support degree on the decision that $F2$ is the diagnosis result in comparison with the method in \[[@B16-sensors-17-00928]\].
Three reasons contribute to the effectiveness and superiority of the new multi-sensor data fusion method. Firstly, the new method is based on the new uncertainty measure, the new measure can address more uncertain information in the Dempster--Shafer evidence theory framework, which contributes to a more accurate experiment result in comparison with \[[@B16-sensors-17-00928]\]. Secondly, the sensor data is preprocessed properly with the new uncertainty measure in the proposed sensor data fusion method, which is very important in combining conflict evidence. Finally, the merits of Dempster's rule, such as satisfying the rule of commutativity and associativity, guarantee the rationality of the fusion result.
7. Conclusions {#sec7-sensors-17-00928}
==============
In this paper, in the Dempster--Shafer evidence theory framework, the weighted belief entropy is proposed based on Deng entropy. The new measure takes advantage of information included in, not only the mass function, but also the scale of the FOD. By addressing more information in a BOE, which means less information loss in information processing, the weighted belief entropy can quantify the uncertainty of evidence effectively. The numerical example shows that this new measure can quantify the uncertainty of evidence more accurately, which is helpful for information processing.
Based on the weighted belief entropy, a multi-sensor data fusion approach is proposed in this paper. A numerical example and an application on fault diagnosis are presented to verify the rationality and effectiveness of the new sensor data fusion method. Both the numerical example and the application indicate that the new measure contributes to a more accurate sensor data fusion method by addressing more uncertain information in the Dempster--Shafer evidence theory framework (BOE).
Further study of this work will be focused on extending the new measure and the proposed multi-sensor data fusion approach to solve more problems in industrial applications.
The authors greatly appreciate the editor's encouragement and the two anonymous reviewers' constructive comments to improve this paper. The work is partially supported by the National Natural Science Foundation of China (Grant No. 61671384), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2016JM6018), the Aviation Science Foundation (Grant No. 20165553036), the Fund of Shanghai Aerospace Science and Technology (Grant No. SAST2016083) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant No. CX201705).
Y.T. and D.Z. designed and performed the research. Y.T. wrote the manuscript. Y.T. and S.X. performed the computation. Y.T. and Z.H. analyzed the data. Z.H. contributed analysis tools. All authors discussed the results and commented on the manuscript.
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.
{#sensors-17-00928-f001}
{#sensors-17-00928-f002}
sensors-17-00928-t001_Table 1
######
Comparison between the weighted belief entropy and Deng entropy with a variable proposition *T*.
Cases Deng Entropy Weighted Belief Entropy
----------------------------------- -------------- -------------------------
$T = \left\{ 1 \right\}$ 2.6623 2.5180
$T = \left\{ {1,2} \right\}$ 3.9303 3.7090
$T = \left\{ {1,2,3} \right\}$ 4.9082 4.6100
$T = \left\{ {1,...,4} \right\}$ 5.7878 5.4127
$T = \left\{ {1,...,5} \right\}$ 6.6256 6.1736
$T = \left\{ {1,...,6} \right\}$ 7.4441 6.9151
$T = \left\{ {1,...,7} \right\}$ 8.2532 7.6473
$T = \left\{ {1,...,8} \right\}$ 9.0578 8.3749
$T = \left\{ {1,...,9} \right\}$ 9.8600 9.1002
$T = \left\{ {1,...,10} \right\}$ 10.6612 9.8244
$T = \left\{ {1,...,11} \right\}$ 11.4617 10.5480
$T = \left\{ {1,...,12} \right\}$ 12.2620 11.2714
$T = \left\{ {1,...,13} \right\}$ 13.0622 11.9946
$T = \left\{ {1,...,14} \right\}$ 13.8622 12.7177
sensors-17-00928-t002_Table 2
######
Basic probability assignment (BPA) of artificial data.
BPA $\mathbf{\mathbf{m}\left( \mathbf{A} \right)}$ $\mathbf{\mathbf{m}\left( \mathbf{B} \right)}$ $\mathbf{\mathbf{m}\left( \mathbf{C} \right)}$ $\mathbf{\mathbf{m}\left( \mathbf{A},\mathbf{C} \right)}$
------------------------------------------------ ------------------------------------------------ ------------------------------------------------ ------------------------------------------------ -----------------------------------------------------------
1st Sensor report: $m_{1}\left( \cdot \right)$ 0.41 0.29 0.3 0
2nd Sensor report: $m_{2}\left( \cdot \right)$ 0 0.9 0.1 0
3rd Sensor report: $m_{3}\left( \cdot \right)$ 0.58 0.07 0 0.35
4th Sensor report: $m_{4}\left( \cdot \right)$ 0.55 0.1 0 0.35
5th Sensor report: $m_{5}\left( \cdot \right)$ 0.6 0.1 0 0.3
sensors-17-00928-t003_Table 3
######
Experimental results with different methods.
Methods $\mathbf{\mathbf{m}\left( \mathbf{A} \right)}$ $\mathbf{\mathbf{m}\left( \mathbf{B} \right)}$ $\mathbf{\mathbf{m}\left( \mathbf{C} \right)}$ $\mathbf{\mathbf{m}\left( \mathbf{A},\mathbf{C} \right)}$
--------------------------------------------------- ------------------------------------------------ ------------------------------------------------ ------------------------------------------------ -----------------------------------------------------------
Deng et al.'s method \[[@B58-sensors-17-00928]\] 0.9820 0.0039 0.0107 0.0034
Zhang et al.'s method \[[@B59-sensors-17-00928]\] 0.9820 0.0033 0.0115 0.0032
Yuan et al.'s method \[[@B11-sensors-17-00928]\] 0.9886 0.0002 0.0072 0.0039
The proposed method 0.9895 0.0003 0.0057 0.0045
sensors-17-00928-t004_Table 4
######
Data for fault diagnosis modelled as BPAs \[[@B16-sensors-17-00928]\].
*Freq*1 *Freq*2 *Freq*3
--------------------------------- -------- -------- --------- -------- -- -------- --------- -- -------- -------- --------- --------
$m_{s_{1}}\left( \cdot \right)$ 0.8176 0.0003 0.1553 0.0268 0.6229 0.3771 0.3666 0.4563 0.1185 0.0586
$m_{s_{2}}\left( \cdot \right)$ 0.5658 0.0009 0.0646 0.3687 0.7660 0.2341 0.2793 0.4151 0.2652 0.0404
$m_{s_{3}}\left( \cdot \right)$ 0.2403 0.0004 0.0141 0.7452 0.8598 0.1402 0.2897 0.4331 0.2470 0.0302
sensors-17-00928-t005_Table 5
######
Weighted belief entropy of sensor reports under different frequencies.
$\mathbf{\mathbf{E}_{\mathbf{W}\mathbf{d}}\left( \cdot \right)}$ $\mathbf{\mathbf{Freq}1}$ $\mathbf{\mathbf{Freq}2}$ $\mathbf{\mathbf{Freq}3}$
------------------------------------------------------------------ --------------------------- --------------------------- ---------------------------
$E_{Wd}\left( m_{s_{1}} \right)$ 0.5657 0.4596 0.7983
$E_{Wd}\left( m_{s_{2}} \right)$ 0.7096 0.3277 1.0257
$E_{Wd}\left( m_{s_{3}} \right)$ 0.7206 0.2207 0.9875
sensors-17-00928-t006_Table 6
######
Weighted belief entropy of sensor reports under different frequencies.
$\mathbf{\mathbf{w}_{\mathbf{S}_{\mathbf{i}}}}$ $\mathbf{\mathbf{Freq}1}$ $\mathbf{\mathbf{Freq}2}$ $\mathbf{\mathbf{Freq}3}$
------------------------------------------------- --------------------------- --------------------------- ---------------------------
$w_{S_{1}}$ 0.2834 0.4560 0.2839
$w_{S_{2}}$ 0.3555 0.3251 0.3648
$w_{S_{3}}$ 0.3610 0.2189 0.3513
sensors-17-00928-t007_Table 7
######
Modified mass function.
$\mathbf{\mathbf{Freq}1}$ $\mathbf{\mathbf{Freq}2}$ $\mathbf{\mathbf{Freq}3}$
----------------------------- -------- -------- --------------------------- -------- -- -------- --------------------------- -- -------- -------- --------------------------- --------
$m_{w}\left( \cdot \right)$ 0.5196 0.0006 0.0721 0.4077 0.7212 0.2788 0.3077 0.4331 0.2172 0.0420
sensors-17-00928-t008_Table 8
######
Sensor data fusion results for fault diagnosis.
$\mathbf{\mathbf{Freq}1}$ $\mathbf{\mathbf{Freq}2}$ $\mathbf{\mathbf{Freq}3}$
--------------- -------- -------- --------------------------- -------- -- -------- --------------------------- -- -------- -------- --------------------------- --------
Fusion result 0.8891 0.0003 0.0427 0.0679 0.9784 0.0216 0.3318 0.6332 0.0349 0.0001
sensors-17-00928-t009_Table 9
######
Comparison of results obtained using proposed method and Jiang et al. method.
$\mathbf{\mathbf{Method}}$ $\mathbf{\mathbf{Freq}1}$ $\mathbf{\mathbf{Freq}2}$ $\mathbf{\mathbf{Freq}3}$
--------------------------------------------------- ------------ -------- --------------------------- -------- -- ------------ --------------------------- -- -------- ------------ --------------------------- --------
Jiang et al.'s method \[[@B16-sensors-17-00928]\] **0.8861** 0.0002 0.0582 0.0555 **0.9621** 0.0371 0.3384 **0.5904** 0.0651 0.0061
Proposed method **0.8891** 0.0003 0.0427 0.0679 **0.9784** 0.0216 0.3318 **0.6332** 0.0349 0.0001
| |
I ended up making some more of the lunch totes and took process pictures to create a free tutorial.
*If you want to make your own tote, but a different size, I've tried to include my thought process to help you think through your own measurements..
Finished Dimensions: 7" x 8.25" x 3"
If your fabric has a pattern that runs vertically, but no distinguishable up or down pattern (e.g. stripes), you can cut the piece using the same patterns as your bag interior. Otherwise, you will need to cut two pieces that are each 10.75" wide x 11" tall.
1. Cut your canvas bag lining.
In this case, I simply cut open the desired bag shape to use as a pattern and traced all around the resulting shape, adding a 1/2 inch seam allowance.
If I didn't have a bag as a ready-made pattern, I could use some basic math to figure out the correct pattern size. Example: the finished bag is 8.25" tall x 7" wide x 3" deep. So to get the length of the needed canvas, add two heights + depth + 1" seam allowance for each side.
8.25" + 8.25" + 3" + 1" + 1" = 21.5"
To get the width of the canvas, the widest part of the bag is 7", but the bag is also 3" deep. So add the width plus the depth plus the sewing seam allowance for each side.
7" + 3" + .5" + .5" = 11"
The middle part is actually the bottom of the bag, which is 3" deep and 7" wide. So add the seam allowance to your pattern.
7" + .5" + .5" = 8"
2. Sew the sides of the canvas bag lining.
Fold the resulting shape in half. Sew with a half inch seam allowance on only the sides of the folded piece.
3. Press open the seams on the canvas bag lining.
I just took the bag, opened it up and slid it over the narrower side of my ironing board so that the iron could glide over the seam. Opening the seams makes sewing your boxed corners much easier and neater and creates cleaner lines.
4. Sew your boxed corners.
When you pressed open your seams, your lining will naturally start creating a box shape. Help the shape along by lining up the center seam of your side panels with the center of the bottom.
Sew a half-inch seam allowance. If your sewing machine has one, use a triple stitch or other reinforcing stitch. Otherwise, just sew over the line a few times.
5. Cut your bag exterior.
Using the canvas lining as a starting point, fold the lining flat to figure out the length and width for the exterior fabric.
Example: Once this particular shape was flattened, I could measure from the bottom of the lining to the top: 11".
And measuring from one side's seam allowance to the other: 10".
Because I wanted to use a fat quarter, I tried to get away with the smallest seam allowance possible - 1/4 inch - to figure out what size pieces I needed to cut. Thus, two pieces that are least 11.5" x 10.5". However, a 1/2 inch seam is more secure.
6. Sew your bag exterior.
Lay your pieces right sides together and sew the sides and bottom using your determined seam allowance (1/4 inch in this tutorial).
7. Box your corners for the bag exterior.
Having sewn all three sides to create a stable shape, this is when I like to create my boxed corners.
My bag is 3" deep, so to get the correct size boxed corner, divide the depth in half (1.5" in this example) and using scissors or a rotary cutter cut out a 1.5" square on each bottom corner.
Press open all your seams and sew your boxed corner just as you did for the canvas lining.
9. Fold over the top of your canvas lining.
Fold over the top of your canvas lining toward the wrong side of the fabric by about an inch on all sides. Press the fold flat.
Then as in the picture above, fold the lining flat to measure the distance from the bottom of the bag to your new top. In this case 10". You will need to fold the top of your exterior bag fabric so that it finishes at the same length.
10. Fold over the top of your exterior bag fabric.
Knowing that the lining and exterior bag fabric have to be the same length, I need to fold over the top just enough so that it finishes at the same size as the lining. Measure from the bottom seam allowance and then fold over the top by the right amount. Press the fold flat.
11. Insert the canvas lining right side up into the exterior bag fabric and pin together.
Press flat the boxed corner for the exterior bag fabric. For the lining, press the boxed corners toward the bottom of the bag. Line up the center of the seams of the lining with the center of the seams of the exterior bag fabric. Pin generously.
13. Topstitch all the way around the bag.
Sew slowly and topstitch about 1/4 inch from the top of the bag all the way around the close the gap between the lining and exterior. To help hide the start and stop sewing marks, I like to begin and end at one of the side seams.
To make handles for your tote, you can sew in your handles while you are topstitching around the bag. Just insert your handles between the lining and bag exterior and make sure that they are placed evenly apart.
Or you can continue on to the next and final step to install eyelets to create rope handles.
Mark and measure the placement of your eyelets. Here I measured 3" from the side and 1" from the top on all sides to mark the placement of my four eyelets.
Using an eyelet plier or similar tool, punch out a starter hole for your eyelet.
Then fiddle with the hole until it is the right size for your eyelet.Then using the eyelet plier again, press the eyelet securely into the fabric.
15. Tie your rope handles.
Make sure that the rope fits into your eyelet. Cut two pieces of rope about 14" in length. Thread each end of the rope through the eyelets and double knot the ends.
And now that you know how easy these totes are to make, sew a bunch assembly-line style to have on hand as needed.
As an aside, the fabrics for the lunch tote are Japanese fabric fat quarters I purchased at the Long Beach Quilt Festival. The vendor is Momen Plus and turns out that the store is in Torrance. Who needs to travel to Tokyo to get a fabric fix, when this store with all of its fabric goodies is just a short drive away? | http://www.serendipityjoy.com/2011/08/tutorial-simple-lunch-tote.html |
Barriers to Entry
Definition - What does Barriers to Entry mean?
Barriers to entry refers to any significant obstacles facing a new entrant into an existing company's market. Both strategic and financial buyers look to acquire companies with high barriers to entry because they are difficult to build internally and they keep competition limited, allowing for higher pricing power. Companies that can demonstrate significant barriers to entry will usually garner a valuation premium from acquirers.
Divestopedia explains Barriers to Entry
Barriers to entry broadly fall into three categories;
- Legal or regulatory barriers include agreements, contracts, patents, trademarks, copyrights and/or regulatory protection. Vendors should clearly define the protection and the extent of the protection.
- Market barriers include brands, customer/supplier relationships, distribution channels, trade secrets, exclusive agreements, location, etc. Vendors should document how they created these market barriers and how they will protect them.
- Capital barriers include significant investments in fixed assets, high costs for regulatory certification, extensive research and development, etc. Documentation of all aspects of capital required for new entries into the marketplace will provide proof of these barriers and will go a long way toward obtaining a premium valuation from a buyer. | https://www.divestopedia.com/definition/1015/barriers-to-entry |
Listing Provided Courtesy Of:
RE/MAX LIFESTYLE REALTY
Property Description
Big and Beautiful. A special combination of spacious 2800 sq ft 5 BR, 2 BA refurbished farmhouse and 3 story finished barn. The house features refinished original tongue and groove oak wood walls, hardwood floors, exquisite light fixtures, large fireplace mantels, and big windows providing plenty of sunlight with pretty farm views. Special features include the rotunda style architecture, kitchen with fireplace and seating area, 8'X31' sunroom with French doors, custom closets, and modern bathrooms.The 3 story Barn is more than a barn. Interior finished on 3 floors, with possibilities for additional living space, events, work space, storage. etc. The barn provides indoor parking, rear exit ramp, wide staircases, high ceilings, multiple entrances. 1.83 ac lovely yard. | https://www.lewisburghomes.com/property/592-201644-628-Lobelia-Rd-Hillsboro-WV-24946 |
DuBois, PA – The City of DuBois hasn’t made a decision about the potential roundabout at the intersection of Beaver Drive and Division Street, but they’ve received plenty of feedback about it.
The city building got around a hundred calls, with about 30 of them in favor of constructing a roundabout and about 70 of the calls against it or suggesting other options.
The roundabout issue will be on the agenda for the next DuBois City Council meeting, which will be Monday, Nov. 13.
PennDOT has offered to pay part of the cost of project, but they have allocated that money for only a roundabout, no other options.
If DuBois goes through with a roundabout, PennDOT would pay for $300,000 and the City of DuBois would pay for the other $350,000.
The city is also looking into the cost of a solar powered traffic signal. They believe a traffic signal could cost anywhere from $400,000 to $500,000, but it doesn’t seem as though PennDOT would cover any of that expense.
City officials still want your feedback. To give them your thoughts, please call the DuBois City Building at 814-371-5521.
Related Stories: | https://www.connectradio.fm/2017/10/24/dubois-feedback-beaver-drive-roundabout/ |
The Cryosphere Working Group organized a field-oriented training course for teaching snow cover quantification techniques at the Finnish Meteorological Institute Arctic Research Center. Contemporary fields method require significant experience and training to achieve high-quality, accurate results, necessitating a field training course. This week-long course was intended to train early career scientists to better utilize field techniques for in situ observations as well as ground-based remote sensing instrumentation, with classroom lectures to support the field activities. By learning advanced field methods in the early career stage, young scientists will help improve quality standards in the Arctic research community in the area of snow science.
Workshop Material
Date and Location:
12 - 18 February 2017 | Sodankylä (Finland)
IASC Working Group / Committees funding the Project: | https://iasc.info/our-work/working-groups/cryosphere/cwg-projects/767-3rd-snow-science-winter-school |
In December 2013, the BC Provincial Government began inviting submissions from the public regarding the rural highway speed limits. The following post is the way Mike Geoghegan sees it. Mike Geoghegan is one of the foremost government and media relations consultants working in British Columbia today. At the provincial government level he served five years as a Ministerial Assistant in the portfolios of Agriculture, Fisheries and Food; and Small Business, Tourism and Culture. For more information check out his company website at www.mgcltd.ca
Let me begin by stating that I am a Road Star, I receive the maximum safe driver discount from ICBC because of my accident free driving record. I attribute my accident free record to the fact that I pay attention to the road and I go with the flow of traffic. Because I do a lot of driving I find that this habit tends to also net me one or two tickets per year. Thus I get the joy of receiving an obnoxious computer generated letter from ICBC threatening some mysterious punitive action because of my reckless behaviour. Imagine how incredibly insulting and patronising such nanny state missives are, especially as someone who insures four vehicles with ICBC.
As someone who has driven extensively in the United States and to a lesser extent Germany let me state that I support speed limits. I have driven on the autobahn where there are no speed limits and passing a truck while a split second later having some BMW six inches off your bumper, left blinker going, is unsettling to say the least. I find it stressful, but I also find driving in British Columbia equally stressful because of our low speed limits and the number of poorly educated drivers we have particularly in the Victoria area.
On several occasions now I have watched in horror at drivers who are stopped on a merge lane because they do not understand the critical difference between a merge and a yield. I have watched cars lazily go into the left lane without passing cars in the right which is the rule on most highways in North America. I frequently drive on the Pat Bay Highway. For most of its length the speed limit is only 80 km/h. No one drives this speed limit, not even the police, except when the cops are out there trolling for dollars. The inevitable result is bottle necks enhanced by the new slow down move over rule which pretty much ensures we now lose a lane and dangerous traffic congestion ensues.
I once talked to a retired RCMP officer about the Pat Bay Highway and he noted that in France the same road would have a speed limit of 130 km/h. That may be a tad high but 80 km/h for most of its length is certainly far too low. The law should reflect what speed most traffic is actually driving at and on the Pat Bay that would be 100 to 110 km/h
Let me contrast the anxiety I feel driving with the flow of traffic in BC, with that of driving in the United States where speed limits are on average 30 per cent higher. First of all when I am going with the flow on a US Interstate, cars are generally at or below the posted speed limit and there is a focus on moving vehicles efficiently. If people are not passing they stay in the right hand lane on a four lane highway. Even under heavy traffic conditions it is often far easier to get around on a given stretch of highway in Washington State than in BC
The Sea to Sky Highway is a particularly amusing example of our province’s penchant for low speed limits. I was driving up to Whistler to attend a UBCM conference shortly after the Sea to Sky Highway had received its billion dollar upgrade. The speed limits were kept at 80 km/h. It was a bright sunny September day with ideal driving conditions and as a result every vehicle was in the right hand lane driving at exactly 110 km/h. We are talking everything from one tonne trucks to sports cars all doing 110 km/h while leaving the left passing lane completely empty. No one wanted to do 120 km/h and risk getting their vehicle impounded but everyone was content to do 110 km/h and risk getting a speeding ticket. That is because the speed limit was kept far too low.
A similar situation happened on the Nanaimo Parkway when it first opened; its speed limit was set at only 80 km/h. So many tickets were issued (the Nanaimo RCMP are noted for their enthusiasm in handing out speeding tickets) that a public backlash ensued and the speed limit was raised to 90 km/h. I was one of the people unfortunate enough to get a ticket back when it was still 80 km/h for going 90 km/h with the result that the state was able to milk me for a lot of money for having the temerity to go with the flow of traffic in the passing lane.
In general all highways that are posted at 80 km/h in BC should be raised to 100 km/h and all 90 km/h should be raised to 110 km/h. There are going to be road situations like the infamous Malahat where speed limits will have to be lower but those signs should be in yellow to indicate that the government is not just being capricious but that this is a dangerously inadequate road and thus drive cautiously.
Now what about those all too rare sections of road where the current speed limit is 100 km/h or even 110 km/h? Again bump them up by 20 km/h to 120 km/h and 130 km/h respectively. There may be sections where you need to keep the speed limit lower than that but overall there should not be a highway in British Columbia with a general speed limit of less than 100 km/h. If there is then you should not call it a highway and certainly not a freeway call it what it is a substandard roadway.
With speed limits that are set to maximise the flow of traffic rather than government revenue, I think we would have far less distracted drivers and fewer accidents. In fact in those places in the United States where speed limits increased, traffic accidents and fatalities declined. We might even start seeing the return of tourists who drive to B.C.
I thank you for your due consideration of this submission. I would have presented it in person to your Nanaimo hearing except quite frankly I avoid driving up island because of the appalling condition of the Malahat and the aforementioned enthusiasm of the Nanaimo RCMP for ticketing drivers on the Island Highway. | http://www.sense.bc.ca/2013/12/16/priorities-trolling-for-dollars-or-sane-speed-limits/ |
They Put A Blindfold On These Kids… What Happened Next Will Warm Your Heart.
There is something pure and yet primitive when it comes to the bond between mother and child. Despite how tired a mom is, she can identify her baby’s cries among other children. So much has been said about a mother’s intuition, her ability to detect or feel when something is not right with her child.
In a new experiment, the tables were turned. Children between the ages of three and nine were blindfolded and led to a line of women. The kids were directed to find their mothers with touch, smell and that invisible bond and instinct. The experience had some of the mom’s quite moved by the findings. | http://www.lifebuzz.com/finding-moms/ |
New this week is Nobel Laureate Orhan Pamuk’s Silent House. Also hitting bookshelves are Heroines by Kate Zambreno, The News from Spain by Joan Wickersham, and more posthumously published work by Kurt Vonnegut. In non-fiction, there’s There Was A Country: A Personal History of Biafra by Chinua Achebe and Short Nights of the Shadow Catcher, National Book Award and Pulitzer Prize-winner Timothy Egan’s biography of Edward Curtis.
Tuesday New Release Day: Pamuk, Zambreno, Wickersham, Vonnegut, Achebe, Egan
The Reconstructionists
“Books are an existential crisis”
Kyle Winkler, in an editorial for Vouched Books (which I’ve mentioned previously), writes that “books are an existential crisis” because we can’t possibly read them all.
Dr. Doyle
From Under a Heavy Plinth
“The story that Lee’s book tells (or tries to tell, because much evidence has been obscured or lost) is not about patience on a monument but about talent buried under a heavy plinth, and discovered only just in time—the late achievement less a measured distillation than a lifesaving decoction.” James Wood reviews Hermione Lee‘s new biography of novelist Penelope Fitzgerald for The New Yorker. Pair with Niamh Ni Mhaoileoin‘s Millions essay on the new age of biography.
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An Opportunity to Recant
Every book reviewer has probably, at one point or another, savaged a book a bit too savagely. But if given the opportunity, would you recant? Would you admit that you’d overstepped? Would you feel good about doing so? At an event last month, Snowball’s Chance author John Reed hosted an event at which NBCC critics did exactly that.
The F-Bomb on the Silver Screen
Wikipedia Find of the Week: A list of films that most frequently use the word “fuck.”
The Future of the Book (& the Future of the ‘Do)
“Better yet, Carpe Wallpaper.”
Jessica Probus’ send-up of Charlotte Perkins Gillman’s The Yellow Wallpaper is brilliant. I present The YOLO Wallpaper. | https://themillions.com/2012/10/tuesday-new-release-day-pamuk-zambreno-wickersham-vonnegut-achebe-egan.html |
Arthur Conan Doyle created Sherlock Holmes as a serialisation in The Strand Magazine before he became the Country’s greatest fictional detective. Of course, there is no connection with Jack the Ripper, but Tony’s characterisation puts the sleuth in the position of examining the clues from the murderous Streets of Whitechapel.
The East End serial killings are a hook to hang this incredible story on. And, on the day, Tony will choose someone from the audience to volunteer to become Dr Watson and help note down the clues as they unfold.
They called it the murderous square mile. It all happened within the space of 12 weeks and the east End of London would never be the same again. Five victims were murdered, but the murder rate in London was so high anyway, that the police were overcome. It took vigilantes to patrol the streets and coppers dressed as women to ward off the ripper’s attentions.
Tony’s talk really fills in the blanks about Victorian London; who lived where, what squalor was really like and who could afford a twopenny leaner? Sherlock and Dr Watson will solve the case with your help.
Tony’s Ripperology qualifications mean he knows the case inside out - which was how some of the victims ended up! | http://tonythecompere.co.uk/sherlock-holmes.html |
This is part of an ongoing series about my father's stroke. In this post, the personal part follows a fairly straightforward gardening entry. Quit at the divider (a row of asterisks) if you're not interested in the memoir portion.
It is, astonishingly, not raining. That's not to say that it won't be raining by the time I finish this post; nor does it mean that it didn't already rain earlier today, because it did. In fact, it snowed. Welcome to Montana.
When it started raining the day before yesterday, I grabbed a raincoat and kept working. I'd set out to do some serious weed control on the flagstone path that lies between my vegetable plot and the strawberry plot in the garden I tend next door. This meant weed cloth, as the worst offender is well-established bindweed.
At first I planned to lift the stones out of the soil, lay down the cloth, and set the stones back in their original positions. Nah. Since I didn't want the cloth to show, I had to dig out the grass and dandelions between the stones, so the "original positions" were soon a matter of guesswork. The path was so overgrown that some were a matter of guesswork even at the beginning.
I got about two thirds of the stones dug up and more or less re-positioned on the first afternoon, but decided that night that a better, more thorough job was called for. So next day I lifted the flags I'd set, dug up the rest, pulled the weed cloth aside, and dug out weeds until I could rake the pebbly soil smooth. This was the point I'd reached when it started to rain.
Settling the flagstones in the stony soup turned out to be a labor-intensive but highly satisfactory job: I was able to line up straight edges, straighten out the whole path, and fit the slabs together in a tight, pleasing pattern.
I would include a picture, but I left my camera in Toronto, and it's still there, along with about five other things I left behind. One thing my mother doesn't need at this point is extra errands, and I'm still kicking myself for leaving her with one.
I'd probably be more impatient if I hadn't had the rare experience of walking in her shoes last month.
While I was visiting, Connie took the first break she'd had since Dad's stroke in November, and went to see her sister in Massachusetts for several days. It was my job to keep up the rhythm she's established for him since he moved into long-term care sometime in February.
Every morning for years, one of my parents would make coffee and bring it back to bed, so every morning Connie gets up at six to take coffee down to Dad at seven. She leaves him when he goes to breakfast at eight, but is back from about ten-thirty to noon, and from two-thirty to five, spending time reading aloud, or walking, or listening to music together.
Finally, in her nightgown and a glorious, midnight blue silk robe that belonged to her grandfather, she slips downstairs at eight o’clock for a goodnight cuddle before she returns upstairs to sleep.
Connie and I had almost six days for me to learn the routines and for Dad to get used to my being there. She kept doing the early-morning coffee visits, but during the day we'd mix things up, so sometimes she'd go down and I'd join her, sometimes the opposite, and sometimes one or the other of us would leave early. And every night, I tucked them into bed, to the vast amusement of the attendants.
This was Con's idea: after all, I'd be saying goodnight while she was gone, and if I showed up at bedtime with her for a few days, then it might be less startling when I turned up alone. So every evening, I kissed them goodnight and headed upstairs, chuckling. Talk about role reversal.
I was glad for the days before Con's departure. Fortunately, she's very organized: for morning coffee, for instance, there are two metal thermoses and two insulated metal cups, all of which get pre-warmed before going downstairs in the neat pockets built into a small canvas bag.
After five plus days of initiation, I knew most of the routines: after dropping Dad at dinner, I knew to lay out clothes for the next day (underwear, undershirt, pants, turtleneck and matching socks, belt) shroud the lamp in a t-shirt so that night attendants would be able to see without turning on the startling over-head light, and lay a waterproof cover over the little couch, in case Dad resisted night changes and sat down on the couch while wet or soiled.
But the first morning that Con was gone, I couldn't find one of the tops to the thermoses that were to hold the early-morning coffee, and I couldn't find a cone with which to make my decaf coffee, and the result was that I didn't get downstairs until, oh my gosh, seven twenty.
As I hustled into Dad's room that first morning, trying to appear relaxed, I met Lenore, one of the marvelous attendants, just coming out. She laughed aloud and shook her finger at me. "You're fired!" she announced jovially. "Twenty minutes late! Your first day on the job and you're fired!"
"Don't tell Connie," I puffed, hurrying past.
The missing cone turned up in the stove drawer (not something I could have predicted), but the thermos cap had been lurking behind an unwashed pot the whole time I hunted for it. Maybe, I thought, this explained why Connie washed dishes after every meal. Note to self for tomorrow: set ALL coffee items out on a CLEAR counter the night before.
In ensuing days, my education continued. I'd been skeptical of Con's reports about how hard it was to get errands done when one had to be back in two hours, but after about twenty-four hours, my skepticism gave way to heartfelt sympathy. I managed to buy a new computer, for instance, only by finding someone who would bring it to me.
So this is why I am not badgering Connie to send me my camera. She has enough to do.
I sense you’ll have more to write as the days pass…I especially loved everything AFTER the asterisks. | http://themanicgardener.com/2010/06/down-the-garden-path.html |
Determine which digit will be at the unit’s place in the square of a number 999.
3
6
1
4
1
As per the rule of square of a number, the unit digit for a square of number is determined by the product of the unit place digit of a given number whose square we have to find. So in the case of 999, unit place digit is 9. So the unit place digit in a square of 999 is, 9 × 9 = 81 i.e 1
So, 9992 has a digit 1 at unit place. | https://byjus.com/question-answer/determine-which-digit-will-be-at-the-units-place-in-the-square-of-a-number/ |
Husband receives a 50-year-old love note from his beloved late wife
A simple
love note, written in the wall, has travelled through time to delight its
intended recipient some 50 years after it was first penned by his wife.
When Germaine
Langdon was preparing to have a little re-panelling done in her Ontario home,
she took the sweet step of writing a little note for her husband in the
drywall. It read: Germaine loves Roy March 17th, 1965.
Roy never
saw it because it was soon covered up by workmen. But more than 50 years later,
their home’s new resident, Rebecca Churáň
was doing a little home improvement work of her own, and uncovered the message.
“When I tore down the paneling in my living room, it revealed
drywall," she wrote
on Facebook. "I was exited [sic] because that meant I did not need to
drywall haha."
But
eventually she decided that the note should be reunited with its intended
recipient, and so she posted its picture on a community Facebook page, appealing
for anyone with information to come forward. Within days, Claudette, daughter
of Roy and Germaine got in touch. Sadly, her mother had passed away in 2006,
but Roy would be over the moon to finally get the message.
At the age
of 92, Roy finally has his love letter from his wife. “The love I could feel he
had for his past wife was almost too hard to take,” Churáň wrote following the
handover meeting.
Image: Facebook/Rebecca Churáň
Author: Rebecca
Rebecca lives in London with her husband, daughter and dachshund. She hopes her dating blogs for Flame Introductions will inspire you to seek out the best London and UK locations for brilliant dates, and discover some tips along the way to help you find your perfect partner.
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Q:
Showing a subset of vectors is linearly independent
Studying “Linear Algebra Step By Step” p. 217, I am trying to understand why my solution is wrong.
Example 3.15
Let $V$ be the vector space of continuous functions defined on the real line. Let $u=\cos(x)$, $v=\sin(x)$ and $w=2$ be vectors in V.
Show that the vectors u, v and w are linearly independent.
I came to the conclusion that set is not linearly independent because I found non-zero scalars $x=2$, $y=1$ and $z=\frac{-1}{2}$ such that the equation
$$2\cos(0)+1\sin(0)+(\frac{-1}{2})2=0$$
is true.
Could someone give me some insight?
A:
You proved correctly that the function$$x\mapsto2\times\cos(x)+1\times\sin(x)+\left(-\frac12\right)\times2$$takes the value $0$ at $0$. And then what? At, say, $\frac\pi4$, it doesn't take the value $0$. In other words, it is not the null function.
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Overloaded
From DDO wiki
Being Overloaded is when your carrying capacity reaches Load: Other (more than 100% load).
This reduces your run speed by 30.8%, caps your maximum dexterity bonus at 1, and gives you a -6 armor check penalty.
You are given the Overloaded status ("You're overloaded!"). | https://ddowiki.com/page/Overloaded |
TECHNICAL FIELD
BACKGROUND ART
DISCLOSURE OF THE INVENTION
BRIEF DESCRIPTION OF THE DRAWINGS
BEST MODES FOR CARRYING OUT THE INVENTION
EMBODIMENT 1
EMBODIMENT 2
EMBODIMENT 3
INDUSTRIAL APPLICABILITY
The present invention relates to a multifunctional notebook, and more particularly, to a multifunctional notebook that can overcome limitations of a conventional folding notebook, organize data in a more visualized manner so that users can identify the data at a glance, and successfully meet users' demands by providing a variety of functions.
FIG. 1
FIG. 1
FIG. 1
10
11
12
20
21
10
is a perspective view of a conventional folding notebook. As shown in , the conventional folding notebook includes a cover , which is composed of a front cover and a back cover . Sheets of inner paper , including a plurality of recording sheets , are bound together with the cover in the form of a notebook. The conventional folding notebook shown in is generally used by students to record assignments or take notes.
21
10
21
The conventional folding notebook, however, has several disadvantages. First, since the recording sheets themselves are separated from one another while being bound together with the cover into a notebook, data written on each of the recording sheets can be perceived as being visually separate. Therefore, in a case where a plurality of data dealing with the same content or closely related to each other are written on different pages of the conventional folding notebook, a viewer may have difficulty visually organizing the data so that the data cannot be successfully perceived at a glance.
21
21
Second, there is a clear limit in the amount of data that can be recorded on each of the recording sheets especially when the conventional folding notebook is one that is handy to carry around. Therefore, in order to record data beyond the limit, the size of the recording sheets should be enlarged, thereby resulting in a notebook that is less convenient to carry.
21
Third, the conventional folding notebook cannot meet users' various demands, such as a demand for making a separate file using part of the recording sheets .
The present invention provides a multifunctional notebook which can visually organize data so that the data can be successfully perceived at a glance and can meet users' various demands by providing a variety of functions.
According to an aspect of the present invention, there is provided a multifunctional notebook. The multifunctional notebook includes a cover which is composed of a front cover and a back cover, and at least one sheet of inner paper which includes a plurality of recording sheets defined by folding the sheet of inner paper in an accordion style so that adjacent folded edges of the inner paper face opposite directions and is fixed to a predetermined part of the inner surface of the cover.
Preferably, the plurality of recording sheets are horizontally connected to one another.
Preferably, the plurality of recording sheets are vertically connected to one another.
Preferably, a perforated line is formed on each of the folded edges of the inner paper so that the plurality of recording sheets can be torn apart from one another.
Preferably, at least one title section, which is used for classifying predetermined data, and an information section, in which the predetermined data is recorded, are provided in a direction perpendicular to a direction along which the plurality of recording sheets are connected to one another.
Preferably, each of the plurality of recording sheets has an index means at one side.
Preferably, the index means is as many perforated hole patterns as there are recording sheets are provided, and the perforated hole patterns are regularly distanced from each other.
Preferably, a perforated line is formed on the plurality of recording sheets so that each of the plurality of recording sheets can be divided into two or more parts along a direction along which the plurality of recording sheets are connected to one another.
The above and other features and advantages of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings in which:
FIG. 1
is a perspective view of a conventional folding notebook;
FIGS. 2 and 3
are perspective views of multifunctional notebooks according to a first embodiment of the present invention;
FIG. 4
FIGS. 2 and 3
is a perspective view of a file made by using some of the recording sheets shown in ;
FIG. 5
FIG. 2
3
is a perspective view illustrating a method of using the multifunctional notebook of or ;
FIG. 6
is a perspective view of a multifunctional notebook according to a second embodiment of the present invention; and
FIG. 7
is a perspective view of a multifunctional notebook according to a third embodiment of the present invention.
Hereinafter, the present invention will be described in greater detail with reference to the accompanying drawings in which preferred embodiments of the invention are shown.
FIGS. 2 and 3
FIG. 2
FIG. 3
are perspective views of multifunctional notebooks according to a first embodiment of the present invention. More specifically, illustrates a multifunctional notebook in which recording sheets are horizontally connected to each other, and illustrates a multifunctional notebook in which recording sheets are vertically connected to each other.
FIGS. 2 and 3
FIGS. 2 and 3
110
111
112
120
110
111
112
120
120
110
Each of the multifunctional notebooks, shown in , includes a cover composed of a front cover and a back cover , and a sheet of inner paper , which is fixed to an inner side of the cover near the interface between the front cover and the back cover . Although illustrate the multifunctional notebooks as including only one sheet of inner paper , the multifunctional notebooks according to the present invention may include more than one sheet of inner paper fixed to the cover .
120
121
120
122
120
The sheet of inner paper includes a plurality of recording sheets , which are defined by folding the inner paper back and forth in an accordion style so that adjacent folded edges of the sheet of inner paper face opposite directions.
121
121
FIG. 2
FIG. 3
The plurality of recording sheets can be horizontally connected to each other, as shown in . Alternatively, the plurality of recording sheets can be vertically connected to each other, as shown in .
122
120
121
120
122
a
a.
A perforated line is formed along each of the folded edges of the sheet of inner paper so that a user can tear apart the recording sheets from one another by tearing the sheet of inner sheet along the perforated line
121
123
124
120
123
124
121
121
121
121
FIGS. 2 and 3
On each of the recording sheets , at least one title section , which is used for identifying the subject of predetermined data written on the corresponding recording sheet, and an information section , in which the predetermined data will be recorded, are arranged along a direction perpendicular to the length of the sheet of inner paper . Since the title section and the information section are provided on each of the recording sheets , a user can record data on the recording sheets in a more organized manner. Even though illustrate two title sections as being provided onto each of the recording sheets , the number of title sections that can be provided onto each of the recording sheets can vary depending on the desired functions of a multifunctional notebook.
121
121
Preferably, an index means is provided at one side of the recording sheets so that the recording sheets can be easily identified.
125
121
125
121
121
125
The index means can be formed using a plurality of perforated hole patterns , which are provided on each of the recording sheets and are regularly distanced from one another. As many perforated hole patterns as there are recording sheets can be provided to each of the recording sheets . Therefore, a user can selectively remove a predetermined number of perforated hole patterns .
125
121
125
125
121
125
125
125
121
121
121
121
a
a
a
b
b
a
b
c
c
More specifically, the user can remove a first perforated hole pattern of a first recording sheet , remove first and second perforated hole patterns and of a second recording sheet , and remove first, second and third perforated hole patterns , and of a third recording sheet . Namely, the user can remove as many perforated patterns as a sequence number of each of the recording sheets from each of the recording sheets . Then, each of the recording sheets can be identified based on how many perforated holes it includes.
FIG. 4
121
121
130
121
As shown in , in the case of making some of the recording sheets into a separate file, the recording sheets can be bound together by passing a binding means through a first perforated hole of each of the recording sheets .
121
121
121
FIG. 5
In the first embodiment of the present invention, a user can record data on each of the recording sheets in the same manner as he/she does in a typical folding notebook, as shown in . The data recorded on the recording sheets of the multifunctional notebook according to the first embodiment of the present invention can be more easily perceived at a glance by simply unfolding the recording sheets .
FIG. 6
FIGS. 2, 3
6
is a perspective view of a multifunctional notebook according to a second embodiment of the present invention. The same reference numerals in , and represent the same elements, and thus their description will not be repeated here.
FIG. 6
220
221
226
220
221
226
221
221
221
226
As described in , the multifunctional notebook includes a sheet of inner paper , which can be torn apart into a plurality of recording sheets . A perforated line is formed along the direction of the length of the sheet of inner paper so that each of the recording sheets can be torn apart into two identical parts along the perforated line . For example, let us assume that a user records English words on the left part of each of the recording sheets and records meanings of those English words in Korean on the right part of each of the recording sheets . In this case, the user can selectively tear off the left or right part of the recording sheets along the perforated line .
FIG. 6
221
221
illustrates the recording sheets as being horizontally connected to one another. However, even if they are vertically connected to one another, the recording sheets can successfully meet the requirements of the multifunctional notebook according to the second embodiment of the present invention.
FIG. 7
FIGS. 2, 3
7
is a perspective view of a multifunctional notebook according to a third embodiment of the present invention. The same reference numerals in and represent the same elements, and thus their description will not be repeated here.
FIG. 7
120
220
120
220
121
221
121
120
123
124
120
121
120
221
220
226
220
As shown in , the multifunctional notebook includes a plurality of sheets of inner paper and . The plurality of sheets of inner paper and include pluralities of recording sheets and , respectively. On each of the recording sheets included in at least the sheet of inner paper , at least one title section , which is used for identifying the subject of predetermined data recorded on the corresponding recording sheet, and an information section , in which the predetermined data is recorded, are arranged along a direction perpendicular to the length of the sheet of inner paper . The recording sheets are connected to one another along the direction of the length of the inner paper . On the recording sheets included in at least the sheet of inner paper , a perforated line is formed along the direction of the length of the sheet of inner paper .
FIG. 7
121
221
121
221
illustrates each of the plurality of recording sheets or as being vertically connected to one another. However, even if they are horizontally connected to one another, the recording sheets or can successfully meet the requirements of the multifunctional notebook according to the third embodiment of the present invention.
The multifunctional notebook according to the present invention provides several advantages. First, since recording sheets are connected to one another, it is possible to identify data recorded on different recording sheets at a glance. Therefore, it is possible to organize data on the recording sheets in a more visualized way.
Second, since small-sized recording sheets, connected to one another, are bound together into a notebook, it is possible for a user to easily carry the notebook and record a considerable amount of data in the notebook.
Third, each plurality of recording sheets of the multifunctional notebook or part of each of the plurality of recording sheets of the multifunctional notebook can be made into an independent file. In addition, each of the recording sheets can be separated into title sections and information sections so that data recorded on the corresponding recording sheet can be more efficiently organized. Therefore, it is possible to meet users' demands by providing a variety of functions.
While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, 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 of the present invention as defined by the following claims. | |
Preview Mosca’s ‘The Wavey EP’Tweet
You can now preview tracks from forthcoming Mosca release ‘The Wavey EP’.
Following his recent smash ‘Done Me Wrong / Bax’ on Glasgow’s Numbers, the London bass man now turns his hand to the tech-edged bass world of Martyn’s 3024 with a smashing EP.
Having reported on the release a couple of weeks back, you can now stream all 4 tracks from the techno-leaning EP, having recently been uploaded on the 3024 Soundcloud.
‘The Wavey EP’ is released on November 7. | http://hyponik.com/news/preview-moscas-the-wavey-ep/ |
How many lecture courses can I take?
You take two, comprising 24 lectures (2 x 12) and 12 seminars (2 x 6) and 8 tutorials (2 x 4).
Which classes am I in?
We will confirm your course enrolment by e-mail immediately after you have paid your Programme fee.
How often do my classes meet?
Each course meets on average 4 times per week for a total of c.10hrs/week.
How many contact hours?
Throughout the Programme, you will have a minimum of 61hrs contact teaching and assessment, and 6hr evening lecture series.
Do the subject streams run concurrently?
Yes.
Do I need to buy books?
The general rule is that you do not need to buy books. However, you should check the course syllabi carefully for any pre-arrival reading.
Can I see the course syllabi? | https://www.exeter.ox.ac.uk/summer-programmes/ecsp/faq/faqs-academics/ |
At Rheem, we are dedicated to bringing comfort to people's lives. As a leading global manufacturer of heating, cooling and water heating equipment, we are innovating all-new ways to deliver just the right temperature while saving energy, water and supporting a more sustainable future. It is an exciting challenge that requires a team of talented, passionate people with a diverse set of skills. From engineers to accountants, sales professionals to support experts, Rheem depends on people to power our innovations. Join Rheem, and help shape the future of products that impact lives-every day.
Qualifications:
Senior Systems Engineer / Systems Architect
The Senior Systems Engineer responsibility is to assist in the design, implementation, and support of Microsoft Technical Solutions. The Engineer will work closely with IT Management to identify, recommend, develop, implement, and support cost-effective technology solutions. The focus of this role is on Microsoft Technical Solutions
Architecture & Design
Leads efforts for the design of Microsoft technical solutions and assists in long range planning
- Reviews existing implementations against Microsoft best-practices, recommending changes and implementing improvements
- Assists in the development, recommendations, and maintenance of Microsoft technical standards, policies, and procedures
- Reviews Disaster Recovery Procedures for Microsoft Systems and recommends changes, maintains documentation, and implements approved changes
- Develops Disaster Recovery annual testing procedures for Microsoft Systems
- Assists in determining the Office 365 / Cloud Strategy. Acts as the Subject Matter Expert for the architecture, planning, implementation, and support for Office 365 and Hybrid-Office 365 implementations
Operational Support
Acts as a primary resource to configure, install, support, and maintain standard Microsoft server hardware, software, and peripherals in both a virtual and non-virtual environment
- A primary resource to design, configure, install, support, and maintain Microsoft Active Directory and Single Sign-on functionality
- Responsible for the design and implementation of the System Patch process using SCCM
- Ensure that systems are regularly patched with SCCM according to location, application, and company policy
- Builds patch compliance reports and provides regular status updates to the Security team
- Performs troubleshooting or assists and mentors junior staff as needed on troubleshooting the most difficult and pervasive technical problems associated with Microsoft applications (e.g., Office, Exchange, Skype for Business), Microsoft servers and network connectivity
- Handles assigned tasks related to Microsoft procurement, documentation, reporting, etc...
- Assists management in the control, establishment, and enforcement of security for Microsoft technology, desktops, and end-users
Project Support
Takes the lead role on Microsoft Technology projects and assist Management with the strategic vision
- Lead project teams for implementations, upgrades, modifications, and enhancements
- Represent the Microsoft interests of the Network Group on major projects of all sizes and scope within the Company
- Handles other duties as assigned
Required Education& Experience :
Bachelor's Degree in Information Technology or related field of study
- Certifications in Microsoft Technologies, MCSE preferred
- Minimum of 7 years working experience as a Microsoft Systems Engineer, Solutions Architect, or equivalent
Required Knowledge, Skills, & Abilities
At least 5 years hands-on working experience with Microsoft Systems Center (SCCM)
- Hands on working experience designing, implementing, and troubleshooting a patch management program utilizing SCCM
- Working experience troubleshooting hardware and software problems with vendor support staff
- Demonstrated experience migrating to Office 365, Hybrid Office 365, or Cloud technology
- At least 7 years hands-on working knowledge of Microsoft Windows server operating systems and a minimum of 3 years working with Server 2012
- At least 10 years hands-on working knowledge of Microsoft Windows desktop operating systems
- Working knowledge of Ethernet networking (TCP/IP, DNS, switching) and a minimum of 1 year experience with routing and internet technologies
- Strong user skills with Microsoft Office (Outlook, Word, Excel, and Powerpoint)
- Ability to develop and use simple project schedules and standard project management terminology
- Strong written and verbal communications skills
- Ability to work after hours (system upgrades, troubleshooting, etc.)
- Ability to provide non-business hour support (remote and onsite) and a rotating "on call" schedule within the Network Group
- Ability to travel on company-related business (other Rheem locations, conferences, training, etc.) with short notice
Preferred Technical Experience :
VMWare ESX
- Project management training
- SCOM, Office 365, Sharepoint, Orchestrator, In-Tune
Rheem is an Equal Opportunity Employer
Notice to Third Party Recruitment Agencies:
Please note that Rheem and its subsidiaries do not accept unsolicited resumes from recruiters or employment agencies. In the absence of an executed Recruitment Services Agreement, there will be no obligation to any referral compensation or recruiter fee.
In the event a recruiter or agency submits a resume or candidate without an agreement, Rheem and its subsidiaries shall explicitly reserve the right to pursue and hire those candidate(s) without any financial obligation to the recruiter or agency. Any unsolicited resumes, including those submitted to hiring managers, will become the property of Rheem. | https://www.themuse.com/jobs/rheem/senior-systems-engineer-systems-architect |
Condensed milk is cow's milk from which water has been removed. Sweetened condensed milk has sugar added; it is a very thick, sweet product that is sold in cans. A related product is evaporated milk but evaporated milk is not sweetened and cannot be substituted for sweetened condensed milk.
SWEETENED CONDENSED MILK
Toasting nuts is an easy way to enhance their flavor. Spread whole nuts on a baking sheet and toast in a 350 degree F. oven, stirring often, or toast in a large skillet over medium heat. Nuts quickly go from toasty to burned, so keep a close watch on them. When you can smell them, they're done.
How to Toast Nuts
Caramel Apple Coffee Cake
Makes two 8-inch round coffee cakes
Caramel-Apple Coffee Cake is a wonderful autumn dessert but since apples are available all
year-round you can make it anytime you desire a heart-warming coffee cake. This cake has a
texture similar to a carrot cake ... it's a dense cake with a slightly spicy flavor and filled with bits of fresh apple. You can omit the caramel topping if you prefer and simply dust the cake with
confectioners' sugar. But the caramel icing adds a special luxurious finish to this simple cake.
Ingredients:
Cake:
2 cups sugar
1 cup vegetable oil
3 eggs, lightly beaten
2 teaspoons vanilla extract
3 cups flour
2 teaspoons cinnamon
1 teaspoon baking soda
1/2 teaspoon salt
3 cups apples, peeled and finely chopped
1 cup pecans, chopped and toasted
Caramel Topping:
2 (14-ounce) cans sweetened condensed milk
1/2 cup brown sugar
1/2 cup butter
1 teaspoon vanilla extract
1-1/2 cups pecans, chopped and toasted
Directions:
To make the cake:
Preheat oven to 350-degrees F.
Grease 2 (8-inch) round baking pans.
In a large bowl, combine sugar, oil, eggs, and vanilla.
Add flour, cinnamon, baking soda, and salt.
Stir until just blended. Batter will be stiff.
Fold in apples and pecans.
Divide batter evenly between prepared baking pans.
Bake 45-50 minutes until tester inserted in center comes out clean.
Allow to cool 10 minutes then remove from baking pans.
Transfer to wire racks and allow to cool 20-30 minutes.
To make the caramel topping:
Place all ingredients, except pecans, in a saucepan.
Bring to a boil over medium-low heat, stirring constantly.
Cook 3-5 minutes until mixture has a pudding-like thickness.
Remove from heat.
Spoon warm caramel topping evenly over coffeecakes.
Sprinkle with 1-1/2 cups pecans.
Caramel Apple Coffee Cake
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Pumpkin Cupcakes
Apple Bread Pudding
Apple Crostata
DESSERTS
>
CAKES WITH FRUIT AND/OR NUTS
> CARAMEL APPLE COFFEE CAKE
MORE APPLE DESSERTS >>
Black Forest Cheesecake
Delicious chocolate cheesecake is layered with cherry cheesecake and topped with whipped cream, chocolate curls and Maraschino cherries. This delicious cheesecake serve 6 to 8 and arrives with a greeting card that you can personalize and is delivered in an elegant gift box.
We may earn a commission when you use one of our links to make a purchase. | https://www.mangiabenepasta.com/apple_7.html |
Late winter and early spring weather brings warm days and storm days. One day the crocuses are peeking through the ground. The next day the ground is covered in snow. The snow melts and those hardly little crocuses are still thriving with their tiny pop of color. Before the really hot weather sets in, check your stash and find some sock yarn that you’ve been saving for a special project. The yarn I used has tiny and larger flecks of color which remind me of early spring flowers growing in the soil.
Category: Knitting Patterns
Pattern Reknit
I had a three balls of Fixation left and I knitted 3 more pairs of Goodbye Summer Socks. Of course I sent two away before I took photos…one for daughter’s birthday, another for coworker who was recovering from medical treatment. Here’s the one that I did take pictures of:
Have you tried it yet? Got a spare ball of Fixation or DK yarn hanging around? Go over and get the pattern on Ravelry. It’s only $1.00!
Someday Baby Blanket Pattern
Someday one of my kids will call and say, “You’re going to be a grandma!” I decided not to wait for that moment to start knitting some little baby things. I started with this blanket in a soft yarn that has excellent drape. It’s machine washable in warm water, but it will need to dry flat. That’s not too bad!
This is an easy blanket to knit, with a 24 row “modified basketweave” stitch pattern, 18 of which are just knit rows. The other rows of this basketweave pattern are a knit 3, purl 3 repeat across the row. It makes for nice texture and something a little more interesting than plain garter stitch. Oh, and the pattern is free! Click the link below!
The blanket measures 28″ x 32″ and should be easy to tote along for families on the go. I recall having a few blankets that were way too large to bring along, so I didn’t want to make this one too big.
For those experienced in knitting for grandkids, what do you suggest I knit next? Follow my blog and make a comment, and I’ll pick a winner to receive 3 balls of Brilliant Blues Universal Yarns Bamboo POP yarn! Winner will be chosen randomly on Sunday, June 14, 2020 at 8pm MST. I will notify you by commenting on your comment, so stay tuned!
Chilly November Legwarmers
So. Cold. Here.
The last part of October gave us temperatures in the teens and twenties! Time to pick up the knitting game a little bit more to stay warm. I came up with these leg-warmers with cables and ribbing, both of which help to keep the leg-warmers in place. They’re a fast knit because there is very little shaping. AND if you know how to cable without a cable needle, you’ll get warm legs even more quickly! Enjoy this free pattern, but remember to abide by the rules of copyright.
chilly november legwarmers
Off Piste Cable Sweater
A few years ago I bought a 6 skein set of gradient yarn at a fiber festival in Idaho Falls. Those skeins sat around and I admired them, but now in my motivated state to knit up the yarn that I have, I started to knit this yarn in a few patterns, but none of them seemed right. So I decided to just start knitting a sweater, without having a pattern. You can find the link below to this pattern. It’s really more of a formula for making a top down sweater.
Off Piste Cable Sweater Link:
off piste cable sweater pattern
Interested in this yarn? I bought it from Blue Savannah. Check out her offerings on Etsy!
Diminutive Placemats
New kitchen needs new placemats. But any placemats that I own are so large that I can’t fit 4 of them on our table or kitchen island without overlapping. So I went shopping for placemats, but they’re all HUGE! And I couldn’t find any that I liked. Additionally, they’re all pretty expensive (times four)!
In an attempt to solve this problem, and since I like the stuff that I make, I thought I would knit some smaller placemats. They’re 12″ x 16″ (as opposed to the usual 14″ x 20″). I have one placemat finished and three to go. I used Lily’s Cream ‘N Sugar yarn in Earth Ombre colorway. They’re machine washable too, unlike many I saw at the store. I like the ikat looking print that the variegated yarn automatically made.
Here’s the pattern for you!
Houndstooth Heaven
Subtitled: How to Upcycle a Sweater
I was in a thrift store a few years back and saw what I affectionately call an “oops” sweater. You know, the kind of sweater where someone didn’t believe the “dry clean only” directions?! In fact, I found three of them, so I bought them with the well-meaning intention of doing something fabulous with them. Several years later I am just getting around to working with them. Here are all the items I made with one sweater:
Much of the sweater body went to make a custom computer case with leather details (I also bought a leather skirt at the thrift store that day–smile). Actually, I finished this right after buying the sweater. The sweater sleeves went to make some water bottle covers and coffee travel cozies. And my feet are showing off the me-sized slippers. I modified a pattern from Purl Soho (here’s the LINK) by sandwiching some plastic canvas between the bottom pieces, blanket stitching it all together, and then adding a back strap. Instant warmth! Or, maybe several hours of sewing and then the warmth.
As for those sweet little baby slippers, I used another pattern from Purl Soho (Felt Baby Slippers). I cut out the pattern pieces with my pinking shearers, pinned them together, and then hand sewed them with sock yarn and a running stitch. Maybe 2 hours tops to complete. You can also check out this patternLINK for baby shoes.
Yeah, I’m not going to be doing this again, except for the baby slippers because they’re so cute! And to be honest, I feel like a super-dork in my slippers, but a warm super-dork!
Goodbye Sandals
It’s that time of year already. It’s time to put the sandals away and start wearing socks again. Because of this, and because I had quite a few skeins of Cascade’s Fixation yarn, I created a pattern for anklets. Choose between striped or one-color socks! You’ll love how they hit right at the top of your shoes! Check out the photo:
What IS IT about stripes? They make my eyes happy and my feet are happier. Here’s the link if you want to buy the pattern:
http://www.ravelry.com/patterns/library/goodbye-sandals
It’s only $1.00 so give it a try. It has complete sock knitting instructions to help you through the more difficult parts.
Deep Winter Knitting at Summer Solstice
I’m currently pretending it is winter and that I don’t live in an arid and hot part of the U.S. I bought this yarn a few weeks ago. It’s “vintage” which means it came from a thrift store. In my defense, when I see 15 skeins of ecru bulky wool for $15, I feel like I need to get my knitting needles clacking and knit something fabulous.
So I made a muse n. (click for link to free pattern!) shrug by Isabell Kraemer and gifted it to my dear daughter. This looks like a manta ray, but it’s pretty cute when on, and certainly it’s going to be a warm sweater!
Iceleaves Shawl–Free Pattern
Dramatic and plush, the Iceleaves shawl is a fast knit using superbulky yarn and size 19 needles. With a gauge of almost 2 stitches per inch, you’ll be done knitting this before you’ve binge-watched two episodes of your favorite series!
This pattern is for your personal use only. Please don’t sell items knit from this pattern, and please don’t pass the pdf along to your fellow-knitters. Instead, refer them to this blog. Click ice-leaves-shawl to download. | https://nancyknit.com/category/knitting-patterns/ |
The Gale Encyclopedia of Fitness. Ed. Jacqueline L. Longe. Vol. 1. Detroit, MI: Gale, 2012. p475-477.
Interval training is any type of physical workout program that involves various intensities of exercise—going from short periods of high, intense work to longer periods of recovery in which only low- or no-intensity work is accomplished. The term can refer to any type of cardiovascular workout, such as running, bicycling, or swimming, in which brief spurts of maximum exertion, called sprint intervals, are intermingled between longer periods of much lower intensity activity, what are called rest intervals. This pair of intervals, or sets of high to low intensity activities are repeated several times to complete an interval training session.
For example, joggers include interval training within their weekly runs by alternating the use of walking and sprinting once or twice a week, in what is called sprint interval training (SIT). Similarly, swimmers can incorporate a couple fast-paced laps for every four or five slower laps.
The recent popularity of interval training over the past several decades has been brought about due to its effectiveness in providing a good cardiovascular work-out. Because the intensity of the workout is varied, it exercises the heart muscle, which improves the cardiovascular system of the body. Interval training helps to improve a person's aerobic capacity because, as one uses interval training on a regular basis, that person is able to exercise longer and at more intense levels. Interval training also provides a comprehensive work-out plan for many types of athletes, along with people who just want to stay healthy and fit.
Interval training is appropriate for most people who are in generally good health. However, if one has problems with the cardiovascular system (such as heart disease), or arthritis or joint problems, then it is recommended that a doctor be consulted before beginning interval training. In addition, if one is over age 45 for men and age 55 for women, it is necessary to first check with a doctor before beginning such a program.
Possibly originating in Sweden where it is called fartlek and meaning “speed play,” the basic idea of interval training is to vigorously exercise for a short amount of time and then slow down for a longer recovery time, only to resume the intensity for another short period followed by another longer break, and to do this many times in succession. This method improves a body's performance, specifically its endurance, speed, and strength.
Step 1: Three to five minutes of warming up on a bicycle that starts out slow and gradually increases in intensity.
Step 2: One minute of moderate or high intensity bicycling, or bike sprinting, followed by one minute of low intensity peddling.
Step 3: Repeating the actions of Step 2 six to eight times.
Step 4: Three to five minutes of cool down that starts at moderate intensity and gradually becomes low intensity and finally no intensity as the interval training ends.
Interval training can also be done with running. The high intensity portion of sprinting is called sprint intervals. They may consist of a time as short as 15 seconds or as long as 20 minutes. An example of sprint interval training is to run at a maximum speed for 30 seconds in a straight line. Running at such fast speeds for 15 minutes would simulate the climbing of a hill, and are also a part of interval training.
Several basic types of interval training are popular with athletes and non-athletes alike. One of them is called high intensity interval training (HIIT). HIIT involves combining very high intensity spurts of exercise with longer amounts of moderate intensity exercise for recovery. It is considered the most strenuous type of interval training but produces the fastest results when it comes to increasing endurance performance and getting physically fit.
Workout music is available that is specially designed to guide one through interval training. Such workout music is available on the Internet and most can be downloaded to a mobile device.
With respect to increasing respiration and the heart rate.
With respect to living or taking place without the need for oxygen, or in the absence of oxygen.
A measure of body fat based on the ratio of height and weight for adults.
The rate (speed) at which biochemical reactions of metabolism take place in living cells, such as those in the human body.
Relating to the heart and blood vessels.
interval training) also jogged, biked, and did aerobic exercise two to three times each week. After two weeks, 75% of the interval-training group doubled their endurance on the bicycles. That is, they were able to double their time that they sprinted at moderate intensities before becoming exhausted. None of the members of the control group showed any improvement in endurance over this two-week period. Since the size of the two groups was small, the researchers stated that further research studies were necessary to verify their conclusions.
BURNING FAT. A study from researchers at McMaster University, along with those from the University of Stirling (Scotland) and the University of Guelph (Canada), reported on the use of interval training to improve cardiovascular fitness and the body's ability to burn fat. The researchers studied eight women in their early twenties. The women intensely cycled for ten sets of four-minutes each; which was then followed by periods of two minutes of rest. In a two-week period, these female participants completed seven of these high-intensity aerobic interval training (HIIT) sessions.
The researchers found that the amount of fat expended in one hour of continuous moderate cycling increased by 36% when compared to the control group (which did not participate in interval training). Overall, the ability of the women's heart and lungs to supply oxygen to their working muscles (what is called cardiovascular fitness) improved by 13%.
Any healthy person can do interval training for improved fitness, health, stamina, and speed. Do to the physical demands of interval training, adequate preparation is necessary. Never go all out when first beginning interval training. Gradually increase performance to prevent injury. Warming up is critical because it gets extra blood into the muscles so they are prepared for the activity.
There is not one generally recommended way to prepare for interval training and to actually do interval training. A good warm-up period is always recommended before doing any exercise. A warm-up period may consist of about five minutes of light jogging or walking with a little extra quickness introduced from time to time. Let the body get accustomed to exercising. Once interval training is started, many exercise experts recommend that the duration of intense activity and moderate activity or rest is varied.
Once interval training is completed, it is a good idea to spend about five minutes cooling down. Light jogging or walking helps the body return to its regular routine. Some stretching exercises can also prevent muscle strain or soreness.
A chronic health condition may prevent one from doing interval training, such as heart disease, respiratory disorder, or cancer. Consult with a medical professional, such as a family doctor, before trying any type of interval training.
A risk of injury (such as with bones, muscles, or tendons) can occur with interval training, especially if one overexerts when first starting the training. Symptoms of overtraining include loss of endurance, strength, and speed; chronic aches and pains; loss of appetite, inability to sleep; overuse injuries such as tendinitis; irritability; irregular resting heart rate, and malaise or a general feeling of fatigue or ill feelings.
Am I in good enough physical shape to use interval training?
Will interval training help me to become physically fit?
How do I determine how hard to exercise with interval training?
Where can I learn more about interval training?
How often should I do interval training each week?
Are there personal trainers locally that specialize in interval training?
Is there anything that would physically prevent me from exercising in this manner?
What types of lifestyle changes will help while doing interval training?
personal trainer or exercise physiologist can assist individuals with establishing safe, effective interval sessions according to their personal goals and health history.
The use of interval training has great benefits for maintaining a healthy and physically fit body. It improves the body's aerobic capacity, which means the cardiovascular system will work more efficiently after experiencing interval training over a long period. It also reduces one's risk for many medical disorders such as heart disease, which in the long run improves cardiovascular fitness. A regular exercise program that includes interval training helps to maintain a healthy weight to height ratio, what is called the body mass index (BMI), by raising the body's potential to expend (burn) fat.
Cook, Gregg, and Fatima d'Almeida-Cook. The Gym Survival Guide: Your Road Map to Fearless Fitness. New York: Sterling, 2008.
Plowman, Sharon A., and Denise L. Smith. Exercise Physiology for Health, Fitness, and Performance. Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins, 2011.
Schoenfeld, Brad. Women's Home Workout Bible. Champaign, IL: Human Kinetics, 2010.
Sutton, Amy L., editor. Fitness and Exercise Sourcebook. Detroit: Omnigraphics, 2007.
Burgomaster, Kirsten A., et al. “Six Sessions of Sprint Interval Training Increases Muscle Oxidative Potential and Cycle Endurance Capacity in Humans.” Journal of Applied Physiology (February 2005). http://jap.physiology.org/content/98/6/1985.abstract?sid=c1a30c65-5a88-4bcb-a5a0-39830c704a7b (accessed November 5, 2011).
Interval Training: Can it Boost Your Calorie-burning Power? Mayo Clinic. (February 6, 2010). http://www.mayoclinic.com/health/interval-training/SM00110 (accessed November 5, 2011).
Talanian, Jason L., et al. “Two Weeks of High-intensity Aerobic Interval Training Increases the Capacity for Fat Oxidation During Exercise in Women.” Journal of Applied Physiology. (December 7, 2006). http://jap.physiology.org/content/102/4/1439.abstract?sid=78b427d9-d026-418a-a85b-36e0ffcb0959 (accessed November 5, 2011).
Weil, Richard. Interval Training. MedicineNet.com . http://www.medicinenet.com/interval_training/article.htm (accessed November 5, 2011).
American Alliance for Health, Physical Education, Recreation and Dance, 1900 Association Dr., Reston, VA, 20191-1598, (703) 476-3400, (800) 213-7193, http://www.aahperd.org .
American College of Sports Medicine, 401 W. Michigan St., Indianapolis, IN, 46206-1440, (317) 637-9200, Fax: (317) 634-7817, http://www.acsm.org .
American Council on Exercise, 4851 Paramount Dr., San Diego, CA, 92123, (888) 825-3636, [email protected], http://www.acefitness.org .
National Coalition for Promoting Physical Activity, 1100 H Street, NW, Ste. 510, Washington, D.C., 20005, (202) 454-7521, Fax: (202) 454-7598, http://www.ncppa.org .
National Strength and Conditioning Association, 1885 Bob Johnson Dr., Colorado Springs, CO, 80906, (719) 632-6722, Fax: (719) 632-6367, (800) 815-6826, http://www.nsca-lift.org .
President's Council on Fitness, Sports and Nutrition, 1101 Wootton Pky., Ste. 560, Rockville, MD, 20852, (240) 276-9567, Fax: (240) 276-9860, http://www.fitness.gov .
Atkins, William A. "Interval Training." The Gale Encyclopedia of Fitness, edited by Jacqueline L. Longe, vol. 1, Gale, 2012, pp. 475-477. Gale Virtual Reference Library, http%3A%2F%2Flink.galegroup.com%2Fapps%2Fdoc%2FCX4021200132%2FGVRL%3Fu%3Dviva_jmu%26sid%3DGVRL%26xid%3D608e430c. Accessed 18 Apr. 2019. | http://go.galegroup.com/ps/i.do?id=GALE%7CCX4021200132&v=2.1&u=viva_jmu&it=r&p=GVRL&sw=w&asid=3f4e83c7d73057a801f6188de9652bda |
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to an apparatus for the manufacture of corrugated pipes of thermoplastic plastics comprising circulating mold segment halves, which are disposed in two opposite rows subsequent to an injection head and of which two at a time combine along a straight molding path to form a closed hollow mold, and which, on their inside, have inside walls forming the corrugation, each of the mold segment halves, not connected with each other, of a row being guided out of the molding path substantially at right angles to the direction of production at the downstream end of the molding path by means of a return device, and being returned to the upstream end of the molding path along a return path, where they are again inserted in the molding path and attached to the mold segment half leading in the direction of production, the return device being a slide with a pivot arm, a coupling member being arranged on the free end of this pivot arm for the releasable coupling to a mold segment half, and drives being provided for continuously moving the coupling member from the downstream end of the molding path to the latter's upstream end and back again, and a wedge element being disposed at the downstream end of the molding path, separating the mold segment halves and cooperating with slopings disposed on the halves.
2. Background Art
An apparatus of the generic type known from U.S. Pat. No. 4,212, 618 ensures that as low as possible a number of circulating mold segment halves is needed. The mold segment halves are separated from each other on the return path and returned at such an average speed that the return period for each mold segment half is less than the time needed by a half to move on the molding path by a distance corresponding to its length. This results in the saving of more than fifty percent of the mold segment halves as compared to conventional apparatuses of continuously circulating mold segment halves. There is but one mold segment half on each return path, which is piloted back to the upstream end of the molding path by continuous, accelerated and again decelerated motion. Owing to the low number of mold segment halves needed, the apparatus can be retrofitted for another diameter of pipe rapidly and at little expense, which is important in particular for pipes of extreme diameters, taking into account that in general only comparatively small quantities of such pipes are produced, there being little sense in preparing an entire apparatus for the manufacture of this pipe diameter. Such an apparatus will also provide for saving in the manufacture of special types of pipes as well as in the manufacture of transition pieces, sockets etc, these special types too only requiring a very limited number of the expensive mold segment halves.
U.S. Pat. No. 4,325,685 discloses an apparatus for the production of corrugated pipes of thermoplastic plastics, in which individual mold segment halves revolve continuously on two closed paths, two mold segment halves joining on a molding path to form a mold segment, and mold segments lying close by close to form a mold, in which a thermally plastic tube discharged by the injection head of an extruder or an injection-molding machine is molded to form a corrugated pipe. The individual mold segment halves have several different profiles, of which one at a time can be put into function. To this end, the mold segment halves are disposed on supports for displacement at right angles to their direction of movement and are moved into their working position by a shunt system. In this way even such mold segment halves can be engaged that mold a socket and/or a spigot of a pipe.
An apparatus for the manufacture of corrugated pipes of thermoplastic plastics is known from DE-G. 93 11 140 U1, in which the mold segment halves, contiguous by twos, are conveyed on a molding path by a driving pinion, which engages with a tooth profile on the lower side of the mold segment halves. The conveyance back is likewise effected by pinions, which are drivable to move sidewise, the mold segment halves thus being movable from the molding path to a return path and from the return path back again to the molding path. Subsequent to the pinions of sidewise conveyance, the return paths are provided with parking stations for mold segment halves that can be inserted in the return paths by their own drives. If a pair of mold segment halves, for instance for the molding of sockets and/or spigots on the pipe to be produced, is to be added to the molding path, then the corresponding additional mold segment halves are inserted in the return path and moved to the upstream end of the molding path, where they are added to the molding path. Simultaneously, a pair of mold segment halves, after being conveyed sidewise, is removed from the molding path at the downstream end of the molding path and prior to entering the return path, is moved into the parking position. If the additional mold segment halves are to be removed from the circuit, then the parked mold segment half is inserted in the respective return path directly prior to these additional mold segment halves being conveyed sidewise away from the molding path, so that the additional mold segment half can be parked again. As a result, the molding path has always the same length only such additional mold segment halves can be inserted that have exactly the length of the usual mold segment halves for the production of the corrugated pipe.
SUMMARY OF THE INVENTION
It is the object of the invention to embody an apparatus of the generic type such that additional mold segment halves can be inserted or, respectively, removed from the molding path at low constructional requirements.
According to the invention this object is attained in that the wedge element is displaceable parallel to the direction of production by means of a displacing drive, and in that grab equipments are provided, which are displaceable counter to the direction of production by means of a supply and removal drive and by means of which one additional mold segment half at a time can be moved to the downstream end of the molding path, removed from the latter in the direction of production and moved into a parking position, and in that the coupling member is movable by means of the drives into two positions at the downstream end of the molding path, the distance of which positions from each other in the direction of production corresponds to the length of the mold segment halves in the direction of production. As a result of the measures according to the invention, additional mold segment halves, for instance for the molding of a socket and/or a spigot within the continuously produced pipe, are moved in front of the downstream end of the mold with their front facing the latter, and thus being inserted in the normal return cycle. The mold segment halves molding the normal corrugated pipe keep on circulating, i.e. the molding path is prolonged by the insertion of additional mold segment halves and, respectively shortened by their removal from the, molding path. In this way it is also possible to insert additional mold segment halves, the length of which not being identical with that of normal mold segment halves. This serves to achieve high flexibility of the apparatus.
Further features, advantages and details of the invention will become apparent from the ensuing description of an example of embodiment taken in conjunction with the drawing.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 is a plan view of an apparatus for the manufacture of corrugated pipes of thermoplastic plastics,
FIG. 2 is a vertical cross-section corresponding to the section line II--II of FIG. 1 of a partial illustration on an enlarged scale as compared to FIG. 1, and
FIG. 3 is a plan view of an apparatus for the manufacture of corrugated pipes of thermoplastic plastics in an illustration on an enlarged scale as compared to FIG. 1, showing the portion of the apparatus that has been changed according to the invention as compared to the prior art.
DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 1 illustrates an apparatus for the manufacture of corrugated pipes of thermoplastic plastics used within the scope of this invention and a portion of which is known from U.S. Pat. No. 4,212,618.
This apparatus has a base 1 with a molding path 2 disposed on it. Mold segments 3 file on this molding path 2, each consisting of two mold segment halves 4, 5. As long as the mold segment halves 4, 5 stick together by twos and as long as adjacent mold segments 3 abut to form a mold, they move straight on the base 1 in a direction of production 6. For continuously driving the mold formed by the mold segments 3, a driving pinion 8 is provided directly behind an injection head 7 of an extruder, the driving pinion 8 passing through a recess 9 in the base 1 and engaging with a tooth profile 10 formed on the respective bottom side of the mold segment halves 4, 5. The driving pinion 8 is non- rotatably disposed on a drive shaft 11 positioned underneath the base 1 and driven via a driving wheel 12 by a motor (not shown). On the molding path 2, the mold segment halves 4, 5 are pressed together by guide rails 13, 14.
A thermally plastic tube is extruded from the injection head 7 into the mold located on the molding path 2, the tube itself being molded to form a pipe 15 with transverse grooves 16 during the motion of the pipe in the direction of production, as it is known for instance from U.S. Pat. No. 3,776,679.
At the downstream end 17, opposite to the injection head 7, of the molding path 2, a wedge plate 18 is disposed on the base 1, which cooperates with slopings 19 disposed on the downstream inner edge--seen in the direction of production 6--of the mold segment halves 4, 5, so that the halves 4, 5 of a mold segment 3, when contacting the wedge plate 18, are moved apart at right angles to the direction of production 6. Of course, no guide rails 13, 14 are provided in this portion. On its wedge faces 20, the wedge plate 18 has rollers 21, which contribute to decrease the friction between the mold segment halves 4, 5 on the one hand and the wedge plate 18 on the other.
In the vicinity of the driving pinion 8, i.e. in the vicinity of the upstream end 22, adjacent to the injection head 7, of the molding path 2, a thrust bearing 23 is provided above the latter, absorbing the forces exercised by the driving pinion 8 upwards on the mold segment halves 4, 5. The thrust bearing 23 has a counter pressure axle 24, which is fixed to the guide rails 13, 14. On the counter pressure axle 24 a bearing 25 is disposed, on which pressing rollers 26 are rotatably supported, resting on the upper side of the mold segment halves 4, 5 and pressing same against the base 1. The thrust bearing 23 is of importance in particular because in the illustrated apparatus for the manufacture of the pipe 15, the depositing of the thermally plastic tube on the inside walls 27 of the mold segment halves 4, 5 is achieved in that air is sucked off the mold cavity 28 of the mold or the, mold segments 3 via channels (not shown in the drawing) formed in the mold segment halves 4, 5. This sucking off takes place via vacuum channels 29 which are formed in the base 1 and which combine with the channels formed in the mold segment halves 4, 5. The formation and arrangement of the vacuum channels in the mold segment halves 4, 5 is illustrated and specified in detail in British patent 971 021, to which reference is made for information. Since the mold segment halves 4, 5 are cooled in addition, the base 1 further comprises cooling water flow pipes 30 and cooling water return pipes 31, through which cooling water is supplied and removed. The design and the arrangement of such cooling water channels in the mold segment halves 4, 5 are illustrated and specified in U.S. Pat. No. 3,776,679, to which reference is made for information. As a result of the thrust bearing 23 pressing the mold segment halves 4, 5 on the base 1, losses of partial vacuum and cooling water are avoided.
On the outside 32 of the mold segment halves 4, 5, clamping prisms 33 are provided, to which a return device 34 can be coupled. Each of the two devices 34 arranged in mirror symmetry to the central longitudinal axis 35 of the molding path 2 has a slide 36, which is guided on a running rail 38 disposed along a return path 37. The running rail 38 is provided with a dove-tail profile, on which the slide 36 is slidably displaceable by a correspondingly adjusted recess. Of course, a roller guidance can be provided for the slide 36, which would ensure the running, reduced in friction, of the slide 36.
A pivot arm 39 formed by two parallel rods is articulated to the slide 36 and has a clamping device 40 articulated to is outer end; on the occasion of linear displacements of the slide 36 and of pivoting movements of the swivel arm 39, the clamping device 40 is always displaced parallel to itself owing to the parallel rod structure. On each clamping device 40, clamping pins 42 are supported, which are actuatable by a linear drive 41 and which engage with adjusted recesses 43 on the respective clamping prism 33, thereby producing a coupling between a return device 34 and an associated mold segment half 4 or 5.
A tandem arrangement of linear drives 44, 45, formed by pneumatic cylinders, is provided for pivoting the pivot arms 39, the free end of the piston rod 46 of the first linear drive 44 being articulated to the slide 36 in the vicinity of the latter's upstream end- -seen in the direction of production 6--while the piston rod 47 of the other linear drive 45 is articulated to the pivot arm 39, namely to a support bearing 48 projecting from the pivot arm 39 in the direction of production 6.
The movement of the slide 36 in the longitudinal direction of the apparatus, i.e. parallel to the central longitudinal axis 35, takes place by means of a drive 49, which may have a pneumatically actuatable piston- cylinder drive 50 as a main element, the piston rod 51 of which is connected with the slide 36. The drive 49 may have two further pneumatically actuatable piston-cylinder drives 52, 53 arranged in a row with the piston-cylinder drive 50 and which are employed for the acceleration, retardation and damping of the movements. The piston rod 54 of the drive 52 is articulated to the drive, 50; the piston rod 55 of the drive 53 is articulated to the running rail 38 in the downstream end portion 56 of the base 1.
Whenever a clamping device 40 is not coupled with a mold segment half 4 or 5, it supports itself on the base 1 by way of a supporting roller 57.
The apparatus specified so far works as described below:
The following proceeds from the position, shown in FIG. 1, of the mold segment halves 4, 5 at the downstream end 17 of the molding path 2, which have been separated partially by means of the wedge plate 18. In this position, the leading edge 58 of the mold segment half 4 operates a switch 59, as a result of which the linear drive 41 is actuated and a locking is produced between the clamping device 40 and the clamping prism 33 of the respective mold segment half 4 or 5. By way of a usual sequence control, the linear drive 44 and the piston-cylinder drive 52 are then acted upon by compressed air such that the piston rods 46, 54 are retracted. As a result, the respective mold segment half 4 or 5 and the clamping device 40 completely move out of the molding path 2 along a curved length 60. At the end of this respective curved length 60, which is at the same time the start of a long straight length 61, parallel to the axis 35, of each return path 37, the piston-cylinder drives 50 and 53 are acted upon by compressed air such that their piston rods 51 and 55 are extracted, whereby the slides 36, with the mold segment half 4 or 5 coupled to them, are accelerated to a speed of as much as 5 m/sec and reversed along the straight length 61 to the upstream portion of the base 1 adjacent to the injection head 7. Right before the final position is reached, a switch 62 is operated, whereby the linear drives 44, 45 are acted upon by compressed air such that their piston rods 46, 47 are extracted. The switch 62 is displaceably and adjustably disposed on a guide rail 62a. As a result, the respective clamping device 40, with the mold segment half 4 or 5, coupled to it, moves along a curved length 63 toward the molding path 2. Simultaneously, a valve (not shown) of the piston-cylinder drive 52 is opened so that the latter's piston rod 54 is extracted by the inertia of the return device 34 and the coupled mold segment half 4 or 5, the mass in motion being braked by the throttling effect of the mentioned valve (not shown). The final damping and braking is made by shock absorbers 64 disposed on the base 1.
When all the piston rods 51, 54, 55 of the piston-cylinder drives 50, 52, 53 are extracted and the shock absorber is pressed in, a switch 65 adjustable on the guide rail 62a and displaceable in latter's longitudinal direction is actuated, whereby the pneumatically actuatable piston-cylinder drives 50 and 53 are acted upon by compressed air in such a way that their piston rods 51 and 55 are retracted. This results in the mold segment half 4 or 5 still coupled to the respective clamping device 40 being moved along a straight length 66 extending at an angle to the axis 35, and that until the downstream front 67 of the respective mold segment half 4 or 5, moved alongside and toward the molding path 2, tightly rests on the facing upstream front 68 of the next downstream mold segment half 4 or 5. Since the closed mold, which consists of mold segments 3, is moved ahead in the direction of production 6 with the aid of the driving pinion 8, and since there are strong frictional forces between the mold segments 3 and the base 1, which may even be augmented by the vacuum actuation mentioned above, the piston-cylinder drives 50, 53 and the linear drives 44, 45,--the latter still in the process of extraction--cannot displace the mold segments 3 forming the mold in the direction of production 6, but they can only tightly press the mold segment halves 4, 5 newly added to the molding path 2 and move them on in the direction of production 6 until the mold segment half 4 leading in the direction of production 6 operates a limit switch 69, which takes place at the beginning of the separation of the two associated mold segment halves 4, 5 leading in the direction of production 6 by the wedge plate 18. By the operation of this switch 69, the linear drives 41 and 44 are acted upon by compressed air such that the clamping pins 42 are moved out of the recess 43 of the clamping prism 33 and the piston rod 46 is retracted. In this way, the clamping device 40 is disengaged from the mold segment half 4 or 5 and then moved along a curved length 70 out of the traveling path of the clamping prisms 33 on the molding path 2. Since the piston-cylinder drives 50, 53 have already been acted upon by compressed air for their piston rods 51, 55 to be retracted, the slide 36 is moved by acceleration along a straight length 71 to take its initial position, where again two mold segment halves 4, 5, partially separated by the wedge plate 18, are coupled to it.
In the embodiments known, the wedge plate is stationarily united with the base 1, for instance by screwing, whereas in the embodiment of the invention according to FIG. 3, it is joined to a displacing drive 72 in the form of a linear drive acting parallel to the axis 35, by means of which the wedge plate 18 can be moved from a position shown in dashed lines in FIG. 3 and corresponding to the position according to FIG. 1, to a position shown in solid lines in FIG. 3. In this latter position, the wedge plate 18 is displaced in the direction of production 6 toward the end portion 56 of the base 1. The distance a between these two positions of the wedge plate 18 equals the dimension b of a mold segment 3a, consisting of two halves 4a, 5a, to be additionally inserted in the molding path 2. In this case, this mold segment 3a is added to the molding path 2, which is extended by the dimension b as a result. The displacing drive 72 is formed by a pneumatically actuatable piston- cylinder drive, of which the cylinder 73 is mounted on the base 1, while the wedge plate 18 is fixed to its piston rod 74. On either side of the displacing drive 72, two supply and removal drives 75 are disposed, which act parallel to the displacing drive 72 and on the base 1, and which are also pneumatically actuatable piston- cylinder drives. On the free end of the respective piston rod 76, a grab equipment 77 is disposed for seizing a mold segment half 4a or 5a. This grab equipment 77 may be a solenoid or a magnetic holding device acting on the advancing front 67a of the mold segment half 4a or 5a. On the path of displacement of the respective grab equipment 77, guide stops 78 are provided on the base 1 along a U-shaped curve, by means of which the position of an additional mold segment half 4a or 5a is set in relation to the base 1 and thus to the molding path 2 when the piston rod 76 of the supply and removal drive 75 is retracted.
FIG. 3 also illustrates the different positions in which the return devices 34 take the mold segment halves 4, 5--as described above-- at the end of the molding path 2, if no additional halves 4a, 5a are on the molding; path 2. This position of the return devices 34 is shown by dashed lines in FIG. 3. The corresponding position of the return devices 34, in case an additional mold segment 3a is on the molding path 2, is shown by solid lines in FIG. 3. The curved lengths 60a, along which the mold segment halves 4, 5 and 4a, 5a, respectively, are guided outward in the case of this constellation, are also shown. The straight length 61a, by which the straight length 61 is extended, corresponds to the dimension b. This extension of the return path 37 becomes possible due to the fact that the drive 49 can be extended by different lengths. In concrete form, this can be realized in that the piston-cylinder drive 50 can be stopped in an intermediate position, in Which the piston rod is extracted by the dimension b. This is the position from which the return of the mold segment halves 4 and 5 takes place if no additional mold segment 3a is on the molding path 2. If, however, an additional mold segment 3a is on the molding path 2, then the piston rod 51 is completely retracted. The corresponding triggering takes place by way of a switch 79, which is operated by the wedge plate 18, when the piston rod 74 of the displacing drive 72 is retracted.
The insertion of an additional mold segment 3a in the molding path and, respectively, the removal of these additional mold segment halves 4a, 5a from the molding path 2 takes place as follows:
According to FIG. 3, the starting point consists in that on each grab equipment 77 of each supply and removal drive 75, an additional mold segment half 4a and 5a is in its inactive position between the guide stops 78. The piston rod 74 of the displacing drive 72 is extracted so that the wedge plate 18 is in its upstream position closer to the injection head 7, as described in detail for FIGS. 1 and 2 above. After a pair of mold segment halves 4, 5 has been guided out of the molding path 2 in the way described above and has been moved outwards along the curved lengths 60 by the return devices 34, the displacing drive 72 is acted upon by compressed air in such a way that its piston rod 74 is retracted into the cylinder 73 and the wedge plate 18 moves away from the injection head 7 by the dimension a. In this case the switch 79 is actuated, triggering an actuation of the supply and removal drives 75 by compressed air in such a way that the latter's piston rods 76 extend counter to the direction of production 6, conveying the additional mold segment halves 4a and 5a located on their grab equipments 77 toward the molding path 2, i.e. upstream. In this case their distance c from each other at right angles to the axis 35 corresponds to the distance c which the mold segment 3 halves 4,5 have from each other when they have been moved apart by the wedge plate 18. The grab equipments 77 are released and the drives 75 are acted upon by compressed air in such a way that their piston rods 76 are again retracted. By means of the switch 79, the triggering of the piston- cylinder drive 50 is changed such that the latter's piston rod 51 is completely retracted so that the return device 34 is moved into the position shown by solid lines in FIG. 3. One return device 34 at a time takes the additional mold segment half 4a or 5a, respectively, and transports it in the manner described along the curved length 60a, the straight supplementary length 61a and the straight length 61 to the start 22 of the molding path 2. When an additional mold segment 3a is inserted in the molding path 2, the latter is extended correspondingly.
If the additional mold segment halves 4a, 5a are to be removed from the molding path 2, then the displacing drive 72 is acted upon by compressed air after separation of the additional halves 4a, 5a at the end of the molding path 2, such that its piston rod 74 extends and moves the wedge plate 18 into its position closer to the injection head 7, so that the ensuing pair of mold segment halves is separated at an earlier time--as specified above. Simultaneously, the switch 79 is again operated, which triggers the described shortening of the displacement path of the piston-cylinder drive 50. Moreover, the piston rods 76 carrying the grab equipments 77 of the supply and removal drives 75 are extracted and seize the additional mold segment halves 4a, 5a to be removed from the circuit. The triggering of the drives 75 is reversed so that the piston rods 76 are retracted, moving the additional mold segment halves 4a, 5a into their parking position between the guide stops 78.
The dimension b of the additional mold segment 3a may be greater or less than the length d of the usual mold segment 3. The additional mold segment 3a may be provided for the molding of a socket 15a on the pipe 15 otherwise provided with transverse grooves 16 over its length, or for the molding of a socket 15a and, additionally, of a spigot (not shown). Taken in conjunction with the mold segment half 5a, FIG. 3 roughly outlines what the inside walls 27a of the additional mold segment halves 4a, 5a are like in such a case.
It may also be suitable to form a socket 15a and a spigot (not shown) one after the other so that when the pipe 15 is severed between the socket 15a and the spigot, pipe sections are produced, having a socket 15a at one end and a spigot at the other. Within a scope given by the length d, the pipe sections may be of arbitrary length. | |
Police investigating string of weekend break-ins
Sioux Falls police are investigating a string of break-ins over the weekend.
Police don’t believe the break-ins are connected, and detectives are working to identify suspects, police spokesman Sam Clemens said.
The first occurred at Cliff Avenue Flea Market and Antiques, 3515 N. Cliff Ave., where at least $3,000 in merchandise was stolen. Management guessed the items were taken between Thursday night and Friday morning, Clemens said.
The thief forced open the back door of the business and took a number of swords, knives, coins and jewelry from the business, Clemens said.
Saturday evening, a thief stole a washer and dryer from a home in the 800 block of North Irene Place, Clemens said.
Also Saturday, a thief stole an undisclosed amount of cash from Safelite Auto Glass, 129 N. Minnesota Ave., after busting a window and entering the business.
On Friday, candy was stolen from a concession stand at Terrace Park. | https://www.argusleader.com/story/news/crime/2014/06/09/police-investigating-string-weekend-break-ins/10234435/ |
TECHNICAL FIELD
BACKGROUND
SUMMARY
DETAILED DESCRIPTION
This invention relates to a system with a closed loop. More particularly, this invention relates to a test system with a configurable closed loop.
Automated Test Equipment (ATE) is used in many industries to efficiently test various electrical and electromechanical devices. For example, manufacturers seek to reduce production time while still achieving a quality for equipment, and the test equipment facilitates testing the operation of equipment and devices for their intended purposes. Test equipment is usually configured to test functionality for certain equipment within a given industry, and sometimes is manufactured specifically to test a particular piece of equipment, which tends to increase the cost of the test equipment. Depending of the complexity of the equipment being tested, the actual testing itself can become quite complicated, requiring significant expertise to operate the test equipment.
One example relates to a test system that can comprise a controller configured to provide a closed loop. The closed loop can comprise a forward transfer function with programmable coefficients that is configured to receive a signal corresponding to a command signal. The closed loop can also comprise a feedback transfer function having programmable coefficients and can be configured to provide a feedback signal that is subtracted from the command signal. The controller can be configured to provide a control signal corresponding to an output of the forward transfer function.
Another example relates to a test system for configuring a closed loop. The closed loop can comprise a controller configured to provide a closed loop, the closed loop configured to receive at least one command signal. The controller can comprise a proportional-integral-derivative (PID) controller with programmable constants. The controller can also comprise a forward transfer function with programmable coefficients that is configured to receive an output of the PID controller. The controller can further comprise a feedback transfer function having programmable coefficients and being configured to provide a feedback signal to the PID controller. The controller can be configured to provide a control signal corresponding to an output of the forward transfer function. The closed loop can further comprise an interface configured to provide an electrical signal to an output for operating a unit under test (UUT) as a function of the electrical signal.
Yet another example relates to a method for configuring a test system. The method can comprise selecting a feedback signal for a closed loop from a plurality of feedback signals. The method can also comprise setting transfer function parameters in a transfer function of a controller for the closed loop. The method can further comprise setting PID controller parameters for a PID controller of the controller for the closed loop.
FIG. 1
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illustrates an example of a test system for implementing a closed loop. The system can include a controller that can receive one or more command signals . The controller could be implemented, for example, as a field programmable gate array (FPGA), a microcontroller, an application specific integrated circuit (ASIC) or the like. The one or more command signals can be analog input signals. In some examples, there can be two command signals . In such a situation, a first of the two command signals can be a relatively constant input signal, while a second of the two command signals can vary. In other examples, more or less command signals could be employed.
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In some examples, the one or more command signals can be provided from and/or controlled by a command module . The command module could be implemented, for example, by a human-machine interface, such as a computer. The command module can be programmed/configured for manual and/or automatic operation. The automatic operation can include automatic application and verification of a test stimulus. The command module can include a user interface that can be configured to provide user input and output. By employing the user interface , a user can select preprogrammed test routines. Such test routines can provide precise, repeatable testing to reduce and/or eliminate errors.
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FIG. 1
The controller can be configured to communicate with a unit under test (UUT) via an interface . The UUT could be implemented, for example, as a mechanical structure, an electromechanical device or an electrical device. As one example, the UUT may be implemented as an aircraft, or some portion thereof. In some examples, the controller can provide a control signal to a current driver of the interface . The control signal could be implemented as a digital signal or an analog signal. In response, the interface can provide a control current corresponding to the control signal to circuitry (e.g., an actuator) in the UUT . In some examples, the actuator could be implemented as an electro-hydraulic valve (EHV). In other examples, the actuator could be implemented as a rotary actuator or a piston. Those skilled will understand other types of actuators and types of UUTs that may be utilized in the system of .
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The interface can include an input configured to receive an analog feedback signal from the UUT . In some examples, the analog feedback signal can be provided from a linear variable differential transformer (LVDT) or other circuitry configured to provide feedback from the UUT to the test system . The analog feedback signal can be implemented, for example, as an AC signal with a magnitude and/or phase corresponding to a position of an actuator detected by the LVDT. In other examples, the analog feedback signal could correspond to a pressure signal, a rotary encoder or other measurement device or related signals. The interface can also include a demodulator that converts the analog feedback signal to a corresponding DC feedback signal. The DC feedback signal can be provided to the controller . In some examples, the interface can provide multiple DC feedback signals to the controller . Analog-to-digital conversion may be utilized to provide the feedback signal as a corresponding digital signal.
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By way of example, the controller can be configured to apply a transfer function to the DC feedback signal. In some examples, the controller can apply multiple transfer functions to a plurality of different DC feedback signals. The controller can also apply a programmable amount of gain to an output of the transfer function applied to the DC feedback signal.
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p
i
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term
term
term
The controller can also provide a gain to each of the command signals . The command signals with the added gain can be provided to a proportional-integral-derivative (PID) controller of the controller . The PID controller could be implemented, for example, to simulate operation of a control loop feedback controller. For example, the PID controller can apply three programmable constants (e.g., parameters), namely, a proportional constant (K) an integral constant (K) and a derivative constant (K). Each of the proportional constant, the integral constant and the derivative constant can be programmed by a user employing the user interface of the command module . The PID controller can sum (i) a proportional term (P) that employs the proportional constant, an integral term (I) that employs the integral constant and a derivative term (D) that employs the derivative constant to provide a PID signal.
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The controller can also apply a forward transfer function to the PID signal to provide a processed signal. The forward transfer function can be implemented as a series of variables with coefficients. Each of the coefficients (e.g., parameters) can be programmed via the user interface of the command module. The controller can also apply a dithering function to the process signal to provide a dithered process signal. Parameters of the dithering function, such as frequency (e.g., 0 Hz to 400 Hz) and magnitude (e.g., 0 V to 10 V) can be programmed via the user interface of the command module .
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The dithered process signal can be provided a control signal to the interface . The interface can include a current driver that can provide the control current to the UUT that corresponds to the dithered process signal. An output limit of the current driver can be controlled, for example, in response to being set by the user of the system . The output limit can define a current limit that can characterize a maximum positive and negative amplitude of the control current output by the current driver of the interface . The actuator (or the structure) of the UUT can be characterized by the analog feedback signal provided from the UUT .
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Parameters of the controller , such as including coefficients of the PID controller, the forward transfer function and the feedback transfer can be set and/or changed by command module in response to user input at the user interface . In some examples, the command module can set and/or change the gain of the controller in response to user input at the user interface . Additionally or alternatively, the command module can select a source of a DC feedback signal employed by the controller in response to user input at the user interface .
FIG. 2
FIG. 2
FIG. 2
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illustrates another example of a system for implementing a closed loop . The closed loop could be implemented on an FPGA . It is to be understood that in other examples, the closed loop could be implemented on a different type of circuit, such as a microcontroller, an ASIC or the like. The closed loop can be employed, for example, to generate signals corresponding to a predetermined transfer function for controlling a UUT . In some examples, the UUT could be implemented to include an EHV . The UUT can provide a first LVDT signal from a first LVDT (labeled in as “LVDT”) and a second LVDT signal from a second LDVT (labeled in as “LVDT”). The first and second LVDT signals can characterize a position of the EHV or other operating condition of the UUT , more generally. The first and second LVDT signals can be provided to an interface . The interface could be implemented, for example, as one or more circuits.
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FIG. 2
For example, the first and second LVDT signals could be provided to corresponding first and second demodulators and (labeled in as “DMOD” and “DMOD”). Each of the first and second the demodulators and can provide first and second feedback signals to the FPGA . The first and second feedback signals could be implemented, for example, as DC signals. The FPGA can apply a first feedback transfer function (G(s)) to the first feedback signal and a second feedback transfer function (G(s)) to the second feedback signal. The first and second feedback transfer functions and could be implemented, for example, as including a multi- (e.g., fourth) order filter, such as can be implemented as a difference equations. Equation 1 characterizes an example of a difference equation that could be employed as the first feedback transfer function . In a similar manner, Equation 1 could be employed to implement the second feedback transfer function as well.
y[x[n]]=a
*y
+a
*y
+a
*y
+a
*y
+b
*x
++b
*x
+b
*x
+b
*x
+b
*x
1
n−1
2
n−2
3
n−3
4
n−4
0
n
1
n−1
2
n−2
3
n−3
4
n−4
Equation 1:
x[n] is the first feedback signal;
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y[x[n]] is a signal output by the first feedback transfer function for a given input signal; and
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a, a, a, a, b, b, b, b, bare coefficients for the first feedback transfer function .
wherein:
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The FPGA can also apply the output of the first and second feedback transfer functions and to respective first and second feedback gain blocks and . Equation 2 characterizes an example of gain that could be applied by the first feedback gain block . In a similar manner, Equation 2 could be employed by the second feedback gain block to apply the second feedback gain.
r[y
]=m*y
n
n
Equation 2:
n
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r[y] is an output of the first feedback gain block ;
n
68
yis an output of the first feedback transfer function ; and
m is a gain coefficient.
wherein:
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A computer can be communicatively coupled to the FPGA . The computer can include a memory for storing machine readable instructions. The computer can also include a processor unit (e.g., a processor core) configured to access the memory and execute the machine readable instructions. In some examples, the computer can communicate with the FPGA via a communications port such as a serial bus, a parallel port, a network port, or the like. A user can employ a user device in communication with the computer to interact with a graphical user interface (GUI) to set the coefficients (e.g., parameters) of the first and second feedback transfer functions and . The user device could be implemented, for example, as a keyboard, a mouse, a combination thereof or the like. In a similar manner, the user device can operate the GUI to set the gain coefficient (e.g., parameters) for the first and second feedback gain blocks and .
FIG. 2
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Additionally, in the example illustrated in , the FPGA receives first and second feedback signals from the UUT via the interface . However, the computer can also be communicatively coupled to the interface such that a user of the system can employ the GUI to provide a configuration signal that can selectively configure the source of the first and second feedback signals. For instance, in some examples, the feedback signals may not originate from an LVDT and/or may not be demodulated by the interface .
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In some examples, the memory can store test data that includes a sequence . In some examples, the sequence can store the parameters and/or an order of command signals for the FPGA for a specific UUT and/or a specific test. The sequence can be associated with a set of parameters that can also be stored in the test data. The parameters can include, for example, data defining coefficients of feedback transfer functions and , and/or gain coefficients for gain block and or the like. For instance, in some environments of application, the coefficients for the first and second feedback transfer functions and can be provided from the manufacturer of the UUT . One of ordinary skill in the art will understand and appreciate that other data could additionally or alternatively be included in the test data
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FIG. 2
The FPGA can apply the output of the first and second feedback gain blocks and to a PID controller . Additionally, the FPGA can receive a first and second command signal (labeled in as “CMD ” and “CMD ”) from the computer . For instance, the test data can be utilized to provide first and second command signals to corresponding inputs of the FPGA, such as based on the test data for performing a test routine. In other examples, the first and second command signals could be provided from another source. The first and second command signals can be provided to corresponding first and second gain blocks and . The first and second gain blocks and can apply first and second gains to the corresponding first and second command signals. In one example, Equation 3 could be employed by the first gain block to apply a gain to the first command signal. In a similar manner, Equation 3 could be employed by the second gain block to apply a gain to the second command signal.
l[c
]=m*c
n
n
Equation 3:
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88
l[c] is an output of the first gain block ;
n
cis the first command signal; and
m is a gain coefficient.
wherein:
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A user can utilize the user device to interact with the GUI to set the gain coefficient (e.g., parameters) of the first gain block and/or the second gain block . The outputs of the first and second gain blocks and can be provided to corresponding inputs of the PID controller of the FPGA .
FIG. 3
FIG. 2
FIG. 3
FIG. 3
FIG. 3
FIG. 2
FIG. 2
FIG. 3
FIG. 3
FIG. 3
FIG. 3
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illustrates an example of a PID controller that could be employed as the PID controller illustrated in . In , a first summing block can subtract a feedback signal (labeled in as “FEEDBACK SIGNAL”) from a command signal (labeled in as “COMMAND SIGNAL”). The command signal could be implemented, for example, as a sum of the output of the first and second gain blocks and illustrated in . The feedback signal could be implemented, for example, as a sum of the output of the first and second feedback gain blocks and illustrated in . The first summing block can provide an error signal (labeled in as “E[N]”). The error signal can be provided to a proportional function block to calculate a proportional term (labeled in as “P_TERM”), an integral function block to calculate an integral term (labeled in as “I_TERM”) and a derivative function block to calculate a derivative term (labeled in as “D_TERM”).
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The proportional function block can employ Equation 4 to calculate the proportional term. The proportional term can make a change to an output that is proportional to a current error value. A high proportional term results in a large change in the output of the PID controller for a given change in the error signal. If the proportional gain is too high, the system can become unstable. In contrast, a small proportional term results in a small output response to a large input error, and a less responsive or less sensitive PID controller . If the proportional term is too low, a resulting control action may be too small when responding to system disturbances.
P
[e[n]]=K
e
term
p
n
Equation 4:
p
Kis a proportional term constant;
e[n] is the error signal; and
term
P[e[n]] is the proportional term for a given error signal.
wherein:
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i
As a further example, the integral function block can employ Equation 5 to calculate the integral term. The contribution to the output of the PID controller from the integral term is proportional to both the magnitude of the error signal and the duration of the error signal. The integral term in the PID controller corresponds to the sum of an instantaneous error over time and gives an accumulated error. The accumulated error is then multiplied by an integral term constant (K). The integral term accelerates movement of the process towards a setpoint and substantially eliminates residual steady-state error that could occur in a pure proportional controller. However, since the integral term responds to accumulated errors from the past, the proportional term can cause the present value to overshoot the setpoint value.
I
[e[n]]=[I
e
*Δt
K
term
term n−1
n
t
+()] Equation 5:
i
Kis the integral term constant;
Δt is a change in time between n and n−1; and
term
I[e[n]] is the integral term for a given error signal.
wherein:
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The derivative function block can employ Equation 6 to calculate the derivative term. The derivative term can be calculated by determining the slope of the error signal over time and multiplying the rate of change of the error signal by a derivative gain K. The derivative term slows the rate of change of the controller output. The derivative term can be used to reduce the magnitude of the overshoot of the setpoint produced by the integral component and improve the combined controller-process stability. However, the derivative term slows the transient response of the PID controller . Additionally, the derivative term in the PID controller is sensitive to noise in the error signal, which can cause the process to become unstable if the noise and the derivative term are sufficiently large.
D
[e[n]]=[
e
−e
Δt]K
term
n
n−1
d
()/ Equation 6:
d
Kis the integral term constant;
Δt is a change in time between n and n−1; and
term
D[e[n]] is the integral term for a given error signal.
wherein:
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FIG. 3
The PID controller can employ a second summing block that can aggregate the proportional term, the integral term and the derivative term together. Equation 7, can be employed by the second summing block to calculate a PID output signal (labeled in as “P[E[N]]”).
Equation 7:
P[e[n]]=P
+I
+D
term
term
term
P[e[n]] is the PID output signal for a given error signal.
wherein:
FIG. 2
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p
i
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Referring back to , a user can employ the user device to interact with the GUI to set a proportional term constant K, an integral term constant Kand/or a derivative term constant Kof the PID controller . Moreover, in some environments of application, the PID controller can be disabled in response to a user input received via the user device of the computer . In such a situation, the output signal of the PID controller could be equal to the error signal input therein. In one example, the PID controller could be disabled by setting the proportional term constant Kequal to one (‘1’) and setting the integral term constant Kand the derivative term constant Kof the PID controller to zero (‘0’). In other examples, the PID controller can be omitted. In such a situation, a summing component that provides a signal corresponding to the difference in the command signals and the feedback signals can be provided in place of the PID controller . Such a disabling or omitting of the PID controller could represent a configuration where no PID controller is necessary and/or desired.
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An output of the PID controller can be provided to a forward transfer function . The forward transfer function can apply a transfer function to the output of the PID controller . In one example, the output of the forward transfer function can be calculated with Equation 8.
f[p
]=a
*f
+a
*f
+a
*f
+a
*f
+b
*p
+b
* p
+b
*p
+b
*p
+b
*p
n
1
n−1
2
n−2
3
n−3
4
n−4
0
n
1
n−1
2
n−2
3
n−3
4
n−4
Equation 8:
n
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pis the output of the PID controller ;
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n
92
f[p] is the output of the forward transfer function for a given p; and
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4
0
1
2
3
4
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a, a, a, a, b, b, b, band bare coefficients for the forward transfer function .
wherein:
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A user of the computer can employ the GUI to set the coefficients for the forward transfer function . In some environments of application the coefficients for the forward transfer function can be provided from the manufacturer of the UUT and stored, for example, in the test data . In other examples, the coefficients can be calculated and/or estimated based on a different transfer function. The FPGA can provide the output of the forward transfer function to a dither function block . The dither function block can apply a dithering to the output of the transfer function. The dither function block can have a frequency and a magnitude. The frequency and the magnitude of the dither function block can be set in response to user input (e.g., provided via the user device ) at the computer provided via the GUI .
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In one example, the frequency of the dither function block can be set in a range of about 0 Hz to about 400 Hz. Moreover, in some examples, the magnitude of the dither can be set in a range from about 0 V to about 10 V. The output of the dither function block can be provided as an output of the FPGA , which output can be referred to as a control signal. The control signal can be provided to a current driver of the interface . The current driver can provide the control current to the EHV , wherein control current can correspond to the output of the FPGA . In response to the control current, the EHV can provide a response (e.g., a mechanical response). The first and/or the second LVDT signal can characterize the response to the EHV . In some examples, the GUI of the computer can provide an output to the user device in the form of graphical indicia (e.g., a graph) that characterizes the response to the EHV . In this manner, the computer can be programmed to measure and/or analyze the response to the EHV based on the parameters set in the FPGA . The results can be stored in results data and used to drive an output that can be presented to the user (e.g., via the GUI ).
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In some examples, user inputs (e.g., received via the user device ) can employ the GUI to change the arrangement of the feedback signals. For instance, in some examples, the user can employ the GUI to change the sources of the feedback signals or what the feedback signals represent, such as may vary according to the context of the system being simulated.
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Employment of the system can allow the user to tune (e.g., set and/or change) parameters of the PID controller , the gain blocks and , the feedback gain blocks and , the transfer functions (the first and second feedback transfer functions and and the forward transfer function ) and the dither function block . Such a tuning allows the system to simulate a large range of stimuli (e.g., in the form of the control current) to the UUT .
FIG. 4
FIG. 2
FIG. 2
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illustrates an example of a test system that includes an FPGA with N number of closed loops , wherein N is an integer greater than or equal to one. The FPGA could be implemented, in a manner similar to the FPGA illustrated in . Moreover, each of the N number of closed loops can be implemented with programmable transfer functions in a manner similar to the closed loop illustrated in .
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FIG. 4
FIG. 2
FIG. 4
FIG. 4
FIG. 4
FIG. 4
The FPGA can receive M number of command signals (labeled in as “CMD ” and “CMD M”), where M is an integer greater than or equal to one. The M number of command signals can include, for example the first and second command signals described with respect to . The FPGA can communicate with an interface that provides stimuli to a UUT . In some examples, each of the N number of closed loops can be associated with a corresponding current driver of the interface . Additionally, each of the corresponding current drivers can be associated with a corresponding input of the UUT , such as an EHV (labeled in as “INPUT ” and “INPUT N”). The UUT can provide K number of output signals from K number of outputs , such as could be implemented as LVDTs (labeled in as “OUTPUT ” and “OUTPUT K”) signals to corresponding K number of demodulators (labeled in as “DMOD” and “DMODK”) of the interface , where K is an integer greater than or equal to one. Each of the K number of demodulators can provide a corresponding feedback signal (labeled in as “FEEDBACK ” and “FEEDBACK K”). The LVDT signals can correspond to sensed parameters of the UUT .
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FIG. 2
FIG. 4
The FPGA and the interface can communicate with a computer . The computer can be implemented in a manner similar to the computer illustrated in , and thus can be an integral part of the test system . The computer can provide the plurality of command signals to the FPGA . A user of the computer can interact with the computer via a user device and employ a GUI of the computer to tune (e.g., set and/or change) transfer function parameters of each of the N number of closed loops . For instance, the user employ the user device to interact with the GUI to tune parameters of a PID controller, gain blocks, as well as other transfer function paths and a dither function in each of the N number of closed loops . Additionally, in some examples, the user can employ the user device to interact with the GUI to selectively monitor and analyze feedback signals for each of the N number of closed loops . Employment of the system illustrated in allows multiple simulated stimuli (e.g., in the form of control currents) to be concurrently provided to multiple EHVs in the UUT , for example.
FIG. 5
FIG. 5
In view of the foregoing structural and functional features described above, example methods will be better appreciated with reference to . While, for purposes of simplicity of explanation, the example method of is shown and described as executing serially, it is to be understood and appreciated that the present examples are not limited by the illustrated order, as some actions could in other examples occur in different orders and/or concurrently from that shown and described herein. Moreover, it is not necessary that all described actions be performed to implement a method.
FIG. 5
FIG. 1
FIG. 2
FIG. 2
FIG. 2
FIG. 2
FIG. 3
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2
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illustrates a flowchart of an example method for configuring a closed loop. The method could be implemented, for example by the system illustrated in and/or the system illustrated in . At , a user can employ a GUI of a computer to select a feedback signal for the closed loop of a controller, such as an FPGA, a microcontroller, an ASIC or the like. At , the user can employ the GUI to set transfer function parameters for the closed loop. The setting of the transfer function parameters can include, for example, setting and/or changing coefficients of difference equations feedback transfer functions (such as the first and second feedback transfer functions and in ) and setting and/or changing coefficients of a forward transfer function (such as the forward transfer function illustrated in ). At , the user can employ the GUI (e.g., the GUI illustrated in ) to set gain parameters, such as a gain constant, for the feedback signal and a command signal. At , the user can employ the GUI to set PID controller parameters (e.g., proportional, integral and derivative constants) for a PID controller of the closed loop. The PID controller could be implemented in a manner similar to the PID controller illustrated in .
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FIG. 2
FIG. 2
At , the user can employ the GUI to set dithering parameters (e.g., magnitude and frequency) for a dither function (e.g., the dither function illustrated in ) of the closed loop. At , a stimulus can be applied to a UUT, such as the UUT illustrated in . Application of the stimulus can include, for example, applying the command signal to the controller, which in turn can apply a control signal to a current source. The current source can apply a corresponding control current to an actuator (e.g., an EHV) of the UUT. The control current can be employed, for example to simulate stimuli to the UUT. What have been described above are examples. It is, of course, not possible to describe every conceivable combination of components or methodologies, but one of ordinary skill in the art will recognize that many further combinations and permutations are possible. Accordingly, the disclosure is intended to embrace all such alterations, modifications, and variations that fall within the scope of this application, including the appended claims. As used herein, the term “includes” means includes but not limited to, the term “including” means including but not limited to. The term “based on” means based at least in part on. Additionally, where the disclosure or claims recite “a,” “an,” “a first,” or “another” element, or the equivalent thereof, it should be interpreted to include one or more than one such element, neither requiring nor excluding two or more such elements.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1
illustrates an example of a test system.
FIG. 2
illustrates another example of a closed loop test system.
FIG. 3
illustrates an example of a proportional-integral-derivative (PID) controller.
FIG. 4
illustrates an example of part of a system that includes a plurality of closed loops.
FIG. 5
illustrates an example flowchart of a method for configuring a closed loop test system. | |
- Physically-Based Editing of Indoor Scene Lighting from a Single Image
Abstract"We present a method to edit complex indoor lighting from a single image with its predicted depth and light source segmentation masks. This is an extremely challenging problem that requires modeling complex light transport, and disentangling HDR lighting from material and geometry with only a partial LDR observation of the scene. We tackle this problem using two novel components: 1) a holistic scene reconstruction method that estimates scene reflectance and parametric 3D lighting, and 2) a neural rendering framework that re-renders the scene from our predictions. We use physically-based indoor light representations that allow for intuitive editing, and infer both visible and invisible light sources. Our neural rendering framework combines physically-based direct illumination and shadow rendering with deep networks to approximate global illumination. It can capture challenging lighting effects, such as soft shadows, directional lighting, specular materials, and interreflections. Previous single image inverse rendering methods usually entangle scene lighting and geometry and only support applications like object insertion. Instead, by combining parametric 3D lighting estimation with neural scene rendering, we demonstrate the first automatic method to achieve full scene relighting, including light source insertion, removal, and replacement, from a single image. All source code and data will be publicly released." | https://www.ecva.net/papers/eccv_2022/papers_ECCV/html/1276_ECCV_2022_paper.php |
FIELD OF THE INVENTION
This invention relates to telecommunications networks and more particularly to a method of and system for resolving contention between different sender/chooser pairs of the spare capacity circuits of a network to restore disrupted connections of the network after a network failure.
BACKGROUND OF THE INVENTION
A telecommunications network comprises a plurality of nodes connected together by means of for example optical fibers. If any of the fibers are cut, the traffic through a portion of the network is disrupted. To remedy this disruption, automatic protection switching is ordinarily provided to move disrupted traffic to dedicated spare circuits promptly, typically in less than 50 milliseconds. But this automatic protection switching requires a high dedicated spare channel capacity.
To avoid automatic protection switching in restoring disrupted traffic, there are some conventional methods that deal directly with each node of the network. Each node consists generally of one or more are digital cross-connect switches. One of these restoration methods is a distributed restoration algorithm (DRA), a variant of which is often referred to as the self-healing network (SHN) method. SHN is an algorithm which rims independently in each of the nodes of a mesh network which have spans connecting adjacent nodes. In order to provide a fast and reliable method of restoring traffic affected by fiber cuts and other failures using SHN, the intelligence is distributed in the network and is based specifically on signalling between nodes. Such signalling may be referred to as the use of signatures and/or messages. Signatures are dynamic in that they are sent on a continuous basis into the nodes, and more specifically into the digital cross-connect hardware in each node where the state of the signature represents a given logic that changes from frame to frame. Upon receipt of these signatures, SHN would react. There are several signature types in SHN and these signatures may be in band or out of band, as they can actually ride with the traffic as part of the payload itself or can superpose on the overhead as part of the supervisory overhead of a signal such as for example in a SONET network.
Each node running SHN conveys the signalling between itself and its adjacent node. Thus, a signature is sent from node to node and each node in turn realizes the logical span(s) to which it is attached. As designed, a logical span contains a multiple number of links and connects two given nodes. A link in turn is a communications channel of any size, for example a DS3 or a DS1 standard communications signal.
A SHN null signature is exchanged between the nodes and carries the information necessary for a node to identify its neighbor(s). Thus, each node knows exactly which other node(s) it is connected to and has an identification of the logical span connecting it to those nodes. The null signatures are sent continuously and thus continuously update each node of its neighbor's presence for a given link. The status, in terms of the functioning of each link, is therefore reinforced continuously.
Whether a link in the network is a spare link or a working link is provisioned by the management of the network which in turn knows where the spare links and the working links of the network are. The spare links in essence are dedicated links that provide a capacity for restoration and which otherwise do not carry any traffic. These spare links are used only when the system detects a failure of a given link, or a set of links, in a logical span by some means, such as for example the detection of a lost signal or a maintenance signal by a line terminating element (LTE) in the cross connect switch of a node.
Once a link is determined to be in alarm, a node, more specifically the cross connect switch in the node, will retrieve the stored information received from the null signatures in an arbitration process to determine what node is connected on the other side of the failed link. In other words, the adjacent nodes sandwiching the failed link each have a node ID. From the arbitration process, one of the nodes is determined to be a sender and the other a chooser. These two adjacent nodes, the sender and the chooser, make up a custodial pair of nodes. A number of different arbitration methods may be used, such as one where numbers (node IDs) are assigned to the different nodes with the node having the lower node ID becoming the sender while the node with the higher node ID becoming the chooser.
Having decided on a custodial pair of nodes, a flooding process for searching alternate routes, or alt-routes, is next started by the sender. Alt-routes are spare routes that traffic disrupted by the failed link may be directed to reach the chooser.
The flooding process in SHN sends signatures into spare links. These flooding signatures or flooding messages carry certain information such as the sender node ID, the chooser node ID and an index. The index is simply a unique number that represents a given flooding route, for example a given flooding demand that will allow the logic in the nodes downstream from the broadcasting node to determine whether two signatures are different or are the result of a multi-cast of the same signature, or whether each signature represents a unique flooding pattern. Nodes downstream from the sender, which may be referred to as tandem nodes, will receive the signatures and detect a state change on the spare paths. The signatures will be multicast out to a particular spare link of each logical span terminates at a tandem node. The spanning out of these signatures throughout the network will reach the chooser eventually through one or more of the tandem nodes if one or more all routes exist.
A chooser recognizes that a flooding signature is meant for it by looking for its own node ID at the chooser node ID field. The chooser then responds to a given unique sender/chooser index combination by sending a complementary restoration signal, or a reverse linking message or signature. This signature travels back through the same path, or the same alt-route, to the sender to inform the sender that it has indeed reserved an alt-route for that particular demand and that the chooser is awaiting the arrival of the restored traffic. Alt-routes may be chosen by a chooser based on any arbitration method since a given sender/chooser index may arrive from several different logical spans, or links within a logical span. Typically, the shortest path, based on a number of hops or repeat counts measured or detected by the chooser node, is chosen.
Regardless of the method of arbitration a chooser uses, it will reserve the particular span that it has reversed linked onto and will typically ignore and discard any other signatures arriving from any other links with that same sender/chooser index. Incoming ports, or precursor ports, and outgoing ports of the tandem nodes along the alt- route are reserved by the reversed linking message so that a particular path through the matrix of each cross connect switch of a tandem node is mapped. The reverse linking signatures are transmitted back to the sender to let the sender know that an alt-route has been reserved by the chooser and the tandem nodes along the alt-route. Any priority function of choosing which traffic to connect onto the alt-route is performed at this time.
A second method for restoring traffic due to failed fiber cuts is a centralized restoration scheme. This second method depends on a centralized intelligence that has a built in knowledge of the different nodes and links of the network, and a defined solution for a particular failed connection. There are advantages and disadvantages to this centralized restoration scheme. One of the disadvantages is that the topology of the network has to be stored in a centralized database and has to be updated every time a change occurs in the network. Thus, the implementation of the centralized restoration scheme becomes more difficult and extensive when the network changes very rapidly, such as for example when links are added, removed, failed, or changes in the network. Such changes occur when spare links are changed to working links or vice versa. In any event, the important aspect of a centralized restoration scheme is reliance on a central intelligence and the ability to dynamically update this intelligence so that it knows the proper state of the network at the time of a failure.
On the other hand, the DRA mentioned previously distributes the intelligence among the different nodes of the network so that the intelligence of the network is gained from the signals and messages from the adjacent nodes and/or the nodes downstream from where the failure occurred. Thus, in the DRA scheme, a far away or far end node can use the network itself and the current state of the network as it is updated so that it knows exactly on which logical span a traffic is to be routed and how many links are on each logical span and what kind of links are on it. This means that the switching commands and the ability to find and reserve alt-routes, as well as the ability to switch the proper traffic into and out of those alt-routes, are all performed in each node individually using a distributed intelligence with a distributed set of rules, logic and mathematical algorithm. Thus, the DRA has the advantage over the centralized restoration scheme of being faster on a network wide level.
There are two different forms of distributed restoration algorithm. One is the span or link based distributed restoration scheme in which SHN is an example of where attempts are made to find alt-route between two custodial nodes. The second form of DRA is a path based scheme in which the shortest and/or most reasonable end-to-end alt-route throughout the network is to be found. The jointed or connected set of links throughout the network of a given circuit forms the alt-route for this scheme. These conventional link based schemes theoretically treat the failure of a single logical span between two nodes, irrespective of the number of links within that span, as a single fiber cut.
However, in actuality, when a fiber cut does occur as, for example, results when trench digging equipment cuts a cable, a number of cuts actually may occur, because a single cable contains many fibers. In addition, all of the cuts may not occur at the same time. Because of the differences in time in which the different links of a span, or the different spans within a cable, are cut, a "greedy characteristic" is introduced into a real life SHN scheme which heretofore was not accounted for. In essence, the greedy characteristic results from the sender of the first cut circuit performing a so-called preemptive activated flooding in which it floods its restoration signals to a sufficient number of the available spare links of the network so as to reserve alt-routes for each link of the spare. This preemptive activated flooding is used by the failed circuit to more quickly find alt-routes in the event of a partial failure of some links of a given span. Thus, it floods as if all of the links of a given span do eventually fail. In other words, with the first cut in a span, a preemptive activated flooding is performed to reserve sufficient spare capacity so that the traffic through most, if not all, of the links of the span can be restored.
But such preemptive activated flooding in fact can locate and reserve an excessive number of alt-routes, i.e., finding more alt-routes than it actually needs for a logical span. The sender of this cut circuit then would hold onto the spare circuits indefinitely until its restoration process is terminated.
Thus, if more than one logical span of the network is cut, or different circuits such as links at different spans are cut at approximately the same time, multiple sender/chooser pairs will become active. A race condition would ensue among the different senders of the cut circuits to contend for the spare capacity and the alt-routes. Accordingly, there is no fair contention process between the multiple senders, as the sender that first initiates flooding and having its reverse linking done before the others have a chance to flood and reserve any alt-routes could in actuality reserve nearly all of the alt- routes in the network for itself. It could therefore prevent other cuts from being repaired expeditiously.
There is therefore a need to provide a method, and a system therefor, of resolving the contention among multiple senders, and their respective demands, for the spare capacity of the network for restoring disrupted traffic after network failures.
SUMMARY OF THE PRESENT INVENTION
To obtain a more equitable resolution of the contention problem, the present invention institutes a set of timers and, by means of their interactions, provides a contention scheme for senders and choosers to share, as much as possible, the limited resources, i.e., the spare capacity and the spare links, of the network.
One of the timers provided is a preactivation timer which prompts the sender to release any spare resources that it has reserved when an alt- route for a particular failed link has been found within a given time period. In particular, in a SHN flooding scenario where all of a sender's links in alarm have been restored and a given time period has passed such that it becomes less and less likely that more links are going to fail, the unused yet reserved alt-routes are forced released so that they may be utilized by other senders to thereby alleviate the greedy characteristic of the SHN preemptive activation type flooding.
The early release of the unused reserved alt-routes is based on the configuration of the preactivation timer which, upon expiration, will force an early sender time-out to release the particular sender's unused yet reserved alt-routes. The configuration of the time period of the preactivation timer is such that the preactivation timer will expire much earlier than the timer provided for the sender time-out, in order to assure that other senders would have sufficient time to utilize the alt- routes released by the particular sender.
Other timers such as a hold-off timer and an alarm validation timer are also configured in the present invention for further enhancing its operation.
It is therefore an objective of the present invention to provide a preactivation timer that allows the present invention to benefit from a faster overall route finding via preemptive activation flooding, while at the same time limiting the disadvantage of excessive reservation of spare links by some sender/chooser pairs to the detriment of other sender/chooser pairs.
It is another objective of the present invention to provide timers whose values are user configureable, thereby giving the network management flexibility in resolving contention of spare capacity by multiple senders.
It is yet a further objective of the present invention to provide an independent preactivation timer for the sender of each custodial pair of unique sender/chooser nodes.
It is yet another objective of the present invention to provide a set of timers whose interactions maximize the efficient restoration of a network due to failed circuits.
BRIEF DESCRIPTION OF THE FIGURES
The above-mentioned objectives and advantages of the present invention will become more apparent and the invention itself will be best understood by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, wherein
FIG. 1 is an illustration of a number of nodes in a telecommunications network in which two senders are formed within a single node in response to a cable failure;
FIG. 2 is a repeat of the FIG. 1 illustration but with details added thereto of the alt-routes being reserved by an first sender (sender B) due to the "greedy characteristic" resulting from the self- healing network (SHN) distributed restoration algorithm (DRA) scheme;
FIG. 3 is an illustration of the relationship between the different timers employed in the instant invention;
FIG. 4 illustrates the relationship between the preactivation timer and the sender time-out for different failed links of a particular span and its comparison with a second span;
FIG. 5 is a block diagram illustrating two digital cross connect switches located at respective adjacent nodes to show the actual physical interconnection between adjacent nodes of the telecommunications network; and
FIGS. 6A and 6B provide a flow diagram illustrating the operation of the instant invention.
DETAILED DESCRIPTION OF THE PRESENT INVENTION
With reference to FIG. 1 it can be seen for illustration purposes 8 nodes of a telecommunications network, namely node 1 to node 8 for example. Within each of these nodes are a number of working links, designated W, and spare links designated S. Each of the nodes may be connected to another node, such as for example an adjacent node as exemplified by nodes 6 and 7, or a node further downstream, such as the connection of node 2 to node 4 by means of an express pipe 10.
For the exemplar embodiment shown in FIG. 1, each node is assumed to be connected to another node by a span, such as 12 shown between nodes 7 and 8. Within each of the spans there are number of links such as for example links 12a, 12b, 12c and 12d. Further, each node has a number of ports, namely Ss and Ws, for providing connection to the links. As was mentioned before, ports W provide connection for the working links while ports S provide connection for the spare links.
The interconnections between nodes 2, 3 and 4 are somewhat different from those of the other nodes for the instant embodiment of FIG. 1 in that in addition to being connected to its adjacent node 3 via links 14a and 14b, node 2 is also connected to node 4 by means of express pipe 10. Thus, for the FIG. 1 embodiment of the instant invention, it should be recognized that a node does not necessarily need to be connected to its adjacent nodes.
In contrast to the prior art in which it was simply assumed that all of the links of a given logical span would fail precisely at the same time when it is cut, the inventors of the instant invention recognized the fact that, in actual practice, when a cut occurs at a span, the links in that span would be cut sequentially. Moreover, as in the case of the embodiment shown in FIG. 1, the fact that node 2 is connected to both nodes 3 and 4 by different spans 10 and 14 means that a cut such as that indicated by cable failure 16 would cut both express pipe span 10 and span 14. Thus, for the FIG. 1 embodiment, a fiber cut would affect both connections between nodes 2 and 3 and nodes 2 and 4. Thus, there is a sender/chooser pair for nodes 2 and 4 and another sender/chooser pair for nodes 2 and 3 resulting from cable cut 16.
For the discussion at hand, for custodial pair of nodes 2 and 4, by means of the arbitration method mentioned above, it is presumed that the sender is node 2 while the chooser is node 4. Likewise, for the custodial pair of nodes 2 and 3, it is assumed that sender is node 2 while chooser is node 3. And in order to differentiate between the two pairs of senders and choosers, for the FIG. 1 embodiment, the first pair of sender/chooser for custodial pair of nodes 2 and 4 is shown to have sender A while the pair of sender/chooser for custodial pair of nodes 2 and 3 is shown to have sender B. Having thus designated two senders A and B in node 2, it nonetheless should be appreciated that instead of both senders being located at one node, it could very well be that both choosers are in one node and the senders in respective different nodes. Or for that matter it could very well be that more than two senders are located in one node while their corresponding multiple choosers are located at different nodes. That notwithstanding, the important point to recognize here is that there are more than one senders vying for the spare capacity, i.e., the spare links, of the network.
As was mentioned previously, SHN distributed restoration may begin by means of preemptive activation flooding. In essence, a preemptive activation flooding enables a sender to quickly find alt- routes in the event of a partial failure of some links of a given span. Putting it in a different perspective, the sender essentially would want to flood its restoration signals or messages to the spare links so as to reserve as much capacity as it needs to provide for what it perceives to be the eventuality that all links of a given span are to fail because of the cut. In other words, the sender wants to provide for all of the links in the event that all of those links were to fail. And by preemptively reserving the alt-routes, the restoration process could be expedited, at least with respect to that particular pair of sender and chooser, since routes have already been reserved for links that might be cut.
Yet such preemptive activated flooding introduces a "greedy characteristic" into the restoration scheme because of the excessive number of alt-routes that are reserved by the particular pair of sender/chooser. And given the fact that conventional SHN provides for only a single iteration of the protocol of flooding and then finding of the alt-routes, the conventional SHN scheme will hold onto all of the reserved alt-routes indefinitely until the entire process is terminated. Such termination of process may be referred to as a "sender timeout".
To elaborate, for the example shown in FIG. 1, if for illustration purposes the custodial pair of sender/chooser represented by sender B of nodes 2 and 3 were to flood and reserve all spare links before the pair of custodial sender/chooser represented by sender A of nodes 2 and 4 were able to do so, then in the case of multiple failures, sender A would not be able to repair its failed link. Putting it differently, a race condition exists among the senders, i.e., there is contention between senders A and B for spare capacity and alt-routes. Thus, if one sender initiates flooding and the reverse linking by its corresponding chooser is done before another sender has a chance to flood and reserve alt- routes, then the second sender would have to wait until the first sender times out. The second sender might not therefore have enough time to reserve any alt-routes released by the first sender, particularly if the respective spans of the first and second senders failed approximately at the same time. There is accordingly no fair contention scheme among the separate senders in conventional SHN logic.
This is particularly illustrated in FIG. 2 in which sender B is assumed to have began its preemptive flooding of restoration signals to other nodes prior to sender A. Thus, as shown, sender B has reserved two alt-routes between nodes 2 and 3 through the available spare links. As shown, the first alt-route, designated 18 comprising sections 18a, 18b and 18c, extends from node 2 to node 6 to node 7 and finally to node 3. The second alt-route reserved by sender B from node 2 to node 3, designated 20 and including sections 20a, 20b, 20c, 20d and 20e, goes from node 2 to node 1 to node 5 to node 6 to node 7 and finally to node 3. And assuming that there are only two spare links for node 2 and each having been reserved by alt-routes 18 and 20, sender A is left with no spare capacity for its restoration of its failed link between nodes 2 and 4.
As shown in FIG. 2, the second alt-route 20 for sender B is not needed since the first alt-route 18 will restore the only link (14b) in alarm between nodes 2 and 3. Note that spare link 14a is not a working link and therefore has no traffic which needs to be rerouted. Yet under the FIG. 2 scenario, the logic provided at the chooser at node 3 will respond by reverse linking for each of the unique sender/chooser index arriving thereat. This is because the chooser in node 3 has no knowledge of the restoration demand. Accordingly, the second alt-route 20 is reserved by sender B for the duration of its operation until its sender time-out, even though alt-route 20 is not needed.
In the meantime, as mentioned above, sender A cannot flood its restoration signals to the adjacent nodes because the spare links for node 2 had all been flooded into or reserved by sender B, who in a race with sender A for the use of the spare links, has already flooded into both spare links. Thus, sender B would wait for the termination of its operation before it will release the spare links to which it has reserved, i.e., alt-route 20. And in the case where the termination of operation for both senders, for example senders A and B, are essentially at the same time, then sender A would not have the time or opportunity to utilize the spare links, i.e., alt-route 20, released by sender B which would become available only nearly at the time that sender A also ceases its restoration operation. Moreover, even if the restoration operation of sender A were to be extended sufficiently to allow it to reserve the now released spare links of sender B, such practice of allowing sender A the opportunity to flood restoration signals to released spare links entails, needless to say, additional restoration time.
To overcome this hoarding problem and particularly the contention problem between multiple sender/chooser pairs, there is instituted in the instant invention a number of timing devices, i.e., timers. One of these timers, hereinafter known as preactivation timer, forces the first sender to release the alt-routes that it had reserved provided that it has found an alt-route to restore the traffic disrupted by all of its failed links. The operation of the preactivation timer, and the other timers of the system of the instant invention, are shown with reference to FIG. 3.
As shown, FIG. 3 is a time diagram illustrating the different timers and events that take place along a time line 22. To begin with, assume that there are only two sender/chooser pairs in the embodiment of FIG. 2. Further assume that by means of an arbitration method in which the lower numbered node is deemed to be the sender, a decision has been made that there are now senders A and B each in node 2 with respective choosers in node 3 and 4. Next, senders A and B are allowed to race by doing their own preemptive activation floodings and retaining their own greedy characteristics. Thus, as shown in the example of FIG. 2, sender B ends up reserving all of the spare links to await the reverse linldng signatures or messages from its corresponding chooser in node 3. And once the reverse linking signatures are received by sender B, it can determine the most efficient alt-route to use. Upon expiration of its preactivation timer, it will furthermore release the other alt-routes it has reserved for the other sender/chooser pair(s) to utilize, in this instance sender A.
These occurrences for sender B are illustrated in FIG. 3. In order to enhance the understanding of FIG. 3, specific times such as 100 ms, 300 ms, 10 sec and 20 sec are shown. But do bear in mind that these times are for illustration purposes and are not meant to limit the instant invention operation to those time periods. As shown, an alarm is detected at line 24, the beginning of the time line, by sender B that there is a failed link which, in this instance, is failed link 14b. See FIG. 2. At that point, a validation of the alarm takes place in accordance with a predetermined time period generated by the system. This is represented by arrow 26 and extends to line 28. This timer may be referred to herein after as an "alarm validation timer".
The purpose of the validation timer is, as its name implies, to validate that the alarm is indeed valid. This is needed because of the fact that the system does not want to begin restoring traffic to alt- routes if the alarm actually signifies some intermittent problems that are repairable by the node itself or intermediate line terminating equipment (LTEs). Such problems include for example equipment failure to which the above-mentioned conventional automatic protection switching, i. e. , switching on the equipment itself, can readily fix. In essence, the present invention system does not want to repair transient failures such as power surges by utilizing restoration. Rather, it focuses onto an actual fiber cut which in a linear transmission system cannot be typically protected against with automatic protection switching. Thus, given a predetermined time period in which there has been a determination that the fault results not from transient or intermittent interruption of traffic, i.e. , it is indeed a fiber cut, the system will take the next action at line 28. For the embodiment of the FIG. 2 example, the alarm validation timer is deemed to have been generated by the system to have a predetermined time period of 100 ms. This timer is independently set for each logical span.
Having thus provided the equipment protection switching time to correct transient failures rather than restore or trying to react immediately to any failure of traffic, the system next begins to perform its preactivation flooding, as indicated by line 30. In other words, at this point of time at line 28, it is deemed that the alarm is validated and preactivation flooding begins.
At the same time, a couple of timers are also generated by the system. The first of the timers is the so-called sender time-out timer shown by line 32. This timer provides a predetermined time period to ensure that the preactivation flooding by the sender, and its subsequent restoration, would not go on indefinitely, thereby tying up the system. In other words, a determination has to be made at some future time at which to declare that restoration is not possible, as for example when there are no alt- routes found. It should further be noted that it is assumed here that sender B has won the race and the second sender such as sender A in the same node is not allowed to flood at all because the first sender has now reserved all of the spare links that it floods into. In this instance, the second sender's sender time-out timer would not begin until the first sender has released the spare routes it had reserved. Under all circumstances, the sender timeout timer does not begin until flooding is actually accomplished on at least one span.
A second timer that is generated by the system which begins to operate at this time is a preactivation timer, as indicated on line 34. The preactivation timer does the following. It sets a predetermined time period during which it waits for the system to find, reserve and restore to an alt-route for the failed link of the sender/chooser pair to which it belongs. The preactivation timer further assures that extra alt- routes are reserved. Putting it differently, because of the greedy characteristic of the sender, the extra alt-routes are held onto for a limited period of time such as for example from 100 ms to 10 sec in the FIG. 3 embodiment, in anticipation of the failure of more links in the same logical span. The amount of time allocated for the preactivation timer is of course arbitrary.
At the expiration of the preactivation timer, designated by line 36 in FIG. 3, all unused alt-routes are released if there are no additional alarms detected on the node for that particular logical span. In other words, each logical span failure has its own preactivation timer and each individual sender, such as for example sender B, has its own sender time- out. Thus, the two senders A and B in the FIG. 2 embodiment each has its own sender time-out timer and each is running its own preactivation timer.
Once the preactivation timer 34 expires, its particular sender, sender B in the example of FIG. 2, is forced to release any unused alt- routes. And since the preactivation timer may be set typically half way or less than half way through the sender time-out, all of the senders which were competing for the spare links are provided extra time to actually locate, flood into and reserve those alt-routes or use those spare links now released by the first sender so as to reserve their own alt-routes. Putting it simply, by providing a preactivation timer, the greedy characteristic of the distributed restoration scheme is "released" ahead of the sender time-out by the first sender in order to allow other senders, which may otherwise time-out at precisely or near the same time as the original sender, time to find their own alt-routes. This therefore provides a more fair contention method based on the premise that reserved alt-routes should be held for a given period in anticipation of further failure of the links in a logical span, but these additional reserved alt- routes ought to be released for the use by other senders after a certain time period which in all likelihood would indicate that there are no other links that will fail within the same logical span, so that other senders may utilize this spare capacity.
Another timer generated by the system of the instant invention is a hold off timer, illustrated by line 38 in FIG. 3. As shown, the hold off timer has a predetermined timer period that extends from line 24 to line 40, a total of approximately 300 ms for this embodiment. This hold off timer is similar to the alarm validation timer in that, instead of holding off the preactivation flooding, it holds off the restoration process of the system until there is a clear determination that such restoration is not premature due to intermittent failures. For example, a hit on traffic through a link could mean the loss of the frame in the traffic or the loss of a signal for any length of time. In electronics, intermittent failures oftentimes entail very short durations. Thus, if there is a failure for example of an optical cable that is intermittent due to either dirt or intermittencies in the interface cards, alarms may be triggered and withdrawn rather rapidly on its own thereby toggling back and forth between the failed and the working states. The hold off timer is implemented to prevent this scenario so that an alarm needs to persist for a predetermined time period, 300 ms in this instant example, before restoration using restorative cross connects are allowed on that failure. Thus, even though flooding begins at line 28 at 100 ms, restoration actually does not take place until an alarm has persisted for an additional 200 ms, as indicated at line 40. This restoration process is indicated by line 42 which extends to the end line 44 of time line 22.
Do note that in FIG. 3, preactivation flooding 30 is shown to extend from line 28 to end line 44. Yet if alt-routes are released and no other links in a logical span are in alarm, then obviously there would not be any flooding. In other words, FIG. 3 shows preactivation flooding to extend all the way to end line 44. Yet, in actuality, such extended flooding would occur only if additional alarms have been detected and not sufficient number of alt-routes have been reserved to satisfy those additional failed links. Of course, flooding continues if no alt-route is found for the first failed link.
For the example shown in FIG. 3, the sender time-out 32 extends to the 20 sec end point. What this means is that the distributed restoration scheme of the instant invention has run its single iteration whereby the first of the multiple sender/chooser pairs will have released any unused alt-routes--whether due to the preactivation timer or the sender time-out. Any unused reserved, now released, spare links may therefore be utilized by some other sender, such as for example sender A.
An illustration of the relationship between the different timers is shown in FIG. 4. Here it is assumed that there are two senders in a particular node with each sender being connected via a logical span to its corresponding chooser node. For the sake of simplicity, the preactivation timer is deemed to have a predetermined time period of 10 sec while the sender time-out timer is deemed to have a predetermined expiration time of 20 sec.
As shown, for logical span number 1 whose time line is designated 46, it is assumed that there are at least 4 links, namely link 1, link 2, link 3 and link 4. When an alarm is validated at time 46a, a sender time- out, designated by downward sloping line 48, begins presumably for 20 sec in accordance with the examples shown in FIG. 3. The preactivation timer, at the same time 46a, begins to countdown its predetermined time period of 10 sec, designated by downward sloping line 50. To provide a time reference, a time of day line 52 is provided to show that the first link 1 failed at 15:34:10.
At time 46b, an alt-route 54 is deemed to have been found for restoring the traffic of failed link 1. As shown, this finding of the alt- route 54 occurs before the expiration of preactivation timer 50. Accordingly, the spare links reserved by sender 1 are not released.
At time 46c, a second link 2 in the same logical span 1 fails. Notice that a second alt-route 56 is then found for the second failed link 2 at time 46d, which remains prior to the expiration of preactivation timer 52. And since no additional failed links are found within the predetermined time period of preactivation timer 50, at time 46e (15:34:20), the preactivation timer 50 expires. At the same time, insofar as the traffic for all so far failed links have been restored via alt-routes, the sender time-out timer is likewise aborted at time 46e.
However, a short time thereafter, at time 46f (15:34:26), yet another link, namely link 3, fails in logical span number 1. With the failure of link 3, the whole process begins anew, as a second preactivation timer 58 begins a second 10 sec predetermined timer period, and a second sender 1 time-out of 20 sec, as indicated by line 60, begins.
As shown, an alt-route 62 is not found for failed link 3 until almost at the end of the predetermined time period of preactivation timer 58, at time 46h. However, before time 46h, at time 46g, yet another link, i.e. , link 4, of logical span 1 fails. And since no additional alt-route is found for link 4, sender time-out 60 for sender 1 is allowed to run its full course until time 46i. At that time, since no other alt-routes are found to restore the traffic of failed link 4, in order not to tie up the system, a determination is made that restoration of failed link 4 is not possible, and all reserved spare alt- routes are released by sender 1.
As further shown in FIG. 4, a second sender 2, which may be equated with sender A in FIG. 2, also resides at the same node. It however is connected to its chooser node by means of a second logical span 2. As shown and with reference to its own time line 64, at time 64a (15:34:17), one of the links, namely link 9, in logical span 2 fails. The preactivation timer, designated 66, for sender 2 begins its countdown of its predetermined time period which is assumed to be the same as the preactivation timer of sender 1. But since all of the alt- routes have been reserved by sender 1, sender 2 would not begin its flooding until shortly after preactivation timer 50 of sender 1 has forced the release of unused spare links that were reserved by sender 1 at time 46e. Thus, for sender 2, its sender time-out 68 does not begin until time 64b, which is shortly after time 46e. And insofar as no alt- route is found for failed link 9 by sender 2 within the duration of sender time-out 68, the traffic traversing failed link 9 is not restored.
For the example shown in FIG. 4 with respect to sender 2, for the sake of clarity, it is assumed that links 3 and 4 of logical span 1 have not failed and that preactivation timer 58 and sender time-out 60 for sender 1 do not exist. For sender 2 in FIG. 4, its sender time-out is shown to have a shorter time duration than the sender time-outs of sender 1.
Thus, FIG. 4 illustrates two things. First, that with respect to sender 1, different sets of preactivation timers and sender time-out timers may be generated for different link failures in the same logical span. And if additional links failed after the expiration of a first preactivation timer, a second preactivation timer may be generated for those additional failed links, such as links 3 and 4. Second, FIG. 4 also shows, with respect to senders 1 and 2 (ignoring the additional failed links 3 and 4 of sender 1), that sender 2 will begin its own sender time- out as soon as the unused spare links previously reserved by sender 1 are forcedly released by the expiration of the preactivation timer of sender 1, in this instance 50 shown in FIG. 4.
The hardware component utilized for the instant invention is shown in FIG. 5. There two digital cross connect switches 74a and 74b, such as model 1633-SX made by the Alcatel Network Systems Company, are illustrated to be connected to each other, as for example between any of the nodes shown in FIG. 2. As shown, each of the digital cross connect switches has a number of ports 70 that are shown to be multiplexed to a line terminating equipment (LTE) such as the SONET LTE 72. Each of the digital cross connect switches 74 has, as shown, two working links 76a and 76b, as well as one spare link 76c and one open link 76d. Do note that working links 76a and 76b correspond to the working links W shown in FIG. 2 and spare link 76c corresponds to the spare link S likewise shown in FIG. 2. For the purpose of the instant invention, it suffices to state that open link 76 is reserved for some later usage as a working link. Each link shown in FIG. 5 is a conventional optical carrier OC-12 fiber, or embedded within a higher order (i.e., OC-48 or OC-192) fiber.
With reference to digital cross connect switch 74a, it can be seen that the interfacing boards indicated as DTNR interface cards 78a and 78b in turn are routed to a number of STS-1 ports 80 for transmission to SONET LTE 72. Although not shown, an intelligence such as a processor resides in each of the digital cross connect switches to act as a generator of the different timers to provide the different predetermined time periods for the instant invention. Also not shown but present in each of the digital cross connect switches is a database storage for storing a mapping which deals with the identification of the various senders, choosers and indexes mentioned previously. A detector that may reside in SONET LTE 72 acts to detect any failure of links between the various digital cross connects switches. The detector may also be resident in the DTNR cards 78a and 78b as detection circuits for interpreting whether a communication failure has occurred at the respective links 76a and 76b.
FIGS. 6A and 6B provide a flow chart for illustrating the operation of the instant invention system. As shown, the process begins at block 600. The alarm validation timer starts with detection of an alarm at block 602. With the detection of an alarm, the alarm validation timer is generated in block 604 by the system to provide a predetermined time period to ensure that the restoration process of the instant invention does not begin unless the automatic protection switching of the node fails to repair the problem. Thus, if the alarm is cleared at block 606, which means that the problem associated with the alarm has been corrected by the automatic protection switching, the process returns to block 602 to await the next alarm detection. Likewise, upon detection of an alarm, in addition to the generation of the alarm validation timer at block 604, a hold off timer is generated by the system in block 608.
Returning to the main branch of the flow chart of the instant invention, if an alarm is not cleared after decision block 606, then a determination is made in block 610 on whether the alarm is validated. If it is not validated, then the process returns back to block 602. If it is in fact validated, then preactivation flooding is activated at block 612. At the same time, a preactivation timer is generated for initiating a predetermined time duration at block 614.
With the initiation of the preactivation flooding, alt-routes or spare links that were found by the flooding are reserved at block 616. At the same time, a sender time-out timer is generated and begins its countdown to sender time-out at block 618 shown in FIG. 6B.
Next, depending on whether the hold off timer has expired, as designated in block 620, restoration of an alt-route begins at block 622. If the hold off timer has not expired, the alarm is cleared in block 624 as it is deemed to have been a transient interruption on the link. Then the process is returned to block 602 to await the next alarm.
Once restoration process has begun in block 622, a determination is made on whether other links are in alarm in block 626. If there are, then these alarms are detected in block 602. If they are not, then the process awaits the expiration of the preactivation timer in block 628. If it has expired, a determination is again made on whether there are other links in the logical span which are in alarm in block 630. If there are, the alt-routes are held and not released in block 632 for restoring the traffic of those other failed links. Thereafter, before restoration process for those other failed links is to take place, the process returns to block 620 to determine whether the hold off timer has expired.
If there are no other links in alarm, as determined in block 630, then all unused alt-routes or spare links are released in block 634. Thereafter, the process is routed to block 636 for a determination of whether the sender time-out has expired. If it has not, then a determination is made on whether or not there is a forced early time-out, such as by the operator of the system, in block 638. If there is no a forced early time-out, the process returns to block 636 to await the expiration of the sender time-out. If there is, the process would end. Similarly, once the sender time-out expires, the process ends.
Inasmuch as the present invention is subject to many variations, modifications and changes in detail, it is intended that all matter described throughout this specification and shown in the accompanying drawings be interpreted as illustrative only and not in a limiting sense. Accordingly, it is intended that the invention be limited only by the spirit and scope of appended claims. | |
It’s all so neat there, so nice and tidy, that even the sprayers are afraid of their mothers and apologize ironically. I am talking about the region where four countries and their languages come together, and the mountains meet the sea. Wait a minute – the sea? Yes, the people living around Lake Constance call it the „Swabian Sea“. On stormy days, the crystal clear, seemingly endless blue surface turns into huge waves, and desperately blinking orange lights call the sailing boats to the harbors.
But when I visited my friends in Meersburg (literally castle at the ocean) last weekend, the lake looked like a mirror. The water reflected the white mountain summits. While the Tramuntana is already in its summer gear, it has been snowing in the Alps just recently. On a sunny spring day like this the contrasting white and green under a blue sky is just estupendo.
On the northern shore where the slopes face the southern sun my friend grows great white wines. Some of them, as the vineyards themselves, carry funny names like Meersburger Jungfernstieg (virgins’ steep path) and Meersburger Bengel (rascal) – inspired by the frivolous goings-on between the grapevines. | https://www.estilopalma.com/2014/05/street-art-4-meersburg/ |
Welcome to ICT Classes 6, 7, 8. Do not do. Due to the situation, the Ministry of Education of the Government of Bangladesh has decided that the students will not be tested this year. That is why the government has published the ICT Assignment Syllabus on October 28, 2020, for the sixth to ninth classes of high schools. Today we have recorded here the syllabus and solution of ICT for the 6th 7th 8th class.
High School ICT Assignment
ICT is a compulsory subject for high school students. School authorities have distributed the ICT syllabus. If you have not yet collected Assessment City, you can quickly download and collect it from my site. Attached here is the assessment with solutions.
ICT Assignment 2020 2nd Week
According to the decision of the government, the annual examination will not be taken this year. That is why the Department of Secondary Higher Secondary has released the ICT assessment of DS HP 6 7 and 8 classes. We’ve beautifully linked destiny here and please follow the article and get new ideas.
ICT Assignment for Class 6 (2020)
Are you a student for class 6? Then you need to take the assignment syllabus and make a solution for 2 weeks. We have to add to our website and see in the below content
ICT Assignment Solution Class 6 PDF
ICT Assignment for Class 7 (2020)
Like other classes, the ICT assignment of class seven has to be submitted to the school. Students must submit assignments to the school within that time. We have attached the assignment of Class Seven here. You can view Seven’s assignments in class from here.
ICT Assignment Solution Class 7 PDF
ICT Assignment for Class 8 (2020)
Due to the situation, the government has decided not to hold the JSC examination this time. That is why the government has published an assignment syllabus instead of the annual examination and the students in their assigned school.
ICT Assignment Solution Class 8 PDF
How to Write A ICT Assignment for all classes?
University students are allowed to write assignments from the East. But this is the first time in history that the Ministry of Education has allowed high school students to view assignments. But since students are small in high school they do not know how to write assignments. Today we have highlighted the method of writing assignments for students here.
Create a cover: Each student needs to create a cover where they will list all the content pages with the table.
Answer the questions: Each student has to write the correct answers to the questions.
Special Note: Each student must use size paper to write the assignment and they must use the first pages for writing.
ICT Assignment Answer 6,7 & 8 class
We know students are looking for solutions to your questions. Questions have been asked from your textbook but you will not get answers from the textbook. That’s why the teachers in my Sparta have found the right solution to your questions and here is the answer sheet. You can get the answers from our website. | https://latestinfo24.com/ict-assignment-for-class-6-7-8-syllabus-solution/ |
In a previous post I explained pinching out dahlias restricting plants to no more than five stems.
Too many stems diverts the plants energy into doing too much.
The same happens once blooming gets underway in earnest. The first blooms arrive atop strong sturdy stems, marvellous!
Then weeks go by and your stems seem to become progressively weaker, snapping under the strain??
What’s happening is the plant in its hurry to complete its life cycle is producing as many flowers as it can.
The heat we have been experiencing means a problem typical in Autumn is happening from the ‘get go’!
Here you can see a Karma Chocolate Dahlia with the main flower bud and then two smaller buds.
Left unchecked, all 3 buds will open.
The lower flowers won’t have stems long enough to use and the strain on the plant will reduce the quality of prime flower.
It makes sense to pinch these flowers out, leaving the main bud to go on and produce a magnificent single flower! | https://swancottageflowers.co.uk/2018/07/25/disbudding-dahlias/ |
Lena does not allow clocks in her house and tells time using an hourglass. But why?
UpStage Theatre will uncover the mystery when it opens Robert Alexander's drama "The Hourglass" at 7 p.m. Oct. 4 in its theater at 1713 Wooddale Blvd. Performances are also scheduled at 7 p.m. Oct. 5 and 3 p.m. Oct. 6.
The play, directed by Ava Brewster-Turner, tells the story of Lena Fletcher, who is bitter and bound to her wheelchair, and her three adult children.
Set in a suburb of Chicago, Lena’s youngest daughter, Mary, has placed her life on hold to care for her mother, while her brother Cliff and sister Dora have moved away. They encourage Mary to do the same.
Meanwhile, the mystery of the hourglass unfolds.
“It’s not nice to let time stand still,” she says, but her children are curious to learn the real reason behind her strange behavior. | |
Saturday, Oct. 1.
“Our state is in dire need of programs that can
offer ex-offenders a full continuum of integrated care that will improve their
functioning and outcomes when they return to their communities,” Commissioner
Marshall Fisher said. “Therefore, when the Department of Mental Health
approached me about supporting its efforts to get this grant, I didn’t
hesitate.”
Fisher said the grant could not have come at a
better time considering the number of incarcerated offenders with mental health
and addiction disorders. There are 3,194 inmates
receiving ongoing mental health treatment and about 15,000 have self-reported
abusing alcohol and drugs.
“We believe individuals with co-occurring mental illness and
substance use disorders represent a group of people who have been
under-identified and may have had difficulties accessing the services they
need,” DMH Executive Director Diana Mikula said. “The Mississippi Second Chance
Act Reentry Program will work to identify these needs and get people the
services that can help them begin their recovery process.”
The grant allows the two departments to do
several things, including improve identification of inmates with co-occurring
substance use and mental health disorders, provide training to staff, integrate
individualized treatment plans and track participant outcomes.
The departments will use mental health assessments to
determine individuals’ needs and collaborate to develop re-entry plans,
including pre- and post-release treatment. Those treatment services will
include cognitive-behavioral therapy, crisis intervention, and recovery support
services such as housing, vocational, and educational services.
As the program begins, it will focus on non-violent
offenders returning to Hinds County. Current plans are to serve 90 individuals
during the three-year pilot program in order to develop a program model that
can be replicated statewide with the receipt of additional federal grant
funding. Unlike similar re-entry models, this program will require people under
community supervision to participate in a minimum number of intensive
outpatient therapeutic hours, based on their individual recidivism risk level.
“Through our collaboration with the Department of
Corrections, we know there are a number of eligible individuals right here in
Hinds County,” Mikula said. “We will be collaborating and using existing
resources in the state mental health system to get these Mississippians the
treatment and support services they need. I know that with all of us working
together, we can create a better tomorrow for the people of our state.”
Published: | https://www.mdoc.ms.gov/Pages/Departments-of-Corrections-and-Mental-Health-Partner-to-Help-Reduce-Recidivism-.aspx |
Can Dogs Eat Raisin Toast?
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Can Dogs Eat Grapes?
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Can Dogs Eat Lychee?
While many fruits and vegetables are safe to eat in moderation by both humans and dogs, there are some fruits you should not feed your dog... | https://can-dogs-eat.au/category/fruit/ |
This shelf facilitates individual access to magnums and allows you to display 7 bottles on one single row. Our patented "Main du Sommelier" system has a body in two materials combining a rigid structure to hold the bottle and a flexible material which adapts to the shape of the bottle and protects it from vibration.
This shelf model contains 7 main du sommelier models with a reworked aesthetic finish and more user-friendly design with regard to positioning the bottle.
It was by working with sommeliers that the idea of developing this patented bottle support came to us. So it seemed logical to name this innovative product after them.
This protective structure gently slides along the guidelines of the shelf in order to adapt the shape of each bottle. | https://en.eurocave.com/accessories/218-sliding-shelf-for-7-magnum-bottles.html |
If you drive a truck, you need to know how to use the gears on a truck to get the best results. These gears are important for the vehicle’s fuel efficiency, and a truck’s manual transmission has a specified range of gears to meet the needs of different situations. Most trucks have a range of about 1000-2500 rpm, and more gears will maximize the efficiency of the engine. Generally, a driver will shift to the fittest gear all the time, depending on the road conditions. High-speed gears save fuel, and low-speed gears give more power when the truck is full.
The average driver won’t use all of the gears on a truck, and will instead skip some of them to save fuel. A truck with 12 gears, for example, wouldn’t start in first gear unless it was heavily loaded. On the other hand, a driver with a 12-speed transmission would start in second or third gear if the truck was empty. The same applies to a driver with a six-speed transmission: they would start in second or third gear if the truck were empty, and a 12-speed transmission would start in third or fourth gear if the truck was pulling a load.
Related Questions / Contents
How Do 18 Gear Trucks Work?
How Do Eighteen Gear Trucks Work? Here are a few tips. First, you should know how to downshift. When you are going downshifting, you should release the clutch slowly to avoid stalling. Also, the clutch is depressed when you are changing gears. This will prevent your brakes from overheating and failing. Once you’ve learned how to downshift, you’ll be able to drive your truck smoothly.
Eighteen-speed transmissions give your truck an extra power level than a traditional truck. It means more energy to pull a heavy load. This feature is very advantageous, since the big engines of semis have a limited power band, so drivers need to shift gears often to keep the engine operating efficiently. Fortunately, this system requires little to no maintenance. Just as with a bicycle, you need to practice shifting to make it easier.
A truck’s first set of gears is called the range switch. The low range is low (Lo) through four or five. The high range is high (no more than 25mph). An eighteen-gear truck can split its gears into a low and high range. An 18-gear truck is an ideal logging truck or mountain driving vehicle. A 13-gear truck, on the other hand, is designed for smoother mountain driving.
Can Trucks Have 18 Gears?
Can Trucks Have Eighteen Gears? The answer to that question depends on what you’re driving. Obviously, a semi-truck will have more gears than an average car. Some have just two, while others have as many as 18. But what happens when you want to change gears in a hurry? Here are some tips. Using the proper gears will make your drive smoother and more enjoyable.
Many truck designs have a number of gears for optimal efficiency. The more gears you have, the less fuel you’ll burn. While three or four gears may be sufficient for most drivers, five or six are too restrictive. And as you know, an 18-speed transmission can make it easier to shift at a slower speed. And if you’re in an environment where you need to go fast, 18 gears can give you an edge.
Another great advantage of an 18-speed transmission is its versatility. This kind of transmission is easy to use, but it requires practice to become comfortable with it. However, you might find that the additional gears are more than enough, and 18 gears are a great thing to have! They also help a truck’s engine run at the proper RPM. This will save fuel and extend its life. As long as you’re careful and pay attention to the manual, an 18-speed transmission will give you the best of both worlds.
What Gear Should I Drive My Truck In?
A truck’s engine is primarily made to run in one of three gears, with the lowest gear being the lowest and the highest gear being the highest. Different types of terrain require different gearing. While driving downhill, drivers should use low gear, as this will help them maintain a slow speed. Low gearing protects brakes, which can become damaged if they are used for extended periods of time.
You should check the speedometer to determine when to change gears. You should drive in the lowest gear when on the road, while higher gearing is better for highways. Second gearing is also preferred when making turns. Third gearing is used for increasing speed and can achieve 30mph. If you need to drive on steep inclines, you should use fourth gear, because it will help you save fuel. However, you shouldn’t drive in this gear on a regular basis.
How Do You Know When to Shift Gears?
Depending on the type of transmission, there are several different ways to shift gears. If you have a manual transmission, start in low gear, then shift up to high gear. To do this, you must use the selector on the shift knob. Switching from one gear to the next during the shift is not a good idea. You can damage the transmission if you do it while it’s running.
The most common way to shift gears on a truck is to press the accelerator pedal and then slowly release the clutch. As you shift up, the truck’s speed will increase, and it’s best to stay in a higher gear while going downhill. Shifting gears is similar to riding a bicycle. It takes practice to become a pro. Always check the RPM on the tachometer, and shift only when it is necessary.
You can use your truck’s engine as a brake by driving in lower gears on long downhill sections. The lower gears require less effort on the brakes, which prevents brake fade. Your engine should sound racing, but the rev counter should not be in red. If you feel the rev counter is climbing to its highest value, shift down. If it’s already too high, it’s time to shift.
How Do You Know When to Switch Gears?
If you’re unfamiliar with shifting, you may wonder, “How do I know when to switch gears on a truck?” You should start by remembering the rule of thumb for a smooth shift. In a low gear, you’ll be moving at one mile per hour. Release the clutch and shift to high gear. Now, you can keep rolling in the second gear while adjusting the clutch.
Changing gears in a truck involves a few factors, including engine speed and terrain. Going uphill will cause your truck’s engine to increase speed, while going downhill will slow down. While the engine speed remains the same, you need to match the road speed with the shifting speed. This process isn’t always intuitive, so practice shifting gears in different situations and pay close attention to the tachometer.
The tachometer will indicate engine RPMs. Shifting to higher gears will reduce fuel consumption. The actual RPMs will vary from vehicle to vehicle, but you should keep in mind that each gear shift is between fifty and one hundred RPMs higher than the previous one. It’s also important to remember that a hill is a great way to test your shift skills, because the vehicle may roll backwards if it’s in the wrong gear. If you’re not careful, it’ll damage your drive train.
How Do You Drive a 10 Speed Truck?
If you want to drive a 10 speed truck, then you must first learn how to shift gears. Although this may seem like a complicated procedure, there are some basic rules to follow. Generally, downshifting is not always necessary. If you are descending a hill, for example, you should shift down to the lowest gear. This will help you match the speed of the truck with the speed of the engine.
As with any big vehicle, you should always be aware of the RPMs of your truck when shifting gears. If you find that you are over three thousand RPMs, switch to the next gear. Not only will this ensure you get the highest gas mileage, but you will also prevent damage to your transmission. To properly shift gears, you should use your middle finger to clutch the shift. This is the best way to shift gears.
Downshifting a 10 speed dump truck requires knowledge of the gears and the transmission. This is because the transmission, rear end gear ratio, and tire size all affect the speed of the engine. By knowing these factors, you will be able to smoothly shift the truck gears and ensure the best possible speed. It is also important to learn how to listen to revs when downshifting the transmission. The right gear will give you the best acceleration and reduce the risk of wheel spin.
How Do You Shift a 10 Speed Truck?
The most common question a truck driver has is, “How do I shift a 10 speed truck?” The answer is actually quite simple: you push the clutch pedal and wait for the input shaft to match. Press and release the clutch pedal when the input shaft matches the gear. This will result in a smooth gear change. However, some trucks are difficult to shift and you may need to use multiple techniques. To avoid the dangers of gear grinding, learn the proper technique before driving your truck.
The gear shifter of a 10 speed truck is a bit more complicated than the one found in a typical car, but still has some similarities. There is a splitter located at the base of the shift handle, which allows you to select the low and high ranges. Low range gears contain gears one through five, while high range gears feature gears six through 10. When the splitter is pressed in the neutral position, the transmission is in sync with the selector.
Learn More Here: | https://www.prettymotors.com/how-do-you-use-the-gears-on-a-truck/ |
A classic visualization of a Fire Watch is a person in a Forest Service fire lookout tower. Fire towers were widely used in the early 1900’s to look for smoke and then report fires from mountain tops in forested areas.
A few of the U.S. Forest service fire lookout towers are still in use.
Today the safety profession uses the term Fire Watch to describe a designated person or team of people actively on the lookout for a fire, often on a construction job site. Many different industries utilize a Fire Watch in their day to day work activities and assessing fire hazards in a Job Safety Analysis (JSA) or Job Hazard Analysis (JHA) is quite common. In certain industries, Fire Watch is a regulatory requirement with specific defined rules that have been defined in the regulations.
Assessing Fire Watch hazards during the preparation of a Job Hazards Analysis, and implementing a Fire Watch when appropriate, is routine in the construction industry, in the U.S. forest Service (USFS), the National Park Service (NPS) and in some cases the forestry industry still uses Fire Watch and lookout towers during periods of extreme fire weather when the risk of fires is high, and in the fire alarm and building sprinkler industry. This last category of building sprinkler systems, is one of the industries where Fire Watch may be mandatory and enforced by regulations.
Understanding Fire Watch is especially important to people who work on, test, and maintain fire sprinkler systems. NFPA 101 Life Safety Code requires that a Fire Watch be instituted anytime a Sprinkler System, Fire Alarm or other Suppression System is hindered or out of service.
During sprinkler system maintenance it is required by law to have the Fire Watch personnel walking around the building and checking each floor for presence of a fire. A best practice is to have each Fire Watch person maintain a log that includes the location inspected along with the time of the visit.
In the construction industry it is a best practice to post a Fire Watch anytime a task involves hot work. Hot work can include welding, grinding, cutting, or other temporary operations where heat is used or equipment / operation may generate sparks. In these cases, Fire Watch personnel is stationed near the work area so they have a clear field of view of the worker and surrounding area. The Fire Watch should have a fire extinguisher of the appropriate size and class for the specific job task and physical location. The Fire Watch should be trained in the operation and use of the specific type of fire extinguisher being utilized as part of the Fire Watch. Preplanning and identification of the hazards and selection of the appropriate safety equipment during the Job Safety Analysis is critical to achieving a positive outcome during these types of operations. 29 CFR § 1915.504 contains details for Fire Watch during work, including training requirements, duties of the employees, equipment employees must be given, and personal protective equipment (PPE) that must be made available and worn.
Sometimes hot work is defined as preforming work on equipment that is energized or pressurized. Whenever possible, this type of hot work should be avoided, but there are times when the equipment or line can not be de-energized or de-pressurized. A Fire Watch may be appropriate for this kind of hot work and should be risk assessed when preparing the Job Hazard Analysis.
When hot work is conducted on ships, there are additional training requirements and certifications for Fire Watch personal that are defined in 29 CFR § 1915.504 and by the Occupational Safety & Health Administration (OSHA and OSHA).
Fire Watch is an important safety tool that should be evaluated during the preparation of the Job Safety Analysis or Job Hazard Analysis as you assess the hazards of your job or tasks.
JSABuilder.com is a fantastic on-line job safety analysis app to assist in preparing your JSA. Set up a free trial account today and follow us on Twitter @JSABuilder, where we Tweet about Health and Safety, provide Safety tips, and updates on current Health and Safety topics. | https://www.jsabuilder.com/resources/fire-watch.php |
Therefore triangle inequality property confirms formation of a triangle if the lengths of the sides are 3, 4 and 5.
It is sufficient to check whether the triangle inequality property holds on largest length, here 5. If it does, then on other lengths, it will certainly do; needs no verification.
Since triangle inequality property does not hold, therefore a triangle cannot be formed if the sides have lengths 5, 10 and 15.
0 < 7 < 6, which is not correct.
7 – 3 < 7 < 7 + 3, i.e.
4 < 7 < 10, which is right.
Between 3 and 7, it is 7 that lies between 4 and 10.
Therefore, third side should be 7.
The square of any side is less than the sum of the squares of the other two sides in an acute triangle.
If the lengths of the sides in a triangle are 4, 5 and 6, then what type of triangle is formed?
Is 42 + 52 > 62 ?
Is 16 + 25 > 36?
Therefore, sides whose lengths are 4, 5 and 6 will form an acute triangle.
Every angle in the triangle is acute.
Find whether a right triangle is formed if the sides are of lengths 9, 40 and 41?
This proves the sides 9, 40 and 41 form a right triangle.
The right angle is formed between the sides 9 and 40, or opposite the side 41.
The square of the longest side in an obtuse triangle is greater than the sum of the squares of the other two sides.
if AC is the longest side opposite the obtuse angle.
What type of triangle is formed if the lengths of its sides are 6, 8 and 11?
Therefore, the triangle contains one obtuse angle. | http://www.math-for-all-grades.com/Triangle-inequality-property.html |
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AuthorRaynor, Nick D.
KeywordTest-taking skills.
Examinations -- Study guides.
Time management -- Tests
Middle school students.
High school students.
Date Published2013-10-21
MetadataShow full item record
AbstractThis research examines the connection between the amount of time a student takes to complete a test and the score that they receive on the test. It is hypothesized that students who take longer to complete their test will actually score lower on the test than the student that finish their tests more quickly. Furthermore, it is thought that female students will have stronger correlations between score and time than will male students. The main discovery that was made is that there was significance in the data regarding strictly time and score. It was shown that students who use less time to take their tests generally scored better than those who took longer to complete the test. However, there was no statistical significance found when breaking down the data into specific categories based on gender, grade level, age, or class. | https://soar.suny.edu/handle/20.500.12648/190 |
IEC 60601-1-9 is based on practical experiences from the industry. The objective of the standard is the improvement of environmental impact, taking into account all stages of a product's life cycle, from initial specification to end-of-life management. It does not provide a simple list of eco-friendly design specifications, but assessment checks based on verifying procedures are in place and evidence is documented to illustrate that environmentally friendly principles were included in the design and development process. The end goal is to minimize significant impact on the environment.
The core requirements of IEC 60601-1-9 can be summed up as "identification," "instruction," and "end-of-life management." In order to demonstrate compliance to IEC 60601-1-9, the following must be submitted: design documents and process descriptions, packaging information, documents on minimizing environmental impact and information related to end-of-life management. Assessments can be done independently from the evaluations of the other parts of the IEC 60601 series. A manufacturer can also use risk analysis to help decide on environmental improvement targets, although this is not required.
The benefits of eco-conscious design in medical electrical equipment can be great, fulfilling requirements or simply indicating a product fills an eco-friendly demand. Using IEC 60601-1-9 as a guide can help support sustainability claims and allow manufacturers to bring greener medical devices to the market. For more insights on how to use IEC 60601-1-9 in designing and developing eco-friendly medical devices, download a copy of our free white paper.
Michael Brousseau is the U.S. Technical Lead for Intertek's Medical business line. In nearly 20 years with Intertek he has worked with electrical manufacturers across a wide range of industries – including medical, IT, industrial, lighting, and more – to meet regulatory, industry, and market requirements around the world.
Tags: 2016 | Medical Devices | Michael Brousseau
Michael Brousseau, | http://www.intertek.com/blog/2016-10-04-med-device/ |
A Guide To Neurogenic Etiologies Of Heel Pain
While heel pain is the most common condition podiatrists see in practice, heel pain can often be complex and occasionally difficult to treat.1 In recent years, we have seen the introduction of new treatments as logical conservative preludes to fasciotomy, including extracorporeal shockwave therapy, injection of the plantar fascia with autologous growth factors and coblation therapy.2 Clinicians are able to employ some of these modalities, such as autologous growth factors, due to a better understanding of the true histological and physiological etiologic mechanism that occurs at the cellular level.3-5 The basic medical science research at the cellular level of tendonopathy has been a critical catalyst in changing our understanding of heel pain etiology. Lemont, et. al., reinforced this point when they observed no histological presence of inflammatory mediators in 50 specimens (100 percent) of plantar fascia that had been resected for the treatment of heel pain.6 These findings must propel us toward a change in our treatment paradigms. Equally important, if not more so, are similar findings and clinical experience in treating other analogous musculoskeletal conditions such as lateral epicondylitis or “tennis elbow.”7,8 While neurogenic etiologies of heel pain comprise the focus of this article, the prevalence of multiple etiology heel pain in clinical practice clearly indicates that our basic understanding of plantar fasciitis is changing and may in fact have been significantly erroneous all this time. Furthermore, the presence of multiple etiology refutes the mistaken tendency to categorize all heel pain as plantar fasciitis when the more correct terminology is plantar fasciosis. The previous catch-all categorization has led to misdiagnosis and less than desirable outcomes in some patients.
Understanding The Array Of Potential Etiologies In Heel Pain
Clinicians often fail to recognize that heel pain can commonly have an isolated neurogenic etiology or it can present concomitantly with other etiological mechanisms.9-11 There is frequently an interplay between the presence of plantar fasciosis and nerve entrapment. Fredericson, et. al., documented via MRI imaging that chronic inflammation of the proximal portion of the plantar fascia can predispose the lateral plantar nerve to entrapment.12 Heel pain etiologies can range from infracalcaneal fat pad atrophy to Reiter’s syndrome (see “A Guide To Potential Heel Pain Etiologies” below).1 More than 2 million patients will be diagnosed with heel pain in a given year, according to estimates from extrapolated data from the American Podiatric Medical Association.13 While the effectiveness of conservative management of plantar fasciitis (fasciosis) is well established, there are no specific studies that document the efficacy of conservative care for managing heel pain when it has a sole neurogenic etiology.1 Given the aforementioned numbers, even for a condition that is successfully diagnosed and treated conservatively more than 90 percent of the time, this still presents approximately 200,000 cases that are of neurogenic or mixed etiology, which may require more definitive and aggressive treatment. Sadly, many cases that fit this description are erroneously attributed to a “recalcitrant” plantar fasciitis status.
Emphasizing The Evolution Of Diagnostic Testing
Differential diagnosis of neurogenic etiologies of heel pain must include tarsal tunnel syndrome, lateral plantar nerve entrapment, medial calcaneal nerve entrapment and what has been described as an entrapment of the first branch of the lateral plantar nerve, which is commonly referred to as Baxter’s nerve. Diabetic peripheral neuropathy can predispose a patient to any of these nerve entrapments with the subsequent presentation of isolated heel pain. Frequently, the diagnosis of an isolated neurogenic cause of heel pain can be problematic and difficult. Technology such as diagnostic ultrasound and MRI can eliminate or substantiate the clinical diagnosis of plantar fasciitis (fasciosis).14 When it comes to determining neurogenic etiologies for the painful heel, one of the biggest problems for clinicians in the past was the lack of anything but electrodiagnostic studies to confirm or substantiate the clinical diagnosis of lower extremity peripheral nerve entrapment. Any experienced clinician knows the frustration of being confronted with overwhelming clinical evidence supporting a diagnosis of a nerve entrapment of the tarsal tunnel only to be informed that the electrodiagnostic studies are “normal.” It is well known that nerve conduction velocity studies are unreliable in the diagnosis of peripheral nerve entrapments in the lower extremity. In my experience, one may have approximately a 50 percent chance of getting a false negative finding in the face of an overwhelming clinical presentation. With the advent of neurosensory testing with the Pressure Specified Sensory Device (PSSD®, Sensory Management Services, LLC), the clinician can now expect a higher level of reliability in confirming the original clinical diagnosis. In a prospective blinded study, Weber demonstrated the sensitivity and specificity of the PSSD compared to standard neurological testing in patients with carpal tunnel syndrome.15 Keep in mind that the median nerve is the single best nerve in terms of reliability for sensitivity and specificity of electrodiagnostic study. Some have advocated making therapeutic decisions for carpal tunnel syndrome in patients with diabetic peripheral neuropathy without the use of electrodiagnostic studies as these diagnostic modalities cannot distinguish those with the syndrome.16 No nerve in the lower extremity even comes close to the median nerve when it comes to the reliability of electrodiagnostic testing. Not only does neurosensory testing with the PSSD modality give the clinician a higher degree of sensitivity, it also allows testing of nerves such as the medial calcaneal nerve which one cannot test with standard electrodiagnostic studies. While the algorithm (see “A Diagnostic Algorithm For Complex, Recalcitrant Heel Pain” below) and heel pain scoring questionnaire (see “How To Use The Heel Pain Scoring System” below) have not been prospectively validated on a large population of patients, these diagnostic tools can give the clinician a good frame of reference for an orderly and stepwise workup of the patient with heel pain. It is critical to take a careful and detailed history in order to determine the true etiology of heel pain. When using the questionnaire during the initial presentation, one can quickly assess the patient. Then assign a score to the patient and institute an appropriate algorithm based upon that score. The scoring is clinical and historical, and the questionnaire includes six patient history questions and five points of clinical evaluation. Diagnostic red flags should include patients who experience pain even at night when they are not on the foot, patients who have increased pain with an orthotic device, and those who say the pain becomes worse the longer they stay on their feet or the more they walk. A family history of diabetes should increase the clinician’s awareness of the possibility of nerve entrapment, even if patients themselves claim not to have diabetes. In many cases, one can further confirm the diagnosis of a neurogenic etiology via the process of elimination with highly reliable modalities such as musculoskeletal sonography. While a normal sonogram of the plantar fascia can eliminate plantar fasciosis as a potential cause, positive sonographic findings of plantar fasciosis cannot rule out a concomitant neural etiology. However, it is very helpful in managing the longstanding patient who has been misdiagnosed and unsuccessfully treated. It can also eliminate fasciosis as a component or contributing factor to the patient’s heel pain. Also be aware when patients present with previously treatedplantar fasciosis which has improved but their heel is still painful after conservative treatment. If they continue to have heel pain, it may be due to a coexistent nerve entrapment where the fasciosis component has been successfully treated. Often, when clinicians question these patients closely, they relate that the nature or type of heel pain changed during the course of treatment. Busy clinicians often miss this subtle difference.
What The Literature Reveals About Nerve Entrapment
Perhaps the most common neurogenic etiology of heel pain is erroneously attributed to Baxter’s nerve. Baxter reported decompression of an entrapment of the first branch of the lateral plantar nerve (which is sometimes referred to as the motor nerve) to the abductor digiti quinti.17 In 1981, Przylucki described this nerve as a potential cause of heel pain years before Baxter’s article.18 Many anatomical texts have also illustrated this nerve. Some of these texts date back to the early part of the 20th century to the point when Sobotta documented its existence.19 However, Roegholt was the first author to suggest that entrapment of this nerve branch could be a cause of heel pain.20 Given the high degree of variability of the neuroanatomy of the medial aspect of the heel, the first branch of the lateral plantar nerve can be a superficial medial calcaneal nerve or a deeper nerve which would be more infracalcaneal as Przylucki described.18 In their true anatomical dissection studies, Louisia and Masquelet identified this nerve in all cadavers.21 They also suggested that proper nomenclature would be the “inferior calcaneal nerve” (ICN). Other names in the literature for this branch include the first branch of the lateral plantar nerve, motor branch to the abductor hallucis muscle, calcaneal branch and Cruvelhier’s medial calcaneal nerve branch. In addition to the nomenclature being wrong for this potential nerve entrapment, there is skepticism if this nerve is really such a prominent neurogenic factor in heel pain. It may be that the medial calcaneal nerve(s) is more commonly a contributor to heel pain. In an important study of 97 heels, Rose, et. al., found a 72 percent incidence of a documented sensory impairment of either the medial calcaneal nerve or the medial calcaneal nerve in combination with the medial plantar nerve.11 This study indicates the prevalence of the medial calcaneal nerve as a neurogenic etiology in heel pain. They also argued that diagnosing medial calcaneal entrapment is difficult. However, with local anesthetic infiltration and a careful injection technique, it is fairly simple to determine whether the medial calcaneal nerve is the sole etiology of heel pain. The medial calcaneal nerve(s) is very superficial and one can easily block them with lidocaine. If the practitioner is careful not to infiltrate the anesthetic deeper than the superficial subdermal layer on the medial aspect of the heel and the patient’s heel pain completely resolves, then this would confirm that the cause of the heel pain is entrapment of the medial calcaneal nerve and not entrapment of the first branch of the inferior calcaneal nerve. Further clinical support for this diagnostic injection would include the lack of impaired sensation along the course of the lateral plantar nerve on the plantar aspect of the foot. This would indicate that the local anesthetic agent did not cause a nerve block of the lateral plantar nerve. It would also mean that its branch, referred to erroneously as Baxter’s nerve or, more properly, the inferior calcaneal nerve, was also not blocked. Additionally, if there is a documented loss of two-point discrimination on the medial skin of the heel, which is innervated by the medial calcaneal nerve(s), then one may confirm entrapment of the medial calcaneal nerve via neurosensory testing. Remember that the first branch of the inferior calcaneal nerve does not have a sensory component to the skin.
Other Key Considerations
Tarsal tunnel syndrome can be subtle and difficult to diagnose, and can have heel pain as its sole component. In a recent study of a series of 25 heels, Oztuna, et. al., found that electrodiagnostic studies documented abnormal sensory nerve conduction of either the lateral plantar nerve or medial plantar nerve in 88 percent of patients with heel pain.22 In 64 percent (14 heels) of the heels, there was an isolated sensory conduction of the lateral plantar nerve.22 The researchers did identify tarsal tunnel in four patients. Interestingly, they used any form of neuropathy, including diabetic peripheral neuropathy, as an exclusion criterion for their controlled study. Clinically, the presence of a provocation sign and a Tinel’s sign are strong indications of entrapment at the level of the tarsal tunnel. While it is very rare, the lateral calcaneal branch coming off the sural nerve is another nerve entrapment that can cause heel pain. There can be a variation in the neuroanatomy where the lateral calcaneal nerve comes all the way under the heel within the infracalcaneal fat pad and provides innervation to the medial aspect of the heel. One can verify this with an anesthetic blockade of only the sural nerve at the lateral aspect of the ankle with subsequent resolution of the patient’s pain. Finally, iatrogenic entrapment from previous heel surgery is common with any medial heel incision. It is nearly impossible with a medial DuVries type incision to retract and protect the branches of the medial calcaneal nerve during open heel surgery. Dellon’s study of the variation of patterns of the medial calcaneal nerve(s) illustrates perfectly why so many medial heel incisions can become problematic for the patient.10,23
In Summary
When ordinary heel pain attributed to plantar fasciosis does not respond to conservative care or changes in nature during the conservative or surgical treatment phase, clinicians should start to think about nerve entrapment as being the culprit. By using a stepwise approach in the diagnosis of chronic, complex heel pain, the practitioner should be able to identify and subsequently treat the patient’s heel pain etiology appropriately. It cannot be stressed enough that high quality ultrasonography is a technology that should see more use in the treatment of heel pain as there are many “cases” of plantar fasciitis (fasciosis) that can be attributed to nerve entrapments. The clinical experience of pain exacerbation from wearing custom orthoses should also arouse suspicion of nerve entrapment for the practitioner as opposed to writing a new orthotic prescription. Dr. Barrett is an Associate Professor within the Arizona Podiatric Medicine Program at the Midwestern University College of Health Sciences. He is a Fellow of the American College of Foot and Ankle Surgeons. Dr. Barrett is a shareholder in the Baltimore-based Sensory Management Services, LLC, which manufactures and sells the Pressure Specified Sensory Device (PSSD).
References:
1. Barrett SJ, O’Malley R. Plantar fasciitis and other causes of heel pain. Am Fam Physician 59(8):2200-6, 1999.
2. Barrett SL, Erredge SE. Growth Factors for Chronic Plantar Fasciitis. Podiatry Today 17(11):37-42, 2004.
3. Rawool NM, Nazarian LN. Ultrasound of the ankle and foot. Semin Ultrasound CT MR 21(3):275-84, 2000.
4. Almekinders LC. Tendinitis and other chronic tendinopathies. J Am Acad Orthop Surg 6(3):157-64, 1998.
5. Almekinders LC, Temple JD. Etiology, diagnosis, and treatment of tendonitis: an analysis of the literature. Med Sci Sports Exerc 30(8):1183-90, 1998.
6. Lemont H, Ammirati KM, Usen N. Plantar fasciitis: a degenerative process (fasciosis) without inflammation. J Am Podiatr Med Assoc 93(3):234-7, 2003.
7. Edwards SG, Calandruccio JH. Autologous blood injections for refractory lateral epicondylitis. J Hand Surg [Am] 28(2):272-8, 2003.
8. Maffulli N, Wong J, Almekinders LC. Types and epidemiology of tendinopathy. Clin Sports Med 22(4):675-92, 2003.
9. Dellon AL. Deciding when heel pain is of neural origin. J Foot Ankle Surg 40(5):341-5, 2001.
10. Kim J, Dellon AL. Neuromas of the calcaneal nerves. Foot Ankle Int, 22(11):890-4, 2001.
11. Rose JD, Malay DS, Sorrento DL. Neurosensory testing of the medial calcaneal and medial plantar nerves in patients with plantar heel pain. J Foot Ankle Surg 42(4):173-7, 2003.
12. Fredericson M, et al. Lateral plantar nerve entrapment in a competitive gymnast. Clin J Sport Med 11(2):111-4, 2001.
13. Association, A.P.M., APMA Survey Suggests Heel Pain Epidemic. APMA web site: www.apma.org, 2001.
14. Kane D, et al. The role of ultrasonography in the diagnosis and management of idiopathic plantar fasciitis. Rheumatology (Oxford) 40(9):1002-8, 2001.
15. Weber RA, et al. A prospective blinded evaluation of nerve conduction velocity versus Pressure-Specified Sensory Testing in carpal tunnel syndrome. Ann Plast Surg 45(3):252-7, 2000.
16. Perkins BA, Olaleye D, Bril V, Carpal tunnel syndrome in patients with diabetic polyneuropathy. Diabetes Care 25(3):565-9, 2002.
17. Baxter DE, Pfeffer GB. Treatment of chronic heel pain by surgical release of the first branch of the lateral plantar nerve. Clin Orthop Relat Res, (279):229-36, 1992.
18. Przylucki H, Jones CL. Entrapment neuropathy of muscle branch of lateral plantar nerve: a cause of heel pain. J Am Podiatry Assoc 71(3):119-24, 1981.
19. Sobotta/Figge, Atlas of Human Anatomy. 1977.
20. Roegholt M. Een nervus calcaneus inferior als overbrenger, Van de pijn bij calcaneodynie of calcaneuss poor en de daaruit volgen therapie. Ned Tijdshr Geneeskd, 84:1898-1902, 1940.
21. Louisia S, Masquelet AC. The medial and inferior calcaneal nerves: an anatomic study. Surg Radiol Anat 21(3):169-73, 1999.
22. Oztuna V, et al., Nerve entrapment in painful heel syndrome. Foot Ankle Int 23(3):208-11, 2002.
23. Dellon AL, Kim J, Spaulding CM. Variations in the origin of the medial calcaneal nerve. J Am Podiatr Med Assoc 92(2):97-101, 2002. | https://www.podiatrytoday.com/article/4735 |
Otter (Lutra lutra)
Otter were once widespread in the Wye, but populations declined sharply during the 1960s and 1970s due to pollution and persistent pesticides, exacerbated by hunting and habitat loss. At present, the majority of the otter population in Great Britain occurs in Scotland and Wales. The otter is still scarce over much of England, where the highest concentrations are in the south-west. However, recent surveys suggest that the otter population is recovering well.
The Wye holds one of the densest and most well-established otter populations in Britain. The river has bank-side vegetation cover, abundant food supply, clean water and undisturbed areas of dense scrub suitable for breeding, making it particularly favourable as otter habitat. The Wye’s population remained even during the lowest point of the UK decline, confirming that the site is particularly favourable for this species and the population likely to be highly stable.
The River Usk is also an important site for otters. They are believed to be using most parts of the main river from Newport upstream and in recent years signs of otters have increased. The upper Usk may have acted as a ‘refuge’ during the decline of the 1950s, and had subsequently acted as a ‘source’ population for recolonisation of south-east Wales.
Otters can be seen swimming or diving and searching for food. Keep an eye out whenever you come across vegetated river banks, islands, reedbeds and woodland, which can also be used for foraging, breeding and resting. Otters feed on fish, large invertebrates (e.g. crayfish) and even ducklings. Quite often a half-eaten fish seen on the banks or in the shallows is the clearest sign an otter has been in the vicinity. The decline of one its favourite food items, the European eel, is a new challenge for the species however. | http://wyeuskfoundation.org/navigation/otter.php |
An excellent opportunity to join the Innovation, Transformation and Change team of our global professional services firm client as Process Improvement & Projects Manager
The Operations & Project Management team works with the various fee-earning business units and core business services to help the business manage matters more effectively (from pricing and scoping through to evaluation) The role is also focused on identifying and delivering necessary changes to working practices and utilising technology to improve efficiency and effectiveness. The ability to drive sustainable change through facilitation, training and promoting benefits is an important part of the value of the team.
This role will give you a breadth of exposure from implementing project management and process improvement disciplines across the teams. The team adopt a consultancy approach where they focus on scoping and matter set-up to ensure the projects are approached in the best way. Underpinning their approach is a training programme to facilitate change and imbed project management behaviours. The role lends itself to a several process improvement opportunities and we work alongside their Commercial Finance, Knowledge and Innovation teams to promote continuous improvement and deliver operational efficiency projects.
Typical responsibilities will include: | https://www.lusona.co.uk/job/process-improvement-and-projects-manager-5547.aspx |
New Zealand Prime Minister Jacinda Ardern announced Tuesday that Australian and New Zealand residents will be able to travel between the two countries without having to quarantine. The trans-Tasman travel bubble will start on Sunday, April 18 at 11:59 p.m.
“This is an important step forward in our COVID response and represents an arrangement I do not believe we have seen in any other part of the world. That is, safely opening up international travel to another country while continuing to pursue a strategy of elimination and a commitment to keeping the virus out,” Arden said.
New Zealand’s Parliament unanimously approved legislation on Wednesday allowing mothers and their partners three days of paid bereavement leave after a miscarriage or stillbirth. Previously, employees were provided with paid leave in case of a stillbirth, the new bill now extends those benefits for those who lose a pregnancy at any point.
Team New Zealand have won the 36th America’s Cup, beating Luna Rossa 7-3 in the best-of-13 series with a dominant 46-second victory in race 10 off the coast of Auckland. The defender retained the Auld Mug, international sport’s oldest trophy, four years after beating Oracle Team USA 7-1 at the 2017 match in Bermuda. It was their fourth America’s Cup triumph after winning in 1995, 2000 and 2017.
Prime Minister Jacinda Ardern reported that New Zealand has purchased enough of Pfizer/BioNTech's Covid-19 vaccine to inoculate its entire population. The government has signed an advanced purchases agreement with the vaccine manufacturer for an additional 8.5 million doses. Pfizer/BioNTech's Covid-19 vaccine will be the country's primary vaccine.
Whilst the Pfizer vaccine does need to be kept at ultra-cold temperatures, this challenge is offset by only having to deal with one vaccine, rather than multiple vaccines with multiple protocols. It will simplify our vaccine roll out," Arden said.
Travel pass – a Covid-19 vaccination passport app developed by the International Air Transport Association – will be tested on Air New Zealand flights between Auckland and Sydney from April on “to streamline the health verification process to help customers know what they need to take their next international trip safely”.
Luna Rossa wrapped up a comprehensive 7-1 win over Ben Ainslie's Ineos Team UK to win the America's Cup Challenger Series in Auckland.
The Italian boat won both of Sunday's races to set up next month's contest against holders Team New Zealand for the 36th America's Cup.
In January, Luna Rossa edged the USA boat American Magic out of the Prada Cup Semi-Final.
Starting from the 1980s Italy has seriously launched the challenge to the America's Cup. On two occasions, in 1992 and 2000 it won the Challenger title, but coming out defeated on both occasions. In 2021 it re-launched the challenge again with Luna Rossa, winning the final at Prada Cup that gives away the title of Challenger 2021.
Despite being a serious challenger to the America's Cup repeatedly since 1983, this is the first time Italy
On Wednesday, Facebook announced users in Australian will no longer be able to find nor share news from neither local or international sources as a response to a proposed Australian legislation that would force platforms to pay publishers for news content.
William Easton, the managing director of Facebook Australia & New Zealand, wrote in a blog post that the "proposed law fundamentally misunderstands the relationship between our platform and publishers who use it to share news content."
“It has left us facing a stark choice: attempt to comply with a law that ignores the realities of this relationship, or stop allowing news content on our services in Australia. With a heavy heart, we are choosing the latter,” he added.
New Zealand schools across the country will be stocked with free period products from June, Prime Minister Jacinda Ardern and Associate Education Minister Jan Tinetti announced at Fairfield College in Hamilton on Thursday.
”There’s lots of barriers that shouldn’t exist for our young people,” Ardern said. “And one of the things stopping our young people from going to school is an issue called period poverty. One in 12 of our students possibly miss school because they don’t have access to period products. That’s just not right and not in a country like New Zealand.”
New Zealand Prime Minister Jacinda Ardern said that genomic sequencing showed that the recent three Covid-19 cases were the variant B117, the more potent variant first detected in the UK, resulting in an Auckland-wide lockdown.
The Ministry of Healthy announced it was investigating the Auckland cases, prioritising "close contacts and casual plus contacts to be tested so we can understand any risk in the community."
New Zealand's Prime Minister Jacinda Ardern on Sunday announced a three-day lockdown in Auckland after three unexplained cases of coronavirus were discovered.
The country had successfully stamped out community spread, after closing its international borders and implementing strict social distancing rules early on in the pandemic.
A 56-year-old woman has tested positive for Covid-19 in New Zealand, after being released from government managed isolation following two negative tests. The woman arrived in Auckland on 30 December after travelling in Spain and the Netherlands for four months.
The woman was released on 13 January and travelled around south Northland with her husband, visiting as many as 30 locations, including popular holiday spots, AirBnBs, and shops.
Political leaders across the globe, have expressed their concern and shock as Pro-Trump supporters stormed the US Capitol and condemned the violence happening on the day the US Senate was to certify the Electoral College results.
"The right of people to exercise a vote, have their voice heard and then have that decision upheld peacefully should never be undone by a mob," so Prime Minister Jacinda Ardern of New Zealand and said she and her countrymen were "devastated" by the events.
Leader of the nationalist League party in Italy, Matteo Salvini, who has been a vocal supporter of Trump, said on Twitter that "violence is never the solution" and Prime Minister Narendra Modi of India called for an "orderly and peaceful transfer of power."
According to JA Bayona, who is directing the new Amazon-exclusive series playing in the Lord of the Rings universe, the production has wrapped up filming in New Zealand. He posted on Instagram that "this is my last photo in New Zealand" but added that his "heart feels a little kiwi no" and that he "can't wait to be back" while also thanking "this extraordinary land and its beautiful people for taking me in".
There is no release date for the series as of yet.
New Zealand agreed Monday on a two-way travel bubble with Australia, allowing quarantine-free travel between the two nations in the first quarter of 2021.
“It is our intention to name a date ... in the New Year once remaining details are locked down,” Prime Minister Jacinda Ardern said at a news conference in Wellington.
97 pilot whales and 3 bottlenose dolphins have died as a result of a mass stranding on the remote Chatham Islands, located 800 kilometers off New Zealand's east coast. New Zealand's Department of Conservation was notified of the incident on Sunday, however rescue efforts were thwarted by the remote location and rough sea conditions.
The US rock band Guns N' Roses plans to perform in a stadium tour in a year's time. In May, the group around the founding members Axl Rose, Slash and Duff McKagan had to cancel their European tour planned for early summer 2020 at short notice. Now they have announced a statium tour for Australia and New Zealand in November 2021. Tickets go on presale on November 23rd.
Zeena Ali has become the first New Zealand police officer to wear a police-issued hijab as part of her official uniform. She had joined the police forces after the Christchurch terror attack and now worked with the police to design a hijab that is both functional for work as a police officer and considerate to her religion.
Nanaia Mahuta will be New Zealand's foreign affairs minister, the first woman and the first Indigenous woman to take that job. Jacinda Ardern promoted Mahuta, who has served as the country's first female member of parliament to wear a moko kauae, a traditional tattoo on her chin, for the past four years.
"I'm privileged to be able to lead the conversation in the foreign space," so Mahuta.
"This is a cabinet and an executive that is based on merit that also happens to be incredibly diverse and I am proud of that," Ardern said Monday.
New South Wales reports seven new Covid-19 cases in the past 24 hours, five of which were locally transmitted.
Premier Daniel Andrews expressed frustration with the Australian Border Force and Kingsford Smith Airport during a press conference over a technicality that allowed 17 travellers from New Zealand to enter Victoria despite the state's lockdown. The identity of the travellers has yet to be determined.
New Zealand Prime Minister Jacinda Ardern has won a second term after a landslide victory in the country's general election. Preliminary results show that Ardern's centre-left Labour Party has won 49% of the vote.
Saturday's result means the Labour Party is projected to win 64 out of 120 parliamentary seats, and be the first party in 24 years with a clear majority. | https://pendect.com/locations/New_Zealand |
As Tartuffe comes closer to nearly conning the family, he becomes more unrestrained and acts invincible as though he got away with his plan before its completion. Ultimately, Tartuffe becomes as bold as to attempt to arrest Orgon, so he could have complete mastery over the house. Since he was blinded sided by his own power, he neglected the consequences of bringing the King into the situation. Due to his past crimes, the tide quickly turned on Tartuffe, and when the officer went to arrest him, Tartuffe could only respond with a surprised, “Who, me?” (87). Tartuffe deluded himself into believing and trusting in a seemingly
Clown characters were based upon the real-life career of court jesters, who were employed by nobles and royalty to entertain them by use of physical and verbal comedy (“Shakespeare’s Clowns and Fools”). Because of their roles as entertainers, jesters were often given more freedom to be blunt than other courtiers and say whatever foolish or even offensive things they desired, because masters and audiences could be amused by the stupidity of their words (Rasmussen and DeJong). Nick Bottom, from A Midsummer Night’s Dream, is one of the best examples of Shakespeare’s use of these genuinely foolish clowns. Throughout the play, Bottom makes thoughtless and incorrect comments on characters and events to provide viewers with comic relief (“A Midsummer Night’s Dream”). To add physical comedy, “Bottom 's head is transformed into that of a donkey, making him the butt of the play 's biggest joke” (Shmoop Editorial Team, “Bottom”).
“King Claudius, as seen in William Shakespeare’s Hamlet, is both intelligent and well-spoken, two traits that, put together, complement his manipulative and dangerous nature. In fact, though it is his conscience that makes Claudius such a complex villain.” (The Manipulative Nature...). With all of that being said Hamlet has a chance right off the bat to claim his throne become a king and rule the land, however instead he fell into a depression. Claudius Speech to Hamlet shortly after his father’s
The comedy wanders around the difficulties and ironies of love as it provides a very accurate description of a relatively common situation that many people experience. Shakespeare excelled in delivering a piece that is comedic, relatable and unpredictable in its essence. As I progress through this essay, I will analyze one of its’ major themes, which is the controversy of love and how it involves some of the characters in the story. Love is often called the most beautiful sentiment a human can ever feel, yet, very often it can cause so much pain and despair, causing it to be very controversial and complicated. This reality is portrayed by Shakespeare in the play, indicating it with one his characters’ quotes; “The course of true love never did run smooth,” comments Lysander, (I.i.134).
The deceitful motives of the characters in Othello derived from popular comedy of early Italians in the sixteenth century. When Shakespeare wrote Othello, he intended to keep the audience on their seats. Common playwright techniques such as “improvised dialog, quick repartee, sham regional dialects, sly mockery, satire, obscene jokes and raillery” are used to amuse the audience (Whalen). Shakespeare focused on emphasizing how the audience will react. Whether they are expected to cry, laugh, or gasp, he put meticulous thought into the plot.
William Shakespeare’s plays are known for having many elements that hook the reader into the drama that lasts from beginning to end. His comedies are especially interesting, typically featuring arguments and feuds between characters, cases of mistaken identity, and at least one couple who experiences a crazy up and down relationship that usually somehow ends up in love by the end of the play. All of these elements are identifiable in Much Ado About Nothing. A deeper look at the characters of Hero and Claudio typifies how this couple is no different. This couple gets together in an unusual way, witnesses plenty of drama and backstabbing moments that lead the reader through the story wondering what is going to become of these two by the end.
He uses the Friar, the Summoner, and the Pardoner to express his views of the church. Chaucer wrote a prologue for the Pardoner and in the prologue the Pardoner states the following about the church, “Then priestlike in my pulpit, with a frown, I stand and when the yokels have sat down, I preach,a s you have heard me say before, and tell a hundred lying mockeries more”(9-12). The Pardoner is calling the people that believe him yokels with is calling them all dumb for believing what he preaches. He is also saying the church isn 't true, and the people that preach aren 't all what they seem to be. Its the use of satire in those
Iago uses manipulation to turn the moor into a murderer. The main reason for Iago's success was based on the social differences between the two. In that time interracial marriage between a black and white person was unacceptable, giving Iago the chance to enrage Brabantio. To begin with, Iago told Roderigo,” I will follow him to serve my turn upon him.” The quote means Iago's intentions are to mislead Othello by gaining his trust and turning him into a killer beast. Once Othello's trust is gain, Othello confides in Iago about Desdemona.
Macbeth had took the two men if they didn’t continue with this mission, they weren’t known as men. Macbeth was too insane to kill another man, but instead he hired two men to proceed the job, This leads to the downfall of Macbeth because it’s affecting him, making him lose his mind more than he is. Shakespeare’s message proves that Macbeth is going overboard with this kingly title. Lady Macbeth and Macbeth had a banquet with the lords and Macbeth had seen Banquo’s ghost at the dinner table, thinking it was full but others thought he was going insane and:/ “were the graced of our Banquo present, who may I rather challenge for unkindness than pity for mischance” (Shakespeare 3.4.47-49).Macbeth was starting to believe Banquo was still present but in reality he wasn’t. The decisions Macbeth is choosing to continue with is affecting the way he’s thinking and living his life.
Shakespeare created such characters and situations in his comedies that are funny and also loved and appreciated by the public but at the same time were critics of society. For example Feste, Touchstone and King Lear’s fool. In his plays the fools help realise who are the actual fools in reality. And not all of the fools are fools, like Speed in ‘Two Gentlemen of Verona’ is very quick and witty. Because according to Shakespeare answering something completely different to what question is asked is a great source of laughter. | https://www.ipl.org/essay/Huckleberry-Finn-Rhetorical-Analysis-Essay-F3ZDJDNFCE86 |
Sometime you need to find all the objects that meet a certain set of criteria – such as “Show me everyone who has a specific form from a particular region”, or “What’s in my pocket?” Filters are the perfect solution.
A filter is a user-created way to select a specific set of objects based on criteria, and that criteria leverages the configurable parts of TejonDb such as Types, statuses, regions, connections, forms, and more.
Filters are built by combining Filter Elements. Each Filter Element requests a specific set of data from the database depending the type of the Filter Element - such as the Type/status, Region, or Connections. If the Filter includes multiple Filter Elements then you can combine the Filter Elements using And and Or groupings.
The actual process of building a filter is as simple as dragging the Filter Elements on to the Filter Designer and then double clicking to open the Filter Element and set it’s properties.
Filters can be simple, such as “find me the active people in Nebraska”, or vey complex, “find me the board members who server more than 2 years, and are now inactive, and were once connected to the active people in Nebraska, but no longer are connected, and have not filled out a Past Board Member Profile Update form.”
Because Filters can be complex, there’s a Filter Analyzer tool to identify how each object was found by the Filter’s Filter Elements.
Once a filter is defined it can be refreshed multiple times, each time finding the data that currently meets the definition of the filter. Because data can move into and out of a filter, there’s a Filter Growth tool to help identify which object were added to a filter or removed from a filter each time the filter was refreshed. | https://tejontech.zendesk.com/hc/en-us/articles/360001049693-Filter-Overview |
Phase 1 Studies evaluate the safety and metabolism of the drug in a small number (20-100) of healthy volunteers and subjects who have the disease studied. Many of these studies require overnight visits at the clinic.
Phase II studies evaluate the effectiveness of the drug and are usually carried out “blinded” with a placebo control group and utilizes several hundred patients. In these studies various doses of the drug are administered to decide the best dosage form to be used.
After the study is completed, a statistical analysis is conducted to determine the benefits and safety of the study drug. Depending on these results the sponsor can continue the process of evaluation through Phase III and apply for FDA approval or discontinue the study or compound.
On completion of these studies, if the safety and value of the drug is evident, Phase III studies are carried out in several hundred to several thousand patients, and on successful completion the pharmaceutical company can apply to the FDA for approval to market the drug.
After approval, Phase IV studies are conducted to further evaluate the drug against other similar marketed drugs and to monitor long term effectiveness and safety.
If you missed last week’s blog, you can read it here. Next week’s blog will focus on the next stage other aspects of the clinical trial process.
The text of this blog comes from the article titled “Clinical Research in the South Coast” by Paul Chervinsky, MD. It was published in the September 2009 edition of The South Coast Insider. | https://nemra-us.com/category/news/ |
Susquehanna International Group LLP bought a new stake in Central Garden & Pet Co (NASDAQ:CENTA) during the 2nd quarter, Holdings Channel reports. The firm bought 18,865 shares of the company’s stock, valued at approximately $465,000.
A number of other large investors have also recently bought and sold shares of CENTA. Mason Street Advisors LLC lifted its holdings in shares of Central Garden & Pet by 3.7% in the 1st quarter. Mason Street Advisors LLC now owns 13,176 shares of the company’s stock worth $306,000 after acquiring an additional 464 shares during the last quarter. Comerica Bank lifted its holdings in shares of Central Garden & Pet by 1.2% in the 1st quarter. Comerica Bank now owns 42,427 shares of the company’s stock worth $1,013,000 after acquiring an additional 486 shares during the last quarter. Piedmont Investment Advisors Inc. lifted its holdings in shares of Central Garden & Pet by 6.2% in the 1st quarter. Piedmont Investment Advisors Inc. now owns 10,339 shares of the company’s stock worth $240,000 after acquiring an additional 606 shares during the last quarter. Rhumbline Advisers lifted its holdings in shares of Central Garden & Pet by 0.7% in the 1st quarter. Rhumbline Advisers now owns 118,022 shares of the company’s stock worth $2,744,000 after acquiring an additional 766 shares during the last quarter. Finally, Arizona State Retirement System lifted its holdings in shares of Central Garden & Pet by 1.4% in the 2nd quarter. Arizona State Retirement System now owns 64,162 shares of the company’s stock worth $1,581,000 after acquiring an additional 874 shares during the last quarter. Institutional investors own 67.10% of the company’s stock.
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Central Garden & Pet stock traded down $0.28 during mid-day trading on Tuesday, reaching $27.45. 7,823 shares of the company’s stock were exchanged, compared to its average volume of 306,961. The company has a market cap of $1.61 billion, a P/E ratio of 14.33, a P/E/G ratio of 2.89 and a beta of 0.12. Central Garden & Pet Co has a twelve month low of $20.50 and a twelve month high of $36.92. The company has a quick ratio of 3.17, a current ratio of 4.84 and a debt-to-equity ratio of 0.67. The company has a fifty day moving average of $24.61 and a 200-day moving average of $24.95.
Central Garden & Pet (NASDAQ:CENTA) last released its earnings results on Thursday, August 1st. The company reported $0.80 earnings per share (EPS) for the quarter, missing the Zacks’ consensus estimate of $0.86 by ($0.06). The business had revenue of $706.58 million for the quarter, compared to analyst estimates of $689.17 million. Central Garden & Pet had a return on equity of 9.66% and a net margin of 4.30%. Equities research analysts expect that Central Garden & Pet Co will post 1.73 earnings per share for the current fiscal year.
A number of equities research analysts have issued reports on the stock. BidaskClub upgraded shares of Central Garden & Pet from a “hold” rating to a “buy” rating in a report on Thursday, September 12th. Zacks Investment Research upgraded shares of Central Garden & Pet from a “sell” rating to a “hold” rating in a report on Tuesday, August 20th. KeyCorp reduced their target price on shares of Central Garden & Pet from $39.00 to $36.00 and set an “overweight” rating on the stock in a report on Friday, August 2nd. Finally, Monness Crespi & Hardt reiterated a “buy” rating and set a $36.00 target price (down from $44.00) on shares of Central Garden & Pet in a report on Friday, August 2nd. One analyst has rated the stock with a sell rating, one has assigned a hold rating and four have given a buy rating to the company’s stock. The company currently has a consensus rating of “Buy” and a consensus price target of $38.50.
Central Garden & Pet Company Profile
Central Garden & Pet Company, together with its subsidiaries, produces and distributes products for the lawn and garden, and pet supplies markets in the United States. It operates through two segments, Pet and Garden. The Pet segment supplies products for dogs and cats, including edible bones, edible and non-edible chews, dog and cat food and treats, toys, pet carriers, grooming supplies, and other accessories; and products for birds, small animals, and specialty pets, such as food, cages and habitats, toys, chews, and related accessories. | |
At CWI, AI research is firmly embedded, as the institute has been involved in AI research from the early beginnings. A number of research groups are advancing AI and its applications, working both from a computer science and a mathematical perspective.
With advances in algorithms and compute power, the importance of Artificial Intelligence as a research topic has grown immensely. AI enables computers to perform tasks at a level that matches or even exceeds human capabilities. AI techniques have also become an computer science tool and helps solve many challenging problems. Intelligent computers are of great value to society as they can be omnipresent and help save us time and effort. Think, for instance, of virtual assistants, image- and speech recognition, and self-driving cars. AI holds great promise for industry areas such as technology, finance, manufacturing, energy, gaming and health.
At CWI, AI research is firmly embedded, as the institute has been involved in AI research from the early beginnings. A number of research groups are advancing AI and its applications, working both from a computer science and a mathematical perspective. Groups involved in top-level AI research are: Machine Learning, Intelligent and Autonomous Systems, Information Access and Life Sciences and Health. Other groups that are involved in AI research are Multiscale Dynamics, Networks & Optimization and Scientific Computing. CWI AI research is applied in domains like, sequential prediction, smart energy systems, data integration and information, financial risk assessment and resilient networks. | https://www.cwi.nl/innovation/research-themes/artificial-intelligence/ai-test |
1. Field of the Invention
The present invention relates to a method, an apparatus, and a program for processing information and, in particular, to a method, an apparatus, and a program that can minimize an adverse effect that occurs when a key required for decrypting stream data is encrypted and an operation for decrypting the key is not completed in time.
2. Description of the Related Art
In recent years, an encryption method has been proposed in which stream data including a plurality of successive units of data is sequentially encrypted on a unit-by-unit basis and an encryption key used for encrypting each of the units of data is changed according to a predetermined rule (refer to, for example, Japanese Unexamined Patent Application Publication No. 2003-143548).
In addition, the development of an encrypting apparatus that encrypts stream data according to such an encryption method and generates meta data including a plurality of encryption keys used for encrypting the stream data and update information for identifying the timings of updating the encryption keys has started.
Furthermore, the development of a decrypting apparatus that decrypts data encrypted using such an encrypting apparatus by using the meta data generated by the encrypting apparatus has started.
Furthermore, in order to enhance the confidentiality of these encryption keys, a technique for encrypting these encryption keys according to a second encryption method and inserting the encryption keys into meta data has been developed.
Accordingly, in this case, to decrypt each of the plurality of encryption keys encrypted according to the second method contained in the meta data, the decrypting apparatus needs to generate each of the plurality of decryption keys and carry out a decrypting operation using each of the decryption keys.
| |
Web Content Accessibility Guidelines (WCAG) is the international standard for making websites and website content more accessible to disabled persons. This covers a wide range of recommendations for making your website content more accessible.
Following these guidelines will make your website’s content more accessible to a wider range of people with disabilities, such as blindness and low vision, deafness and hearing loss, learning disabilities, cognitive limitations, limited movement, speech disabilities, photosensitivity and combinations of these.
A website using the WCAG recommendations will often make your web content more usable to users in general and help rank better with search engines because of it’s clean systematic approach.
In 2005, the Ontario legislature passed the Accessibility for Ontarians with Disabilities Act (AODA). It was passed with the intent of improving access to goods, services, facilities, accommodation, employment, buildings, structures and premises in Ontario for all individuals with disabilities.
This means if you are a large organization (over 50 employees) you are required by law to ensure that new websites or those undergoing a significant redesign (new look, navigation and/or change to content) to comply with WCAG 2.0 Level A.
- Text Alternatives
Ensure text alternatives are in place for non-text content such as images or video. This could be as simple as using larger print, symbols, or simpler language.
- Adaptable
Adaptable content means your site may be presented in different ways. This could be a simpler layout, while still maintaining the same information and structure.
- Distinguishable
Ensure your text is readable by providing a strong colour contrast between text and background and that the font size is at least 14 points or easily re-sizeable.
Links and controls should be easily identifiable with keyboard or mouse focus.
- Keyboard Accessible
Your entire website should be completely keyboard accessible without using a mouse.
- Provide Enough Time
Make sure that any content that is set to change automatically (such as banners) has pause or manual control as people with dyslexia or other reading disabilities may need more time to take in the information.
- Do Not Cause Seizures
Avoid rapidly flashing images/objects or any other elements that are known to cause seizures.
- Navigable
Make your links visually distinguishable, and structure your site intuitively to help users navigate and find content and always easily identify where they currently are.
- Readable
Ensuring your product, service or message content is easily readable and understandable enables everyone easy comprehension.
Make sure your text is distinguishable and easy to read in size, style, colour and format.
- Predictable
Keep a consistent style / structure across the different pages of your site.
Such things as keeping your navigation in a consistent location and notifying users if links will direct them away form your site or open new windows help keep your site predictable.
- Input Assistance
Any forms or request for user input should be clearly explained, keyboard accessible and even provide ‘help’ links. If a form is rejected because of incorrect or missing fields, these should be very clearly marked with instructions on how to fix to proceed.
- Compatibility
Make sure your website is compatible with screen readers and other assistive technology softwares and tools. | https://cortezcreations.org/services/web-content-accessibility-guidelines/ |
According to Nikki Chambers, hazards scientist at RMS, this week’s heavy summer monsoon rain has caused flash flooding and landslides in western and central parts of Sri Lanka. This event has damaged homes, affected an estimated 100,000 people, and displaced over 27,000 people. It arrives after a severe drought that has lasted around five months, which threatened to decimate the rice and tea plantations.
With climate projections indicating a rising rainfall trend in the wet zone and decreasing rainfall trend in the dry zone, the risks associated with water-related climate variability are expected to intensify. As a result Sri Lanka is experiencing increased climate variability and extremes, including more intense floods, droughts, and storms, a pattern that is reflected throughout the region
Flood insurance in this region is given only in combination with windstorm/cyclone cover. Industry reports suggest there is take-up of about 20 per cent of this type of cover mainly from industrial and commercial organizations. Private dwellings rarely have the cover.
Sri Lanka has experienced severe drought over the last three years followed by relentless monsoonal rain. In January and February 2011 floods and landslides caused displacement across the eastern and central regions of Sri Lanka. More than one million people were affected and in excess of 33,000 families were displaced in temporary relocation centers across the island. There were 64 deaths recorded but in terms of people displaced and farmland inundated, the floods were even more devastating than the tsunami of December 2004. Whilst these floods were a major loss to the market, total flood claims in 2011 were lower than in 2010, at LKR 753mn ($6.81 million).
Extreme weather variations have implications on the quality of the tea crop, Sri Lanka’s most important export. Tea exports are estimated to have reaped $1.5 billion in export revenues in 2013, but extreme weather conditions are likely to have a negative impact on the quality of the crop. The government is currently investigating a national crop insurance scheme to help farmers cope with increasingly severe and disruptive weather and resulting crop losses.
The destructive recent flood events have sparked worldwide awareness of the potential devastation of these catastrophes, calling for an industry-wide reevaluation of risk quantification.
Source: RIMS
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Here are more articles you may enjoy. | https://www.claimsjournal.com/news/international/2014/06/06/249959.htm |
Synopsis : Information regarding vegetarian and vegan diet lifestyle including the difference between the two, how to get enough protein, and tips for becoming a vegetarian with example recipes.
There are all types of vegetarians, those who give up all dairy products including eggs and cheese, and those who simply eat fruits and vegetable and nothing else.
The choice is up to you when you are thinking about becoming a vegetarian, but before you throw away that cottage cheese, realize that you will need to do other things that will meet the nutritional needs that your body will be denied without that serving of cottage cheese.
The practice of living on products of the plant kingdom, with or without the use of eggs and dairy products, but excluding entirely the consumption of any part of the body of an animal as food (including chicken, fish and seafood).
Vegetarians who refuse to consume foods other than fruits, grains, vegetables, nuts and seeds. Vegans are particularly noteworthy because they do not intend to consume eggs and dairy products. Thus, vegans' vitamins and nutrients needs are consisting of calcium, protein, iron and Vitamin B12. A raw vegan diet consists of unprocessed vegan foods that have not been heated above 115 degrees Fahrenheit (46 degrees Celsius).
sed to describe a vegetarian who does not eat eggs, but does eat dairy products. People who do not eat beef, pork, poultry, fish, shellfish or animal flesh of any kind, but do eat eggs and dairy products are lacto-ovo vegetarians ("lacto" comes from the Latin for milk, and "ovo" for egg).
Refers to people who do not eat meat or dairy products but do eat eggs.
Are like lacto-vegetarians. But these groups of vegetarians do not limit their dairy foods intake to low-fat. They consume even the fresh and high-fat dairy products. Vitamin needs of these vegetarians are like those of the lacto-vegetarians.
People who eat chicken and fish but not other types of meat like beef, lamb and pork. Thus, these vegetarians' vitamins needs are far lower compared to their other counterparts since they can assimilate more vitamins from wider food sources.
"Flexitarian" is a term recently coined to describe those who eat a mostly vegetarian diet, but occasionally eat meat.
A vegaquarian is someone that eats only vegetables, grains, dairy products and fish as part of a lifestyle decision.
The macrobiotic diet, revered by some for its healthy and healing qualities, includes unprocessed vegan foods, such as whole grains, fruits and vegetables, and allows the occasional consumption of fish.
Occasionally used to describe those who abstain from eating all meat and animal flesh with the exception of fish. Although the word is not commonly used, more and more people are adopting this kind of diet, usually for health reasons or as a stepping stone to a fully vegetarian diet.
Woman holding two containers of strawberries in front of her face - Photo by Elijah O'Donell on Unsplash.
You may want to start off slow and work your way towards totally becoming a vegetarian.
Your body, believe it or not, will go through some changes when it is being denied something that they are used to having. Instead of completely cutting out meat abruptly, think about eating fish or chicken instead and then gradually phasing that out if that's where you want to be in the long run.
Another essential part to becoming a vegetarian is to know what nutrients are contained in the foods that you will be eating.
Those who don't support the vegetarian lifestyle do so mainly because they feel like the body will be deprived of important vitamins and minerals it needs to be healthy. However, those who have successfully switched to a vegetarian lifestyle know that there are plenty of substitutions that can be made to help make up for the gap that is left by a meatless diet.
Do your research and know that broccoli as well as many dark greens like kale and spinach contain tons of calcium and eating them will give you more than enough to be healthy. Know as well that nuts and grains provide a great source of protein, so if you can get enough of them into your diet, you will also be meeting those nutritional needs.
Becoming a vegetarian can be one of the best things you can do for your body as well as for your life. Those who have already done so have found that they feel better, they have more energy, and they even are able to lose weight without feeling hungry all the time. Take the time to research becoming a vegetarian and then take your time towards this satisfying lifestyle.
It can be very difficult to switch to a meatless way of eating, so you should know what you're getting into before you get into it. Examine the pros as well as the cons, but know that becoming a vegetarian involves more than just not eating meat.
What Do Vegetarians Get Protein From?
Being vegetarian does not mean your diet will be lacking in protein. Most plant foods contain protein and in fact it would be very difficult to design a vegetarian diet that is short on protein. The need of protein for the human body is about a nickel's weight worth, the excess is basically excreted in urine. Based on research, the need for amino acids is highly exaggerated as only 16% or our body is Protein.
Moreover, the irony of the whole protein debate is that being overly concerned about sufficient sources of protein for vegetarians may not even be that necessary as it's been proven that excess dietary protein may lead to health problems.
Of course we all need a certain amount of protein everyday to remain healthy. However, based on misinformation to this effect, several people view the daily consumption of a high-protein diet as beneficial and this in itself may actually be wrong.
According to the French Hygienist, Albert Mosseri, diseases and conditions which can be caused or aggravated by too much protein intake include: Leukemia, Skin Diseases and even Cancer.
Based on the John Robbins work titled: Diet for a New America , the number of people in the US suffering from diseases caused by protein excess is a mind-boggling 40,000,000 compared to a measly 3 people suffering from the deficiency of this substance.
For some sufficient sources of protein for vegetarians, here are some recommended items.
Green Leaves: Believe or not, these babies have sufficient amounts of protein and of extremely high quality, containing all the essential amino acids. They are highly absorbent and will not ferment in the intestines nor poison the body.
Legumes (though not necessarily advocated...are a good protein supply for a vegetarian).
Although milk is a source of calcium, you certainly don't need milk to get plenty of calcium. The milk of any animal is basically too rich humans. It is highly acidic and mucus forming.
Now, to answer the question-can vegans get enough sustenance for calcium needs? Here's some calcium-rich foods to try: spinach, collard greens, kale, , fortified orange juice, sesame seeds, broccoli, almonds, carrots.
Briefly Folks, according to nutritionist, Albert Mosseri; sufficient proof that anemia is not caused by lack of iron in a vegetarian diet is that the disease actually regresses during fasting!
Sure, the truth is If you used to eat meat, you may already have enough B12 stored in your body to be recycled and re-used for up to twenty or thirty years.
Bowl containing various vegetables and salad ingredients - Photo by Anna Pelzer on Unsplash.
There are four major groups of vegetarians, in relation to the kind of food they eat and the vitamins they generate from these food sources.
The principal aim of vegetarians is to drastically cut, if not eliminate, the absorption of fats from food to prevent cholesterol build up that leads to obesity, hypertension, heart ailments, strokes and a host of other diseases.
But by doing so, they compromise their bodies assimilation of other vitamins and nutrients needed for better functioning. Thus, experts note that most vegetarians experience mild to severe deficiencies to some nutrients, minerals and vitamins.
Most vegetarians need more vitamin B12. This is because this vitamin is particularly found only in animal meat. However, to meet the vegetarian's needs for this vitamin, they can resort to eating breakfast cereals, brewers' yeast and soy beverages.
Because vegetarians' vitamin supplies are somehow made limited, they are also subjected to vitamin D deficiency. The need for this vitamin can be satisfied by exposure to direct sunlight because vitamin D is synthesized by the body's skin.
Zinc is a mineral that most vegetarians need more. That is because this is much needed for improved growth among teenagers.
Protein is one nutrient that can only be found mostly in dairy products. But the strict vegetarians' needs for protein can be met by consuming soy products, which are the only plant-sourced food to contain as much protein as dairies.
Experts and dietitians advise that before you subject yourself to any vegetarianism diet practices, you must first research about them. Get to know the potential vitamin needs that might miss by avoiding several foods.
If you are a vegetarian and your vitamin needs are still not met, consult your doctor to ask about vitamin supplements suited for you.
Remember, vegetarianism is good, but you need to source out those vitamins you need from other sources if you want to maximize the dietary discipline's results.
Vegetarianism in America study (2008), published by Vegetarian Times shows that 3.2 percent of U.S. adults, or 7.3 million people, follow a vegetarian-based diet. Approximately 0.5 percent, or 1 million, of those are vegans, who consume no animal products at all. In addition, 10 percent of U.S., adults, or 22.8 million people, say they largely follow a vegetarian-inclined diet.
Vegan Diet Improves Diabetes Markers in Overweight Adults - Study shows a plant-based diet improves beta-cell function and insulin sensitivity in overweight adults with no history of diabetes.
Tofu - How to Get Your Friends to Try It - Tofu is becoming a bigger part of western diets, especially for people who want fast and easy to cook dishes that can help keep them trim.
Starting a Vegetarian or Vegan Lifestyle Guide - Useful information and guidelines to help start a vegan or vegetarian diet and new way of life.
World Vegetarian Day - Oct 1 - Give Vegetarianism a Try and Win Up to $1000 - Non-vegetarians who pledge to abstain from all meat fish and fowl during Vegetarian Awareness Month will be entered in a random drawing for cash prizes.
Vegetarians Have Lower Risk of Heart Disease, Stroke and Diabetes - Loma Linda University study suggests metabolic syndrome is significantly less prevalent in vegetarians.
Citation: Disabled World. (2019/01/21). Vegetarian - Vegan: Recipes, News and Information. Retrieved 2019-04-19, from https://www.disabled-world.com/fitness/vegetarian/ Direct Link: Vegetarian - Vegan: Recipes, News and Information - Information regarding vegetarian and vegan diet lifestyle including the difference between the two, how to get enough protein, and tips for becoming a vegetarian with example recipes. | https://www.disabled-world.com/fitness/vegetarian/ |
The Graphic Design capstone project provides a simulation of an extended client design project. Students will take a project from concept to final presentation. Students work closely with the department head, interpreting a project brief, developing design elements, and designing a logo, brochure, and package design. The project is executed in three stages with feedback and discussion at each stage. Students are expected to discuss, present, and critique their work with a high level of professionalism, and implement research strategies that contribute to the overall finished project.
Final project work by Michelle Panta
A portfolio project for Graphic Design majors
Instructor-Led Course
Feedback from design professionals
Creative Projects
Stretch your skills, grow your portfolio
Learn at Your Own Pace
Self-paced and scheduled programs available
Course Outline
1 - Choosing a Client
You will present your research and concept for initial feedback.
2 - Researching and Conceptualizing
Prepare images, colors, and typography based on the concept and submit them for additional feedback.
3 - Preparing the Design
Present your final deliverables: a polished logo, brochure, and package design.
Course Outcomes
Students in this course can expect to learn to:
- Research a design concept for a new product.
- Present relevant research sources along with a written analysis and explanation of how they contributed to your concept.
- Present the development of a design concept using sketches, tearsheets, mood boards, and any other methods of your choice to present design concepts.
- Prepare a distinctive color palette based on the principles of color harmony.
- Research and present appropriate typefaces and design typography to support the branding or communication goal of the client and project.
- Create an effective identity design for brochure and package design as well as other applications such as business cards, billboards, and Web sites.
- Create a four-page brochure and six-sided fold-up carton design for a package/product.
- Deliver a written presentation of an entire project that demonstrates critical thinking ability, professional project presentation skills, and the ability to develop/explain your creative process.
- Create a complete project that exhibits professional competence in print design genres including logo/branding design, brochure layout, and packaging.
Course Registration
Interested in this course? This course is available to students enrolled in the Associate of Occupational Studies program.
Software and Supplies
To take this course you'll need:
- Computer with Internet connection.
- Adobe Photoshop, Illustrator, and InDesign or equivalent programs.
- Experience in the above software.
Who’s Teaching
Course developed by Joss Parsey
Getting Started
Enrolling online is easy and convenient.
Chat with our knowledgeable admissions staff to select course and program options.
Complete your registration entirely online.
Related Programs
Did you know? You can take this course as part of an award-winning certificate or degree program. | https://www.sessions.edu/online-courses/graphic-design-capstone/ |
What are sub-brands and why are they needed?
The Boston College wordmark is the core element in the visual identity system. It is the official logo of the University, and is what is most strongly associated with the Boston College brand. In order to be effective, all logo treatments must be consistent and accurate, and as such, coordinated through University Communications.
The primary challenge is to align these entities behind a single, unified institutional brand. The institution of Boston College has many decades of history and name recognition, and our central brand has already been leveraged.
Until recently, there has been no logic in the treatment of school, office, or department names. The color treatment, seal and/or wordmark use, and typography were not consistent. The multiplicity of identity styles across the varying schools and departments added to confusion and a possible negative reflection of the main BC brand.
New wordmarks for schools and other University entities
Distinct sub-brand wordmarks are being created and will be available for schools, offices, departments, and other University-affiliated groups to identify themselves, while maintaining a cohesive University brand identity. The original Boston College wordmark will remain the same and dominate the wordmarks. The sub-brand will incorporate the names of the schools, departments, offices, and other entities in a cascading hierarchy, with school names being level 1 of the hierarchy. | https://www.bc.edu/content/bc-web/offices/office-of-university-communications/policies-guidelines/subbrands.html |
A&S Support Coordinators will assist participants connect with the supports and services they need to achieve their personal goals. This process starts with the development of the participant’s individualized support plan (NJISP) and his/hers Person Centered Planning Tool (PCPT). Each participant will be assigned a Support Coordinator (SC) that will get to know each participant and their family. The SC will schedule an initial meeting to meet the participant and their family/support and inquire about current support needs, community resources, and natural supports (family, neighbors, and community) that are available to the participant. Programs and resources by local, state, and federal agencies will be explored. A&S support coordinators will provide linkage and coordinate with all appropriate supports that best suits the participant. This will result in a unique service plan that will become each participant’s blueprint for the future. Once a plan is developed, the SC will approve the plan and assist in the implementation of the plan. Each Coordinator will continue to follow up and stays in communication with families to assist with any revisions or changes as necessary through monthly contact, quarterly face-to-face visits and an annual home visit.
What we do as Support Coordinators:
- Identify the client’s support needs and preferences
- With the participant and family, will develop the NJ Person Centered. Planning Tool (PCPT) and NJ Individual Service Plan (NJISP).
- Identify and locate services that include: community supports, the government supports beyond DDD, and /or natural support based on funds available in the participant’s individual budget. Linking participant and their families to available resources and agencies
- Ongoing monitoring of established supports and services to make sure services are running smoothly.
- Responding to emergencies and other service-related needs of the participant and/or family. | https://www.aandssupportservices.com/administrators-support-coordinators/ |
CITP’s Tech Policy Clinic submitted a Comment to the Federal Trade Commission in connection with its review of the COPPA Rule to protect children’s privacy online. Our Comment explains why it is important to update the COPPA Rule to keep it current with new privacy risks, especially as children spend increasing amounts of time online on a variety of connected devices.
What is the Children’s Online Privacy Protection Act (COPPA)?
As background, Congress in 1998 gave the FTC authority to issue rules that govern how online commercial service providers should collect, use or disclose information about children under the age of 13. The FTC issued the first version of the Rule in 2000 which requires providers to place parents in control over what information is collected from their young children online. The Rule applies to both providers of services directed to children under 13 as well as those serving a general audience who have actual knowledge that they are collecting, using, or disclosing personal information from children under 13. This Rule was subsequently revised, after a period of public comment, in 2013 to account for technological developments, including the pervasive use of mobile apps. In 2019, the FTC announced it was revisiting the Rule in light of ongoing questions about the efficacy of the Rule in a data-fueled online marketplace and soliciting public comment on potential improvements to the Rule.
Core Recommendations to Update the COPPA Rule
Our Comment makes three main points:
- We encourage the FTC to develop rules that promote external scrutiny of provider practices by making the provider’s choices about how they are complying with the Rule available in a transparent and machine-readable format.
- We recommend that the FTC allow providers to rely on an exemption from collecting or tracking information related to “internal operations” only under extremely limited circumstances, otherwise the exception risks swallowing the rule.
- We offer some suggestions on how education technology providers should be responsive to parents and recommend that the FTC conduct further studies about how such technology is being used in practice.
We elaborate on each point below.
Enabling Effective External Compliance Checks Through Transparency
One of the central challenges with the COPPA Rule today is that it is very difficult for external observers (parents, researchers, journalists or advocacy groups) to understand how an online provider has decided to comply with the Rule. For example, it is not clear if a site believes it is in compliance with the Rule because it argues that none of its content is directed at children or because it has implemented rules that seek appropriate consent before gathering information about users. Making a provider’s choices on compliance transparent will enable meaningful external scrutiny of practices and hold providers to account.
Under the COPPA Rule providers are responsible for determining whether or not a service is child directed by looking to a variety of factors. If the service is directed at children, then the provider must ensure they have verified parental consent before collecting information about users. If the audience is of mixed age, then the provider must ensure that it does not collect information about users under the age of 13 without parental consent.
The determination about whether a service is child directed, as the FTC explains, includes factors such as “its subject matter, visual content, use of animated characters or child-oriented activities and incentives, music or other audio content, age of models, presence of child celebrities or celebrities who appeal to children, language or other characteristics of the Web site or online service, as well as whether advertising promoting or appearing on the Web site or online service is directed to children . . . [and] competent and reliable empirical evidence regarding audience composition, and evidence regarding the intended audience.” If the service is child directed and children under the age of 13 are the primary audience, then it is “primarily child directed.” If services that are child directed, but do not target children as the primary audience, they are “child directed, but mixed audience” services under the COPPA Rule.
If a mixed audience service seeks to collect information about users it can choose to implement an age gate to ensure it does not collect data about underage users. An age gate is, a mechanism that asks users to provide their age or date of birth in an age-neutral way.
Our principal recommendation is that the COPPA Rule should be revised to explicitly facilitate external scrutiny by requiring providers to make their design choices more open to external review. Specifically, we suggest that the FTC should make sites or services disclose, in a machine-readable format, whether they consider themselves, in whole or part, “directed to children” under COPPA. This allows academic researchers (or parents) to examine what the provider is actually doing to protect children’s privacy.
We also recommend that the FTC establish a requirement that, if a website or online service is using an age gate as part of its determination that it is not child directed, it must publicly post a description of the operation of the age gate and what steps it took to validate that children under 13 cannot circumvent the age gate.
In addition, drawing on our work on online dark patterns, we suggest that the FTC examine the verifiable parental consent mechanisms used by providers to ensure that parents are being given the opportunity to make fully informed and free choices about their child’s privacy.
Finally, we suggest some ways that platforms such as iOS or Android can be enlisted by the FTC to play a more effective role in screening users and verifying ages.
Restrict Providers from Relying on the “Internal Operations” Exception
Another significant issue with current practices is that providers rely on an exception for providing parental notice and obtaining consent before collecting personal information when they use persistent identifiers for “internal operations.” The 2013 revisions to the Rule included this new exception, but required it to be used for a limited set of circumstances necessary to deliver the service. It appears many providers now use that exception for a wide variety of purposes that go well beyond what is strictly necessary to deliver the service. In particular, users have no external way to verify whether certain persistent identifiers, such as cookies, are being used for impermissible purposes. Therefore, our Comment urges the FTC to require providers to be transparent about how they rely on the “internal operations” exception when using certain persistent identifiers and limit the circumstances when the providers are allowed to use such an exception.
Give Parents Control Over Information Collected by Educational Technology Service Providers
Finally, our Comment addresses the FTC’s query about whether a specific exception for parental consent is warranted for the growing market of providers of educational technology services to children (and their parents) in the classroom and at home. We recommend that the FTC should study the use of educational technology in the field before considering a specific exception to parental consent. In particular, we explain that any rule should cover the following issues: First, parents should be told, in an accessible manner, what data educational technology providers collect about their children, how that data is used, who has access to the data, and how long it is retained. Parents should also have the right to request that data about their children are deleted. Second, school administrators should be given guidance on how to make informed decisions about selecting educational technology providers, develop policies that preserve student privacy, and train educators to implement those policies. Third, the rule should clarify how school administrators and educational technology providers are accountable to parents for how data about their children are collected, used and maintained. Fourth, the FTC needs to clearly define what is meant by “educational purposes” in the classroom in considering any exceptions for parental consent.
* The Comment was principally drafted by Jonathan Mayer and Mihir Kshirsagar, along with Marshini Chetty, Edward W. Felten, Arunesh Mathur, Arvind Narayanan, Victor Ongkowijaya, Matthew J. Salganik, Madelyn Sanfilippo, and Ari Ezra Waldman. | https://freedom-to-tinker.com/2020/01/ |
TRENTON — The White House has delayed implementing two of the top recommendations of the presidential opioid commission chaired by New Jersey Gov. Chris Christie, but the Trump administration sent several officials to Trenton on Monday to advance a third program — a public-private partnership with the pharmaceutical industry.
Standing next to Christie, counselor to the president Kellyanne Conway said President Donald Trump has made the opioid epidemic a priority, which is why he established the Commission on Combating Drug Addiction and the Opioid Crisis in the first place.
“Opioid addiction is a scourge across the land, it literally has touched every state, every demographic group. So we feel that since it’s touched everyone in that way, it is a challenge that should be shared and worn by all,” said Conway, who is a resident of Bergen County.
On Monday, Conway and Christie met with representatives from 14 pharmaceutical companies, including Purdue Pharma, Johnson & Johnson and Allergan, to continue building a research collaboration between industry and the federal government that was announced by National Institutes of Health Director Francis Collins earlier this year.
The partnership, Christie said, will "fast track" the development of non-opioid pain medication, as well as new medication-assisted treatment options.
NIH will function as a “clearinghouse” to share information between companies and help identify which compounds in the development pipeline have the “most potential,” the governor said.
Collins said the research would also focus on new overdose reversal treatments, “because there’s concerns that the current methods may not be strong enough,” particularly for people who have overdosed on fentanyl.
Several of the companies represented at the meeting have been the subject of state-based lawsuits over allegations of deceptive marketing practices related to prescription opioids.
Asked about the responsibility of pharmaceutical companies in fueling the opioid crisis, Christie said he "didn't spend any time this morning talking about pending litigation because they wouldn't want to talk about it anyway."
While the Trump administration has embraced the partnership with the pharmaceutical industry, it has yet to act on the main recommendation from the commission’s interim report, which was to declare the opioid epidemic a national emergency.
It has been more than a month since Trump said he intended to make the formal declaration.
The commission’s interim report also proposed waiving a longstanding prohibition on using Medicaid funds to pay for residential substance abuse treatment.
Since the 1960s, the federal government has barred certain health care facilities with more than 16 beds — classified as Institutions for Mental Disease — from receiving federal matching funds to treat Medicaid patients.
The Christie administration applied to remove this restriction as part of a comprehensive Medicaid waiver application submitted to the Trump administration earlier this year.
New Jersey, along with four other states, is still waiting on guidance from the U.S. Centers for Medicare and Medicaid Services as to whether this additional substance abuse treatment funding will be made available.
The opioid commission was supposed to submit its final report in October, but Christie recently asked for the deadline to be pushed back to Nov. 1. | https://www.politico.com/states/new-jersey/story/2017/09/18/white-house-backs-pharma-partnership-after-delaying-other-opioid-commission-recommendations-114555 |
Lose Yourself in These 5 Must-Visit Libraries around Jakarta
Libraries, in general, don’t necessarily have a stunning reputation among Indonesian locals, which is probably why you don’t really hear about them that often. But this doesn’t mean Indonesian people don’t like books or enjoy reading. In fact, a lot of the local people you’ll meet are most likely bookworms themselves. Little did you know, Jakarta is actually home to a lot of really cool and unique libraries where you can lose yourself in really great books and escape the bustling city life of Jakarta. You can also go to libraries to work or study if you need a calm ambiance.
So, here we provide a list of libraries in Jakarta that you should go check-out:
1. Perpustakaan Nasional RI (The National Library of Indonesia)
Housing the most complete collection of books in the whole city, The National Library of Indonesia is surely the heart of knowledge in Jakarta. So, you will find tons of books with various genres ranging from fiction romantic novels to geopolitical guides.
The building itself is comprised of 27 floors – all filled with books. Each floor also has its own sections for different genres and subjects. For example, you’ll be able to find children’s books, which consist of a great collection of national classics and has a colorful interior. You can also find books for the elderly there along with books in braille. If you don’t know what book you’re looking for and have some time on your hands, immediately head to the 21st or 22nd floor. Here you will find many books ranging from non-fiction to literature. Another great thing that might interest you is the various old newspapers, films, and ancient texts that you can go check out here. So, at this rate, you might even be able to learn about Jakarta’s vast history in one day.
For non-members of the library, you may not borrow and take home books from the library. That is why PNRI wants to ensure every visitor with great hospitality and comfort, therefore they also provide cozy sofas, sturdy tables, and plenty of power plugs, and free wifi. But, if you are interested in making a membership, you can head on down to the Membership Room and fill out an application (make sure to bring your ID).
Address: Jl. Medan Merdeka Sel. No.11, RW.2, Gambir, Kec. Senen, Central Jakarta, Special Region of Jakarta 10110
Telp: (021) 1500914
Opening Hours:
- Monday to Thursday 8.30-18.00
- Friday to Sunday 9.00-16.00
2. Rimba Baca
Having one of the coziest interiors ever, Rimba Baca is a family library in South Jakarta made up of two floors that consist of both children and adult books. You will find that the first floor houses mostly children’s books, ranging from encyclopedias to fiction novels and activity books. Most of the books are in English but there also ones in Bahasa Indonesia, Chinese, Indian, and even Korean! There’s also a really cool art room for kids to have fun drawing and coloring.
The second floor comprises of adult books with genres such as fantasy, fiction, design, cooking, politics, biographies, comics, and religion. Again, the majority of the books are in English but there also some great Indonesian selections as well. There are sofas, chairs, and carpets provided for you to cozy up with your book.
This library also has a membership program to enter, but they don’t allow anyone to borrow the books to take home. For instance, if you’re a non-member adult who wants to head to the 2nd floor, it cost Rp.30.000,00 (~$2). If you bring a child, it costs Rp.30.000,00 for them and Rp.10.000,00 for the accompanying adult. Although the membership program allows you to borrow books, it is more suitable/beneficial for a family because it cost Rp.375.000,00 per year (~$25).
Address: Jl. Intan RSPP No.21B, RW.2, Cilandak Bar., Kec. Cilandak, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12430
Telp: (021) 7664517
Opening Hours: Monday to Sunday 10.00 – 19.00
3. OMAH Library
For those of you looking for books about architecture and design, the On Meeting Architecture Hub (OMAH) library is certainly the place for you. An as architect himself, OMAH’s founder Realrich Sjarief aims to use this library to help rising architects have access to architectural books in Indonesia. Hence, you’ll be able to find around 1,500 theoretical books, case studies, and monographs.
Other than that, this library in Tangerang also contains fiction novels and book son philosophy in both English and Bahasa. The library is open to the public for free but you’re not allowed to take home any of the books. Before you can visit the library, make sure to contact them in advance because the library itself is located in Realrich Sjaief’s private studio.
Address: Kompleks Taman Villa Meruya, Taman Amarilis II Blok F2 No. 15, Tangerang
Email: [email protected]
Opening Hours: Weekends 10.00-18.00
4. Kwitang14
Established in 2014 by members of Cinema Poetica, Kwitang14 is a small quiet library in Central Jakarta that houses books on culture, design, and sociopolitical issues. Cinema Poetica is a group of film journalists, activists, critics, and researchers all sharing the love for films. Therefore, the majority of these books are donated by the members themselves. You can find over English 200 books and also check their catalog online. There are 4 tables and 8 chairs provided, along with a cozy carpeted corner with lots of soft pillows, so you can lie down.
In order to read these books, you need to bring your ID with you. You are not allowed to borrow the books but are welcome to spend as long as you like. The great thing about this library is that you can come and read their books outside of their opening hours by contacting them a day in advance. Kwitang14 also hosts an event called Nonton Dikwit, where you are invited to watch and participate in film discussions. In addition, there are no entrance or administrative fees!
Address: Jl. Kwitang Raya No. 14, Senen, Central Jakarta
Email: [email protected]
Opening Hours: Friday to Sunday 12.00-18.00 (contact in advance if you want to come outside of opening hours)
5. Freedom Institute Jakarta
For local bookworms, Freedom Institute is a familiar name. It quickly gained popularity due to its modern wide interior and cool Indonesian paintings. This library in South Jakarta houses thousands of unique books with various genres and topics. There are also books published by the Freedom Institute themselves.
To enter the library, you need to become a member. But don’t worry, you just need to fill out a form and show them your ID. Moreover, there is no membership fee and you are immediately given your membership card.
This library provides free wifi, couches, desks, and even meeting rooms that are open to the public for no cost at all. A lot of university students tend to come here to study so it may be a little bit crowded during the weekdays. Furthermore, you are not allowed to borrow any books but you may photocopy the pages that you need.
Address: Wisma Bakrie, Jl. H. R. Rasuna Said No.Kav, B-1, Kuningan, Menteng, South Jakarta City
Telp: 021 3100349
Opening Hours:
- Monday 9.00-18.00
- Tuesday to Friday 10.00-18.00
6. Erasmus Huis
This instagrammable library offers a cozy ambiance, cool room temperature, and free wifi. This library belongs to The Netherland Embassy in Jakarta, therefore most of the books are in Dutch. However, don’t worry because there are books in English and Indonesian, too. Moreover, if you want to visit this library, there is no entrance fee. But, if you want to borrow a book, you have to register as a member first. To be a member, you will be charged Rp30.000,00 for public and Rp15.000,00 for students.
Address: Dutch Embassy Indonesia, Jalan Haji R. Rasuna Said Blok C No.3, Kuningan Timur, South Jakarta
Opening Hours:
- Monday – Thursday 9.00 – 16.00
- Friday 9.00 – 14.00
- Saturday 10.00 – 13.00
7. Goethe-Institut Jakarta
Goethe Institut, an organization that actively promotes German culture and offers cultural cooperation, has an open-for-public library in Jakarta. Therefore, everyone can read or use the media in this library for free. In addition, you will be informed with information about Germany, including books, music, films, and game collections. However, if you want to borrow something from the library, you have to own a membership card and domiciled in Jabodetabek only. To register for membership, you will have to fill a form in the library. Also, don’t forget to bring your ID with Jabodetabek address!
Address: Jl. Dr. GSSJ Ratulangi No. 9, Gondangdia, Menteng, Central Jakarta
Phone: (021) 3914042
Opening Hours:
- Monday 09.00 – 17.00
- Tuesday – Friday 09.00 – 17.00
- Saturday 10.000 – 16.00
8. Indonesian Ministry of Education and Culture (Kemdikbud) Library
Located beside the f(x) Sudirman Mall, precisely in Building A of Kemdikbud Indonesia, this library in Central Jakarta has many collections of Indonesian books. However, their foreign film and audio collections are also quite broad, from history films to cartoons. If you want to watch the film, they have a theatre room there, equipped with a small TV and headset for each person. Moreover, the entrance fee is free and you don’t have to be a member. But, if you want to borrow a book, make sure you bring your ID and an Rp6.000,00 stamp.
Address: Indonesian Ministry of Education and Culture, Building A, 1st Floor, Jl. Jenderal Sudirman, Senayan, Central Jakarta
Website: https://perpustakaan.kemdikbud.go.id/
Opening Hours: | https://www.flokq.com/blog/libraries-jakarta |
A Patagonia employee breastfed her baby in a meeting. Her male VP's response is a masterclass in workplace values.
Talk about a "family-friendly workplace."
08.16.19
Patagonia has taken "family-friendly workplace" to a whole new level, and people are noticing.
The outdoor clothing and gear company has made a name for itself by putting its money where its mouth is. From creating backpacks out of 100% recycled materials to donating their $10 million tax cut to fight climate change to refusing to sell to clients who harm the environment, Patagonia leads by example.
That dedication to principle is clear in its policies for parents who work for them, as evidenced by a viral post from Holly Morisette, a recruiter at Patagonia. | https://www.upworthy.com/tag/childcare |
We all think we know what it is to be compassionate, and when someone claims to be compassioante we think we know what is meant by it. So how would we describe compassion in today’s terms, and how did Schopenhauer and Shantideva interpret the term? The Oxford English Dictionary defines compassion as ‘The feeling or emotion, when a person is moved by the suffering or distress of another, and by the desire to relieve it; pity that inclines one to spare or to succour’. Within this definition there are several keys terms that these two men discuss, these include – the emotions of the individual acting compassionately, suffering, pity and succour. Nancy Snow brings some clarity into how compassion can be seen from a modern philosophical perspective when she writes ‘the ability to identify with another’s distress makes the other’s suffering real to those who feel compassion, and facilitates benevolent desires for the other’s good’. and that it differs from pity as the individuals feels “with” not “for” the sufferer.
When considering how the views of Shantideva and Schopenhauer differ, it is helpful to see the background, culture and time the two men lived. Shantideva, an 8th Century Indian Buddhist monk, was a follower of Buddhism. Buddhism is a practice and lifestyle that can be said to cross the boundaries of religion and philosophy, and the BBC describes Buddhism on its “Religions” page of it’s website as ‘a tradition that focuses on personal spiritual development. Buddhists strive for a deep insight into the true nature of life and do not worship gods or deities’. This description in itself seems paradoxical as all other major religions have one one or many deities. Buddhism can still be thought of as an “Eastern” religion, only taking root in western civilisation in the late 19th and early 20th Centuries.
Like many religions, such as Christianity, Buddhism has many factions, but the major two types are Theravada (translated as “Teaching of the Elders”) and Mahayana (meaning “The Great Vehicle.”). The former group believe that only Buddhists that explicitly follow the teachings of the Buddha and live as monks can achieve nirvana (a transcendent state of enlightenment free from desire or suffering and the goal of Buddhists), by contrast the Mahayana believe all people can reach nirvana. A feature of Mahayana Buddhism, therefore, is that it has a wider variety beliefs (arguably looser or less strict), and a more comprehensive canon of writings and literature to draw from.
Followers of the Mahayana approach will strive for a lifestyle known as bodhisattva. Suzanne Newcombe describes a bodhisattva as ‘a person who not only strives for individual enlightenment but also commits to continue to be reincarnated through multiple lifetimes in order to bring enlightenment to all beings’ and key to this she continues, is ‘experiencing compassion for everything that suffers’. And herein lies the start of one of the major differences between the compassion of the Western understanding of the term, and the Eastern teaching of this style of Buddhism – compassion in this context is universal (ie to all living creatures, not only fellow man) and the term “experiencing” infers the living and feeling of the emotion of the sufferer, as opposed to just recognition and a feeling of pity. The universality of compassion with particular regards to suffering leads to, and supports the Buddhist construct of “no self” or “anattā” – the view that we are always changing and have no permanence, and do not exist in a hierarchical sense to our fellow beings. Shantideva followed these Buddhist beliefs.
Much of the actual life story of Shantideva is mixed with tales and legends of a mythical quality involving levitation, appearance and disappearance, personal manifestations and performance of miracles. In today’s context these accounts seem sensational, but when put into context of religious texts written in the first millennia CE (Christian and Muslim) this is not unusual. But, importantly, we know of the life of Shantideva because of his major work “The Way of the Bodhisattva” which it is claimed he recited in one sitting. Through these writings we can understand his views on Buddhist ideals and views on compassion.
By way of contrast much more is known about the life of western philosopher Arthur Schopenhauer (1788–1860). Schopenhauer was a German philosopher who had multiple published papers, essays and books throughout his lifetime detailing his views on philosophy and compassion. But like Shantideva, it can be problematic looking at Schopenhauer’s life and works through today’s cultural lens, as he is now thought of as anti-Semitic and misogynistic. That said, Schopenhauer did not wish to be remembered for his actions or lifestyle, rather than his words. The connection between Shantideva and Schopenhauer, however, can be established, in so much as we know from Schopenhauer’s writings and possessions about his key interest in Eastern philosophy and religion, in particular Hinduism and Buddhism, eventually self-identifying as a Buddhist. This last point is endorsed in his own published work, noted in the book “The World as Will and Representation” (1818).
A key comparison between the thoughts of Schopenhauer and Shantideva is their thoughts on suffering being universal, inclusive and inescapable. Although a universal Buddhist principal, Shantideva’s beliefs being of the Mahayana stream are aligned to not only the understanding and the relief of suffering, but through compassion, sharing the emotion. Schopenhauer aligned his thoughts on suffering to the first two noble truths of Buddhism – all life is suffering and this suffering is caused by trying to escape from the suffering through distraction and desires (although Schopenhauer puts it in terms of the futility to escape striving). This comparison on universal suffering is also reinforced with the shared Buddhist belief of “no self”. Schopenhauer held the view that further to escaping the futility of striving, if one believes in “self” then they will not escape suffering, because a person will put their individual needs before others leading to the detrimental promotion of ego. Shantideva is very unequivocal on the point of no self, and states there is no difference between his suffering and the suffering of others when he writes ‘Suffering has no “possessor,” therefore, no distinctions can be made in it. Since pain is pain, it is to be dispelled. What use is there in drawing boundaries?’ Hence there is no possible hierarchy between individuals.
Schopenhauer parallels the Buddhist’s third and fourth noble truths with a three-fold approach to enlightenment and the cessation of suffering, one of which involves immersing oneself in the pursuit of compassion for others, a promotion of an altruistic lifestyle and being morally aware. But the link and parallel to Shantideva is further exhibited if we study what Schopenhauer was referring to in this approach, in that leading a moral and altruistic life by definition leads to a selfless and charitable life full of the compassion for others – the two things cannot be mutually exclusive. This leads Schopenhauer to a circular or self-supporting argument, in that in order to understand how others act morally through auteurism, we must act altruistically ourselves, and this understanding of ourselves through the understanding of others leads to compassion for others by sharing their suffering. So here the parallel with Shantideva is strengthened – if we share the suffering of others by feeling the sadness and pain they feel, as if it were our own, then compassion will bring us to the point of acting to alleviate their suffering as if it were our own. Compassion can be seen as the trigger for activity (not the passivity of sympathy or pity).
Moreover, we can understand this push towards “active” compassion from both Schopenhauer and Shantideva from a perspective of motive, ie. what is driving the action? In both cases, it is not a rational choice, nor a balanced judgement on the right course of action, rather it comes from an emotional feeling, and this emotion leads to compulsion to act. So Shantideva and Schopenhauer both feel compassion and act compassionately through the desire and need to alleviate the suffering in others, not to make themselves feel good, or simply because it is the right and moral thing to do. But does desire become confused with duty? It could be argued that Shantideva’s compassion is more dutiful as it sits inside a wider religious doctrine rather than a purely autonomous philosophical belief.
However, if the focus is solely on the motive, on the process, on the emotional attachment to the sufferer, on the lack of “self”, and on auteurism that both Shantideva and Schopenhauer both seem to concur, then it may well be possible to miss the outcome of compassion in which they appear to differ. For Schopenhauer the outcome or result of the act of compassion is not a positive experience, as at best it leads to serenity, but for him it highlights or reinforces the futility of the struggle of life itself which many could read as a negative experience. Thus Schopenhauer would describe himself as a pessimist. Shantideva, on the other hand, sees compassion as a positive experience, and through compassion it is possible to escape from sorrow and negativity – ‘Thus for everything that lives, As far as are the limits of the sky, May I be constantly their source of livelihood, Until they pass beyond all sorrow’ (Shantideva Verse 22). But to infer that Shantideva finds this merely a mildly positive experience would be underplaying his true beliefs, as elsewhere in his writings he states the joyfulness that can be gained through compassion – ‘The ocean-like immensity of joy Arising when all beings will be freed, Will this not be enough? Will this not satisfy? The wish for my own freedom, what is that to me?’ (Shantideva Verse 108). This is very different from the thoughts of Schopenhauer who writes ‘The will now turns away from life; it shudders at the pleasures in which it recognizes the affirmation of life’.
The further contrasts between the two sets of beliefs are less apparent. Schopenhauer appears to suggest that compassion is just a step or road marker on a route-map (albeit an important one) to the discovery and attainment of “no self”, whereas Shantideva sees this as the ongoing route to wisdom and nirvana. Indeed it could be said that Schopenhauer only sees that compassion is a transitory life phase as he writes ‘His will turns about; it no longer affirms its own inner nature […] but denies it. The phenomenon by which this becomes manifest is the transition from virtue to asceticism’. Asceticism in this context is a purposeful withdrawal from sensual pleasures and emotions in order to obtain a spiritual calmness, and can often lead to living the life of a monk. The denial of pleasure and emotion necessarily will lead to the cessation of compassion. This leads on to a linked, though supported, argument that Shantideva looks at the universality of cessation of all suffering as a goal in compassion rather than the alleviation of suffering in individuals as a salve for the cessation of suffering in one’s self.
Another crucial difference may be seen in the way the two men describe and view compassion as a virtue isolation. Shantideva can be seen to regard compassion more wholistically, in respect that compassion sits in a suite of other virtues. When commentating on Shantideva, Carolyn Price writes that ‘compassion does not operate on its own, but in cooperation with other virtues: hope, courage, self-confidence and joyfulness’, whereas Schopenhauer writes about compassion very much in isolated and ring-fenced virtuous terms.
As a closing point it is worth noting that the way Schopenhauer and Shantideva lived their lives was very different. The former did not live the compassionate lifestyle that he proposed in his in writings, whereas, the latter certainly did. As already discussed, Schopenhauer did not see any hypocrisy in not living by his words, but one might judge his views on compassion as somewhat more theoretical and untested (certainly by himself), whereas the compassion of Shantideva has been put in practice throughout the centuries by many generations of his followers.
In conclusion the comparisons between the views of Schopenhauer and Shantideva on compassion are centred on the shared experienced of suffering, the desire and duty to relieve suffering, and the promotion of “no self”. They differ in the areas of the purpose and outcome of compassion (in relieving suffering), and in the universality of all suffering with the continual need to pursue a life of compassion, hence inheriting a positive emotional outcome as a product of the deed. The reasons behind their views differing can be put into the context of where and when they lived, their lifestyles and how they lived, how they perceived the purpose of their lives, and fundamentally the schisms, parallels and cross-overs between religion and philosophy. | https://the-sage-page.com/buddhism-and-the-philosophy-of-compassion/ |
Aiming to build a more sustainable residential development, the City of Port Phillip investigated the incorporation of alternative water sources for internal use within the proposed Balaclava community housing project. These alternative water sources included rainwater collected from rooftops, stormwater collected from paved surfaces, and greywater from bathroom sinks, showers, baths and washing machines.
From a technical perspective the collection, treatment and distribution of the proposed alternative water sources was feasible. However significant uncertainty surrounded issues such as quality, regulation and indoor use of these alternative water sources.
The Project
The City of Port Phillip gained funding through the Smart Water Fund to identify regulatory gaps and risks associated with using alternative water sources in a community housing project. This project acts as research and a feasibility study.
Government and industry professionals assessed risks associated with alternative water sources and other issues including collection, storage, treatment and appropriate end use.
The project was originally designed as a demonstration site collecting and treating stormwater, greywater and rainwater for re-use in toilets, showers and washing machines.
The absence of regulatory guidance, water quality knowledge and risk awareness, particularly relating to stormwater and greywater recycling, meant that the demonstration aspects of the project were amended.
Lessons Learnt
The project identified a need for greater regulatory guidance in utilising alternative water sources in residential developments, particularly for stormwater. More work needs to be done to determine stormwater quality and risk factors associated with various stormwater catchments and end use to receive broad re-use acceptance from Department of Human Services and EPA Victoria.
The Benefits
This project illustrates the potential for substituting recycled stormwater, greywater and rainwater in place of drinking quality water. Collecting and recycling stormwater and rainwater can reduce destructive peak flows and contaminants entering waterways during heavy rains. Reusing greywater reduces the load on the sewage system and the marine environment. "This project helps identify gaps in regulation, knowledge and accountability that need to be addressed in order to realise the water saving potential of residential development projects," said Gary Spivak, Housing Development Officer, City of Port Phillip. | https://waterportal.com.au/swf/projects/item/133-lessons-for-development-industry-city-of-port-phillip-balaclava |
In December 2015, representatives of governments from around the world will meet in Paris to discuss the terms of a legally binding global agreement for action on climate change. This meeting represents the 21st Session of the Conference of Parties (COP21) to the United Nations Framework Convention on Climate Change (UNFCCC), which is the current global arrangement for collective state action on climate change. The ultimate aim of this arrangement is to prevent human interference with the climate from bringing about dangerous levels of climate change. With this end in mind, the purpose of COP21 is to get states to commit to some sort of legally binding agreement on climate change that will come into force in 2020.
Given that climate change is now largely undisputed and a central priority of the global political agenda, COP21 has become the most significant and highly anticipated conference on climate change to date, drawing public attention and inspiring political discussion around the world. As questions over the science of climate change have faded, the urgency of the action needed has become startlingly clear. The result is that COP21 in Paris is now seen as a ‘make or break’ opportunity for world leaders to act. Provided a new agreement arises in Paris, there will be continued discussions over the final details of this agreement in the coming years. This is just the start of the process towards a comprehensive agreement.
But looking back at previous COP meetings throughout the history of the UNFCCC leaves little room for optimism over the chances of a meaningful agreement arising in Paris. Since its creation over two decades ago, the UNFCCC has brought about little in the way of meaningful action on climate change. Instead, there is an alarming disjuncture between what’s collectively required to avoid dangerous climate change and what action has actually been taken so far by individual states, leading to much political, academic and public debate, not only about how to instigate action within the UNFCCC, but also whether it is a suitable forum for addressing climate change at all.
Some authors attribute the lack of action in the UNFCCC to a perceived lack of fairness among its participants, which in turn has created a political stalemate as parties argue over intractable positions. In response to this challenge, many philosophers and political theorists have considered what’s fair in relation to climate change. Traditional discussions of fairness in the UNFCCC focus on distributive aspects, which relate to the fair distribution of costs and benefits. Climate change is a both a global and an intergenerational problem for which there is much at stake. Many of those who will experience the very worst effects of climate change will have had little responsibility for bringing it about. There will be many winners and losers in the years to come. As a result, there has always been a strong divide in the COP negotiations between poorer nations, who demand more action from those that have historically caused climate change, and the rich, who expect greater action from rapidly developing economies.
Little, however, has been said about procedural fairness in relation to the UNFCCC, which concerns the way that decisions are made. If distributive fairness relates to the costs and benefits that arise from the actions of the UNFCCC, procedural fairness concerns how decisions about these actions are made. In fact, very little has been said about the procedural rules of the UNFCCC at all. Many of its procedural rules have not yet been formally adopted, operating instead on an ad hoc basis. In particular, the UNFCCC has not yet adopted any rules over voting, with the result that decisions are made by consensus, which allows a single party to obstruct action even if there is agreement among the rest of the group. This has lead to both stalemate and outcomes that consistently reflect the ‘lowest common denominator’ where ambition and leadership is desperately needed. Further, procedural fairness is not just important in its own right, but also because it can provide a way of reaching agreement amongst those who disagree over distributive issues. Given the stalemate that exists in the UNFCCC and the urgent need for action on climate change, a review and analysis of the UNFCCC’s procedural rules is long overdue.
To this end, this book identifies which rules should govern the decisions of the UNFCCC. In specific, it develops a set of rules so that the decisions of the UNFCCC are made in a fair way. As such, this book isn’t about what should be decided in the UNFCCC, but rather how its decisions should be made. I argue that if a decision is made in accordance with these rules, then an agreement will gain long-term support and endorsement. In doing this, I also show that, on account of its universal membership, the UNFCCC is the only appropriate forum for international action on climate change. This book therefore makes a twofold contribution to the debate preceding the UNFCCC COP21 meeting in Paris 2015 and its aftermath in the years to come; first, by determining several practical policy measures for instigating action on climate change and second, by arguing that states should continue to support international action on climate change within the UNFCCC. It does this by linking analytical political philosophy with applied public policy. Given the growing academic and political debate taking place on the future of the UNFCCC, and the need for policy guidance at a practical level, the book provides an important contribution to an otherwise neglected issue area that will be of interest to both academics and practitioners working in the field, including state delegations, NGOs, and international organisations. What’s more, many of the arguments in this book will apply to other multilateral agreements to address climate change. Its recommendations will not only guide the UNFCCC in the immediate years to come, but also action on climate change in many other forums.
The book ultimately develops several practical policy measures for the design of the UNFCCC. It does so in four steps. First, it considers the various principles of distributive fairness that have been advocated in the UNFCCC and shows that, not only is there disagreement over what is fair in this context, but also that there is reasonable disagreement over how the costs and benefits of climate change should be fairly distributed. This is important because it means that deliberation and discussion is unlikely to bring about an agreed outcome. Second, having shown this, the book then argues that procedural fairness is an important way of reaching a mutually acceptable outcome when there is reasonable disagreement over how to distribute costs and benefits. As a result, the current use of consensus-based decision-making is partly responsible for the political inertia in the UNFCCC and there is a consequent need to revise its procedural rules.
Third, the book develops several principles that should govern the decision-making processes of the UNFCCC, including principles governing who should participate, the terms on which decisions should be made, what voting method should be used, and how actors should bargain. It does this by analysing principles of procedural fairness and considering how they can be applied in the context of climate change. Finally, it argues that the UNFCCC is the only appropriate forum for addressing climate change at the global level. It does this by arguing that procedural justice is a fundamental part of any effective climate change agreement. Drawing on the earlier arguments, the book suggests that procedural justice requires that a fair climate agreement have universal representation. Given that the UNFCCC is the only forum that provides universal membership, it is the only appropriate forum for effectively addressing climate change. As such, the book serves as both an academic study of procedural justice and climate change as well as a guide for policy-making for international cooperation on climate change.
1.2 Climate Change and the UNFCCC
The fact that the earth’s climate is undergoing fundamental changes due to human activity is now undisputed (UNFCCC 1992; IPCC 2007, 2012; Stern 2007; Garnaut 2009). The Assessment Reports of the Intergovernmental Panel on Climate Change (IPCC) are the most comprehensive studies to date on climate change and the impacts that it has on human interests.1 The most recent of these, the IPCC Fifth Assessment Report published in 2013, represents the most comprehensive study of the climate ever undertaken (IPCC 2013). This report states that climate change is occurring, that this is very likely due to human activity, and that unabated action will result in further climate change (IPCC 2014 Synthesis Report). The potential implications of climate change include severe and irreversible changes to the climate system, which are expected to have extreme consequences for fundamental human interests on a global scale.2 This includes sea level rise and an increase in the incidence of extreme weather events such droughts. It is widely thought that this will threaten basic human rights to food, water, health and shelter and could represent an existential risk to some countries (Caney 2009; OHCHR 2009; OHCHR and UNEP 2012).3
The IPCC also states that climate change mitigation is a global commons problem, for which collective action to reduce emissions of greenhouse gases will provide greater aggregate gains than continued unrestricted emissions (Toth et al. 2001, p. 653; IPCC WG3 TS.4.4). As such, the potential benefits of avoiding severe climate change are expected to outweigh the anticipated costs of achieving this objective (IPCC 2007; Stern 2007; Garnaut 2009).4 This has been reiterated by the Global Commission on the Economy and Climate, a group of experts, commissioned to analyse the economic implications of addressing climate change (the Global Commission on the Economy and Climate 2014).
Given that climate change is a global problem and that no single actor is responsible for a significant proportion of total emissions, achieving climate mitigation is often seen as requiring an international, if not fully global response (IPCC 2001, 2007). The United Nations Framework Convention for Climate Change (UNFCCC) is the existing international agreement for international cooperation on climate change and the Conference of the Parties to the UNFCCC (COP) is the official negotiating forum for collective decision-making in the Convention (UNFCCC 1992).5 This is an international agreement among nation states to cooperate on climate change. The ultimate objective of the Convention, which and has been signed and ratified by 196 states, is to ‘stabilise greenhouse gas concentrations in the atmosphere at a level that prevents dangerous interference with the climate system’ (UNFCCC 1992, Article 2).
The legal instrument of the UNFCCC is the Kyoto Protocol (1997), which puts legally binding commitments on states to reduce their greenhouse gases (UNFCCC 1997). The Marrakech Accords (2001), the Bali Action Plan (2007), and the Durban Platform (2011) are subsequent agreements that have been adopted to continue action through the UNFCCC. Whilst the recent COP15 negotiations in Copenhagen highlighted the limits of the UNFCCC process, the outcome of COP16 in Cancun and COP17 in Durban renewed optimism in its ability to deliver collective action on climate change.6 In particular, COP17 established a second commitment period under the Kyoto Protocol, as well as the Ad-hoc Working Group on the Durban Platform: an agreement to negotiate an agreed outcome with legal force by 2015, which will become operational in 2020. The recent COP18 in Doha (UNFCCC 2012) committed to build on the framework put in place at Durban and this process was reaffirmed at COP19 and COP20 in Warsaw 2013 and Lima in 2014 respectively (UNFCCC 2013; UNFCCC 2014).
Although there is some dispute over what dangerous climate change exactly entails, avoiding dangerous anthropogenic interference with the atmosphere is now broadly seen as limiting global temperature increases to within 2 °C of those before the industrial revolution. The IPCC states that in order to keep a 50 % chance of meeting this target, it is necessary to limit atmospheric concentrations of green house gases to between 480 ppm and 530 ppm, which in turn requires drastic reductions in the overall levels of global green house gas emissions. But little action is taking place to mitigate the activities that cause climate change and the international community has struggled to come up with a collective response to this problem. On current trends, temperature increases could exceed 4 °C by the end of this century, which would lead to extreme and irreversible impacts (Global Commission on the Economy and Climate 2014). Some think that the lack of action achieved by the UNFCCC requires a major reassessment is needed of the current focus to implement action through the UNFCCC. It would be more worthwhile pursuing international action in other international forums and to focus attention elsewhere.
There are many other multilateral arrangements that coordinate cooperative action on climate change where it might be much easier to stimulate action.7 These are agreements amongst limited numbers of states to address climate change, including traditional international institutions that are now incorporating climate change into their mandates, such as: the Group of Eight Industrialised Countries (G8), the Group of Twenty (G20) and the UN Security Council. Given that the G8 and G20, as well as agreement set up to specifically address climate change such as the Major Economies Forum on Climate Change and Energy (MEF).8
There are also many arrangements between state and non-state actors at the international and national level.9 Examples include the Netherlands Voluntary Agreement on Energy Efficiency and the Australia Greenhouse Challenge Plus Program (Gupta et al. 2007, p. 761). National laws and policies are also critical areas of climate policy (Levi and Michonski 2010). For this reason, some authors argue that power over collective action for climate change is increasingly located beyond the intergovernmental system (Kingsbury et al. 2005; Pattberg and Stripple 2008; Biermann et al. 2009; Biermann 2010; Corbera and Schroeder 2011). Others argue that climate change politics is decentralised, or ‘fragmented’, reflecting the multiplicity of actors and power relations that exist beyond the traditional interstate system (Biermann et al. 2010). As such, the failure of centralised approaches to action on climate change, and the increasing prevalence of alternative forms of cooperation, has lead some to suggest that action might be better pursued in forums outside of the UNFCCC (Prins and Rayner 2007a, 2007b; Grasso and Timmons Roberts 2013).
These different international arrangements aren’t mutually exclusive, and many work alongside one another. However, focusing international efforts to address climate change in one arena does limit the resources that can be put into achieving outcomes in other areas, so there are tensions between these different forums for cooperation. For one thing, the UNFCCC can be perceived as the overall institution that should deliver action on climate change, so waiting for a top down agreement to arise may prohibit action in other areas as states anticipate action to come about. The costs of the annual COPs aren’t insignificant either. Given what’s at stake, the lack of action active by the UNFCCC thus far, and the emerging diversification of alternative arrangements for international cooperation, it’s worth considering whether the UNFCCC is still the most appropriate forum for addressing climate change.
1.3 Guiding Principles for International Cooperation on Climate Change
In light of the different institutional arrangements and institutions that exist in relation to climate change, a number of authors have evaluated the UNFCCC and proposed options for its reform.10 Many of these evaluations and proposals are based on implicit assumptions about the normative desirability of different arrangements and the role that they should play. The IPCC Fourth Assessment Report defines several principles and criteria that can be used to either evaluate existing cooperative arrangements or guide their design (IPCC 2014). Typically, the overall desirability of an institution relates to its performance, or ‘effectiveness’ in reaching an overall objective (for example, achieving climate stabilisation). But many refer to other normative criteria when making proposals about climate institutions, including justice, legitimacy, and economic efficiency.
The literature on climate change typically divides normative criteria into two categories: substantive criteria, which relate to the outcomes of an institution, and procedural criteria, which relate to the processes that generate these outcomes. These criteria are interlinked, in the sense that they can either complement and conflict with one another in different situations. For example, an institution that achieves economic efficiency may not yield the best environmental outcome (Philibert and Pershing 2001). On other occasions they are mutually supportive; an institution that is neither equitable, nor politically feasible, is unlikely to achieve its goals (Rajamani 2000).
Substantive criteria can also relate to the procedural design of an institution, just as procedural criteria can be matters of substantive concern. For instance, it might be desirable to design an institution that achieves a substantive end, such as economic efficiency. This involves ensuring that the outcomes of the agreement are those that minimise the economic cost of the agreement. But it also involves designing the procedural aspects of the institution so that these minimise the economic cost of the agreement as well. This might involve designing procedures that minimise transaction costs, or that do not place high information costs on participating actors. In this instance, a substantive normative criterion has implications for the procedural design of the institution. Consequently, whilst a distinction can be made between procedural and substantive criteria of institutional design, this does not limit the aspects of institutional design that each type of criterion applies to.
Further, some of the criteria proposed here have both procedural and substantive elements. For instance, the criterion of legitimacy, which is defined and discussed in the following section, has elements that govern both of these criteria. Separating these elements is common in the literature on institutional design. For example, Fritz Scharpf has labeled these ‘input legitimacy’ and ‘output legitimacy’, which respectively relate to procedural and substantive elements (Scharpf 1999). Both Thomas Franck, and Buchanan and Keohane also make a distinction between these two features of legitimacy (Franck 1995; Buchanan and Keohane 2006). The reason for separating such criteria into their substantive and procedural components, even when some of these criteria concern both of these dimensions, is to show that, in certain cases, they matter to both process and outcome. This is something that is sometimes overlooked in the literature. I separate these two features to demonstrate that one can focus on the procedural aspect of legitimacy irrespective of the substantive ends that it brings about.
Substantive criteria relate to the outcomes that are brought about by the institution. These criteria are important regardless of the process through which they arise. For instance, one might argue that achieving important ends such as avoiding dangerous climate change is the most pressing concern at the moment and that it doesn’t matter how this end is actually achieved, so long as this goal is reached. The literature on multilateral climate change institutions often refers to five substantive criteria for institutional design: effectiveness; justice, or equity; efficiency, or cost-effectiveness; legitimacy; and political feasibility.11 These criteria are valuable in themselves, but they are also interdependent and interlinked.
Effectiveness relates to the extent to which an institution meets its intended objective (Höhne et al. 2002, p. 33). In the case of climate change, this is typically defined in terms of meeting an emissions target or achieving certain adaptation goals. For example, the primary objective of the UNFCCC is to stabilise greenhouse gas concentrations in the atmosphere at a level that prevents dangerous interference with the climate system (UNFCCC 1992, Article 2). This is often proposed as the primary objective of any international agreement, and many authors advocate secondary principles that are instrumental to achieving this end. For instance, some argue that a high level of participation is a fundamental criterion of institutional design for climate change policy (OHCHR 2009, p. 23; Hare et al. 2010; Bosetti and Frankel 2012). Others claim that compliance and enforcement are essential elements of a multilateral climate change agreement (Barrett 2003; Barrett and Stavins 2003; Victor 2006). However, to a large extent, participation and enforceability are only desirable insofar as they are instrumental towards achieving emissions reductions or some other end.
In addition to effectiveness, there are three further substantive principles that are often given as guiding principles for climate policy: efficiency, legitimacy and distributive equity. Efficiency dictates that the economic costs of addressing climate change are minimised (Gupta et al. 2007, p. 750). Broadly speaking, a legitimate institution is one that has both the right to govern as well as a level of support amongst those on whom it imposes power (Franck 1995; Dingwerth 2005; Bodansky 2007). Distributive equity relates to both justice and fairness and concerns how the relative benefits and costs of climate change should be distributed amongst states. There are other elements of equity that are important in relation to climate change, including intergenerational equity, or intranational equity. However these elements are beyond the scope of this book. Further, whilst equity, justice and fairness sometimes have different meanings in different contexts, this isn’t such a concern for the content of this book. Here, following the convention of much of the literature on this subject, I use these terms interchangeably.12
But the design of a multilateral climate change agreement is not simply a matter of promoting certain substantive outcomes: procedural values also have a role to play here. Procedural values are those that relate to how an outcome is reached, regardless of what that outcome actually is. When thinking about climate change, this concerns the design of decision-making processes that determine outcomes, which are the institutional procedures for making collective choices (Krasner 1982, p. 186).
There are two procedural normative criteria that are of particular concern for institutional design: procedural efficiency and procedural justice. On the one hand, procedural efficiency relates to the ability to actually make a decision. That is, it concerns how issues such as how easy it is for a group to agree on something. There are various proposals for facilitating decision-making in multilateral climate change institutions, including:
Procedural justice, on the other hand, concerns whether the means by which an outcome is reached is fair regardless of what the outcome actually is (Banuri et al. 1995, p. 83–5, 117; Rayner and Thompson 1998, p. 319; Albin 2001; Grasso 2007; 2010, p. 4). It relates to who participates in a decision-making process, as well as the fairness of that process. The basis of procedural justice is grounded in different ways according to different theories of justice. Whilst some argue that procedural justice is based on a fundamental duty of equal respect for the opinions of others,17 others claim that procedural justice is important because it enables affected parties to maintain their dignity (Schlosberg 1999, p. 12–13, 90; Paavola 2005, p. 313–4), or that it carries important instrumental value towards meeting other ends (Toth 1999, p. 2).
Whilst many authors acknowledge the importance of procedural fairness, this issue is often overlooked in the literature on climate change, and formal mechanisms to facilitate procedural justice are missing from most policy proposals.18 This is strange given the importance that many place on the value of procedural justice in political institutions generally, as well as in specific relation to climate change. The climate negotiations at COP15 highlighted that the COP is seen as an illegitimate venue for negotiations due to the exclusive nature of its decisions. At these negotiations, Venezuela, Cuba, Nicaragua and Bolivia all renounced the Copenhagen Agreement on procedural grounds.19 Others have questioned the legitimacy of the G8 and MEF on procedural grounds, arguing that they exclude key actors and are insufficiently transparent (Karlsson-Vinkhuyzen and McGee 2013, p. 67).
To be sure, some authors argue that there is no intrinsic merit to procedural design and that decision-making processes should be designed with the sole intention of promoting certain desirable outcomes. For instance, Richard Arneson argues democracy should be regarded as ‘a tool or instrument that is to be valued not for its own sake but entirely for what results from having it’ (Arneson 2004). In specific relation to climate change, one might hold that the overall goal of international cooperation should be to avoid dangerous climate change, and that other values should only be taken into account to the extent that they promote this end. According to these sorts of arguments, decision-making processes should be designed to achieve desired outcomes, rather than to promote values that are independent of these ends.
But in response to this objection, there are at least four reasons for considering procedural values in the context of climate change. First, as mentioned above, many authors do in fact argue that there is something intrinsically just about the process by which outcomes are reached.20 This view is supported by empirical studies of human behaviour, as well as the claims that arise in the negotiations of the UNFCCC (IISD 2010; Grasso 2010, p. 99; Winkler and Beaumont 2010, p. 640). It seems reasonable to assume that there may be some cases in which the process is valued independently of the outcome achieved.
Second, the absence of procedural justice in the UNFCCC has contributed to its political deadlock. Despite several unsuccessful attempts to adopt rules for voting and broader decision-making, the Parties of the COP have so far failed to agree on its procedural rules, meaning that the COP continues to rely on the draft rules of procedure, which do not specify a voting procedure.21 Consequently, decisions are made by consensus, leading to ‘lowest common denominator’ outcomes, and blocking tactics within negotiations (Prins and Rayner 2007b).
Third, as I show in Chap. 2, climate change is an issue that is characterised by reasonable disagreement over substantive values. This means that no single answer is likely to gain the support of actors, even if they are arguing about the common good, and in good faith. I show that procedural justice is instrumentally important because it allows us to reach a mutually acceptable outcome when there is reasonable disagreement about substantive ends. In Chap. 8, I go on to argue that procedural justice is still important even if people give up on a comprehensive agreement for climate change.
Fourth, climate change is characterised by extreme uncertainty, and this makes it difficult for actors to reach agreement on the substantive outcomes of climate institutions. Some authors argue that, when outcomes are uncertain, actors put an emphasis on the quality of the procedure, over substantive outcomes (Toth 1999, p. 2; Foti et al. 2008). For this reason, procedural justice is an important precondition to creating and operating climate institutions.
Regardless of what one thinks about the intrinsic value of procedural justice there are good reasons for thinking about the procedural fairness of the UNFCCC and climate policy more generally. In fact, one of the central arguments of this book is that procedural justice is a fundamental element of effective climate change institutions. This book develops this idea further and uses it to develop a set of principles for fair decision-making in the UNFCCC.
1.4 Literature Review
Before explaining how this will be done, it’s worth reflecting on the existing literature on procedural justice and the UNFCCC. Whilst there is a great deal of research on the role of justice and morality in climate change, many of these studies almost completely overlook procedural justice. Theorists and philosophers have examined issues of fairness and justice extensively since climate change became a matter of political concern.22 Debate has largely focused on: which principles should guide the distribution of the benefits and burdens of climate change; the fair distribution of emission rights; what rights and duties people have regarding climate change; and, to a limited extent, fair adaptation to climate change. Whilst many authors acknowledge that procedural justice is an important issue in this area, few political theorists have taken up this question.
There has, however, been a recent ‘procedural turn’ in the literature on multilateral governance, as authors have turned their attention to issues of inclusiveness and transparency (Bäckstrand 2006, p. 467; Bäckstrand 2010; Dryzek and Stevenson 2011, 2012b; Stevenson 2011). There is growing consensus in both the academic and policy literature that principles of ‘good’ governance should apply to decisions in international organisations. Core elements of good governance include: transparency, participation, accountability, and the review and refinement of policy choices over time. Other studies specifically consider the fairness of international negotiation processes (Albin 2003, p. 13; Chasek and Rajamani 2003), often suggesting that the effective representation of all stakeholders and the impartial consideration of all claims are necessary conditions for fair negotiations, or that parties should have more equal starting positions in terms of negotiating capacity.
This procedural turn in literature on multilateral governance is reflected in the gradual accommodation of procedural matters in the treaty texts and constitutions of several multilateral institutions. For example, the Aarhus Convention on Access to Information, Public Participation in Decision-Making and Access to Justice in Environmental Matters (1998), which assign rights to information, participation and accountability in environmental decision-making.23 Authors increasingly recognise that democratic values, such as representation, deliberation and inclusion are becoming common elements of the rhetoric of many other multilateral institutions (Bäckstrand 2010, p. 670).
These values are typically underpinned by a substantive right to live in an environmental adequate for health and well-being. Alternatively, they are advocated as instrumental values for the achievement of other ends. For instance, Karen Bäckstrand argues that the institutional effectiveness of environmental governance mechanisms is tied to procedural values such as representation, participation, accountability and transparency (Bäckstrand 2006, p. 468). As such, the promotion of these democratic values is instrumental towards achieving substantive ends, rather than intrinsically valuable. These studies often consider multilateral institutions more generally, rather than climate change institutions in specific. Whilst climate change institutions are a part of multilateral institutions more generally, there are also many important differences between climate change institutions, and other environmental agreements. Therefore, despite this procedural turn in environmental governance, more attention is needed on the procedural design of the UNFCCC.
Whilst specific references to procedural justice are often absent from the literature on climate change, this is not to say that procedural justice has not featured in the analysis of institutions that share many of the features of those that concern climate change. An example of this is the broad literature on the ‘democratic deficit’ that exists in global institutions.24 Following the increased interdependence of the new global order, there has been a revaluation of several notions of legitimacy and democracy in international politics. This reflects the idea that there is now a high level of interdependence between individuals in different countries, and that a democratic deficit has arisen due to the ‘transfer of decision-making authority away from nation states towards a variety of unelected or unaccountable international bodies’ (Bodansky 2007). As a result, many argue that greater levels of inclusion should take place in the decision-making processes of international institutions,25 or that there should be greater means through which accountability can be exercised in international institutions.26 The areas of transnational democracy, cosmopolitan democracy, discursive democracy and stakeholder democracy are all advocated as institutional innovations that reduce the democratic deficit of multilateral institutions in this way (Bäckstrand 2008, p. 79). | https://lawexplores.com/introduction-27/ |
The Port of Coatzacoalcos is an important industrial port and heart of the region’s petrochemical industry. While it is not a well-known tourist destination, it has ample infrastructure and services to support conventions at its Zabludosky-designed convention center and theater. The Port of Coatzacoalcos offers culture, music, and cuisine second to none on Mexico’s eastern shores. The city specializes in preparing delicious seafood.
The Port of Coatzacoalcos’s climate is very comfortable, averaging about 25ºC (77ºF) throughout the year. Rainy season lasts about two or three months, but the rest of the year is full of sun, which is great for sun tanning at the beach. Boat trips and tours in the Bay are available, and the ships with clear bottoms are especially popular.
In a forested landscape with rich plant and animal life, the area around the Port of Coatzacoalcos is an ecological tourist’s dream. Near the city are beautiful parks and other areas with many breathtaking waterfalls. Local native peoples will guide you through this tropical paradise.
The Port of Coatzacoalcos is also in an important historic region. In fact, its name comes from the ancient Olmec culture that thrived here from 1400 to 400 BC. Several archaeological zones are nearby that document the flourishing culture of the ancient peoples. Ten of 17 Olmec heads were found nearby in San Lorenzo Tenochtitlán, and other priceless artifacts were discovered in Azuzul that rival anything found in Egypt. | http://www.worldportsource.com/ports/cruising/MEX_Puerto_de_Coatzacoalcos_259.php |
CA’s Northern Rural Counties’ 135k Recall Signers Are Not ‘Highest Support for Newsom Recall’ as Claimed
5 So Cal counties’ recall signers provided 54% of total valid signatures.
By Katy Grimes, May 8, 2021 10:55 am
The California Secretary of State’s office released a final recall petition report on Wednesday, showing that a total of 1,719,943 valid signatures were verified out of 2,161,349 signatures submitted two months ago – just under an 80% validation rate, the Globe reported Thursday.
“Highest support for Newsom recall comes from California’s rural, northeastern counties, final state numbers show,” KTLA’s headline reported Friday.
Knowing that the population of California’s rural counties is a fraction of the state’s population, this didn’t add up. The total population of Modoc County is 8,635. Plumas County population is 18,939. We aren’t talking numbers large enough to even total 1,719,943. The U.S. Census and state report that just under 1% of the total California population live in rural counties, which makes the KTLA headline dubious.
“Support for the petition to recall Gov. Gavin Newsom is highest in conservative, sparsely populated California counties in parts of the Sierra Nevada and the state’s rural, remote northeast, newly released data shows,” KTLA reported, focused on percentages of registered voters in rural counties.
This statement misconstrues the statistical data.
The article however, starts with noting total recall signatures in the state, as opposed to the percentage of registered voters who signed the recall petition, which is the entire basis of their headline and story:
“The California secretary of state’s office released its final report Wednesday, verifying more than 1.7 million signatures have been certified as valid in the effort to recall the Democratic governor.”
Looking at the number of actual signatures by registered voters in the counties is probably more instructive. The Secretary of State reports:
The top five counties with verified recall petition signatures are:
Orange County: 285,452 submitted, 215, 714 validated
Riverside County: 186,806 submitted, 146, 804 validated
San Bernardino County: 130,382 submitted, 106,475 validated
San Diego County: 238,095 submitted, 179,039 validated
Los Angeles County: 328,224 submitted, 264, 495 validated
The total of these five counties’ verified recall signatures is 912,526, out of the statewide 1,719,943 million – a little under 54% of the total validated recall signatures.
“The sparsely populated California counties in parts of the Sierra Nevada and the state’s rural, remote northeast” may have as a percentage of registered voters had the most support, but the total of those 15 counties is 135,558 verified signatures out of the 1.7 million submitted, as follows:
El Dorado County: 26,777 submitted, 22,103 validated
Amador County: 6,017 submitted, 4,966 validated
Placer County: 58,515 submitted, 45,868 validated
Yuba County: 7,947 submitted, 5,836 validated
Sutter County: 8,269 submitted, 6,544 validated
Butte County: 19,329 submitted, 15,942 validated
Sierra County: 493 submitted, 406 validated
Plumas County: 2,057 submitted, 1674 validated
Lassen County: 3,731 submitted, 2,855 validated
Shasta County: 24,534 submitted, 18,943 validated
Modoc County: 1,221 submitted, 908 validated
Siskiyou County: 6,019 submitted, 4,921 validated
Glenn County: 2,967 submitted, 2,523 validated
Colusa County: 1,821 submitted, 1,537 validated
Tehama County: 6,713 submitted, 5,207 validated
The total of those 15 rural counties is 135,558 verified signatures, of the 1.7 million total verified. This isn’t even 10% of the 1,719,943 million total validated signatures – it’s a little under 8% of the state’s recall petition signatures.
While percentage of registered voters is a valid measurement, is should be with context.
Could KTLA’s headline be in search of a story? “Highest support for Newsom recall comes from California’s rural, northeastern counties, final state numbers show.”
It isn’t until the 10th paragraph the KTLA article addressed the percentage of California’s registered voters who signed the recall petition: “In the end, more than 1.7 million valid signatures from registered voters were counted. That’s nearly 7.8% of the state’s more than 22 million voters.”
What’s the point of the article? The headline is supposed to tell the story, rather than the data. The rural counties provided a little less than 8% of the recall signatures (In line with the total registered voters who signed the recall), while the five southern California counties provided more than half – nearly 55% — of the valid recall signatures.
When the numbers do the talking, we see the bigger picture.RECALL newsom-heatlie-final
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11 thoughts on “CA’s Northern Rural Counties’ 135k Recall Signers Are Not ‘Highest Support for Newsom Recall’ as Claimed”
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Very glad to see this effective counter-punch to KTLA’s attempted spin. As you probably know, KTLA, once a fine local news station, is now joined-at-the-hip to the Los Angeles Times, which is itself joined-at-the-hip to continuation of Gavin Newsom as governor.
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And Gavin Newsom and the LA Times and KTLA are all joined at the hip to the Propaganda of the National Security State and Intelligence Agencies. Has anyone actually looked at the LATimes New Owner and his intelligence ties and financial conflicts in Puerto Rico and with CIA fronts?
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Showandtell nails it everytime! I’m a native Californian who bailed to Texas 2 years ago but still and always will read Katy Grimes’ excellent articles regarding California politics. My grandparents and most of my native born California family would by appalled with the current political situation of our magnificent state even though the majority were democrats.
So grateful for the California Globe and its followers. The Golden State has been STOLEN by low information idiots but it will be restored to sanity with time and the persistence of thinking individuals of all races and backgrounds. Carry on my brothers and sisters of “The crown jewel of the new dispensation”….Mark Twain
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D Carmi: As we used to write on postcards, “Having a wonderful(?) time, wish you were here!”
But I can well understand why you and many others either cannot or will not stay in California in these terrible times. Very best wishes to you.
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Nice push back on the data manipulation to support their narrative – that the recall effort is just a product of Trump supporters.
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That is a pathetic comment…. This has nothing to do with Trump… Get over it… If you cannot see what is going on with this once great state, you are part of the problem.
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Stupid, hateful, lying liberals thought this was some sort of insult. I am proud to live in a rural area and to have signed to recall Noisome the goobenor.
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CW: This seems like an offshoot of the “deplorables and unredeemables” nonsense that Newsom and his hangers-on themselves manufactured out of whole cloth. But really, what do they have if they don’t have their fake narrative of mocking the Recall by demonizing their made-up stereotypes?
I also think this dishonest KTLA spin is a way to divert attention from the unexpectedly huge number of Recall signers in L.A. County, which is thought to be majority Dem and thus automatic (they think) Newsom backers. But is L.A. County a slam-dunk to retain Newsom? It doesn’t look like it. Not at all.
Speculation: There are 88 municipalities in L.A. County, many of which absorbed new U.S. citizens over many years and most may be registered Democrats for a number of reasons, not least because Dem politicians promised and doled out goodies to new immigrants in hopes of buying their votes. Probably many who then became citizens have since wised up as they noticed their new country becoming like the one they left. Thus many LEGAL immigrants, now citizens, although technically registered Democrats, don’t vote “D”. Add to that the plenty of other Democrat voters who are also fed up with Newsom and want him gone.
Good thing Katy Grimes did this analysis. Otherwise the KTLA fake headline and brightly-colored map disinformation would have gone unanswered.
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There are lies, there are damned lies and then there’s the media.
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I think that some of these rural petition gathering efforts have a genuine grassroots aspect to them. I love rural California – the people are wonderful, and California’s natural landscape is incomparable. I wish the state would go back to the constitutional design that was destroyed in Reynolds v. Sims where each county had equal representation in the Senate. That way, there would be a real balance to legislation, and you wouldn’t need Prop 13.
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Neanderthals, Love Ya
Unfortunate, all the moochers in urban hell holes think otherwise….they will quickly feel…..inflation and kitchen table scarcities …… far far more punishing than being only “donut rich”. | https://californiaglobe.com/articles/cas-northern-rural-counties-135k-recall-signers-are-not-highest-support-for-newsom-recall-as-claimed/ |
NEW YORK (Reuters Health) - Staying connected with family
and friends may delay memory decline among the elderly, new
research confirms.
"Our results suggest that increasing social integration may
be an important component of efforts to protect older Americans
from memory decline," Dr. Lisa F. Berkman from the Department
of Society, Human Development, and Health at Harvard School of
Public Health, Boston and colleagues conclude in a report in
the American Journal of Public Health.
They looked at the impact of social integration on changes
in memory over 6 years in 16,638 Americans aged 50 and older
enrolled in the Health and Retirement Study. Memory was gauged
by immediate and delayed recall of a 10-word list, and social
integration was assessed by marital status, volunteer activity,
frequency of contact with children, parents, and neighbors.
The average memory score declined from 11.0 in 1998 to 10.0
in 2004, the investigators found.
ADVERTISEMENT
People with high social integration and low social
integration had similar memory scores in 1998 but that changed
over the subsequent 6 years. People who were highly socially
integrated in 1998 suffered slower rates of memory decline over
time than their less social peers. Memory among the least
socially integrated declined at twice the rate as among the
most socially integrated.
"Being in the highest level of social integration
ameliorated more than half of the age-related decline in
memory," Berkman and colleagues state.
These findings are consistent with several prior studies,
all of which found that being socially engaged was associated
with a lower rate of cognitive decline and a lower risk of
dementia, the team notes.
| |
What is meant by recognizing individual differences?
What is meant by recognizing individual differences?
Individual differences are the ways in which people differ from each other. It is important for managers to understand individual differences because they influence the feelings, thoughts, and behavior of employees. Individual differences can be divided into two categories: personality differences. capacity differences.
What is the meaning of individual differences?
Individual differences stand for the variation or deviations among individuals in regard to a single characteristic or number of characteristics. It is stand for those differences which in their totality distinguish one individual from another.
What are examples of individual differences?
Shortness or tallness of stature, darkness or fairness of complexion, fatness, thinness, or weakness are various physical individual differences. 2. Differences in intelligence: There are differences in intelligence level among different individuals.
How do you deal with individual differences?
Amer E.
- Differentiate instruction.
- Capitalize on learning styles.
- Incorporate multiple intelligences into curriculum.
- Capitalize on student interests.
- Involve students in educational goals.
- Use computerized instruction.
- Group students effectively.
- Consider outside placement options.
What makes lumber different from other wood products?
Lumber is a wood product, sawn and shaped from timbers of harvested trees. By its nature, wood is not of uniform consistency and therefore will contain defects that impact the appearance of the lumber that is created from the wood material, and which may impact the structural characteristics as well.
How are the different grades of lumber determined?
Wane: A wane is when there is missing wood or an untrimmed edge along the side or corner of a board. As stated above, the various grades of lumber are determined by the appearance of the wood and the number of defects. These grades are determined by the U.S. Department of Commerce and the American Lumber Standards Committee.
Why is it important to acknowledge individual differences?
It is important to allow for individual differences (e.g. some southerners may not be hospitable) and to acknowledge that the context of the situation also has a great deal of influence on someone’s behavior. For example, I may behave a certain way at a corporate meeting and quite differently when at home interacting with family members.
What’s the difference between No 3 and No 3 lumber?
No. 3 lumber allows for more defects—as long as they don’t go all the way through the wood. Knots are allowed of any quality, as long as they are well spaced. Lumber of this grade has strength and stiffness values that make it suitable for use as a vertical member of a wall. | https://www.handlebar-online.com/usefull-tips/what-is-meant-by-recognizing-individual-differences/ |
The papers of painter and teacher Morton Traylor measure 3.4 linear feet and date from 1936 to 2003. The papers document his career as an artist and administrator of the Virginia Art Institute through biographical material, correspondence, writings, personal business records, printed material, photographs, and scrapbooks. The bulk of the collection consists of photographs, slides, and albums of artwork by Traylor. Three scrapbooks document his education and early career through clippings, photographs, exhibition materials, and letters.
The papers of California art historian, writer, instructor, and curator, Melinda Wortz (1940-2002) date from 1958-1992, and measure 17.45 linear feet. The collection includes documentation of Wortz's tenure at the University of California, Irvine (UCI), where she specialized in collecting and presenting the California "light and space" artists during the 1970s and 1980s. Wortz's papers include biographical information, personal and professional correspondence, interview transcripts and sound recordings, professional and student writings and notes, diaries of five trips abroad, UCI administrative, dossier, and teaching files, general subject and artist files, printed material, several pieces of artwork; and photographs.
The papers of Los Angeles Abstract Classicist painter and educator Frederick Hammersley measure 34.75 linear feet and date from circa 1860-2009, bulk 1940-2009. The papers contain biographical materials, 32 diaries, family and professional correspondence, personal business and financial records, estate records, writings, graphic design projects, teaching files, printed materials, scrapbooks, photographs, and works of art.
The papers of California pop artist and teacher Mel Ramos measure 0.6 linear feet and date from 1959 to 1984. The collection documents Ramos's career as an artist through correspondence with Lawrence Alloway, Dwan Gallery, Roy Lichtenstein, David Stuart, and Tom Wesselman, among others; a few inventories, invoices, and loan agreements; documentation of his work with the San Francisco Art Institute; and exhibition announcements and catalogs. Writings include two manuscripts on Ramos and the Pop Art movement, a one-page interview of Ramos, and poetry by Robin Skelton. Of interest in the collection, are files containing photographs, photo-collages, and clippings used for paintings such as "Elephant Seal," "Virnaburger," and "Manet's Olympia."
The papers of sculptor, painter, jewelry designer, and teacher Claire Falkenstein measure 42.8 linear feet and date from 1917 to her death in 1997. There is extensive correspondence with fellow artists, collectors, critics, friends, museums, and galleries. The collection also contains biographical materials, much of it collected and organized by Falkenstein, personal and business records, writings, diaries, exhibition files, commission files, teaching files, photographs, original artwork, scrapbooks, and printed materials. There is a short motion picture film of an interview with Falkenstein featuring the windows she designed for St. Basil's Church in Los Angeles.
The Molly Saltman "Art and Artists" interviews measure 2.4 linear feet and contain 62 sound recording interviews and lectures with art collectors, teachers, actors, and artists. The interviews were conducted by Molly Saltman from 1966-1967 as part of the "Art and Artists" radio series broadcast on the KPAL radio station in Palm Springs, California. Several of the interviews and lectures consist of more than one reel.
The records of the Woman's Building feminist arts organization in Los Angeles measure 33.4 linear feet and date from 1970-1992. Originally founded by artist Judy Chicago, graphic designer Sheila Levant de Bretteville, and art historian Arlene Raven in 1973, the Woman's Building served as an education center and public gallery space for women artists in southern California. The records document both the educational and exhibition activities and consist of administrative records, financial and legal records, publications, curriculum files, exhibition files, grant funding records and artist's works of arts and prints. A significant portion of the collection documents the Women's Graphic Center, a typesetting, design, and printing service operated by The Woman's Building.
The papers of ceramicist and educator Laura Andreson measure 1.9 linear feet and date from 1932 to 1991. The collection is comprised of correspondence, professional files, gallery records, writings and notes, artwork, and photographic materials that document her pioneering work in ceramics.
The Mabel Alvarez papers measure 2.3 linear feet and date from 1898 to 1987. The papers include scattered biographical information, scattered letters, unpublished prose, printed materials, sketchbooks, expense books, notebooks, diaries and journals, address books, photographs, and scrapbooks documenting the life and career of Los Angeles painter Mabel Alvarez.
The papers of Southern California painter Stanton Macdonald-Wright measure 3.2 linear feet and date from 1907 to 1973. The collection contains correspondence with family, friends, and artists, including Morgan Russell, and his wife Suzanne Binon, Michel and Suzanne Seuplor, Ann and John Summerfield, and Bethany Wilson. Also found are writings, six diaries, travel journals, printed materials, and artwork. | https://sova.si.edu/search?q=Art%20teachers%20--%20California%20--%20Los%20Angeles |
The papers of painter Helen DeMott measure 7.9 linear feet and date from 1896-1997. DeMott's painting career from 1940-1996 is documented through her numerous sketchbooks and original artwork. Also found is biographical material, correspondence, writings and poems, scrapbooks, printed material, photographic material, audio and video recordings, and scattered material from collagist Ray Johnson.
The papers of New York City art critic, writer, and lecturer Forbes Watson date from 1840-1967 with the bulk of materials dating from 1900-1960 and measure 13.5 linear feet. Found are biographical materials, correspondence, business records relating to the Arts Publishing Corporation, records documenting Watson's work for the Public Works of Art Project and the Section of Painting and Sculpture, reference files, an exhibition file from the Pepsi-Cola Company's Third Annual Exhibition, writings and notes, ten scrapbooks and loose pages, printed materials, and photographs.
The papers of painter and educator Edwin Ambrose Webster measure 2.7 linear feet and date from 1821 to 1968. Found within the papers are biographical material; business and personal correspondence; writings; teaching and research files, including information on Webster's participation in the 1913 Armory show; printed material; artwork; and photographic materials of Webster, his family and friends, and his work.
Papers of painter Elisabeth Weber-Fulop measure 0.2 linear feet and date from 1921 to 1966. Biographical material, letters, printed material, and photographs document Weber-Fulop's career and artwork.
The papers of Boston area painters Esther Baldwin Williams and daughter Esther Williams measure 2.1 linear feet and date from 1887 to 1984. The scattered papers of both women include biographical information, personal business records, correspondence, writings and notes, two diaries, four sketchbooks, printed materials, photographs, and one photograph album.
The papers of California art historian, writer, instructor, and curator, Melinda Wortz (1940-2002) date from 1958-1992, and measure 17.5 linear feet. The collection includes documentation of Wortz's tenure at the University of California, Irvine (UCI), where she specialized in collecting and presenting the California "light and space" artists during the 1970s and 1980s. Wortz's papers include biographical information, personal and professional correspondence, interview transcripts and sound recordings, professional and student writings and notes, diaries of five trips abroad, UCI administrative, dossier, and teaching files, general subject and artist files, printed material, several pieces of artwork; and photographs.
The papers of art critic, editor, and gallery director Sidney Woodward date from 1823 to 1963, bulk 1915-1932, and measure 3.5 linear feet. The majority of the collection consists of personal and professional correspondence and collected letters that pertain to Woodward's relationships with various artists, galleries, and arts organizations. Also included in this collection are two biographical documents; lecture notes and collected writings; printed material including books relating to the topic of art, exhibition catalogs, and newspaper clippings; a few personal photographs and reference photographs of paintings; and scrapbooks containing newspaper clippings, art reproductions, and printed material from the Casson Galleries.
The Eugene C. Worman research material on William H. Bartlett measures 4.1 linear feet and dates from 1835-1995. The collection reflects Worman's interest in Bartlett's career as an illustrator, and includes material on Bartlett's work and travels, his publisher, George C. Virtue, and the museums and institutions in which his artwork is represented. Records include biographical material, correspondence, notes, writings, articles, printed material, reproductions, photographs, slides, and transparencies.
The papers of art critic and photographer Max Kozloff measure 1.4 linear feet and date from circa 1950-2015. The collection provides a glimpse into the work life of a prolific twentieth century American art critic through biographical material, correspondence with artists and critics, interviews, many unpublished writings, and printed material.
The records of New York City World House Galleries measure 9.8 linear feet and date from 1927 to 1991, with the bulk of them dating from 1953 to 1980. The collection documents the gallery's general business affairs, sales, and relationships with artists from 1953-1968, and later gifts and sales by founder entrepreneur and art collector Herbert Mayer. Artists for which files are found include Jean Dubuffet, Ernst Ludwig Kirchner, Paul Klee and Georgio Morandi, among many others. Additional records include correspondence, inventory records, sales and purchase records, records of gifts and auctions, and shipping and consignment records. | https://sova.si.edu/search?f=data_source%3AArchives+of+American+Art&s=10&n=10&t=C&q=* |
Mean scores for osteoporosis health belief subscales of descriptive studies.
The findings were that women who received the active powder lost only half as much bone as participants taking the placebo. She was previously diagnosed with prolactinoma and had been treated with cabergoline for 3 years.
About mg of calcium is lost daily to breast milk . Node also has a firm belief that the next era of naturopathic medicine will see a resurgence of in-patient facilities which use fasting, earthing, hydrotherapy and homeopathy to bring people back from chronic diseases of modern living; he is involved in numerous conversations and projects to bring about this vision.
Besides, pharmacists are most often thought of as only dispensers of medications. Scale modification included deletion of the subscales of benefits and barriers related to calcium 12 items and exercise 12 items. Articles were also limited to English language.
Although the precise mechanism of action is not completely understood, these agents strongly inhibit osteoclast-mediated bone resorption. Introduction Pregnancy and lactation-associated osteoporosis PLOfirst suggested by Nordin and Roper , is a very rare condition that can cause multiple vertebral compression fractures.
Subjects were required to sign the consent form in order to participate in the study.
Modifying the OHBS and OSES questionnaires to predict other health behaviours related to osteoporosis, such as vitamin D intake and drug therapy initiation would be beneficial in tailoring osteoporosis education interventions for both research and practice.
Because of polycystic ovary disease, she went through menopause at age 38 and, despite years of hormone replacement therapy HRTcalcium supplements, and weight-bearing exercise, she developed osteoporosis when she was still in her forties. It is important to note that only two trials and the one group pretest-posttest study reported results for more than two OHBS subscales [ 141719 ], and only two trials reported OSES subscale scores, highlighting the need for more experimental research in this area [ 1417 ].
The preceding review of the literature suggested that women who have osteoporosis are generally unaware of their skeletal status [ 910 ]. Twenty-two articles met the inclusion criteria.
From the literature search, citations of articles identified as potentially suitable for inclusion were exported to reference software, EndNote X for Windows 7, for reference management. Further, a hypothesis stating that the more severe the perception of severity of and susceptibility to osteoporosis the greater the likelihood of screening in a pharmacy, exhibited a weak positive correlation between perceptions of severity of and susceptibility to osteoporosis and the intention to screen in a pharmacyand, resp.
This lack of recognition can be attributed to the high cost of screening and limited access to bone density measuring devices. Lack of concern and knowledge can be attributed to lower perceptions of susceptibility [ 56 ] and severity of the disease [ 7 ]. Of the intervention studies reviewed, several showed improved outcomes; however, these results must be interpreted with caution.
Mean scores for osteoporosis self-efficacy subscales of descriptive studies. Unfortunately, once you have an osteoporotic fracture, you are at high risk of having another. The 42 items are separated into seven subscales: Men appear to have greater self-efficacy in performing exercise From a lifestyle perspective, Silverstein says things haven't changed all that much.
One study reported that women with knowledge of their own low bone density levels were more likely to change their health behavior to prevent fractures than women with normal bone density levels [ 1112 ].
However, association between the perceptions of susceptibility and screening intentions were not statistically significant Table 3.
People may not know that they have osteoporosis until their bones become so weak that a sudden strain, bump, or fall causes a fracture or a vertebra to collapse. Chervenak says that the gold standard for bone density testing is dual energy X-ray absorptiometry, or DXA, a painless test that takes just a few minutes.
Hip fracturein particular, usually requires prompt surgery, as serious risks are associated with it, such as deep vein thrombosis and pulmonary embolismand increased mortality. In a recent study of more than 7, men and women age 55 and older, 56% of non-vertebral fractures in women and 79% of non-vertebral fractures in men occurred in participants who were not diagnosed with osteoporosis according to the T ≤ cutoff (Schuit et al., ).
In a study whose results surprised even the researchers who conducted it, gardening went a long way to help reduce the risk for osteoporosis among the 3, women age 50 and older involved in the study. 35 rows · The Z-score combined with risk factors, including a history of fragility fracture, is then used.
To assess whether young women who participate in an osteoporosis prevention program based on the Health Belief (Rosenstock, ) and Self-Efficacy Models (Bandura, ) demonstrate higher levels.
Calcium deficiencies in young people can account for a significant difference in peak bone mass and can increase the risk for hip fracture later in life. Surveys indicate that teenage girls in the United States are less likely than teenage boys to get enough calcium. The study enrolled women, aged 50 or more years, to participate in the Oklahoma American Indian Women’s Osteoporosis Study. | https://cuvukopaqe.stylehairmakeupms.com/a-study-of-osteoporosis-in-young-women-49146kr.html |
Department of Landscape Architecture
Dr. Liang-Yi Yen is currently working as a professor of the Department of Landscape Architecture at Fu Jen Catholic University. His areas of expertise include urban planning, urban design, community planning, cultural heritage, urban social movements, and cultural geography. Dr. Yen's concerns of research are mainly with spatial and social justice, and he has integrated research into social engagement. Therefore, his primary research projects in the last decade are all related to major urban issues in Xinzhuang, where Fu Jen Catholic University is located, including preservation movement for Lo-Sheng Sanatorium, construction and operation of Zhong-Gang Drainage Project, Xinzhuang old street preservation movement, and anti-eviction movement of Wenzaizun. As he took part in these official projects or civil movements, he had, on one hand assisted, local residents to formulate movement strategies and advocate public discourse, but also observed and analyzed the development of these controversial events at a closer distance. Given with such context, he is able to investigate the urban politics of Xinzhuang in the 21st century, and further clarify the relationship between urban development, urban planning, and urban social movements in theory.
In addition to themes of urban politics, Dr. Yen is also devoted to studying the relationship between cultural landscape and contemporary society of consumption. In contemporary times, cultural landscape is mostly regarded as an industry that help promote economic development, but it also creates the problems of social exclusion, such as gentrification, forced relocation of indigenous people, and avoidance of uneven distribution of public resources. Over the past few years, Dr. Yen has led graduate students to carry out in-depth investigations into Dihua Street of Taipei, ceramics street of Yingge, Qingjing Farm of Nantou, Dongshan Township of Yilan, and Hongken tulou of Fujian, Shapowei, Xiamen of Fujian, Xikou, Zhejiang, and so forth. All of these efforts are made with the intent as he attempts to appreciate the background of tourism culture from cultural landscape and its impact on the livelihood of local residents, and propose such tourism policies of greater social inclusiveness. | https://spark.fju.edu.tw/content/urban-social-movement-critical-planning |
Rare Minerals Illuminate 17,000-year old Questions
Scientists learned it straight from the bull's muzzle: cave painting shows evidence of ancient trade. In collaboration with French museums and research facilities, Stanford researchers have found evidence of scarce manganese oxide mineral exchange between prehistoric peoples of the French Pyrenees.
The results of their study, concerning the mineral composition of the 17,000-year old "Great Bull of Lascaux" lithograph in Dordogne, France, were published in the November 2006 edition of the 13th International Conference on X-Ray Absorption Fine Structure.
"This cave painting is among the world's oldest and most exquisite," said collaborator and Stanford Synchrotron Radiation Laboratory (SSRL) researcher and Faculty Chair Gordon Brown. "Archeologists have been concerned about the interpretation of this rock art and its pigments since it was discovered."
To minimize damage to the celebrated art, the researchers obtained microscopic black pigment samples collected by archeologists: one from the bull's ears and another from his muzzle. They then used an X-ray absorption method at SSRL Beamline 11-2 and at the European Synchrotron Radiation Facility to identify manganese oxide minerals in the samples. Absorption spectra revealed an "unanticipated" variety of manganese oxide minerals, including a rare occurrence of hausmannite (Mn3O4), never before encountered in prehistoric pigments.
Learning the mineral composition reveals its geographic origin, and may expose bits about the culture of early humans who made it. Finding hausmannite in the southwest region of Europe could mean that the area's manganese oxide source has been exhausted or forgotten—or, as the researchers propose, that prehistoric humans traded among each other, supplying the cave artists with ores imported from elsewhere in the region.
French scientists Francois Farges, Emily Chalmin, and others collaborated with Brown on this research. | https://phys.org/news/2007-03-rare-minerals-illuminate-year.html |
The European Commission (EC) has launched the ‘Effective Systems for Authenticity and Traceability in Food System’ Grant Program.
Scope
To contribute to the goals of the farm to fork strategy, the EU will scale up its fight against food fraud to create a level playing field for operators and strengthen the powers of control and enforcement authorities. The new EU Official Controls Regulation includes key provisions in relation to food fraud. Recently, the issue of food fraud has been thrust into the spotlight and is of increasing concern to society and to the food industry. It can have very different impacts on consumers, ranging from direct health threats (e.g. consumption of toxic adulterants and contaminants) to violation of consumer rights (e.g. mislabeling).
With the complexity of the global market and the addition of e-commerce, the safety risks of food fraud are likely to increase. Therefore, there is a constant need for sensitive and accurate authentication methods and innovative traceability methods to prevent food fraud and help the industry and official control authorities. Maintaining the integrity of European foods is vital to protect both consumers and the legitimate producers, industry and retail, and foster consumer confidence in the authenticity of all food products.
Areas
Successful proposals are expected to address both areas (area A and area B):
- Area A:
- Take stock and determine the current state-of-the-art, identify gaps, and suggest short-, medium- and long-term strategies for closing gaps in research addressing various aspects of fraud such as societal and economic drivers, fraud opportunities, mitigation and prevention measures.
- Quantify the economic dimension of the food fraud problem and understand the behaviour of food criminals perpetrating food fraud.
- Carry out translational research on fraud detection methods to provide the required evidence base for harmonisation and standardisation of methods and harmonisation of strategies for regulatory use.
- Develop and validate rapid food fraud detection tools and real-time in-situ/on-line analytical methods for testing authenticity and quality.
- Develop and implement new food fraud detection models (based on data, by applying artificial intelligence techniques) and tracing methods through the use of new and emerging technologies, such as blockchain and smart labeling tools.
- Build common platforms and tools for sharing information among stakeholders.
- Area B:
- Support the development of an early warning system (EWS) for detection and possible further prevention of fraudulent practices and an efficient use of artificial intelligence, taking into consideration the data protection rules in place.
- Evaluate the utility of different food-authenticity-related databases existing in Member States and the EU institutions, and create a central database / data portal for further use of these data by authorized users to improve fraud detection and enforcement actions by the competent authorities.
- Develop tools that increase consumers’ confidence in the authenticity and quality of the food supply, in line with the relevant legal frameworks.
- Investigate food chain stakeholders’ attitudes towards adulterated food to understand better their motivation to commit fraud and trade-in inferior quality goods.
Funding Information
The check will normally be done for the coordinator if the requested grant amount is equal to or greater than EUR 500,000, except for:
- public bodies (entities established as a public body under national law, including local, regional or national authorities) or international organizations; and
- cases where the individual requested grant amount is not more than EUR 60,000 (low value grant).
Expected Outcomes
Project results are expected to contribute to all of the following outcomes:
- A robust knowledge base of the underlying reasons for / drivers of food fraud (eg economic and social) and the extent of food fraud.
- Innovative strategies and solutions (tools and devices) to prevent fraudulent practices by improving traceability and safeguarding authenticity, and fostering solutions for fraud prevention.
- Improved assistance to control bodies and authorities in fraud prevention.
- Improved transparency through digital solutions (such as IoT, artificial intelligence, blockchain and distributed ledger technologies) that meet consumer demand for food transparency, with a focus on demonstrating authenticity of food as a way to reduce food fraud and boost consumer confidence in food origin and quality.
- Contribution to further development of policies for food authentication and traceability and for fighting food fraud / food crime.
- Support official control by providing guidance on detection and mitigation of fraudulent practices.
Eligibility Criteria
To be eligible for funding, applicants must be established in one of the eligible countries, ie:
- the Member States of the European Union, including their outermost regions;
- the Overseas Countries and Territories (OCTs) linked to the Member States;
- eligible non-EU countries:
- countries associated to Horizon Europe
- low- and middle-income countries. | https://www2.fundsforngos.org/latest-funds-for-ngos/cfps-to-support-ri-in-combating-food-fraud-and-improving-food-systems/ |
Suburban St. Louis Proposed Development
M+H was selected to Master Plan a mixed use development for a 150 acre, primarily undeveloped property in suburban St. Louis, Missouri. Retail, office, restaurant, entertainment and single and multi-family residential spaces were to be incorporated with existing municipal, religious and educational facilities.
Through extensive site analysis, M+H became intimately familiar with the current site characteristics such as topography, vegetation, wildlife, lakes, ponds, streams, man-made structures, vistas and views, as well as pedestrian and vehicular circulation and connections on and off site. Multiple design solutions were produced to communicate this information to the various interest groups including the owner, neighbors and governing authorities.
Site concepts were designed to achieve the owner’s development objectives and space requirements based on assimilation of this analysis and owner sensitivities to the natural environment and site features.
Taking the planning task one step farther, M+H suggested an architectural language intended to provide an overall identity for the project. Important architectural elements of the site concept were detailed. Images of these selected design components were provided to communicate the identity and the realization of the opportunity. | http://mha.us.com/project/mixed-use-master-plan/ |
Authors:
Martha Matashu, North-West University, South Africa
Abstract:
Corona Virus Diseases -19 (COVID-19) exposed high gaps of inequalities and social injustices that exist in societies. This raises questions about the adequacy of the existing human rights education frameworks to achieve the right to education to the end of achieving sustainable development and social justice in societies in general and in specific developing countries. This study submits the argument that the observed inequalities and social injustices provide evidence that the conceptualisation of education based on the human rights approach alone is insufficient to attain the rights to education and the goal behind this right. This conceptual paper thus assesses the grounds for an alternative conceptualisation of an educational framework that can provide a normative basis for the right to education, social justice, and sustainable development in societies. This paper begins with a discussion of the right to education. A proposal is suggested to incorporate the human capital theory and the capabilities approach instead of discarding the human rights-based approach or leaving it to stand alone. The incorporation of the human rights, human capital, capabilities approach to the universal rights to the education system will enrich the human rights-based education framework to provide a comprehensive perspective for attaining the normative basis for rights to education, the development of people's capacities to their full potentials, creation of conditions necessary for capabilities to be realized and the rights to be exercised. Such an integrated education approach is envisaged to contribute toward building sustained development and social justice in societies. | https://submit.iafor.org/submission/submission64618/ |
When the Automobile Club de l’Ouest issued a call for tenders for the exclusive supply of the chassis for the Hydrogen prototypes that will compete in the 2024 24 Hours of Le Mans, ORECA and RBAT decided to join forces, pooling their expertise in a bid-winning combination.
Both firms have a keen interest in the ACO’s hydrogen programme which includes the creation of a distinct hydrogen class in 2024, and so teamed up for the first time in their history in a joint bid. ORECA will draw on its expertise of its Design Office and its production skills as well as its endurance racing knowledge and experience, while RBAT will bring its expertise in racing car design, very much focused on aerodynamics, vehicle dynamics, simulation and energy recovery optimisation. The initial task for the partners will be to undertake and provide a detailed feasibility study for the vehicle concept.
RBAT and ORECA thus join Plastic Omnium, the exclusive supplier of the hydrogen prototype fuel tanks ultimately for the cars set to make their Endurance debut in 2024. | https://newsroom.lemans.org/en/press/red-bull-advanced-technologies-and-oreca-to-supply-hydrogen-class-chassis-in-2024 |
What COVID-19 Taught Us About the Supply Chain
One hot topic that has arisen during the COVID-19 pandemic is the importance of rethinking current supply chains and the benefits enabled by both their digitalisation and the use of virtual inventories. The combination of additive manufacturing (AM) and digitisation will likely encourage industries to rethink their approach to supply chains.
The importance of reevaluating current supply chains stems from the inherent differences between traditional manufacturing and AM solutions. Traditional manufacturing by nature requires a global supply network with physical warehouses and physical shipping/logistics. One of the key characteristics of traditional manufacturing is mass production, where the greater the production quantity, the lower the price per part
During these last few months, a chain of events led to multiple supply chain failures. The initial outbreak in China combined with the country’s increased role in the production of world goods, began a ripple effect of problems. Factory shut-downs in China caused some physical inventories to deplete and as the virus began to spread, it became a global pandemic. In terms of supply chains, the intention to limit the spread of the virus by minimising travel made it extremely difficult to move goods. The shortage and acute need for parts, especially medical parts, grew and vulnerabilities were experienced both insofar as manufacturing, as well as in supply chain logistics.
New awareness
The pandemic has shown that the risks of supply chain disruption are higher when manufacturing is centralised and transportation is widespread and the emergency brought awareness of AM as a technology and as an enabler of digital supply chains. But neither the technology nor the business models are new and the geographical and time associated benefits of AM became clear because of the way the AM ecosystem came through in times of need.
Specifically in the medical field, AM is already widely used in pre-operative patient-specific anatomical models, such as surgical guides. Within manufacturing, AM enables localised manufacturing and is used for production tooling and high-end critical parts, as well as for maintenance and emergency spare parts.
A recent industry webinar, in which I participated, also included Stratasys’ EMEA president, Andy Langfeld, who discussed how the PPE shortage during the pandemic uncovered the classical risk of the global supply chain today. He pointed to the AP-HP hospital network in Paris which addressed this through 3D printing and set up an internal production method within just 48 hours. Doctors can order industry-compliant parts from an internal catalog as needed, demonstrating how AM can help overcome supply chain failures.
Not just a pandemic solution
There are other reasons for supply chain failures such as geo-political issues like the tariff wars between the USA and China, and Brexit. Evaluating digital supply chain effectiveness for a company is relevant now and in the future.
When comparing production costs, looking only at those derived from manufacturing makes sense IF the supply chain is the same for items produced by the compared manufacturing methods. While AM might be more costly per part in the manufacturing, it can save significant costs when it comes to the supply of a part. Digital supply chains, in general, have much lower costs: a digital supply chain is shorter, modular, and obviously less physical, cutting the costs related to keeping an inventory, warehouses, overproduction, transportation, and more.
In times of crisis, there still could be difficulties in the digital supply chain but these are restricted mostly to the supply of raw materials. The agility of digital enables quick reactions and changes when needed. We have seen over these past months factories repurposing to manufacture medical equipment, but in traditional manufacturing the time and costs of such a switchover are significant. In contrast, secured virtual inventories and AM can be flexible and nimble essentially hot-swapping one location for another, or one product for another.
Vulnerabilities of a digital nature
With all these advantages, it makes one wonder why digital supply chains with AM aren’t more popular. There are vulnerabilities that stem from digital production and digital supply chains that need to be addressed. Traditional production can ensure almost 100% consistency and repeatability in the physical product because parts are produced en masse. When the part is digital it’s not yet produced. Therefore it is important to keep repeatability across times and locations to ensure 100% consistency – whenever or wherever the part is eventually produced.
Enforcing repeatability in AM can be done by tracking and controlling the production process using SaaS software, such as LEO Lane’s. This ensures the correct machine, and the correct settings are used, thereby accounting for different material characteristics. Another vulnerability for both physical and digital parts is theft. When a physical part is stolen, the economic loss is the value of that one part. However, when a digital part is stolen, the economic ramifications are much worse: an unprotected digital part is a blueprint to output as many parts as desired. Again, this is certainly an important consideration when setting up a digital supply chain, with the same software solutions offering protection of the virtual inventory..
In view of COVID-19, it is likely that we will need to be able to work from any location for some time. Using cloud and SaaS solutions makes it easier to integrate with companies’ existing systems and still have access from different places. AM and digital supply chains offer an alternative, or a parallel alternative to the existing supply chain, in order to self-sustain and remain strong against possible disruptions.
Whether it is to supply spare parts in an emergency or simply for everyday use, the benefits of digital supply chains are increasingly being embraced and leveraged by many companies. | https://linklinejournal.com/what-covid-19-taught-us-about-the-supply-chain/ |
The transport of classic vehicles is subject to a variety of tasks. The spectrum ranges from restoration objects, which are not in running order, to regular classic cars of American or European origin to valuable collectables in original paint and individual pieces in showroom quality.
We are familiar with the specific requirements of the transport of classic vehicles and treat each car with the utmost care. The respective import regulations concerning required documents and conditions are constantly monitored by us. In the U.S. we arrange an assessment by independent experts and a fiduciary handling of the purchase price upon request. Collection from the dealer and delivery, as required also with closed trailers, sea freight, air cargo and customs clearance.
At Pangaea we offer you everything from one source. Our dedicated team will inform you in advance about customs regulations, charges and transit time for your planning. | https://www.pangaeacargo.com/en/usa-vehicle-transport/classic-car-shipping.html |
Grass patch heights supporting herbivores
Rina Grant drove around the Kruger National Park and found it curious that one seems to always find animals on the short grass areas rather than areas where there is lots of grass. In her post-doctoral study, Grant looked at possible reasons, and found that the grasses on these sites were indeed more nutritious.
As an expansion of this, published in the African Journal of Range & Forage Science, Volume 36, Issue 1, 2019 “When less is more: heterogeneity in grass patch height supports herbivores in counter-intuitive ways” looks at whether animals really selected the short grass patches or whether it was easier to see them there.
The study observes which patches were frequently utilised, by doing regular monthly road counts, grass height observations and dung counts on selected short grass patches in the Kruger National Park. Grant thought that one may find different patterns of utilization in the different areas of Kruger.
“Because it is interesting and exciting driving in Kruger and especially looking at where animals are, I had the opportunity to get inputs from many scientists on the design of the project and the interpretation of the results,” Grant said.
Herbivores are an integral part of the African landscape and have evolved with the vegetation to create the savanna landscape. Managers of these landscapes can benefit from a better understanding of how indigenous herbivores use the landscape to which they are adapted.
Smaller-framed impala and blue wildebeest (meso-herbivores) were most regularly seen on these nutritious patches, while from dung deposits it was clear that the even larger-framed buffalo (mega-herbivores) spent time there. This preference can be explained by considering the nutritional needs and food intake of the herbivores. Smaller-framed herbivores seem to be able to satisfy their dietary requirements on the high-quality forage patches, while larger-framed herbivores seem to supplement the quality forage by also spending foraging time on areas of higher grass biomass.
From this insight, Grant and her co-authors propose that range management should take herbivore preferences into account and allow herbivores to select and concentrate their foraging on the most nutritious forage. This approach, according to the paper, is likely to decrease inputs while allowing animals to maintain or increase production.
Grant’s co-authors
Judith Botha: Grant has worked with Botha for about 20 years. They started by looking at the use of dung analysis to evaluate the nutritional status of herbivores, but later she specialized in statistics and she did the sophisticated statistical analysis for this paper.
Thelani Grant: Thelani Grant was very keen to do a MSc related to this project and joined Grant on all the field trips. She used some of the data collected for her MSc thesis.
Mike J S Peel: Peel is the head of the wildlife research group of the Agricultural Research Council in Nelspruit. He provided important input to the project and offered the opportunity to look at systems on private reserves.
Izak P J Smit: A project on the effect of waterholes on the surrounding vegetation developed into a PhD and later to Smit joining SANParks as the program manager responsible for remote sensing. Apart from joining Grant on some field trips, he gave advice on the design of the project. His thinking helped to make the manuscript understandable.
Photograph: Rina Grant on one of her many expeditions. | https://www.nisc.co.za/news/118/announcements-and-notices/grass-patch-heights-supporting-herbivores |
Component Diagram :
A component diagram provides a physical view of the system. Its purpose is to show the dependencies that the software has on the other software components (e.g., software libraries) in the system. The diagram can be
shown at a very high level, with just the large-grain components, or it can be shown at the component package level.2
Modeling a component diagram is best described through an example. Below Diagram shows four components: Reporting Tool, Billboard Service, Servlet 2.2 API, and JDBC API. The arrowed lines from the Reporting Tool component to the Billboard Service, Servlet 2.2 API, and JDBC API components mean that the Reporting Tool is dependent on those three components.
Deployment Diagram:
The deployment diagram shows how a system will be physically deployed in the hardware environment. Its purpose is to show where the different components of the system will physically run and how they will communicate with each other. Since the diagram models the physical runtime, a system’s production staff will make considerable use of this
diagram.
The notation in a deployment diagram includes the notation elements used in a component diagram, with a couple of additions, including the concept of a node. A node represents either a physical machine or a virtual machine node (e.g., a mainframe node). To model a node, simply draw a three-dimensional cube with the name of the node at the top of the cube. Use the naming convention used in sequence diagrams: [instance name] : [instance type] (e.g., “w3reporting.myco.com : Application Server”).
The deployment diagram above shows that the users access the Reporting Tool by using a browser running on their local machine and connecting via HTTP over their company’s intranet to the Reporting Tool. This tool physically runs on the Application Server named w3reporting.myco.com. The diagram shows the Reporting Tool component
drawn inside of IBM WebSphere, which in turn is drawn inside of the node w3.reporting.myco.com. The Reporting Tool connects to its reporting database using the Java language to IBM DB2’s JDBC interface, which then communicates to the actual DB2 database running on the server named db1.myco.com using native DB2 communication. In addition to talking to the reporting database, the Report Tool component communicates via
SOAP over HTTPS to the Billboard Service.
UML Objects oriented Concepts:
UML can be described as the successor of object oriented analysis and design.
An object contains both data and methods that control the data. The data represents the state of the object. A class describes an object and they also form hierarchy to model real world system. The hierarchy is represented as inheritance and the classes can also be associated in different manners as per the requirement.
The objects are the real world entities that exist around us and the basic concepts like abstraction, encapsulation, inheritance, polymorphism all can be represented using UML.
So UML is powerful enough to represent all the concepts exists in object oriented analysis and design. UML diagrams are representation of object oriented concepts only. So before learning UML, it becomes important to understand OO concepts in details.
Following are some fundamental concepts of object oriented world:
- Objects: Objects represent an entity and the basic building block.
- Class: Class is the blue print of an object.
- Abstraction: Abstraction represents the behavior of an real world entity.
- Encapsulation: Encapsulation is the mechanism of binding the data together and hiding them from outside world.
- Inheritance: Inheritance is the mechanism of making new classes from existing one.
- Polymorphism: It defines the mechanism to exists in different forms. | https://aerointerview.com/2016/06/uml-v/ |
Maintenance Engineer will perform a variety of maintenance, repair and continuous improvement functions on the plant equipment and machinery with limited direction and guidance. Support manufacturing operations in a spirit of teamwork and cooperation in order to improve overall plant OEE. Troubleshoot and resolve issues in a timely fashion, safely, professionally and efficiently, complete machine repairs and rebuilds per the original design.
Qualification : Mechanical Engineering
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Quality Engineer
|Taylor, MI||
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This position is for a Quality Engineer in Tier-I automotive manufacturing plant. Position is responsible for maintaining complete Quality Management systems in compliance to IATF 16949 standards and our customer specific requirements.
Qualification : Mechanical Engineering
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Manufacturing Engineer
|Taylor, MI||
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Production Engineer will establish and maintain all documentation related to manufacturing process (Standard Operating Procedures, Process Flow Diagrams, work instruction, Inspection Standards, etc.) Participate in design work holding and tool holding design approval process. Lead capacity planning and productivity improvement activities. Utilize CAD to design layouts and necessary work holding fixtures and parts. | http://angstrom-usa.com/careers.html |
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