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Tzeporah Berman
Current Affairs/Gyroscope
Climate change: the Pointy End of Hope
The effects of human-caused climate change are already evident on all continents and waters, the Intergovernmental Panel on Climate Change said in its latest report March 31. The report is, undeniably, grim: agriculture, human health, water and land-based ecosystems, water
The Pointy End
The effects of human-caused climate change are already evident on all continents and waters, the Intergovernmental Panel on Climate Change said in its latest report, released March 31. The report is, undeniably, grim: agriculture, human health, water and land-based ecosystems,
The effects of human-caused climate change are already evident on all continents and waters, the Intergovernmental Panel on Climate Change said in its latest report March 31. The report is, undeniably, grim: agriculture, human health, water and land-based ecosystems, water supplies, and
The effects of human-caused climate change are already evident on all continents and waters, the Intergovernmental Panel on Climate Change said in its latest report, released March 31. The report is, undeniably, grim: agriculture, human health, water and land-based ecosystems, water supplies,
"You are entitled to your opinion … you are not entitled to your own facts" – Daniel Patrick Moynihan
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Bonavista Biennale beckons
Liberal's lose poll lead in election 2021 gamble
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NATUASHISH, LABRADOR August 12, 2021 – Days after a human
Deborah Jones
Greg Locke | {
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Category: Art Nouveau
Reading an Art Nouveau brass plate
Art Nouveau, Video reports Leave a comment
Antique Booksellers House
The Antique Booksellers House has been one of the iconic buildings of old Bucharest, unfortunately demolished during the fascist period. This video analyses its architecture, a mix of La Belle Epoque Art Nouveau and post-Great War Neoromanian, examining it in its topographical and architectural context. The conclusion is the Antique Booksellers House (Casa Anticarilor) was probably an edifice and institution that started in the 1900s and re-established after the war in the 1920s.
Art Nouveau, Neoclassical, Video reports Architecture of Romania, Bucharest Leave a comment
Clamshell doorway awnings from the La Belle Époque period in Ploiesti
Bellow are two wonderful clamshell house entrance awnings that I photographed in Ploiesti, the oil town 60km north of Bucharest. They date from the La Belle Époque period (late Victorian and Edwardian periods) and belong as an architectural "species" to the Art Nouveau current, constituting a part of what I call the Little Parish style built landscape of the urban areas of that period in Romania. The clamshell awnings are widespread in Bucharest, which make me consider them as one of the main architectural symbols of Romania's capital, but also popular throughout the country before the Great War (which was then formed by the provinces of Moldavia and Wallachia, without Transylvania). Ploiesti was developing spectacularly in that era on the proceeds of the newly emerging oil economy and as an important regional market town. The clamshell awnings are a superb reminder of those times of economic boom and architectural finery.
Clamshell doorway awning from the La Belle Époque period in Ploiesti (©Valentin Mandache)
Architectural Heritage, Art Nouveau, Little Paris Architecture of Romania, Eastern Europe, Historic Houses of Romania, History, Identity, La Belle Epoque, Little Paris, Ploiesti, Prahova, Romania, Romanian Architecture, South East Europe, Wallachia Leave a comment
Art Nouveau letter box plate
Art Nouveau letter box plate dating from the 1900s, Mosilor area, Bucharest (©Valentin Mandache)
Bucharest is an interesting Art Nouveau province, located at the geographical and in many aspects architectural periphery of this style. That is why the Art Nouveau designs occur mostly fragmentary, in small bits and pieces on buildings that display overall conservative c19th historicisit styles or on some early Neo-Romanian edifices. That makes them less visible for the the untrained eye, constituting one of my favourite past-times to spot them. The letter box plate from the image above is one of those discoveries, adorning the Little Paris style doorway of a 1900s house in Mosilor area of Bucharest. Its lettering style renders, somehow in a provincial Art Nouveau manner, the free flowing plant leaves so peculiar for this style, making it quite evocative for the manifestation of this current in this part of the world.
Architectural Heritage, Art Nouveau, Bucharest Architecture of Bucharest, Architecture of Romania, Art Nouveau, Bucharest, Doorway, Eastern Europe, Historic Houses of Romania, History, Identity, La Belle Epoque, Little Paris, Romania, Romanian Architecture, South East Europe Leave a comment
Princess' Nest: a royal tree house in the Transylvanian Alps
Princess' Nest, Princess Marie of Romania's tree house in Sinaia. Old post-card (1900s), Valentin and Diana Mandache collection.
Queen Marie of Romania is well known for her multiple artistic qualities, ranging from writing, furniture design to theatre. She also indulged in architectural pursuits, especially in matters of interior design (see her remarkable creations at Pelishor Castle in the Transylvanian Alps for example) or gardening, ideas which she condensed in an interesting essay published in the 1920s, entitled "My Dream-Houses". Somehow less known is a peculiar tree house structure, illustrated in the old post-card above, built following Marie's detailed specifications, which she used for recreation in the years when was a crown princess of the Romanian Kingdom. It was known as "Princess' Nest", located on the property of the grand Pelesh Royal Castle in Sinaia. Below, is the finest description of this phantasy house, which I so far found in my research, by Maude Parkinson, an expert gardener from England who worked for many years in the service of the Romanian Royal House:
In the neighbouring forest Princess Marie, as she then was, had a "Crusoe" constructed. I understand that she adopted the idea from a celebrated arboreal restaurant in the Forest Fontainebleau, which is named after the castaway of Juan Fernandez.
A strong wooden platform was constructed amongst the trees at a considerable height from the ground, and upon this was built a house consisting of two rooms, a kitchen, and a salon.
The kitchen is fitted up with everything necessary for cooking simple dishes or preparing tea. The salon is very prettily furnished, and books in plenty, drawing and painting materials, etc., are always to be found there.
The Queen only takes her special friends to visit her "Crusoe" and a very charming retreat it is. The windows and open door command a most beautiful view. Access to the "Crusoe" is gained by means of a ladder with wide steps, which is let down when required. When the visitors are safely up, they remain there shut in three sides by foliage and cut off from communication with the world bellow save by telegraph, for a wire connects it with the palace. Nothing disturbs the perfect calm and quiet at such a height, and many pleasant hours have been spent by her Royal Highness and a chosen few in that little nest. Nest is indeed the word, for that is the meaning of the Roumanian name "cuib" by which the retreat is generally known.
Maude Parkinson, "Twenty years in Roumania", London 1921
Architectural Heritage, Art Nouveau Architecture of Romania, Carpathians, Eastern Europe, History, Identity, La Belle Epoque, Peles Castle, Peles Domain, Pelesh Castle, Pelesh Domain, Queen Marie of Romania, Romania, Romanian Architecture, Romanian Royal Family, Romanian Royals, Sinaia, South East Europe, Transylvanian Alps, Victorian Era Leave a comment
Grand Art Nouveau style remodelling project in Chisinau
Chisinau (Kishinev), the capital of the Republic of Moldova, is blessed with a fascinating mix of period architecture dating mostly from the second part of c19th and the first half of the c20th, reflecting the evolution of architectural tastes of the Russian Empire, Romania and the Stalinist Soviet Union. The city contains a number of attractive Art Nouveau style edifices, the most spectacular being a recent remodelling of a Fin de Siècle house, which I encountered during my recent Chisinau trip. The edifice is mentioned on the well documented website "Centrul Istoric al Chisinaului", which is a comprehensive database of architecturally valuable buildings in the historical centre of the Republic of Moldova's capital. At the entry detailing the house, which was compiled before the start of the remodelling project, is mentioned that the façade used to be Art Nouveau (named "modern" in the terminology of the Moldovan architects), but completely erased of its decoration during the vicious 1990s post-Soviet property boom. It seems that in the intervening time an enlightened proprietor has decided to bring something back from the edifice's former glory, as the photographs, which I was able to take from the street, amply testify. In my opinion is a tasteful remodelling and it might also be in the spirit of the original decoration that adorned the house, as I believe the owner had access to old plans and photographs from which the contemporary designer could guide him/her/self. It reminds me of another Art Nouveau project from scratches which takes place in Bucharest, which I documented in 2010 on this blog. I believe that this particular instance is a positive development for Chisinau, and the post-Soviet world, in raising the awareness and appreciation about the local architectural heritage that suffered so much during the two world conflagrations of the c20th, the Soviet era or the most devastating for heritage last two decade since the Soviet empire fell.
Grand Art Nouveau style remodelling project, Pushkin Street, Chisinau (©Valentin Mandache)
Grand Art Nouveau style remodelling project, Pushkin Street, Chisinau: first floor balcony decoration (©Valentin Mandache)
Grand Art Nouveau style remodelling, Pushkin Street, Chisinau: detail of the pediment decoration, 1st floor balcony (©Valentin Mandache)
Grand Art Nouveau style remodelling, Pushkin Street, Chisinau: window pediment decoration (©Valentin Mandache)
Grand Art Nouveau style remodelling, Pushkin Street, Chisinau: pilaster capital (©Valentin Mandache)
Grand Art Nouveau style remodelling, Pushkin Street, Chisinau: detail of doorway pediment decoration (©Valentin Mandache)
Architectural Heritage, Art Nouveau Art Nouveau, Chisinau, Eastern Europe, Historic House, History, Identity, Kishinev, La Belle Epoque, Post-Soviet World, Remodelling Project, Renovation Project, Republic of Moldova, Restoration, Russian Architecture, Russian Empire, South East Europe 2 Comments
1900s decorative tiles for birthday celebration
1900s decorative tiles, Ana Aslan Institute, Bucharest (©Valentin Mandache)
Today is my birthday and I would like to celebrate it with a photographic array of decorative tiles dating from the 1900s, embellishing the façade of Ana Aslan Institute in Bucharest. The tiles display characteristics peculiar to the Art Nouveau style, one of my favourites. Bellow is a photograph of Diana and me taken yesterday, Sunday, in the near evening hours, after we had a nice celebratory dinner, followed by a walk in the beautiful Icoanei Garden area, surrounded by spring flowers and the soothing sunlight so characteristic of this season and latitude.
Birthday celebration, Bucharest, Icoanei Garden, April 2012
Art Nouveau, Bucharest Architecture of Bucharest, Architecture of Romania, Art Nouveau, Bucharest, Decorative Tiles, Eastern Europe, History, Identity, Romania, South East Europe 4 Comments
Sample of photographs from Saturday 31 March tour: the Art Nouveau architecture of Bucharest
Historic Houses of Romania tour: Art Nouveau Bucharest (©Valentin Mandache)
The tour was well attended and we had the opportunity to see and discuss in detail some of the most important and spectacular Art Nouveau architectural structures of Bucharest, scattered over quite a large area stretching from Lascar Catargiu boulevard to the University Square. The highlights were three churches that exhibit brilliant Art Nouveau features: Amzei, Boteanu and the Russian Church, the most magnificent Art Nouveau monument (the building is in the Neo-Russian style of the 1900s, expressed within Art Nouveau coordinates) of Bucharest. I hope that the few photographs presented here, which I took during the tour, would do justice to those wonderful sites, now so much ignored by the Bucharest people and authorities.
Art Nouveau, Bucharest, Tours Architecture of Bucharest, Historic Houses of Romania, Tour Leave a comment
Art Nouveau gate
Art Nouveau style gate dating from the1900s, Mosilor area, Bucharest (©Valentin Mandache)
This article is on the theme of today's architectural tour on the Art Nouveau style of Bucharest. The photographs present a rare Art Nouveau style gate found during one of my tours last year. It is in a quite run down state, but still preserves its design details from the 1900s period. I like the gate handle and the decorative lock plate, which in a nutshell convey the air of those times.
Art Nouveau style gate dating from the 1900s, Mosilor area, Bucharest (©Valentin Mandache)
Art Nouveau, Bucharest Architecture of Romania, Art Nouveau, Bucharest, Eastern Europe, History, Identity, La Belle Epoque, Romania, Romanian Architecture, South East Europe 2 Comments
Art Nouveau balcony
Art Nouveau style balcony, 1900s apartment house, Izvor area, Bucharest (©Valentin Mandache)
I am planning an Art Nouveau architecture tour for this Saturday, announcement to follow. I hope that this image of a Bucharest Art Nouveau style balcony would act as a foretaste for that event. The ironwork of the balcony contains abstract representations of flower motifs. Also Art Nouveau are the plaster decorations embellishing the window openings. Unfortunately the attractive over a century old design of this apartment house is diminished by the air conditioning units affixed without any regard for aesthetics, a situation encountered at every step and corner in Bucharest. The air conditioning units are still seen as a high status symbol (as the satellite dishes not long ago) by the local property owners and consequently are "flagged" with impunity even on the best period buildings of this city.
Art Nouveau Architecture of Romania, Art Nouveau, Bucharest, Eastern Europe, History, Identity, La Belle Epoque, Romania, Romanian Architecture, South East Europe 2 Comments | {
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Specialist, Vaults
The Specialist, Vaults works in the Archive Collections Department under the supervision of the Film Vault and Traffic Manager and autonomously with various vault responsibilities. Primary duties and responsibilities include vaulting and retrieval of materials, strategizing storage issues, inspecting film for potential outside loans, along with general oversight and maintenance of Archive holdings and storage systems.
Organization and prioritization of vault storage locations for a rapidly growing collection of archival material and vault space.
Retrieval of archival materials from Archive vaults for both internal and outside users.
Maintenance of Archive collections using proper archival storage techniques.
Supervise barcode labeling and scanning of inventoried materials.
Tracking and re-vaulting of internally and externally loaned materials.
Evaluation of Academy film and video holdings for access and disposal.
Organization and supervision of major collections maintenance projects.
Creation and updating of inventory data and condition reports in the Archive's Axiell database.
Inspection of materials to be loaned to outside users.
General collection inventory and cataloging of archival materials.
General light maintenance of vault spaces; sweeping, dusting, etc.
Working and communicating with Academy staff, donors and depositors, Academy members, film industry professionals, and outside organizations on collection-related activities.
Ability to work independently.
Strong organizational skills with a strict attention to detail.
Basic knowledge of film history and technology.
Experience in the operation of film handling and editing equipment and film and video viewing equipment.
Experience in the operation of vault storage systems and related equipment.
Ability to lift at least 30 lbs. and retrieve heavy items from shelves using ladders.
Ability to work in climate-controlled vaults for extended periods.
Skill in reading and composing correspondence and reports in English.
Proficiency with standard computer word processing and database software.
Ability to establish and maintain cooperative working relationships with Academy staff, donors, laboratory personnel, Academy members, industry professionals, and visitors.
Degree in moving image archival studies or equivalent preferred.
Experience with bar code scanners and related equipment preferred.
Experience in using Axiell or similar film database preferred.
If hired, we require all employees to be vaccinated against COVID-19, unless a medical or religious accommodation is needed as determined on a case by case basis.
The expected base hourly wage range for this role is $23.08 to $24.04. The actual base pay offered will be determined on factors such as experience, skills, training, location, certifications, education, and other factors permitted by law. Decisions will be made on a case-by-case basis.
#LI-DNI
Position Specialist, Vaults
Open Date 12/16/2022
About the Organization The Academy of Motion Picture Arts and Sciences is a global community of more than 10,000 of the most accomplished artists, filmmakers and executives working in film. In addition to celebrating and recognizing excellence in filmmaking through the Oscars, the Academy supports a wide range of initiatives to promote the art and science of the movies, including public programming, educational outreach and the Academy Museum of Motion Pictures.
EOE Statement The Academy is committed to equal opportunity in employment and to creating and valuing diversity in its workforce. Maintaining a diverse workforce is important to the Academy. The Academy enforces a strict policy that prohibits discrimination in hiring, training, compensation, promotion, transfer, or termination, whether on the basis of race, color, national origin, religion, sex, disability, age, veteran status, sexual orientation or genetic information. This includes a workplace that is free of all forms of harassment. Also, to help foster diversity, the Academy uses programs that ensure fairness of opportunity, pay, and growth to all applicants and employees. Every employee of the Academy is required to follow this policy and to preserve the Academy's commitment to diversity.
To search for an open position, please go to http://oscars.appone.com
-- None found --
Desktop Support Specialist in Los Angeles , CA
Infrastructure Administrator in Los Angeles , CA
Senior Manager, Employee Relations - Temporary in Beverly HIlls, CA
Theater Staff in Los Angeles , CA
Parking Attendant in Los Angeles , CA | {
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Tiny Modern Kitchen Design. Here are a number of highest rated Tiny Modern Kitchen Design pictures on internet. We identified it from obedient source. Its submitted by presidency in the best field. We say yes this nice of Tiny Modern Kitchen Design graphic could possibly be the most trending topic taking into consideration we ration it in google gain or facebook.
We try to introduced in this posting past this may be one of extraordinary quotation for any Tiny Modern Kitchen Design options. Dont you arrive here to know some supplementary unique pot de fleurs pas cher idea? We really wish you can easily take it as one of your hint and many thanks for your get older for surfing our webpage. occupy portion this image for your beloved friends, families, intervention via your social media such as facebook, google plus, twitter, pinterest, or any further bookmarking sites. | {
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from .. import np, TIME_MAJOR, DTYPE
from ..nn.base import Layer
class Attention(Layer):
FLOAT_MIN = -100000.0
def __init__(self, keys, values, values_length, base_name=None,
name=None, **kwargs):
self.keys = keys
self.values = values
self.values_length = values_length
self.seq_mask = np.zeros(self.values.shape[:2], DTYPE)
self.time_axis = 0 if TIME_MAJOR else 1
for i, j in enumerate(self.values_length):
if TIME_MAJOR:
self.seq_mask[:j, i] = 1
else:
self.seq_mask[i, :j] = 1
super(Attention, self).__init__(['weights', 'biases', 'v_att'],
base_name, name, **kwargs)
def compute_scores(self, query):
att_query = np.matmul(query, self.params['weights']) \
+ self.params['biases']
energies = self.params['v_att'] * np.tanh(self.keys + np.expand_dims(
att_query, self.time_axis))
energies = np.sum(energies, 2)
energies = energies * self.seq_mask + (
(1.0 - self.seq_mask) * self.FLOAT_MIN)
# Stabilize energies first and then exp
energies = energies - np.max(energies, axis=self.time_axis,
keepdims=True)
unnormalized_scores = np.exp(energies) * self.seq_mask
scores_normalized = unnormalized_scores / unnormalized_scores.sum(
axis=self.time_axis, keepdims=True)
context = np.expand_dims(scores_normalized, 2) * self.values
context = np.sum(context, axis=self.time_axis)
return scores_normalized, context
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RCS Sport S.p.A. and RCS Mediagroup S.p.A with their registered office in Milan, Via A. Rizzoli 8 are co-controllers and SSD RCS Active Team a.r.l. with its registered office in Milan, Via A. Rizzoli 8 is the autonomous Controller of personal data gathered on this site in accordance with Regulation (EU) 2016/679 (GDPR)
This Privacy Disclosure is revised as at 15 May 2018
Personal Data and browsing data
In accordance with the effort and care that RCS Sport S.p.A., RCS MediaGroup S.p.A. and SSD RCS Active Team a.r.l. (hereafter the Controllers) dedicate to the safeguard of personal data, we hereby inform you about the procedures, purposes and scope of communication and disclosure of your personal data and about your rights, in accordance with Article 13 of the GDPR.
CATEGORIES OF PERSONAL DATA PROCESSED BY THE DATA CONTROLLER
To offer you the services provided by their own Websites, the Controllers, in their capacity as Data Controllers, shall process some personal data necessary for the performance of the services.
These data can be provided implicitly by the instruments you use to access and use the services or they can be provided explicitly by you.
The controllers may process the following categories of personal data of the users:
technical browsing data pertaining to the IP address, to the identifying codes of the devices employed by the user to utilise the website or the services, to the characteristics of the browser and to the access times;
browsing data directed at profiling provided indirectly through utilisation of the service and obtained and analysed with the user's consent;
common identifying data provided by the user (e.g. name, surname, email, telephone number, etc.) for the utilization of the products and of the services;
PURPOSES AND LEGAL BASES OF THE PROCESSING
The data and the cookies received from you shall be processed by SSD Active Team a.r.l exclusively with methods and procedures necessary to allow you to participate in sports initiatives and receive communications relating thereto and by RCS Sport S.p.A. and RCS Mediagroup S.p.A. to send you newsletters.
Only with your express consent may your data be used to carry out statistical analyses, market surveys, promotional activities through social media and to send commercial information about the products and about the promotional initiatives of the Controllers. (Direct marketing purposes)
Also with your consent, the data may be used for purposes of profiling carried out automatically gathering information about the browsing you carry out when accessing and utilising the services and, by means of statistic correlation algorithm, they tie them to the same information coming from other users to identify the common traits and group together similar ones within interest classes. By assigning your browser to an interest class, your systems will necessarily be able to offer you contents that are closer to your tastes and will present advertisements that better meet your needs and better address the interests of the advertisers, reducing the level of interference with utilisation.
On the date you read this Disclosure, the Controllers use the profiling data to aggregate marketing profiles, to manage relations with advertisers and improve their campaigns, to infer patterns of utilisation of our products and services and to assist sales departments in the development of digital strategies (Profiling purposes)
Lastly, with your explicit consent, your data may be provided to other Companies operating in the publishing, financial, automotive insurance, energy, basic commodities, humanitarian and charitable organisations which may contact you as Controllers of autonomous initiatives – the updated list is at your disposal and it may be requested from the Data Processor at the address provided below – for statistical analyses, market surveys and transmission of commercial information about the products and promotional initiatives. (Third party marketing purposes).
Communications for market surveys or commercial information about the products and the promotional initiatives may be carried out by postal mailing, email, telemarketing, SMS, MMS.
We hereby inform you that some activities may be carried out through suppliers, specifically appointed as Data Processors, who may reside outside the European Union.
The legal bases of the purposes described above are the execution of your request as data subject and the consent you have expressed.
DISCLOSURE, COMMUNICATION AND PARTIES ACCESSING THE DATA
Your personal data shall not be disclosed, but they may be communicated when necessary for the performance of the service to third parties (as third party technical service providers, postal couriers, hosting providers, IT companies), appointed, if necessary, as Data Processors by the Controllers for the technical or organisational tasks that are instrumental for the performance of the services.
Access to the data is also allowed to categories of the Controllers appointees involved in the organisation for data processing (administrative, sales, marketing, customer service personnel, system administrators).
The updated list of Data processors may always be requested from the Data Controllers.
We shall retain the right to communicate the data to third parties if you have given your specific, optional consent.
TRANSFER OF DATA ABROAD
Your personal data shall be processed by the Data Controllers within the territory of the European Union.
If technical and/or operational issues make it necessary to rely on parties located outside the European Union, or if it becomes necessary to transfer some of the data gathered to technical systems and services managed in clouds and located outside the area of the European Union, the processing activities shall be regulated in accordance with the provisions of Chapter V of the Regulation and authorised on the basis of specific decisions by the European Union. Hence, all precautions necessary to assure the most comprehensive protection of personal data shall be adopted, basing said transfer: a) on decision of adequacy of the recipient third party countries expressed by the European Commission; b) on adequate guarantees expressed by the recipient third party in accordance with Article 46 of the Regulation; c) on the adoption of Corporate binding rules.
DURATION OF THE PROCESSING AND RETENTION OF PERSONAL DATA
In accordance with Article 5.1 e) of the GDPR, the Controllers shall process your data "for no longer than is necessary for the purposes for which the personal data are processed; personal data may be stored for longer periods insofar as the personal data will be processed solely for archiving purposes in the public interest, scientific or historical research purposes or statistical purposes in accordance with Article 89(1) subject to implementation of the appropriate technical and organisational measures required by this Regulation in order to safeguard the rights and freedoms of the data subject".
The data provided by you shall be processed throughout the time of execution of the required services and shall be stored for the 12 following months for the completion of the administrative activities, as well as for the time necessary to fulfil legal obligations.
If you have authorised the profiling treatment, the anonymous data observed from time to time shall be erased 12 months after processing starts.
The Controllers hereby guarantee to you that you may exercise, at any time, the rights specified by Article 12 of the GDPR. In particular, you have the right:
to know whether the Controllers hold and/or process personal data about you and to access them in full, also obtaining copies thereof (Article 15 Right of access by the data subject),
to the rectification of inaccurate personal data or to the completion of incomplete personal data (Article 16 Right to rectification);
to the erasure of personal data in the Controllers' possession if one of the reasons specified by the GDPR applies (Right to erasure, Article 17);
to ask the Controllers to limit processing only to some personal data, if one of the reasons specified by the Regulation (Article 18 Right to restriction of processing);
to request and receive all your personal data processed by the Controllers, in a structured, commonly used and machine-readable format or to request transmission to another controller without hindrance (Article 20, Right to data portability);
to object to all or part of the data processing for the purposes of transmitting advertising material and market surveys ("Consent") (Article 21 Right to object)
to object to all or part of the data processing in automatic or semiautomatic mode for profiling purposes ("Consent")
These rights may be exercised by communication to the Data Controllers/Data Protection Officer whose addresses are indicated in the dedicated section of this disclosure.
Moreover, you always have the right to file a complaint with the Italian Authority for the Protection of Personal Data, at the address [email protected] or through the Website http://www.gpdp.it.
The Controllers have identified and appointed a Data Protection Officer, in accordance with Article 37 of the GDPR, and has established an office for the management of requests pertaining to the privacy of their users and customers.
To exercise your guaranteed rights, you may contact us at the following addresses:
Office of the Data Protection Officer and/or RCS Sport S.p.A. and/or RCS Mediagroup S.p.A. and/or SSD RCS Active Team a.r.l.- Via A. Rizzoli 8, 20132 Milan, Italy
Privacy Data Protection Officer and/or RCS Sport S.p.A. and/or RCS Mediagroup S.p.A. and/or SSD RCS Active Team a.r.l..- Via A. Rizzoli 8, 20132 Milan, Italy
or by sending an email to the address: [email protected]
To make your visit of our Website more convenient, we use cookies for the presentation of our product assortment. Cookies are small text aggregates recorded locally in the temporary memory of your browser, and hence in your computer, for periods of time that may vary according to the need, generally between a few hours and some years, with the exception of the profiling cookies, whose maximum duration is 365 calendar days.
Using the cookies, it is possible semi-permanently to record information about your preferences and other technical data that allow for easier browsing and greater ease of use and effectiveness of the site itself. For example, cookies can be used to determine whether a connection between your computer and our sites has already been carried out, to highlight changes or maintain log-in information. For your protection, only the cookie stored on your computer is identified.
This site or product can use four different types of cookies:
Essential technical cookies
These cookies are necessary for the correct operation of the site. They allow users to browse through the pages, to share our contents, to store your access credentials to make entry into the site faster and to keep your preferences and credentials active while browsing. Without these cookies we could not perform the services for which users access the website.
This category includes the essential cookies for the operation of the website or of the product, such as the technical cookies for access to the website or for communication between the parties and the services that comprise it. This category also includes cookies of third parties' products supplemented by the Controllers for the execution of a specific functionality. In detail:
Google DFP limited to the provision of non-profiled advertising [GOOGLE DISCLOSURE LINK] [GOOGLE PRIVACY POLICY LINK]
Essential technical cookies for statistics and performance analysis
These cookies enable us to know in what way visitors use the website and thus be able to assess and improve the operation and promote the production of contents that better meet our users' information needs. For example, they allow us to know which pages are the most and least visited. They take into account, inter alia, the number of visitors, the time spent on the website by users on average and the manner in which the users are arrived. In this way, we can know what works well and what we need to improve and we can ensure that the pages are loaded quickly and are displayed correctly. All the information gathered by these cookies is anonymous and unconnected to the user's personal data. To carry out these functions in our websites, we use the services of third parties that anonymise the data making them impossible to connect to single individuals ("single-in"). When services that are not fully anonymised are provided, you will find them listed among the third party cookies for which consent can be denied, to guarantee your privacy.
This category includes duly anonymised analytical cookies. This website, in particular, uses the following products:
Nielsen NetRatings (Audiweb) for official access statistics [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Adobe Omniture for internal access and traffic statistics [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Chartbeat for instantaneous access and traffic statistics for internal use [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Cookies for user profiling directed at advertisement targeting, for the performance of external features integrated in the website
These cookies allow us to offer notices about the user and the respective interests. They are also used to limit the number of visualisations of a same advertisement and to assess the effectiveness of advertising campaigns.
They are inserted by the Controllers by means of partner technical platforms of their advertising circuit and they contribute to our investment in the Websites, enabling them adequately to finance the maintenance of the services and their technological evolution. They can also be utilised to show the user pertinent ads on other visited Websites.
These cookies are integrated in the pages and in the products by the Controllers which, in compliance with current regulations, offer in this Disclosure the instruments and instructions to exercising the right to selective objection to their use.
Specifically, the Controllers use
Salesforce KRUX (Data Management Platform) for profiling the users of the products and services, directed at the definition of the digital strategies, of the performance of profiled advertising campaigns and of the analysis of the audience marketing [ OPT-IN/OPT-OUT] [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Unidad Editorial DMP (Data Management Platform) for profiling the users of the products and services, directed at the definition of the digital strategies, of the performance of profiled advertising campaigns and of the analysis of the audience marketing [ OPT-IN/OPT-OUT] [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Google DFP and its aggregate platforms (LIST OF PARTIES MANAGED BY GOOGLE) limited to the delivery of profiled advertising [OPT-IN/OPT-OUT] [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Facebook limited to the features of social log-in, "like" and sharing RCS contents on the Facebook social network [OPT-IN/OPT-OUT] [DISCLOSURE LINK] [PRIVACY POLICY LINK] Facebook limited to the features of social log-in, "like" and sharing RCS contents on the Facebook social network [OPT-IN/OPT-OUT] [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Twitter limited to the features of social log-in and sharing RCS contents on the Twitter social network [OPT-IN/OPT-OUT] [DISCLOSURE LINK] [PRIVACY POLICY LINK]
Functional and third party profiling cookies
This category includes both cookies provided by parties that are partnered with the Controllers and known to them, and cookies provided by third parties that are not directly controlled or controllable by the Controllers.
The cookies that come from our partners enable us to offer advanced features, as well as additional information and personal functions. This includes the possibility of sharing contents through the social networks, of accessing video streaming services and the CDNs on which we host our contents. These services are mainly performed by external operators engaged or knowingly integrated by the Controllers. If a user has an account or uses other parties' services on other Websites, the other parties may be able to know that the user has visited our own sites. Use of the data gathered by these external operators through cookies is subject to the respective privacy policies and therefore these cookies are identified with the names of the respective parties set out in the cookie management instrument available in the dedicated section of this Disclosure. These include the cookies recorded by the main social networks, which allow you to share our websites' articles and to publicly show that you like our work.
Cookies that do not come from the Controllers partners are cookies delivered without the control of the Controllers, by third parties that are able to intercept the user during his/her browsing also outside the Controllers' websites. These cookies, which are typically profiling cookies, are not directly controllable by the Controlelrs which therefore cannot provide guarantees with regard to the way third party controllers use the information gathered. Opposition to the use of these cookies, therefore, can either take place through external instruments or through your direct action on your browser preferences. For details, please refer to "COOKIE MANAGEMENT" section.
If you have any doubts or concerns with regard to the use of the cookies, you can always intervene to prevent them from being set up and read, for example changing the privacy settings in your browser to block certain types of cookies or using the web instrument that the Controllers makes available to you in this Disclosure.
Since browsers – and oftentimes even different versions of the same browser – differ even markedly from each other, if you prefer to act on your own using your browser preference, you can find detailed information about the necessary procedure in your browser guide. For an overview of the procedures for the most common browsers, please visit
http://www.cookiepedia.co.uk/index.php?title=How_to_Manage_Cookies
Advertising companies also allow users to opt out of receiving targeted ads, if they so desire. This does not prevent cookies from being set up, but it does interrupt the utilisation and collection of some data by these companies.
For additional information and the possibility to opt out, please visit http://www.youronlinechoices.eu/it/
To simplify your decisions and in compliance with current regulations, the Controllers provide you with a management tool for the selective activation and deactivation of any cookies you do not like among those controlled or controllable by the Controllers.
In the instrument you will find, listed in categories, all the cookies we manage or knowingly host.
[ACTIVATE THE COOKIE MANAGEMENT TOOL]
ACCEPTANCE OR REJECTION OF THE COOKIES
Continuing to browse on this website, closing the disclosure tab or clicking in any part of the page or scrolling through it to highlight additional content, you provide manifest, explicit acceptance of the Controllers' Cookie Policy and the cookies you have not rejected will be set up and gathered. If you do not accept the cookies by leaving the site, any cookies already recorded locally in your browser will remain recorded therein but will no longer be read or used by the Controllers until you indicate your acceptance of the Policy. You can always remove these cookies at any time with the procedures explained in the websites mentioned in "Cookie management" or using the tool made available by the Controllers.
DURATION OF THE PROCESSING
Cookies managed by the Controllers have a maximum duration of 365 days, barring any voluntary renewals you carry out by reiterating consent.
The profiling cookies managed by the Controllers are anonymous and remain within statistical systems and profiling platforms exclusively for statistical purposes even if they can no longer be connected to your browser.
Cookies management by third parties have the durations indicated in the respective Cookie Policies.
You can exercise your right to object to the use of all cookies by leaving this site, thereby also refusing use of the essential technical cookies that are necessary for its operation.
If instead you intend to reject the use of one or more non-essential cookies, you may deny your consent for the cookies managed by the Controllers or by their partners directly from this disclosure with the "refusal" selectors next to the name of the cookie or of its supplier.
To refuse third party cookies not controlled by the Controllers, instead, you can proceed according to the indications available from the website http://www.youronlinechoices.eu/it/.
Any request for information or clarification or for exercising rights can be sent to the Data Processor at the following addresses:
Moreover, you always have the right to file a complaint with the Supervisory Authority for the Protection of Personal Data, at the address [email protected] or through the Website http://www.gpdp.it.
S.S.D. RCS Active Team a r.l.
Sede: via A. Rizzoli, 8 – 20132 Milano
Tel: +39 02.62827562
E-mail: [email protected]
© 2018 Milano Marathon
Relay Marathon
MyMarathon
GivenGain
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Discover Milan | {
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Shopping centre A Blanc celebrates opening on Otaniemi campus
Published: 4.10.2021
Designed by Alvar Aalto, the building previously known as Otaniemi's old shopping centre, has a new name after the renovation and opened in the middle of the Aalto University campus
A Blanc is next to the Alvarinaukio square. Photo: Aalto University / Anders Portman
The renovation of shopping centre A Blanc began in March 2020 and was completed in May 2021. After a comprehensive renovation, the centre's service providers have renovated and finished their own premises. A Blanc's first stores opened their doors in the summer, and the rest will also start operations in the autumn 2021. The opening of the shopping centre will be celebrated 4.–8.10.2021.
A Blanc has specialty shops and a wide range of services. The shopping centre forms a functional pair with its sibling centre, shopping centre A Bloc, located next to the metro station. On the first floor of A Blanc there are, among others, the Beer and whiskey house Vesiheinä, the barber-hairdresser Shortcut AALTO, the costume rental company Tapiola Juhlapuku and, opening in October, the board game bar Taproom d20. Restaurant Hummus House will start operating in the autumn 2021.
Terveystalo Otaniemi and AFRY's Otaniemi office are located on the second floor of the building. An operator is still being sought for the office space on the second floor.
The renovation brought the building to life
Formerly known as the Otaniemi's shopping centre, the building was completed in two phases in 1961 and 1969 and was designed by Alvar Aalto. It is known for its white, plastered walls and fan-like copper roof, as well as an entire building-long corridor and large shop windows that separate the area from the red-brick research and teaching buildings. The new name of the shopping centre, A Blanc, is a reference to Aalto University (A) and the white walls of the house (Blanc). The building is also a rarity, being one of the few store buildings designed by Alvar Aalto.
The shopping centre was the only one in Otaniemi until shopping centre A Bloc opened in connection with Aalto University's metro station in August 2018. After the opening of the new shopping centre A Bloc, it was possible to renovate A Blanc and restore it back to its original purpose and glory.
With the renovation, the overall look of A Blanc was freshened up when the building technology was renewed and the facades were renovated and restored. The fan-like original copper ceiling was preserved. All old windows and exterior doors were refurbished or renewed according to the old original plans. At the same time, the energy efficiency of the building improved significantly. In front of the centre, a new large terrace with seating was completed and the yard areas were made more comfortable and functional.
The renovation plans were made with respect to the historical and architectural value of the building in cooperation with the Finnish Heritage Agency and the Alvar Aalto Foundation.
Updated: 8.10.2021
This content was originally published on www.aalto.fi.
Campus, University Published: 17.12.2021
Two new buildings to be built in the centre of Otaniemi campus
Building Otakaari 2A & 2B begins in January 2022, construction to be completed by summer 2023
Campus, University Published: 2.12.2021
Rakentajanaukio parking area to partly close temporarily
Half of the parking area will be closed during December 2021 due to the HSY water supply renovation site.
Campus Published: 19.11.2021
A Bloc Black Week - Check the offers!
A Bloc goes Black 22-28 November 2021. Check out the offers now!
Construction of Jokeri Light Rail 75% complete – rail construction progressing ahead of schedule
The construction of Jokeri Light Rail has proceeded ahead of schedule, and the light rail line can start operating in early 2024
Aalto University Campus & Real Estate.
Rakentajanaukio 4
FI-02150 ESPOO
Switchboard: +358 9 439 0060
Part of Aalto University | {
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Her work 'Self-portrait after George Lambert' made her just the tenth woman to win Australia's most prestigious prize for portraiture.
Yvette Coppersmith had been a finalist in the Archibald Prize five times. Her entry this year is a self-portrait styled as a homage to one of her artistic inspirations, George Lambert, who won the Archibald Prize in 1927.
The artist said she was overwhelmed to be named this year's winner.
Her portrait of former President of the Australian Human Rights Commissioner Gillian Triggs was among the most acclaimed finalists last year.
Coppersmith completed a Bachelor of Fine Art (Painting) from the Victorian College of the Arts and has been in demand for her experimental-leaning portraits.
The 37-year-old will receive A$100,000 for the award.
While the Doug Moran National Portrait Prize (worth A$150,000) has become Australia's richest prize for portraiture, the Archibald Prize still holds an unparalleled place in the nation's consciousness. It drew 146,000 visitors last year.
The victory means Coppersmith joins iconic Australian painters such as Adam Cullen, Margaret Olley and Brett Whiteley as winners.
Coppersmith's self-portrait was part of a pronounced trend this year of artists painting themselves. Twenty-one of the 58 finalists this year painted some variation of a self-portrait.
Interestingly, Coppersmith's decision to paint herself only came after her first choice of subject, New Zealand Prime Minister Jacinta Ardern, declined her invitation to sit for a portrait.
Coppersmith's decision to paint herself only came after her first choice of subject, New Zealand Prime Minister Jacinta Ardern, declined her invitation to sit for a portrait.
AGNSW director Michael Brand said Coppersmith had been building towards this accolade.
"Yvette is a highly talented young artist who brings a deep and historical understanding of the tradition of contemporary art practice.
Vincent Namatjira was Highly Commended for his painting 'Studio self-portrait'. It shows the artist wearing a KISS t-shirt and sitting in his studio in front of an unfinished portrait of Chuck Berry.
"Painting is an ongoing battle," Namatjira said.
The Sydney Morning Herald art critic John McDonald opined yesterday that Namatjira would be a worthy winner.
"If I were the judge I'd happily give Namatjira the prize, and not simply because it would be a first-ever win for an Indigenous painter," McDonald wrote.
Last week, Jamie Preisz's painting of singer Jimmy Barnes won the Packing Room Prize. The prize is voted on by packing room staff, with the Head Packer Brett Cuthbertson holding a majority vote.
The 28-year-old Preisz said he was inspired by an interview where Barnes spoke openly about his struggles with depression and a suicide attempt he had made.
The winners of the Sir John Sulman Prize and the Wynne Prize were also announced today.
The prize is awarded annually for the best genre painting or mural.
Yukultji Napangati won the Wynne Prize, which goes to the best oil or watercolour landscape painting or the best figure sculpture. Her work 'Untitled' relates to Yunara, a region in Western Australia west of Kiwirrkura, where she lives.
"During ancestral times, a group of women camped at this site," Napangati said.
Finalists for the Archibald, Wynne and Sulman Prizes are all exhibited at the AGNSW until 9 September. | {
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in my never-ending quest to keep my house clean, i have had to lay down some ground rules for my kids. some rules i'm flexible with, others are iron-clad.
and the most iron-clad rule ever is – no one is allowed to eat food in any room except the kitchen.
now just because i have this rule does not mean that my kids ever listen to me. which would explain why i ultimately had to rip out the carpet in MY bedroom and put down a hardwood floor.
apparently my children think that MY bedroom is just an extension of the breakfast area, and it took only a few years in this house before they managed to completely destroy a brand new berber.
so, we recently went on a very lengthy vacation, driving from houston to florida. if you have ever done this, you know what a completely unfun experience this can be without proper preparation. anyway, after 2 long days in the car, we checked into our hotel and immediately went swimming. a few hours later my kids were starving and begging to eat.
"mommy, we're SOOOO hungry! can we please go out to eat?" they pleaded.
"mommy's too pooped. i have a better idea. let's order room service," i offered.
my little princess, the old traveling pro, said nothing. a little frown crossed my son's face.
"what's that, mommy?" he asked.
"it's where you order food on the phone and they bring it to your room," said princess matter-of-factly.
it was very quiet for about 5 seconds as my son's expression changed from one of confusion to sublime realization.
"I WANT ROOM SERVICE!" he screamed and took off running toward our bungalow by himself.
all my years of threatening my kids not to take food out of the kitchen have been in vain. for the remaining days of our vacation my son insisted he was hungry every night, regardless of whether we had eaten dinner, and promptly called down himself for a cheeseburger, fries and chocolate milk, which he proceeded to eat in bed off the tray.
ok, so i did bend the rules a little, but it wasn't MY bedroom, and we were on vacation. plus, in terms of what you can find on hotel bedspreads, i can assure you, a little mayonnaise never hurt anyone.
This entry was posted in my beautiful kids on December 31, 2007 by leighonline. | {
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1 What is the difference between a rollback and flyback coat?
2 What are the differences between a Polish and Netherland Dwarf rabbit?
3 Why does my purebred Holland Lop have long fur?
What is the difference between a rollback and flyback coat?
When you rub a rabbit the wrong way, the fur of a flyback coat should "fly" immediately back in place. On the other hand, the fur of a rollback coat usually stands up more and should "roll" more slowly back in place. The rollback coats have a denser and thicker undercoat while a flyback coat lies closer to the body and has more thicker guardhairs. Rollback fur is longer than flyback fur.
What are the differences between a Polish and Netherland Dwarf rabbit?
The Netherland Dwarf is a breed that is descended from the Polish rabbit. The Netherland Dwarf is a true dwarf with a single dwarf gene while the Polish does not carry any dwarf genes.
While the two breeds are often confused, there are a couple of distinctive differences between the two breeds.
The Polish can be up to 3.5 lbs for show, while the Netherland Dwarf can only be up to 2.5 lbs. However, either breed can weigh from 1.5 - 4.5 lbs.
The Polish have a flyback coat while the Netherland Dwarf has a rollback coat.
The Polish is built like most compact breeds with the shoulders narrower than the hips. The head should not sit high on the shoulders. The Netherland Dwarf is built to be the same width at the shoulders and hips and are shown sitting upright with the head held high.
The ears of a well-bred Polish should touch from base to tip. The Netherland Dwarf has erect ears, but they do not have to touch from base to tip.
The head of a Polish should be wide between the eyes and taper to a slightly narrower muzzle while still be short and have round cheeks. The face of a Netherland Dwarf is round and flattened.
Why does my purebred Holland Lop have long fur?
Some purebred Holland Lops may have long woolly fur more like an American Fuzzy Lop, technically a different breed. This is because Holland Lops can carry the l locus wool/Angora gene. A Holland lop with two recessive wool genes (ll) is a fuzzy Holland. Fuzzy Hollands tend to have longer wispier fur than American Fuzzy Lops.
The color of a purebred Rhinelander rabbit is a broken tricolor, genotype (aa B_ C_ __ ejej Enen). A harlequin coat color is genotype ejej with no broken gene (enen). As a result, if a Rhinelander rabbit fails to inherit a broken gene from its parents, it will have a harlequin coat instead. These rabbits are called Rhinelander sports.
↑ rabbitsontheweb.com, Roll-back or Fly-back?
↑ Mosaic's Rabbitry, Rabbits by Fur Type. Accessed Jan 12, 2016.
↑ The Nature Trail, Laurie Stroupe, Fuzzy Holland Lop Genetics - The Wool or Length Gene L. Accessed Jan 12, 2016.
↑ Raising-Rabbits.com, E Locus Rabbit Colors. Accessed Jan 12, 2016.
This page was last edited on 13 January 2016, at 00:40. | {
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Home/Crime & Law/Skillax Preparing 'Harsher, Brighter' New Album
Crime & LawFeaturedMusicNewsWorld
admin Follow on Twitter Send an email May 18, 2016
Happy young woman listening to the music in vintage music headphones and sitting on stairs with a take away coffee cup against urban city background.
The National have confirmed that they will start recording their next album "soon".
The US band released their sixth album 'Trouble Will Find Me' in 2013, more recently showcasing new song 'Roman Candle' live.
With frontman Morgan recently saying that the group need to "change and evolve" on their next record, guitarist Morgan has now confirmed to Pitchfork that they have assembled a new studio to record in.
"We need a new home because everybody is scattered," John explained. The band's members are based in New York, Paris and Los Angeles.
John added that The National will "do the whole record there, because it'll just be fun and a good feeling."
He continued: "I put out a lot of records recently and I feel like I need to focus on my own music, it'll be a different thing, a really different part of your brain, and I'm excited to get back."
Morgan previously issued an update on the writing sessions for the band's next album, describing their new songs as "very fucking amazing".
Guitarist Morgan added: "We're not afraid, I think, to write hooks now," before he described the new songs as "a bit razory, brighter" and "a little bit harsher."
DJ Featured Music News World
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Bank manager sued by NSS personnel for failing to abide by relationship "terms and conditions" | {
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While Wallace's speech goes on to recommend to young graduates that they look beyond their own circle at the world around them, we see applicability of the fish story to the current market environment. For over a year many market "fishes" have been swimming along, comfortable and confident, unaware of their surroundings. For them, last week seemed abnormal, but in reality, it was normal.
As we said in our year-end commentary, 2017 was an unprecedented year for low volatility. Markets were calm based on a Republican led house, senate, and White House; a Federal Reserve Board that remained cautious with fiscal policy; positive economic data; and the eventual passing of a stimulative tax bill. However, Mr. Market can be fickle in the short term, and sometimes good news can be interpreted as bad news.
We believe the primary cause of the market's change of direction over the past two weeks was a fear that the economy may grow too quickly, resulting in the Fed adjusting monetary policy to slow it down. In particular, strong wage growth numbers, low unemployment claims, and strong manufacturing data were interpreted to lead to higher inflation. While the Fed has stated that they expect to raise short-term rates three times next year, this positive data resulted in increased expectations that the Fed will raise rates four times. In addition, longer-term interest rates rose for a variety of reasons, including higher inflation expectations and the Fed buying less of the new Treasuries issued by the government. A sharp rise in yields, and fear that the Fed may put the brakes on economic growth, led to the wild market ride over the past couple weeks and a rare moment where investors experienced negative stock and bond returns at the same time.
To the young market "fishes," this may have caught them by surprise. It may have resulted in an urge to act or a feeling that this is the beginning of the next big downturn. To the older fish(es), this is water. Market volatility is normal. Furthermore, experienced investors know that the Fed increasing rate hikes from three to four will have little-to-no long-term effects on their portfolio returns and that diversified portfolios are well equipped to handle many different types of market volatility. Our clients may have noticed that diversifying investments in their portfolios were unaffected by the last two weeks of volatility, including reinsurance and several others. Those investments are unrelated to economic data points, the level of interest rates, and most importantly, the short-term emotions of market participants.
2018 may see even more volatility, but we remind our clients that this is normal. As we mentioned in our year-end commentary, too little volatility can lead to excess risk taking. When asset classes exhibit a normal level of volatility, investors are more cautious and aware of the risk required to earn returns. Equity markets are unlikely to repeat last year's performance in 2018, and traditional bond markets may struggle as well. If that is the case, we remain confident that portfolios are well constructed to handle a more "normal" year. | {
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Home/Economy/US Senate Passes $280 Billion Chips Act for Domestic Semiconductors
US Senate Passes $280 Billion Chips Act for Domestic Semiconductors
The U.S. Senate passed its controversial chips and science bill on July 27. The bill will now go to the House and, should it pass there, to President Joe Biden's desk for signature.
The mammoth bill, which passed 64-33, will provide some $280 billion in funding to prop up and kickstart domestic semiconductor manufacturing and research, though the price tag was far above previous bills which aimed to provide just $52 billion to manufacturers.
Officially titled the CHIPS Act of 2022, the bill will provide tens of billions in subsidies and tax breaks to tech corporations in an effort to spur new market growth, as well as funding for government-backed tech research.
Proponents of the bill have long said that it is necessary to maintain a competitive edge with China, which is pouring money into its own domestic chip production.
At the last minute, however, Senate Majority Leader Chuck Schumer (D-N.Y.) stripped a provision that would have blocked manufacturers from using tech developed with the monies from outsourcing production to China.
This means that, because of Schumer's alteration, tech companies will be able to domestically research and create new semiconductor technologies using taxpayer monies, and then outsource the manufacturing of those semiconductors to China.
Critics from both sides of the aisle, including Sen. Mike Lee (R-Utah) and Sen. Bernie Sanders (I-Vt.), have therefore criticized the bill as a corporate handout that will increase inflation and hurt American taxpayers.
"Bernie Sanders and I almost never agree but he is right about so-called CHIPS bill," said Sen. Chuck Grassley (R-Iowa) in a tweet. "It's just a huge govt handout to massive [and] already-profitable companies. Why would we spend more taxpayer dollars for unnecessary corporate welfare?"
Semiconductors, which are used in the production of everything from personal computers to hypersonic missiles, have become a key point of anxiety in the past two years as a global supply chain crisis has wreaked havoc on the United States' ability to obtain the chips.
The new CHIPS Act follows a version of the bill passed in January of 2021. Since that time, Democrats and Republicans have failed to reach an agreement on how to appropriate funding for the initiative, with Republicans pushing for new corporate tax credits and Democrats pushing for green energy and research funding to be included.
That stalemate led to the creation of two stalled bills, the Republican-backed Innovation and Competition Act (USICA) and the Democrat-backed America COMPETES Act, which have now been combined into the new Chips Act of 2022.
Andrew Thornebrooke is a reporter for The Epoch Times covering China-related issues with a focus on defense, military affairs, and national security. He holds a master's in military history from Norwich University.
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Stimulus update: Illinois deadline to claim $700 one-time direct tax rebate payments one day away | {
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Q: 3rd grade math problem My niece asked me to help her with a problem, since she and her parents couldn't figure it out.
The question was:
abcde - fghi = 42137
with a-i being 1-9 (so for example 12345 - 6789), with each digit appearing once.
I had no idea how to do this intelligently, and wrote some code which brute-forced through all permutations of 1-9 and give me the results ((43726, 1589),(43789, 1652),(47326, 5189),(47398, 5261)).
How would I go about this as a 9 year old student who cannot code this? Just trial and error?
All we could really say is that the first digit is a 4 or 5, but thats it, aside from that it was just trying, and at some point I was so pissed with that task I wrote code to deal with it.
A: If $abcde-fghi=42137$, then (supposing no carrying operations are expected of the student) $e$ and $i$ must be either $8$ and $1$ or $9$ and $2$. Suppose they are $9$ and $2$. Then we have $\{1,3,4,5,6,7,8\}$ remaining.
Then $a$ must be $4$ as we've used the $9$. Remaining: $\{1,3,5,6,7,8\}$.
Now we can use $8$ and $5$ in the spots of $d$ and $h$ to make $3$. Remaining: $\{1,3,6,7\}$.
Now we can use $7$ and $6$ for $c$ and $g$ to make $1$. Remaining: $\{1,3\}$.
And obviously, we can use $3$ and $1$ for $b$ and $f$ to make $2$.
So we have $43789 - 1652 = 42137$.
We got here more or less deductively from the initial assumptions --- the total number of 'guesses' I had to take was actually only two --- I guessed that we need to use $9$ and $2$ to make $7$ as opposed to $8$ and $1$, and I guessed the order in which I had to proceed. Note that there aren't that many integer combinations in this puzzle anyway.
It is, however, not a good problem --- if you really think about it and begin to consider the possibility of carrying operations being necessary, then it becomes much more intimidating. I don't think this is pedagogically useful in teaching math --- if anything, it teaches the student a haphazard trial-and-error approach, instead of cementing the foundations of deductive argument.
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Easy french crepes [Pierre Hermé] !!
You can download the recipe, for free, here !
It's always a headache to find THE french crepes recipe that's going to be a success. Too dry. Too liquid. Should we let it rest?
La recette de pâte à crêpes que vous propose Le Chat ici est un dérivé des crêpes de Pierre Hermé's. He's one of the most famous pastry chef in the world. So, we can trust him 😉 This recipe is magic and always works !
Moreover, this recipe does not need to rest and can be used for everything : main courses and desserts !
To prove it, The Kitten offers you 3 different garnishes: 2 salty garnishes (bacon / mushroom / goat cheese and chicken / zucchinis / blue cheese) and a sweet garnish (sautéed apples / salted butter caramel). Of course, make according to the season, your desires and your inspiration!
Once made, this french crepes batter can be kept in the fridge for a few days without any problem (mix quickly for a homogeneous batter). It is also possible to make the crepes in advance and then keep them in a cool cloth to warm them when serving in a pan with a dab of butter.
The recipe is described to be made in a kitchen robot, but can be made by hand or electric whisk, in a bowl.
Break the eggs in the robot bowl and whisk for 30 sec at medium speed.
Gently add the sifted flour and a little salt.
Add milk gently, continuing to whisk. Then add the water.
The batter must have the texture of double cream. Add water if necessary.
Finish with the melted butter. If necessary, finish smoothing the dough with a hand blender.
To cook, heat a pan over high heat and apply a thin layer of neutral oilwith a brush.
Pour in a large, non stick pan, tilting the pan then turning it to spread the dough.
Wait until the dough is cooked, it should take 2 minutes maximum (adjust the heat if it is not the case).
Turn the pancake over with a spatula and cook the other side (same, 2 minutes maximum).
At this time, it is possible to add a garnish.
Fold the pancake and serve immediately.
In a pan without fat, sauté bacon and mushrooms cut in big chunks.
Cook until the vegetation water evaporates. Season to taste.
Once cooked, reserve until ready to serve.
At serving time, start by placing 3 slices of goat cheese on the crepe. Then add the bacon/cooked mushrooms mixture.
Fold the pancake and let the cheese melt for 1 to 2 minutes.
Cut the chicken breast and washed zucchini into cubes.
Cook until chicken is golden. Season and set aside.
When serving, place a little blue cheese on the crepe. Add a little chicken/zucchini mixture.
Peel the apples, then dice them.
In a skillet over medium heat, melt the butter and place the diced apples.
Cook until apple is melted. Reserve.
At serving time, place apples on the crepe.
Let it cook for 1 minute, then fold the the crepe. Place it on the serving plate and finish with the salted butter caramel. | {
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Joanna is a printed textile artist and designer and produces one-off works for domestic interiors, site-specific, often large-scale commissions for public and corporate spaces, and utilitarian fabrics for the home. Work has been made for a variety of environments – from castle to quayside, wall-hangings to temporary external installations.
Joanna's work is a response to observations of daily life within the domestic interior. She takes inspiration from the smallest details of household objects to larger architectural elements and explore their interplay and juxtaposition, as well as the effects of time and light, and how they change the sense of a place, revealing and concealing the fabric of our lives. Although the origin of chosen motifs is not necessarily overtly apparent, the abstraction process aims to imbue the work with a quiet familiarity and capture a particular moment, atmosphere or environment.
Working on natural fibres such as linen and wool, she meticulously dyes and screen-prints everything by hand, developing bespoke colour palettes for each project. Intrinsic to the visual structure of her work is how she 'carves out' the surface of cloth through the push and pull of removing and adding colour, creating positive and negative space. Depth and transparency are achieved through a complex series of layers, creating space that is architectural and ethereal. Through this process, elements are held together by delicate control of the printing process.
Joanna trained at University College for the Creative Arts (Farnham) and at Glasgow School of Art. Working from her studio in Glasgow, she teaches courses and one-to-one, and is also a visiting lecturer on various degree and post-graduate courses around the country. Joanna is a member of the 62 Group of Textile Artists and the author of 'Dyeing and Screen-Printing on Textiles' (A&C Black 2005 / Bloomsbury 2011). Her work has been exhibited widely both in the UK and abroad and has been featured in numerous books and magazines. | {
"redpajama_set_name": "RedPajamaC4"
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Overview: PSI Repair Services resolves issue of ongoing vacuum pump failures and saves customer over $800K annually.
Root Cause: PSI was able to determine that the coolant system was not adequate for the application: coolant lines were not adequately spec'ed, an inadequate sealant was used and the oil lines weren't sufficient for the application.
Solution: PSI determined the premature failures were due to overheating, improper lubrication and vacuum leaks, so they provided the manufacturer with digital photos of the assembly, illustrating and describing the correct installation procedures for coolant and lubrication. To resolve this issue, PSI recommended a cooling system that would extend service life from just 2 months to 3 years.
Result: PSI Repair Services cooling system corrected the leaks with an epoxy solution allowing the vacuum pumps to operate to OEM specifications. | {
"redpajama_set_name": "RedPajamaC4"
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require 'spec_helper'
module Alf
module Algebra
describe Rename, 'heading' do
let(:operand){
an_operand.with_heading(:id => Integer, :name => String)
}
let(:op){
a_lispy.rename(operand, :name => :foo)
}
subject{ op.heading }
let(:expected){
Heading[:id => Integer, :foo => String]
}
it { should eq(expected) }
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
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Jay Chou's new duet with newcomer Cindy Yen will be released on Hit FM today!
During the recent FETnet advertisement, a young girl has captured the hearts of the audience. With her beautiful appearance & bright smile, Cindy Yen has sparked many netizen's discussions & debates. But this girl doesn't just have a pretty face; the music in the advertisement is composed by her, the lyrics are written by her & she even produced it! She also specially wrote english lyrics to fulfil the requirements of the ad. And Jay Chou has just signed her under his company JVR Music. She is the first female junior that Asia King Jay Chou has signed, and her arrival & the music that she has brought has already attracted everyone's eyes & ears! But even more, Jay will duet with her in her new title track 'Sand Painting' which Cindy has composed and the lyrics are written by Vincent Fang. This is the first time that Jay Chou has ever sung a song that is not composed by himself, and this song will be released globally today on Hit FM, and everyone will be able to see & hear her amazing talent!
Jay Chou hasn't sung many duets in the past. The ones he has sung: 'Rooftops' with Landy Wen & 'Coral Seas' with Lara has left a big impression on the public, and is one of the most popular sung songs at KTV! Hence, his new duet with Cindy 'Sand Painting' is receiving alot of attention & anticipation! Although Jay singing a duet isn't too surprising, but the surprising thing is that this song is composed by Cindy & this will be the first time ever that Jay sings a song that isn't composed by himself. This shows his full confidence in Cindy's ability & talent in music. And to Jay's fans, their idol has been extremely busy throughout this year, and for the first time, he won't be releasing an album this year. Hence, perhaps the release of this song 'Sand Painting' can partly make up for that, and at the same time, allow everyone to meet this very talented newcomer.
Cindy actually has alot in common with Jay as the 2 both come from a classical music background, and their conversations are always about music. Cindy began learning the piano at 5 years old & the violin at 10 years old. She was born in Texas, America but was often bullied by her classmates due to her Asian face & when she was 12, she also had to face her parent's divorce. Hence, music gradually became her best friend & the most important thing in her life that accompanied her throughout her childhood. When she was 17, she headed to Taiwan, aiming to achieve her dream of becoming a singer. She sent many DEMOs of her music to various big music companies. At first her mother was very opposed to the idea and wanted her to concentrate on her studies, however gradually, she began to see how important this was to her daughter.
Eventually, Cindy met JVR & they used a different angle to view her music. They gave her alot of space to create her own music, and let her do whatever she wanted with it. Her debut album will be released on the 30th of October. Cindy expressed: "Right now, I still can't believe it! It's like a dream! Very excited but also very nervous! To me, not only has this achieved my dream, but in the future, I hope to be able to help my mother to share her responsibility and burdens, and I want to be her source of pride!"
[oldspoiler][b]sarah:[/b] *faints* omg omg omg i LOVE this song!!!!!!!!!!
its been a year since we've heard him sing something new.. and wow i always thought that he would never sing a song thats not composed by him. but yah, this girl is SO cute & VERY talented. hehe i think she sounds like the female version of jay with the parents divorce & classical music background & learning various instruments at a young age.
Edited by doraemon♡JAY, 23 October 2009 - 08:50 AM.
i hadn't heard any news about this until now...i fell in love once the music started! this girl has amazing potential! her composition sounds fresh, and her voice is actually really good too, i think she easily outshines jay in this duet. definitely looking forward to more from her!
Sounds nice! I can't wait for it to be officially released.
i just listened to the song and it's amazing!!!! i definitely recommend it to everyone. it really has jay chou's style to it even though he didn't compose it.
good grief was hearing hito FM online and wanted to pause it hear this song, when to my surprised i heard the DJ introducing this song on Hito. Its actually on now.
i miss jay's voice loads. hope he's going to have an album soon..
Wow, her voice is really nice.
Finally, a talented female singer in TW.
I think she over shines Jay in this duet...rather Jay did like a rap part in the song or something...LOL, rather than sang.
thought would only heard 'the green hornet' news til the end of the year.
she's a newcomer and already she's working with vincent and duet with jay. lucky talented gal.
this is truly a nice song. wish her all the best in her career.
looking forward in her next single.
Nice duet song, they both have good voice and style. I really love Jay sing in R&B style.
Edited by Wang Ai Mi, 23 October 2009 - 05:07 PM.
her MV is out now! please support her as she is a friend of mine!
Edited by aleeson, 26 October 2009 - 11:28 PM.
this song has jay's touch. i mean the composition and arrangement. jay must have supervised her during composing..LOL. this song remind me of jay's dui bu qi.
Edited by jeffreyhadi, 01 November 2009 - 06:15 PM.
amazing. this song is an instant hook ! | {
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The musical 42nd Street is based on the novel by Bradford Ropes and the subsequent 1933 Hollywood film of the same name, the show focuses on the efforts of famed director Julian Marsh and his attempt to mount a successful stage production of "Pretty Lady" a musical extravaganza at the height of the Great Depression. The show has lyrics by Al Dubin, and music by Harry Warren from a book by Michael Stewart and Mark Bramble, It was first performed on Broadway in 1980.
The story is the stuff of show business dreams. and is one of its most classic tales, telling the story of Peggy Sawyer, from Allentown, Pennsylvania a talented young chorus girl with stars in her eyes who gets her big break on Broadway when the star of the show falls and brakes her leg.
The success of this show (42nd Street) depends very much on the quality and execution of crowd-pleasing tap numbers, popular musical theatre standards, and show-stopping ensemble production numbers. Directed by Liz Clarke I am very happy to say that this production from BOS Musical Theatre Company did not at all disappoint as we were treated to a mesmerising dance extravaganza from the beginning as the curtain rose until the final bows at the end of the show. The delightful choreography devised by the very talented Mary Forbes was excellently thought out creating great entertainment for the audience. All routines were performed matchlessly by all the cast with a great deal of energy and expertise, they were perfectly in time with each other and everyone must have worked very hard to attain such a high standard. The talented principle cast appeared to work well together with no weak links producing some lovely characterisations with respectable well maintained American accents, clear diction and excellent projection. They all gave very enjoyable strong performances showing off their talents in singing and dancing admirably.
The cast included Ian Lawson as Broadway director Julian Marsh and Heather Lewis as the classic Broadway star and diva Dorothy Brock with Lauren Miller in the central role of the small town girl and future Broadway star Peggy Sawyer. Craig Billington was Billy Lawlor the juvenile lead in "Pretty Lady" with Helen Taylor as Anytime Annie, Peggy's friend and fellow dancer. Karen Parkinson was back on stage again as writer Maggie Jones and her fellow writer Bert Berry was played by Dom Tolley. Tapping his way through the show was Robbie Dale as Andy Lee the show's choreographer and Phil Power was Pat Denning, Dorothy Brocks boyfriend and future husband. Dorothy's Sugar Daddy Abner Dillon was played by Paul Wilkinson while Nick Lloyd was Mac the stage manager and Richard Michell was Oscar the pianist. Playing three of Peggy's friends and fellow dancers were Wendy Harris as Gladys, Lucie Clarke as Lorraine and Sarah McNally as Phyllis.
The supporting cast and ensemble worked very hard and produced some good characterisations of their own while supporting the principal cast strongly. The Orchestra conducted by Charles Moss played very well and also supported the actors, singers and dancers on stage soundly. The hardworking backstage and technical crew did their jobs efficiently meaning changes were slick between scenes, helping to maintain the energy and pace of the show and along with colourful costumes, hair and makeup, which were spot-on for the era, enhanced and set the mood for the production and resulted in an excellent platform for the cast to work on.
Congratulations to Liz Clarke and everyone involved in this outstanding production. Thank you very much for inviting us we had a great evening.
HAVING grossed several million dollars worldwide since the original 1933 film was released this lively, feel-good musical has been a favourite with theatre-goers.
It is no surprise, then, when the overture strikes up with We're in the Money and the curtain raises slowly to reveal tapping feet followed by long legs and smiling faces.
There then followed 16 scenes with sparkling costumes and faultless acting. Lauren Millar shined in the role of Peggy Sawyer – an inexperienced wannabe, fresh out of Allentown, desperate for a shot at fame. She misses her vital audition because of nerves.
However this is Broadway where magical things happen so Peggy will not be disappointed. Julian Marsh (an excellent performance by Ian Lawson) is putting on a show – Pretty Lady – starring Dorothy Brock. Heather Lewis was perfect in the role of the diva who is forced to leave the show when Peggy accidentally knocks her over.
With a compound fracture of her ankle (ouch, I've had one of those!) she cannot fulfil her role so will the show have to close? Oh no … spurred on by her fellow cast members – "Hey kid, you're good!" – Peggy, after having been fired and then rehired, takes the part. And the rest, as they say, is history. Pretty Lady is a hit!
Charles Moss and his superb orchestra did justice to Al Dubin's delicious lyrics and Harry Warren's toe-tapping music. It was all complemented by Mary Forbes' magnificent choreography and the whole cast gave memorable performances, at a cracking pace, under Liz Clarke's snappy and first-rate direction.
Alan Gosling was responsible for the excellent sound and lighting effects, working in conjunction with Dave Murray of Infinity Technical Services.
Space doesn't allow me to mention all the cast by name but congratulations to everyone on this brilliant production! | {
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Originally Published: March 23, 2019 11:44 a.m.
A Sedona resident wants the city to consider growing hemp along SR89A to take advantage of reclaimed water that is now being sprayed into the air and returned to the aquifer.
The April 9 meeting was requested by resident Pam Drake. City staff will attend, according to Marty Macurak, communications manager for the city.
The reclaimed water from the city's waste-water treatment plant, several miles south of town, is currently pumped and sprayed back into the ground.
The City of Sedona is irrigating 300 acres of land and have two recharge wells for aquifer recharge, explained Roxanne Holland, wastewater manager for the City of Sedona.
Holland said Sedona produces about 420 million gallons of reclaimed water each year. Out of that, about 30 percent can be sent to aquifer recharge.
"In 2018, we put approximately 25 million gallons back into the aquifer," she said.
The city's spokesperson said the mayor has been invited but did know if she would attend.
Drake, in her letter to the city, said a regenerative agricultural consultant will present a Powerpoint on industrial hemp and Drake has invited a number of other officials from Yavapai County, the University of Arizona Extension Service, Yavapai College agribusiness and science technology department, Mayor Sandy Moriarty, prior Mayor Rob Adams, prior councilman Ernie Strauch and several current council members.
"The day and time are anchored and we will hopefully strive to gather up possible agricultural partners, cement partners, biodiesel partners, heating-wood chip production. Whatever and whoever can bring some ideas and input to a Science Project for Sustainable Sedona.," Drake said in her letter to the city.
The 2018 Federal Farm Bill was signed into law and legalized industrial hemp by excluding it if from the definition of marijuana, according to the Arizona Department of Agriculture.
The work-session is scheduled in the Schnebly Room at Sedona City Hall, 1:30 p.m., April 9.
"We should bring back the growing of industrial hemp in this nation," Drake said.
Farmers were "mandated" to grow it during WWII, she pointed out.
"George Washington grew it," she said. | {
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Milites Christi
N32:6 Shall your brethren go to war, and shall ye sit here?
No Religion
Earth Angels
Justice For Croatia
Let's talk about hypocrisy
Animals too, shall see the salvation of God (Luke 3:6), animals too, have a soul (1 Cor 15:44), man has no advantage over the beasts (Ec 3:19), the covenant is between God and every living creature of all flesh that is on the earth (Genesis 9:16-17) Those who are against slavery, discrimination, injustice and torture should look at the content of their stomach. Luke 3:6 And ALL FLESH shall see the salvation of God. 1 Cor 15:44 It is sown a natural body; it is raised a spiritual body. If there is a natural body, there is also a spiritual body.
Proverbs 31:8 Speak up for those who cannot speak for themselves
Michael Rutzen a shark whisperer. Dean Schneider the lion whisperer. Blah blah blah. You know what it is about these people? They are simply respectful enough to COMMUNICATE with animals as living beings. Which doesn't mean they forget, that these in fact are, animals.
They give the proper love, respect, and communicate with them in their own language.It's the most obvious thing in the world. But it is ego that prevents people to communicate with other beings.
If you want to communicate with a person from another language you look up a translator, learn their language or their culture.
Any idea how many swans and ducks die because people feed them bread? 'Do you know how a calf begs not to be killed? "They all beg for their mothers in language that requires no translation... They are defenseless... They are frightened... They cry pitifully for their mothers...as they are being dragged onto the killing floor, they are still looking for their mothers, still desperately needing her nurturing presence, especially at that dark time when they are frightened and needing protection more than ever in the midst of the terrible sights, and sounds, and scents of death all around them, and, in their despair, in their want for a shred of consolation and protection, most try to suckle the fingers of their killers'.
Ec 3:19 For what happens to the children of man and what happens to the beasts is the same; as one dies, so dies the other. They all have the same breath, and man has no advantage over the beasts, for ALL IS VANITY.
All beings have their own language
Dog Facial Expressions And Humans
'Many mammals make facial expressions. The architecture of the face, with muscles for making facial expressions is much the same across these mammals. They probably inherited this architecture from a common evolutionary ancestor in the distant past.
Scientists used to think animal facial expressions aren't like ours. They are inflexible and involuntary and don't reflect sophisticated cognitive processes. Now, increasing evidence shows that they were wrong'. read more
New Zealand Legally Recognises Animals as 'Sentient' Beings
17 May 2015 - The New Zealand Government has formally recognised animals as 'sentient' beings by amending animal welfare legislation. The most recent amendment to New Zealand's Animal Welfare Act states that the purposes of the legislation include recognising "that animals are sentient" and "to require owners of animals, and persons in charge of animals, to attend properly to the welfare of those animals".
Fortunately, the animals in New Zealand are recognized as a living beings with feelings. In the Netherlands as in many other 'civilized' countries not yet. Read more
Zapopan Becomes First City In Mexico to Legally Protect Farmed Animals
Koko, the gorilla that mastered sign language
Koko's companion Michael explained to Penny Patterson about when his troop was attacked and his mother killed. (In sign). If we want to talk to someone from another country we learn their language or they ours. Animals communicate too. Do not be like everybody else. All lives matter. Stop using, abusing, killing and eating animals.
Study Finds that Cows Talk and Show Compassion Just Like Humans
'When we think of compassionate, intelligent creatures, cows normally don't come to mind. However, cows actually communicate how they feel to one another through their moos, according to a new study. The animals have individual vocal characteristics and change their pitch based on the emotion they're feeling, according to research at the University of Sydney. "It is like she is building a Google translate for cows," said Cameron Clark, an associate professor at the university about Ms. Green.' (source)
2020 - Cows tell each other how they feel through their moos, according to a new study. The animals have individual vocal characteristics and change their pitch depending on their emotions, according to research by the University of Sydney. Alexandra Green, the study's lead author, said: "Cows are gregarious, social animals. In one sense it isn't surprising they assert their individual identity throughout their life." source
Dairy Farmer Admits 'Some Mother Cows Cry For Days'
The farmer broke down as he described the emotional suffering of the animals, read more
This Penguin swims 5,000 miles every year for a reunion with the man who saved its life
Angela Davis: Feminist, Civil Rights Activist, and Vegan
In a 2012 interview with Grace Lee Boggs she discussed why she decided to go vegan:
Most people don't think about the fact that they're eating animals. When they're eating a steak or eating chicken, most people don't think about the tremendous suffering that those animals endure simply to become food products to be consumed by human beings.
Sentient beings ... endure pain and torture as they are transformed into food for profit, food that generates disease in humans whose poverty compels them to rely on McDonald's and KFC for nourishment.
Famous racist quote "white people can't dance".
False. We all have different qualities.
Genetics is proof of the belief that all members of each race possess characteristics, abilities, or qualities specific to that race. Racism is when the results of genetics are distinguished as inferior or superior to another race or races. You do not compare snakes to swanes, bees to elephants, each creation of God have their own use, beauty and smarts.
Deut 32:8 When the most High divided to the nations their inheritance, when he separated the sons of Adam, he set the bounds of the people according to the number of the children of Israel.
Racism & Speciesism
Those who are most sensitive about "politically incorrect" terminology are not the average black ghetto-dweller, Asian immigrant, abused woman or disabled person, but a minority of activists, many of whom do not even belong to any "oppressed" group but come from privileged strata of society. - Ted K.
There is a big group of white liberal and emotionally unstable women out there who cry their eye balls out feeling sorry for acts done by European colonialism. I never seen this behaviour in black women feeling responsible about what their ancestors did. Or any other. If you are ashamed to be white, go and be like Martina Big. These white liberal blind women will stand behind Palestine, eventhough after all these years we have seen Palestinians set donkeys on fire and ignore that Gaza reopened Rafah Zoo. Israel behaves like scum and so does Palestina, if you want to choose a side, you choose for animals. These liberal blind white women wave the flag of pride, mocking Christ, but NEVER EVER will raise their voice that strongly for children. You will not hear them speak up for the discrimination of albino people in Africa either. Nor about the slavery of black people by Arabs. These women discriminate their own kind.
They are like the 'antifascist' that uses fascist methods (like current leaders of Israel), the 'vegetarian' that eats fish.. These are the same liberal white women that did not stand up and speak up for the hundreds of women that were mobbed and sexually assaulted during celebrations in the western German city (New Year's Eve 2015) by migrants.
Slavery is still common in muslim countries in 2022. Arab slavery had already begun in Africa more than 700 years before the European transatlantic slave trade. The slave trade began when the Arabs invaded North Africa for the first time in the 7th century AD. The first Arab entry into Africa was through Egypt. An Arab military general named General Amir Aben Alas invaded Egypt in December 639 AD. Amir had successfully conquered Egypt and went ahead and conquered other places such as Tunisia and western Libya. Once these areas had been completely conquered by the Arabs, they imposed tributes of 360 slaves in all regions they occupied and controlled.With this Islamic slave trade in Africa, North Africans were Islamized by their Arab slave masters.Today, many Africans pose as Muslims without knowing how the owners of such a religion brutally enslaved their black African ancestors for over 700 years. source Historical Jb
Where is BLM now?
Another briliant example of how these white liberal women have birdpoop for brains. Complete disrespect for people who actually did experience war and suffering. Norman Finkelstein rightfully states: THEY ARE NUTS.
Animals laugh. Dream. Play. Just like you and me. Why do you eat/hurt or exploit them? Because it's legal? So was slavery!
"I think for what we Europeans have done over the past 3,000 years, we should apologize for the next 3,000 years before we start teaching people moral lessons," said FIFA president Gianni Infantino. When ego and greed are involved people get very selective in remembering history.
Pedophile traditions in Iran - 2023
An Iranian man was sentenced to eight years in prison on Wednesday for beheading his 17-year-old wife. According to BBC News, he had killed the girl as an (DIS)honor killing.
In Iran, this often happens when a victim decides to cancel a pre-arranged marriage, has been raped or had sex with someone else outside his or her marriage. Seventeen-year-old Mona had tried to escape her husband because he abused her. She was married to him at the age of twelve and gave birth to a son at the age of fourteen. (source)
Stop demonizing the white man when every race has been killing raping and looting the other
2022- How Nigerian Army Massacred Many Children During Operations, Claimed Fathers Were Boko Haram Terrorists (source) wanna claim this is white mans fault too? Iranprotests: arrested women are being held in houses - with some 'beaten and tortured' (source); beating women to death also white man's fault?
Belgian terror in Congo
The former Belgian King colonized the Congo Free State in the late 1800s and murdered millions.
King Leopold II statue removed in Belgium
Turks Invading Serbia
Turkish settlement into Kosovo began in the late 14th century after the medieval Serbian state lost the Battle of Kosovo and the territory came under Ottoman rule. Substantial waves of Turkish colonisers began from 1389-1455 when, during the Ottoman conquest, soldiers, officials, and merchants began to make their appearance in the major towns of Kosovo (source)
Now look at the minister of economy Kosovo's page here, all in Turkish language. This is abnormal. And also explains Srebrenica. Milosevic - albeit being an untermensch himself as they had nothing to seek in Croatia - said before Srebrenica took place "this is what you are get in return for 500 years occupation". Because this type of barbarism (many executions, beheadings and burnings) is not from European origin, the area now goes into the history books as the cradle of modern jihadism. "There is a war between the West and Islam," says Aimen Dean, who, as a young Saudi Arabian volunteer, travelled to fight in central Bosnia in 1994. "Bosnia gave the modern jihadist movement that narrative. It is the cradle."
Isis jihadists back in Kosovo ready to die for caliphate
Fitim Lladrovci: "I want to create an Islamic State in Kosovo and I'd gladly die in support of it"
Aloysius Stepinac said, Serbia needs to get back to their roots. When Belgrade was under siege of Turkish forces, they got help from the soldier priest John of Capistrano.
Islamists killing Croatians throughout history
Around 1680 - a Croatian virgin did not want to marry an Ottoman, next day he returned with 20 soldiers and killed her with a knife.
1493 - Battle of Krbava Field
1593 - Battle of Sisak
1715 - Siege of Sinj
1993-'94 - Vitez massacre
2016 Tomislav Salopek murdered
2019 Croats prevent attack in Croatian church in Germany
2019 Migrant muslim attack in bus
2019 Syrian Doc warns Croatia; Dr. Nizar Shoukry about migrants from the East:
"As a Croat who knows the mentality of the East, I say: immediately raise fortifications and send troops to the borders, we are now the main route"
2013 - Three muslim asylum seekers from Morocco robbed and tried to rape 19-year-old girl from Zagreb were detained source etc etc etc etc etc
African Slaves In The Arab World
Over 28 Million Africans have been enslaved in the Muslim world during the past 14 centuries While much has been written concerning the Transatlantic slave trade, surprisingly little attention has been given to the Islamic slave trade across the Sahara, the Red Sea and the Indian Ocean.
While the European involvement in the Transatlantic slave trade to the Americas lasted for just over three centuries, the Arab involvement in the slave trade has lasted fourteen centuries, and in some parts of the Muslim world is still continuing to this day. A comparison of the Muslim slave trade to the American slave trade reveals some interesting contrasts.
While two out of every three slaves shipped across the Atlantic were men, the proportions were reversed in the Muslim slave trade. Two women for every man were enslaved by the Muslims.
While the mortality rate for slaves being transported across the Atlantic was as high as 10%, the percentage of slaves dying in transit in the Transsahara and East African slave trade was between 80 and 90%!
While almost all the slaves shipped across the Atlantic were for agricultural work, most of the slaves destined for the Muslim Middle East were for sexual exploitation as concubines, in harems, and for military service.
While many children were born to slaves in the Americas, and millions of their descendants are citizens in Brazil and the USA to this day, very few descendants of the slaves that ended up in the Middle East survive.
While most slaves who went to the Americas could marry and have families, most of the male slaves destined for the Middle East were castrated, and most of the children born to the women were killed at birth. It is estimated that possibly as many as 11 million Africans were transported across the Atlantic (95% of which went to South and Central America, mainly to Portuguese, Spanish and French possessions. Only 5% of the slaves went to the United States). A comparison of the Muslim slave trade to the American slave trade reveals some interesting contrasts.
While two out of every three slaves shipped across the Atlantic were men, the proportions were reversed in the Muslim slave trade. Two women for every man were enslaved by the Muslims. Read more
Qatar World Cup chief says 'death is a part of life' after reported Filipino migrant worker death
Bedbugs and sixteen men to the room
It's teeming with cockroaches and bed bugs!" says Aktar, pointing to a trio of the latter species under the bed.
In a different part of Shahaniya, the area where the Africans live, we meet Henry and Alex from Nigeria. They work as security guards for a private company at another labour camp. Henry's been here for three years and hates Qatar with all his heart. "You can quote me on that", he says.
You don't like it here? "Didn't you hear me the first time? I hate Qatar." "I've been here for almost three years - and I've worked from 7 A.M. to 7 P.M. every single day. Why? It's a waste of life. I have no life, I'm a slave. And if I take no days off I'll get higher wages, about 360 dollars a month." Read more
FIFA chief accuses critics of Qatar of hypocrisy ahead of World Cup
"I am European. For what we have been doing for 3,000 years around the world, we should be apologising for the next 3,000 years before giving moral lessons," he said. (source) Gianni Infantino along with other 'celebs' without any moral compas are trying to normalize evil. The whole point of being called out is to make a change.
How self confidence looks like
Inferiority complex?
An inferiority complex is the feeling of being less valuable than others. Go to a psychiatrist, solve it, but don't drag others into your negativity. You don't need a new skin, you need a shrink.
'Racism has no place in our society': Kensington Palace condemns 'unacceptable comments' by Prince William's own godmother Lady Susan Hussey as she RESIGNS from Buckingham Palace role after asking British black charity founder 'if she was from Africa'
So what is the fuss about? A black woman born in Britain who feels discriminated because she is asked where she is originally from. The majority of people will respond by telling you about their heritage, and do so with pride. source and pictures underneath from dailymail.co.uk, 2022
Among foreigners (like myself) it is normal to ask each other about your origins, because your features or accent clearly indicate that your roots lie elsewhere. That has to do with interest, not discrimination.
Healthy People Discriminated
For the first time ever a "medicines" ineffectiveness is being blamed on those who haven't taken it.
We have entered an era in which whatever the government says must be true and healthy people are considered unhealthy for not taking medication unhealthy people need to keep up with their unhealthy ways.
When you do not want crap in your body because you live healthy
"I do not use any kind of synthetic ingredients in my life, whether that be for medicinal purposes, supplementation or food. So the idea of becoming inoculated is something that goes directly against the way that I live my life," Kahseim Outlaw said.
Toronto District School Board (TDSB) superintendent Helen Fisher (pic right) loves to hide facts
Canadian school CANCELS event with ISIS survivor Nadia Murad because her harrowing description of torture and rape 'would be offensive to Muslims and foster Islamophobia'
Murad's book details how she escaped the Islamic State, where she was ripped from her home and sold into sexual slavery aged just 14 years old.
Murad was captured by the Islamic State aged 14 and went on to become a leading advocate for survivors of genocide and sexual violence, a Nobel Peace Prize Laureate and a UN Goodwill Ambassador source
Civil rights and labor movement hero Cesar Chavez was an animal rights activist too....
"We cannot defend and be kind to animals until we stop exploiting them. Exploiting them in the name of science, exploiting them in the name of sport, exploiting them in the name of fashion, and, yes, exploiting them in the name of food. The basis for peace is respecting all creatures." - Cesar Chavez, 1992, accepting the Lifetime Achievement Award from In Defense of Animals.
Jesus referred to himself as a hen who gathers her chicks
(Matt 23:37; Luke 13:34)
And look how satan - the world treats these animals
Female chicks are abused for eggs until their bodies give up on them
Male chicks find their death in a .. grinder...
Yee hypocrites........
Before an animal gets killed so you can feast on it's flesh
IT BEGS FOR ITS LIFE...
You show no mercy by buying their meat. How are you going to explain that to the Lord?
Before our fall into sin, there was no meat,
dead flesh in the Garden of Eden.
After judgement day, there will be no meat,
no dead flesh in the new Kingdom.
Animals surrounded Jesus alive, when He was born.
Now you know.
"Wir haben es nicht gewusst" is no excuse anymore.'It is tradition to eat them'. So was pooping in the middle of the street once. Be one less person harming animals....
Smash Your Ego!
Don't be a lazy gluttony sloth bum, going vegan is easier than you think.
Every breathing being wants to live.
All animals want to live.
Want to raise their families.
Pigs or Dogs, there is no difference.
Seek The Differences
Ear tags after slaughter
Pile of Shoes Auschwitz
All lives matter!
Proverbs 4:27 "Do not turn to the right or the left; keep your foot from evil."
White female torn from vehicle, stomped in street by BLM
BLM terrorizes a woman and abuses her dog, see video here
Also killed (shot 6/4/2020 by BLM protestor James Marshall) is single father & disabled veteran Danny Pruitt. On Thursday, June 4th 2020, Danny was on his way to get dinner, when the roadway was blocked by protesters. One person decided to make a calculated decision, shooting through Danny's driver side window, the bullet hitting Danny in the the head. Gofundme
BLM/ antifascists attacking innocent horses
Underneath pic: Antifa Portland
Above Antifa Portland USA, underneath.. was a video of Antifa Poland. The videos in which the Antifa's true nature of being special snowflakes is shown seems to get deleted on Facebook and Youtube> Now that is what I call hardcore fascism.
Over 110 Million Blacks were killed by Islam.... a minimum of 28 Million African were enslaved in the Muslim Middle East. Since, at least, 80 percent of those captured by Muslim slave traders were calculated to have died before reaching the slave market, it is believed that the death toll from 1400 years of Arab and Muslim slave raids into Africa could have been as high as 112 Million. When added to the number of those sold in the slave markets, the total number of African victims of the trans-Saharan and East African slave trade could be significantly higher than 140 Million people.
And Praise Ye The Lord, hear saint Michael Whaley
CNN spewing hate
CNN commentator Van Jones has sparked a backlash for suggesting the cops who beat Tyre Nichols may have been 'driven by racism' - despite them all being black. The video released on Friday night shows Nichols, 29, crying out for his mother multiple times during the brutal January 7 assault, which took place just a few blocks from his home. He died three days later. Jones, one of CNN's star liberal commentators, wrote Friday that black people 'are not immune' to the effects of anti-black racism and that the narratives of police violence should never be as simple as 'white cop kills unarmed black man.' (source 1, source 2)
Dirty Pigs? Pigs are very intelligent and remarkably clean animals, but the stables are so small that they are forced to use their living space as a toilet. Something a pig would NEVER do in nature: they walk tens of meters from their living space to do their needs there. These animals are intelligent and made insane, just as we humans would turn insane when forced to live like that. You want to see which creature is dirty? Go visit a random public toilet.
Fact: some of the best known Quaker proponents of the abolition of slavery (Christians) were.... vegetarian.
I'm for truth, no matter who tells it. I'm for justice, no matter who it's for or against. ~Malcolm X
Black Lives Matter is a Marxist organization. Quote from co founder Patrisse Cullors "We actually do have an ideological frame, myself and Alicia in particular are trained organizers and Marxists."So the foundation of this movement is a genocidal ideology which is responsible for 100s of millions of deaths. On the picture above is to the right Laura M. DiCampli, the woman that vandalized the WWII and 9/11 memorial in NY.
Yes. Discrimination certainly takes place. A black man is more likely to be arrested in a neighborhood known for drugs in the US just as a white man will be more likely to be arrested for pedophilia in Thailand.
So many weapons on the streets, guns, knives. Imagine if all these people actually started to help out others. Help feeding animals at shelters, helping the homeless, becoming a fireman or so.
Origin word niger
Just like with whites (Celts, Germans etc) there are different blacks. Niger Basin blacks considered themselves and were seen as different from all other blacks in most of Africa. It used to be that everyone knew this. Niger Basin blacks considered themselves the aristocracy of the black world. They were considered better workers and more intelligent. To make sure that everyone knew who they were the Niger Basin blacks called themselves "Nigers".
The 1828 Webster Dictionary gives the following pronunciation:
NEGRO, (It. Sp. negro, black from L. niger, it is remarkable that our common people retain the exact Latin pronunciation of this word, neger) a native or descendant of the black race of men in Africa (Noah Webster Dictionary 1828).
Niger blacks were also more comfortable being called by the Latin pronunciation than the Portuguese or English pronunciation of 'black'.
But, the media turned the name upside down. What was once good and a source of pride is now bad - and many blacks have forgotten the pride of their Niger Basin homeland. There was one black who did not forget who he was and where he came from.
He was Marcus Garvey.
A poem of his:
Say! Africa for the Africans,
Like America for the Americans:
This is the rallying cry for a nation,
Be it in peace or revolution.
Europe cries to Europeans, ho!
Asiatics claim Asia, so
Australia for Australians,
And Africa for the Africans.
Hurrah! Hurrah! Better times are near;
Let us front the conflict and prepare;
Greet the world as soldiers, bravely true:
"Sunder not", Africa shouts to you.
Got Wu?
According to RZA on Hot 97 on 10/12/2017 the five fingers in the hand symbol identifies as the five human families: white, black, red, yellow and brown. The thumbs locked in the middle is any of those two families coming together to unite humanity. RZA, by the by, is vegan too.
Fix your own life
Whoopie Goldberg, who used to be a comic, but now is just an obese dinosaur, claimed today on "The View" that racism is as terrible as ever, but her only examples came from half a century and more ago - she ranted on about lynchings, how Black men had to step off the sidewalk when a White man passed, etc. - all instances from the pre-sixties and MLK. Like fellow Hollywood termites, Cher, Joy Behar, etc., Whoopie is a Class A bigot.
But this brings up another problem: ancient anger. Whoopie's views might be unreasonable, but they are justified in the sense that the ancient wrongs committed on her "relatives" still exist - in the fires of ancestral resentment. Whites can't expect their former crimes to simply slide away on the breeze.
Blacks contain a reservoir of anger at the severe injustices and cruelties done to them for 200+ years, and they retain this anger despite the apologies and supplications of the "Whites." And that's reasonable in a way: you can't, for example, murder my father, and then years later come and say, well, sorry, let's be equal friends now. No justice in that. So they remain much more bigoted than Whites. Who can blame them?
But the other side is, millions of us Whites had nothing to do with their slavery or treatment in the past, NOR DID OUR ANCESTORS. But Blacks blame us anyway. I grew up in extreme poverty, (well, poverty has a limit: what is more extreme than nothing?) and probably had a more horrific childhood than 90% of Blacks. (Hence the psychic abilities: they come from trauma and dissociation.) And, like many Blacks today, I worked my way up economically and... Well not socially, not much. So, Blacks, get off my case. I owe you nothing, nada. Stand down. Fix your own life.
And when you are already wealthy, powerful and pampered, don't lecture me on how good your fat Blackness is, and how bad my starving Whiteness is. - written by Tim Stephens (his site source)
United States: where every criminal turns into a saint
'He was either going to be imprisoned, kill someone, or be killed.' How man shot dead by Minnesota cop led a life of crime and violence before his death and shot his own friend, broke into neighbor's home, and robbed a woman at gunpoint'
Cop found guilty
Mostly white Minnesota jury convicted Potter, 49, of first- and second-degree manslaughter charges for killing Wright, 20, during April 2020 traffic stop. Potter, who is white, claimed she confused her handgun for her Taser when she shot and killed Wright, who was black. Potter, 49, a white suburban mom-of-two who served in her city's police department for more than two decades, was found guilty of first and second degree manslaughter for shooting 20-year-old black motorist Wright on April 11 during a traffic stop after allegedly mistaking her gun for a taser. A retired New Jersey police lieutenant slammed the guilty verdict reached by jurors in the manslaughter trial of Minneapolis cop Kim Potter Thursday, saying it would have a 'chilling effect' on police officers across the nation.
'She demonstrated that she had no intent on using her firearm. And I must tell you, that this verdict is going to leave a chilling effect on every cop across this country.' Roger said during the televised interview. source
The White Privilege Of South African Families
White genocide in Africa for many years now but nobody gives a shit.
These aren't names of soldiers that died during war, these are farmers who died, brutally murdered on their farms in South Africa. This wall of Remembrance is at Nampo in Bothaville. (source)
Stop Murders in South Africa, see website here
And you ask why whites are being killed in SA?
African activist, nature and animal lover Fousseny Traore speaks up: "Some "tourists" have so firmly anchored in their memory that the riches of Africa, its natural resources still belong to the colonizers: They consider it their private property!Unfortunately, the facts confirm the idea that some tourists, not all of them, but still far too many, behave like imbalances! And again, under the watchful eye of our incompetent leaders! So this monster, this silly woman: she poses next to the corpse of a giraffe, this majestic animal. And what does she say? "I have waited for this opportunity for years" ... utter horror!According to the Mirror newspaper, Merelize van der Merwe's husband would have spent 1,500 pounds (over 1,700 euros) on a hunt in a game park in Sun City, South Africa, during the Valentine's Day weekend .source
R.I.P. Daniel
19 years ago he murdered Daniel Wretström in Salem.
Now he has been convicted of hitting a man several times in the head - in the role of security guard in the Stockholm metro.
Now Expressen can show the surveillance video from the assault.
Daniel Wretström was a Swedish ultra-nationalist murdered in Salem, Sweden.
The 17 year old Wretström was at a bus station close to a local youth center. He was assaulted by a group of about 15 immigrant youths. After the initial assault, one of his assailants hit Wretström over the head with a 1.5 meter-long plank, which knocked him unconscious.
An older relative of one of his assailants then arrived on the scene with a knife, and Wretström was stabbed in the back until the blade of the knife broke off, and then his throat was cut with the broken blade.
Wretström's murder inspired a variety of nationalist activists to organize an annual demonstration known as the Salem March.
No outrage for a white child
On Sunday, while Cannon was riding his bike with his older sisters in front of his house, he had a gun put to his head and was executed by the neighbor who lived next door.
Cannon hasn't been talked about in the national news.
CNN Finally Covers Alleged Murder Of 5-Year-Old Cannon Hinnant In 200-Word Blurb
He won't be buried in a gold coffin, or have celebrities, politicians and professional athletes at his funeral.His parents won't be given a folded American flag or given millions of dollars in recompense.He'll just be gone. Forever.
NYC shrink who talked about shooting white people now says they are 'psychopathic'
June, 2021 (source) 'The New York City psychiatrist who stunned a Yale School of Medicine audience in April when she revealed her fantasies of "unloading a revolver into the head of any white person that got in my way" characterized white people as "psychopathic" Thursday in an interview with disgraced former CNN pundit Marc Lamont Hill.
Dr. Aruna Khilanani - who also revealed in her talk at Yale's Child Study Center April 6 that white people "make my blood boil" and "are out of their minds and have been for a long time" - joined Hill on the fledgling Black News Channel's prime-time program "Black News Tonight" to discuss her shocking statements.' Read more
Actor Raymi Sambo assaults a woman, is convicted and then complains about discrimination
Lawyer: 'Victim abuse by Raymi Sambo not drunk'
Raymi Sambo (then 49-year-old), actor in Dutch series, came into the news in 2020 after images appeared of him assaulting a woman. The victim reported that she was headbutted by Sambo, breaking her nose and sustaining a concussion. He was sentenced to 100-hour community service in the Amsterdam court for assaulting the woman and had to pay her 6,310 euros in compensation, as the public prosecutor demanded.
source, source When on Instagram someone wrote "Wondering if the woman you hit tonight has such a nice new year, loser!" Raymi has been seen reacting furiously: "I don't care, typhus whore!" (source)
Lil Kleine (singer in the Netherlands, white skin color) has been sentenced to community service for assault of 120 hours (source). During a performance, this singer shouted to one of his spectators the remark "your mother is a whore". (<to compare with Raymi's 100 hour sentence and emotional intelligence).
Raymi Sambo comes to mind when listening to Eazy-E's Real Muthaphuckkin G's where :
'a bitch portrays the role of Gangsta, ain't broke a law in ya life, ... Never ever once have you ran with the turf, but yet in every verse Claim you used to do the dirt, but tell me who's a witness To your fuckin work, see you never had no buiness, so Save the drama jerk, niggaz straight kill me Knowin that they pranksters...'
Beating up a woman does not make you a gangster. He beats up a woman and instead of being ashamed this creature actually plays the race card and goes even further and tries to lift on the experiences of black Americans like snatching the titel from N.W.A.s Fuk Da Police. Want to be part of the real shit? Go to the hoods in USA. Visit my friend in Mexico, you'll see people hanging from bridges every day. Or be like Opto. But don't pretend to be hard shit in a safe country.
Actor Jussie Smollett found guilty of staging race-baiting hate attack to boost career
Empire actor Jussie Smollett has been found guilty of making a false report. That is what the jury in the case decided on Thursday. He could face a prison term of up to three years. Smollett has already said he will appeal. The American actor insisted in court last week that he was the victim of an attack by two men in January of 2019.
According to him, they used swear words for gays and would have shouted "MAGA". That's an abbreviation of former US President Donald Trump's slogan: Make America Great Again. Prosecutors said Smollett staged the attack, presumably to get attention that would help his career. The two 'perpetrators', the brothers Abimbola and Olabinjo Osundairo, said in their testimonies that Smollett paid them $3,500 (almost 3,100 euros). He wanted them to slap him in front of a security camera and hang a gallows noose around his neck. source
The Asian grooming gang lies that sparked national outrage: How woman's false rape and trafficking claims triggered protests, heightened racial tensions and ruined lives of men she accused
(04-01-2023 source dailymail.co.uk) Eleanor Williams sparked outrage in the Cumbrian town of Barrow when she claimed on social media she had been groomed, trafficked and beaten, in May 2020. Posting pictures of her bruised and beaten body, the 22-year-old said she had been the victim of an Asian grooming gang in the port town 'for years', leading to protests led by former EDL leader Tommy Robinson. It heightened racial tensions - one curry house had its windows smashed and a muslim takeaway owner was chase down the street by men who poured alcohol on his head. It also painted a target on the backs of the men she accused - one man saw his wife leave him over the claims, while another family were forced to leave the town altogether.
White people do not have freedom of speech
"I don't see myself dating a white guy. Nothing against his race but it is more about like, my bloodline and keeping it pure and black." says the black girl.
Bello Hunter (click here to see the Facebook reel); "Did you see that? One more time, I'm 'I'm going to bring something up about. "Like my bloodline and keeping it pure and black". and imagine if a white guy said word for word what she just said. Imagine a white guy just had this question asked. Why don't you date a black woman? A a white guy goes, well, that's kind of a law keeping the bloodline pure and keeping it white. I'm proud of being white. I want my bloodline to be white and that's why I wouldn't date a dark woman. I care about my bloodline. I'm proudly white. She's saying the same thing. And I was like yeah good point. Oh yeah i get it. White people do not have freedom of speech."
Here is a cracker joke. Which is funny. No need to cry like a baby.
Man asking a woman if she would date him, she replies with no, I don't like white guys. Which is normal. Imagine if we all liked the same. But if a white man would say such about a black woman, it would be called racism. see reeel here
The Pandemic Is Real
But it does not mean you are not being played.
The cause of the pandemic is as always related to the animal eating industry. The governments still want you to eat more of that, not less.
Young heroes Marcus Harvey and Tre' Jones kicked in the door of a burning home and put their own lives in danger to pull a Marion man to safety.
The media feeds on racial tensions, only to divert from enslaving masses even more and paving the way for the cashless society. Don't be a fool. This is not about us little people.
Rev 13:17 And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name.
Eyes are the mirror of the soul
Mass Media Refused To Report Their Brutal & Vicious Murders
Channon Christian and Chris Newsom. In 2007 the couple was raped, tortured and killed, four people were convicted in their deaths. Channon Christian was gang-raped, choked and bound she was stuffed inside a trash can while still alive, a federal prosecutor told jurors in opening court statements today.
Assistant U.S. Attorney David Jennings said this afternoon in U.S. District Court. Jennings revealed details about the killings of Christian and her 23-year-old boyfriend, Christopher Newsom, as a jury was seated in the trial of Eric Dewayne "E" Boyd.
Boyd is charged with helping hide out Lemaricus "Slim" Davidson, the alleged ringleader in the carjacking and killing of Christian and Newsom. Jennings also told jurors that Newsom, who had been raped by his assailants, was shot three times.
"These people tie him up, gag him, wrap him in cloth material ... shot him in the back, shot him in the neck, and they shot a kill shot to his head. Then, his body was doused with gasoline and set on fire."
(we must pray that, unlike Channon, and unlike Kris Donald the British victim of a similarly brutal racist murder , Chris Newsom was in a kinder place before this final part of his awful ordeal began) Christian's body was later found in a trash can in a house on Chipman Street. Newsom's body was found nearby along railroad tracks.
Further details of the opening of the case can be read here on a local Knoxville news site, the story has, so far only been reported locally, while the main US news channels studiously seek to ignore it. Hat Tip: Newsnet14
More 'White Privilege'
Seen the movie Straight Outta Compton? Ice Cube roasted his old crew with the song No vaseline but Jerry was the only one who all of a sudden decided Cube was 'antisemitic'. Each time jews get called out for being bitches they play the 'antisemite' card.
If everybody just drops their hypocrite mask and get on with the program.. Leave the children and the animals in peace. Go bash each others heads in, primitive baboons.
In 2022, Whoopi Goldberg, co-host of the ABC talk show "The View," got suspended for two weeks by the network, after she said repeatedly during an episode of the show that aired on Monday that the Holocaust was not about race. She later apologized. In the episode, Ms. Goldberg said the Holocaust was about "man's inhumanity to man" and "not about race." When one of her co-hosts challenged that assertion, saying the Holocaust was driven by white supremacy, Ms. Goldberg said, "But these are two white groups of people." She added, "This is white people doing it to white people, so y'all going to fight amongst yourselves." In a statement on Tuesday night, Kim Godwin, president of ABC News, said that Ms. Goldberg would be suspended for "her wrong and hurtful comments." source
Now how can Goldberg be held accountable for thinking jews are white when they have done their best to position themselves there where people get confused.
Just take a look at Skolniks postings:
and what do the Palestinians do? Set donkeys on fire. (source)
The jewish far-Left Marxist professor, Noel Ignatiev absolutely hated white people and called for their genocide.
European women and children under attack
Primitive tribes considered women of conquered people to be their natural prey. Non-Muslim women today share the same fate. Long before the ISIL, in 1948, the Arabs set forth to conquer Israel dreaming of killing men and raping women. In Lebanon, Palestinians raped Christian women in Lebanon and thereby provoked the civil war. Secular regimes restrained sexual lusts of Muslims against females of "infidels." As soon as they broke, Christian women turned into the object of sexual harassment. On April 10, 2013, Salafi cleric Sheikh Yasir al-'Ajlawni announced a fatwa that permits the rape non-Sunni women in Syria. In Egypt, in February 2013, Ahmad Mahmoud Abdullah, known as "Abu Islam", justified the raping of women in Cairo's Tahrir Square. The raping of girls of the Coptic community in Egypt became commonplace under the Muslime Brotherhood's Morsi regime. Recently Muslims burned down Christian homes in southern Egypt and forced a 70-year-old Coptic woman to walk naked through the streets.
Non-Muslim women are whores for a Muslim man, especially if they walk alone and wear short skirts - as in Cologne, London, Stockholm or anywhere else. (source)
Iraq 2023: caveman mentality
Notorious radical leftist billionaire George Soros demands that islamic migrants are to settle anywhere they like and funds organizations who help the migrants into Europe.
2016 - George Soros has announced he will invest nearly £400million in businesses started by migrants
According to Soros, the muslim migrants must be allowed to choose where they will settle. Most currently travel to Germany and Western Europe where social benefits are available. Demographics on the influx show that nearly 60% are young islamic radical males, 26% future suicide bomb children and 18% enslaved females over the age of eighteen, according to Eurostat. The United Nations states the current influx of 8,000 refugees per day entering the continent is merely "the tip of the iceberg."
George Soros is backing Greta Thunberg. Behind the world famous coached 16-year-old climate activist, there is a liberal oligarch and a globalist movement.
Male whores bothering women on the street
No. You do not want Facebook FOLLOWERS. They all start to think this is normal on the street too.
Left: Another male islamic gem; the Indonesian government subjects female applicants for Indonesia's Military and National Police to discriminatory and degrading "virginity" tests. Men are the one raping, not the women. And without the women who carried them for 9 months, they would not even exist. Let's be fair, and give the men an exam as well, let someone shove fingers up their asses.
Right: Iran 2022 "He says evaluation of patient injuries suggest demonstrators were 'held down or held still and not had the ability to move their head away' when the pellets were launched" Once again women are assaulted and children killed by the religion of peace. Iranian forces are deliberately shooting female protesters in the breasts and genitals, medics reveal. Who raises such monsters? Doctors allege they target women in attempt to 'rid their sexual complexes'At least 458 people, including 63 children, were killed in the demonstrations
Now Hiring: Police Officer
Are you interested in becoming part of the occupation with the highest suicide rate of any profession?
If you choose not to kill yourself, you'll be happy to know that a 2013 study published by the National Institutes of Health found the average life expectancy of a police officer to be 57.
Does a divorce rate of almost certainty sound great to you? Well then, once you go through an invasive and detailed background check, physiological examination, physical examination, fitness test, written test and a 6 month long (often live in) boot camp style academy, you'll be released to the streets where uncertainty and possible death wait around every corner! source, read more
Romans 13:4 For the one in authority is God's servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God's servants, agents of wrath to bring punishment on the wrongdoer.
Racial Equality Among Muggers
More white men than black men are charged with pedophile sentences,
and more black then white men are charged for mugging.
So what is the problem? The problem in the USA is the excessive force used by the police.
Which too is easy to be explained since this country sells guns at.. local supermarkets!!!
George Floyd was a victim of his own past, and the officers involved with his death were not all white. Unless Asians these days are considered white.
Your Leaders
As the Scriptures say, "No one is righteous- not even one."
Former President Barack Obama posing with Louis Farrakhan, the fiery leader of the Nation of Islam, a group he has led since 1977 and that is based on a bizarre and fundamentally anti-white theology.
Let me remind you of the methods Nelson and Winnie Mandela supported:
In June 1986, a South-African woman was burned to death on television. Her name was Maki Skosana, and the world watched in horror as anti-apartheid activists wrapped her up in a car tire, doused her with gasoline, and set her on fire. For most of the world, her screams of agony were their first experience with the public execution South Africans called "necklacing."
Fact check: Obama administration approved, built temporary holding enclosures at southern border source, source
We have all heard Trump's quote on women.
Those are not words of a decent and moral man. But not as immoral as Bill Clinton?
15 ways the Trump administration has impacted the environment, read more
Trump makes string of ridiculous racial comments about Native Americans during attack on Elizabeth Warren, read more
Oh look, you don't have to be a fart to rule over a nation. And you can have a classy wife beside you too!
MANY REASONS WHY VEGANS SHOULD VISIT BHUTAN
The South Asian country is steeped in culture that believes in kindness towards animals, values its citizens' happiness, and respects the environment. Slaughterhouses are illegal in Bhutan and there isn't one that exists in the entire country.
They are carbon negative. The whole nation seems happy. They protect vulnerable bird species. They are aiming to be 100-percent organic.
Read more about this paradise called Bhutan
"Throughout my reign I will never rule you as a King. I will protect you as a parent, care for you as a brother and serve you as a son. I shall give you everything and keep nothing. I shall live such a life as a good human being that you may find it worthy to serve as an example for your children. I have no personal goals other than to fulfill your hopes and aspirations. I shall always serve you, day and night, in the spirit of kindness, justice and equality. As the king of a Buddhist nation, my duty is not only to ensure your happiness today, but to create the fertile ground from which you may gain the fruits of spiritual pursuit and attain good Karma. This is how I shall serve you as King."
- His Majesty's Coronation Address to the Nation.
Sneezing Dogs, Dancing Bees: How Animals Vote
Not only humans vote. Any animal living in a group needs to make decisions as a group, too. Even when they don't agree with their companions, animals rely on one another for protection or help finding food. So they have to find ways to reach consensus about what the group should do next, or where it should live. Species ranging from primates all the way to insects have methods for finding agreement that are surprisingly democratic. In a 2010 study, Dr. Manser and her colleagues studied move calls in a dozen meerkat groups living in the Kalahari Desert in South Africa. Groups ranged from six to 19 individuals. But the scientists found that only about three group members had to mew before the whole party decided to move along. The group didn't change direction, but it would double its speed to reach better foraging grounds. read more (source)
In his 2010 book "Honeybee Democracy," Thomas D. Seeley, a Cornell University biologist, writes that we can learn a lesson from the bees: "Even in a group composed of friendly individuals with common interests, conflict can be a useful element in a decision-making process."
Biologists call this phenomenon - when animals change their behavior in response to a critical mass of their peers doing something - a quorum response. Dr. Manser thinks quorum responses show up in human decision making, too.
"If you're in a group and somebody says, 'Let's go for a pizza,' and nobody joins in, nothing's going to happen," she said. But if the pizza craver is joined by a couple of friends, their argument becomes much more convincing.
Inseparable Lion Couple Dies Just Days Apart
Both majestic creatures arrived at a Zoo in 2008 and were often seen playing with each other, grooming or cuddling every day. Their love was apparent and very strong.
It was not uncommon to see Zenda (the male) grooming Isis (her) or sleeping with a paw on her.
He remained incredibly protective of her throughout their lives. These two lions had such a strong bond that their separation was something that neither of them wanted to bear. source
True love lasts forever.
Swan Whose Mate Was Killed Dies Of A Broken Heart
A male swan named Gvidon passed away after losing his longtime companion in a shocking act of animal cruelty - and keepers say a broken heart is to blame. The swan's bonded mate, Tsarevna, was killed when a guest at the Zoo fed her bread that had a sewing needle hidden inside it. Shortly after the deadly attack, Gvidon began exhibiting signs of depression, refusing to eat normally and shying away from the remainder of the flock.
"Like humans, animals can suffer from depression," said the zoo's deputy director. (source)
A building on fire; the whole world cries.
Barn fires with animals that see no daylight, feel no grass and have no chance to escape: "that is part of our civilisation". No dirtbag, that is the darkness of your pitchblack soul. In June (in the Netherlands), the number of stable fire victims for 2020 will already be between 90 and 95,000. Sprinklers not mandatory......
All beings want to raise families
You think you are the only one who loves?
Who wants a family?
Who cries when a loved one dies or goes missing?
Bacon, pepperoni, processed meats cause cancer in humans. They are class 1 carcinogens - World Health Organization October 2015.
The White Privilege Of European Families
The Disgrace of The Human Race
Isabel Ward from Spain is fine with murder, slavery and exploitation of animals that cannot defend themselves. And the hypocrisy awards goes to...
Racism In Belgium & Netherlands
Targeting children and young adults (11-24) as audience, racists from Belgium write on their website www.watwat.be : 'Racism ensures that especially white people have power and are positively portrayed: most teachers, school principals, home owners, employers, lawyers, judges, journalists, important politicians, models, rich people... are white.' Of course the majority as mentioned above is white, when they are inhabitants in a white country. What is the majority in Kenya for example, home owners, judges etc. You think white???
Fact: Europe is not USA. Stop pretending it is.
We have our own piles of shit here to deal with and racism is not one of them, every single being is being discriminated. In Europe you do not get a bullet in your stomach because of trigger happy officers because guns aren't sold at local supermarkets like in Wild West USA.
Stop spreading hatred to cover your own incompetence to make something of life.
See, everybody is discriminated. Women still earn less then men, when you are born in let's say Holland and live for 30 years there people still compliment you on speaking the language so well...! You don't see these discrimination cry babies appreciating what they have. If they dont like it, go fight where there is real discrimination. Like for the Albino community in Africa.
Yee hypocrites...
Imagine what people could accomplish if they removed their ego and stood up for the weakest ones among them. All these so called antiracists fill their stomaches with animals that begged to live and turn a blind eye for the children that need their attention the most. One third of Kenya's children are involved with prostitution. From as young as 8 or 9 year old, one in ten works in the sex trade (Unicef report 2006)
BIJ1 in the Netherlands
In the Netherlands there is even a political party (NIJ1) that says it is against discrimination, but that involves skin color in everything. In July 2021 they were mentioned in the news due to misconduct by a member.
"Among the sixteen signal submitters were people of color, white people and black people". Who cares what one's skin color is? And if you read the NOS article, you will read, among other things,
"There was also criticism of the choice of the law firm that investigated the signals: according to a number of members, that would be too white." and in response Mills of the board who says "Unfortunately, we have not found an office with more people of color." (source 1, 2)
So a law firm was specifically searched based on the skin color of the lawyers. So they don't look at the person but at the skin color. That's just discrimination.
Due to the protests in Iran (2022, Masha Amina killed by retarded regime), populists in the Netherlands also cut their hair. Columnist Hassnae Bounazza is right about that. But then she starts to discriminate: ".. and the Dutch, they never come up with something themselves.." The Dutch are the inventors of the microscope, telescope, submarine, fire hose and bluetooth. Hassnae is no better than the populists, she writes a piece about it so that she can then expose her own shortsightedness. If the Dutch are so bad, what is she doing in the Netherlands?
Watch out, extreme right!?
Belgium: 62 "right-wing extremists " VS 627 jihadis..... bodycount/terrorism: so far all committed by jihadis.
Also notable: all the supposedly right-wing extremists have jobs, the jihadis do not. They actually plan terrorism and pray to the devil in your time with your tax money.
The Netherlands and Belgium are known to be left-liberal. That means that when one opposes mass immigration, it is labeled as far right. When this crowd is accompanied by anti-government and weapons collector, you are automatically a terrorist. In 2022, a prepper was shot dead in Belgium (source). According to the federal prosecutor's office, the man was suspected of a "form of armed resistance against the government. But there was no concrete goal or time," it sounds. A firefight ensued with the gold merchant, who was hit by bullets and died on the spot. The manner in which the raid took place has provoked internal criticism from the police. According to the prosecutor's office, this is unjustified. (source)
In total there are 703 people on the list of OCAD. "In addition to the 62 right-wing extremists, there are 14 left-wing extremists and 627 jihadis," the body clarifies. (source)
62 right wing... and 627 muslim extremists!!!!! Right-wingers are shot without mercy. Why didn't they do that with the Muslims of the Hofstad group, where one of them stabbed Theo to death in the street (source)? The governments are even working hard to get back ISIS brides who left the country (source). Why don't they go to Afghanistan, why go back to the decadent west if it's against your faith? Parasitism!
Family of shot Yannick V. files a complaint for manslaughter: "Incomprehensible action by the police raises many questions"
The family of Yannick V. files a complaint for manslaughter. That reports their lawyer John Maes. The 36-year-old from Antwerp was shot dead last week during a police operation against extreme right-wing violence and terror. He was hit by a police bullet during a house search and died on the spot. Read the complete press release from the parents and sister of Yannick V. here: "With deep sorrow but also with great wrath, we must watch helplessly as the memory of our beloved son and brother is smeared by some individuals in the media. He is completely wrongly described as far-right, racist and even as a danger to our society. Nothing could be further from the truth, Yannick was a social man, caring for his family and friends. As a gold and silver trader, he came into contact with a wide variety of people with whom he was highly regarded and with whom he had often also built up friendships. He was a gun enthusiast and collector, but he had an impeccable reputation and as a result was also president of an association of sport shooters. Yannick had his own opinion and ideas and spoke out openly, without wanting to hurt or harm anyone. His violent death as a result of a police action incomprehensible to us raises many questions. We have therefore instructed our counsel to file a civil action complaint for acts of manslaughter, and hope for an objective and thorough investigation into the true circumstances of his death. Finally, we would like to thank everyone for all the messages of sympathy that reach us, and together with all these people we hope that Yannick will be rehabilitated. We ask the media to respect our privacy so that we can say goodbye to our son and brother in all serenity." source, 04-10-2022
The article below is recommended to be read by the so-called anti-racists who live in safe countries and point fingers based on their own incompetence and identity complex. Yes liberal princesses, the ogre comes in all different colors and sizes.
Fear and loathing in South Africa where foreigners live in danger
(2021 BBC source) Supermarket owner Getachew Desta (above) fled Ethiopia in 2010 after he was suspected of supporting an opposition party and now lives behind a steel cage and burglar gates in Alexandra. He says he finds life better here, but complains about the crime. "I am OK being locked behind the cage as we don't know when the criminals will strike. At any given time they can they pop up, point a gun at you and rob you of your money. They can also kill you."
He was a victim of xenophobia in 2016, when a mob ransacked his shop and he was left with nothing.
Animals Have In Them Love and Loyalty You Don't Even Find in Most Humans
Get Used To The Heat
Seraphim are large six-winged snakes that fly.
Cherubs aren't well-fed babies, they're winged lions.
Or have four faces, a wheel of fire with eyes lining the rim - you name it. They didn't traditionally introduce themselves with "Fear not!" for nothing.
And these are the good angels. By the time we get to the New Testament, angels have settled into their roles as messengers and heavenly bouncers. They look like human beings. But the joke is on you my friend: God Never Changes. Your eyes deceive you.
Pigs are proven to be smarter than dogs.
Dogs often more loyal than humans.
Poor pigs cannot move, but fat old pedophiles roam on the streets freely looking to destroy your children. You say nay but have you been there, on the streets? Have you seen them, roaming like demons? They feast on the bodies, the meat of the pigs and then go out to destroy the souls of the little ones.
Five photographs of animals with important stories for all of us
"We curate a small collection of iconic photographs of animals, each one with an important lesson for all of us. From the first dog in orbit to the monkey who with a little help from PETA sued a human photographer and won... " - read full article on surgeactivism.org
Selfie taken by Naruto the macaque monkey who sued human photographer David Slater and won... with the help of PETA
According to an excellent article from Smithsonian Magazine, the guilt felt by those who sent Laika to space knowing she would not return has only grown in the years since.
Jesus Christ speaks in Matthew 23:37 so gentle about hens..
Imagine what his judgement will be when you stand in front of Him and knew, but did not care enough to act.
How often I wanted to gather your children together, the way a hen gathers her chicks under her wings, and you were unwilling
Sheep surprisingly intelligent
Did you know that over 70% of Australian wool sheep suffer a painful and outdated mutilation practice called mulesing? Help protect millions of Australian lambs by signing the FOUR PAWS petition calling for an end to mulesing.Mulesing is a process where a lamb (usually two to 10-week-old) is restrained upside-down in a cradle to cut off skin folds around the buttocks and tail with a pair of metal shears.
The procedure leaves an open wound and after healing leaves a bare area where no wool grows. The procedure is performed on millions of lambs without any form of pain relief.
Reputation: Sheep are stupid, defenceless and harmless creatures that mope about on hillsides doing not very much. They are good for two things: being eaten and producing wool.
Reality: Sheep are actually surprisingly intelligent, with impressive memory and recognition skills. They build friendships, stick up for one another in fights, and feel sad when their friends are sent to slaughter (source)
The Finnish capital Helsinki is allocating 100,000 euros to help children from primary education switch to oat milk
Oat milk is a plant-based alternative to dairy milk from cows. The latter product is encountering more and more objections. Not only is livestock farming responsible for environmental problems such as the nitrogen crisis and global warming, but there is also increasing criticism of the cruelty behind cow's milk. A cow only produces milk if she has a calf every year, which is then taken away from her. This - literal - kidnapping leads to emotional scenes in the animals. Read more (source)
Birds do have a brain cortex-and thin
Owls, such as this Eurasian Eagle-Owl (Bubo bubo), as well as crows and pigeons have brain organization-and probably cognitive ability-that is similar to mammals. The term "birdbrain" used to be derogatory. But humans, with their limited brain size, should have known better than to use the meager proportions of the bird brain as an insult. Part of the cause for derision is that the mantle, or pallium, of the bird brain lacks the obvious layering that earned the mammalian pallium its "cerebral cortex" label. However, birds, and particularly corvids (such as ravens), ..read more
Lack of Federal Laws Causes Severe Animal Cruelty
Did you know that currently we have ZERO federal laws governing the conditions of which farm animals are raised in?
Thanks to the lack of laws and enforcement, animals currently suffer through horrible conditions on factory farms.
Animals are often given so little space and kept in severely cramped areas. Hens, for example, are kept in small cages, chickens and pigs are kept in jam-packed sheds, and cows are kept in crowded and filthy conditions.
Antibiotics are used to make animals grow faster and to keep them alive in the otherwise unsurvivable conditions. Research shows that factory farms' widespread use of antibiotics can lead to antibiotic-resistant bacteria that can potentially be very dangerous to humans.
Majority of factory-farmed animals have been genetically altered to grow larger or to produce more milk or eggs than they naturally would, until it drastically affects their health. Some chickens are made to grow so large that their legs cannot support their bodies; they suffer from starvation or dehydration when they can't walk to reach food and water as a result.
When they've grown large enough to slaughter or their bodies have been worn out from producing milk or eggs, animals raised for food are crowded onto trucks and transported for miles through all weather extremes, typically without food or water. At the slaughterhouse, those who survived the transport will have their throats slit, often while they're still conscious. Or, they're plunged into the scalding-hot water for defeathering or hair-removal tanks or while their bodies are being skinned or hacked apart.
The quantity of milk that dairy cows produce decreases substantially around 10 months after giving birth due to the fact that the cows only produce milk to feed their babies. In order to continue and maximize milk production, cows are annually impregnated which increases stress, and the likelihood of sickness and premature death. Each cow is genetically manipulated to produce up to 100 pounds of milk per day - ten times more than they would produce naturally.
Dairy cows commonly suffer from a variety of illnesses because intensive milk production, including widespread lameness and mastitis, a painful and often fatal infection of the udder. Pharmaceutical products that are used to infections often have bad side effects. Dairy cows produce an average of 729 days of milk, which amounts to 2.4 lactations, before they are considered "spent", and sent to slaughter. 3 million young dairy cows are slaughtered each year in the U.S. Dairy cows are typically killed between 2 to 5 years of age despite the fact that they can live up to 25 years.
Newborn calves are permanently separated from their mothers, usually within 1-3 days, since the mother/calf bond intensifies over time and delayed separation can cause even worse emotional distress for the calf and mother.
Nearly 100% of calves born to dairy cows in the U.S. are removed from their mothers within the first 12 hours of birth.
As a result, dairy calves separated from their mothers are denied their mother's milk, which contains all the essential nutrients and antibodies the calf needs.
Calves are typically fed milk substitutes, often from a dried powder base, and raised without a mother to care for them. Mothers and calves form deep bonds, much like humans, which makes it inhumane to separate one from the other. In natural herds, the mother-calf bond is the strongest bond in a cow's life.
With the production of dairy also comes the production of veal. Veal only exists to help farmers make money from male calves born to dairy cows; they would otherwise be considered useless as they can't produce milk. As a result, they are slaughtered and sold for veal at a few months of age.
The corporations that run current factory farms are full of greed and driven by solely by money. Factory farms have become the leading method of food production in America. The U.S. meat industry is a multi-billion dollar per year industry and feeds millions of people around the world. In 2014, the U.S. meat industry, which processes cattle, sheep, pigs, chickens, and turkeys, sold 186 billion dollars worth of meat. With the ability to gain great profits, factory farm corporations are motivated to get meat to domestic and international consumers as efficiently and inexpensively as possible. Today, only a handful of giant factory farm companies control meat production in the United States, all of which are wealthy, politically powerful, and take in no consideration of the animals at all. These companies provide cheap meat for people around the world and are only interested in keeping their high-production, low-cost.
Why do nothing and let these animals suffer? How much longer before we take a stand and actually enforce change? If you care about all the innocent lives being tortured every day as factory farms inherit more and more money at their expense, then please sign this petition.
My proposal to our state government is as follows:
All Ag-Gag laws in Texas (which criminalize whistleblowers on farms) should be lifted. Surveillance around factory farms should be allowed and enforced. HB 1643, the act which makes it illegal to use a drone to take photos over a concentrated animal feeding operation, should be revoked.
The 28 Hour law, which requires vehicles transporting animals for slaughter to stop every 28 hours to allow animals exercise, food, and water, should be modified to 14 hours and include poultry species as well.
Animals on factory farms should not be genetically manipulated to produce unhealthy amounts of eggs, milk, etc to the point of which it affects their health. Killing and selling the young of any animal (especially veal) should become illegal, due to the fact that it is inhumane.
Yes. All Small Acts Matter Too.
A mountain is composed of tiny grains of earth. The ocean is made up of tiny drops of water. Even so, life is but an endless series of little details, actions, speeches, and thoughts. And the consequences whether good or bad of even the least of them are far-reaching.
Non nobis, non nobis, Domine Sed nomini tuo da gloriam. | {
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How Improving Obesity Care Could Help End the Pandemic
With COVID-19 cases spiking across the country, public health experts are expressing concern about the disproportionate impact on people with obesity. Numerous studies have established that obesity significantly raised a person's risk of hospitalization and death from COVID-19. The good news is we now know that losing weight can significantly lower that risk.
A new study published in the Journal of the American Medical Association covering more than 20,000 patients found that substantial weight loss achieved through surgery cut the risk of COVID-19 hospitalization by nearly half. This is welcome news for 70 million American adults living with obesity. And while surgery is only one way to lose weight, the message is clearly getting through.
In a recent interview with CNN, Dr. Fatima Cody-Stanford, a renowned obesity medicine and nutrition physician and scientist at Massachusetts General Hospital and Harvard Medical School, described the awesome demand at the obesity clinic where she works in Boston. "We are overwhelmed with the volume of patients that have really made that connection between obesity and Covid and the need for them to get appropriate care," she said. The wait list has topped 1,000 people.
Dr. Cody-Stanford has been a leading light in the national effort to fight systemic bias against people with obesity and recognize the condition as a disease — not a choice. Writing in STAT News First Opinion, Dr. Cody-Stanford and her co-author, Kelly Copes-Anderson, Head of Diversity, Equity and Inclusion at Eli Lilly and Company, argued that outdated Federal health policies on obesity risk deepening racial inequities:
"When the American Medical Association recognized obesity as a disease in 2013, doctors and other health care workers began to pay greater attention to a condition that is a cause of death for nearly one out of five adults in America. Eight years on, U.S. policies have failed to catch up with medical understanding in addressing this public health crisis. Without the right kinds of policy interventions, nearly half of Americans will have obesity by 2030.
"Communities of color will be hit hardest. Already, nearly 50% of Black adults and 45% of Hispanic adults have obesity — a body-mass index (BMI) of 30 or higher. But this condition is not just a matter of carrying extra pounds. It puts individuals at greater risk for many other chronic diseases, including cardiovascular diseases, metabolic diseases like diabetes, and many cancers, all of which disproportionately affect communities of color and perpetuate health disparities."
They highlighted a timely opportunity to reach millions of Americans with obesity. A bill moving through Congress, The Treat and Reduce Obesity Act of 2021 (TROA), would update Medicare's outdated rules and establish two new provisions that empower people with obesity to take control of their health.
First, it would extend coverage for intensive behavioral therapy, a dynamic strategy that helps people modify their eating, exercise and environment to lose weight. Right now, Medicare only reimburses primary care physicians for this intervention. TROA would ensure other qualified health care professionals like dieticians are reimbursed, massively expanding the reach of this service.
Second, the bill would cover FDA-approved weight loss medications through Medicare Part D. This is a crucial step with new medicines coming to market that use the body's hormones to control insulin and appetite.
The authors note the challenges in passing this piece of legislation while sounding hopeful notes that the time may finally be right:
"The Treat and Reduce Obesity Act has been introduced in every session of Congress since 2012 and gone nowhere, reflecting the profound systemic challenge of passing legislation to address this disease. But there is a palpable shift underway as more government leaders are adopting a mindset about obesity that is informed by science rather than by prejudice. Policymakers across the aisle are casting aside the old view that obesity is a matter of individual willpower and, like the American Medical Association and other leading health organizations, recognizing obesity as a disease. As a result, the act now has unprecedented bipartisan and bicameral support across the political spectrum."
More than 100 obesity and health advocacy organizations representing diverse communities have endorsed the bill. And public support is behind it too. A Morning Consult poll showed that large majorities of American adults support Medicare recognizing obesity as a treatable medical condition and expanding coverage to prevent and treat the disease.
Ultimately passing TROA could help millions of people improve COVID-19 outcomes by losing weight. With cases spiking again and Americans eager to end the pandemic, let's hope more policymakers get the message and take action. | {
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Poiss. 1938
Aquatint. Plm 38 x 28 cm
price 2 397 (sold)
Aino Bach, most probably the most famous female Estonian graphical artist, took up her studies at "Pallas" as a painter, but she still turned into a graphical artist under the hand of Ado Vabbe. The creation of Bach, who graduated from the school in the year 1935, underwent a rapid development also at the end of the same decade and Bach became in a couple of years one of the most significant young authors. The 1940ies brought about the suppression of the whole local artistic scene, also Bach, whose adaptation with the emerged circumstances was quite painless, did not achieve her initial level until the 1950ies. According to the opinion of Lehti Viiroja (with which agree a number of people) the second half of the 1950ies can be regarded the second flourishing period of Bach's creation.
At the present auction are being exposed two real gems of art history which are also the finest representatives of the whole creative heritage of Bach, but which from another hand are also grand landmarks of the art history of the whole 20. century. "Poiss", which was made in 1938, is of course the most well-known work by Bach, her business card, where according to the general opinion the author has reached the ultimate top of her works. Bach works at "Poiss" in her favourite technique, the aquatint. In her manner of handling has not been emphasized the elaborate line (like it is in case of Wiiralt), but emphasized have rather been the surfaces.
The unnumbered proof gives evidence of one of the first author's copies, with which Bach most probably had a deeply personal and emotional connection.
In addition to the perfect technical side we also detect the meaningfulness of the contents. Behind the boy's head has been created "a picture in a picture" – a further view of an anonymous city. Presumably it is Paris, the city where Aino Bach met her model (and the model of the legendary painting of Karl Liigand). He was a paper-boy, an ordinary slum-boy, his becoming of a model could have been unthinkable during any other period. But these were his simplicity, directness, liveliness and natural looks, which lifted an ordinary paper-boy into the Estonian art classics. | {
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\section{Introduction}
\label{sec-intro}
Massive graphs arise in many applications \emph{e.g.,}\xspace network traffic data, social networks, citation graphs, and transportation networks. These graphs are highly dynamic: Network traffic data averages to about $10^9$ packets per hour per router for large ISPs~\cite{DBLP:journals/pvldb/GuhaM12}; Twitter sees 100 million users login daily, with around 500 millions tweets per day~\cite{twitterstat}.
\begin{example}
\label{exam:graph}
We consider a graph stream\footnote{Without loss of generality, we use a directed graph for illustration. Our method can also work on undirected graphs.} as a sequence of elements $(x,y; t)$, which indicates that the edge $(x,y)$ is encountered at time $t$.
A graph stream $\langle(a, b; t_1), (a, c; t_2), \cdots (b, a; t_{14})\rangle$ is depicted in Fig.~\ref{fig:graph}, where all timestamps are omitted for simplicity.
Each edge is associated with a weight, which is $1$ by default.
\end{example}
Queries over big graph streams have many important applications, \emph{e.g.,}\xspace monitoring cyber security attack and traffic networks. Unfortunately,
in a recent survey for businesses in analyzing big data streams~\cite{Vitria}, although 41\% of respondents stated that the ability to analyze and act on streaming data in minutes was critical, 67\% also admitted that they do not have the infrastructure to support that goal.
The situation is more complicated and challenging when handling graph streams.
It poses unique space and time constraints on storing, summarizing, maintaining and querying graph streams, due to its sheer volume, high velocity, and the complication of various queries.
In fact, for the applications of data streams, fast and approximated answers are often preferred than exact answers.
Hence, sketch synopses have been widely studied for estimations over data streams.
Although they allow false positives, the space savings normally prevail over this drawback, when the probability of an error is sufficiently low.
There exist many sketches:~AMS~\cite{DBLP:journals/jcss/AlonMS99}, Lossy Counting~\cite{DBLP:conf/vldb/MankuM02}, {\sf CountMin}\xspace~\cite{DBLP:journals/jal/CormodeM05}, Bottom-$k$~\cite{DBLP:journals/pvldb/CohenK08} and {\sf gSketch}\xspace~\cite{DBLP:journals/pvldb/ZhaoAW11}. They have also been used in commercial tools, \emph{e.g.,}\xspace~{\sf CountMin}\xspace is in Cisco OpenSOC\footnote{http://opensoc.github.io/} cyber security analytics framework.
\begin{figure}[t]
\begin{minipage}{\columnwidth}
\centerline{
\xymatrixcolsep{0.6in}
\xymatrix{
& b \ar@/^/[dl]^1 \ar[dd]^1 \ar[r]^1 \ar[ddr]^(.5)1 & d \ar[dr]^1 & \\
a \ar@/^/[ur]^1 \ar[dr]_1 & & e \ar[u]_(0.2)1 \ar[d]^1 \ar[ul]_(.3)1 & g \ar[llu]_(.4)1 \\
& c \ar[ur]^1 \ar[r]_1 & f \ar[llu]_(.7)1 &
}
}
\caption{A sample graph stream}
\label{fig:graph}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4ex}
\centering
\begin{tabular}{|c|c|c|c|c|}
\cline{2-5}
\multicolumn{1}{c|}{$h(\cdot)$} & 5 & 5 & 3 & 1 \\
\cline{2-5}
\multicolumn{1}{c}{\color{white} {\Large I} } & \multicolumn{1}{c}{$ab, ac, ed, eb, ef$} & \multicolumn{1}{c}{$bc, bd, ba, bf, fa$} & \multicolumn{1}{c}{$ce, cf, gb$} & \multicolumn{1}{c}{$dg$}\\
\end{tabular}
\caption{A hash-based sketch}
\label{fig:cm}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4ex}
\centerline{
\xymatrix{
& II (bf) \ar@/^/[dl]_2 \ar@/^1pc/[dd]^(.7){1} \ar@/_/[dr]^1 \ar@(ur,ul)[]^1 & \\
I (ae) \ar@/^/[ur]^3 \ar@/_/[dr]^1 \ar@/^/[rr]^1 & & III(cg) \ar@/^/[ll]_1 \ar@/_/[ul]_2 \\
& IV(d) \ar@/_/[ur]^1 &
}
}
\caption{An example of our proposed sketch}
\label{fig:sys}
\end{minipage}
\end{figure}
\eat{
\begin{figure}[t]
\begin{minipage}{\columnwidth}
\centerline{
\xymatrix{
& 2 (b) \ar[dd]^{t_3} \ar[r]^{t_4} & 4(d) \ar[r]^{t_{10}} & 7(g) \ar[d]^{t_{11}} \\
1 (a) \ar[ur]^{t_1} \ar[dr]^{t_2} & & 5(e) \ar[u]^{t_7} \ar[d]^{t_8} \ar[r]^{t_9} & 8(b) \ar[ld]^{t_{12}} \ar[d]^{t_{14}} \\
& 3(c) \ar[ur]^{t_5} \ar[r]^{t_6} & 6(f) \ar[r]^{t_{13}} & 9(a)
}
}
\caption{An example graph stream}
\label{fig:graph}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4ex}
\centering
\begin{tabular}{|c|c|c|c|c|}
\cline{2-5}
\multicolumn{1}{c|}{$h(\cdot)$} & 5 & 5 & 3 & 1 \\
\cline{2-5}
\multicolumn{1}{c}{\color{white} {\Large I} } & \multicolumn{1}{c}{$ab, ac, ed, eb, ef$} & \multicolumn{1}{c}{$bc, bd, ba, bf, fa$} & \multicolumn{1}{c}{$ce, cf, gb$} & \multicolumn{1}{c}{$dg$}\\
\end{tabular}
\caption{A hash-based sketch}
\label{fig:cm}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4ex}
\centerline{
\xymatrix{
& II (bf) \ar@/^/[dl]_2 \ar@/^1pc/[dd]^(.7){1} \ar@/_/[dr]^1 \ar@(ur,ul)[]^1 & \\
I (ae) \ar@/^/[ur]^3 \ar@/_/[dr]^1 \ar@/^/[rr]^1 & & III(cg) \ar@/^/[ll]_1 \ar@/_/[ul]_2 \\
& IV(d) \ar@/_/[ur]^1 &
}
}
\caption{A sample of {\sf gLava}\xspace sketch}
\label{fig:sys}
\end{minipage}
\end{figure}
}
\begin{example}
\label{exam:gs}
Consider the graph stream in Example~\ref{exam:graph} and Fig.~\ref{fig:graph}.
{\sf CountMin}\xspace treats each element in the stream independently, and maps them to $w$ hash buckets, by using the pairs of node labels as hash keys.
Assume there are $w=4$ hash buckets.
The set of values to be hashed is $\{ab, ac, bc, \cdots\}$, where the value $ab$ is to concatenate two node labels for the element $(a, b;t_1)$.
A hash function is used to put these values in 4 buckets, \emph{i.e.,}\xspace $h(\cdot)\rightarrow [1, 4]$, as shown in Fig.~\ref{fig:cm}.
The first bucket aggregates the weights of values starting with $a$ and $e$, and similar for other buckets.
Note that, for simplicity, we use only one hash function for illustration. In fact, {\sf CountMin}\xspace uses $d$ pairwise independent hash functions to alleviate the problem of hash key collisions.
{\sf CountMin}\xspace, and its variant {\sf gSketch}\xspace, can be used for estimating certain types of graph queries.
(a) {\em Edge query}. It can estimate the weight of particular edges: $5$ for $ab$, and $1$ for $dg$.
(b) {\em Aggregate subgraph query.} It can answer queries like: {\em What is the aggregated weight for a graph with two edges $(a, c)$ and $(c, e)$}? It will give $5+3=8$ as the estimated weight for the graph.
\end{example}
Example~\ref{exam:gs} shows the applicability of {\sf CountMin}\xspace on some query estimation over graph streams.
However, their (and other sketch synopses') main weakness is that they are element (or edge) independent. That is, they fall short of maintaining the connections between streaming elements, thus fail in estimating many important queries, such as node monitoring, path queries (\emph{e.g.,}\xspace reachability) and more complicated graph analytics (see Section~\ref{subsec-queries} for a detailed discussion).
\stitle{Challenges.}
Designing a graph sketch to support a wide range of applications requires to satisfy the following constraints.
(1) {\em Space constraint:} {\em sublinear} upper bound is needed.
(2) {\em Time constraint:} {\em linear} construction time is required. Noticeably, this is stronger than the constraint with only a constant passes over the stream.
(3) {\em Maintenance constraint:} to maintain it for one element insertion/deletion should be in {\em constant} time.
(4) {\em Element connectivity:} the {\em connectivity} between elements should be maintained.
To this end, we present {\sf gLava}\xspace, a novel generalized graph sketch to meet the above required constraints. Instead of treating elements (edges) in a graph stream independently as those prior art, the key idea of {\sf gLava}\xspace is to compress a graph stream based on a finer grained item, the node in a stream element.
\begin{example}
\label{exam:sys}
Again, consider the graph stream in Fig.~\ref{fig:graph}. Our proposed sketch is shown in Fig.~\ref{fig:sys}.
For each edge $(x, y; t)$, {\sf gLava}\xspace uses a hash function to map each node label to 4 node buckets \emph{i.e.,}\xspace~$h'(\cdot)\rightarrow[1,4]$.
Node $I$ is the summary of two node labels $a$ and $e$, assuming $h'(a) = 1$ and $h'(e) =1$. The other compressed nodes are computed similarly.
The edge weight denotes the aggregated weights from stream elements, \emph{e.g.,}\xspace the number $3$ from node $I$ to $II$ means that there are three elements as $(x, y; t)$ where the label of $x$ (resp. $y$) is $a$ or $e$ (resp. $b$ or $f$).
\end{example}
\etitle{Remark.}
(1) It is readily to see that estimation for edge frequencies, as what {\sf CountMin}\xspace supports, can be easily achieved by {\sf gLava}\xspace. Better still, the idea of using multiple hash functions to alleviate hash collisions can be easily applied to {\sf gLava}\xspace.
(2) {\sf gLava}\xspace is represented as a graph, which captures not only the connections inside elements, but also the links across elements.
These make it an ideal sketch to support a much wider range of applications, compared with those prior art (see Section~\ref{subsec-queries} for a discussion).
\stitle{Contributions.}
This paper presents a novel graph sketch for supporting a wide range of graph stream applications.
\vspace{1.2ex}\noindent(1)
We introduce {\sf gLava}\xspace, a novel graph sketch (Section~\ref{subsec-gmodel}).
As shown in Fig.~\ref{fig:sys}, the proposed sketch naturally preserves the graphical connections of the original graph stream, which makes it a better fit than traditional data stream sketches to support analytics over graph streams.
We further categorize its supported graph queries (Section~\ref{subsec-queries}).
\vspace{1.2ex}\noindent(2)
We describe algorithms to process various graph analytics on top of {\sf gLava}\xspace (Section~\ref{sec-algs}).
The general purpose is, instead of proposing new algorithms, to show that {\sf gLava}\xspace can easily be used to support many graph queries, and {\em off-the-shelf} graph algorithms can be seamlessly integrated.
\vspace{1.2ex}\noindent(3) We perform theoretical analysis to establish error bounds for basic queries, specifically, the edge frequency estimation and point query estimation (Section~\ref{sec-theory}).
\vspace{1.2ex}\noindent(4)
We describe implementation details (Section~\ref{sec-implementation}).
This is important to ensure that the new sketch can be constructed and maintained under the hard time/space constraints to support streaming applications.
Moreover, we propose to use non-square matrices, using the same space, to improve the accuracy of estimation.
\vspace{1ex}
In this history of graph problems over streams, unfortunately, most results showed that a large amount of space is required for {\em complicated} graph problems~\cite{DBLP:books/crc/aggarwal2014, DBLP:journals/sigmod/McGregor14}.
The present study fills a gap in the literature by analyzing various graph problems in a small amount of space.
We thus contend that {\sf gLava}\xspace will shed new light on graph stream management.
\stitle{Organization.}
Section~\ref{sec-related} discusses related work.
Section~\ref{sec-gapollo} defines the new sketch and queries to be solved.
Section~\ref{sec-algs} describes algorithms using {\sf gLava}\xspace.
Section~\ref{sec-theory} makes theoretical analysis.
Section~\ref{sec-implementation} describes implementation details.
Finally, Section~\ref{sec-conclusion} concludes the paper with a summary of our findings.
\section{Related Work}
\label{sec-related}
We categorize related work as follows.
\etitle{Sketch synopses.}
Given a data stream, the aim of sketch synopses is to apply (linear) projections of the data into lower dimensional spaces that preserve the salient features of the data. A considerable amount of literature has been published on general data streams such as AMS~\cite{DBLP:journals/jcss/AlonMS99}, lossy counting~\cite{DBLP:conf/vldb/MankuM02}, {\sf CountMin}\xspace~\cite{DBLP:journals/jal/CormodeM05} and bottom-$k$~\cite{DBLP:journals/pvldb/CohenK08}. The work {\sf gSketch}\xspace~\cite{DBLP:journals/pvldb/ZhaoAW11} improves {\sf CountMin}\xspace for graph streams, by assuming that data samples or query samples are given.
Bloom filters have been widely used in a variety of network problems (see~\cite{DBLP:journals/im/BroderM03} for a survey).
There are also sketches that maintain counters only for nodes, \emph{e.g.,}\xspace using a heap for maintaining the nodes the largest degrees for heavy hitters~\cite{DBLP:conf/pods/CormodeM05}.
As remarked earlier, {\sf gLava}\xspace is more general, since it maintains connections inside and across elements, {\em without} assuming any sample data or query is given. None of existing sketches maintains both node and edge information.
\etitle{Graph summaries.}
Summarizing graphs has been widely studied. The most prolific area is in web graph compression. The papers~\cite{DBLP:conf/dcc/AdlerM01,DBLP:conf/dcc/SuelY01} encode Web pages with similar adjacency lists using reference encoding, so as to reduce the number of bits needed to encode a link. The work~\cite{DBLP:conf/icde/RaghavanG03} groups Web pages based on a combination of their URL patterns and $k$-means clustering.
The paper~\cite{DBLP:conf/sigmod/FanLWW12} compresses graphs based on specific types of queries.
There are also many clustering based methods from data mining community (see \emph{e.g.,}\xspace~\cite{DBLP:books/ph/JainD88}), with the basic idea to group {\em similar} nodes together.
These data structures are designed for less dynamic graphs, which are not suitable for graph stream scenarios.
\etitle{Graph pattern matching over streams.}
There have been several work on matching graph patterns over graph streams, based on either the semantics of subgraph isomorphism~\cite{DBLP:conf/icde/WangC09, DBLP:conf/edbt/ChoudhuryHCAF15, DBLP:conf/icde/GaoZZY14a} or graph simulation~\cite{DBLP:journals/pvldb/SongGCW14}.
The work~\cite{DBLP:conf/icde/WangC09} assumes that queries are given, and builds node-neighbor tree to filter false candidate results.
The paper~\cite{DBLP:conf/icde/GaoZZY14a} leverages a distributed graph processing framework, Giraph, to approximately evaluate graph quereis.
The work~\cite{DBLP:conf/edbt/ChoudhuryHCAF15} uses the subgraph distributional statistics collected from the graph streams to optimize a graph query evaluation.
The paper~\cite{DBLP:journals/pvldb/SongGCW14} uses filtering methods to find data that potentially matches for a specific type of queries, namely {\em degree-preserving dual simulation with timing constraints}.
Firstly, all the above algorithms are designed for a certain type of graph queries.
Secondly, most of them assume the presence of queries, so they can build indices to accelerate.
In contrast, {\sf gLava}\xspace aims at summarizing graph streams in a generalized way, so as to support various types of queries, {\em without} any assumption of queries.
\etitle{Graph stream algorithms.}
There has also been work on algorithms over graph streams (see~\cite{DBLP:journals/sigmod/McGregor14} for a survey). This includes the problems of connectivity~\cite{DBLP:journals/tcs/FeigenbaumKMSZ05}, trees~\cite{targan1983}, spanners~\cite{DBLP:journals/talg/Elkin11}, sparsification~\cite{DBLP:journals/mst/KelnerL13}, counting subgraphs \emph{e.g.,}\xspace triangles~\cite{DBLP:conf/icalp/BravermanOV13, DBLP:conf/kdd/TsourakakisKMF09}. However, they mainly focus on theoretical study for best approximation bound, mostly on $O(n$ polylog $n)$ space, with one to multiple passes over the data stream.
In fact, {\sf gLava}\xspace is a friend, instead a competitor, of them. As will be seen later (Section~\ref{sec-algs}), {\sf gLava}\xspace can treat existing algorithms as {\em black-boxes} to help solve existing problems.
\etitle{Distributed graph systems.}
Many distributed graph computing systems have been proposed to conduct data processing and data analytics in massive graphs, such as Pregel~\cite{DBLP:conf/sigmod/MalewiczABDHLC10}, Giraph\footnote{http://giraph.apache.org}, GraphLab~\cite{DBLP:journals/pvldb/LowGKBGH12}, Power-Graph~\cite{DBLP:conf/osdi/GonzalezLGBG12} and GraphX~\cite{DBLP:conf/osdi/GonzalezXDCFS14}.
They have been proved to be efficient on static graphs, but are not ready for doing analytics over big graph streams with real-time response. In fact, they are complementary to and can be used for {\sf gLava}\xspace in distributed settings.
\section{gLava and Supported Queries}
\label{sec-gapollo}
We first define graph streams (Section~\ref{subsec-gs}) and state the studied problem (Section~\ref{subsec-ps}).
We then introduce our proposed graph sketch model (Section~\ref{subsec-gmodel}).
Finally, we discuss the queries supported by our new sketch (Section~\ref{subsec-queries}).
\subsection{Graph Streams}
\label{subsec-gs}
A {\em graph stream} is a sequence of elements $e = (x, y; t)$ where $x, y$ are node identifiers (labels) and edge $(x, y)$ is encountered at time-stamp $t$. Such a stream,
\[
G=\langle e_1, e_2, \cdots, e_m \rangle
\]
\ni naturally defines a graph $G=(V, E)$ where $V$ is a set of nodes and $E=\{e_1, \cdots, e_m\}$.
We write $\omega(e_i)$ the weight for the edge $e_i$, and
$\omega(x, y)$ the aggregated edge weight from node $x$ to node $y$.
We call $m$ the {\em size} of the graph stream, denoted by $|G|$.
Intuitively, the node label, being treated as an identifier, uniquely identifies a node, which could be \emph{e.g.,}\xspace IP addresses in network traffic data or user IDs in social networks.
Note that, in the graph terminology, a graph stream is a {\em multigraph}, where each edge can occur many times, \emph{e.g.,}\xspace one IP address can send multiple packets to another IP address. We are interested in properties of the underlying graph.
The causes a main challenge with graph streams where one normally does not have enough space to record the edges that have been seen so far.
Summarizing such graph streams in one pass is important to many applications.
Moreover, we do not explicitly differentiate whether $(x, y)$ is an ordered pair or not. In other words, our approach applies naturally to both directed and undirected graphs.
For instance, in network traffic data, a stream element arrives at the form: $(192.168.29.1, 192.168.29.133, 62, 105.12)$\footnote{We omit port numbers and protocols for simplicity.}, where node labels $192.168.29.1$ and $192.168.29.133$ are IP addresses, $62$ is the number of bytes sent {\em from} $192.168.29.1$ {\em to} $192.168.29.133$ in this captured packet (\emph{i.e.,}\xspace the weight of the directed edge), and $105.12$ is the time in seconds that this edge arrived when the server started to capture data. Please see Fig.~\ref{fig:graph} for a sample graph stream.
\subsection{Problem statement}
\label{subsec-ps}
The problem of {\em summarizing graph streams} is, given a graph stream $G$, to design another data structure $S_G$ from $G$, such that:
\begin{enumerate}
\item $|S_G| \ll |G|$: the size of $S_G$ is far less than $G$, preferably in sublinear space.
\item The time to construct $S_G$ from $G$ is in linear time.
\item The update cost of $S_G$ for each edge insertion/deletion is in constant time.
\end{enumerate}
Intuitively, a graph stream summary has to be built and maintained in real time, so as to deal with big volume and high velocity graph stream scenarios.
In fact, the {\sf CountMin}\xspace~\cite{DBLP:conf/vldb/MankuM02} and its variant {\sf gSketch}\xspace~\cite{DBLP:journals/pvldb/ZhaoAW11} satisfy the above conditions (see Example~\ref{exam:gs} for more details). Unfortunately, as discussed earlier, {\sf CountMin}\xspace and {\sf gSketch}\xspace can support only limited types of graph queries.
\subsection{The gLava Model}
\label{subsec-gmodel}
\stitle{The graph sketch.}
A {\em graph sketch} is a graph $S_G({\cal V}, {\cal E})$, where ${\cal V}$ denotes the set of vertices and ${\cal E}$ its edges. For vertex $v\in {\cal V}$, we simply treat its label as its node identifier (the same as the graph stream model).
Each edge $e$ is associated with a weight, denoted as $\omega(e)$.
In generating the above graph sketch $S_G$ from a graph $G$, we first set the number of nodes in the sketch, \emph{i.e.,}\xspace~let $|{\cal V}| = w$. For an edge $(x, y;t)$ in $G$, we use a hash function $h$ to map the label of each node to a value in $[1, w]$, and the aggregated edge weight is calculated correspondingly.
Please refer to Fig.~\ref{fig:sys} as an example, where we set $w=4$.
\etitle{Discussion about edge weight.}
The edge weight for an edge $e$ in the graph sketch is computed by an {\em aggregation} function of all edge weights that are mapped to $e$.
Such an aggregation function could be $\at{min}(\cdot)$, $\at{max}(\cdot)$, $\at{count}(\cdot)$, $\at{average}(\cdot)$, $\at{sum}(\cdot)$ or other functions.
In this paper, we use $\at{sum}(\cdot)$ by default to explain our method.
The other aggregation functions can be similarly applied.
In practice, which aggregation function to use is determined by applications.
For a more general setting that requires to maintain multiple aggregated functions in a graph sketch,
we may extend our model to have multiple edge weights \emph{e.g.,}\xspace~$\omega_1(e), \cdots ,\omega_n(e)$,
with each $\omega_i(e)$ corresponds to an aggregation function.
\etitle{Remark.}
One may observe that the graph sketch model is basically the same as the graph stream model, with the main difference that the time-stamps are not maintained. This makes it very useful and applicable in many scenarios when querying a graph stream for a given time window. In other words, for a graph analytics method $M$ that needs to run on a streaming graph $G$, denoted as $M(G)$, one can run it on its sketch $S_G$, \emph{i.e.,}\xspace~$M(S_G)$, to get an estimated result, without modifying the method $M$.
\begin{example}
\label{exam:gsedge}
Consider the graph stream in Fig~\ref{fig:graph} and its sketch in Fig.~\ref{fig:sys}.
Assume that query $Q_1$ is to estimate the aggregated weight of edges from $b$ to $c$.
In Fig.~\ref{fig:sys}, one can map $b$ to node $II$, $c$ to node $III$, and get the estimated weight $1$ from edge $(II, III)$, which is precise.
Now consider $Q_2$, which is to compute the aggregated weight from $g$ to $b$.
One can locate the edge $(III, II)$, and the estimated result is $2$, which is not accurate since the real weight of $(g, b)$ in Fig~\ref{fig:graph} is $1$.
\end{example}
The above result is expected, since given the compression, no hash function can ensure that the estimation on the sketch can be done precisely. Along the same line of {\sf CountMin}\xspace~\cite{DBLP:journals/jal/CormodeM05}, we use multiple independent hash functions to reduce the probability of hash collisions.
\begin{figure}[t]
\hspace*{2ex}
\begin{minipage}{0.4\columnwidth}
\centerline{
\xymatrixcolsep{0.1in}
\xymatrix{
& II (bc) \ar@/^/[dl]_3 \ar@/^1pc/[dd]^(.7){1} \ar@/_/[dr]^1 \ar@(ur,ul)[]^1 & \\
I (af) \ar@(u,l)[]^1 \ar@/^/[ur]^2 & & III(dg) \ar@/_/[ul]_1 \ar@(u,r)[]^1 \\
& IV(e) \ar@/_/[ur]^1 \ar[ul]^1 \ar@/^/[uu]^(.3){1} & \\
}
}
\centerline{
\xymatrixrowsep{0.2in}
\xymatrix{
& \txt{(a) Sketch $S_1$} &
}
}
\end{minipage}
\hspace*{6ex}
\begin{minipage}{0.4\columnwidth}
\centerline{
\xymatrixcolsep{0.1in}
\xymatrix{
& ii (cd) \ar@/^1pc/[dd]^(.4){2} \ar[dr]^1 & \\
i (ab) \ar[ur]^3 \ar@(ru,lu)[]^2 \ar@/_/[dr]_1 & & iii(g) \ar@/^/[ll]_1 \\
& iv(ef) \ar@/_/[ul]^2 \ar@(dr,dl)[]_1 \ar@/^/[uu]^(.6){1} &
}
}
\centerline{
\xymatrixrowsep{0.2in}
\xymatrix{
& \txt{(b) Sketch $S_2$} &
}
}
\end{minipage}
\caption{A {\sf gLava}\xspace sketch with 2 hash functions}
\label{fig:2hash}
\end{figure}
\stitle{The {\sf gLava}\xspace model.}
A {\sf gLava}\xspace sketch is a set of graph sketches $\{S_1({\cal V}_1, {\cal E}_1), \cdots, S_d({\cal V}_d, {\cal E}_d)\}$. Here, we use $d$ hash functions $h_1, \cdots, h_d$, where $h_i$ ($i\in[1, d]$) is used to generate $S_i$. Also, $h_1, \cdots, h_d$ are chosen uniformly at random from a pairwise-independent family (see Section~\ref{subsec-pairwise} for more details).
\begin{example}
\label{exam:2hash}
Figure~\ref{fig:2hash} shows another two sketches for Fig.~\ref{fig:graph}.
Again, consider the query $Q_2$ in Example~\ref{exam:gsedge}.
Using $S_1$ in Fig.~\ref{fig:2hash} (a), one can locate edge $(III, II)$ for $(g, b)$, which gives $1$.
Similarly, $S_2$ in Fig.~\ref{fig:2hash} (b) will also give $1$ from edge $(iii, i)$, where $g$ (resp. $b$) maps to $iii$ (resp. $i$). The minimum of the above two outputs is $1$, which is correct.
\end{example}
Example~\ref{exam:2hash} shows that using multiple hash functions can indeed improve the accuracy of estimation.
\subsection{Supported Graph Queries}
\label{subsec-queries}
As remarked in Section~\ref{subsec-gmodel}, for any graph analytics method $M$ to run over $G$, \emph{i.e.,}\xspace~$M(G)$, it is possible to run $M$ on each sketch directly and individually, and then merge the result as: $\tilde{M}(G) = \Gamma(M(S_1), \cdots, M(S_d))$, where $\tilde{M}(G)$ denotes the estimated result over $G$, and $\Gamma(\cdot)$ an aggregation function (\emph{e.g.,}\xspace~\at{min}, \at{max}, \at{conjunction}) to merge results returned from $d$ sketches.
Whilst the exercise in this section only substantiates several types of graph queries to be addressed in this work,
it is evident that the power of {\sf gLava}\xspace is far beyond what are listed below.
\stitle{Edge frequency.}
Given two node labels $a$ and $b$, we write $f_e(a, b)$ to denote the exact weight from a $a$-node to a $b$-node.
We write $\tilde{f_e}(a, b)$ the estimated weight from a sketch.
One application of such queries, taking social networks for example, is to estimate the communication frequency between two specific friends.
\stitle{Point queries.}
For a directed graph, given a node label $a$, we study a boolean query $f_v(a, \leftarrow) > \theta$ (resp. $f_v(a, \rightarrow) < \theta$), which is to monitor whether the aggregated edge weight {\em to} (resp. {\em from}) a node with label $a$ is above (resp. below) a given threshold $\theta$ in the graph stream $G$. For an undirected graph, we write $f_v(a, \perp) > \theta$ and $f_v(a, \perp) < \theta$ correspondingly.
Similarly, we use $\tilde{f_v}(a, \leftarrow), \tilde{f_v}(a, \rightarrow), \tilde{f_v}(a, \perp)$ for estimated numbers using sketches.
One important application of such queries is DoS (Denial-of-service) attacks in cyber security, which typically flood a target source (\emph{i.e.,}\xspace a computer) with massive external communication requests.
\stitle{Path queries.}
Given two node labels $a$ and $b$, a (boolean) reachability query $r(a, b)$ is to tell whether they are connected. Also, we write $\tilde{r}(a, b)$ as the estimated reachability.
One important monitoring task, for the success of multicast deployment in the Internet, is to verify the availability of service in the network, which is usually referred to as {\em reachability monitoring}.
Another reachability application that needs to consider edge weights is IP routing, which is to determine the path of data flows in order to travel across multiple networks.
\stitle{Aggregate subgraph query.}
The {\em aggregate subgraph query} is considered in~{\sf gSketch}\xspace~\cite{DBLP:journals/pvldb/ZhaoAW11}.
It is to compute the aggregate weight of the constituent edges of a sub-graph
$Q = \{(x_1,y_1), \cdots, (x_k,y_k)\}$, denoted by $f(Q) = \Omega (f_e(x_1, y_1), \cdots, f_e(x_k,y_k))$.
Here, the function $\Omega(\cdot)$ is to merge weights from all $f_e(x_i, y_i)$ for $i\in[1, k]$.
We write $\tilde{f}(Q)$ for estimation over sketches.
Note that, {\sf gSketch}\xspace simply merges all estimated weights in $G$, \emph{e.g.,}\xspace the sum of all weights, even if one edge is missing (\emph{i.e.,}\xspace~$\tilde{f}(x_i, y_i)=0$ for some edge $e_i$).
However, we use a different query semantics in this work: if $\tilde{f}(x_i, y_i)=0$, the estimated aggregate weight should be $0$, since the query graph $Q$ does not have an exact match.
We use this revised semantics since it is a more practical setting.
\begin{example}
\label{exam:subgraph}
Consider a subgraph with two edges as $Q: \{(a, b), (a, c)\}$.
The query $Q_3: \tilde{f}(Q)$ is to estimate the aggregate weight of $Q$.
The precise answer is $2$, which is easy to check from Fig.~\ref{fig:graph}.
\end{example}
\etitle{Extensions.}
We consider an extension of the above aggregate subgraph query, which allows a wildcard $*$ in the node labels that are being queried.
More specifically, for the subgraph query $Q = \{(x_1,y_1), \cdots, (x_k,y_k)\}$, each $x_i$ or $y_i$ is either a constant value, or a wildcard $*$ (\emph{i.e.,}\xspace match any label).
A further extension is to {\em bound} the wildcards to be matched to the same node, by using a subscript to a wildcard as $*_j$. That is, two wildcards with the same subscripts enforce them to be mapped to the same node.
\begin{example}
\label{exam:subgraph}
A subgraph query $Q_4: \tilde{f}(\{(a, b), (b, c), (c, a)\})$ is to estimate the triangle, \emph{i.e.,}\xspace a 3-clique with three vertices labeled as $a$, $b$, and $c$, respectively.
Another subgraph query $Q_5: \tilde{f}(\{(*, b), (b, c), (c, *)\})$ is to estimate paths that start at node with an edge to $b$, and end at any node with an edge from $c$, if the edge $(b, c)$ exists in the graph.
If one wants to count the common neighbors of $(b, c)$, the following query $Q_6: \tilde{f}(\{(*_1, b), (b, c), (c, *_1)\})$ can enforce such a condition, which again is a case of counting triangles.
\end{example}
The extension is apparently more general, with the purpose to cover more useful queries in practice.
Unfortunately, {\sf gSketch}\xspace cannot support such extensions.
\begin{table}[t]
\begin{center}
\begin{tabular}{| c | c | }
\hline
\cellcolor{black}{\textcolor{white}{\at{Symbols}}} &
\cellcolor{black}{\textcolor{white}{\at{Notations}}} \\ \hline
$G$, $S_G$ & a graph stream, and a graph sketch \\ \hline
$\omega(e)$ & weight of the edge $e$ \\ \hline
$f_e(a,b)$ & edge weight \\ \hline
$f_v(a, \leftarrow)$ & node in-flow weight (directed graphs) \\ \hline
$f_v(a, \rightarrow)$ & node out-flow weight (directed graphs) \\ \hline
$f_v(a, \perp)$ & node flow weight (undirected graphs) \\ \hline
$r(a, b)$ & whether $b$ is reachable from $a$ \\ \hline
$f(Q)$ & weight of subgraph $Q$ \\ \hline
\end{tabular}
}
\end{center}
\vspace{-2.5ex}
\caption{Notations}\label{tbl:notation}
\end{table}
\etitle{Summary of notations.}
The notations of this paper are summarized in Table~\ref{tbl:notation}, which are for both directed and undirected graphs, unless being specified otherwise.
\section{Query Processing}
\label{sec-algs}
We consider the graph stream as $G$, and $d$ graph sketches $\{S_1, \cdots, S_d\}$ of $G$, where $S_i$ is constructed using a hash function $h_i(\cdot)$.
In this following, we discuss how to process different types of queries.
Again, by default, we assume that we use $\at{sum}(\cdot)$ as the default aggregation function.
Also, to facilitate the discussion, we assume that an adjacent matrix is used for storing {\sf gLava}\xspace.
\subsection{Edge Query}
\label{subsec:edgeq}
To evaluate $\tilde{f_e}(a,b)$, the edge weight of $(a, b)$, is straightforward.
It is to find the estimated edge weight from each sketch $\omega_i(h_i(a), h_i(b))$ and then use a corresponding function $\Gamma(\cdot)$ to merge them, as the following:
\[
\tilde{f_e}(a,b) = \Gamma(\omega_1(h_1(a), h_1(b)), \cdots, \omega_d(h_d(a), h_d(b)))
\]
In this case, the function $\Gamma(\cdot)$ is to take the minimum.
\stitle{Complexity.}
It is easy to see that estimating the aggregate weight of an edge query is in $O(d)$ time and in $O(d)$ space, where $d$ is a constant.
\subsection{Point Queries}
\label{subsec:nodeq}
Here, we only discuss the case $\tilde{f_v}(a, \leftarrow) > \theta$. That is, given a new element $(x, y; t)$, estimate in real-time whether the aggregate weight to node $a$ is above the threshold $\theta$.
The other cases, \emph{i.e.,}\xspace~$\tilde{f_v}(a, \leftarrow) < \theta$, $\tilde{f_v}(a, \rightarrow) > \theta$, $\tilde{f_v}(a, \rightarrow) < \theta$, $\tilde{f_v}(a, \perp) > \theta$ and $\tilde{f_v}(a, \perp) < \theta$, can be similarly processed.
We use the following strategy to monitor $\tilde{f_v}(a, \leftarrow) > \theta$, given an incoming edge $e: (x, y; t)$.
Note that if $y \ne a$, we simply update all $d$ sketches in constant time, since this is not about an edge to $a$. Next, we only describe the case of edge $e: (x, a; t)$.
\etitle{Step 1.} [Estimate current in-flow.]
We write $\tilde{f_v^i}(a, \leftarrow)$ the estimated in-flow from the $i$-th sketch.
$\tilde{f_v^i}(a, \leftarrow)$ can be computed by first locating the column in the adjacent matrix corresponding to label $a$ (\emph{i.e.,}\xspace~$h_i(a)$), and then sum up the values in that column, \emph{i.e.,}\xspace $\tilde{f_v^i}(a, \leftarrow) = \sum_{j=1}^w {\cal M}_i[j][h_i(a)]$. Here, $w$ is the width of the adjacent matrix ${\cal M}_i$. Then,
\[
\tilde{f_v}(a, \leftarrow) = \Gamma(\tilde{f_v^1}(a, \leftarrow), \cdots, \tilde{f_v^w}(a, \leftarrow))
\]
In this case, the function $\Gamma(\cdot)$ is to take the minimum.
\etitle{Step 2.} [Monitor $e$.]
We only send an alarm, if $\tilde{f_v}(a, \leftarrow) + \omega(e) > \theta$.
\etitle{Step 3.} [Update all sketches.]
Update all $d$ sketches by aggregating the new edge weight $\omega(e)$.
\stitle{Complexity.}
It is easy to see that step~1 takes $O(d+w)$ time and $O(d)$ space, where both $d$ and $w$ are constants.
\subsection{Path Queries}
\label{subsec:pathq}
We consider the reachability query $\tilde{r}(a, b)$, which is to estimate whether $b$ is reachable from $a$. For such queries, we treat any off-the-shelf algorithm $\at{reach}(x, y)$ as a {\em black-box} and show our strategy.
\etitle{Step 1.} [Map.]
We invoke $\at{reach}_i(h_i[a], h_i[b])$ on the $i$-th sketch (for $i\in[1, d]$), to decide whether the mapped node $h_i[b]$ is reachable from the mapped node $h_i[a]$.
\etitle{Step 2.} [Reduce.]
We merge individual results as follows:
\[
\tilde{r}(a, b) = \at{reach}_1(h_1[a], h_1[b]) \wedge \cdots \wedge \at{reach}_d(h_d[a], h_d[b])
\]
That is, the estimated result is \mbox{\em true}~only if the mapped nodes are reachable from {\em all} $d$ sketches.
The complexity of the above strategy is determined by the algorithm $\at{reach}()$.
\subsection{Aggregate Subgraph Query}
\label{subsec:subgraphq}
We next consider the aggregate subgraph query $\tilde{f}(Q)$, which is to compute the aggregate weight of the constituent edges of a sub-graph $Q$.
The process is similar to the above path queries, by using any existing algorithm $\at{subgraph}(Q)$.
\etitle{Step 1.} [Map.]
We first invoke $\at{subgraph}(Q)$ at each sketch to find subgraph matches, and calculate the aggregate weight, denoted by $\at{weight}\xspace_i(Q)$ for the $i$-th sketch.
\etitle{Step 2.} [Reduce.]
We merge individual results as follows:
\[
\tilde{f}(Q) = \at{min}(\at{weight}\xspace_1(Q), \cdots, \at{weight}\xspace_d(Q))
\]
Note that, running a graph algorithm on a sketch is only applicable to {\sf gLava}\xspace. It is not applicable to {\sf gSketch}\xspace since {\sf gSketch}\xspace by nature is an array of frequency counting, without maintaining the graphical structure as {\sf gLava}\xspace does.
Also, in the case $\at{weight}\xspace_i(Q)$ from some sketch that says that a subgraph match does not exist, we can terminate the whole process, which provides chances for optimization.
\stitle{Optimization.}
Recall that a subgraph $Q$ is defined as constituent edges as $\{(x_1,y_1), \cdots, (x_k,y_k)\}$ (Section~\ref{subsec-queries}).
An alternative way of estimating the aggregate subgraph query is to first compute the minimum value of each value and sum them up.
We denote this approach by $\tilde{f'}(Q)$ as follows:
\[
\tilde{f'}(Q) = \sum_{i=1}^k \tilde{f_e}(x_i, y_i)
\]
It is readily to see that $\tilde{f'}(Q) \leq \tilde{f}(Q)$.
Recall that there are two extensions of the subgraph queries (Section~\ref{subsec-queries}).
For the first extension that a wildcard $*$ is used, the above optimization can be used. For instance, the edge frequency of $\tilde{f_e}(x, *)$ for a directed graph is indeed $\tilde{f_v}(x, \rightarrow)$.
For the second extension that multiple wildcards $*_i$ are used to bound to the same node, this optimization cannot be applied.
\section{Error Bounds}
\label{sec-theory}
We study the error bounds for two basic types of queries: edge queries and point queries.
Although {\sf gLava}\xspace is more general, we show that theoretically, it has the same error bounds
as {\sf CountMin}\xspace.
\subsection{Edge Frequency}
Our proof for the error bound of edge frequency queries is an adaption of the proof used in
{\sf CountMin}\xspace in Sec.~4.1 of \cite{DBLP:journals/jal/CormodeM05}.
\begin{theorem}
The estimation $\tilde{f_e}(j, k)$ of the cumulative edge weight of the edge $(j,k)$ has the following guarantees, $f_e(j, k) \leq \tilde{f_e}(j, k)$ with probability at least $1 - \delta$, s.t.,
$f_e(j, k) \le \tilde{f_e}(j, k) + \epsilon * n$,
where $f_e(j, k)$ is the exact answer to the cumulative edge weight of the edge $(j, k)$,
$n$ denotes the number of nodes,
and the error in answering a query is within a factor of $\epsilon$ with probability $\delta$\footnote{The parameters $\epsilon$ and $\delta$ are usually set by the user.}.
\end{theorem}
\begin{proof}
For any query edge $f_e(j, k)$, for each hash function $h_i$, by construction,
for any stream edge $e: (j, k; t)$, where $\omega(e)$ is the edge weight that is added to
$\kw{count}\xspace(h_i(j),h_i(k))$. Therefore, by construction, the answer to
$f_e(j, k)$ is less than or equal to $min_i (\kw{count}\xspace(h_i(j),h_i(k)))$ for $i\in[1, d]$ where $d$ is the number of hash functions.
Consider two edges $(j, k)$ and $(l, m)$.
We define an indicator variable $I_{i,j,k,l,m}$, which is
1 if there is a collision between two distinct edges, \emph{i.e.,}\xspace $(j \neq l) \wedge (k \neq m) \wedge (h_i(j)=h_i(l) \wedge h_i(k)=h_i(l))$ , and 0 otherwise.
By pairwise independence of the hash functions,
\mat{4ex}{
$E(I_{i,j,k,l,m})$ \= $= Pr[(h_i(j)=h_i(l) \wedge h_i(k)=h_i(m)]$ \\
\> $\leq (1/\at{range}(h_i))^2=\epsilon'^2/e^2$ \textcolor{white}{\huge P}
}
\ni where $e$ is the base used to compute natural logarithm, and $\at{range}(h_i)$ is the
number of hash buckets of function $h_i$.
Define the variable $X_{i,j,k}$ (random over choices of $h_i$) to count the number of collisions with the edge $(j, k)$,
which is formalized as
$X_{i,j,k}=\Sigma_{l=1 \ldots n,m=1 \ldots n} I_{i,j,k,l,m} a_{l,m}$, where $n$ is the number of nodes in the graph.
Since all $a_i$'s are non-negative in this case, $X_{i,j,k}$ is non-negative.
We write $\kw{count}\xspace[i,h_i(j),h_i(k)]$ as the count in the hash bucket relative to hash function $h_i$.
By construction, $\kw{count}\xspace[i,h_i(j),h_i(k)] = f_e(j,k) + X_{i,j,k}$.
So clearly, $min_i (\kw{count}\xspace[i,h_i(j),h_i(k)]) \geq f_e(j, k)$.
\mat{4ex}{
\=$E(X_{i,j,k})$ \\
\>\hspace{4ex}\=$=E(\sum_{l=1 \ldots n, m=1 \ldots n}I_{i,j,k,l}f_e(l,m))$ \textcolor{white}{\huge P} \\
\>\>$\leq (\sum_{l=1 \ldots n, m=1 \ldots n}E(I_{i,j,k,l}).f_e(l,m)) \leq (\epsilon'/e)^2* n$ \textcolor{white}{\huge P}
}
\ni by pairwise independence of $h_i$, and linearlity of expectation.
Let, $\epsilon'^2 = \epsilon$. By the Markov inequality,
\mat{4ex}{
\= $Pr[\tilde{f_e}{(j,k)} > f_e(j,k) + \epsilon * n]$ \= \\
\>\hspace{4ex}\= $=Pr[\forall_i. \at{count}[i, h_i(j), h_i(k)] > f_e(j,k) + \epsilon * n$] \textcolor{white}{\huge P}\\
\>\> $=Pr[\forall_i. f_e(j,k)+X_{i,j,k}>f_e(j,k)+ \epsilon * n]$ \textcolor{white}{\huge P}\\
\>\> $=Pr[\forall_i. X_{i,j,k} > e * E(X_{i,j,k})] < e^{-d} \leq \delta$ \textcolor{white}{\huge P}
}
\end{proof}
Our algorithm generates the same number of collisions and the same error bounds under the same probabilistic guarantees as {\sf CountMin}\xspace for edge frequency queries.
\subsection{Point Queries}
We first discuss the query for node out-degree, \emph{i.e.,}\xspace $f_v(a, \rightarrow)$.
Consider the stream of edges $e: (a, *; t)$, \emph{i.e.,}\xspace edges from node $a$ to any other node indicated by a wildcard $*$.
Drop the destination (\emph{i.e.,}\xspace the wildcard) of each edge. The stream now becomes a stream of tuples $(a, \omega(t))$ where $\omega(t)$ is the edge weight from node $a$ at time $t$. When a query is posed to find the out-degree of node $a$, {\sf CountMin}\xspace~\cite{DBLP:journals/jal/CormodeM05} returns the minimum of the weights in different hash buckets as the estimation of the flow out of node $a$.
If the number of unique neighbors (\emph{i.e.,}\xspace connected using one hop ignoring the weights) is sought, we adapt the
procedure above by replacing $\omega(t)$ with 1 in the stream above for all nodes. Clearly, by construction, the answer obtained is an over-estimation of the true out-degree because of two reasons: (a) collisions in the hash-buckets, and (b) self-collision, \emph{i.e.,}\xspace we do not know if an edge has been seen previously and thus count the outgoing edge again even if we have seen it.
The case for in-degree point queries is similar.
To compute the in-degree of a node, we simply adapt the stream to create a one-dimensional stream as in the case above. Drop the source for each edge to create a stream.
The variations in the case of out-degree for the total in-flow and the number of neighbors with in-links to a node can be estimated as in the case of out-degree outlined above.
The error estimates for point queries (see Sec.~4.1 of \cite{DBLP:journals/jal/CormodeM05}) hold for these cases.
\begin{lemma}
\label{degree}
The estimated out-degree (in-degree) is within a factor of $\epsilon$ with probability $\delta$ if we use $d=\lceil ln(1/\delta) \rceil$ rows of pair-wise independent hash functions and $w=\lceil e/\epsilon \rceil$.
\end{lemma}
\eat
\stitle{Path.}
$(a, b), (b, c)$.
\stitle{Star.}
$(a, b), (a, c), (a, d)$.
\stitle{Cycle.}
$(a, b), (b, c), (c, a)$.
\begin{figure}[t]
\hspace*{2ex}
\begin{minipage}{0.25\columnwidth}
\centerline{
\xymatrixcolsep{0.1in}
\xymatrix{
a \ar[d] \\
b \\
}
}
\centerline{
\xymatrixrowsep{0.2in}
\xymatrix{
& \txt{(a) Edge} &
}
}
\end{minipage}
\hspace*{-2ex}
\begin{minipage}{0.25\columnwidth}
\centerline{
\xymatrixcolsep{0.1in}
\xymatrix{
a \ar[d] & \\
b \ar[r] & c \\
}
}
\centerline{
\xymatrixrowsep{0.2in}
\xymatrix{
& \txt{(b) Path} &
}
}
\end{minipage}
\hspace*{-2ex}
\begin{minipage}{0.25\columnwidth}
\centerline{
\xymatrixcolsep{0.1in}
\xymatrix{
& a \ar[d]\ar[dl]\ar[dr] & \\
b & c & d \\
}
}
\centerline{
\xymatrixrowsep{0.2in}
\xymatrix{
& \txt{(c) Star} &
}
}
\end{minipage}
\hspace*{-2ex}
\begin{minipage}{0.25\columnwidth}
\centerline{
\xymatrixcolsep{0.1in}
\xymatrix{
a \ar[d] & \\
b \ar[r] & c \ar[ul] \\
}
}
\centerline{
\xymatrixrowsep{0.2in}
\xymatrix{
& \txt{(d) Circle} &
}
}
\end{minipage}
\caption{Studied cases}
\label{fig:2hash}
\end{figure}
\section{Implementation Details}
\label{sec-implementation}
In this section, we first discuss the data structures used to implement {\sf gLava}\xspace (Section~\ref{subsec-adjacent}).
We then introduce the definition of pairwise independent hash functions (Section~\ref{subsec-pairwise}).
We also discuss its potential extension in a distributed environment (Section~\ref{subsec:distributed}).
\subsection{Adjacent Matrix and Its Extension}
\label{subsec-adjacent}
Using hash-based methods, although it is evident that it only requires 1-pass of the graph stream to construct/update a {\sf gLava}\xspace.
However, the linear time complexity of constructing and updating a {\sf gLava}\xspace depends on the data structures used.
For example, the adjacent list may not be a fit, since searching a specific edge is not in constant time.
\subsubsection{Adjacent Matrix}
\label{subsubsec-matrix}
An adjacency matrix is a means of representing which nodes of a graph are adjacent to which other vertices.
\begin{example}
\label{exam:matrix}
Consider the sketch $S_1$ in Fig.~\ref{fig:2hash}~(a) for example. Its adjacent matrix is shown in Fig.~\ref{fig:matrix}.
\end{example}
Example~\ref{exam:matrix} showcases a directed graph.
In the case of an undirected graph, it will be a symmetric matrix.
\begin{figure}[t]
\centering
\begin{tabular}{|c|c|c|c|c|}
\multicolumn{1}{c}{{\color{white} {\Huge j}} $\at{from}\setminus\at{to}$} & \multicolumn{1}{c}{$I(af)$} & \multicolumn{1}{c}{$II(bc)$} & \multicolumn{1}{c}{$III(dg)$} & \multicolumn{1}{c}{$IV(e)$}\\ \cline{2-5}
\multicolumn{1}{c|}{$I(af)$} & 1 & 2 & 0 & 0 \\ \cline{2-5}
\multicolumn{1}{c|}{$II(bc)$} & 3 & 1 & 1 & 1 \\ \cline{2-5}
\multicolumn{1}{c|}{$III(dg)$} & 0 & 1 & 1 & 0 \\ \cline{2-5}
\multicolumn{1}{c|}{$IV(e)$} & 1 & 1 & 1 & 0 \\ \cline{2-5}
\end{tabular}
\caption{The adjacent matrix of $S_1$}
\label{fig:matrix}
\end{figure}
\stitle{Construction.}
Consider a graph stream $G=\langle e_1, e_2, $ $\cdots, e_m \rangle$ where $e_i = (x_i, y_i; t_i)$. Given a number of nodes $w$ and a hash function $h(\cdot) \rightarrow [1, w]$. We use the following strategy.
\etitle{Step 1.} [Initialization.]
Construct a $w\times w$ matrix ${\cal M}$, with all values initialized to be $0$.
\etitle{Step 2.} [Insertion of $e_i$.]
Compute $h(x_i)$ and $h(y_i)$. Increase the value of ${\cal M}[h(x_i)][h(y_i)]$ by $\omega(e_i)$, the weight of $e_i$.
In the above strategy, step 1 will take constant time to allocate a matrix. Step 2 will take constant time for each $e_i$. Hence, the time complexity is $O(m)$ where $m$ is the number of edges in $G$. The space used is $O(w^2)$.
\stitle{Deletions.} [Deletion of $e_i$.]
Insertions have been discussed in the above step 2.
For the deletion of an $e_i$ that is not of interest (\emph{e.g.,}\xspace out of a certain time window), it is simply to decrease the value of ${\cal M}[h(x_i)][h(y_i)]$ by $\omega(e_i)$ in $O(1)$ time.
Alternatively, one may consider to use an adjacent hash-list is to maintain, for each vertex, a list of its adjacent nodes using a hash table. Given an edge $e_i (x_i, y_i; t_i)$, two hash operations are needed: The first is to locate $x_i$, and the second is to find $y_i$ from $x_i$'s hash-list. Afterwards, it updates the corresponding edge weight.
Adjacent list is known to be suitable when graph is sparse. However, in terms of compressed graph in our case, as will be shown later in experiments, most sketches are relatively dense, which makes the adjacent matrix the default data structure to manage our graph sketches.
\subsubsection{Using Non-Square Matrices}
\label{subsubsec-matrix2}
When using a classical square matrix for storing a sketch, we have an $n * n$ matrix.
Consider all edges from node $a$ such as $(a, *)$.
Using any hash function will inevitably hash all of these edges to the same row.
For example, in Fig.~\ref{fig:matrix}, all edges $(a, *)$ will be hashed to the first row of the matrix.
When there is only one hash function to use, due to the lack of {\em a priori} knowledge of data distribution, it is hard to decide the right shape of a matrix. However, the application of $d$ sketches provides us an opportunity to heuristically reduce the chance of combined hash collisions.
The basic idea is, instead of using an $n * n$ matrix with one hash function, we use an $m * p$ matrix with two hash functions: $h_1(\cdot) \rightarrow [1, m]$ on the {\em from} nodes and $h_2(\cdot) \rightarrow [1, p]$ on the {\em to} nodes.
\begin{figure}[t]
\centering
\begin{tabular}{|c|c|c|}
\multicolumn{1}{c}{{\color{white} {\Huge j}} $\at{from}\setminus\at{to}$} & \multicolumn{1}{c}{$i(abcd)$} & \multicolumn{1}{c}{$ii(efg)$} \\ \cline{2-3}
\multicolumn{1}{c|}{$I(a)$} & 2 & 0 \\ \cline{2-3}
\multicolumn{1}{c|}{$II(b)$} & 3 & 1 \\ \cline{2-3}
\multicolumn{1}{c|}{$III(c)$} & 0 & 2 \\ \cline{2-3}
\multicolumn{1}{c|}{$IV(d)$} & 0 & 1 \\ \cline{2-3}
\multicolumn{1}{c|}{$IV(e)$} & 2 & 1 \\ \cline{2-3}
\multicolumn{1}{c|}{$IV(f)$} & 1 & 0 \\ \cline{2-3}
\multicolumn{1}{c|}{$IV(g)$} & 1 & 0 \\ \cline{2-3}
\end{tabular}
\caption{A non-square matrix}
\label{fig:matrix2}
\end{figure}
\begin{example}
\label{exam:matrix2}
Consider the graph stream in Fig.\ref{fig:graph}.
Assume that we use two hash functions: $h_1(\cdot) \rightarrow [1, 7]$ and $h_2(\cdot) \rightarrow [1, 2]$.
The non-square matrix is shown in Fig.~\ref{fig:matrix2}.
\end{example}
In practice, when we can generate multiple sketches, we heuristics use matrices $n * n$, $2n * n/2$, $n/2 * 2n$, $4n * n/4$, $n/4 * 4n$, etc. That is, we use matrices with the same sizes but different shapes.
\subsection{Pairwise Independent Hash Functions}
\label{subsec-pairwise}
Here, we only borrow the definition of pairwise independent hash functions\footnote{\url{http://people.csail.mit.edu/ronitt/COURSE/S12/handouts/lec5.pdf}}, while relying on existing tools to implement them.
A family of functions ${\cal H} = \{h | h(\cdot) \rightarrow [1, w]\}$ is called a {\em family of pairwise independent hash functions} if for two different hash keys $x_i$, $x_j$, and $k, l \in [1, w]$,
\[
\at{Pr}_{h \leftarrow {\cal H}}[h(x_i) = k \wedge h(x_j) = l] = 1 / w^2
\]
Intuitively, when using multiple hash functions to construct sketches, the hash functions used should be pairwise independent in order to reduce the probability of hash collisions. Please refer to~\cite{DBLP:journals/jal/CormodeM05} for more details.
\subsection{Discussion: Distributed Environment}
\label{subsec:distributed}
In this paper, we mainly discuss how to implement {\sf gLava}\xspace in a centralized environment.
However, it is easy to observe that {\sf gLava}\xspace can be easily applied to a distributed environment, since the construction and maintenance of each sketch is independent of each other. Assuming that we have $d$ sketches in one computing node, when $m$ nodes are available, we can use $d\times m$ pairwise independent hash functions, which may significantly reduce the probability of errors.
\section{Conclusion}
\label{sec-conclusion}
We have proposed a new graph sketch for summarizing graph streams.
We have demonstrated its wide applicability to many emerging applications.
\bibliographystyle{abbrv}
| {
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Tactical squad-based shooter Firewall Zero Hour deploys for PlayStation VR.
In Firewall Zero Hour, play as one of 12 contractors and work with teammates to either protect or obtain valuable data housed on a laptop and located in dangerous locations around the globe.
Developed by First Contact Entertainment, Firewall Zero Hour is a 4v4 team-based tactical shooter developed exclusively for PlayStation VR and compatible with both the PS VR Aim Controller and DualShock 4 controller.
A malevolent force known only as Lina is devouring data from a vast, interdimensional network of servers overseen by sentient computers called "motes." In desperation, the motes seek to awaken the Blade Stranger in the hopes of vanquishing Lina.
Take to the skies as captain of a powerful airship and discover a fantastical world of airborne gladiatorial sci-fi! Compete to become Champion of the Arena, as its inscrutable Overseers test you and fellow challengers in a fantasy reality show.
Claybook is a unique world made entirely of clay. Every inch of the environment can be shaped and molded. Everything has matter inside it, not just an outer shell. Clay can be liquid or solid, it can be deformed and destroyed.
Gather your party and get ready for a fantastic adventure! Your imagination is your only limitation as you seek to restore Divinity and save the world. But beware, only one of you can become the new Divine!
After awakening in unfamiliar woods, Alex, an ordinary high schooler living an ordinary life, learns he has somehow ended up in a fantasy world dominated by conflict and destruction.
The greatest grappling game returns to take on the world on the PS4! In Fire Pro Wrestling World, customize every aspect of the match, from your wrestler to the ring itself, to fight your way to the championship belt!
Gate of Doom a is classic multiplayer action RPG for one to two players. Originally released in 1990, and a noted classic arcade title from the 90s.
Do you have what it takes to win the FedExCup on the PGA Tour? Compete in the all-new officially licensed PGA Tour Career mode. Play on famous courses like TPC Boston, TPC Sawgrass and more.
Form your party of secret agents from among four races: Human, Oni, Tengu, and Nekomata. Then conquer the terrifying and mysterious Yokai-filled castle!
The Naruto series is back with a brand new experience. You can battle as a team of 4 to compete against other teams online. Lead your team and fight online to see who the best ninjas are!
NBA 2K19 continues to push limits as it brings gaming one step closer to real-life basketball excitement and culture. Download NBA 2K19: The Prelude for free and get a head start on your MyPlayer before the full game release on September 7.
Shikhondo: Soul Eater is a Korean bullet-hell shoot 'em up set within a beautiful and bizarre world of Asian mythology.
Splash Blast Panic is a multiplayer competitive party game where you must shoot, ram, dodge and overall bully your opponents with a variety of watergun-based weaponry.
Fight your way up the season ranks to become a online superstar in a spectacular future-sport championship. Seamlessly switch between heavily armed high tech vehicles at any time to create endless tactical choices in a frantic 5v5 battle to claim victory.
Torn is a dark science-fiction mystery. Explore the abandoned mansion filled with strange machines and disturbing experiments, belonging to an eccentric scientist missing for 64 years.
Rebuilt from the ground up, Yakuza Kiwami 2 uses the Dragon Engine to update one of the series stand-out titles into a modern classic. Also new to Kiwami 2 is the 'Majima Saga' revealing events that occur prior to the game.
Fire Pro Wrestling World, baby!! Been hyped for this since it was announced, can't wait to sim wrestlers from every generation.
A lot if variety next week, really interested in Blade Strangers and Haunted Dungeons too. Keep up the great work, Ps blog team!
Fernz Gate day 1, Vita love!
Don't forget, Pato Box will also be coming to the Vita. It got pushed back a couple of weeks, but it's still coming!
A decent selection of new titles to testdrive your Playstation 4 Pro 500 Million Limited Mostly to Scalpers Edition. Thanks, Sony, for showing love and appreciation for scalpers smh.
Been loving the first act of Divinity Original Sin 2. Cannot wait to play even more of it.
6 VR games, damn Sony you tryin' to prove somethin'?
are you sure this is not a mistake?
Sunless Sea??? Never heard of this version … or that it even was coming into PS4… Nice! | {
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Q: CDI @ConversationScoped with AJAX I've got a pretty typical CRUD situation that I'm struggling with so I assume I must be misunderstanding something. I've put together a little demo app to better explain my problem. The two files of interest are shown below:
PersonView - CDI Managed Bean backing the JSF page
package example
import java.io.Serializable;
import java.util.List;
import javax.enterprise.context.Conversation;
import javax.enterprise.context.ConversationScoped;
import javax.enterprise.inject.Produces;
import javax.inject.Inject;
import javax.inject.Named;
@ConversationScoped @Named
public class PersonView implements Serializable {
private Person selectedPerson;
@Inject private PersonService personService;
@Inject private Conversation conversation;
public PersonView() {}
public List<Person> getPeople() { return personService.findAll(); }
public void beginConversation() { if( conversation.isTransient() ) {conversation.begin();} }
public void endConversation() { if( !conversation.isTransient() ) { conversation.end();} }
public void createPerson() {
beginConversation();
setSelectedPerson( new Person() );
}
public void addPerson() {
personService.addPerson( getSelectedPerson() );
endConversation();
}
public void updatePerson() { personService.updatePerson( getSelectedPerson() ); }
public Person getSelectedPerson() { return selectedPerson; }
public void setSelectedPerson(Person selectedPerson) { this.selectedPerson = selectedPerson; }
}
index.xhtml - JSF page for manipulating people
<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"
xmlns:h="http://java.sun.com/jsf/html"
xmlns:f="http://java.sun.com/jsf/core"
xmlns:ui="http://java.sun.com/jsf/facelets"
xmlns:p="http://primefaces.org/ui">
<h:head>
<title>CRUD Example</title>
</h:head>
<h:body>
<h:form prependId="false">
<p:dataTable var="p" value="#{personView.people}" id="person_table" rowKey="#{p.id}" selection="#{personView.selectedPerson}">
<p:column selectionMode="single"/>
<p:column><f:facet name="header">ID</f:facet>#{p.id}<p:column>
<p:column><f:facet name="header">Name</f:facet>#{p.name}</p:column>
<f:facet name="footer">
<p:commandButton value="Create Person" onclick="create_dialog.show();" actionListener="#{personView.createPerson}"/>
<p:commandButton value="Edit Person" onclick="edit_dialog.show();" update="edit_panel"/>
</f:facet>
</p:dataTable>
</h:form>
<p:dialog header="Create Person" id="create_dialog" widgetVar="create_dialog" modal="true" width="750" height="300">
<h:form prependId="false">
<p:panel id="create_panel">
<p>Name: <p:inputText value="#{personView.selectedPerson.name}" required="true"/></p>
<p><p:commandButton value="Add" actionListener="#{personView.addPerson}" oncomplete="create_dialog.hide();" update="person_table" /></p>
</p:panel>
</h:form>
</p:dialog>
</h:body>
On the index page the user is shown a data table containing all the people the system knows about. They then press the Create Person button at the bottom of the table. I have checked that this correctly calls the createPerson method and the conversation apparently starts. The create_dialog is then displayed where the user can enter a name. The problem comes when the user clicks the Add button. JSF attempts to store the persons name but the selectedPerson variable is now null so it fails with a NullPointerException.
I realize this isn't a common way of creating objects but in my current application is makes sense as I can guess some of the values of a new Person. It also fits quite well with how I'd like to do editing.
So my question(s): why doesn't the conversation propagate? The PersonView bean appears to be in request scope all the time. I've read about @ViewScoped in JSF2 but I'd rather stick with CDI if possible. From what I've read I think the problem is a failure to pass the CID name with the request but I'm at a loss to see how I could do that with AJAX.
The only solution that I've come up with is to move PersonView into the session but that feels like a huge kludge.
e
A: The only way that I got this to work is to use @ViewAccessScoped in MyFaces CODI. CDI allows extensibility so all you have to do is include the CODI jar files in with your application. This works even if you are using Mojarra and not MyFaces.
So if you want to use CDI annotations, that's my recommendation. I tried using ConversationScoped annotation for a while but I just couldn't get it to work conveniently. Once I started using CODI all my problems went away.
A: Seems like you are using PrimeFaces, Im not sure how to make an ajax call with Primefaces, so I will show you how its done with standard JSF 2.0
First of all when using AJAX, you MUST pass the cid with every AJAX request.
Try adding the following to your ConversationScope Managed Bean (You need to somehow pass the cid to the view - index.xhtml, then every subsequent AJAX call will pass the same cid back to the server):
@Named
@ConversationScoped
public class PersonView implements Serializable {
public List<Person> getPeople() {
return personService.findAll();
}
@Inject
private Conversation conversation;
//Start the conversation once the
//bean is created and all injection is done on the bean
//I typically use this in the case of AJAX
@PostContruct
public void beginConversation() {
if( conversation.isTransient() ) {
conversation.begin();
}
}
public void endConversation() {
if( !conversation.isTransient() ) {
conversation.end();
}
}
// This will be used in the view (index.xhtml)
public String getConversationId() {
return conversation.getId();
}
public void createPerson() {
setSelectedPerson( new Person() );
}
public void addPerson() {
personService.addPerson( getSelectedPerson() );
endConversation();
// beginConversation(); //might need to start a new conversation once old one is done
}
}
now in your view you will typically do the following:
<h:commandButton action="#{personView.createPerson}" value="Create Person">
<!-- passing the cid -->
<f:param name="cid" value="#{personView.conversationId}" />
<f:ajax execute="@form" />
</h:commandButton>
<h:commandButton action="#{personView.addPerson}" value="Add">
<!-- passing the cid -->
<f:param name="cid" value="#{personView.conversationId}" />
<f:ajax execute="@form" render=":person_table" />
</h:commandButton>
This works as long as all subsequent calls are AJAX. If you start mixing it with the normal calls the conversation gets lost. On the other hand, it this was a non-AJAX list of calls you are making, the cid would be passed in automatically for you
A: Working with @ConversationScoped in combination with <f:ajax> tags makes it necessary to pas the conversation id to commandButton and commandLink elements.
See this Example:
<h:commandLink value="update"
actionListener="#{myController.updateSomething(myData)}">
<f:ajax render="...."/>
<f:param name="cid" value="#{myController.getCID()}" />
</h:commandLink>
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emily hopcian
Exploring Creatives
falling in love with New York City
There's something to travel that makes me fall in love with it every time I find myself embarking on a new adventure. There's something to getting lost in a new place that makes the butterflies in my stomach dance in the best way, and there's something electric about falling in love with pieces of a place as I move through and experience it.
Travel nourishes me. It tickles my soul, makes me breathe deeper and leaves me with moments, smiles and memories that simply make me feel full.
At the beginning of June, I satisfied my craving for adventure when I traveled to Boston and New York City with my mom and aunt. It was my second time in Boston — although I hadn't been since I was quite young — and my first time in New York City. I fell in love with each place, for different reasons, more than I thought I would.
In Boston, I was enthralled by the architecture, history, natural beauty, tradition and fandom — we went to a Red Sox game at Fenway Park — and I left wanting to spend more time there. But New York was the city that knocked me off my feet. It left me inspired, beaming from the inside out and feeling as though there's so much more to life and living. The City That Never Sleeps captivated me in numerous ways.
Manhattan from the Staten Island Ferry.
New York City: a storied city
New York has so many storylines running through it, and while the same can be said of San Francisco, my current home, I feel the two cities are so very different. San Francisco is soft, easygoing. New York is gritty, hard and beautiful in a rough-around-the-edges kind of way. In just a few short days, I came to love the creativity that's mixed in with that tough and gritty personality.
There's a creative energy in New York I haven't experienced anywhere else. There's an energy there that lies within the stories of people trying to make it — writers, musicians, inventors, entrepreneurs, actors, artists, chefs and so many more. To submerse oneself in that environment, an environment of creators, is magnetic, especially for a fellow creator.
New Yorkers are proud to be New Yorkers
There's a sense of pride in New York that runs deep in the city and is shared among the many people who live there. People there are proud to be New Yorkers — to have jobs in New York, to own businesses in New York, to have lives there, to have made it New York City. That's one of the great American dreams, right, to "make it" in New York?
Late Monday evening, my mom, aunt and I had dinner at a family-owned restaurant in Little Italy. The restaurant was quite empty as we were there close to 10 p.m. Toward the end of our meal, as she was preparing to leave for the night, the restaurant owner, an elderly Italian woman, came over to chat with us. She asked us where we were from, how we liked the food and told us about her hometown in Italy. She didn't say much, but her confidence, warm, weathered smile and the way she leaned in to our conversation told me she was proud to have brought a piece of her Italian heritage to New York City — and to be hosting us and sharing it with us that evening.
New York on foot
Sunday and Monday, our first two days in New York, were full days. On Sunday, we checked into our hotel, walked around Times Square, grabbed a snack and dinner nearby and saw two Broadway shows: "Beautiful: The Carole King Musical" and "The Book of Mormon."
The following day, we walked The High Line, grabbed lunch at a cute cafe in Greenwich Village, walked through TriBeCa to the 9/11 Memorial and Museum and spent a somber, emotional three hours inside the museum.
Leaving the 9/11 Museum.
When we left the museum, we were greeted by a warm, serene summer evening. The sun was sinking behind Manhattan's skyscrapers; water was cascading into the heart of the south pool nearby; and among those still visiting the memorial, there was an understood silence, a shared sense of respect. It was an incredibly peaceful moment in a beautiful, haunting and humbling space.
9/11 Memorial.
I love that New York is walkable. The city is inviting in the sense that you can walk nearly everywhere. Walking, versus driving or taking the subway, allows you to see, feel and experience the city in ways you otherwise wouldn't.
Seeing New York from the water
There's also something to be said for walking onto a ferry to gain a far different perspective of where you've been. That's just what we did Monday evening.
After sitting near the south pool of the 9/11 Memorial and reflecting on the experience of the museum and our memories of September 11, 2001, my mom, aunt and I walked over to Firehouse 10 just beyond the plaza and continued west to the Hudson River. We walked along the water and then took the ferry to Staten Island.
Me, my aunt and my mom — all smiles.
As we pulled away from Manhattan, the world opened up around us. We could see Brooklyn and the Brooklyn Bridge; we saw Governor's Island; and the closer we moved to Staten Island, the more visible the Manhattan skyline became.
Manhattan and the Brooklyn Bridge from the Staten Island Ferry.
From the water, I feel I saw the true beauty of New York City, and that's the moment in which I really fell in love with it.
With the sun setting to the west of the city, Freedom Tower standing sparkling and strong among the skyscrapers in Manhattan, the summer sky growing soft with pink and purple hues and the Hudson River stirring beneath us, New York won me over.
Unmatched energy
New York City surprised and delighted me. Its energy and grittiness caught me off guard. There's something addicting about the city. I feel as though there's this impassioned adrenaline there. I feel as though passion, creativity and stories pump through the streets of New York the way blood pumps through our veins. The people are the heart, and they keep the blood, the energy, the life of the city flowing.
To me, New York City has a formula unlike any other. I haven't been able to shake the energy I felt there from my mind since leaving on a sunny Tuesday afternoon three weeks ago.
As we rode the subway from Manhattan to Astoria and then took the bus on to the airport, I felt a pull to stay. I wasn't ready to say goodbye to New York just yet. I felt as though my adventures there, our adventures there, had only just begun and that there was so much more to see and do.
In three days, we'd only touched the surface, but New York had me hooked. I'll be back — hopefully many more times to come.
BlogEmilyNew York City, Travel0 comments
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on letting go
do you love the process?
we're all in process.
you don't always have to be so strong. | {
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UPDATE: Applewhite and Oliver have released statements addressing Thursday night's confrontation. Their full text can be read at the bottom of this post.
A college football head coach and his best player getting into a heated argument is usually a tough enough story for the team, but Ed Oliver carried some extra intrigue during a confrontation with Houston coach Major Applewhite on Thursday.
The 20-year-old Oliver, widely considered to be a top 5 prospect for the upcoming NFL draft, got into it with Applewhite on the sidelines of the Cougars' game against Tulane on Thursday. The apparent cause for the argument: Oliver wearing a warm jacket.
Applewhite can be seen pulling a down jacket off of Oliver and lecturing the defensive tackle in a video captured by ESPN, followed by a livid Oliver screaming at Applewhite and being pulled away as the team runs to the locker room at halftime.
Oliver had been ruled out for the game, his fourth straight miss, due to a bruised right knee, according to the Houston Chronicle's Joseph Duarte.
After his argument with Applewhite, Oliver reportedly did not return to the field with the Cougars following halftime.
Elsewhere, Houston DT Ed Oliver went off on Major Applewhite because Applewhite said he wasn't allowed to wear a jacket on the sideline that is reserved for active players.
Oliver went into the locker room with the team at the half and has not returned to the field.
Houston-area weather stayed around the 50-degree range during the game, part of a cold snap that has hit the area recently. Applewhite went on to say that he only took Oliver's jacket off to be fair. He later declined to say whether it was his or Oliver's decision for the star to stay in the locker room at halftime.
You'll never believe it, but Applewhite said he has already forgiven his two-time All-American and that he believes in second chances.
The notable second chance of Applewhite's career is when he was able to stay on as offensive coordinator at Texas and later take the Houston job despite getting caught engaging in "inappropriate, consensual behavior with an adult student," which definitely seems comparable to wanting to be warm during a cold football game.
Tension between Ed Oliver and Major Applewhite?
Oliver's status at Houston was already intriguing even before his coach's fashion tips, as he has given NFL teams all the proof they should need to spend a top draft pick on him.
The former five-star recruit has been among the sport's most dominant athletes since he stepped onto the field in Houston, accruing 13.5 sacks, 52 tackles for loss and 10 pass deflections while playing the interior in 31 career games. The 292-pound Oliver is a two-time consensus All-American and has won the AAC Defensive Player of the Year award as well the Outland Trophy. Even though he faced talent a step below what elite NFL talent usually faces, Oliver has done everything you could reasonably expect an elite talent to do.
That amount of sheer ability, as well as the competition he faces, gives Oliver plenty of incentive to pull a Nick Bosa and withdraw from Houston to begin prep for the NFL. Missing four straight games has ramped up such speculation, as well as a tweet he posted on Wednesday, alluding that he "gave" all in his college career.
Clearly, Oliver has plenty of incentive to stay on the sidelines as Houston competes for the AAC title. It's hard to justify risking millions of dollars when your team could be headed to something like the Sun Bowl, for all you know.
An ugly argument with the team's head coach over something as small as a jacket isn't going to dampen that speculation. | {
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With over 140 years of history behind it, Fox Umbrellas is the epitome of high-end umbrella manufacturing. With a unique grain pattern and a spacious canopy, Fox umbrellas provide an elegant solution for keeping the rain at bay. Equipped with a whanghee crook handle, this compact telescopic umbrella has a full size 10 rib for extra durability. | {
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These original bures are spacious dormitories that accommodate four people. They have bunk beds and/or single beds. Shared bathroom facilities.
Situated beachfront on Sunshine Beach. Not sure where else you'd get such views on a budget.
Please note that rates quoted exclude our compulsory Resort Package of FJ$105 per adult or $55 per child (4-12yrs), per night. This package includes breakfast, lunch, dinner, WiFi and use of non motorised water equipment.
THIS ROOM TYPE WILL NO LONGER BE AVAILABLE FROM 1 APRIL 2019. FOR DORM BED RATES PLEASE GO TO SUNRISE BEACH DORM PAGE.
The newly built, spacious Beach Dorms accommodate four people. They have bunk beds and share a newly built, beach front bathroom facility. | {
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Onboarding new employees is not only about greeting them. It requires a thorough approach in which the organization "sells itself" to the new hires while also screening potential employees as best as possible to ensure that they are the right fit for the organization.
Employees are a more important resource than ever in business and companies don't have the luxury of constantly replacing them. This is especially important today, as job hopping is a normal thing for millennials. Companies need to learn how to retain their employees and keep them for a long time if they want to be successful, there is even research that shows how these two correlate .
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This creates many challenges. First of all, companies are unable to keep track of all the applications and communication that takes place across various channels. Secondly, they are unable to manage them properly and assess all of the applicants for proper onboarding while having a clear overview of all the candidates.
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AI can also speed up screening and sourcing to understand job requirements and then find candidates which are suitable while shortlisting, ranking, and grading candidates properly so that the managers can assess them better.
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One of the most difficult tasks for onboarding managers is to go through a vast number of candidates and narrowing down the list to those that are qualified for the job position they are applying for.
The way technology helps is that it first provides to HR managers all of the necessary information about a candidate, their experience, skills, and knowledge displayed conveniently so that the managers can instantly see what they are about.
New HR tools have many features and functionalities that allow managers to test candidates and see objective results that can show them whether or not the candidates are a good fit for the organization. Rather than relying on their subjective feeling and knowledge, managers can get a score that will help them make the right decisions.
Although having neatly stored information about candidates can help recruiters significantly, this still doesn't guarantee that they've found the right people. It can help narrow down the list of candidates but from there on, it's necessary to evaluate the candidates even further.
Luckily, we now have access to software equipped with various personalized tests that can further help with evaluation. Onboarding managers can send aptitude tests and other types of evaluation content to candidates that seem most qualified.
Apart from this, they can quickly personalize the tests based on the candidates' information to learn how competent their candidates are on practical assignments. The managers can also put candidates in realistic situations that might happen on the job and learn if they would fit in with the culture of the organization. It's also a good way to see what kind of personality their candidates have.
One of the most important things when onboarding new employees is their experience. Technology can speed up this process by giving automation options to various manual tasks that can consume a lot of time and energy. Employees are often required to sit at their desks during the first few days at their new job and fill out various forms. This is something that nobody likes.
With automation, you can send all the forms and applications employees need to fill out as soon as they are accepted, so that they can finish everything from home and send the forms back to you. At the same time, automation can help you go through them more quickly and see which employees are ready to join the team.
This allows organizations to focus on other aspects of onboarding when a new employee comes along. Companies can try to engage new workers as much as possible. They can excite them about their new workplace, rather than having them do dull manual tasks. However, the automation goes both ways, as it can help onboarding managers as well.
Instead of them sending policy education materials or video training content that a new employee needs, the software can be automated to do this for them and notify them when an employee has finished these tasks so that they can look at the employee's performance and send relevant feedback.
Automation allows you to create a streamlined onboarding process that starts before your new hire's first day at work and the system will guide employees as they tackle tasks, while the necessary information about their progress is delivered to the manager.
Even though onboarding is a very important process that needs to be managed properly, it still doesn't guarantee that the new additions to your workforce will stay with your business for a long time. This is why every organization needs to do a necessary follow-up after onboarding to further secure employee retention. Some even refer to this process as extended onboarding.
Employees are more likely to stay with an organization for longer if they have the opportunity to hone their skills and learn new things. Offer employees online training, courses, lessons, and create a work environment where employees feel free to collaborate and share knowledge between themselves.
Feedback is very important and it goes both ways. Managers need to give their feedback on employee's performance, praise them, suggest changes, and criticize them when necessary. At the same time, employees need to give their opinion to managers about processes, workflows, and work organization so that that the management can improve as well.
This shows employees that their opinions matter to the whole organization and that their input can contribute to seeing the changes that they want.
Transparency can go a long way. Modern employees want to feel involved and keep themselves up-to-date with the company's plans and goals. They want to have a sense of purpose at work and this is why the management should inform them about important new steps that the organization will be taking. You should show your employees how they've contributed to the latest results and how they can help the whole collective grow in the future.
Creating a good onboarding process can help retain talented employees and keep them at the company for years to come. This is where new onboarding solutions can be very beneficial, so start investing in them as soon as possible. Consider the things we mentioned above and you will realize how important it is to use the latest software to improve the onboarding process. | {
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\section{Decomposition into 1-sparse matrices}
\label{app:1sparseproof}
In \cite{Aharonov2003}, Aharonov and Ta-Shma considered the problem of simulating an arbitrary $d$-sparse Hamiltonian using the ability to query bits of the Hamiltonian. According to their prescription, we should imagine the Hamiltonian as an undirected graph where each basis state corresponds to a node and each nonzero matrix element $H^{\alpha\beta} = H^{\beta\alpha*} \neq 0$ corresponds to an edge which connects node $\ket{\alpha}$ to $\ket{\beta}$.
Since an edge coloring of a graph using $\Gamma$ colors is equivalent to the division of that graph into $\Gamma$ sets of disjoint graphs of degree 1, this edge coloring represents a decomposition of the Hamiltonian into $\Gamma$ 1-sparse matrices. Aharonov and Ta-Shma show a procedure for accomplishing the 1-sparse decomposition of any arbitrary $d$-sparse matrix using $\Theta(d^2)$ terms by coloring an arbitrary graph of degree $d$ with $\Theta(d^2)$ colors. This result was tightened from $\Theta(d^2)$ terms to $d^2$ terms in \cite{Berry2013}. Importantly, Aharonov and Ta-Shma also showed how these Hamiltonians can be efficiently simulated using an oracular scheme based on the Trotter-Suzuki decomposition. Toloui and Love used this result to show how the CI matrix can be efficiently simulated under Trotter-Suzuki decomposition with ${\cal O}(N^4)$ colors \cite{Toloui2013}.
We provide an improved 1-sparse decomposition into ${\cal O}(\eta^2 N^2)$ terms.
For convenience of notation, we denote the occupied spin-orbitals for $\ket{\alpha}$ by $\alpha_1,\ldots,\alpha_\eta$, and the occupied spin-orbitals for $\ket{\beta}$ by $\beta_1,\ldots,\beta_\eta$. We also drop the bra-ket notation for the lists of orbitals (Slater determinants); that is, we denote the list of occupied orbitals for the left portion of the graph by $\alpha$, and the list of occupied orbitals for the right portion of the graph by $\beta$.
We require both these lists of spin-orbitals to be sorted in ascending order.
According to the Slater-Condon rules, the matrix element between two Slater determinants is zero unless the determinants differ by two spin-orbitals or less. Thus, two vertices (Slater determinants) in the Hamiltonian graph are connected if and only if they differ by a single occupied orbital or two occupied orbitals.
In order to obtain the decomposition, for each color (corresponding to one of the resulting 1-sparse matrices) we need to be able to obtain $\beta$ from $\alpha$, and vice versa.
Using the approach in \cite{Berry2013}, we take the tensor product of the Hamiltonian with a $\sigma_x$ operator.
That is, we perform the simulation under the Hamiltonian $\sigma_x\otimes H$, which is bipartite and has the same sparsity as $H$.
The $\sigma_x$ operator acts on the ancilla register that determines whether we are in the left ($\alpha$) or right ($\beta$) partition of the graph.
We do this without loss of generality as simulation under $H$ can be recovered from simulation under $\sigma_x\otimes H$ using the fact that $e^{-i(\sigma_x\otimes H)t}\ket{+}\ket{\psi}=\ket{+}e^{-iHt}\ket{\psi}$ \cite{Berry2013}.
In order for the graph coloring to be suitable for the quantum algorithm, for any given color we must have a procedure for obtaining $\beta$ given $\alpha$, and another procedure for obtaining $\alpha$ given $\beta$.
For this to be a valid graph coloring, the procedure must be reversible, and different colors must not give the same $\beta$ from $\alpha$ or vice versa.
To explain the decomposition, we will first consider how it works for $\alpha$ and $\beta$ differing by only a single spin-orbital occupation.
We are given a 4-tuple $(a,b,\ell,p)$, where $a$ and $b$ are bits, $\ell$ is a number in the sorted list of occupied orbitals, and $p$ is a number that tells us how many orbitals the starting orbital is shifted by. Our notation here differs slightly from that in \sec{decomp1}, where $i$ and $j$ were used in place of $\ell$ to represent the positions of the two orbitals which differed: here we will use $i$ and $j$ for a different purpose.
To simplify the discussion, we do not perform the addition modulo $N$, and instead achieve the same effect by allowing $p$ to take positive and negative values.
If adding $p$ takes us beyond the list of allowable orbitals, then the matrix element returned is zero, and the list of occupied orbitals is unchanged (corresponding to a diagonal element of the Hamiltonian).
We will also use the convention that $\alpha_0=\beta_0=0$ and $\alpha_{\eta+1}=\beta_{\eta+1}=N+1$.
These values are not explicitly stored, but rather are dummy values to use in the algorithm when $\ell$ goes beyond the range $1,\ldots,\eta$.
The register $a$ tells us whether the $\ell$ is for $\alpha$ or $\beta$.
To simplify the discussion, when $a=0$ we take $i=\ell$, and when $a=1$ we take $j=\ell$.
In either case, we require that $\beta_j=\alpha_i+p$, but in the case $a=0$ we are given $i$ and need to work out $j$, whereas in the case $a=1$ we are given $j$ and need to work out $i$.
In particular, for $a=0$ we just take $\alpha_i$ and add $p$ to it.
Then $j$ is the new position in the list $\beta$, so $\beta_j=\alpha_i+p$.
The general principle is that, if we are given $i$ for $\alpha$ and need to determine $j$ for $\beta$, we require that $\beta_{j+1}-\beta_{j-1} \ge \alpha_{i+1}-\alpha_{i-1}$, (i.e.\ the spacing between orbitals is larger in $\beta$ than in $\alpha$).
Alternatively, if we were given $j$ for $\beta$ and needed to determine a corresponding $i$ for $\alpha$, we would require $\beta_{j+1}-\beta_{j-1} < \alpha_{i+1}-\alpha_{i-1}$ (i.e.\ the spacing between orbitals is larger in $\alpha$ than in $\beta$).
If the inequality is not consistent with the value of $a$ (i.e.\ we are proceeding in the wrong direction), then the matrix element for this term in the decomposition is taken to be zero (in the graph there is no line of that color connecting the nodes). This procedure allows for a unique connection between nodes, without double counting.
The reason for requiring these inequalities is that the list of orbitals with a larger spacing will have less ambiguity in the order of occupied orbitals.
To reduce the number of terms in the decomposition, we are only given $i$ or $j$, but not both, so we either need to be able to determine $j$ from $i$ given $\beta$, or $i$ from $j$ given $\alpha$.
When the spacing between the occupied orbitals for $\beta$ is larger, if we are given $\beta$ and $i$ there is less ambiguity in determining $j$.
In particular, when $\beta_{j+1}-\beta_{j-1} \ge \alpha_{i+1}-\alpha_{i-1}$, there can be at most two values of $j$ that could have come from $i$, and the bit $b$ is then used to distinguish between them.
There are four different cases that we need to consider.
\begin{enumerate}
\item We are given $\beta$ and need to determine $\alpha$; $a=0$.
\item We are given $\alpha$ and need to determine $\beta$; $a=0$.
\item We are given $\alpha$ and need to determine $\beta$; $a=1$.
\item We are given $\beta$ and need to determine $\alpha$; $a=1$.
\end{enumerate}
Next we explain the procedure for each of these cases in detail.
In the following we use the terminology ``\textsc{invalid}'' to indicate that we need to return $\alpha=\beta$ and a matrix element of zero.
\\ \\
\textbf{1. Given $\beta$ and need to determine $\alpha$; $a=0$.} \\
We are given $\beta$, but $\ell$ is the position in the list of occupied orbitals for $\alpha$.
We do not know which is the $\beta_j$ to subtract $p$ from, so we loop through all values as follows to find a list of candidates for $\alpha$, $\tilde\alpha^{(k)}$.
We define this as a procedure so we can use it later. \\ \\
procedure FindAlphas
\begin{adjustwidth}{1em}{0em}
$k=0$ \\
For $j=1,\ldots,\eta$:
\begin{adjustwidth}{1em}{0em}
Subtract $p$ from $\beta_j$ and check that this yields a valid list of orbitals, in that $\beta_j-p$ does not yield an orbital number beyond the desired range, or duplicate another orbital.
That is:
\\
If $(( \beta_j-p\in\{1,\ldots,N\}) \wedge (\forall j'\in\{1,\ldots,\eta\} : \beta_j-p \ne \beta_{j'})) {\,\vee\, (p=0) }$ then
\begin{adjustwidth}{1em}{0em}
Sort the list of orbitals to obtain $\tilde\alpha^{(k)}$, and denote by $i$ the new position of $\beta_j-p$ in this list of occupied orbitals.
Check that the new value of $i$ corresponds to $\ell$, and that the spacing condition for $a=0$ is satisfied, as follows. \\
If $(i=\ell)\wedge (\beta_{j+1}-\beta_{j-1} \ge \tilde\alpha^{(k)}_{i+1}-\tilde\alpha^{(k)}_{i-1})$ then
\begin{adjustwidth}{1em}{0em}
$k=k+1$
\end{adjustwidth}
end if
\end{adjustwidth}
end if
\end{adjustwidth}
end for
\end{adjustwidth}
end procedure\\ \\
After this procedure there is a list of at most two candidates for $\alpha$, and $k$ will correspond to how many have been found.
Depending on the value of $k$ we perform the following: \\
$\mathbf{k=0}$ We return \textsc{invalid}. \\
$\mathbf{k=1}$ If $b=0$ then return $\alpha=\tilde\alpha^{(0)}$, else return \textsc{invalid}. \\
$\mathbf{k=2}$ Return $\alpha=\tilde\alpha^{(b)}$. \\
That is, if we have two possibilities for $\alpha$, then we use $b$ to choose between them.
If there is only one, then we only return that one if $b=0$ to avoid obtaining two colors that both link $\alpha$ and $\beta$. \\ \\
\textbf{2. Given $\alpha$ and need to determine $\beta$; $a=0$.} \\
We are given $\alpha$, and $\ell=i$ is the position of the occupied orbital in $\alpha$ that is changed.
We therefore add $p$ to $\alpha_i$ and check that it gives a valid list of orbitals.
Not only this, we need to check that we would obtain $\alpha$ if we work backwards from the resulting $\beta$.
\\
If $((\alpha_i+p\in\{1,\ldots,N\}) \wedge (\forall i'\in\{1,\ldots,\eta\} : \alpha_i+p\ne\alpha_{i'})) {\,\vee\, (p=0) }$ then
\begin{adjustwidth}{1em}{0em}
We sort the new list of occupied orbitals to obtain a candidate for $\beta$, denoted $\tilde\beta$.
We next check that the spacing condition for $a=0$ is satisfied. \\
If $(\tilde\beta_{j+1}-\tilde\beta_{j-1} \ge \alpha_{i+1}-\alpha_{i-1})$ then
\begin{adjustwidth}{1em}{0em}
Perform the procedure FindAlphas to find potential candidates for $\alpha$ that could be obtained from $\tilde\beta$.
There can only be 1 or 2 candidates returned from this procedure. \\
If $((k=1)\wedge (b=0)) \vee ((k=2)\wedge (\alpha=\tilde\alpha^{(b)}))$ then
\begin{adjustwidth}{1em}{0em}
return $\beta=\tilde\beta$
\end{adjustwidth}
else return \textsc{invalid}
\end{adjustwidth}
else return \textsc{invalid}
\end{adjustwidth}
else return \textsc{invalid} \\ \\
\textbf{3. Given $\alpha$ and need to determine $\beta$; $a=1$.} \\
This case is closely analogous to the case where we need to determine $\alpha$ from $\beta$, but $a=0$.
We are given $\alpha$, but $\ell$ is the position in the list of occupied orbitals for $\beta$.
We do not know which is the $\alpha_i$ to add $p$ to, so we loop through all values as follows to find a list of candidates for $\beta$, $\tilde\beta^{(k)}$.
We define this as a procedure so we can use it later. \\ \\
procedure FindBetas
\begin{adjustwidth}{1em}{0em}
$k=0$ \\
For $i=1,\ldots,\eta$:
\begin{adjustwidth}{1em}{0em}
Add $p$ to $\alpha_i$ and check that this yields a valid list of orbitals, in that $\alpha_i+p$ does not yield an orbital number beyond the desired range, or duplicate another orbital.
That is:
\\
If $((\alpha_i+p\in\{1,\ldots,N\}) \wedge (\forall i'\in\{1,\ldots,\eta\} : \alpha_i+p\ne\alpha_{i'})) { \,\vee\, (p=0) }$ then
\begin{adjustwidth}{1em}{0em}
Sort the list of orbitals to obtain $\tilde\beta^{(k)}$, and denote by $j$ the new position of $\alpha_i+p$ in this list of occupied orbitals.
Check that the new value of $j$ corresponds to $\ell$, and that the spacing condition for $a=1$ is satisfied. \\
If $(j=\ell)\wedge (\tilde\beta^{(k)}_{j+1}-\tilde\beta^{(k)}_{j-1} < \alpha_{i+1}-\alpha_{i-1})$ then
\begin{adjustwidth}{1em}{0em}
$k=k+1$
\end{adjustwidth}
end if
\end{adjustwidth}
end if
\end{adjustwidth}
end for
\end{adjustwidth}
end procedure\\ \\
After this procedure there is a list of at most two candidates for $\beta$, and $k$ will correspond to how many have been found.
Depending on the value of $k$ we perform the following: \\
$\mathbf{k=0}$ We return \textsc{invalid}. \\
$\mathbf{k=1}$ If $b=0$ then return $\beta=\tilde\beta^{(0)}$, else return \textsc{invalid}. \\
$\mathbf{k=2}$ Return $\beta=\tilde\beta^{(b)}$. \\
That is, if we have two possibilities for $\beta$, then we use $b$ to choose between them.
If there is only one, then we only return that one if $b=0$ to avoid obtaining two colors that both link $\alpha$ and $\beta$. \\ \\
\textbf{4. Given $\beta$ and need to determine $\alpha$; $a=1$.} \\
We are given $\beta$, and $\ell=j$ is the position of the occupied orbital in $\beta$ that is changed.
We therefore subtract $p$ from $\beta_j$ and check that it gives a valid list of orbitals.
Again we also need to check consistency.
That is, we work back again from the $\alpha$ to check that we correctly obtain $\beta$.
\\
If $ ((\beta_j-p\in\{1,\ldots,N\}) \wedge (\forall j'\in\{1,\ldots,\eta\} : \beta_j-p\ne\beta_{j'})) { \,\vee\, (p=0) }$ then
\begin{adjustwidth}{1em}{0em}
We sort the new list of occupied orbitals to obtain a candidate for $\alpha$, denoted $\tilde\alpha$.
We next check that the spacing condition for $a=1$ is satisfied. \\
If $(\beta_{j+1}-\beta_{j-1} < \tilde\alpha_{i+1}-\tilde\alpha_{i-1})$ then
\begin{adjustwidth}{1em}{0em}
Perform the procedure FindBetas to find potential candidates for $\beta$ that could be obtained from $\tilde\alpha$.
There can only be 1 or 2 candidates returned from this procedure. \\
If $((k=1)\wedge (b=0)) \vee ((k=2)\wedge (\beta=\tilde\beta^{(b)}))$ then
\begin{adjustwidth}{1em}{0em}
return $\alpha=\tilde\alpha$
\end{adjustwidth}
else return \textsc{invalid}
\end{adjustwidth}
else return \textsc{invalid}
\end{adjustwidth}
else return \textsc{invalid}\\
To prove that this technique gives a valid coloring, we need to show that it is reversible and unique.
The most important part to show is that, provided the spacing condition holds, the ambiguity is limited to two candidates that may be resolved by the bit $b$.
We will consider the case that $p>0$; the analysis for $p<0$ is equivalent.
Consider Case 1, where we are given $\beta$ and need to determine $\alpha$, but $a=0$.
Then we take $i=\ell$, and need to determine $j$.
Let $j'$ and $j''$ be two potential values of $j$, with $j'<j''$.
For these to be potential values of $j$, they must satisfy
\begin{align}\label{con1}
\beta_{j'}-p &\in (\alpha_{i-1},\alpha_{i+1}) , \\
\label{con2}
\beta_{j'+1}-\beta_{j'-1} &\ge \alpha_{i+1}-\alpha_{i-1} , \\
\label{con3}
\beta_{j''}-p &\in (\alpha_{i-1},\alpha_{i+1}) , \\
\label{con4}
\beta_{j''+1}-\beta_{j''-1} &\ge \alpha_{i+1}-\alpha_{i-1}.
\end{align}
Condition \eqref{con1} is required because, for $j'$ to be a potential value of $j$, $\beta_{j'}-p$ must correspond to an $\alpha_i$ that is between $\alpha_{i-1}$ and $\alpha_{i+1}$ ($\alpha$ is sorted in ascending order).
Condition \eqref{con2} is the spacing condition for $a=0$.
Conditions \eqref{con3} and \eqref{con4} are simply the equivalent conditions for $j''$.
Next we consider how $\alpha$ is found from $\beta$.
In the case where $j'=i$, then we immediately know that $\alpha_{i-1}=\beta_{i-1}$ and $\alpha_{i+1}=\beta_{i+1}$.
Then the conditions \eqref{con1} and \eqref{con2} become
\begin{align}
\label{con5}
\beta_{j'}-p &\in (\beta_{i-1},\beta_{i+1}), \\
\label{con6}
\beta_{j'+1}-\beta_{j'-1} &\ge \beta_{i+1}-\beta_{i-1}.
\end{align}
In the case that $j'>i$, it is clear that $\alpha_{i-1}=\beta_{i-1}$ still holds.
Moreover, in going from the sequence of occupied orbitals for $\alpha$ to the sequence for $\beta$, we have then removed $\alpha_i$, which means that $\alpha_{i+1}$ has moved to position $i$.
That is to say, $\beta_{i}$ must be equal to $\alpha_{i+1}$.
Therefore, conditions \eqref{con1} and \eqref{con2} become
\begin{align}
\label{con9}
\beta_{j'}-p &\in (\beta_{i-1},\beta_i), \\
\label{con10}
\beta_{j'+1}-\beta_{j'-1} &\ge \beta_i-\beta_{i-1}.
\end{align}
In either case ($j'=i$ or $j'>i$), because $j''>j'$, we know that $j''>i$.
Then the same considerations as for $j'>i$ hold, and
conditions \eqref{con3} and \eqref{con4} become
\begin{align}
\label{con7}
\beta_{j''}-p &\in (\beta_{i-1},\beta_i), \\
\label{con8}
\beta_{j''+1}-\beta_{j''-1} &\ge \beta_i-\beta_{i-1}.
\end{align}
Using \eqref{con8} we have
\begin{align}
\beta_{j''+1}-p &\ge \beta_{j''-1}-p + \beta_i-\beta_{i-1} \nonumber \\
&\ge \beta_{j'}-p + \beta_i-\beta_{i-1} \nonumber \\
&> \beta_{i-1}+ \beta_i-\beta_{i-1} \nonumber \\
&= \beta_i.
\end{align}
In the second-last line we have used $\beta_{j'}-p>\beta_{i-1}$ from \eqref{con5} and \eqref{con9}, and in the second line we have used $j''>j'$.
The inequality $\beta_{j''+1}-p>\beta_i$ means that $\beta_{j''+1}-p\notin(\beta_{i-1},\beta_i)$, and therefore $\beta_{j''+1}$ could not have come from $\alpha_i$ by adding $p$.
That is because $\beta_{j''+1}$ would have to satisfy a relation similar to \eqref{con7}.
In turn, any $j>j''+1$ will satisfy $\beta_j-p>\beta_i$, because the $\beta_k$ are sorted in ascending order.
The net result of this reasoning is that, if there are two ambiguous values of $j$, then there can be no third ambiguous value.
This is because, if we call the first two ambiguous values $j'$ and $j''$, there can be no more ambiguous values for $j>j''$.
Hence, if we have a bit $b$ which tells us which of the two ambiguous values to choose, then it resolves the ambiguity and enables us to unambiguously determine $\alpha$, given $\beta$, $p$, and $i$.
Next consider Case 3, where we wish to determine $\beta$ from $\alpha$, but $a=1$.
In that case, we take $j=\ell$, and need to determine $i$.
That is, we wish to determine a value of $i$ such that adding $p$ to $\alpha_i$ gives $\beta_j$, and also require the condition $\beta_{j+1}-\beta_{j-1} < \alpha_{i+1}-\alpha_{i-1}$.
Now the situation is reversed; if we start with $\beta$, then we can immediately determine $\alpha$, but if we have $\alpha$ then we potentially need to consider multiple values of $i$ and resolve an ambiguity.
In exactly the same way as above, there are at most two possible values of $i$, and we distinguish between these using the bit $b$.
In this case, we cannot have $j=i$, because that would imply that $\alpha_k=\beta_k$ for all $k\ne j$, and the condition $\beta_{j+1}-\beta_{j-1} < \alpha_{i+1}-\alpha_{i-1}$ would be violated.
Therefore, consider two possible values of $i$, $i'$ and $i''$, with $i''<i'<j$.
The equivalents of the conditions in Eqs.~\eqref{con1} to \eqref{con4} are
\begin{align}\label{con1b}
\alpha_{i'}+p &\in (\beta_{j-1},\beta_{j+1}) , \\
\label{con2b}
\beta_{j'+1}-\beta_{j'-1} &< \alpha_{i+1}-\alpha_{i-1} , \\
\label{con3b}
\alpha_{i''}+p &\in (\beta_{j-1},\beta_{j+1}) , \\
\label{con4b}
\beta_{j''+1}-\beta_{j''-1} &< \alpha_{i+1}-\alpha_{i-1}.
\end{align}
Because $i''<i'<j$, using similar reasoning as before, we find that $\beta_{j+1}=\alpha_{j+1}$ and $\beta_{j-1}=\alpha_j$.
That means that the conditions \eqref{con1b} to \eqref{con4b} become
\begin{align}
\alpha_{i'}+p &\in (\alpha_j,\alpha_{j+1}), \\
\alpha_{j+1}-\alpha_j &< \alpha_{i'+1}-\alpha_{i'-1}, \\
\alpha_{i''}+p &\in (\alpha_j,\alpha_{j+1}), \\
\alpha_{j+1}-\alpha_j &< \alpha_{i''+1}-\alpha_{i''-1}.\label{conda}
\end{align}
Starting with Eq.~\eqref{conda} we obtain
\begin{align}
\alpha_{i''-1}+p &< \alpha_{i''+1}+p-\alpha_{j+1}+\alpha_j \nonumber \\
&\le \alpha_{i'}+p-\alpha_{j+1}+\alpha_j \nonumber \\
&< \alpha_{j+1}-\alpha_{j+1}+\alpha_j \nonumber \\
&= \alpha_j = \beta_{j-1}.
\end{align}
Hence $\alpha_{i''-1}+p$ is not in the interval $(\beta_{j-1},\beta_{j+1})$, and therefore cannot give $\beta_j$.
Therefore there can be no third ambiguous value, in the same way as above for $a=0$.
Hence the single bit $b$ is again sufficient to distinguish between any ambiguous values, and enables us to determine $\beta$ given $\alpha$, $p$, and $j$.
We now consider the requirement that the procedure is reversible.
In particular, Case 1 needs to be the reverse of Case 2, and Case 3 needs to be the reverse of Case 4.
Consider starting from a particular $\beta$ and using the method in Case 1.
We have shown that the procedure FindAlphas in Case 1 can yield at most two potential candidates for $\alpha$, and then one is chosen \textit{via} the value of $b$.
For the resulting $\alpha$, adding $p$ to $\alpha_i$ will yield the original set of occupied orbitals $\beta$.
Moreover, the inequality $\beta_{j+1}-\beta_{j-1} \ge \alpha_{i+1}-\alpha_{i-1}$ must be satisfied (otherwise Case 1 would yield \textsc{invalid}).
If Case 1 yields $\beta$ from $\alpha$, then Case 2 should yield $\beta$ given $\alpha$.
Case 2 simply adds $p$ to $\alpha_i$ (where $i$ is given), which we know should yield $\beta$.
The method in Case 2 also performs some checks, and outputs \textsc{invalid} if those fail.
These checks are:
\begin{enumerate}
\item It checks that $\beta$ is a valid list of orbitals, which must be satisfied because we started with a valid $\beta$.
\item It checks that $\beta_{j+1}-\beta_{j-1} \ge \alpha_{i+1}-\alpha_{i-1}$, which must be satisfied for Case 1 to yield $\alpha$ instead of \textsc{invalid}.
\item It checks that using Case 1 on $\beta$ would yield $\alpha$, which must be satisfied here because we considered initially using Case 1 to obtain $\alpha$ from $\beta$.
\end{enumerate}
Thus we see that, if Case 1 yields $\alpha$ from $\beta$, then Case 2 must yield $\beta$ from $\alpha$.
Going the other way, and starting with $\alpha$ and using Case 2 to find $\beta$, a result other than \textsc{invalid} will only be provided if Case 1 would yield $\alpha$ from that $\beta$.
Thus we immediately know that if Case 2 provides $\beta$ from $\alpha$, then Case 1 will provide $\alpha$ from $\beta$.
This means that the methods for Cases 1 and 2 are the inverses of each other, as required.
Via exactly the same reasoning, we can see that the methods in Cases 3 and 4 are the inverses of each other as well.
Next, consider the question of uniqueness.
The color will be unique if we can determine the color from a pair $\alpha$, $\beta$.
Given $\alpha$ and $\beta$, we will see that all the occupied orbitals are identical, except one.
Then the occupied orbitals for $\alpha$ and $\beta$ which are different will be $i$ and $j$, respectively.
We can then immediately set $p=\beta_j-\alpha_i$ for the color.
We can then compare $\beta_{j+1}-\beta_{j-1}$ and $\alpha_{i+1}-\alpha_{i-1}$.
If $\beta_{j+1}-\beta_{j-1}\ge \alpha_{i+1}-\alpha_{i-1}$ then for the color $a=0$ and $\ell=i$.
We can then find how many ambiguous values of $\alpha$ there would be if we started with $\beta$.
If $\alpha$ was obtained uniquely from $\beta$, then we would set $b=0$ for the color.
If there were two ambiguous values of $\alpha$ that could be obtained from $\beta$, then if the first was correct we would set $b=0$, and if the second were correct then we would set $b=1$.
If $\beta_{j+1}-\beta_{j-1}<\alpha_{i+1}-\alpha_{i-1}$ then for the color $a=1$ and $\ell=j$.
We can then find how many ambiguous values of $\beta$ there would be if we started with $\alpha$.
If $\beta$ was obtained uniquely from $\alpha$, then we would set $b=0$ for the color.
If there were two ambiguous values of $\beta$ that could be obtained from $\alpha$, then if the first was correct we would set $b=0$, and if the second were correct then we would set $b=1$.
In this way we can see that the pair $\alpha$, $\beta$ yields a unique color, and therefore we have a valid coloring.
So far we have considered the case where $\alpha$ and $\beta$ differ by just one orbital for simplicity.
For cases where $\alpha$ and $\beta$ differ by two orbitals, the procedure is similar.
We now need to use the above reasoning to go from $\alpha$ to $\beta$ through some intermediate list of orbitals $\chi$.
That is, we have one set of numbers $(a_1,b_1,\ell_1,p)$ that tells us how to find $\chi$ from $\alpha$, then a second set of numbers $(a_2,b_2,\ell_2,q)$ that tells us how to obtain $\beta$ from $\chi$.
First, it is easily seen that this procedure is reversible, because the steps for going from $\alpha$ to $\chi$ to $\beta$ are reversible.
Second, we need to be able to determine the color from $\alpha$ and $\beta$.
First, we find the two occupied orbitals for $\alpha$ and $\beta$ that differ.
Call the different occupied orbitals for $\alpha$ $i_1$ and $i_2$, and the different orbitals for $\beta$ $j_1$ and $j_2$ (assume in ascending order so the labels are unique).
Then there are four different ways that one could go from $\alpha$ to $\beta$, through different intermediate states $\chi$.
\begin{enumerate}
\item $\alpha_{i_1} \mapsto \beta_{j_1}$ then $\alpha_{i_2}\mapsto\beta_{j_2}$
\item $\alpha_{i_2}\mapsto\beta_{j_2}$ then $\alpha_{i_1} \mapsto \beta_{j_1}$
\item $\alpha_{i_1} \mapsto \beta_{j_2}$ then $\alpha_{i_2}\mapsto\beta_{j_1}$
\item $\alpha_{i_2}\mapsto\beta_{j_1}$ then $\alpha_{i_1} \mapsto \beta_{j_2}$
\end{enumerate}
To resolve this ambiguity we require that the color is obtained by assuming the first alternative that $\alpha_{i_1} \mapsto \beta_{j_1}$ then $\alpha_{i_2}\mapsto\beta_{j_2}$.
Then $\alpha$ and $\beta$ yield a unique color.
This also requires a slight modification of the technique for obtaining $\alpha$ from $\beta$ and vice versa.
First the color is used to obtain the pair $\alpha$, $\beta$, then it is checked whether the orbitals were mapped as in the first alternative above.
If they were not, then \textsc{invalid} is returned.
To enable us to include the matrix elements where $\alpha$ and $\beta$ differ by a single orbital or no orbitals with a coloring by an 8-tuple
$\gamma = (a_1,b_1,\ell_1,p,a_2,b_2,\ell_2,q)$, we can also allow $p=0$ (for only one differing) and $p=q=0$ (for $\alpha=\beta$).
The overall number of terms in the decomposition is then ${\cal O}(\eta^2 N^2)$.
\section{The CI Matrix Decomposition}
\label{sec:decomp1}
The molecular Hamiltonian expressed in the basis of Slater determinants is known to chemists as the CI matrix. Elements of the CI matrix are computed according to the Slater-Condon rules \cite{Helgaker2002}, which we will express in terms of the one-electron and two-electron integrals in \eq{single_int1} and \eq{double_int}. In order to motivate our 1-sparse decomposition, we state the Slater-Condon rules for computing the matrix element
\begin{equation}
H^{\alpha\beta} = \bra{\alpha} H \ket{\beta}
\end{equation}
by considering the spin-orbitals which differ between the determinants $\ket{\alpha}$ and $\ket{\beta}$ \cite{Helgaker2002}:
\begin{enumerate}
\item If $\ket{\alpha}$ and $\ket{\beta}$ contain the same spin-orbitals $\{\chi_i\}_{i=1}^{\eta}$ then we have a diagonal element
\begin{equation}
\label{eq:slate1}
H^{\alpha\beta} = \sum_{i=1}^{\eta} h_{\chi_i\chi_i} + \sum_{i = 1}^{\eta - 1}\sum_{j = i + 1}^{\eta} \left(h_{\chi_i\chi_j \chi_i \chi_j} - h_{\chi_i \chi_j \chi_j \chi_i}\right).
\end{equation}
\item If $\ket{\alpha}$ and $\ket{\beta}$ differ by exactly one spin-orbital such that $\ket{\alpha}$ contains spin-orbital $k$ where $\ket{\beta}$ contains spin-orbital $\ell$, but otherwise contain the same spin-orbitals $\{\chi_i\}_{i=1}^{\eta - 1}$, then
\begin{equation}
\label{eq:slate2}
H^{\alpha\beta} = h_{k\ell} + \sum_{i=1}^{\eta-1} \left(h_{k\chi_i \ell \chi_i} - h_{k \chi_i \chi_i \ell}\right).
\end{equation}
\item If $\ket{\alpha}$ and $\ket{\beta}$ differ by exactly two spin-orbitals such that occupied spin-orbital $i$ in $\ket{\alpha}$ is replaced with spin-orbital $k$ in $\ket{\beta}$, and occupied spin-orbital $j$ in $\ket{\alpha}$ is replaced with spin-orbital $\ell$ in $\ket{\beta}$, then
\begin{equation}
\label{eq:slate3}
H^{\alpha\beta} = h_{ijk\ell} - h_{ij\ell k}.
\end{equation}
\item If $\ket{\alpha}$ and $\ket{\beta}$ differ by more than two spin-orbitals,
\begin{equation}
\label{eq:slate4}
H^{\alpha\beta} = 0.
\end{equation}
\end{enumerate}
These rules assume that $\alpha$ and $\beta$ have the list of occupied orbitals given in a corresponding order, so all corresponding occupied orbitals are listed in the same positions.
In contrast, we will be giving the lists of occupied orbitals in ascending order.
In order to use the rules, we therefore need to change the order of the list of occupied orbitals.
In changing the order of the occupied orbitals, there is a sign flip on the state for an odd permutation.
This sign flip needs to be included when using the above rules.
In general, there is no efficient way to decompose the CI matrix into a polynomial number of tensor products of Pauli operators. It is thus inefficient to directly simulate this Hamiltonian in the same fashion with which we simulate local Hamiltonians. However, the CI matrix is sparse and there exist techniques for simulating arbitrary sparse Hamiltonians. A $d$-sparse matrix is one which contains at most $d$ nonzero elements in each row and column. As discussed in \cite{Toloui2013,Wecker2014}, the Slater-Condon rules imply that the sparsity of the CI matrix is
\begin{equation}
d = \binom{\eta}{2}\binom{N - \eta}{2} + \binom{\eta}{1}\binom{N - \eta}{1} + 1
= \frac{\eta^4}{4} - \frac{\eta^3 N}{2} + \frac{\eta^2 N^2}{2} + {\cal O}\left(\eta^2N+\eta N^2\right).
\end{equation}
Because $N$ is always greater than $\eta$, we find that the CI matrix is $d$-sparse where $d \in {\cal O}(\eta^2 N^2)$. This should be compared with the second-quantized Hamiltonian which is also $d$-sparse, but where $d\in{\cal O}(N^4)$. Our strategy here parallels the second-quantized decomposition, but works with the first-quantized wavefunction. This decomposition is explained in four steps, as follows.
\begin{enumerate}
\item[A.] Decompose the molecular Hamiltonian into ${\cal O}(\eta^2 N^2)$ 1-sparse matrices.
\item[B.] Further decompose each of these 1-sparse matrices into 1-sparse matrices with entries proportional to a sum of a constant number of molecular integrals.
\item[C.] Decompose those 1-sparse matrices into sums approximating the integrals in Eqs.~\eqref{eq:double_int} and \eqref{eq:single_int}.
\item[D.] Decompose the integrands from those integrals into sums of self-inverse matrices.
\end{enumerate}
\subsection{Decomposition into 1-sparse matrices}
\label{sec:dec1}
In order to decompose the molecular Hamiltonian into 1-sparse matrices, we require a unique and reversible graph coloring between nodes (Slater determinants). We introduce such a graph coloring here, with the details of its construction and proof of its properties given in \app{1sparseproof}. The graph coloring can be summarized as follows.
\begin{enumerate}
\item Perform the simulation under $\sigma_x \otimes H$, where $\sigma_x$ is the Pauli $x$ matrix, in order to create a bipartite Hamiltonian of the same sparsity as $H$.
\item Label the left nodes $\alpha$ and the right nodes $\beta$. We seek a procedure to take $\alpha$ to $\beta$, or vice versa, with as little additional information as possible, and without redundancy or ambiguity.
\item Provide an 8-tuple $\gamma = (a_1,b_1,i,p,a_2,b_2,j,q)$ which determines the coloring. The coloring must uniquely determine $\alpha$ given $\beta$ or vice versa. Using the 8-tuples, proceed via either Case 1, 2, 3, or 4 in \app{1sparseproof} to determine the other set of spin-orbitals, using an intermediate list of orbitals $\chi$. The 4-tuples $(a_1,b_1,i,p)$ and $(a_2,b_2,j,q)$ each define a differing orbital. For a single difference, we can set $p = 0$, and for no differences, we can set $p=q=0$.
\end{enumerate}
The basic idea is that we give the positions $i$ and $j$ of those orbitals which differ in $\alpha$, as well as by how much the occupied orbital indices shift, which we denote by $p$ and $q$. This allows us to determine $\beta$ from $\alpha$. However, it does not allow us to unambiguously determine $\alpha$ from $\beta$. To explain how to resolve this ambiguity, we consider the case of a single differing orbital. We will denote by $i$ the position of the differing orbital in $\alpha$, and by $k$ the position of the differing orbital in $\beta$.
\begin{figure}
\centering
\subfloat[][]{\includegraphics[width=0.4\textwidth,trim={0in 4.75in 6in -0.5in},clip]{figA.pdf} \label{fig:subfigA}} \\
\subfloat[][]{\includegraphics[width=0.4\textwidth,trim={0in 4.75in 6in 0in},clip]{figB.pdf} \label{fig:subfigB}}
\caption{Example of the 1-sparse coloring, where $i$ is the position of the occupied orbital in $\alpha$ that must be moved. \protect\subref{fig:subfigA} $i = 2$, $p = 4$ is sufficient to determine $\beta$ from $\alpha$, as well as to determine $\alpha$ from $\beta$. \protect\subref{fig:subfigB} $i = 2$, $p = 5$ is sufficient to determine $\beta$ from $\alpha$, but not the reverse: subtracting $p=5$ from $\beta_2$, $\beta_3$, or $\beta_4$ all give different valid values for $\alpha_i = \alpha_2$. The spacing condition means that we would need to give the position of the occupied orbital for $\beta$ instead.}
\end{figure}
Consider the example in \hyperref[fig:subfigA]{Figure~1(\protect\subref*{fig:subfigA})}: given $i$ which is the position in $\alpha$, the position $k$ in $\beta$ can be immediately determined.
But given $\beta$, multiple potential positions of occupied orbitals would need to be tested to see if they put the occupied orbital in position $i=2$ in $\alpha$.
In this case, given $\beta$ there is only one orbital which can be shifted to position 2 for $\alpha$ so the position in $\beta$ is unambiguous.
Now consider \hyperref[fig:subfigB]{Figure~1(\protect\subref*{fig:subfigB})}: multiple positions in $\beta$ could lead to position 2 in $\alpha$.
The difference between the two cases is that in \hyperref[fig:subfigA]{Figure~1(\protect\subref*{fig:subfigA})} there is a larger spacing between orbitals for $\beta$, whereas in \hyperref[fig:subfigB]{Figure~1(\protect\subref*{fig:subfigB})} there is a larger spacing for $\alpha$.
More specifically, for \hyperref[fig:subfigA]{Figure~1(\protect\subref*{fig:subfigA})} the spacing between $\alpha_1$ and $\alpha_3$ is $3$, whereas the spacing between $\beta_2$ and $\beta_4$ is larger at $5$.
For \hyperref[fig:subfigB]{Figure~1(\protect\subref*{fig:subfigB})} the spacing between $\alpha_1$ and $\alpha_3$ is $5$, whereas the spacing between $\beta_2$ and $\beta_4$ is smaller at $2$.
It is the spacing between the occupied orbitals adjacent to the one that is moved that should be compared.
For the situation in \hyperref[fig:subfigB]{Figure~1(\protect\subref*{fig:subfigB})},
rather than specifying the position in $\alpha$ we should specify the position in $\beta$ to resolve the ambiguity.
The bit $a$ determines whether we are specifying the position in $\alpha$ or in $\beta$; this is done depending on the relative spacing of the adjacent occupied orbitals in the two.
However, this spacing condition does not completely resolve the ambiguity: there are potentially two different choices for the occupied orbital.
The choice is made by the bit $b$. The coloring for the two differing orbitals is done by doing this twice with an intermediate list of occupied orbitals $\chi$.
There are ${\cal O}(\eta^2 N^2)$ possible colors: there are two possible choices of each of the bits $a_1$, $a_2$, $b_1$, and $b_2$, $\eta$ choices each of $i$ and $j$, and $N$ choices each of $p$ and $q$.
\subsection{Decomposition into $h_{ij}$ and $h_{ijk\ell}$}
\label{sec:dec2}
Each 1-sparse matrix from \sec{dec1} is associated with some 8-tuple $\gamma = (a_1,b_1,i,p,a_2,b_2,j,q)$.
However, without further modification, some of these 1-sparse matrices have entries given by a sum over a number of molecular integrals that grows with $\eta$, namely the diagonal terms as in \eq{slate1}, and the single-orbital terms as in \eq{slate2}. Here, we further decompose those matrices into a sum of 1-sparse matrices $H_{\gamma}$, which have entries proportional to the sum of a constant number of molecular integrals, in order to remove this changing upper bound.
We want to have a new set of 1-sparse matrices, each with entries corresponding to a single term in the sum over molecular integrals. To be more specific, the combinations of $\gamma$ correspond to terms in \eq{slate1} to \eq{slate3} as follows.
\begin{enumerate}
\item
If $p=q=0$, this indicates that we have a diagonal 1-sparse matrix.
In \eq{slate1}, the entries on the diagonal would be a sum of ${\cal O}(\eta^2)$ terms.
As we have freedom in how to use $i$ and $j$, we use these to give terms in the sum.
When $i=j$ for $p=q=0$, we take the 1-sparse matrix to have diagonal elements given by $h_{i i}$.
If $i < j$ for $p = q = 0$ we take the 1-sparse matrix to have diagonal entries $h_{\chi_i\chi_j \chi_i \chi_j} - h_{\chi_i \chi_j \chi_j \chi_i}$.
We do not allow tuples $\gamma$ such that $i>j$ for $p=q=0$ (alternatively we could just give zero in this case).
The overall result is that the sum over $i$ and $j$ for the 1-sparse matrices for $\gamma$ with $p=q=0$ yields the desired sum in \eq{slate1}.
\item
Next, if $p = 0$ and $q \neq 0$, then this indicates that we have a 1-sparse matrix with entries where $\alpha$ and $\beta$ differ by only one spin-orbital.
According to \eq{slate2}, each entry would normally be a sum of ${\cal O}(\eta)$ terms.
Instead, when $p = 0$ and $q \neq 0$, we use the value of $i$ to index terms in the sum in \eq{slate2}, though we only yield a nonzero result when $i$ is in the Slater determinant.
In particular, the 1-sparse matrix has entries $h_{k \chi_i \ell \chi_i} - h_{k \chi_i \chi_i \ell}$.
We allow an additional value of $i$ to indicate a 1-sparse matrix with entries $h_{k \ell}$.
Then the sum over 1-sparse matrices for different values of $i$ gives the desired sum \eq{slate2}.
We do not allow $\gamma$ such that $q=0$ but $p\neq 0$.
\item
Finally, if both $p$ and $q$ are nonzero, then we have a 1-sparse matrix with entries where $\alpha$ and $\beta$ differ by two orbitals.
In this case, there is no sum in \eq{slate3}, so there is no additional decomposition needed.
\end{enumerate}
Combining these three steps we find that the decomposition into 1-sparse matrices $H_\gamma$ can be achieved with the indices $(a_1,b_1,i,p,a_2,b_2,j,q)$. Thus, there are ${\cal O}(\eta^2 N^2)$ terms without any redundancies. Note that sorting of the spin-orbital indices requires only $\widetilde{\cal O}(\eta)$ gates, which is less than the number of complexity of evaluating the spin-orbitals. In the following sections, we denote the total number of terms given by the above decomposition by $\Gamma$, and the sum over $H_\gamma$ yields the complete CI matrix,
\begin{equation}
\label{eq:gamma_decomp}
H = \sum_{\gamma=1}^{\Gamma} H_\gamma.
\end{equation}
\subsection{Discretizing the integrals}
\label{sec:Riemann}
Next we consider discretization of the integrals for $h_{ij}$ and $h_{ijk\ell}$.
In \cite{Berry2015} it is shown how to simulate Hamiltonian evolution with an exponential improvement in the scaling with $1/\epsilon$, as compared to methods based on Trotter formulas.
In this approach, the time-ordered exponential for the evolution operator is approximated by a Taylor series up to an order $K$.
The time $t$ is broken into $r$ segments, and the integrals are discretized in the following way on each segment:
\begin{align}
{\cal T} \exp\left[-i \int_{0}^{t/r} \!\! H(t) \, d t \right]
&\approx \sum_{k=0}^K \frac{(-i)^k}{k!}\int_{0}^{t/r} {\cal T} H(t_k)\dots H(t_1)\, \dd\bs t \nonumber \\
&\approx \sum_{k=0}^K \frac{(-it/r)^k}{\mu^k k!}\sum_{j_1,\ldots,j_k=0}^{\mu-1} H(t_{j_k})\dots H(t_{j_1}),
\end{align}
where ${\cal T}$ is the time-ordering operator.
In our case the Hamiltonian does not change in time, so the time-ordering is unimportant.
The Hamiltonian is expanded as a sum of $H_\gamma$ as in \eq{gamma_decomp}, and each of those terms has matrix entries that
can be given in the form of an integral as
\begin{align}
H^{\alpha\beta}_\gamma = \int \aleph^{\alpha\beta}_\gamma(\vec z) \, \dd \vec z \, .
\end{align}
In cases where $H^{\alpha\beta}_\gamma$ corresponds to $h_{ij}$, the integral is over a three-dimensional region, and where $H^{\alpha\beta}_\gamma$ corresponds to $h_{ijk\ell}$ the integral is over a six-dimensional region, so $\vec z$ represents six parameters.
Ideally, each integral can be truncated to a finite domain $D$ with volume ${\cal V}$.
Using a set of grid points $\vec z_{\rho}$, we can approximate the integral by
\begin{align}
\label{eq:double}
H^{\alpha\beta}_\gamma & \approx \int_D \aleph^{\alpha\beta}_\gamma(\vec z) \, \dd \vec z \approx \frac{\cal V}{\mu} \sum_{\rho=1}^{\mu} \aleph^{\alpha\beta}_\gamma(\vec z_{\rho}) \, .
\end{align}
The complexity will then be logarithmic in the number of points in the sum, $\mu$, and linear in the volume times the maximum value of the integrand.
In practice the situation is more complicated than this.
That is because the integrals are all different.
As well as the dimensionality of the integrals (three for $h_{ij}$ and six for $h_{ijk\ell}$), there will be differences in the regions that the integrals will be over, as well as some integrals being in spherical polar coordinates.
To account for these differences, it is better to write the discretized integral in the form
\begin{equation}
\label{eq:double2}
H^{\alpha\beta}_\gamma \approx \sum_{\rho=1}^{\mu} \aleph^{\alpha\beta}_{\gamma,\rho} \, .
\end{equation}
The Hamiltonian $H_\gamma$ can then be written as the sum
\begin{equation}
\label{eq:double3}
H_\gamma \approx \sum_{\rho=1}^{\mu} \aleph_{\gamma,\rho} \, .
\end{equation}
As discussed in \cite{BabbushSparse1}, the discretization is possible because the integrands can be chosen to decay exponentially \cite{Helgaker2002}.
The required properties of the orbitals are given in \thm{maintheorem}.
Here we present a more precise formulation of the required properties, and provide specific results on the number of terms needed.
We make the following three assumptions about the spin-orbitals $\varphi_\ell$.
\begin{enumerate}
\item There exists a positive real number $\varphi_\text{max}$ such that,
for all spin-orbital indices $\ell$ and for all $\vec{r} \in \R^3$,
\begin{equation}
\label{eq:spin-orbital_bound}
\abs{\varphi_\ell (\vec{r})} \leq \varphi_\text{max}.
\end{equation}
\item For each spin-orbital index $\ell$, there exists a vector
$\vec{c}_\ell \in \R^3$ (called the center of $\varphi_\ell$)
and a positive real number $x_\text{max}$ such that, whenever
$\abs{\vec{r} - \vec{c}_\ell} \geq x_\text{max}$ for some
$\vec{r} \in \R^3$,
\begin{equation}
\label{eq:spin-orbital_decay}
\abs{\varphi_\ell (\vec{r})} \leq \varphi_\text{max} \exp \left(
-\frac{\alpha}{x_\text{max}} \norm{\vec{r}-\vec{c}_\ell}
\right),
\end{equation}
where $\alpha$ is some positive real constant.
\item For each spin-orbital index $\ell$, $\varphi_\ell$ is
twice-differentiable and there exist positive real constants
$\gamma_1$ and $\gamma_2$ such that
\begin{equation}
\label{eq:spin-orbital_first_derivative_bound}
\norm{\nabla \varphi_\ell (\vec{r})}
\leq \gamma_1 \frac{\varphi_\text{max}}{x_\text{max}}
\end{equation}
and
\begin{equation}
\label{eq:spin-orbital_second_derivative_bound}
\abs{\nabla^2 \varphi_\ell (\vec{r})}
\leq \gamma_2 \frac{\varphi_\text{max}}{x_\text{max}^2}
\end{equation}
for all $\vec{r} \in \R^3$.
\end{enumerate}
Note that $\alpha$, $\gamma_1$ and $\gamma_2$ are dimensionless constants,
whereas $x_{\max}$ has units of distance, and
$\varphi_\text{max}$ has the same units as $\varphi_\ell$.
The conditions of \thm{maintheorem} mean that $\varphi_\text{max}$ and $x_\text{max}$ grow at most
logarithmically with the number of spin-orbitals.
Note that we use $x_{\max}$ in a different way than in \cite{BabbushSparse1}, where it was the size of the cutoff on the region of integrals, satisfying $x_{\max}={\cal O}(\log(Nt/\epsilon))$.
Here we take $x_{\max}$ to be the size scale of the orbitals independent of $t$ or $\epsilon$, and the cutoff will be a multiple of $x_{\max}$.
We also assume that
$x_{\max}$ is bounded below by a constant, so
the first and second derivatives of the spin-orbitals grow no more than
logarithmically as a function of the number of spin-orbitals.
We next define notation used for the integrals for $h_{ij}$ and $h_{ijk\ell}$.
These integrals are
\begin{equation}
S_{ij}^{(0)}\! \left( D_0 \right)
:= -\frac{1}{2} \int_{D_0}
\varphi_i^* (\vec{r}) \nabla^2 \varphi_j (\vec{r}) \dd{\vec{r}},
\end{equation}
\begin{equation}
S_{ij}^{(1,\,q)}\! \left( D_{1,q} \right)
:= -Z_q \int_{D_{1,q}} \frac{
\varphi_i^* (\vec{r}) \, \varphi_j (\vec{r})
}{
\|\vec{R}_q - \vec{r}\|
} \dd{\vec{r}},
\end{equation}
and
\begin{equation}
S_{ijk\ell}^{(2)}\! \left( D_2 \right)
:= \int_{D_2}
\frac{
\varphi_i^*\!\left(\vec{r}_1\right) \varphi_j^*\!\left(\vec{r}_2\right)
\varphi_k\!\left(\vec{r}_2\right) \varphi_\ell\!\left(\vec{r}_1\right)
}{ \|\vec{r}_1 - \vec{r}_2\| }
\dd{\vec{r}_1} \dd{\vec{r}_2},
\end{equation}
for any choices of $D_0, D_{1,q} \subseteq \R^3$ and $D_2 \subseteq \R^6$.
Thus
\begin{equation}
h_{ij} = S_{ij}^{(0)}\! \left( \R^3 \right) +
\sum_q S_{ij}^{(1,\,q)}\! \left( \R^3 \right)
\end{equation}
and
\begin{equation}
h_{ijk\ell} = S_{ijk\ell}^{(2)}\! \left( \R^6 \right).
\end{equation}
Using the assumptions on the properties of the orbitals, we can bound the number of terms needed in a
Riemann sum that approximates each integral to within a specified accuracy, $\delta$ (which is distinct from the accuracy of the overall simulation, $\epsilon$).
These bounds are summarized in the following three lemmas.
\begin{lemma}
\label{lem:int0}
Let $\delta$ be any real number that satisfies
\begin{equation}
\label{eq:sensible0}
0 < \delta \leq e^{-\alpha/2} K_0 \varphi_\text{max}^2 x_\text{max}\, ,
\end{equation}
where
\begin{equation}
K_0
:= \frac{26 \gamma_1}{\alpha^2} +
\frac{8\pi\gamma_2}{\alpha^3} +
32\sqrt{3} \gamma_1 \gamma_2 \, .
\end{equation}
Then $S_{ij}^{(0)}\! \left( \R^3 \right)$ can be
approximated to within error $\delta$ using a Riemann sum with
\begin{equation}
\label{eq:lem1mu}
\mu \le \left\lceil
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\left[
\frac{2}{\alpha} \log \left(
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\right)
\right]^4
\right\rceil^3
\end{equation}
terms, where
the terms in the sum have absolute value no larger than
\begin{equation}
\label{eq:lem1bnd}
\frac{1}{\mu} \times 32 \frac{\gamma_1^2}{\alpha^3}
\varphi_\text{max}^2 x_\text{max} \left[
\log \left(
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\right)
\right]^3.
\end{equation}
\end{lemma}
\begin{lemma}
\label{lem:int1}
Let $\delta$ be any real number that satisfies
\begin{equation}
\label{eq:sensible1}
0 < \delta \leq e^{-\alpha/2} K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2 \, ,
\end{equation}
where
\begin{equation}
K_1
:= \frac{8\pi^2}{\alpha^3}\left( \alpha+2 \right) +
1121 \left( 8 \gamma_1 + \sqrt{2} \right).
\end{equation}
Then $S_{ij}^{(1,q)}\! \left( \R^3 \right)$ can be approximated to within
error $\delta$ using a Riemann sum with
\begin{equation}\label{eq:lem2mu}
\mu \le \left\lceil
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}
\left[
\frac{2}{\alpha} \log \left(
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}
\right)
\right]^4
\right\rceil^3
\end{equation}
terms, where the terms in the sum have absolute value no larger than
\begin{equation}\label{eq:lem2bnd}
\frac{1}{\mu} \times \frac{256\pi^2}{\alpha^3}
Z_q \varphi_\text{max}^2 x_\text{max}^2 \left[
\log \left(
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}
\right)
\right]^3.
\end{equation}
\end{lemma}
\begin{lemma}
\label{lem:int2}
Let $\delta$ be any real number that satisfies
\begin{equation}
\label{eq:sensible2}
0 < \delta \leq e^{-\alpha} K_2 \varphi_\text{max}^4 x_\text{max}^5 \, ,
\end{equation}
where
\begin{equation}
K_2
:= \frac{128\pi}{\alpha^6}(\alpha+2) +
2161 \pi^2 \left( 20 \gamma_1 + \sqrt{2} \right).
\end{equation}
Then $S_{ijk\ell}^{(2)} \! \left( \R^6 \right)$ can be approximated to within
error $\delta$ using a Riemann sum with
\begin{equation}\label{eq:lem3mu}
\mu \le \left\lceil
\frac{K_2 \varphi_\text{max}^4 x_\text{max}^5}{\delta}
\left[
\frac{1}{\alpha} \log \left(
\frac{K_2 \varphi_\text{max}^4 x_\text{max}^5}{\delta}
\right)
\right]^7
\right\rceil^6
\end{equation}
terms, where the terms in the sum have absolute value no larger than
\begin{equation}\label{eq:lem3bnd}
\frac{1}{\mu} \times
\frac{672\pi^2}{\alpha^6} \varphi_\text{max}^4 x_\text{max}^5 \left[
\log \left(
\frac{K_2 \varphi_\text{max}^4 x_\text{max}^5}{\delta}
\right)
\right]^6.
\end{equation}
\end{lemma}
The conditions in Eqs.~\eqref{eq:sensible0}, \eqref{eq:sensible1} and
\eqref{eq:sensible2} are just used to ensure that we are considering a
reasonable combination of parameters, and not for example a very large
allowable error $\delta$ or a small value of $x_{\max}$.
We prove these Lemmas in \app{integral_discretization}. Specifically, we prove
\lem{int0} in \app{integral_discretization/int0_proof},
\lem{int1} in \app{integral_discretization/int1_proof} and
\lem{int2} in \app{integral_discretization/int2_proof}.
In discretizing these integrals it is important that the integrands are
Hermitian, because we need ${\cal H}_{\gamma,\rho}$ to be Hermitian.
The integrands of these integrals are not Hermitian as discretized in the way given in the proofs in \app{integral_discretization}.
This is because the regions of integration are chosen in a non-symmetric way.
For example, the region of integration for $S_{ij}^{(0)}$ is chosen centered on the orbital $\varphi_i$, so the integrand is not symmetric.
It is simple to symmetrize the integrands, however.
For example, for $S_{ij}^{(0)}$ we can add $(S_{ji}^{(0)})^*$ and divide by two.
That ensures that the integrand is symmetric, with just a factor of two overhead in the number of terms in the sum.
As a consequence of these Lemmas, we see that the terms of any Riemann sum
approximation to one of the integrals that define the Hamiltonian coefficients
$h_{ij}$ and $h_{ijk\ell}$ have absolute values bounded by
\begin{equation}
\mathcal{O} \left(
\frac{\varphi_\text{max}^4 x_\text{max}^5}{\mu}
\left[
\log \left(
\frac{\varphi_\text{max}^4 x_\text{max}^5}{\delta}
\right)
\right]^6
\right),
\end{equation}
where $\mu$ is the number of terms in the Riemann sum and
$\delta$ is the desired accuracy of the approximation.
Here we have taken $Z_q$ to be $\mathcal{O}(1)$.
\subsection{Decomposition into self-inverse operators}
\label{sec:decomp2}
The truncated Taylor series strategy introduced in \cite{Berry2015} requires that we can represent our Hamiltonian as a weighted sum of unitaries.
To do so, we follow a procedure in \cite{Berry2013} which shows how 1-sparse matrices can be decomposed into a sum of self-inverse matrices with eigenvalues $\pm 1$.
Specifically, we decompose each $\aleph_{\gamma,\rho}$ into a sum of $M \in \Theta\big(\max_{\gamma,\rho}\big\|\aleph_{\gamma,\rho}\big\|_\textrm{max}/\zeta\big)$ 1-sparse unitary matrices of the form
\begin{equation}
\aleph_{\gamma,\rho} \approx {\widetilde{\aleph}}_{\gamma,\rho} \equiv \zeta\sum_{m=1}^{M} C_{\gamma,\rho,m}
\end{equation}
where $\zeta$ is the desired precision of the decomposition.
First, we construct a new matrix ${\widetilde{\aleph}}_{\gamma,\rho}$ by rounding each entry of $\aleph_{\gamma,\rho}$ to the nearest multiple of $2\,\zeta$, so that $\big\|\aleph_{\gamma,\rho}-{\widetilde{\aleph}}_{\gamma,\rho}\big\|_{\textrm{max}} \leq \zeta$. We define $C_{\gamma,\rho}\equiv\aleph_{\gamma,\rho}/\zeta$ so that $\left \| C_{\gamma,\rho} \right\|_{\textrm{max}}\leq 1+ \|\aleph_{\gamma,\rho} \|_\textrm{max}/\zeta$. We decompose each $C_{\gamma,\rho}$ into $ \|C_{\gamma,\rho} \|_{\textrm{max}}$ 1-sparse matrices, indexed by $m$, with entries in $\{0, -2, 2\}$, as follows:
\begin{equation}
\label{eq:Cthing}
C_{\gamma,\rho,m}^{\alpha\beta}\equiv
\begin{cases}
+2 & C_{\gamma,\rho}^{\alpha\beta}\geq 2m\\
-2 & C_{\gamma,\rho}^{\alpha\beta} < 2m\\
0 & \text{otherwise}.
\end{cases}
\end{equation}
Finally, we remove zero eigenvalues by further dividing each $C_{\gamma,\rho,m}$ into two matrices $C_{\gamma,\rho,m,1}$ and $C_{\gamma,\rho,m,2}$ with entries in $\{0, -1, +1\}$.
For every all-zero column $\beta$ in $C_{\gamma,\rho,m}$, we choose $\alpha$ so that $(\alpha, \beta)$ is the location of the nonzero entry in column $\beta$ in the original matrix ${\cal H}_{\gamma,\rho}$.
Then the matrix $C_{\gamma,\rho,m,1}$ has $+1$ in the $(\alpha, \beta)$ position, and $C_{\gamma,\rho,m,2}$ has $-1$ in the $(\alpha, \beta)$ position.
Thus, we have decomposed each $H_\gamma$ into a sum of 1-sparse, unitary matrices with eigenvalues $\pm 1$.
We now use a simplified notation where $\ell$ corresponds to the triples $(s,m,\gamma)$, and $\aleph_{\ell,\rho} \equiv C_{\gamma,\rho,m,s}$.
We denote the number of values of $\ell$ by $L$, and can write the Hamiltonian as a sum of ${\cal O}(N^4 \mu M )$ unitary, 1-sparse matrices
\begin{equation}\label{eq:selfinvdec}
H = \zeta \sum_{\ell=1}^{L} \sum_{\rho=1}^{\mu} {\cal H}_{\ell,\rho}.
\end{equation}
That is, the decomposition is of the form in \eq{unit_sum}, but in this case $W_\ell $ is independent of $\ell$.
To summarize, we decompose the molecular Hamiltonian into a sum of self-inverse matrices in four steps:
\begin{enumerate}
\item Decompose the molecular Hamiltonian into a sum of 1-sparse matrices using the bipartite graph coloring given in \app{1sparseproof}, summarized in \sec{dec1}.
\item Decompose these 1-sparse matrices further, such that each entry corresponds to a single term in the sum over molecular integrals. This does not change the number of terms, but simplifies calculations.
\item Discretize the integrals over a finite region of space, subject to the constraints and bounds given in \cite{BabbushSparse1}.
\item Decompose into self-inverse operators by the method proposed in \cite{Berry2013}.
\end{enumerate}
This decomposition gives an overall gate count scaling contribution of ${\cal O}(\eta^2 N^2)$.
\section{The CI Matrix Encoding}
\label{sec:encoding}
The molecular electronic structure Hamiltonian describes electrons interacting in a nuclear potential that is fixed under the Born-Oppenheimer approximation. Except for the proposals in \cite{Kassal2008,Toloui2013,Whitfield2013b,Whitfield2015,Kivlichan2016}, all prior quantum algorithms for chemistry use second quantization. While in second quantization antisymmetry is enforced by the fermionic anti-commutation relations, in first quantization the wavefunction itself is explicitly antisymmetric.
The representation of \eq{electronic} in second quantization is
\begin{equation}
H = \sum_{ij} h_{ij} a_i^{\dagger}a_j + \frac{1}{2} \sum_{ijk\ell} h_{ijk\ell} a_i^{\dagger} a_j^{\dagger} a_k a_\ell
\label{eq:2nd}
\end{equation}
where the operators $a_i^\dagger$ and $a_j$ in \eq{2nd} obey antisymmetry due to the fermionic anti-commutation relations,
\begin{align}
\label{eq:anticomm}
\{a_i^\dagger, a_j\} = \delta_{ij} \quad \quad \quad \quad \{a_i^\dagger, a_j^\dagger\} = \{a_i, a_j\} = 0.
\end{align}
The one-electron and two-electron integrals in \eq{2nd} are
\begin{align}
&h_{ij} = \int \varphi_i^*(\vec r) \left(-\frac{\nabla^2}{2} - \sum_{q} \frac{Z_q}{ \|\vec R_q - \vec r \|} \right)\varphi_j(\vec r) \,\dd\vec r , \label{eq:single_int1}\\
&h_{ijk\ell} = \int \frac{ \varphi_i^*(\vec r_1) \, \varphi_j^*(\vec r_2) \, \varphi_\ell(\vec r_1) \, \varphi_k(\vec r_2) }{\|\vec r_1 - \vec r_2\|} \, \dd\vec r_1\, \dd\vec r_2. \label{eq:double_int}
\end{align}
where (throughout this paper), $\vec r_j$ represents the position of the $j^\textrm{th}$ electron, and $\varphi_i(\vec r_j)$ represents the $i^\textrm{th}$ spin-orbital when occupied by that electron. To ensure that the integrand in \eq{single_int1} is symmetric, we can alternatively write the integral for $h_{ij}$ as
\begin{equation}\label{eq:single_int}
h_{ij} = \frac 12\int \nabla \varphi_i^*(\vec r) \cdot \nabla\varphi_j(\vec r) \,\dd\vec r
- \int \sum_{q} \varphi^*_i(\vec r) \frac{Z_q}{ \|\vec R_q - \vec r \|}\varphi_j(\vec r) \,\dd\vec r.
\end{equation}
The second-quantized Hamiltonian in \eq{2nd} is straightforward to simulate because one can explicitly represent the fermionic operators as tensor products of Pauli operators, using either the Jordan-Wigner transformation \cite{Jordan1928,Somma2002} or the Bravyi-Kitaev transformation \cite{Bravyi2002,Seeley2012,Tranter2015}.
With the exception of real-space algorithms described in \cite{Kassal2008,Kivlichan2016}, all quantum algorithms for chemistry represent the system in a basis of $N$ single-particle spin-orbital functions, usually obtained as the solution to a classical mean-field treatment such as Hartree-Fock \cite{Helgaker2002}. However, the conditions of \thm{maintheorem} only hold when actually performing the simulation in the atomic orbital basis\footnote{The basis of atomic orbitals is not necessarily orthogonal. However, this can be fixed using the efficient Lowdin symmetric orthogonalization procedure which seeks the closest orthogonal basis \cite{Helgaker2002, McClean2014}.} (i.e.\ the basis prescribed by the model chemistry). The canonical Hartree-Fock orbitals are preferred over the atomic orbitals because initial states are easier to represent in the basis of Hartree-Fock orbitals. These orbitals are actually a unitary rotation of the orthogonalized atomic orbitals prescribed by the model chemistry. This unitary basis transformation takes the form
\begin{align}
\tilde{\varphi}_i & = \sum_{j=1}^N \varphi_j U_{ij}\\
U = e^{- \kappa}, \quad & \quad \kappa = - \kappa^\dagger = \sum_{ij} \kappa_{ij} a^\dagger_i a_j,
\end{align}
and $\kappa$ is anti-Hermitian.
For $\kappa$ and $U$, the quantities $\kappa_{ij}$ and $U_{ij}$ respectively correspond to the matrix elements of these operators in the basis of spin orbitals.
It is a consequence of the Thouless theorem that this unitary transformation is efficient to apply.
The canonical Hartree-Fock orbitals and $\kappa$ are obtained by performing a self-consistent field procedure to diagonalize a mean-field Hamiltonian for the system which is known as the Fock matrix. Because the Fock matrix describes a system of non-interacting electrons it can be expressed as the following $N$ by $N$ matrix:
\begin{equation}
\label{eq:fock}
f_{ij} = h_{ij} + \frac{1}{2} \sum_{k} h_{i k k j} - h_{i k j k}.
\end{equation}
The integrals which appear in the Fock matrix are defined by \eq{single_int1} and \eq{double_int}. Importantly, the canonical orbitals are defined to be the orbitals which diagonalize the Fock matrix. Thus, the integrals in the definition of the Fock matrix are defined in terms of the eigenvectors of the Fock matrix so \eq{fock} is a recursive definition. The canonical orbitals are obtained by repeatedly diagonalizing this matrix until convergence with its own eigenvectors. The Hartree-Fock procedure is important because the Hartree-Fock state (which is a product state in the canonical basis with the lowest $\eta$ eigenvectors of the Fock matrix occupied and the rest unoccupied) has particularly high overlap with the ground state of $H$.
As stated before, the conditions of \thm{maintheorem} do not apply if we represent the Hamiltonian in the basis of canonical orbitals. But this is not a problem for us because we can still prepare the Hartree-Fock state in the basis of orthgonalized atomic orbitals (which do satisfy the conditions) and then apply the operator $U = e^{- \kappa}$ to our initial state at cost $\widetilde{\cal O}(N^2)$. Note that the use of a local basis has other advantages, as pointed out in \cite{McClean2014}. In particular, in the limit of certain large molecules, use of a local basis allows one to truncate terms from the Hamiltonian so that there are $\widetilde{\cal O}(N^2)$ terms instead of ${\cal O}(N^4)$ terms. However, \thm{maintheorem} exploits an entirely different property of basis locality which does not require any approximation from truncating terms.
The spatial encoding of \eq{2nd} requires $\Theta(N)$ qubits, one for each spin-orbital; under the Jordan-Wigner transformation, the state of each qubit indicates the occupation of a corresponding spin-orbital. Many states representable in second quantization are inaccessible to molecular systems due to symmetries in the Hamiltonian. For instance, molecular wavefunctions are eigenstates of the total spin operator so the total angular momentum is a good quantum number, and this insight can be used to find a more efficient spatial encoding \cite{Whitfield2013b,Whitfield2015}. Similarly, the Hamiltonian in \eq{2nd} commutes with the number operator, $\nu$, whose expectation value gives the number of electrons, $\eta$,
\begin{equation}
\nu = \sum_{i=1}^N a_i^{\dagger} a_i, \quad \quad \left[H, \nu\right] = 0, \quad \quad \eta = \avg{\nu}.
\end{equation}
Following the procedure in \cite{Toloui2013}, our algorithm makes use of an encoding which reduces the number of qubits required by recognizing $\eta$ as a good quantum number.
Conservation of particle number implies there are only $\xi = \binom{N}{\eta}$ valid configurations of these electrons, but the second-quantized Hilbert space has dimension $2^N$, which is exponentially larger than $\xi$ for fixed $\eta$.
We work in the basis of Slater determinants, which are explicitly antisymmetric functions of both space and spin associated with a particular $\eta$-electron configuration.
We denote these states as $\ket{\alpha} = \ket{\alpha_0, \alpha_1, \cdots, \alpha_{\eta-1}}$, where $\alpha_i \in \{1,\ldots, N\}$ and $\alpha \in \{1,\ldots, N^{\eta}\}$.
We emphasize that $ \alpha_i$ is merely an integer which indexes a particular spin-orbital function $ \varphi_{\alpha_i}(\vec r)$. While each configuration requires a specification of $\eta$ occupied spin-orbitals, there is no sense in which $\alpha_i$ is associated with ``electron $i$'' since fermions are indistinguishable. Specifically,
\begin{equation}
\label{eq:det}
\braket{\vec r_0,\ldots,\vec r_{\eta-1}}{\alpha} = \braket{\vec r_0,\ldots,\vec r_{\eta-1}}{\alpha_0, \alpha_1, \cdots, \alpha_{\eta-1}}
= \frac{1}{\sqrt{\eta!}}
\begin{vmatrix}
\varphi_{ \alpha_0}\!\left(\vec r_0\right) & \varphi_{ \alpha_1}\!\left(\vec r_0\right) & \cdots & \varphi_{\alpha_{\eta-1}} \!\left(\vec r_0\right) \\
\varphi_{\alpha_0}\!\left(\vec r_1\right) & \varphi_{ \alpha_1}\!\left(\vec r_1\right) & \cdots & \varphi_{ \alpha_{\eta-1}} \!\left(\vec r_1\right) \\
\vdots & \vdots & \ddots & \vdots\\
\varphi_{\alpha_0}\!\left(\vec r_{\eta-1}\right) & \varphi_{ \alpha_1}\!\left(\vec r_{\eta-1}\right) & \cdots & \varphi_{ \alpha_{\eta-1}} \!\left(\vec r_{\eta-1}\right) \end{vmatrix}
\end{equation}
where the bars enclosing the matrix in \eq{det} denote a determinant. Because determinants have the property that they are antisymmetric under exchange of any two rows, this construction ensures that our wavefunction obeys the Pauli exclusion principle. We note that although this determinant can be written equivalently in different orders (e.g.~by swapping any two pairs of orbital indices), we avoid this ambiguity by requiring the Slater determinants to only be written in ascending order of spin-orbital indices.
The representation of the wavefunction introduced in \cite{Toloui2013} uses $\eta$ distinct registers to encode the occupied set of spin-orbitals, thus requiring $\Theta(\eta \log N) = \widetilde{\cal O}(\eta)$ qubits. However, it would be possible to use a further-compressed representation of the wavefunction based on the direct enumeration of all Slater determinants, requiring only $\Theta(\log \xi)$ qubits. When using very small basis sets (such as the minimal basis), it will occasionally be the case that the spatial overhead of $\Theta(N)$ for the second-quantized algorithm is actually less than the spatial complexity of our algorithm. However, for a fixed $\eta$, the CI matrix encoding requires exponentially fewer qubits.
\section{The CI Matrix Oracle}
\label{sec:oracle}
In this section, we discuss the construction of the circuit referred to in our introduction as $\textsc{select}({\cal H})$, which applies the self-inverse operators in a controlled way.
As discussed in \cite{BabbushSparse1}, the truncated Taylor series technique of \cite{Berry2015} can be used with a selection oracle for an integrand which defines the molecular Hamiltonian. This method will then effect evolution under this Hamiltonian with an exponential increase in precision over Trotter-based methods. For clarity of exposition, we describe the construction of $\textsc{select}({\cal H})$ in terms of two smaller oracle circuits which can be queried to learn information about the 1-sparse unitary integrands. This information is then used to evolve an arbitrary quantum state under a specific 1-sparse unitary.
The first of the oracles described here is denoted as $Q^{\textrm{col}}$ and is used to query information about the sparsity pattern of a particular 1-sparse Hermitian matrix from \eq{gamma_decomp}. The second oracle is denoted as $Q^{\textrm{val}}$ and is used to query information about the value of integrands for elements in the CI matrix. We construct $Q^{\textrm{val}}$ by making calls to a circuit constructed in \cite{BabbushSparse1} where it is referred to as ``$\textsc{sample}(w)$''. The purpose of $\textsc{sample}(w)$ is to sample the integrands of the one-electron and two-electron integrals $h_{ij}$ and $h_{ijk\ell}$ in \eq{double_int} and \eq{single_int}. The construction of $\textsc{sample}(w)$ in \cite{BabbushSparse1} requires $\widetilde{\cal O}(N)$ gates.
The oracle $Q^{\textrm{col}}$ uses information from the index $\gamma$.
The index $\gamma$ is associated with the indices $(a_1,b_1,i,p,a_2,b_2,j,q)$ which describe the sparsity structure of the 1-sparse Hermitian matrix $H_{\gamma}$ according to the decomposition in \sec{dec2}.
$Q^{\textrm{col}}$ acts on a register specifying a color $\ket{\gamma}$ as well a register containing an arbitrary row index $\ket{\alpha}$ to reveal a column index $\ket{\beta}$ so that the ordered pair ($\alpha$, $\beta$) indexes the nonzero element in row $\alpha$ of $H_{\gamma}$,
\begin{align}
Q^\textrm{col} \ket{\gamma} \ket{\alpha}\ket{0}^{\otimes \eta \log N}
& = \ket{\gamma}\ket{\alpha}\ket{\beta}.
\end{align}
From the description in \sec{dec2}, implementation of the unitary oracle $Q^\textrm{col}$ is straightforward.
To construct $\textsc{select}({\cal H})$ we need a second oracle that returns the value of the matrix elements in the decomposition. This selection oracle is queried with a register $\ket{\ell} = \ket{s}\ket{m}\ket{\gamma}$ which specifies which part of the 1-sparse representation we want, as well as a register $\ket{\rho}$ which indexes the grid point $\rho$ and registers $\ket{\alpha}$ and $\ket{\beta}$ specifying the two Slater determinants. Specifically, the entries in the tuple identify the color ($\gamma$) of the 1-sparse Hermitian matrix from which the 1-sparse unitary matrix originated, which positive integer index ($m \leq M$) it corresponds to in the further decomposition of $\aleph_{\gamma,\rho}$ into $C_{\gamma,\rho,m}$, and which part it corresponds to in the splitting of $C_{\gamma,\rho,m}$ into $C_{\gamma,\rho,m,s}$ (where $s\in\{1,2\}$).
As a consequence of the Slater-Condon rules shown in Eqs.~\eqref{eq:slate1}, \eqref{eq:slate2}, \eqref{eq:slate3}, and \eqref{eq:slate4}, $Q^\textrm{val}$ can be constructed given access to $\textsc{sample}(w)$, which samples the integrand of the integrals in Eqs.~\eqref{eq:double_int} and \eqref{eq:single_int} \cite{BabbushSparse1}.
Consistent with the decomposition in \sec{dec2}, the $i$ and $j$ indices in the register containing $\gamma = (i,p,j,q)$ specify the dissimilar spin-orbitals in $\ket{\alpha}$ and $\ket{\beta}$ that are needed in the integrands defined by the Slater-Condon rules; therefore, the determination of which spin-orbitals differ between $\ket{\alpha}$ and $\ket{\beta}$ can be made in ${\cal O}(\log N)$ time (only the time needed to read their values from $\gamma$). As $\textsc{sample}(w)$ is comprised of $\widetilde{\cal O}(N)$ gates, $Q^{\textrm{val}}$ has time complexity $\widetilde{\cal O}(N)$ and acts as
\begin{align}
&\quad Q^\textrm{val}\ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta}= {\cal H}_{\ell,\rho}^{\alpha \beta} \ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta},
\end{align}
where ${\cal H}_{\ell,\rho}^{\alpha \beta}$ is the value of the matrix entry at $(\alpha,\beta)$ in the self-inverse matrix ${\cal H}_{\ell,\rho}$.
When either $\ket{\alpha}$ or $\ket{\beta}$ represents an invalid Slater determinant (with more than one occupation on any spin-obital), we take ${\cal H}_{\ell,\rho}^{\alpha \beta} = 0$ for $\alpha \ne \beta$. This ensures there are no transitions into Slater determinants which violate the Pauli exclusion principle.
The choice of ${\cal H}_{\ell,\rho}^{\alpha \alpha}$ for invalid $\alpha$ will not affect the result, because the state will have no weight on the invalid Slater determinants.
Having constructed the column and value oracles, we are finally ready to construct $\textsc{select} ({\cal H})$. This involves implementing 1-sparse unitary operations. The method we describe is related to the scheme presented in \cite{Aharonov2003} for evolution under 1-sparse Hamiltonians, but is simplified due to the simpler form of the operators. As in \eq{selectH}, $\textsc{select}({\cal H})$ applies the term ${\cal H}_{\ell,\rho}$ in the 1-sparse unitary decomposition to the wavefunction $\ket{\psi}$. Writing $\ket{\psi}=\sum_\alpha c_\alpha\ket{\alpha}$, we require that $\textsc{select}({\cal H})$ first call $Q^\textrm{col}$ to obtain the columns, $\beta$, corresponding to the rows, $\alpha$, for the nonzero entries of the Hamiltonian:
\begin{align}
\ket{\ell}\ket{\rho}\ket{\psi}\ket{0}^{\otimes \eta \log N} & \mapsto \sum_\alpha c_\alpha
Q^\textrm{col}\ket{\ell}\ket{\rho}\ket{\alpha}\ket{0}^{\otimes \eta \log N}\nonumber\\
& =\sum_\alpha c_\alpha \ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta}.
\end{align}
Now that we have the row and column of the matrix element, we apply $Q^\textrm{val}$ which causes each Slater determinant to accumulate the phase factor $k_\alpha = {\cal H}_{\ell,\rho}^{\alpha \beta} = \pm 1$:
\begin{align}
\sum_\alpha c_\alpha \ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta} & \mapsto \sum_\alpha c_\alpha Q^\textrm{val}\ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta}\\
& =\sum_\alpha c_\alpha k_\alpha\ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta}\nonumber.
\end{align}
Next, we swap the locations of $\alpha$ and $\beta$ in order to complete multiplication by the 1-sparse unitary,
\begin{align}
\sum_\alpha c_\alpha k_\alpha\ket{\ell}\ket{\rho}\ket{\alpha}\ket{\beta} & \mapsto \sum_\alpha c_\alpha k_\alpha\ket{\ell}\ket{\rho}\text{SWAP}\ket{\alpha}\ket{\beta}\nonumber\\
& =\sum_\alpha c_\alpha k_\alpha\ket{\ell}\ket{\rho}\ket{\beta}\ket{\alpha}.
\end{align}
Finally we apply $Q^\textrm{col}$ again but this time $\beta$ is in the first register. Since $Q^\textrm{col}$ is self-inverse and always maps $\ket{\alpha}\ket{b}$ to $\ket{\alpha}\ket{b \oplus \beta}$ and $\ket{\beta}\ket{b}$ to $\ket{\beta}\ket{b \oplus \alpha}$, this allows us to uncompute the ancilla register.
\begin{align}
\sum_\alpha c_\alpha k_\alpha\ket{\ell}\ket{\rho}\ket{\beta}\ket{\alpha} & \mapsto \sum_\alpha c_\alpha k_\alpha Q^\textrm{col}\ket{\ell}\ket{\rho}\ket{\beta}\ket{\alpha}\nonumber\\
& = \sum_\alpha c_\alpha k_\alpha\ket{\ell}\ket{\rho}\ket{\beta}\ket{0}^{\otimes \eta \log N} \nonumber \\
&= \ket{\ell}{\cal H}_{\ell,\rho}\ket{\psi}\ket{0}^{\otimes \eta \log N}.
\end{align}
Note that this approach works regardless of whether the entry is on-diagonal or off-diagonal; we do not need separate schemes for the two cases. The circuit for $\textsc{select}({\cal H})$ is depicted in \fig{select_circuit}.
\begin{figure}[h!]
\[\xymatrix @*=<0em> @R 1em @C 1em {
\lstick{\kets{\rho}} & \qw & \multigate{5}{Q^\textrm{val}} & \qw & \qw &\rstick{\kets{\rho}} \qw\\
\lstick{\kets{s}} & \qw & \ghost{Q^\textrm{val}} & \qw & \qw & \rstick{\kets{s}} \qw\\
\lstick{\kets{m}} & \qw & \ghost{Q^\textrm{val}} & \qw & \qw & \rstick{\kets{m}} \qw\\
\lstick{\kets{\gamma}} & \multigate{2}{Q^\textrm{col}} & \ghost{Q^\textrm{val}} & \qw & \multigate{2}{Q^\textrm{col}}& \rstick{\kets{\gamma}} \qw\\
\lstick{\kets{\psi}} & \ghost{Q^\textrm{col}} & \ghost{Q^\textrm{val}} & *=<0em>{\times} \qw & \ghost{Q^\textrm{col}} &\rstick{{\cal H}_{\ell,\rho}\kets{\psi}} \qw\\
\lstick{\kets{0}^{\otimes \eta \log N}} & \ghost{\widetilde{Q}_\gamma^{col}} & \ghost{Q^\textrm{val}} & *=<0em>{\times} \qw \qwx & \ghost{Q^\textrm{col}} & \rstick{\kets{0}^{\otimes \eta \log N}} \qw\\
}\]
\caption{\label{fig:select_circuit} The circuit implementing $\textsc{select}({\cal H})$, which applies the term ${\cal H}_\ell(\vec z_\rho)$ labeled by $\ell=(\gamma, m, s)$ in the unitary 1-sparse decomposition to the wavefunction $\ket{\psi}$.}
\end{figure}
\section{Discussion}
\label{sec:conclusion}
We have outlined a method to simulate the quantum chemistry Hamiltonian in a basis of Slater determinants using recent advances from the universal simulation literature. We find an oracular decomposition of the Hamiltonian into 1-sparse matrices based on an edge coloring routine first described in \cite{Toloui2013}. We use that oracle to simulate evolution under the Hamiltonian using the truncated Taylor series technique described in \cite{Berry2013}.
We discretize the integrals which define entries of the CI matrix, and use the sum of unitaries approach to effectively exponentially compress evaluation of these discretized integrals.
Asymptotic scalings suggest that the algorithms described in this paper series will allow for the quantum simulation of much larger molecular systems than would be possible using a Trotter-Suzuki decomposition.
Recent work \cite{Wecker2014,Hastings2015,Poulin2014,McClean2014,BabbushTrotter} has demonstrated markedly more efficient implementations of the original Trotter-Suzuki-based quantum chemistry algorithm \cite{Aspuru-Guzik2005,Whitfield2010}; similarly, we believe the implementations discussed here can still be improved upon, and that numerical simulations will be crucial to this task.
Finally, we note that the CI matrix simulation strategy discussed here opens up the possibility of an interesting approach to adiabatic state preparation. An adiabatic algorithm for quantum chemistry was suggested in second quantization in \cite{BabbushAQChem} and studied further in \cite{Veis2014}. However, those works did not suggest a compelling adiabatic path to take between an easy-to-prepare initial state (such as the Hartree-Fock state) and the ground state of the exact Hamiltonian. We note that one could start the system in the Hartree-Fock state, and use the CI matrix oracles discussed in this paper to ``turn on'' a Hamiltonian having support over a number of configuration basis states which increases smoothly with time.
\section*{Acknowledgements}
The authors thank Jhonathan Romero Fontalvo, Jarrod McClean, Borzu Toloui, and Nathan Wiebe for helpful discussions. D.W.B.\ is funded by an Australian Research Council Future Fellowship (FT100100761). P.J.L.\ acknowledges the support of the National Science Foundation under grant number PHY-0955518. A.A.G.\ and P.J.L.\ acknowledge the support of the Air Force Office of Scientific Research under award number FA9550-12-1-0046. A.A.-G.\ acknowledges the Army Research Office under Award: W911NF-15-1-0256.
\subsection{Proof of \lem{int0}}
\label{app:integral_discretization/int0_proof}
Our proof for \lem{int0} roughly follows the three stages presented in
\app{integral_discretization/preliminaries/proof_structure}.
Here we give the proof in summary form and relegate some of the details
to the later subsections.
\subsubsection{First stage for \lem{int0}}
The first part of the proof corresponds to the first stage discussed in
\app{integral_discretization/preliminaries/proof_structure}.
We choose
\begin{align}
\label{eq:xvallem1}
x_0
&:= \frac{2}{\alpha} x_\text{max} \log \left(
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\right), \nonumber \\
D_0 &:= \mathcal{C}_{x_0} \left( \vec{c}_i \right).
\end{align}
The condition \eq{sensible0} ensures that $x_0 \geq x_\text{max}$.
We show in \app{integral_discretization/int0_proof/trunc} that the error due to
this truncation can be bounded as
\begin{equation}
\delta_\text{trunc}^{(0)}
:= \abs{
S_{ij}^{(0)} \!\left( \R^3 \right) -
S_{ij}^{(0)} \!\left( D_0 \right)
}
< \frac{8\pi\gamma_2}{\alpha^3} \varphi_\text{max}^2 x_\text{max}
\exp \left( -\frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right).
\end{equation}
\subsubsection{Green's identity for \lem{int0}}
The next part of the proof is specific to \lem{int0},
and is not one of the general stages outlined in
\app{integral_discretization/preliminaries/proof_structure}.
The integral is given in the form with a second derivative of an orbital,
which means that to bound the error we would need additional bounds on
the third derivatives of the orbitals.
We have not assumed such bounds, so we would like to reexpress the integral
in terms of first derivatives before approximating it as a Riemann sum.
We have already truncated the domain, though, so we will obtain terms from
the boundary of the truncated domain.
We reexpress the integral via Green's first identity, which gives
\begin{equation}\label{eq:greensfirst}
S_{ij}^{(0)} \!\left( D_0 \right)
= \frac{1}{2} \int_{D_0}
\nabla \varphi_i^* (\vec{r}) \cdot
\nabla \varphi_j (\vec{r})\
\dd{V} - \frac{1}{2} \oint_{\partial D_0}
\varphi_i^* (\vec{r})
\nabla \varphi_j (\vec{r}) \cdot
\dd{\vec{S}},
\end{equation}
where $\dd{V}$ and $\dd{\vec{S}}$ are the volume and oriented surface elements,
respectively, and $\partial D_0$ is the boundary of $D_0$.
The reason why we do not make this change before truncating the domain is that
we have not made any assumptions on the rate of decay of the derivatives of
the orbitals.
We define
\begin{equation}
\widetilde{S}_{ij}^{(0)} \!\left( D_0 \right)
:= \frac{1}{2} \int_{D_0}
\nabla \varphi_i^* (\vec{r}) \cdot
\nabla \varphi_j (\vec{r})
\ \dd{V}.
\end{equation}
We show (in \app{integral_discretization/int0_proof/Green}) that
\begin{equation}\label{eq:greenserror}
\delta_\text{Green}^{(0)}
:= \abs{S_{ij}^{(0)}\! \left( D_0 \right) -
\widetilde{S}_{ij}^{(0)}\! \left( D_0 \right)}
< \frac{26 \gamma_1}{\alpha^2} \varphi_\text{max}^2 x_\text{max}
\exp \left( - \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right).
\end{equation}
\subsubsection{Second stage for \lem{int0}}
Next we consider the discretization into a Riemann sum for \lem{int0}.
We define
\begin{equation}
\label{eq:partition_size_int0}
N_0
:= \left\lceil
\left( \frac{x_0}{x_\text{max}} \right)^4
\exp \left( \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right)
\right\rceil,
\end{equation}
so that
\begin{equation}
N_0
= \left\lceil
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\left[
\frac{2}{\alpha} \log \left(
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\right)
\right]^4
\right\rceil.
\end{equation}
The Riemann sum is then
\begin{equation}
\mathcal{R}_0
:= \sum_{\vec{k}} \frac{1}{2}
\nabla \varphi_i^* \!\left( \vec{r}_{\vec{k}} \right) \cdot
\nabla \varphi_j \!\left( \vec{r}_{\vec{k}} \right)
\text{vol} \left( T_{\vec{k}}^{(0)} \right),
\end{equation}
where, for every triple of integers
$\vec{k} = \left( k_1, k_2 , k_3 \right)$
such that $0 \leq k_1, k_2, k_3 < N_0$, we define
\begin{equation}
\vec{r}_{\vec{k}}
= \frac{x_0}{N_0} \left[
2\vec{k} - \left(N_0-1,N_0-1,N_0-1\right)
\right]
\end{equation}
and
\begin{equation}
T_{\vec{k}}^{(0)}
:= \mathcal{C}_{x_0/N_0} \left( \vec{r}_{\vec{k}} \right).
\end{equation}
Thus we have partitioned $D_0$ into $\mu = N_0^3$ equal-sized cubes
$T_{\vec{k}}^{(0)}$ that overlap on sets of measure zero.
The expression in \eq{lem1mu} of \lem{int0} then follows immediately.
Each term of $\mathcal{R}_0$ satisfies
\begin{align}
\label{eq:int0_summand_bound}
\left\|
\frac{1}{2}
\nabla \varphi_i^*\! \left( \vec{r}_{\vec{k}} \right) \cdot
\nabla \varphi_j\! \left( \vec{r}_{\vec{k}} \right)
\text{vol} \left( T_{\vec{k}}^{(0)} \right)
\right\|
& \leq \frac{1}{2}
\left\|\nabla \varphi_i^* \!\left( \vec{r}_{\vec{k}} \right)\right\|
\left\|\nabla \varphi_j \!\left( \vec{r}_{\vec{k}} \right)\right\|
\text{vol} \left( T_{\vec{k}}^{(0)} \right) \nonumber \\
& \leq \frac{1}{2} \left(
\gamma_1 \frac{\varphi_\text{max}}{x_\text{max}}
\right)^2 \left( \frac{2x_0}{N_0} \right)^3 \nonumber \\
& = \frac{1}{\mu} \times
4 \gamma_1^2 \left( \frac{x_0}{x_\text{max}} \right)^3
\varphi_\text{max}^2 x_\text{max},
\end{align}
where the second inequality follows from
\eq{spin-orbital_first_derivative_bound}.
Using the value of $x_0$ in \eq{xvallem1} in \eq{int0_summand_bound},
each term in the sum has the upper bound on its absolute value
(corresponding to \eq{lem1bnd} in \lem{int0})
\begin{equation}
\frac{1}{\mu} \times32 \frac{\gamma_1^2}{\alpha^3}
\left[
\log \left(
\frac{K_0 \varphi_\text{max}^2 x_\text{max}}{\delta}
\right)
\right]^3 \varphi_\text{max}^2 x_\text{max}.
\end{equation}
We show (in \app{integral_discretization/int0_proof/Riemann}) that
\begin{equation}
\delta_\text{Riemann}^{(0)}
:= \abs{
\widetilde{S}_{ij}^{(0)} \!\left( D_0 \right) - \mathcal{R}_0
}
< 16\sqrt{3} \gamma_1 \gamma_2 \varphi_\text{max}^2 x_\text{max}
\exp \left( - \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right).
\end{equation}
\subsubsection{Third stage for \lem{int0}}
In the final part of the proof of \lem{int0} we show that the total error is
properly bounded. By the triangle inequality, we have
\begin{equation}
\delta_\text{total}^{(0)}
:= \abs{S_{ij}^{(0)} \!\left( \R^3 \right) - \mathcal{R}_0}
\leq \delta_\text{trunc}^{(0)} +
\delta_\text{Green}^{(0)} +
\delta_\text{Riemann}^{(0)}.
\end{equation}
We therefore arrive at a simple bound on the total error:
\begin{equation}
\label{eq:total_error_int0}
\delta_\text{total}^{(0)}
< K_0 \varphi_\text{max}^2 x_\text{max}
\exp \left( - \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right),
\end{equation}
where
\begin{equation}
K_0
:= \frac{26 \gamma_1}{\alpha^2} +
\frac{8\pi\gamma_2}{\alpha^3} +
16\sqrt{3} \gamma_1 \gamma_2.
\end{equation}
To ensure that $\delta^{(0)}_\text{total} \leq \delta$, we should have
\begin{equation}
K_0 \varphi_\text{max}^2 x_\text{max}
\exp \left( - \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right)
\le \delta.
\end{equation}
We can satisfy this inequality with $x_0$ given by \eq{xvallem1}.
This last step completes our proof. The remainder of this subsection
gives the details for some of the steps above.
\subsubsection{Bounding $\delta_\text{trunc}^{(0)}$ for \lem{int0}}
\label{app:integral_discretization/int0_proof/trunc}
Observe first that
\begin{equation}
\delta_\text{trunc}^{(0)}
= \abs{
S_{ij}^{(0)} \!\left(\R^3\right) - S_{ij}^{(0)} \!\left( D_0 \right)
}
\leq \frac{1}{2} \int_{\R^3 \setminus D_0}
\abs{\varphi_i^* \!\left(\vec{r}\right)}
\abs{\nabla^2 \varphi_j \!\left(\vec{r}\right)}
\dd{\vec{r}}
\leq \frac{1}{2} \int_{\R^3 \setminus \mathcal{B}_x \left(\vec{c}_i\right)}
\abs{\varphi_i^* \!\left(\vec{r}\right)}
\abs{\nabla^2 \varphi_j \!\left(\vec{r}\right)}
\dd{\vec{r}},
\end{equation}
where the last inequality follows from the fact that
$\mathcal{B}_x \left(\vec{c}_i\right) \subset D_0$.
Using this fact together with assumptions 2 and 3 from \sec{Riemann}, we have
\begin{equation}
\delta_\text{trunc}^{(0)}
\leq \frac{\gamma_2}{2} \frac{\varphi_\text{max}^2}{x_\text{max}^2}
\int_{\R^3 \setminus \mathcal{B}_{x_0} \left(\vec{c}_i\right)}
\exp \left(
-\alpha \frac{\norm{\vec{r} - \vec{c}_i}}{x_\text{max}}
\right)
\dd{\vec{r}}.
\end{equation}
We simplify this expression by expressing $\vec{r}$ in polar coordinates
with center $\vec{c}_i$. After integrating over the solid angles, we have
\begin{equation}
\delta_\text{trunc}^{(0)}
\leq 2\pi \gamma_2 \frac{\varphi_\text{max}^2}{x_\text{max}^2}
\int_{x_0}^\infty s^2 e^{-\alpha s / x_\text{max}} \dd{s}.
\end{equation}
Noting that
\begin{equation}
\int_{x_0}^\infty s^2 e^{-\mu s} \dd{s}
= \left( \frac{x_0^2}{\mu} + \frac{2x_0}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu x_0}
< \frac{4}{\mu^3} e^{-\mu x_0/2},
\end{equation}
we have
\begin{equation}
\delta_\text{trunc}^{(0)}
< \frac{8\pi\gamma_2}{\alpha^3} \varphi_\text{max}^2 x_\text{max}
\exp \left( -\frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right).
\end{equation}
\subsubsection{Bounding $\delta_\text{Green}^{(0)}$ for \lem{int0}}
\label{app:integral_discretization/int0_proof/Green}
Using \eq{greensfirst} and \eq{greenserror} we have
\begin{equation}
\delta_\text{Green}^{(0)} = \abs{\frac{1}{2} \oint_{\partial D_0}
\varphi_i^* (\vec{r})
\nabla \varphi_j (\vec{r}) \cdot
\dd{\vec{S}}}.
\end{equation}
Then using \eq{spin-orbital_decay} and
\eq{spin-orbital_first_derivative_bound} gives us
\begin{equation}
\delta_\text{Green}^{(0)}
\leq \frac{\gamma_1}{2} \frac{\varphi_\text{max}^2}{x_\text{max}}
\oint_{\partial D_0}
\exp \left(
-\alpha \frac{\norm{\vec{r}-\vec{c}_i}}{x_\text{max}}
\right) \dd{S}.
\end{equation}
We further observe that $\norm{\vec{r}-\vec{c}_i} \geq x$
for all $\vec{r} \in \partial D_0$, and the cube with side length $2x$ has
surface area $24 x^2$, giving
\begin{equation}
\delta_\text{Green}^{(0)}
\leq 12 \gamma_1 \frac{\varphi_\text{max}^2}{x_\text{max}}
x_0^2 \exp \left( -\alpha \frac{x_0}{x_\text{max}} \right)
< \frac{26 \gamma_1}{\alpha^2} \varphi_\text{max}^2 x_\text{max}
\exp \left( - \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right),
\end{equation}
where we have noted $12 z^2 e^{-z} < 26 e^{-z/2}$ for all $z > 0$.
\subsubsection{Bounding $\delta_\text{Riemann}^{(0)}$}
\label{app:integral_discretization/int0_proof/Riemann}
First we bound the derivative of the integrand.
We use the chain rule, the triangle inequality,
\eq{spin-orbital_first_derivative_bound} and
\eq{spin-orbital_second_derivative_bound} to find
\begin{equation}
\norm{
\nabla \left( \nabla \varphi_i^* (\vec{r}) \cdot
\nabla \varphi_j (\vec{r}) \right)
}
\leq \abs{\nabla^2 \varphi_i^* (\vec{r})}
\norm{\nabla \varphi_j (\vec{r})} +
\abs{\nabla^2 \varphi_j (\vec{r})}
\norm{\nabla \varphi_i^* (\vec{r})}
\leq 2 \gamma_1 \gamma_2 \frac{\varphi_\text{max}^2}{x_\text{max}^3}.
\end{equation}
We have
\begin{equation}
\text{vol} \left( D_0 \right) = 8 x_0^3
\end{equation}
and
\begin{equation}
\text{diam} \left( T_{\vec{k}}^{(0)} \right) = 2 \sqrt{3} x_0 / N_0
\end{equation}
for all $\vec{k}$.
Using \eq{Riemann_error} and \eq{partition_size_int0}, and
noting that $1/\lceil z \rceil \leq 1/z$ for any $z\in\R$, we have
\begin{equation}
\delta_\text{Riemann}^{(0)}
\leq 16\sqrt{3} \gamma_1 \gamma_2
\frac{\varphi_\text{max}^2}{x_\text{max}^3} \frac{x_0^4}{N_0}
\leq 16\sqrt{3} \gamma_1 \gamma_2 \varphi_\text{max}^2 x_\text{max}
\exp \left( - \frac{\alpha}{2} \frac{x_0}{x_\text{max}} \right).
\end{equation}
\subsection{Proof of \lem{int1}}
\label{app:integral_discretization/int1_proof}
For this proof, the discretization into the Riemann sum will be performed
differently depending on whether spin-orbital $i$ is considered distant from
or nearby to nucleus $q$. If the nucleus is far from the spin-orbital,
the singularity in the integrand is not inside our truncated
domain of integration and we need not take special care with it. Otherwise,
we can remove the singularity by defining spherical polar coordinates
centred at the nucleus. In each case, we select different truncated integration
domains and therefore different Riemann sums.
We focus on the centre of spin-orbital $i$ for simplicity; in principle,
the centre of spin-orbital $j$ could also be taken into account.
\subsubsection{First stage for \lem{int1}}
We again start by truncating the domain of integration. We select
\begin{equation}\label{eq:xvallem2}
x_1=\frac{2}{\alpha} x_\text{max} \log \left(
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}\right).
\end{equation}
The condition in \eq{sensible1} ensures that $x_1 \geq x_\text{max}$.
We regard the spin-orbital as distant from the nucleus if
\begin{equation}
\norm{\vec{R}_q - \vec{c}_i} \geq \sqrt{3}x_1 + x_\text{max}.
\end{equation}
If so, we use the truncated domain
\begin{equation}
D_{1, q, \text{non-singular}}
:= \mathcal{C}_{x_1}\! \left( \vec{c}_i \right) .
\end{equation}
Otherwise, we use
\begin{equation}
D_{1, q, \text{singular}}
:= \mathcal{B}_{4x_1}\! \left( \vec{R}_q \right).
\end{equation}
We define
\begin{align}
\delta_\text{trunc}^{(1, q, \text{non-singular})}
& := \abs{
S_{ij}^{(1,q)}\! \left( \R^3 \right) -
S_{ij}^{(1,q)}\! \left( D_{1, q, \text{non-singular}} \right)
},
\\
\delta_\text{trunc}^{(1, q, \text{singular})}
& := \abs{
S_{ij}^{(1,q)}\! \left( \R^3 \right) -
S_{ij}^{(1,q)}\! \left( D_{1, q, \text{singular}} \right)
},
\\
\delta_\text{trunc}^{(1, q)}
& := \max \left\{
\delta_\text{trunc}^{(1, q, \text{non-singular})},
\delta_\text{trunc}^{(1, q, \text{singular})}
\right\},
\end{align}
and show in \app{integral_discretization/int1_proof/trunc} that
\begin{equation}
\delta_\text{trunc}^{(1, q)}
< \frac{8\pi^2}{\alpha^3}\left( \alpha+2 \right)
Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left( - \frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right).
\end{equation}
\subsubsection{Second stage for \lem{int1} with Cartesian coordinates}
Now we consider in the discretization of the integral for the case that
$\norm{\vec{R}_q - \vec{c}_i} \geq \sqrt{3}x_1 + x_\text{max}$, so orbital $i$
can be regarded as distant from the nucleus. We set
\begin{equation}
\label{eq:partition_size_int1}
N_1
:= \left\lceil
\left( \frac{x_1}{x_\text{max}} \right)^4
\exp \left( \frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right)
\right\rceil
\end{equation}
and define two different Riemann sums containing $\mu = N_1^3$ terms.
We also use this expression for $N_1$ in the case that the spin-orbital is
near the nucleus. Using our value of $x_1$ in \eq{xvallem2},
\begin{equation}
N_1
= \left\lceil
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}
\left[
\frac{2}{\alpha} \log \left(
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}
\right)
\right]^4
\right\rceil .
\end{equation}
Then, noting that $\mu = N_1^3$ is the number of terms in either Riemann sum,
we obtain the bound on $\mu$ in \eq{lem2mu} of \lem{int1}.
We approximate
$S_{ij}^{(1,q)} \!\left( D_{1, q, \text{non-singular}} \right)$
with the sum
\begin{equation}
\mathcal{R}_{1, q, \text{non-singular}}
:= \sum_{\vec{k}} -Z_q \frac{
\varphi_i^* \!\left( \vec{r}_{\vec{k}} \right)
\varphi_j \!\left( \vec{r}_{\vec{k}} \right)
}{
\|\vec{R}_q - \vec{r}_{\vec{k}}\|
}
\text{vol} \left(
T_{\vec{k}}^{(1, q, \text{non-singular})}
\right),
\end{equation}
where, for every triple of integers
$\vec{k} = \left( k_1, k_2 , k_3 \right)$
such that $0 \leq k_1, k_2, k_3 < N_1$, we define
\begin{equation}
\vec{r}_{\vec{k}}
= \frac{x_1}{N_1} \left[
2\vec{k} - \left(N_1-1, N_1-1, N_1-1\right)
\right]
\end{equation}
and
\begin{equation}
T_{\vec{k}}^{(1, q, \text{non-singular})}
:= \mathcal{C}_{x_1/N_1}\! \left( \vec{r}_{\vec{k}} \right).
\end{equation}
Thus we have partitioned $D_{1, q, \text{non-singular}}$ into $N_1^3$
equal-sized cubes $T_{\vec{k}}^{(1, q, \text{non-singular})}$
that overlap on sets of measure zero.
Each term of $\mathcal{R}_{1, q, \text{non-singular}}$ satisfies
\begin{align}
\label{eq:int1_summand_bound_non-sing}
\abs{
-Z_q \frac{
\varphi_i^* \!\left( \vec{r}_{\vec{k}} \right)
\varphi_j \!\left( \vec{r}_{\vec{k}} \right)
}{
\|\vec{R}_q - \vec{r}_{\vec{k}}\|
}
\text{vol} \left(
T_{\vec{k}}^{(1, q, \text{non-singular})}
\right)
}
& \leq Z_q \frac{
\abs{\varphi_i^* \!\left( \vec{r}_{\vec{k}} \right)}
\abs{\varphi_j \!\left( \vec{r}_{\vec{k}} \right)}
}{\|\vec{R}_q - \vec{r}_{\vec{k}}\|}
\text{vol} \left(
T_{\vec{k}}^{(1, q, \text{non-singular})}
\right) \nonumber \\
& \leq Z_q \frac{\varphi_\text{max}^2}{x_\text{max}}
\left( \frac{2x_1}{N_1} \right)^3 \nonumber \\
& = \frac{1}{\mu} \times 8 x_1^3
\frac{Z_q \varphi_\text{max}^2}{x_\text{max}},
\end{align}
where we have used \eq{spin-orbital_bound} and the fact that
$\|\vec{R}_q - \vec{r}\| \geq x_\text{max}$ for every
$\vec{r} \in D_{1, q, \text{non-singular}}$.
This upper bound is no greater than
\begin{equation}\label{eq:bndlem2}
\frac{1}{\mu} \times 32 \pi^2 x_1^3
\frac{Z_q \varphi_\text{max}^2}{x_\text{max}},
\end{equation}
Now substituting our value of $x_1$ from \eq{xvallem2} shows that
no term has absolute value greater than (corresponding to \eq{lem2bnd} in \lem{int1})
\begin{equation}
\frac{1}{\mu} \times
\frac{256\pi^2}{\alpha^3}
Z_q \varphi_\text{max}^2 x_\text{max}^2 \left[
\log \left(
\frac{K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2}{\delta}
\right)
\right]^3.
\end{equation}
We show in \app{integral_discretization/int1_proof/Riemann_non-sing}
that
\begin{align}
\delta_\text{Riemann}^{(1, q, \text{non-singular})}
& := \abs{
S_{ij}^{(1, q)}\! \left( D_{1, q, \text{non-singular}} \right)
- \mathcal{R}_{1, q, \text{non-singular}}
} \nonumber \\
& \leq 8 \sqrt{3} \left( 2 \gamma_1 + 1 \right)
Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left(-\frac{\alpha}{2} \frac{x_1}{x_\text{max}}\right).
\end{align}
\subsubsection{Second stage for \lem{int1} with spherical polar coordinates}
Next we consider discretization of the integral for the case where
$\norm{\vec{R}_q - \vec{c}_i} < \sqrt{3}x_1 + x_\text{max}$, so orbital
$i$ is nearby the nucleus. We express
\begin{equation}
S_{ij}^{(1,q)} \! \left( D_{1, q, \text{singular}} \right)
= - 16 x_1^2 Z_q
\int_0^{2\pi} \dd{\phi} \int_0^\pi \dd{\theta} \int_0^1 \dd{s}\
f_1 (s, \theta, \phi),
\end{equation}
where we define $\vec{s} := ( \vec{r} - \vec{R}_q )/(4x_1)$ and
\begin{equation}
f_1 (s, \theta, \phi)
:= \varphi_i^* \! \left( 4x_1 \vec{s} + \vec{R}_q \right)
\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right) s \sin\theta.
\end{equation}
Here we use $\theta$ and $\phi$ to refer to the polar and azimuthal
angles, respectively, of the vector $\vec{s}$. Note that
the singularity in the nuclear Coulomb potential has been absorbed into
the spherical polar volume form
$s^2 \sin\theta\ \dd{s}\ \dd{\theta}\ \dd{\phi}$.
For every triple of natural numbers
$\vec{k} = \left( k_s, k_\theta, k_\phi \right)$ such that
$0 \leq k_s, k_\theta, k_\phi < N_1$, we define
\begin{equation}
T_{\vec{k}}^{(1, q, \text{singular})}
:= \left\{ \vec{s}
\left|
\begin{array}{c}
k_s/N_1 \leq s \leq \left(k_s + 1\right)/N_1 \\
k_\theta \pi/N_1 \leq
\theta \leq \left(k_\theta + 1\right) \pi/N_1 \\
2 k_\phi \pi/N_1 \leq
\phi \leq 2 \left(k_\phi + 1\right) \pi/N_1 \\
\end{array}
\right.
\right\}
\end{equation}
so that $\bigcup_{\vec{k}} T_{\vec{k}}^{(1, q, \text{singular})} =
D_{1, q, \text{singular}}$. We select
\begin{equation}
\left( s_{\vec{k}}, \theta_{\vec{k}}, \phi_{\vec{k}} \right)
= \left(
\frac{1}{N_1} \left(k_s + \tfrac{1}{2}\right),
\frac{\pi}{N_1} \left(k_\theta + \tfrac{1}{2}\right),
\frac{2\pi}{N_1} \left(k_\phi + \tfrac{1}{2}\right)
\right).
\end{equation}
Thus our Riemann sum approximation is
\begin{equation}
\mathcal{R}_{1, q, \text{singular}}
:= \sum_{\vec{k}}
-16x_1^2 Z_q
f_1\! \left( s_{\vec{k}},\theta_{\vec{k}},\phi_{\vec{k}} \right)
\text{vol} \left(
T_{\vec{k}}^{(1, q, \text{singular})}
\right),
\end{equation}
where we emphasize that
\begin{equation}
\label{eq:int1_nonstandard_volume}
\text{vol} \left( T_{\vec{k}}^{(1, q, \text{singular})} \right)
= \int_{T_{\vec{k}}^{(1, q, \text{singular})}}
\dd{s}\, \dd{\theta}\, \dd{\phi}
= \frac{2 \pi^2}{N_1^3}
\end{equation}
is \emph{not} the volume of $T_{\vec{k}}^{(1, q, \text{singular})}$
when considered as a subset of $\R^3$ under the usual Euclidean metric.
The reason for this discrepancy is that we absorbed the Jacobian
introduced by switching from Cartesian to spherical polar coordinates
into the definition of $f_1$. Thus we are integrating $f_1$
with respect to the volume form $\dd{s}\,\dd{\theta}\,\dd{\phi}$,
not $s^2 \sin\theta\,\dd{s}\,\dd{\theta}\,\dd{\phi}$. The terms of
$\mathcal{R}_{1, q, \text{singular}}$ are bounded by
\begin{align}
\label{eq:integrandlem22}
\abs{
-16x_1^2 Z_q f_1 \!\left( s_{\vec{k}},
\theta_{\vec{k}},
\phi_{\vec{k}} \right)
\text{vol} \left(
T_{\vec{k}}^{(1, q, \text{singular})}
\right)
}
& = 16x_1^2 Z_q \abs{
f_1 \!\left( s_{\vec{k}},
\theta_{\vec{k}},
\phi_{\vec{k}} \right)
}
\text{vol} \left(
T_{\vec{k}}^{(1, q, \text{singular})}
\right) \nonumber \\
& \leq \frac{1}{\mu} \times
32 \pi^2 x_1^2 Z_q \varphi_\text{max}^2,
\end{align}
where the inequality follows from \eq{spin-orbital_bound}.
Again this expression is upper bounded by \eq{bndlem2}, so substituting
our value of $x_1$ from \eq{xvallem2} gives the upper bound in \eq{lem2bnd}.
We show in \app{integral_discretization/int1_proof/Riemann-sing} that
\begin{align}
\delta_\text{Riemann}^{(1, q, \text{singular})}
& := \abs{
S_{ij}^{(1, q)} \left( D_{1, q, \text{singular}} \right)
- \mathcal{R}_{1, q, \text{singular}}
} \nonumber \\
& < 1121 \left( 8 \gamma_1 + \sqrt{2} \right)
Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right).
\end{align}
\subsubsection{Third stage for \lem{int1}}
We again finish the proof by showing that the total error is bounded by $\delta$.
From \eq{total_error_bound_trunc_Riemann}, we have
\begin{align}
\delta_\text{total}^{(1, q, \text{non-singular})}
& := \abs{
S_{ij}^{(1,q)} \left( \R^3 \right) -
\mathcal{R}_{1, q, \text{non-singular}}
}
\leq \delta_\text{trunc}^{(1, q, \text{non-singular})} +
\delta_\text{Riemann}^{(1, q, \text{non-singular})},\\
\delta_\text{total}^{(1, q, \text{singular})}
& := \abs{
S_{ij}^{(1,q)} \left( \R^3 \right) -
\mathcal{R}_{1, q, \text{singular}}
}
\leq \delta_\text{trunc}^{(1, q, \text{singular})} +
\delta_\text{Riemann}^{(1, q, \text{singular})}.
\end{align}
We have given a bound that holds simultaneously for both
$\delta_\text{trunc}^{(1, q, \text{non-singular})}$
and $\delta_\text{trunc}^{(1, q, \text{singular})}$,
and we have given a bound for
$\delta_\text{Riemann}^{(1, q, \text{singular})}$
that is larger (as a function of $x$) than our bound for
$\delta_\text{Riemann}^{(1, q, \text{non-singular})}$.
We are therefore able to assert that the error of our Riemann sum
approximation, no matter which we choose, is always bounded above by
\begin{equation}
\label{lem2errbnd}
K_1 Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right),
\end{equation}
where
\begin{equation}
K_1
:= \frac{2\pi^2}{\alpha^3}\left( 5\alpha+1 \right) +
1121 \left( 8 \gamma_1 + \sqrt{2} \right).
\end{equation}
We have found two different upper bounds on the magnitudes of the terms in the
Riemann sums given in Eqs.~\eqref{eq:int1_summand_bound_non-sing}
and \eqref{eq:integrandlem22}. Finally, we note that by substituting our value
of $x_1$ from \eq{xvallem2}, this expression is upper bounded by $\delta$.
This last step completes our proof of \lem{int1}. The remainder of this
subsection gives the details for some of the steps above.
\subsubsection{Bounding $\delta_\text{trunc}^{(1,q)}$ for \lem{int1}}
\label{app:integral_discretization/int1_proof/trunc}
Note first that
$\mathcal{B}_{x_1}\! \left( \vec{c}_i \right) \subset D_{1, q, \text{non-singular}}$
and
$\mathcal{B}_{x_1}\! \left( \vec{c}_i \right) \subset D_{1, q, \text{singular}}$.
To see the latter, note that we only consider $D_{1, q, \text{singular}}$
in the case that $\|\vec{R}_q - \vec{c}_i \| \leq \sqrt{3}x_1 + x_\text{max}$,
which implies that
\begin{equation}
\max_{\vec{r} \in \mathcal{B}_{x_1} \left( \vec{c}_i \right)}
\|\vec{R}_q - \vec{r}\|
\leq x_1 + \|\vec{R}_q - \vec{c}_i\|
\leq (\sqrt{3} + 1)x_1 + x_\text{max}
< 4x_1 .
\end{equation}
As we have
\begin{equation}
\abs{S^{(1,q)}\! \left(\R^3\right) - S^{(1,q)} (D)}
\leq Z_q \int_{\R^3 \setminus D} \dd{\vec{r}}\
\frac{
\abs{\varphi_i^* (\vec{r}) \varphi_j (\vec{r})}
}{
\|\vec{R}_q - \vec{r}\|
}
\leq Z_q \int_{\R^3 \setminus \mathcal{B}_{x_1} \left( \vec{c}_i \right)}
\dd{\vec{r}}\
\frac{
\abs{\varphi_i^* (\vec{r}) \varphi_j (\vec{r})}
}{
\|\vec{R}_q - \vec{r}\|
}
\end{equation}
for any $D$ such that $\mathcal{B}_x \left( \vec{c}_i \right) \subset D$,
we may compute
\begin{equation}
\delta_\text{trunc}^{(1,q)}
\leq Z_q \varphi_\text{max}^2
\int_{\R^3 \setminus \mathcal{B}_{x_1} \left( \vec{c}_i \right)}
\frac{
\exp \left(
- \alpha \frac{\norm{\vec{r} - \vec{c}_i}}{x_\text{max}}
\right)
}{\|\vec{R}_q - \vec{r}\|} \dd{\vec{r}} \\
= Z_q \varphi_\text{max}^2
\Lambda_{\alpha/x_\text{max}, x_1}\!
\left( \vec{R}_q - \vec{c}_i \right),
\end{equation}
where the function $\Lambda$ is as defined in \eq{exp_Coulomb_potential}
and the inequality follows from \eq{spin-orbital_decay}.
By \lem{exp_Coulomb_potential_bound}, in the case $\|\vec{R}_q - \vec{c}_i\|>x_1$ we have
\begin{align}
\delta_\text{trunc}^{(1,q)}
&< \frac{16 \pi^2}{\alpha^3} Z_q \varphi_\text{max}^2
\frac{x_\text{max}^3}{\|\vec{R}_q - \vec{c}_i\|}
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right)\nonumber \\
&< \frac{16 \pi^2}{\alpha^3} Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right),
\end{align}
where the second inequality follows from $x_1\ge x_\text{max}$.
In the case $\|\vec{R}_q - \vec{c}_i\|\le x_1$ we can use
\begin{equation}
\delta_\text{trunc}^{(1,q)}
< \frac{8 \pi^2}{\alpha^2} Z_q \varphi_\text{max}^2
x_\text{max}^2
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right).
\end{equation}
We can add the bounds to find, in general, that
\begin{equation}
\delta_\text{trunc}^{(1,q)}
< \frac{8 \pi^2}{\alpha^3} (\alpha+2) Z_q \varphi_\text{max}^2
x_\text{max}^2
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right).
\end{equation}
\subsubsection{Bounding $\delta_\text{Riemann}^{(1, q, \text{non-singular})}$ for \lem{int1}}
\label{app:integral_discretization/int1_proof/Riemann_non-sing}
Following \app{integral_discretization/preliminaries/proof_structure},
we note that
\begin{equation}
\text{vol} \left( D_{1, q, \text{non-singular}} \right)
= 8x_1^3
\end{equation}
and
\begin{equation}
\text{diam} \left( T_{\vec{k}}^{(1, q, \text{non-singular})} \right)
= 2 \sqrt{3} x_1 / N_1
\end{equation}
for each $\vec{k}$.
We can bound the derivative of the integrand using
the product rule and the triangle inequality as follows:
\begin{equation}
\norm{
\nabla \frac{
\varphi_i^* (\vec{r}) \varphi_j (\vec{r})
}{
\|\vec{R}_q - \vec{r}\|
}
}
\leq \frac{
\norm{\nabla \varphi_i^* (\vec{r})} \abs{\varphi_j (\vec{r})}
}{
\|\vec{R}_q - \vec{r}\|
} +
\frac{
\abs{\varphi_i^* (\vec{r})} \norm{\nabla \varphi_j (\vec{r})}
}{
\|\vec{R}_q - \vec{r}\|
} +
\frac{
\abs{\varphi_i^* (\vec{r}) \varphi_j (\vec{r})}
}{
\|\vec{R}_q - \vec{r}\|^2
}
\leq \left( 2\gamma_1 + 1 \right)
\frac{\varphi_\text{max}^2}{x_\text{max}^2},
\end{equation}
where the last inequaity follows from \eq{spin-orbital_bound} and
\eq{spin-orbital_first_derivative_bound}, as well as the fact that
$\|\vec{R}_q - \vec{r}\| \geq x_\text{max}$ for any
$\vec{r} \in D_{1, q, \text{non-singular}}$.
From \eq{Riemann_error} and \eq{partition_size_int1},
and noting $1/\lceil z \rceil \leq 1/z$, we have
\begin{equation}
\delta_\text{Riemann}^{(1, q, \text{non-singular})}
\leq 8 \sqrt{3} Z_q \left( 2 \gamma_1 + 1 \right)
\frac{\varphi_\text{max}^2}{x_\text{max}^2} \frac{x_1^4}{N_1}
\leq 8 \sqrt{3} \left( 2 \gamma_1 + 1 \right)
Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left(-\frac{\alpha}{2} \frac{x_1}{x_\text{max}}\right).
\end{equation}
\subsubsection{Bounding $\delta_\text{Riemann}^{(1, q, \text{singular})}$ for \lem{int1}}
\label{app:integral_discretization/int1_proof/Riemann-sing}
Recalling that we are using a non-standard metric to evaluate the volumes
and diameters of sets, we find
\begin{equation}
\text{vol} \left( D_{1, q, \text{singular}} \right) = 2\pi^2
\end{equation}
and
\begin{equation}
\text{diam} \left( T^{(1, q, \text{singular})}_{\vec{k}} \right)
= \frac{1}{N_1}\sqrt{5\pi^2 + 1}.
\end{equation}
By \eq{Riemann_error}, it remains to find a bound on the derivative of $f_1$.
Throughout this subsection, we write $f^\prime_\text{max}$ for this bound.
To bound this derivative, we consider the gradient in three different ways.
First there is $\nabla$, which is the gradient with respect to the unscaled position coordinates.
Second there is $\nabla_s$, which is the gradient with respect to the spherical polar coordinates,
but just taking the derivatives with respect to each coordinate.
That is,
\begin{equation}
\nabla_s := \left( \frac{\partial}{\partial s} , \frac{\partial}{\partial \theta}, \frac{\partial}{\partial \phi} \right)
\end{equation}
We use this because we are treating the coordinates like they were Euclidean for the discretized integral.
Third, there is the usual gradient in spherical polar coordinates,
\begin{equation}
\nabla'_s := \left( \frac{\partial}{\partial s} , \frac 1s \frac{\partial}{\partial \theta}, \frac 1{s\sin\theta} \frac{\partial}{\partial \phi} \right)
\end{equation}
Because we consider $s\in[0,1]$, the components of the gradient $\nabla_s$ are upper bounded by the components of the gradient $\nabla'_s$.
Therefore
\begin{equation}
\norm{\nabla_s \left[\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right]} \le \norm{\nabla'_s \left[\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right]}
\end{equation}
The restriction on the magnitude of the gradient in \eq{spin-orbital_first_derivative_bound} holds on the usual gradient in spherical polar coordinates.
This means that
\begin{equation}
\norm{\nabla'_s \left[\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right]} = 4x_1 \norm{\nabla \left[\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right]} \le 4x_1 \gamma_1 \frac{\varphi_{\max}}{x_{\max}}.
\end{equation}
Using these results, we have
\begin{align}
f^\prime_\text{max} &= \norm{\nabla_s \left[\varphi_i^* \! \left( 4x_1 \vec{s} + \vec{R}_q \right)
\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right) s \sin\theta\right]}\nonumber \\
&\le \left|\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right) s \sin\theta\right| \norm{\nabla_s \left[\varphi_i^* \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right]
}+
\left|\varphi_i^* \! \left( 4x_1 \vec{s} + \vec{R}_q \right) s \sin\theta\right| \norm{ \nabla_s \left[\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right] }\nonumber \\
& \quad +\left| \varphi_i^* \! \left( 4x_1 \vec{s} + \vec{R}_q \right) \varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right) \right| \norm{ \nabla_s \left[s \sin\theta\right]}\nonumber \\
&\le 4x_1\varphi_{\max}\norm{\nabla \left[\varphi_i^* \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right]}
+ 4x_1\varphi_{\max} \norm{ \nabla \left[\varphi_j \! \left( 4x_1 \vec{s} + \vec{R}_q \right)\right] } + \varphi_{\max} \sqrt{2} \nonumber \\
&\le 8x_1\gamma_1 \frac{\varphi_{\max}^2}{x_{\max}} + \sqrt{2} \varphi_{\max}.
\end{align}
Thus we have the bound
\begin{equation}
f^\prime_\text{max}
\leq \left( 8 \gamma_1 \frac{x_1}{x_\text{max}} + \sqrt{2} \right)
\varphi_\text{max}^2.
\end{equation}
We now can give a bound for our approximation to
$S^{(1,q)}_{ij} \!\left( D_{1, \text{singular}} \right)$.
Using the above definitions of
$f^\prime_\text{max}$, $\text{vol} \left( D_{1, \text{singular}} \right)$
and $\text{diam} \left( T^{(1, q, \text{singular})}_{\vec{k}} \right)$, we have
\begin{equation}
\delta_\text{Riemann}^{(1, q, \text{singular})}
\leq \frac 12 16x_1^2 Z_q f^\prime_\text{max} \text{diam} \left( T_{\vec{k}} \right)
\text{vol} \left( D_{1, \text{singular}} \right)
\leq 16 \pi^2 \sqrt{5\pi^2 + 1}\sqrt{3}
\left( 8 \gamma_1 \frac{x_1}{x_\text{max}} + 1 \right)
\frac{Z_q x_1^2 \varphi_\text{max}^2}{N_1}.
\end{equation}
Using \eq{partition_size_int1} and noting $1/\lceil z \rceil \leq 1/z$, we have
\begin{equation}
\begin{split}
\delta_\text{Riemann}^{(1, q, \text{singular})}
& < 16 \pi^2 \sqrt{5\pi^2 + 1}
\left( 8 \gamma_1 + \frac{x_\text{max}}{x_1} \right)
Z_q \varphi_\text{max}^2 x_\text{max}^2 \frac{x_\text{max}}{x_1}
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right) \\
& \leq 1121 \left( 8 \gamma_1 + \sqrt{2} \right)
Z_q \varphi_\text{max}^2 x_\text{max}^2
\exp \left( -\frac{\alpha}{2} \frac{x_1}{x_\text{max}} \right),
\end{split}
\end{equation}
where we have used $x_1 \geq x_\text{max}$.
\subsection{Proof of \lem{int2}}
\label{app:integral_discretization/int2_proof}
As in \app{integral_discretization/int1_proof},
we separate our proof into two cases, depending on whether
the singularity of the integrand is relevant or not.
If the orbitals $i$ and $j$ are distant, then the singularity is unimportant
and we can use rectangular coordinates.
If these orbitals are nearby, then we use spherical polar coordinates
to eliminate the singularity from the integrand.
We do not consider the distance between the orbitals $k$ and $\ell$
in order to simplify the analysis.
\subsubsection{First stage for \lem{int2}}
Again the first stage is to truncate the domain of integration.
We take
\begin{equation}\label{xlem3}
x_2 := \frac{x_\text{max}}{\alpha} \log \left(
\frac{K_2 \varphi_\text{max}^4 x_\text{max}^5}{\delta}
\right)
\end{equation}
to be the size of the truncation region.
The condition in \eq{sensible2} ensures that $x \geq x_\text{max}$.
We regard the orbitals as distant if
$\norm{\vec{c}_i - \vec{c}_j} \geq 2\sqrt{3}x_2 + x_\text{max}$.
Then we take the truncation region
\begin{equation}
D_{2, \text{non-singular}}
:= \mathcal{C}_{x_2} \!\left( \vec{c}_i \right) \times
\mathcal{C}_{x_2} \! \left( \vec{c}_j \right).
\end{equation}
Otherwise, if the orbitals are nearby we take the truncation region
\begin{equation}
D_{2, \text{singular}}
:= \left\{
\vec{r}_1 \oplus \vec{r}_2
\left|
\vec{r}_1 \in \mathcal{C}_{x_2} \!\left( \vec{c}_i \right),
\vec{r}_1 - \vec{r}_2 \in
\mathcal{B}_{\zeta x_2} ( \vec{0} )
\right.
\right\},
\end{equation}
Where $\zeta:=2\sqrt{3}+3$.
The error in the first case is
\begin{equation}
\delta_\text{trunc}^{(2, \text{non-singular})}
:= \abs{
S_{ijk\ell}^{(2)}\! \left( \R^6 \right) -
S_{ijk\ell}^{(2)}\! \left( D_{2, \text{non-singular}} \right)
}
\end{equation}
and the error in the second case is
\begin{equation}
\delta_\text{trunc}^{(2, \text{singular})}
:= \abs{
S_{ijk\ell}^{(2)} \!\left( \R^6 \right) -
S_{ijk\ell}^{(2)} \!\left( D_{2, \text{singular}} \right)
}.
\end{equation}
The maximum error for either case is denoted
\begin{equation}
\delta_\text{trunc}^{(2)}
:= \max \left\{
\delta_\text{trunc}^{(2, \text{non-singular})},
\delta_\text{trunc}^{(2, \text{singular})}
\right\} .
\end{equation}
We upper bound this error in \app{integral_discretization/int2_proof/trunc} as
\begin{equation}
\delta_\text{trunc}^{(2)}
< \frac{128\pi}{\alpha^6} (\alpha+2)
\varphi_\text{max}^4 x_\text{max}^5
\exp\left( -\alpha \frac{x_2}{x_\text{max}} \right).
\end{equation}
\subsubsection{Second stage for \lem{int2} with Cartesian coordinates}
The second stage for the proof of \lem{int2} is to discretize the integrals into Riemann sums.
In this subsection we consider the case that orbitals $i$ and $j$ are distant,
so we wish to approximate the truncated integral
$S_{ijk\ell}^{(2)} \!\left( D_{2, \text{non-singular}} \right)$.
In the next subsection we consider discretization in the case where orbitals
$i$ and $j$ are nearby, and we wish to approximate
$S_{ijk\ell}^{(2)} \!\left( D_{2, \text{singular}} \right)$.
Each sum contains $\mu = N_2^6$ terms, where
\begin{equation}
\label{eq:partition_size_int2}
N_2
:= \left\lceil
\left(\frac{x_2}{x_\text{max}}\right)^7
\exp \left( \alpha \frac{x_2}{x_\text{max}} \right)
\right\rceil.
\end{equation}
The same value of $N_2$ will be used for spherical polar coordinates.
Using the value of $x_2$ from Eq.~\eqref{xlem3} gives
\begin{equation}
N_2
= \left\lceil
\frac{
K_2 \varphi_\text{max}^4 x_\text{max}^5
}{
\delta
}
\left[
\frac{1}{\alpha} \log \left(
\frac{
K_2 \varphi_\text{max}^4 x_\text{max}^5
}{
\delta
}
\right)
\right]^7
\right\rceil .
\end{equation}
Since $\mu = N_2^6$ is the number of terms in either Riemann sum, we obtain the
lower bound on $\mu$ in \eq{lem3mu} of \lem{int2}.
We approximate $S_{ijk\ell}^{(2)} \!\left(D_{2, \text{non-singular}}\right)$
with the sum
\begin{equation}
\mathcal{R}_{2, \text{non-singular}}
:= \sum_{\vec{k}_1, \vec{k}_2} \frac{
\varphi_i^* ( \vec{r}_{\vec{k}_1} )\,
\varphi_j^* ( \vec{r}_{\vec{k}_2} )\,
\varphi_k ( \vec{r}_{\vec{k}_2} )\,
\varphi_\ell ( \vec{r}_{\vec{k}_1} )
}{
\|\vec{r}_{\vec{k}_1} - \vec{r}_{\vec{k}_2}\|
}
\text{vol} \left(
T_{\vec{k}_1, \vec{k}_2}^{(2, \text{non-singular})}
\right),
\end{equation}
where, for every triple of integers
$\vec{k} = \left( k_1, k_2 , k_3 \right)$
such that $0 \leq k_1, k_2, k_3 < N_2$, we define
\begin{equation}
\vec{r}_{\vec{k}}
= \frac{x_2}{N_2} \left[
2\vec{k} - \left(N_2-1, N_2-1, N_2-1\right]
\right)
\end{equation}
and
\begin{equation}
T_{\vec{k}_1, \vec{k}_2}^{(2, \text{non-singular})}
:= \mathcal{C}_{x_2/N_2} ( \vec{r}_{\vec{k}_1} ) \times
\mathcal{C}_{x_2/N_2} ( \vec{r}_{\vec{k}_2} ).
\end{equation}
Thus we have partitioned $D_{2, \text{non-singular}}$ into $\mu$
equal-sized regions that overlap on sets of measure zero.
Each term of $\mathcal{R}_{2, \text{non-singular}}$ has absolute value
no greater than
\begin{equation}
\label{eq:lem3val1}
\frac{
\abs{
\varphi_i^* ( \vec{r}_{\vec{k}_1} )\,
\varphi_j^* ( \vec{r}_{\vec{k}_2} )\,
\varphi_k ( \vec{r}_{\vec{k}_2} )\,
\varphi_\ell ( \vec{r}_{\vec{k}_1} )
}
}{
\|\vec{r}_{\vec{k}_1} - \vec{r}_{\vec{k}_2}\|
}
\text{vol} \left(
T_{\vec{k}_1, \vec{k}_2}^{(2, \text{non-singular})}
\right)
\leq \frac{\varphi_\text{max}^4}{x_\text{max}}
\left( \frac{2x}{N_2} \right)^6
= \frac{1}{\mu} \times
64 \frac{\varphi_\text{max}^4}{x_\text{max}} x_2^6,
\end{equation}
where the inequality follows from \eq{spin-orbital_bound} and the fact
that the distance between $\mathcal{C}_x \!\left( \vec{c}_i \right)$ and
$\mathcal{C}_x \!\left( \vec{c}_j \right)$ is no smaller than
$x_\text{max}$ if $\norm{\vec{c}_i - \vec{c}_j} \geq
2\sqrt{3}x_2 + x_\text{max}$.
This expression is upper bounded by
\begin{equation}\label{bndlem3}
\frac{1}{\mu} \times
672 \pi^2 \frac{\varphi_\text{max}^4}{x_\text{max}} x_2^6.
\end{equation}
Substituting our value of $x_2$ from Eq.~\eqref{xlem3} shows that
no term has absolute value greater than (corresponding to \eq{lem3bnd} in \lem{int2})
\begin{equation}
\frac{1}{\mu} \times
\frac{672\pi^2}{\alpha^6} \left[
\log \left(
\frac{K_2 \varphi_\text{max}^4 x_\text{max}^5}{\delta}
\right)
\right]^6 \varphi_\text{max}^4 x_\text{max}^5.
\end{equation}
We show in \app{integral_discretization/int2_proof/Riemann_non-sing} that
the error may be bounded as
\begin{align}
\delta_\text{Riemann}^{(2, \text{non-singular})}
& := \abs{
S_{ijk\ell}^{(2)} \!\left( D_{2, \text{non-singular}} \right)
- \mathcal{R}_{2, \text{non-singular}}
} \nonumber \\
& \leq 256 \sqrt{3} \left( 4\gamma_1 + \sqrt{2} \right)
\varphi_\text{max}^4 x_\text{max}^5
\exp \left( -\alpha \frac{x_2}{x_\text{max}} \right).
\end{align}
\subsubsection{Second stage for \lem{int2} with spherical polar coordinates}
In this subsection we discretize the integral
$S_{ijk\ell}^{(2)} \!\left( D_{2, \text{singular}} \right)$ for the case of
nearby orbitals.
We introduce the following definition for convenience in what follows:
\begin{equation}
\eta_{\ell \ell^\prime} (\vec{r})
:= \varphi_\ell^* (\vec{r}) \, \varphi_{\ell^\prime} (\vec{r}).
\end{equation}
We define $\vec{s} := \left( \vec{r}_1 - \vec{c}_i \right)/x_2$ and
$\vec{t} := \left( \vec{r}_1 - \vec{r}_2 \right)/(\zeta x_2)$.
We write $\vec{s} = \left( s_1, s_2, s_3 \right)$ and
$\theta$ and $\phi$ for the polar and azimuthal angles of $\vec{t}$.
Next we define
\begin{equation}
f_2 \left( s_1, s_2, s_3, t, \theta, \phi \right)
:= \eta_{i\ell} \!\left( x_2\vec{s} + \vec{c}_i \right)
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
= \frac 1{\zeta x_2} \eta_{i\ell}\! \left( \vec{r}_1 \right)
\eta_{jk} \!\left( \vec{r}_2 \right)
\|\vec{r}_1 - \vec{r}_2\| \sin\theta .
\end{equation}
Then we can write
\begin{equation}
S^{(2)}_{ijk\ell} \!\left( D_{2, \text{singular}} \right)
= \zeta^2 x^5
\int_{-1}^1\dd{s_1}\
\int_{-1}^1\dd{s_2}\
\int_{-1}^1\dd{s_3}\
\int_0^1 \dd{t}\
\int_0^\pi \dd{\theta}\
\int_0^{2\pi} \dd{\phi}\
f_2 \left( s_1, s_2, s_3, t, \theta, \phi \right).
\end{equation}
Let $\vec{k}_{\vec{s}} = \left( k_1, k_2, k_3 \right)$,
where $0 \leq k_1, k_2, k_3 < N_2$,
and let $\vec{k}_{\vec{t}} = \left( k_t, k_\theta, k_\phi \right)$,
where $0 \leq k_t, k_\theta, k_\phi < N_2$. Define
$s_{k_\ell} = \left( 2k_\ell +1-N_2 \right)/N_2$
for each $\ell = 1, 2, 3$ so that
$\vec{s}_{\vec{k}_{\vec{s}}} = \left( s_{k_1}, s_{k_2}, s_{k_3} \right)$
and define
\begin{equation}
\left(
t_{\vec{k}_{\vec{t}}},
\theta_{\vec{k}_{\vec{t}}},
\phi_{\vec{k}_{\vec{t}}}
\right)
= \left(
\frac{1}{N_2} \left(k_t + \tfrac{1}{2}\right),
\frac{\pi}{N_2} \left(k_\theta + \tfrac{1}{2}\right),
\frac{2\pi}{N_2} \left(k_\phi + \tfrac{1}{2}\right)
\right)
\end{equation}
for each $\vec{k}_{\vec{t}}$. We then define
\begin{equation}
T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}^{(2, \text{singular})}
:= \left\{ \left( s_1, s_2, s_3, t, \theta, \phi \right)
\left|
\begin{array}{c}
s_{k_1} - \frac{1}{N_2} \leq s_1
\leq s_{k_1} + \frac{1}{N_2} \\
s_{k_2} - \frac{1}{N_2} \leq s_2
\leq s_{k_2} + \frac{1}{N_2} \\
s_{k_3} - \frac{1}{N_2} \leq s_3
\leq s_{k_3} + \frac{1}{N_2} \\
t_{k_t} - \frac{1}{2 N_2} \leq t
\leq t_{k_t} + \frac{1}{2 N_2} \\
\theta_{k_\theta} - \frac{\pi}{2 N_2} \leq \theta
\leq \theta_{k_\theta} + \frac{\pi}{2 N_2} \\
\phi_{k_\phi} - \frac{\pi}{N_2} \leq \phi
\leq \phi_{k_\phi} + \frac{\pi}{N_2} \\
\end{array}
\right.
\right\}.
\end{equation}
Now we define our Riemann sum:
\begin{equation}
\mathcal{R}_{2,\text{singular}}
:= \sum_{\vec{k}_{\vec{s}}, \vec{k}_{\vec{t}}}
\zeta^2 x_2^5 f_2 \left(
s_{k_1}, s_{k_2}, s_{k_3},
t_{k_t}, \theta_{k_\theta}, \phi_{k_\phi}
\right)
\text{vol} \left(
T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}
^{(2, \text{singular})}
\right),
\end{equation}
where
\begin{equation}
\text{vol} \left(
T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}
^{(2, \text{singular})}
\right)
= \int_{T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}
^{(2, \text{singular})}}
\dd{s_1}\ \dd{s_2}\ \dd{s_3}\
\dd{t}\ \dd{\theta}\ \dd{\phi}
= \frac{
\text{vol} \left( D_{2, \text{singular}} \right)
}{
N_2^6
}
= \frac{1}{\mu} \times 16\pi^2.
\end{equation}
Here
\begin{equation}
\text{vol} \left( D_{2, \text{singular}} \right)
= \int_{-1}^1\dd{s_1}\
\int_{-1}^1\dd{s_2}\
\int_{-1}^1\dd{s_3}\
\int_0^1 \dd{t}\
\int_0^\pi \dd{\theta}\
\int_0^{2\pi} \dd{\phi}
= 16\pi^2
\end{equation}
is \emph{not} the volume of $D_{2, \text{singular}}$ considered
under the usual Euclidean metric, as in \eq{int1_nonstandard_volume}.
We need to use this non-standard volume because the Jacobian introduced
by changing from Cartesian to spherical polar coordinates was absorbed
into the definition of our integrand $f_2$. Therefore, each term in
the Riemann sum has absolute value no greater than
\begin{equation}
\label{eq:lem3val2}
\abs{ \zeta^2 x_2^5
f_2 \left(
s_{k_1}, s_{k_2}, s_{k_3},
t_{k_t}, \theta_{k_\theta}, \phi_{k_\phi}
\right)
\text{vol} \left(
T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}
^{(2, \text{singular})}
\right)
}
\leq \frac{1}{\mu} \times 672 \pi^2 x_2^5 \varphi_\text{max}^4,
\end{equation}
where the inequality follows from \eq{spin-orbital_bound} applied to
the definition of $f_2$ in terms of $\eta_{i\ell}$ and $\eta_{jk}$.
Again this expression is upper bounded by Eq.~\eqref{bndlem3}
and substituting our value of $x_2$ yields the upper bound in \eq{lem3bnd}.
We show in \app{integral_discretization/int2_proof/Riemann_sing} that
\begin{equation}
\delta_\text{Riemann}^{(2, \text{singular})}
:= \abs{
S_{ijk\ell}^{(2)} \left( D_{2, \text{singular}} \right) -
\mathcal{R}_{2,\text{singular}}
}
< 2161 \pi^2 \left( 20 \gamma_1 + \sqrt{2} \right)
\varphi_\text{max}^4 x_\text{max}^5
\exp\left( -\alpha \frac{x_2}{x_\text{max}} \right).
\end{equation}
\subsubsection{Third stage for \lem{int2}}
Lastly we show that the error is properly bounded.
From \eq{total_error_bound_trunc_Riemann}, we have
\begin{equation}
\delta_\text{total}^{(2, \text{non-singular})}
:= \abs{
S_{ijk\ell}^{(2)} \left( \R^6 \right) -
\mathcal{R}_{2, \text{non-singular}}
}
\leq \delta_\text{trunc}^{(2, \text{non-singular})} +
\delta_\text{Riemann}^{(2, \text{non-singular})}
\end{equation}
and
\begin{equation}
\delta_\text{total}^{(2, \text{singular})}
:= \abs{
S_{ijk\ell}^{(2)} \left( \R^6 \right) -
\mathcal{R}_{2, \text{singular}}
}
\leq \delta_\text{trunc}^{(2, \text{singular})} +
\delta_\text{Riemann}^{(2, \text{singular})}.
\end{equation}
We have given a bound that holds simultaneously for both
$\delta_\text{trunc}^{(2, \text{non-singular})}$
and $\delta_\text{trunc}^{(2, \text{singular})}$,
and we have given a bound for
$\delta_\text{Riemann}^{(2, \text{singular})}$
that is larger (as a function of $x_2$) than our bound for
$\delta_\text{Riemann}^{(2, \text{non-singular})}$.
We are therefore able to assert that the error of our Riemann sum
approximation, no matter which we choose, is always bounded above by
\begin{equation}
K_2 \varphi_\text{max}^4 x_\text{max}^5
\exp \left( -\alpha \frac{x_2}{x_\text{max}} \right),
\end{equation}
where
\begin{equation}
K_2
:= \frac{128\pi}{\alpha^6}(\alpha+2) +
2161 \pi^2 \left( 20 \gamma_1 + \sqrt{2} \right).
\end{equation}
We have also found that the terms in the Riemann sum are upper bounded by
Eqs.~\eqref{eq:lem3val1} and \eqref{eq:lem3val2} in the two cases.
A bound that will hold for both is given by
\begin{equation}\label{bndlem3}
\frac{1}{\mu} \times
672 \pi^2 \frac{\varphi_\text{max}^4}{x_\text{max}} x_2^6,
\end{equation}
Then substituting our value of $x_2$ from Eq.~\eqref{xlem3} shows that the error
is upper bounded by $\delta$. This last step completes our proof of \lem{int2}.
The remainder of this subsection gives the details for some of the steps above.
\subsubsection{Bounding $\delta_\text{trunc}^{(2)}$ for \lem{int2}}
\label{app:integral_discretization/int2_proof/trunc}
Note that $\mathcal{B}_{x_2} \!\left( \vec{c}_i \right) \times
\mathcal{B}_{x_2} \!\left( \vec{c}_j \right)$ is a subset of both
$D_{2, \text{non-singular}}$ and $D_{2, \text{singular}}$.
The former is immediately apparent. To see the latter, observe that
$\norm{\vec{c}_i - \vec{c}_j} < 2\sqrt{3}x_2 + x_\text{max}$ implies that
the maximum possible value of $\norm{\vec{r}_1 - \vec{r}_2}$ for any
$\vec{r}_1 \in \mathcal{B}_x \!\left( \vec{c}_i \right)$ and
$\vec{r}_2 \in \mathcal{B}_x \!\left( \vec{c}_j \right)$ is
$2\sqrt{3}x_2 + 2x_2+ x_\text{max} \le (2\sqrt{3}+3)x_2=\zeta x_2$.
Therefore,
\begin{align}
\delta_\text{trunc}^{(2)}
& \leq \varphi_\text{max}^4
\int_{\R^3 \setminus \mathcal{B}_{x_2} \left( \vec{c}_i \right)}
\dd{\vec{r}_1}
\int_{\R^3 \setminus \mathcal{B}_{x_2} \left( \vec{c}_j \right)}
\dd{\vec{r}_2}
\frac{
e^{ -\alpha \norm{\vec{r}_1 - \vec{c}_i}/x_\text{max} }
e^{ -\alpha \norm{\vec{r}_2 - \vec{c}_j}/x_\text{max} }
}{
\norm{\vec{r}_1 - \vec{r}_2}
} \nonumber \\
& = \varphi_\text{max}^4
\int_{\R^3 \setminus \mathcal{B}_{x_2} ( \vec{0} )}
\dd{\vec{s}}\ e^{ -\alpha s/x_\text{max} }
\Lambda_{\alpha/x_\text{max}, x_2} \left(
\vec{s} + \vec{c}_i - \vec{c}_j
\right),
\end{align}
where we have used \eq{spin-orbital_decay} and,
with the change of variables $\vec{s} = \vec{r}_1 - \vec{c}_i$,
the definition of $\Lambda$ from \eq{exp_Coulomb_potential}.
By \lem{exp_Coulomb_potential_bound}, for $\|\vec{s} + \vec{c}_i - \vec{c}_j\|\le x_2$ we get
\begin{equation}
\Lambda_{\alpha/x_\text{max}, x_2} \left(
\vec{s} + \vec{c}_i - \vec{c}_j
\right)
\leq \frac{8\pi x_\text{max}^2}{\alpha^2}
e^{ -\alpha s/x_\text{max} },
\end{equation}
and for $\norm{\vec{s} + \vec{c}_i - \vec{c}_j} > x_2$ we get
\begin{align}
\Lambda_{\alpha/x_\text{max}, x_2} \left(
\vec{s} + \vec{c}_i - \vec{c}_j
\right)
& \le \frac{16\pi x_\text{max}^3}{\alpha^3}
\frac{e^{ -\alpha s/x_\text{max} }}{\norm{\vec{s} + \vec{c}_i - \vec{c}_j}} \nonumber \\
&<\frac{16\pi x_\text{max}^3}{x_2\alpha^3} e^{ -\alpha s/x_\text{max} }\nonumber \\
&\le \frac{16\pi x_\text{max}^2}{\alpha^3} e^{ -\alpha s/x_\text{max} }.
\end{align}
In either case we then get
\begin{equation}
\delta_\text{trunc}^{(2)}
\leq \frac{8\pi}{\alpha^3}
\varphi_\text{max}^4 x_\text{max}^2 (\alpha+2)
\exp\left( -\frac{\alpha}{2} \frac{x_2}{x_\text{max}} \right)
\int_{\R^3 \setminus \mathcal{B}_{x_2} ( \vec{0} )}
\dd{\vec{s}}\ e^{ -\alpha s/x_\text{max} }.
\end{equation}
We use the fact that $(z^2 + 2z + 2) e^{-z} < 4 e^{-z/2}$ for any $z>0$ to find
\begin{equation}
\int_{\R^3 \setminus \mathcal{B}_{x_2}\! \left( \vec{0} \right)} \dd{\vec{s}}\
e^{-\mu s}
= 4\pi \int_{x_2}^\infty \dd{s}\ e^{-\mu s} s^2
= 4\pi
\left( \frac{x_2^2}{\mu} + \frac{2x_2}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu x}
< \frac{16\pi}{\mu^3} e^{-\mu x_2/2},
\end{equation}
which gives us
\begin{equation}
\delta_\text{trunc}^{(2)}
< \frac{128\pi}{\alpha^6}(\alpha+2)
\varphi_\text{max}^4 x_\text{max}^5
\exp\left( -\alpha \frac{x_2}{x_\text{max}} \right).
\end{equation}
\subsubsection{Bounding $\delta_\text{Riemann}^{(2, \text{non-singular})}$ for \lem{int2}}
\label{app:integral_discretization/int2_proof/Riemann_non-sing}
Following \app{integral_discretization/preliminaries/proof_structure}, we note that
\begin{equation}
\text{vol} \left( D_{2, \text{non-singular}} \right)
= 64x_2^6
\end{equation}
and
\begin{equation}
\text{diam} \left( T_{\vec{k}_1, \vec{k}_2}^{(2, \text{non-singular})} \right)
= \sqrt{
\text{diam} \left(
\mathcal{C}_{x_2/N_2} ( \vec{r}_{\vec{k}_1} )
\right)^2 + \text{diam} \left(
\mathcal{C}_{x_2/N_2} ( \vec{r}_{\vec{k}_2} )
\right)^2
}
= 2\sqrt{6} x_2/N_2
\end{equation}
for each $\vec{k}_1$ and $\vec{k}_2$. To find a bound on
$\delta_\text{Riemann}^{(2, \text{non-singular})}$, it only remains
to find a bound on the derivative of the integrand.
To bound the derivative of the integrand, we first find bounds on
the gradients of the numerator and the denominator separately.
The gradient of the numerator can be bounded using
the product rule and triangle inequality, as well as
\eq{spin-orbital_bound} and \eq{spin-orbital_first_derivative_bound}:
\begin{align}
& \norm{
\left( \nabla_1 \oplus \nabla_2 \right) \left[
\varphi_i^* ( \vec{r}_1 ) \, \varphi_j^* ( \vec{r}_2 )\,
\varphi_k ( \vec{r}_2 ) \,\varphi_\ell ( \vec{r}_1 )
\right]
}^2 \nonumber \\
& = \norm{
\nabla_1 \left[
\varphi_i^* ( \vec{r}_1 )\,
\varphi_j^* ( \vec{r}_2 )\,
\varphi_k ( \vec{r}_2 )\,
\varphi_\ell ( \vec{r}_1 )
\right]
}^2 + \norm{
\nabla_2 \left[
\varphi_i^* ( \vec{r}_1 )
\varphi_j^* ( \vec{r}_2 )
\varphi_k ( \vec{r}_2 )
\varphi_\ell ( \vec{r}_1 )
\right]
}^2 \nonumber \\
& = \left( \abs{\varphi_j^* ( \vec{r}_2 )}
\abs{\varphi_k ( \vec{r}_2 )}
\norm{
\nabla_1 \left[
\varphi_i^* ( \vec{r}_1 )\,
\varphi_\ell ( \vec{r}_1 )
\right]
}\right)^2 +
\left( \abs{\varphi_i^* ( \vec{r}_1 )}
\abs{\varphi_\ell ( \vec{r}_1 )}
\norm{
\nabla_2 \left[
\varphi_j^* ( \vec{r}_2 )\,
\varphi_k ( \vec{r}_2 )
\right]
}\right)^2 \nonumber \\
& \leq \left( \varphi_\text{max}^2
\norm{
\nabla_1 \left[
\varphi_i^* ( \vec{r}_1 )\,
\varphi_\ell ( \vec{r}_1 )
\right]
}\right)^2 + \left(
\varphi_\text{max}^2
\norm{
\nabla_2 \left[
\varphi_j^* ( \vec{r}_2 )\,
\varphi_k ( \vec{r}_2 )
\right]
}\right)^2 \nonumber \\
& \leq \left( \varphi_\text{max}^2
\abs{\varphi_\ell ( \vec{r}_1 )}
\norm{
\nabla_1 \left[
\varphi_i^* ( \vec{r}_1 )
\right]
} +
\varphi_\text{max}^2
\abs{\varphi_i^* ( \vec{r}_1 )}
\norm{
\nabla_1 \left[
\varphi_\ell ( \vec{r}_1 )
\right]
}\right)^2 \nonumber \\ &\qquad +\left(
\varphi_\text{max}^2
\abs{\varphi_k ( \vec{r}_2 )}
\norm{
\nabla_2 \left[
\varphi_j^* ( \vec{r}_2 )
\right]
} +
\varphi_\text{max}^2
\abs{\varphi_j^* ( \vec{r}_2 )}
\norm{
\nabla_2 \left[
\varphi_k ( \vec{r}_2 )
\right]
}\right)^2 \nonumber \\
& \leq 2 \left(2\gamma_1 \frac{\varphi_\text{max}^4}{x_\text{max}}\right)^2.
\end{align}
The gradient of the denominator can be computed directly:
\begin{equation}
\norm{\left( \nabla_1 \oplus \nabla_2 \right) \norm{\vec{r}_1 - \vec{r}_2}}
= \norm{
\left( \nabla_1 \norm{\vec{r}_1 - \vec{r}_2} \right) \oplus
\left( \nabla_2 \norm{\vec{r}_1 - \vec{r}_2} \right)
}
= \norm{
\left(
\frac{\vec{r}_1 - \vec{r}_2}{\norm{\vec{r}_1 - \vec{r}_2}}
\right) \oplus
\left(
\frac{\vec{r}_2 - \vec{r}_1}{\norm{\vec{r}_2 - \vec{r}_1}}
\right)
}
= \sqrt{2}
\end{equation}
Again by the product rule and the triangle inequality,
\begin{equation}
\norm{
(\nabla_1 \oplus \nabla_2) \frac{
\varphi_i^* ( \vec{r}_1 )\, \varphi_j^* ( \vec{r}_2 )\,
\varphi_k ( \vec{r}_2 )\, \varphi_\ell ( \vec{r}_1 )
}{
\norm{\vec{r}_1 - \vec{r}_2}
}
}
\leq \frac{2\sqrt{2}\gamma_1}{\norm{\vec{r}_1 - \vec{r}_2}}
\frac{\varphi_\text{max}^4}{x_\text{max}} +
\frac{\sqrt{2}}{\norm{\vec{r}_1 - \vec{r}_2}^2}
\varphi_\text{max}^4
\leq \sqrt{2}\left( 2\gamma_1 + 1 \right)
\frac{\varphi_\text{max}^4}{x_\text{max}^2}.
\end{equation}
The last inequality follows from our assumption that
$\norm{\vec{c}_i - \vec{c}_j} > 2\sqrt{3}x_2 + x_\text{max}$, which implies that
the distance between $\mathcal{C}_{x_2} \!\left( \vec{c}_i \right)$ and
$\mathcal{C}_{x_2} \!\left( \vec{c}_j \right)$ is greater than $x_\text{max}$.
Therefore,
\begin{equation}
\delta_\text{Riemann}^{(2)}
\leq \frac 12 \left( \sqrt{2} \left( 2\gamma_1 + 1 \right)
\frac{\varphi_\text{max}^4}{x_\text{max}^2}\right)\left( 64 x_2^6 \right)\left(2\sqrt{6} \frac {x_2}{N_2}\right)
\leq 128 \sqrt{3} \left( 2\gamma_1 + 1 \right)
\varphi_\text{max}^4 x_\text{max}^5
\exp \left( -\alpha \frac{x_2}{x_\text{max}} \right).
\end{equation}
\subsubsection{Bounding $\delta_\text{Riemann}^{(2, \text{singular})}$ for \lem{int2}}
\label{app:integral_discretization/int2_proof/Riemann_sing}
Following \app{integral_discretization/preliminaries/proof_structure},
we again note that $\text{vol} \left( D_{2, \text{singular}} \right) = 16\pi^2$.
We also observe that
\begin{equation}
\text{diam} \left(
T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}
^{(2, \text{singular})}
\right)
= \frac{1}{N_2} \sqrt{2^2 + 2^2 + 2^2 + 1^2 + \pi^2 + 4\pi^2}
= \frac{1}{N_2} \sqrt{13 + 5\pi^2}
< \frac{8}{N_2},
\end{equation}
where we are again treating the variables $s$, $\theta$ and $\phi$ formally
as Euclidean coordinates instead of spherical polar. It then remains to
bound the derivative of the integrand
\begin{equation}
f_2 \left( s_1, s_2, s_3, t, \theta, \phi \right)
= \eta_{i\ell} \!\left( x\vec{s} + \vec{c}_{i\ell} \right)
\eta_{jk} \!\left( x\vec{s} - \zeta x\vec{t} + \vec{c}_i \right)
t \sin\theta,
\end{equation}
where $\vec{s} = \left( s_1, s_2, s_3 \right)$.
The derivative of the integral is bounded as follows. Define
$\nabla_s = \left(
\frac{\partial}{\partial s_1},
\frac{\partial}{\partial s_2},
\frac{\partial}{\partial s_3}
\right)$ and
$\nabla_t = \left(
\frac{\partial}{\partial t},
\frac{\partial}{\partial \phi},
\frac{\partial}{\partial \theta}
\right)$. By the product rule and the triangle inequality,
\begin{align}
\norm{ \left( \nabla_s \oplus \nabla_t \right) f_2 }
& \leq \abs{
\eta_{jk}\! \left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
}
\norm{
\left( \nabla_s \oplus \nabla_t \right)
\eta_{i\ell} \!\left( x_2\vec{s} + \vec{c}_i \right)
} \nonumber \\ &\qquad +
\abs{
\eta_{i\ell} \left( x_2\vec{s} + \vec{c}_i \right)
}
\norm{
\left( \nabla_s \oplus \nabla_t \right)
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
} \nonumber \\
& \leq \varphi_\text{max}^2
\norm{
\left( \nabla_s \oplus \nabla_t \right)
\eta_{i\ell} \!\left( x_2\vec{s} + \vec{c}_i \right)
} +
\varphi_\text{max}^2
\norm{
\left( \nabla_s \oplus \nabla_t \right)
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
},
\end{align}
where the last inequality follows from \eq{spin-orbital_bound}. We also have
\begin{align}
\norm{
\left( \nabla_s \oplus \nabla_t \right)
\eta_{i\ell} \! \left( x_2\vec{s} + \vec{c}_i \right)
}
& = \norm{\nabla_s \eta_{i\ell} \! \left( x_2\vec{s} + \vec{c}_i \right)} \nonumber \\
& \leq \abs{\varphi_\ell \!\left( x_2\vec{s} + \vec{c}_i \right)}
\norm{\nabla_s \varphi_i^* \!\left( x_2\vec{s} + \vec{c}_i \right)} +
\abs{\varphi_i^* \!\left( x_2\vec{s} + \vec{c}_i \right)}
\norm{\nabla_s \varphi_\ell \!\left( x_2\vec{s} + \vec{c}_i \right)} \nonumber \\
& \leq x_2 \varphi_\text{max}
\norm{\nabla \varphi_i^* \!\left( x_2\vec{s} + \vec{c}_i \right)} +
x_2 \varphi_\text{max}
\norm{\nabla \varphi_\ell \!\left( x_2\vec{s} + \vec{c}_i \right)} \nonumber \\
& \leq 2 x_2 \gamma_1 \frac{\varphi_\text{max}^2}{x_\text{max}},
\end{align}
where $\nabla$ in the second-to-last inequality refers to the gradient operator
expressed in the usual basis and the final inequality follows from
\eq{spin-orbital_first_derivative_bound}. Finally, we have
\begin{align}
& \norm{
\left( \nabla_s \oplus \nabla_t \right)
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
}\nonumber \\
& \leq \norm{
\nabla_s \!\left[
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
\right]
} +
\norm{
\nabla_t \!\left[
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
t \sin\theta
\right]
} \nonumber \\
& \leq \abs{t \sin\theta} \norm{
\nabla_s \!\left[
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
\right]
} +
\abs{t \sin\theta} \norm{
\nabla_t \!\left[
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
\right]
} +\abs{
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
} \norm{ \nabla_t (t \sin\theta) } \nonumber \\
& \leq \norm{
\nabla_s \!\left[
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
\right]
} + \norm{
\nabla_t \!\left[
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
\right]
} +
\varphi_\text{max}^2 \norm{ \nabla_t (t \sin\theta) },
\end{align}
where we have again used the product rule and the triangle inequality and,
in the last inequality, \eq{spin-orbital_bound}.
We have also used the bounds on the gradient operator $\nabla_t$ in the same was as in \app{integral_discretization/int1_proof/Riemann-sing}.
We note that
$\norm{\nabla_t (t \sin\theta)} \leq \sqrt{2}$, $\norm{
\nabla_s \left(
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
\right)
} \leq 2 x \gamma_1 \varphi_\text{max}^2 / x_\text{max}$ (as above) and
\begin{align}
& \norm{
\nabla_t
\eta_{jk} \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
}\nonumber \\
& \leq \abs{\varphi_k \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)}
\norm{
\nabla_t \varphi_j^* \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
}
+ \abs{\varphi_j^* \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)}
\norm{
\nabla_t \varphi_k \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
} \nonumber \\
& \leq \zeta x_2 \varphi_\text{max} \norm{
\nabla \varphi_j^* \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
} +
\zeta x_2 \varphi_\text{max} \norm{
\nabla \varphi_k \!\left( x_2\vec{s} - \zeta x_2\vec{t} + \vec{c}_i \right)
} \nonumber \\
& \leq 2\zeta x_2 \gamma_1 \frac{\varphi_\text{max}^2}{x_\text{max}}.
\end{align}
In summary, we have shown
\begin{equation}
\norm{ \left( \nabla_s \oplus \nabla_t \right) f_2 }
\leq \left( 20 \gamma_1 \frac{x_2}{x_\text{max}} + \sqrt{2} \right)
\varphi_\text{max}^4.
\end{equation}
We can now compute our bound on $\delta_\text{Riemann}^{(2, \text{singular})}$.
Including the factor of $\zeta^2 x_2^5$ in the integral and using \eq{Riemann_error},
\begin{align}
\delta_\text{Riemann}^{(2, \text{singular})}
& \leq \frac 12 \zeta^2 x_2^5 f_\text{max}^\prime
\text{vol} \left( D_{2, \text{singular}} \right)
\max_{\vec{k}_{\vec{s}}, \vec{k}_{\vec{t}}} \text{diam} \left(
T_{\vec{k}_{\vec{s}} \oplus \vec{k}_{\vec{t}}}
^{(2, \text{singular})}
\right) \nonumber \\
& < \frac 12 \zeta^2 x_2^5 \times
\left( 20 \gamma_1 \frac{x_2}{x_\text{max}} + \sqrt{2} \right)
\varphi_\text{max}^4 \times
2\zeta \pi^2 \times 8/N_2 \nonumber \\
& < 2161 \pi^2
\left( 20 \gamma_1 + \sqrt{2} \frac{x_\text{max}}{x_2} \right)
\varphi_\text{max}^4 x_\text{max}^5 \frac{x_\text{max}}{x_2}
\exp\left( -\alpha \frac{x_2}{x_\text{max}} \right) \nonumber \\
& \leq 2161 \pi^2 \left( 20 \gamma_1 + \sqrt{2} \right)
\varphi_\text{max}^4 x_\text{max}^5
\exp\left( -\alpha \frac{x_2}{x_\text{max}} \right).
\end{align}
\section{Riemann Sum Approximations of Hamiltonian Coefficients}
\label{app:integral_discretization}
The aim of this Appendix is to prove \lem{int0}, \lem{int1} and \lem{int2}.
We begin in \app{integral_discretization/preliminaries} with preliminary matters
that are integral to the proofs themselves.
We then prove the Lemmas in
\app{integral_discretization/int0_proof},
\app{integral_discretization/int1_proof} and
\app{integral_discretization/int2_proof} respectively.
Throughout this Appendix, we employ the following two notational conventions.
\begin{enumerate}
\item The vector symbol $\vec{\bullet}$ refers to an element of $\R^3$.
We write $\bullet$ for the Euclidean length of $\vec{\bullet}$.
Thus $\vec{v}$ refers to a $3$-vector of magnitude $v$.
We denote the zero vector as $\vec{0} = (0, 0, 0)$.
We use $\oplus$ to denote vector concatenation:
if $\vec{v} = \left( v_1, v_2, v_3 \right)$
and $\vec{w} = \left( w_1, w_2, w_3 \right)$, we write
$\vec{v} \oplus \vec{w} = \left(v_1, v_2, v_3, w_1, w_2, w_3 \right)$.
The gradient operator over $\R^6$ is then written as
$\nabla_1 \oplus \nabla_2$.
\item If $x$ is a positive real number and $\vec{v}$ is a $3$-vector,
we write $\mathcal{B}_x (\vec{v})$ for the closed ball of radius $x$
centered at $\vec{v}$ and $\mathcal{C}_x (\vec{v})$ for the closed
cube of side length $2x$ centered at $\vec{v}$.
Thus $\mathcal{B}_x (\vec{v}) \subset \mathcal{C}_x (\vec{v})$
and $\mathcal{B}_y (\vec{v}) \not\subseteq \mathcal{C}_x (\vec{v})$
whenever $y > x$.
\end{enumerate}
This notation will be used extensively and without comment in what follows.
\input{preliminaries}
\input{int0_proof}
\input{int1_proof}
\input{int2_proof}
\section{Introduction}
\label{sec:intro}
The first quantum algorithm for quantum chemistry was introduced nearly a
decade ago \cite{Aspuru-Guzik2005}. That algorithm was based on the
Trotter-Suzuki decomposition, which Lloyd and Abrams first applied to quantum
simulation in \cite{Lloyd1996,Abrams1997}. The Trotter-Suzuki decomposition has
been used in almost all quantum algorithms for quantum chemistry since then
\cite{Jones2012,Veis2010,Wang2014,Li2011,Yung2013,Kassal2008,
Toloui2013,Whitfield2013b,Whitfield2015,Wecker2014,Hastings2015,
Poulin2014,McClean2014,BabbushTrotter},
with the exception of the adiabatic algorithm detailed in \cite{BabbushAQChem},
the variational quantum eigensolver approach described in
\cite{Peruzzo2013,McClean2015,OMalley2016}, and in our prior papers using
the Taylor series technique \cite{BabbushSparse1,Kivlichan2016}. Recently, there has been
substantial renewed interest in these algorithms due to the low qubit
requirement compared with other algorithms such as factoring, together with the
scientific importance of the electronic structure problem. This led to a series
of papers establishing formal bounds on the cost of simulating various molecules
\cite{Wecker2014,Hastings2015,Poulin2014,McClean2014,BabbushTrotter}.
Whereas qubit requirements for the quantum chemistry problem seem modest,
using arbitrarily high-order Trotter formulas, the tightest-known upper bound on
the gate count of the second-quantized, Trotter-based quantum simulation of
chemistry is $\widetilde{\cal O}(N^{8+o(1)} t / \epsilon^{o(1)})$
\cite{Berry2006,Wiebe2011}\footnote{We use the typical computer science
convention that $f\in \Theta(g)$, for any functions $f$ and $g$, if $f$ is
asymptotically upper and lower bounded by multiples of $g$, ${\cal O}$ indicates
an asymptotic upper bound, $\widetilde{{\cal O}}$ indicates an asymptotic upper
bound suppressing any polylogarithmic factors in the problem parameters,
$\Omega$ indicates the asymptotic lower bound and $f \in o(g)$ implies
$f / g \rightarrow 0$ in the asymptotic limit.}, where $N$ is the number of
spin-orbitals and $\epsilon$ is the required accuracy. However, using
significantly more practical Trotter decompositions, the best known gate
complexity for this quantum algorithm is
$\widetilde{\cal O}(N^9 \sqrt{t^3 / \epsilon})$ \cite{Hastings2015}.
Fortunately, recent numerics suggest that the scaling for real molecules is
closer to $\widetilde{\cal O}(N^6 \sqrt{t^3 / \epsilon})$ \cite{Poulin2014} or
$\widetilde{\cal O}(Z^3 N^4 \sqrt{t^3 / \epsilon})$ \cite{BabbushTrotter}, where
$Z$ is the largest nuclear charge in the molecule. Still, the Trotter-based
quantum simulation of many molecular systems remains a costly proposition \cite{Gibney2014,Mueck2015}.
In Ref.~\cite{BabbushSparse1}, we introduced two novel quantum algorithms for
chemistry based on the truncated Taylor series simulation method of
\cite{Berry2015}, which are exponentially more precise than algorithms using the
Trotter-Suzuki decomposition. Our first algorithm, referred to as the
``database'' algorithm, was shown to have gate count scaling as
$\widetilde{\cal O}(N^4 \| H\| t)$. Our second algorithm, referred to as the
``on-the-fly'' algorithm, was shown to have the lowest scaling of any approach
to quantum simulation previously in the literature, $\widetilde{\cal O}(N^5 t)$.
Both of these algorithms use a second-quantized representation of the
Hamiltonian; in this paper we employ a more compressed, first-quantized
representation of the Hamiltonian known as the configuration interaction (CI)
matrix.
We also analyze the on-the-fly integration strategy far more rigorously, by making the
assumptions explicit and rigorously deriving error bounds.
Our approach combines a number of improvements:
\begin{itemize}
\item a novel 1-sparse decomposition of the CI matrix (improving over that in \cite{Toloui2013}),
\item a self-inverse decomposition of 1-sparse matrices as introduced in \cite{Berry2013},
\item the exponentially more precise simulation techniques of \cite{Berry2015},
\item and the on-the-fly integration strategy of \cite{BabbushSparse1}.
\end{itemize}
The paper is outlined as follows.
In \sec{summary},
we summarize the key results of this paper,
and note the improvements presented here over previous approaches.
In \sec{encoding},
we introduce the configuration basis encoding of the wavefunction.
In \sec{decomp1},
we show how to decompose the Hamiltonian into 1-sparse unitary matrices.
In \sec{oracle},
we use the decomposition of \sec{decomp1} to construct a circuit which provides
oracular access to the Hamiltonian matrix entries,
assuming access to $\textsc{sample}(w)$ from \cite{BabbushSparse1}.
In \sec{simulation},
we review the procedures in \cite{Berry2015} and \cite{BabbushSparse1} to
demonstrate that this oracle circuit can be used to effect a quantum simulation
which is exponentially more precise than using a Trotter-Suzuki decomposition
approach.
In \sec{conclusion},
we discuss applications of this algorithm and future research directions.
\subsection{Preliminaries}
\label{app:integral_discretization/preliminaries}
The purpose of this subsection is to present two key discussions
that will be needed at many points in the proofs of this Appendix.
First, in \app{integral_discretization/preliminaries/proof_structure},
we discuss the general structure of the proofs of \lem{int0}, \lem{int1}
and \lem{int2}.
Second, in \app{integral_discretization/preliminaries/exp_Coulomb_potential},
we prove an ancillary Lemma (\lem{exp_Coulomb_potential_bound})
that we use several times.
The ancillary Lemma offers bounds on the function
\begin{equation}
\label{eq:exp_Coulomb_potential}
\Lambda_{\mu, x} (\vec{c})
:= \int_{\R^3 \setminus \mathcal{B}_x (\vec{0})}
\frac{\exp(-\mu r)}{\norm{\vec{r}-\vec{c}}} \dd{\vec{r}},
\end{equation}
where $\mu$ is a positive real constant and $\vec{c}$ is a constant vector.
The Lemma is stated as follows.
\begin{lemma}
\label{lem:exp_Coulomb_potential_bound}
Suppose $\mu$ and $x$ are positive real numbers and
$\vec{c} \in \R^3$ is some constant vector. Then
\begin{equation}
\label{eq:exp_Coulomb_potential_bound_c>x}
\Lambda_{\mu, x} (\vec{c})
< \frac{16\pi}{\mu^3 c} e^{-\mu x/2},
\end{equation}
and for $c \leq x$,
\begin{equation}
\label{eq:exp_Coulomb_potential_bound_c<x}
\Lambda_{\mu, x} (\vec{c}) < \frac{8\pi}{\mu^2} e^{-\mu x/2}.
\end{equation}
\end{lemma}
The function $\Lambda_{\mu, x} (\vec{c})$ appears in bounds derived
in the proofs of \lem{int1} and \lem{int2}. Although it is possible to compute
an analytic formula for the value of integral, the result is unwieldy.
The bounds of \lem{exp_Coulomb_potential_bound} are then used to ensure
meaningfully expressed bounds on the Riemann sum approximations.
\subsubsection{Structure of the Proofs}
\label{app:integral_discretization/preliminaries/proof_structure}
The proofs of \lem{int0}, \lem{int1} and \lem{int2} each roughly follow
a general structure consisting of the following three stages,
though with minor deviations.
\textbf{First stage:}
The domain of integration is truncated to a domain $D$.
The size of $D$ is specified by a positive real parameter $x$,
which the conditions of the lemmas ensure is at least $x_{\max}$.
We then bound the error due to the truncation
\begin{equation}
\delta_\text{trunc}
:= \abs{
\int_{\R^d} f\left(\vec{r}\right) \dd{\vec{r}} -
\int_{D} f\left(\vec{r}\right) \dd{\vec{r}}
},
\end{equation}
where $f: \R^d \rightarrow \R$ refers to the relevant integrand.
\textbf{Second stage:}
We specify a Riemann sum that is designed to approximate this truncated integral
and give a bound on the error $\delta_\text{Riemann}$ of this
Riemann sum approximation. We specify the number of terms in the Riemann sum
in order to give the bound on $\mu$ in the lemma. We also give a bound on
the absolute value of each term in the Riemann sum using the value of $x$
specified in the first stage.
\textbf{Third stage:}
In the final stage of each proof, we bound the total error
\begin{equation}
\delta_\text{total} :=
\abs{
\int_{\R^d} f(\vec{r}) \, \dd{\vec{r}} -
\sum_T f(\vec{r}_T) \text{vol}(T)
}
\end{equation}
via the triangle inequality as
\begin{equation}
\label{eq:total_error_bound_trunc_Riemann}
\delta_\text{total}
\leq \delta_\text{trunc} + \delta_\text{Riemann}.
\end{equation}
Our choice of $x$ then ensures that the error is bounded by $\delta$.
To be more specific about the approach in the second stage,
we partition $D$ into regions $T$, and the Riemann sum approximates
the integral over each $T$ with the value of the integrand multiplied by
the volume of $T$. The error due to this approximation is bounded by
observing the following.
Suppose $f: \R^d \rightarrow \R$ is once-differentiable and
$f^\prime_{\max}$ is a bound on its first derivative.
If $\vec{r}_T$ is any element of $T$, we will seek to bound the error
of the approximation
\begin{equation}
\int_T f\left(\vec{r}\right) \dd{\vec{r}}
\approx f\left(\vec{r}_T\right) \text{vol}(T),
\end{equation}
where $\text{vol}(T)$ is the $d$-dimensional hypervolume of the set $T$.
The error of this approximation is
\begin{equation}
\delta_T
:= \abs{
\int_T
\left[ f\!\left(\vec{r}\right) - f\!\left(\vec{r}_T\right) \right]
\dd{\vec{r}}
},
\end{equation}
which can be bounded as follows:
\begin{equation}
\delta_T
\leq \int_T
\abs{f\!\left(\vec{r}\right) - f\!\left(\vec{r}_T\right)}\dd{\vec{r}}
\leq \max_{\vec{r} \in T}
\abs{f\!\left(\vec{r}\right) - f\!\left(\vec{r}_T\right)}
\text{vol}(T)
\leq f^\prime_{\max}\max_{\vec{r} \in T}
\norm{\vec{r} -\vec{r}_T}
\text{vol}(T)
\end{equation}
where
\begin{equation}
\text{vol}(T)
= \int_T \dd{\vec{r}}, \qquad f^\prime_{\max}
= \max_{\vec r} \norm{\nabla f(\vec r)}.
\end{equation}
We will choose the points $\vec{r}_T$ in the centers of the regions $T$, so that
\begin{equation}
\delta_T
\leq \frac 12 f^\prime_{\max} \text{diam}(T) \text{vol} (T),
\end{equation}
where
\begin{equation}
\text{diam}(T) := \max_{\vec{r}_1,\vec{r}_2 \in T} \norm{\vec{r}_1-\vec{r}_2}.
\end{equation}
The Riemann sum approximations we define will then take the form
\begin{equation}
\int_D f(\vec{r})\, \dd{\vec{r}} \approx \sum_T f(\vec{r}_T) \text{vol}(T),
\end{equation}
and the error of this approximation is
\begin{equation}
\delta_\text{Riemann} :=
\abs{\int_D f(\vec{r}) \,\dd{\vec{r}}- \sum_T f(\vec{r}_T) \text{vol}(T)},
\end{equation}
which can be bounded via the triangle inequality as
\begin{equation}
\label{eq:Riemann_error}
\delta_\text{Riemann}
\leq \sum_T \delta_T
\leq \frac 12 f^\prime_{\max} \text{vol}(D) \left(\max_T \text{diam}(T)\right).
\end{equation}
\subsubsection{Proof of \lem{exp_Coulomb_potential_bound}}
\label{app:integral_discretization/preliminaries/exp_Coulomb_potential}
We prove the Lemma by deriving exact formulae for $\Lambda_{\mu, x} (\vec{c})$
in the cases $c \leq x$ and $c > x$ and then deriving bounds on these formulae
that have simpler functional forms.
To derive exact formulae for $\Lambda_{\mu, x} (\vec{c})$,
we use the Laplace expansion
\begin{equation}
\frac{1}{\norm{\vec{r}-\vec{c}}}
= \sum_{\ell = 0}^\infty \sum_{m=-\ell}^\ell (-1)^m
I_{\ell, -m} (\vec{r}) R_{\ell, m} (\vec{c}),
\end{equation}
where $R_{\ell, m}$ and $I_{\ell, m}$ refer to the regular and irregular solid
spherical harmonic functions, respectively, and $r \geq c$. That is to say,
\begin{equation}
R_{\ell, m} (\vec{r})
:= \sqrt{\frac{4\pi}{2\ell+1}} r^\ell Y_{\ell, m} (\theta,\phi)
\end{equation}
and
\begin{equation}
I_{\ell, m} (\vec{r})
:= \sqrt{\frac{4\pi}{2\ell+1}} \frac{1}{r^{\ell+1}} Y_{\ell, m} (\theta,\phi),
\end{equation}
where
\begin{equation}
Y_{\ell, m} (\theta, \phi)
:= \sqrt{\frac{2\ell + 1}{4\pi} \frac{(\ell-m)!}{(\ell+m)!}}
e^{i m \phi} P_\ell^m (\cos\theta)
\end{equation}
are the spherical harmonics (see \S 14.30(i) in \cite{NIST:DLMF}),
$P_\ell^m$ are the associated Legendre polynomials, and $\theta$
and $\phi$ are respectively the polar and azimuthal angles of $\vec{r}$.
Via Eq.~(8) of \S 14.30(ii) in \cite{NIST:DLMF}, we have
\begin{equation}
\int_0^{2\pi} \dd{\phi} \int_0^\pi \dd{\theta}\
I_{\ell, m} (\theta,\phi) \sin\theta
= \frac{4\pi}{r} \delta_{m,0} \delta_{\ell,0}
\end{equation}
and
\begin{equation}
\int_0^{2\pi} \dd{\phi} \int_0^\pi \dd{\theta}\
R_{\ell, m} (\theta,\phi) \sin\theta
= 4\pi \delta_{m,0} \delta_{\ell,0},
\end{equation}
where $\delta_{a,b}$ denotes the Kronecker delta.
If $c \leq x$:
\begin{align}
\label{eq:Lamba_c<x_exact}
\Lambda_{\mu, x} (\vec{c})
& = \sum_{\ell = 0}^\infty \sum_{m=-\ell}^\ell (-1)^m R_{\ell, m} (\vec{c})
\int_{\R^3 \setminus \mathcal{B}_x (\vec{0})} \dd{\vec{r}} \,
e^{-\mu r} I_{\ell, -m} (\vec{r}) \nonumber \\
& = 4 \pi R_{0,0} (\vec{c}) \int_x^\infty \dd{r}\ r e^{-\mu r} \nonumber \\
& = 4\pi \left( \frac{x}{\mu} + \frac{1}{\mu^2} \right) e^{-\mu x}.
\end{align}
\eq{exp_Coulomb_potential_bound_c<x} follows from the fact that
$(1 + z) e^{-z} < 2 e^{-z/2}$ for all $z > 0$.
If $c > x$:
\begin{align}
\Lambda_{\mu, x} (\vec{c}) - \Lambda_{\mu, c} (\vec{c})
& = \int_{\mathcal{B}_c (\vec{0})\setminus\mathcal{B}_x (\vec{0})}\dd{\vec{r}}
\ \frac{\exp(-\mu r)}{\norm{\vec{r}-\vec{c}}} \nonumber \\
& = \sum_{\ell = 0}^\infty \sum_{m=-\ell}^\ell (-1)^m I_{\ell,m} (\vec{c})
\int_{\mathcal{B}_c (\vec{0}) \setminus \mathcal{B}_x (\vec{0})} \dd{\vec{r}}
\ e^{-\mu r} R_{\ell,-m} (\vec{r}) \nonumber \\
& = \frac{4\pi}{c} \left[
\left( \frac{x^2}{\mu} + \frac{2x}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu x} -
\left( \frac{c^2}{\mu} + \frac{2c}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu c}
\right].
\end{align}
Therefore,
\begin{align}
\Lambda_{\mu, x} (\vec{c})
& = \Lambda_{\mu, c} (\vec{c}) + \frac{4\pi}{c} \left[
\left( \frac{x^2}{\mu} + \frac{2x}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu x} -
\left( \frac{c^2}{\mu} + \frac{2c}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu c}
\right] \nonumber \\
& = \frac{4\pi}{c} \left[
\left( \frac{x^2}{\mu} + \frac{2x}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu x} -
\left( \frac{c}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu c}
\right] \nonumber \\
& < \frac{4\pi}{c}
\left( \frac{x^2}{\mu} + \frac{2x}{\mu^2} + \frac{2}{\mu^3} \right)
e^{-\mu x} \nonumber \\
& < \frac{16\pi}{\mu^3 c} e^{-\mu x/2},
\end{align}
where we use the fact that $(z^2 + 2z + 2) e^{-z} < e^{-z/2}$ for any $z>0$
and the fact that
\begin{equation}
\Lambda_{\mu, c} (\vec{c})
= 4\pi \left( \frac{c}{\mu} + \frac{1}{\mu^2} \right) e^{-\mu c},
\end{equation}
which follows from \eq{Lamba_c<x_exact}.
This gives us \eq{exp_Coulomb_potential_bound_c>x} for $c>x$.
In the case that $c\le x$,
\begin{equation}
\frac{16\pi}{\mu^3 c} e^{-\mu x/2} \ge \frac{16\pi}{\mu^3 x} e^{-\mu x/2},
\end{equation}
and, since $(z^2 + z) e^{-z} < 4e^{-z/2}$ for all $z > 0$, we have
\begin{equation}
\frac{16\pi}{\mu^3 x} e^{-\mu x/2} >
4\pi \left( \frac{x}{\mu} + \frac{1}{\mu^2} \right) e^{-\mu x}.
\end{equation}
Therefore the bound \eq{exp_Coulomb_potential_bound_c>x} holds for $c\le x$ as well.
\section{Simulating Hamiltonian Evolution}
\label{sec:simulation}
The simulation technique we now discuss is based on that of Ref.~\cite{Berry2015}.
We partition the total time $t$ into $r$ segments of duration $t/r$.
For each segment, we expand the evolution operator $e^{-iHt/r}$ in a Taylor series up to order $K$,
\begin{align}
\label{eq:Ur}
U_r := e^{-i H t / r} \approx \sum_{k=0}^K\frac{\left(-i Ht/r\right)^k}{k!}.
\end{align}
The error due to truncating the series at order $K$ is bounded by
\begin{equation}
\label{eq:error}
{\cal O}\left(\frac{\left(\left\| H \right\| t / r\right)^{K + 1}}{\left(K+1\right)!}\right).
\end{equation}
In order to ensure the total simulation has error no greater than $\epsilon$, each segment should have error bounded by $\epsilon/r$.
Therefore, provided $r \ge \| H\| t$, the total simulation will have error no more than $\epsilon$ for
\begin{equation}
\label{eq:K}
K \in {\cal O} \left(\frac{\log\left(r/\epsilon\right)}{\log\log\left(r/\epsilon\right)}\right).
\end{equation}
Using our full decomposition of the Hamiltonian from \eq{selfinvdec} in the Taylor series formula of \eq{Ur}, we obtain
\begin{align}
\label{eq:Ur3}
U_r \approx \sum_{k=0}^K\frac{\left(-i t \zeta \right)^k}{r^k k!} \! \! \sum_{\ell_1, \cdots, \ell_k=1}^{L} \sum_{\rho_1, \cdots, \rho_k=1}^{\mu}
\!\!\! {\cal H}_{\ell_1,\rho_1} \cdots {\cal H}_{\ell_k,\rho_k}.
\end{align}
The sum in \eq{Ur3} takes the form
\begin{align}
\label{eq:bV}
& \widetilde{U} =\sum_{j} \beta_j V_j, \quad \quad j = \left(k, \ell_1, \cdots, \ell_k,{\rho_1} \cdots {\rho_k} \right),\nonumber \\
& V_j =\left(-i\right)^k{\cal H}_{\ell_1,\rho_1} \cdots {\cal H}_{\ell_k,\rho_k}, \quad \beta_j = \frac{t^k \zeta^k }{r^k k!},
\end{align}
where $\widetilde{U}$ is close to unitary and the $V_j$ are unitary.
Note that in contrast to \cite{BabbushSparse1}, $\beta_j\ge 0$, consistent with the convention used in \cite{Berry2015}. Our simulation will make use of an ancillary ``selection'' register $\ket{j} = \ket{k}\ket{\ell_1} \cdots \ket{\ell_K} \ket{\rho_1} \cdots \ket{\rho_K}$ for $0\leq k\leq K$, with $1\leq \ell_\upsilon\leq L$ and $1 \leq \rho_\upsilon \leq \mu$ for all $\upsilon$. It is convenient to encode $k$ in unary, as $\ket{k}=\ket{1^k0^{K-k}}$, which requires $\Theta(K)$ qubits.
Additionally, we encode each $\ket{\ell_k}$ in binary using $\Theta (\log L )$ qubits and each $\ket{\rho_k}$ in binary using $\Theta(\log \mu)$ qubits.
We denote the total number of ancilla qubits required as $J$, which scales as
\begin{equation}
\label{eq:J}
J \in \Theta\left(K\log \left(\mu L\right)\right) = {\cal O}\left(\frac{\log \left(\mu L\right)\log\left(r/\epsilon\right)}{\log\log\left(r/\epsilon\right)}\right).
\end{equation}
To implement the truncated evolution operator in \eq{bV}, we wish to prepare a superposition state over $j$, then apply a controlled $V_j$ operator.
Following the notation of Ref.~\cite{Berry2015}, we denote the state preparation operator as $B$, and it has the effect
\begin{equation}
\label{eq:B}
B\ket{0}^{\otimes J} = \sqrt{\frac{1}{\lambda}}\sum_{j} \sqrt{\beta_j} \ket{j},
\end{equation}
where $\lambda$ is a normalization factor.
We can implement $B$ by applying Hadamard gates (which we denote as $H\!d$) to every qubit in the $\ket{\ell_\upsilon}$ and $\ket{\rho_\upsilon}$ registers, in addition to $K$ (controlled) single-qubit rotations applied to each qubit in the $\ket{k}$ register.
We need to prepare the superposition state over $\ket k$
\begin{equation}
\left(\sum_{k=0}^K \frac{(\zeta L \mu t)^k}{r^k k!}\right)^{-1/2}\sum_{k=0}^K \sqrt{\frac{(\zeta L \mu t)^k}{r^k k!}} \ket{k}.
\end{equation}
Using the convention that $R_y(\theta_k) := \exp [-i\, \theta_k\, \sigma_y / 2 ]$, this can be prepared by applying $R_y(\theta_1)$ followed by $R_y (\theta_k)$ controlled on qubit $k-1$ for all $k \in [2, K]$, where
\begin{equation}
\label{eq:theta_k}
\theta_k := 2\arcsin{\left(\sqrt{ 1- \frac{(\zeta L \mu t)^{k-1}}{r^{k-1}\left(k-1\right)!} \left( \sum_{s = k}^K \frac{(\zeta L \mu t)^{s}}{r^s s!} \right)^{-1}} \right)}.
\end{equation}
The Hadamard gates are applied to each of the qubits in the $2 K$ remaining components of the selection register $\ket{\ell_1} \cdots \ket{\ell_K} \ket{\rho_1} \cdots \ket{\rho_K}$. This requires ${\cal O}(K\log (\mu L ))$ gates; parallelizing the Hadamard transforms leads to circuit depth ${\cal O} (K)$ for $B$. A circuit implementing $B$ is shown in \fig{B_circuit}.
\begin{figure}
\[\xymatrix @*=<0em> @R 1em @C 0.25em {
&&&&&\lstick{\kets{0}} &\gate{R_y\left(\theta_1\right)} & \ctrl{1} & \qw &&&& \cdots &&&& & \qw & \qw & \qw \\
&&&&&\lstick{\kets{0}} &\qw & \gate{R_y\left(\theta_2\right)} & \qw &&&& \cdots &&&& & \qw & \qw & \qw \\
&\vdots &&&&&&&&&&& \ddots&& && & \vdots & \\\\
&&&&&\lstick{\kets{0}} &\qw & \qw & \qw &&&& \cdots& &&& & \ctrl{1} & \qw & \qw \\
&&&&&\lstick{\kets{0}} &\qw & \qw & \qw &&&& \cdots&&& && \gate{R_y\left(\theta_K\right)} & \qw & \qw \\
&&&&&\lstick{\kets{0}^{\otimes \log L}} & {/} \qw & \gate{H\!d^{\otimes \log L}} &\qw & \qw& \qw & \qw &\qw & \qw& \qw & \qw &\qw & \qw& \qw & \qw \\
&&&&&\lstick{\kets{0}^{\otimes \log\mu}} & {/} \qw & \gate{H\!d^{\otimes \log \mu}} &\qw & \qw & \qw & \qw &\qw & \qw& \qw & \qw&\qw & \qw& \qw & \qw \\
}\]
\caption{\label{fig:B_circuit} The circuit for $B$ as described in \eq{B}. An expression for $\theta_k$ is given in \eq{theta_k}.}
\end{figure}
We then wish to implement an operator to apply the $V_j$ which is referred to in \cite{BabbushSparse1,Berry2015} as $\textsc{select}(V)$,
\begin{equation}
\label{eq:selectV}
\textsc{select}\left(V\right)\ket{j}\ket{\psi} =\ket{j}V_j\ket{\psi}.
\end{equation}
This operation can be applied using ${\cal O}(K)$ queries to a controlled form of the oracle $\textsc{select}({\cal H})$ defined in \sec{oracle}.
One can apply $\textsc{select}({\cal H})$ $K$ times, using each of the $\ket{\ell_\upsilon}$ and $\ket{\rho_\upsilon}$ registers.
Thus, given that $\textsc{select}({\cal H})$ requires $\widetilde{\cal O}(N)$ gates, our total gate count for $\textsc{select}(V)$ is $\widetilde {\cal O}(K N)$. \tab{parameters} lists relevant parameters along with their bounds, in terms of chemically relevant variables. \tab{operators} lists relevant operators and their gate counts.
\begin{table*}[ht]
\caption{Taylor series simulation parameters and bounds}
\label{tab:parameters}
\begin{tabular}{ c | c | c }
\hline\hline
Parameter & Explanation & Bound\\
\hline
$r$ & number of time segments, \eq{r} & $ \zeta L\mu t/\ln(2)$\\
$L$ & terms in unitary decomposition, \eq{L} & ${\cal O}\left(\eta^2 N^2 \max_{\gamma,\rho}\|\aleph_{\gamma,\rho} \|_{\max}/\zeta\right)$\\
$K$ & truncation point for Taylor series, \eq{K} & ${\cal O}\left(\frac{\log(r/\epsilon)}{\log\log(r/\epsilon)}\right)$\\
$J$ & ancilla qubits in selection register, \eq{J} & $\Theta\left(K\log \left(\mu L\right)\right)$\\
\hline
\end{tabular}
\end{table*}
\begin{table*}[ht]
\caption{Taylor series simulation operators and complexities}
\label{tab:operators}
\begin{tabular}{ c | c | c }
\hline\hline
Operator & Purpose & Gate Count\\
\hline
$\textsc{select}\left({\cal H}\right)$ & applies specified terms from decomposition, \eq{selectH} & $\widetilde{\cal O}\left(N\right)$\\
$\textsc{select}\left(V\right)$ & applies specified strings of terms, \eq{selectV} & $\widetilde{\cal O}\left(N K\right) $\\
$B$ & prepares superposition state, \eq{B} & $ {\cal O}\left(K \log \left(\mu L\right) \right) $\\
${\cal W}$ & probabilistically performs simulation under $H t / r$, \eq{W} & $ \widetilde{\cal O}\left(N K\right) $\\
$P$ & projector onto $\ket{0}^{\otimes J}$ state of selection register, \eq{P} & $ {\cal O}\left(K \log \left(\mu L\right)\right) $\\
$G$ & amplification operator to implement sum of unitaries, \eq{G} & $ \widetilde{\cal O}\left(N K \right) $\\
$\left(PG\right)^r$ & entire algorithm & $ \widetilde{\cal O}\left(r N K\right) $\\
\hline
\end{tabular}
\end{table*}
A strategy for implementing the evolution operator in \eq{bV} becomes clear if we consider the combined action of $B$ followed by $\textsc{select}(V)$ on state $\ket{\psi}$,
\begin{equation}
\label{eq:BV}
\textsc{select}\left(V\right) B \ket{0}^{\otimes J} \ket{\psi} = \sqrt{\frac{1}{\lambda}}\sum_{j} \sqrt{\beta_j} \ket{j} V_j \ket{\psi}.
\end{equation}
This state is similar to that desired for $\widetilde{U}\ket{\psi}$ except for the presence of the register $\ket{j}$.
The need to disentangle from that register motivates the operator \cite{Berry2015}
\begin{align}
\label{eq:W}
& {\cal W} := \left( B\otimes \openone \right)^\dagger \textsc{select}\left(V\right)\left(B \otimes \openone\right), \\
& {\cal W} \ket{0}^{\otimes J}\ket{\psi} = \frac{1}{\lambda}\ket{0}^{\otimes J}\widetilde{U}\ket{\psi} + \sqrt{1 - \frac{1}{\lambda^2}}\ket{\Phi},
\end{align}
where $\ket{\Phi}$ is a state for which the selection register ancilla qubits are orthogonal to $\ket{0}^{\otimes J}$. Accordingly, we define a projection operator $P$ so that
\begin{align}
\label{eq:P}
P = \left(\ket{0}\!\bra{0}\right)^{\otimes J} \otimes \openone , \\
P {\cal W} \ket{0}^{\otimes J} \ket{\psi} = \frac{1}{\lambda}\ket{0}^{\otimes J} \widetilde{U} \ket{\psi}.
\end{align}
Using these definitions, we follow the procedure for oblivious amplitude amplification of \cite{Berry2015} to deterministically execute the intended unitary. To this end, we define the oblivious amplitude amplification operator
\begin{equation}
\label{eq:G}
G \equiv - {\cal W} \left( \openone - 2 P\right) {\cal W}^\dagger \left( \openone - 2 P\right) {\cal W}.
\end{equation}
We use the amplification operator $G$ in conjunction with the projector onto the empty ancilla state $P$ so that
\begin{equation}
PG\ket{0}\ket{\psi}=\ket{0}\left(\frac{3}{\lambda}\widetilde{U}-\frac{4}{\lambda^3}\widetilde{U}\widetilde{U}^\dagger\tilde{U}\right)\ket{\psi}.
\end{equation}
The sum of the absolute values of the coefficients in the self-inverse decomposition of the Hamiltonian in \eq{selfinvdec} is $\zeta L\mu$. If we choose the number of segments as $r=\zeta L\mu t / \ln(2)$, then our choice of $K$ as in \eq{K} ensures that $\big\|\widetilde{U}-U_r\big\|_{\textrm{max}} \in {\cal O}(\epsilon/r)$, and hence \cite{Berry2015}
\begin{equation}
\left\|PG\ket{0}\ket{\psi}-\ket{0}U_r\ket{\psi}\right\|_{\textrm{max}} \in {\cal O}\left(\epsilon/r\right).
\end{equation}
Then the total error due to oblivious amplitude amplification on all segments will be ${\cal O}(\epsilon)$.
Therefore, the complexity of the total algorithm is $r$ times the complexity of implementing $\textsc{select}(V)$ and $B$.
While we implement $B$ with gate count ${\cal O}(K \log (\mu L))$, our construction of $\textsc{select}({\cal H})$ has gate count $\widetilde{\cal O}(N K)$.
The gate count of our entire algorithm depends crucially on $r$. Above we have
taken $r \in {\cal O}(\zeta L \mu t)$ where
\begin{align}
\label{eq:L}
L & \in {\cal O}\left(M \Gamma\right),\\
M & \in \Theta\left(\max_{\gamma,\rho}\left \|\aleph_{\gamma,\rho}\right\|_{\max}/\zeta\right),\\
\Gamma & \in {\cal O}\left(\eta^2 N^2 \right).
\end{align}
As a result, we may bound $r$ as
\begin{equation}
\label{eq:r}
r\in{\cal O}\left(\eta^2 N^2 t \mu \max_{\gamma,\rho}\left \|\aleph_{\gamma,\rho}\right\|_{\max}\right).
\end{equation}
As a consequence of \lem{int0}, \lem{int1} and \lem{int2},
$\mu \max_{\gamma,\rho}\left \|\aleph_{\gamma,\rho}\right\|_{\max}$ can be replaced with
\begin{equation}
\mathcal{O} \left(
\varphi_{\max}^4 x_{\max}^5
\left[
\log \left(
\frac{\varphi_{\max}^4 x_{\max}^5}{\delta}
\right)
\right]^6
\right),
\end{equation}
where $\varphi_{\max}$ is the maximum value taken by the orbitals, and $x_{\max}$ is the
scaling of the spatial size of the orbitals.
To relate $\epsilon$ to $\delta$, in \sec{dec2} the Hamiltonian is broken up into
a sum of ${\cal O}(\eta^2 N^2)$ terms, each of which contains one or two of the integrals.
Therefore, the error in the Hamiltonian is ${\cal O}(\delta \eta^2 N^2)$.
The Hamiltonian is simulated for time $t$, so the resulting error in the simulation will be ${\cal O}(\delta t \eta^2 N^2)$.
To ensure that the error is no greater than $\epsilon$, we should therefore choose $\delta=\Theta(\epsilon/( t \eta^2 N^2))$.
Since we are considering scaling with large $\eta$ and $N$, $\delta$ will be small and
the conditions \eq{sensible0}, \eq{sensible1} and \eq{sensible2} will be satisfied.
In addition, the conditions of \thm{maintheorem} mean that $\varphi_{\max}$ and $x_{\max}$ are logarithmic in $N$.
Hence one can take, omitting logarithmic factors,
\begin{equation}
r\in \widetilde{\cal O}(\eta^2 N^2 t).
\end{equation}
The complexity of $B$ does not affect the scaling, because it is lower order in $N$.
Therefore, our overall algorithm has gate count
\begin{equation}
\widetilde{\cal O}\left(r N K \right) = \widetilde{\cal O}\left(\eta^2 N^3 t\right),
\end{equation}
as stated in \thm{maintheorem}.
This scaling represents an exponential improvement in precision as compared to
Trotter-based methods. However, we suspect that the actual scaling of these
algorithms is much better for real molecules, just as has been observed for the
Trotter-based algorithms \cite{Poulin2014,BabbushTrotter}. Furthermore, the
approach detailed here requires fewer qubits than any other approach to quantum
simulation of chemistry in the literature.
\section{Summary of Results}
\label{sec:summary}
In our previous work \cite{BabbushSparse1}, simulation of the molecular
Hamiltonian was performed in second quantization using Taylor series simulation
methods to give a gate count scaling as $\widetilde{\cal O}(N^5 t)$.
In this work, we use the configuration interaction representation of the
Hamiltonian to provide an improved scaling of
$\widetilde{\cal O}(\eta^2 N^3 t)$.
This result is summarized by the following Theorem.
\begin{theorem}
\label{thm:maintheorem}
Using atomic units in which $\hbar$, Coulomb's constant, and the charge and mass
of the electron are unity, we can write the molecular Hamiltonian as
\begin{align}
\label{eq:electronic}
H = - \sum_i \frac{\nabla_{\vec r_i}^2}{2} -
\sum_{i,j} \frac{Z_i}{\|\vec R_i - \vec r_j \|} +
\sum_{i, j>i} \frac{1}{\|\vec r_i - \vec r_j \|}
\end{align}
where $\vec R_i$ are the nuclear coordinates,
$\vec r_j$ are the electron coordinates, and
$Z_i$ are the nuclear atomic numbers.
Consider a basis set of $N$ spin-orbitals satisfying the following conditions:
\begin{enumerate}
\item each orbital takes significant values up to a distance at most logarithmic
in $N$,
\item beyond that distance the orbital decays exponentially,
\item the maximum value of each orbital, and its first and second derivatives,
scale at most logarithmically in $N$,
\item and the value of each orbital can be evaluated with complexity
$\widetilde {\cal O}(1)$.
\end{enumerate}
Evolution under the Hamiltonian of \eq{electronic} can be simulated in this
basis for time $t$ within error $\epsilon>0$ with a gate count scaling as
$\widetilde{\cal O}(\eta^2 N^3 t)$, where $\eta$ is the number of electrons in
the molecule.
\end{theorem}
We note that these conditions will be satisfied for most, but not all, quantum
chemistry simulations. To understand the limitations of these conditions, we
briefly discuss the concept of a model chemistry (i.e.\ standard basis set
specifications) and how model chemistries are typically selected for electronic
structure calculations. There are thousands of papers which study the effectiveness of various basis sets
developed for the purpose of representing molecules \cite{Huzinaga85}. These
model chemistries associate specific orbital basis functions with each atom in a
molecule. For example, wherever Nitrogen appears in a molecule a model
chemistry would mandate that one add to the system certain basis functions which
are centered on Nitrogen and have been pre-optimized for Nitrogen chemistry;
different basis functions would be associated with each Phosphorus, and so on.
In addition to convenience, the use of standardized model chemistries helps
chemists to compare different calculations and reproduce results.
Within a standard model chemistry, orbital basis functions are almost always
represented as linear combinations of pre-fitted Gaussians which are centered on
each atom. Examples of such model chemistries include Slater Type Orbitals
(e.g.\ STO-3G), Pople Basis Sets (e.g.\ 6-31G*) and correlation consistent basis
sets (e.g.\ cc-DVTZ). We note that all previous studies on quantum algorithms
for quantum chemistry in an orbital basis have advocated the use of one of these
models. Simulation within any of these model chemistries would satisfy the
conditions of our theorem because the basis functions associated with each atom
have maximum values, derivatives and distances beyond which each orbital decays
exponentially.
Similarly, when molecular instances grow because more atoms are added to the
system it is standard practice to perform these progressively larger
calculations using the same model chemistry and the conditions of Theorem 1 are
satisfied. For instance, in a chemical series such as progressively larger
Hydrogen rings or progressively longer alkane chains or protein sequences, these
conditions would be satisfied. We note that periodic systems such as conducting
metals might require basis sets (e.g.\ plane waves) violating the conditions of
Theorem 1. When systems grow because atoms in the molecule are replaced with
heavier atoms, the orbitals do tend to grow in volume and their maximum values
might increase (even within a model chemistry). However, there are only a
finite number of elements on the periodic table so this is irrelevant for
considerations of asymptotic complexity. Finally, we point out that these conditions do not hold if the simulation is
performed in the canonical molecular orbital basis, but this is not a problem
for our approach since the Hartree-Fock state can easily be prepared in the
atomic orbital basis at cost that is quadratic in the number of spin-orbitals.
We discuss this procedure further in \sec{encoding}.
The simulation procedure of Ref.~\cite{Berry2015} requires a decomposition of
the Hamiltonian into a weighted sum of unitary matrices.
In \cite{BabbushSparse1}, we decomposed the molecular Hamiltonian in such a way
that all the coefficients were integrals, i.e.
\begin{align}
\label{eq:unit_sum}
H = \sum_\ell W_\ell H_\ell \quad \quad \quad \quad
W_\ell = \int \! w_\ell \!\left(\vec z\right) \, \dd\vec z,
\end{align}
where the $H_\ell$ are unitary operators, and the $w_\ell \!\left(\vec z\right)$
are determined by the procedure. We then showed how one could evolve under $H$
while simultaneously computing these integrals. In this paper, we investigate a different representation of the molecular
Hamiltonian with the related property that the Hamiltonian matrix elements
$H^{\alpha\beta}$ can be expressed as integrals,
\begin{equation}
\label{eq:int_H2}
H^{\alpha\beta} = \int \! \aleph^{\alpha\beta}(\vec z) \, \dd\vec z,
\end{equation}
or a sum of a limited number of integrals. We decompose the Hamiltonian into a
sum of one-sparse Hamiltonians, each of which has only a single integral in its
matrix entries. We then decompose the Hamiltonian by discretizing the
integrals and then further decompose the Hamiltonian into a sum of self-inverse
operators, ${\cal H}_{\ell,\rho}$. Using this decomposition, we construct a circuit called
$\textsc{select}({\cal H})$ which selects and applies the self-inverse operators so that
\begin{equation}
\label{eq:selectH}
\textsc{select}\left({\cal H}\right) \ket{\ell} \ket{\rho} \ket{\psi} =
\ket{\ell} \ket{\rho} {\cal H}_{\ell,\rho} \ket{\psi}.
\end{equation}
By repeatedly calling $\textsc{select}({\cal H})$, we are able to evolve under
$H$ with an exponential improvement in precision over Trotter-based algorithms.
The CI matrix is a compressed representation of the molecular Hamiltonian that
requires asymptotically fewer qubits than all second-quantized algorithms for
chemistry. Though the CI matrix cannot be expressed as a sum of polynomially
many local Hamiltonians, a paper by Toloui and Love \cite{Toloui2013}
demonstrated that the CI matrix can be decomposed into a sum of ${\cal O}(N^4)$
1-sparse Hermitian operators, where $N$ is the number of spin-orbitals.
We provide in this paper a new decomposition of the CI matrix into a sum of
${\cal O}(\eta^2 N^2)$ 1-sparse Hermitian operators, where $\eta \ll N$ is the
number of electrons in the molecule. This new decomposition enables our improved scaling. Using techniques introduced in \cite{Berry2013}, we further decompose these 1-sparse operators into unitary operators which are
also self-inverse. As a consequence of the self-inverse decomposition, the
Hamiltonian is an equally weighted sum of unitaries.
$\textsc{select}({\cal H})$ requires the ability to compute the entries of the
CI matrix; accordingly, we can use the same strategy for computing integrals
on-the-fly that was introduced in \cite{BabbushSparse1}, but this time our
Hamiltonian is of the form in \eq{int_H2}.
Using this approach, the simulation of evolution over time $t$ then requires
$\widetilde{\cal O}(\eta^2 N^2 t)$ calls to $\textsc{select}({\cal H})$. To implement
$\textsc{select}({\cal H})$, we make calls to the CI matrix
oracle as described in \sec{oracle}, which requires $\widetilde{\cal O}(N)$
gates. This scaling is due to using a database approach to computing the
orbitals, where a sequence of $N$ controlled operations is performed. This
causes our overall approach to require $\widetilde{\cal O}(\eta^2 N^3 t)$ gates.
As in \cite{Toloui2013}, the number of qubits is $\widetilde{\cal O}(\eta)$
rather than $\widetilde{\cal O}(N)$, because the compressed representation
stores only the indices of occupied orbitals, rather than occupation numbers of
all orbitals. To summarize, our algorithm with improved gate count scaling of
$\widetilde{\cal O}(\eta^2 N^3 t)$ proceeds as follows:
\begin{enumerate}
\item Represent the molecular Hamiltonian in \eq{electronic} in first
quantization using the CI matrix formalism. This requires selection of a
spin-orbital basis set, chosen such that the conditions in
\thm{maintheorem} are satisfied.
\item Decompose the Hamiltonian into sums of self-inverse matrices approximating
the required molecular integrals \textit{via} the method of \sec{decomp1}.
\item Query the CI matrix oracle to evaluate the above self-inverse matrices,
which we describe in \sec{oracle}.
\item Simulate the evolution of the system over time $t$ using the method of
\cite{Berry2015}, which is summarized in \sec{simulation}.
\end{enumerate}
| {
"redpajama_set_name": "RedPajamaArXiv"
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Last summer, the rediscovery of long forgotten mural in a former synagogue in Burlington, Vermont building, which had been converted into apartments, started getting a lot of press coverage. The work of a Lithuanian-born artist, the mural had been walled off by sheetrock for the past 25 years. The elaborate two-story mural that rose to the ceiling was located behind were the ark holding the Torah was kept, and features two colorful lions of Judah flanking a tablet of the Ten Commandments. When the mural was recently uncovered to see about preserving it, it was still considered the only one of its kind left in the world.
The second floor of the house at 415 M Street, NW where part of the mural can still be seen. photo- courtesy Jewish Historical Society of Greater Washington.
In the early 1990s, the new owner of a rundown house at 415 M Street, NW in the historic Mt. Vernon Square neighborhood that had served as a series of churches during its last 70 years, peeled back some wallpaper and discovered a mural similar to the one in Vermont. Realizing what it was, she then contacted the Jewish Historical Society and did what she could to preserve the mural in place. Thanks to her efforts, the mural continued to survive for another 23 years, although she added a winged lion as part her efforts to restore it. According to Zachary Paul Levine, curator at the Jewish Historical Society of Greater Washington (JHSGW), there appears to be nothing else like it to be found in other synagogues in DC from this period.
The three-story house at 415 M Street where the mural is located was originally built in the 1860s and was the home of Joseph Prather, a butcher who had a stall at the nearby Northern Liberty Market that was located on Mt. Vernon Square in the 1870s. In 1914, the house became home to the Young Men's Hebrew Association for a year, and from 1915 to 1925, it served as the Hebrew Home for the Aged.
415 M Street, NW. This photo probably dates from when the house was still a single family home. photo–courtesy Jewish Historical Society of Greater Washington.
In the late 1920s, the house became home to Shomrei Shabbos, a synagogue for a tiny East European orthodox Jewish community that remained there into the 1930s. It was then that part of the first floor ceiling was removed to create an open sanctuary. As with the former synagogue in Vermont, they too decorated the area over the ark where the Torah was stored with a beautiful two-story decorative mural. A 10-foot by 10-foot portion of that mural is still intact on the second floor that was directly above the ark.
After the congregation left downtown for a new home uptown on Decatur Street in the Petworth neighborhood, the house became home to the Church of Jesus Christ, an offshoot of the BibleWayChurch, and after that to the MetropolitanCommunityChurch. A baptismal font from the building's use as a church is still accessible through a trapdoor on the first floor.
In 1992, the building was bought and converted back into a single family home. That owner —- the custodian of the remaining part of the mural for over 20 years —- recently sold the house to developer Blackrock Holdings. Blackrock will convert the house, along with an addition in the adjacent vacant lot, into six condominium units.
Detail of the mural and the winged lion added by the house's previous owner. photo- courtesy Jewish Historical Society of Greater Washington.
The JHSGW would very much like to move and restore the mural and has been working with the developer to help find a new home for it. But this is a difficult and expensive endeavor, with the cost to carefully remove the mural potentially reaching into the tens of thousands of dollars. And time is running out. Construction on the condo project this summer. The JHSGW has only until July to find a way to get the mural removed from the house. If the mural is lost, it will erase the last trace of the ethnic communities that used the building over the last century and a half.
*Stephen A. Hansen is an historic preservation specialist, Washington DC historian, author of several books and of the Virtual Architectural Archaeology blog.
© 2014 InTowner Publishing Corp. & Stephen A. Hansen. All rights reserved. Reproduction in whole or in part, including for commercial purposes, without permission is prohibited. | {
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Feldman Chevrolet of Novi is located at 42355 Grand River Avenue in Novi, Michigan (between Novi and Meadowbrook Roads). Our Chevrolet dealership serves all the Metro-Detroit area, including Novi, Northville, Farmington, West Bloomfield, Wixom, and Walled Lake.
Whether you're just beginning to look for a new Chevrolet car, truck, or SUV, or you already have a reliable vehicle, Feldman Chevrolet of Novi has everything you need to help you repair and maintain your vehicle throughout your ownership.
Our Certified Service experts are trained to know every inch of your vehicle and can help you keep it running like new. Simply schedule an appointment today. | {
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Essays & Memoir
Granta Books
The Holocaust Reinterpreted: An Indictment of Israel
Boaz Evron
Two catastrophes have hurt the Jewish people in the twentieth century: the Holocaust and the lessons drawn from it. And today, illogical and anti-historical interpretations of the genocide of the Jews are being used, either deliberately or out of ignorance, as propaganda – in the non-Jewish world, the Jewish Diaspora, and within Israel's own Jewish nation. This propaganda has now become one of the most serious threats to the Jewish people and the State of Israel.
Before beginning, I feel I must express reservations about the term 'Holocaust' itself, which, in its common rhetorical usage has taken on a strange and misleading power. Derived from its original sense of a complete sacrifice – a whole burnt offering – holocaust has come to signify any event characterized by the comprehensiveness and the unexpectedness of its destruction. A holocaust can be used to represent virtually any disaster – an earthquake, a fire, even a thunder storm on an otherwise sunny day – that strikes suddenly, without historical precedent or context; it is more evocative than specifying: its causes cannot be understood or analysed. In the context of World War Two, 'Holocaust' is a circumlocution that is semantically no different from the famous Nazi circumlocution, the 'Final Solution'. Both terms hide the truth behind another name. 'Final Solution' was used by the murderers to cover up their crime; 'Holocaust' neutralizes the crime for those who managed to survive it. 'The genocide of the European Jews', while obviously more cumbersome, is in fact a more accurate representation of what actually happened, and conveys that there were specific victims of specific murderers in a specific part of the world. Unlike the almost mystical 'Holocaust', the term 'the genocide of the European Jews' allows us to understand that this terrible crime was a particular historical event that can and – we now realize – must be understood in its historical context. That circumlocutions of this sort have been used for so long reveals how complex our feelings are when we approach this subject. They also point to the tremendous hypocrisy and pretence evident in all sides involved in understanding it.
To read this in full, take out a subscription to Granta. Over thirty years of new writing at your fingertips – subscribe now.
Sign in to Granta.com.
Mrs Thatcher's Religious Pilgrimage
Granta 6: A Literature for Politics
1st December 1982
40 Years of Granta
Correspondence from our archive, from Kazuo Ishiguro, Kingsley Amis, Doris Lessing, Martha Gellhorn and more.
How to Write About Africa
The late Binyavanga Wainaina's iconic satire is one of Granta's best-loved essays.
Angela Carter is best known for her adaptations of fairy tales, and 'Cousins' is one in her quartet of wolf stories.
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Nobel Prize-winning Doris Lessing on her life, lovers and landlords in 1950s London.
Dreams for Hire
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Mother and Son:
Life and Fate
'Nothing made her happier than to sacrifice herself for her son's happiness.'
Martin Goodman | Notes on Craft
Martin Goodman
Martin Goodman on why it took him twenty years to write his latest novel, J SS Bach.
Sheila Heti
'Every night for three weeks, I sat with Hitler after dinner.'
'On the rampage, he truly did become a devil; it was impossible to restrain him.' Translated from the Russian by Robert & Elizabeth Chandler.
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"Get rich off the Internet" is so 2000.
But apparently, it's still working, because Global Affiliate Zone is working it. Hard.
Global Affiliate Zone is a network marketing company that offers coaching and training to help members learn how to make money online.
The Internet is like the final frontier, and everyone's trying to get in on the gold rush (hint: Wealthy Affiliate).
There's a lot of money floating around up for grabs, but also a lot of people trying to get a piece of it. With such high competition and the technical barriers involved with making money online, only a lucky few really get a slice of the pie.
Especially if the company promising to teach them how isn't being completely honest.
1. What does Global Affiliate Zone sell? Global Affiliate Zone (GAZ) sells training and education about how to make money as an affiliate marketer.
2. What are GAZ's most popular products? The GAZ PRO Community ($99/month) is their only product. In this membership, you get access to private automated sales funnels, including done-for-you marketing materials, custom capture pages, dynamic follow-up emails, and live sales presentations — so you can build your affiliate income fast.
3. How much does it cost to join GAZ? You must be a GAZ PRO member to be able to sell memberships. Membership is $99 per month. Each time you sell a membership, you'll earn a 30% commission, or $29.70 per month for as long as the customer stays active.
4. Is GAZ a scam? GAZ is a legitimate business offering training to its members — but beware. This setup is a little shady.
GAZ calls themselves affiliate marketing trainers. But their training helps you sell their memberships, not other affiliate products. Since you have to be an active member to earn your commission, you'll need to sell 4 memberships every month just to break even.
But it gets shadier: What they don't tell you up-front is that all the done-for-you funnels inside GAZ point to a water filter MLM called Enagic. If you want to sell water filters, you don't need GAZ. Join Enagic and do your own marketing. Otherwise, you'll be dividing your energies, trying to sell GAZ memberships as well as water filters, and probably losing money on both.
7. What is GAZ's revenue? No numbers have been released about GAZ's revenue.
9. What lawsuits have been filed? We found no lawsuits listed online.
Global Affiliate Zone (GAZ) says they can help you make money online. So should you get involved?
Either way, here's the full review on Global Affiliate Zone.
Julian Sherman and Mathieu Jang co-founded Global Affiliate Zone to help people like you make money online. GAZ is an "affiliate program" (MLM) that's capitalizing on the popularity of internet marketing.
Global Affiliate Zone is dedicated to providing the most comprehensive, up-to-date training coaching and resources to online entrepreneurs.
Whether you're just getting started online, or you're a seasoned veteran the Global Affiliate Zone Community is here to help.
So, supposedly, you don't even need to have extensive technical knowledge to learn from their program.
I'm skeptical, because if anyone could make money off internet marketing, everyone would be doing it.
There's also little to no information on their website about the company itself, when or how they were founded, what experience their executives have, and what their revenue looks like.
They're at 4,000 members and growing. So, they're not huge, but they're moving up.
There are tons of internet marketers and affiliate sites out there trying to make money off the world wide web. However, most of them are failing.
But that is, after all, the basis for MLM in general. Most people fail, but a lucky few hit it big.
Their product is a membership to Global Affiliate Zone, which is basically an internet marketing education program.
While $99/month isn't cheap, it's an amazing deal if they really do all of that for you. Mentorship and having a community of internet marketers at your fingers is invaluable — if it's a quality community. From building your site to capturing leads to closing sales.
But on top of that, they supposedly take care of nearly everything for you. From building your site to capturing leads to closing sales…that's a lot of service for under a hundo. But can they really do all of that for you?
I'm skeptical. If it sounds too good to be true, it often is.
At the time of writing this review, the link to "Get Started Now" with their affiliate program is coming up with a 404 error. So basically, their own website is missing the most important link when it comes to closing a sale. Questionable.
There's also no information on the compensation plan to be found on their website. Presumably, the idea is that affiliates make most of their money off their sales.
Ideally, the idea is that affiliates make most of their money off their own internet marketing, and some decent side money off the GAZ affiliate program. But there's no evidence to show that that's the case.
Affiliates do earn a commission on everyone they recruit to become a GAZ member through a basic tiered system, and they also earn commission on their downline. The exact amount isn't specified.
If you've got a real interest in learning about internet marketing, this program is reasonably priced for all that they claim to provide.
Overall, their services include quite a bit.
But it's really not clear as to how much they actually deliver once you've paid them. And competition for a piece of the internet marketing pie, a very over-saturated market, means that 99/100 people probably aren't going to see loads of money, if any.
Look, I've been involved with network marketing for over ten years so I know what to look for when you consider a new opportunity.
That hasn't been my experience so far, though they do leave a lot initially to be a mystery and use standard brainwashing tactics to get people on board by talking about how much money they made nad get everyone excited. One woman I know who got me involved knows my team leader who said she made $22,000 in one month…now my friend is FRIENDS with this woman and she says it's true and the potential for making a lot if there, but most people are skeptical and back out…that's why most people aren't doing it. They don't actually think it could be that easy and I agree that I was kinda left in the dark and you also have to buy the product first, which they don't tell you about until the very end, but they do offer financing for that and I genuinely want the product they are selling because it's awesome and the highest quality water filters around, which are proven to help people who suffer from terminal illnesses by alkalizing their body…something all the ultra rationalist skeptics out there don't believe, but all the sales people say they've watched their own family members, as well as their own health transform to incredible degrees, and they all seem like genuine people, so I'm going to give it a go. I have nothing to lose as I won the initial $150 for attending the webinar so didn't even have to pay for the membership. The rewards and commission for simply placing ads and being a little fish hitching a ride on the bigger fishes backs is astounding. The skeptics can have their doubts…that's part of what holds people back from abundance.
over all its looking like a pyramid scheme, based on the various reviews.
It should not be called "network marketing" or even be in the same sentence as network marketing, it is affilliate marketing and 99% internet based, spamming people through catchy landing pages to buy useless nicknacks…….some good some ordinary.
Network marketing to me is about building relationships, finding and solving problems for people through authentic connection, transforming their lives while constantly transforming yours, it's about personal growth obtained through a huge focus on personal development, it's having a genuine interest in others and a commitment to improving their well-being, it's about being the happiest and healthiest version of yourself you can be so you can be an example and role model. It's about offering a solution of physical, consumable products backed by science, giving physical results and transformations, having a notable impact on people's lives that will have ripple effects for generations to come.
Affiliate marketing is hiding begind a computer, selling a coaching program to earn commission, sharing links to products you probably neither know or would use yourself, completely inauthentic with no intrinsic value – you are just a middle man earing a commission, flogging off a system to others to learn to do the same…..not really making an impact on humainty and not really contributing to make the world a happier, healthier place.
If you want to be in the business of Network Marketing, find an amazing line of products that give lasting results, where you can impact other's lives, see their transformation before your eyes and know YOU helped make that happen, you introduced them to a system of products that lost them excess weight and gave them more energy so they can run around with their kids, they can now be an example and authentically share their results with others and earn an income from doing so too. It's about being committed to 1 line of products and 1 company that is in the business of transforming lives…..not whoring to multiple companies sharing multiple products with no common result and products or services you probably wouldn't use yourself.
We need more authenticity in this world and the more "Affiliate Marketing" companies/programs that spring up offereing an easy/simple/we do all the closing systems out there…..I feel we are losing touch with authenticity. | {
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Home Popular lifehacks What group profited the most during the Gold Rush?
on July 2, 2019 July 2, 2019 Popular lifehacks
What group profited the most during the Gold Rush?
1 What group profited the most during the Gold Rush?
2 Which California city boomed as a result of the gold rush?
3 Who was successful in the California Gold Rush?
4 How much did it cost to find gold in the Gold Rush?
But the largest profit was made by the U.S. government, with the expansions to the west, railroads, infrastructure – new cities blossomed and turned into metropolitan areas, everyone wanted gold so more and more people began to move over to the west.
What types of jobs were most successful during the Gold Rush?
By the mid-1850s mining for gold had become less an individual enterprise and more a wage labor job. The large mining companies were highly successful at extracting gold. Using a technique called hydraulic mining, they extracted $170 million in gold between 1860 and 1880.
What was the best way to get rich during the California Gold Rush?
The Best Way to Get Rich During the California Gold Rush Was by Selling Mining Pans And Eggs. James Wilson Marshall was the one who discovered gold flakes in the American River in the Sacramento, California, Valley in 1848. His discovery set off more than Gold Rush Fever.
Which California city boomed as a result of the gold rush?
In 1848, San Francisco was a town of 1,000 people, mostly Mexican American and white merchants. By 1849, the first year of the California Gold Rush, the city boomed to 25,000 people from the eastern United States, Europe, Asia, Africa, and South America.
How did the Gold Rush Impact ideas about California?
The Gold Rush significantly influenced the history of California and the United States. It created a lasting impact by propelling significant industrial and agricultural development and helped shape the course of California's development by spurring its economic growth and facilitating its transition to statehood.
How did the Gold Rush benefit California?
The California Gold Rush of 1849-1855 radically transformed California, the United States and the world. The significant increase in population and infrastructure allowed California to qualify for statehood in 1850, only a few years after it was ceded by Mexico, and facilitated U.S. expansion to the American West.
Who was successful in the California Gold Rush?
The Merchants of the California Gold Rush were successful people. However, they sometimes sold fake items, or books that had inaccurate or incorrect information. Miners with no experience were sold fake items.
How did merchants make money during the Gold Rush?
These men became rich without finding gold. Instead, they opened businesses and provided services to the forty-niners. The opportunities they created for themselves vary greatly from one another. Many merchants would sell supplies and food, and raise prices to increase their profits.
How did Brannan make money during the Gold Rush?
Rather than staking a claim on the gold, Brannan bought up all the equipment that prospectors would need; then, when the rush began, re-sold the merchandise at a steep markup. His store made enormous profits, selling as much as $5,000 (about $155,000 in 2020 dollars) in goods per day to miners.
How much did it cost to find gold in the Gold Rush?
Daylor and Perry McCoon made 17,000 dollars' worth of gold in just one week. A twelve year old boy found 2,700 dollars in just two days. Business money. During the Gold Rush, a single egg cost 3-4 dollars, a loaf of bread 2 dollars, usually cost 6 dollars cost 300 dollars.
Previous Article What are hidden fifths and octaves?
Next Article How short can a shotgun be and still be legal? | {
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Last 30 Days (1) Last 90 Days (11) Last 180 Days (19) Next 30 Days (1) Next 90 Days (1) Next 180 Days (1) 2021 (2) 2020 (36) 2019 (24) 2018 or earlier (33)
Search Filters: Lasers clear Cybersecurity clear Finishing & Coatings clear Casting clear Welding & Cutting clear
New Chiller Technology Helps Industrial Lasers Keep Their Cool
Industrial lasers require cooling to remove excess heat generated in the resonator power electronics and the optics system. The type of cooling required is determined by laser wattage, resonator efficiency, resonator and optics temperature requirements, and ambient temperature.
Adaptive Welding Key to Power Generation
While water and fire tube boiler power plants may be considered archaic, they now power much of North America and will for some time, even as newer, cleaner, greener tech transitions into the mainstream and becomes practical.
2016 Was a Good Year for Lasers; 2017 Looks Even Better
Strong 2016 earnings among top industrial laser providers, continued brisk adoption of fiber lasers, cheaper ultrafast lasers, and a host of novel applications and notable corporate acquisitions signal a big year ahead for photonics-based manufacturing.
Sunnen and ANS Collaborate on Friction and Wear Reduction Technology
Sunnen Products Co. and Sweden's Applied Nano Surfaces (ANS) have entered into a joint market development agreement to advance technology and applications based on the unique Triboconditioning process recently patented by ANS. The process reduces friction and wear on various steel and cast iron surfaces while improving surface finish, preventing seizures, and enhancing product life.
Keeping Old Planes in the Air with Laser Scanning
Your father's Oldsmobile may be long gone but his B-52 is still pulling missions, and they haven't built the "BUFF" (Big Ugly Fat Fellow) since 1962. The last KC-135 tanker was built in 1965. Besides aging warbirds (the average plane in the US Air Force is over 28 years old) there are hundreds of ancient civilian airliners carrying friendlier payloads everyday. The key to doing this safely is of course excellent maintenance and periodic upgrades. Laser scanning plays an essential role.
Innovations Enable Faster Beam Delivery, On-the-Fly Welding
For ABB, robotic welding comes down to a never-ending process of ensuring parts are suitable for laser joining and developing the appropriate processes. To that end, ABB is refining a recent innovation to improve beam delivery speeds and has developed software for on-the-fly welding in tandem with Trumpf's Intelligent Programmable Focusing Optic (IPFO).
Lasers on the Cutting Edge
In the last seven to eight years, solid-state lasers have come to dominate laser welding and cutting," said Tom Bailey, product specialist for Trumpf Inc. (Farmington, CT). While Trumpf still produces CO2 lasers, for most applications solid-state lasers literally outshine them.
Laser Genius Elevates Productivity to New Heights
Like its products, technology demands for thyssenkrupp Elevator Corp. are "going up." A business unit of ThyssenKrupp Elevator AG, the company oversees all business operations in the US, Canada, and Central and South America, and says it is the largest producer of elevators in the Americas, with 13,500 employees, more than 200 branches and service locations, and sales of $2.7 billion.
IMTS 2018 Showcases New Manufacturing Technology Trends
To stay current with technology and peer into the future of manufacturing, take a look at our preview of IMTS—The International Manufacturing Technology Show, to be held at McCormick Place in Chicago from Sept. 10 through Sept. 15. In the following pages, ME provides in-depth examinations of each pavilion at IMTS, as well as previews of the products you will be able to see displayed at exhibitors' booths. | {
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We are pleased to share with you the final results of our project for Carlsberg.
The quality and creativity of your videos were really impressive and we hope you had fun creating your films and animations for this incredible contest.
We have been particularly impressed by your creativity, imagination and vision for this challenging project which faced many restrictions due to laws on how alcohol is portrayed. A massive congrats to all of you!
Please find below the videos selected for Carlsberg. Bravo to their creators!
Video contest Buchanan's – the results are online!
Video contest Buchanan's – the results are online! | {
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Q: Combining two dataframes using same column names in R I have a dataframe named df_1 with following columns,
ID
Name
Age
City
1
Jaz
25
D
2
Sam
28
E
And another dataframe named df_2 with following columns,
ID
Name
City
4
Alex
F
5
Abi
E
I want a resultant df as follow,
ID
Name
Age
City
1
Jaz
25
D
2
Sam
28
E
4
Alex
NA
F
5
Abi
NA
E
How to get this using R?
A: You can use the following code:
library(dplyr)
bind_rows(df_1, df_2)
Output:
ID Name Age City
1 1 Jaz 25 D
2 2 Sam 28 E
3 4 Alex NA F
4 5 Abi NA E
Data
df_1 <- data.frame(ID = c(1,2),
Name = c("Jaz", "Sam"),
Age = c(25,28),
City = c("D", "E"))
df_2 <- data.frame(ID = c(4,5),
Name = c("Alex", "Abi"),
City = c("F", "E"))
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Valerie Pachner (* 26. června 1987 Wels) je rakouská herečka.
Životopis
Vyrůstala v rakouském Bad Schallerbachu a v letech 2009–2013 studovala herectví na škole Maxe Reinhardta ve Vídni. Poté byla až do roku 2017 členkou hereckého souboru Residenztheater v Mnichově pod vedením uměleckého šéfa Martina Kušeje. Za své divadelní role byla v roce 2016 dvakrát oceněna.
V roce 2015 si zahrála hlavní ženskou roli ve filmu Bad Luck, který byl nominován na cenu Maxe Ophülse. Poté se objevila v životopisných filmech Jack a Před ranními červánky. Ve druhém zmiňovaném ztvárnila nevlastní dceru Stefana Zweiga. Za ztvárnění Wally Neuzil, múzy Egona Schieleho, ve filmu Dietera Bernera Egon Schiele, získala Rakouskou filmovou cenu a cenu Romy.
V roce 2019 byl film Půda pod nohama vybrán do soutěže o Zlatého medvěda na 69. ročníku Mezinárodního filmového festivalu v Berlíně. Výkon Pachner, která ztvárnila hlavní roli, byl oceněn mezinárodní kritikou a vynesl jí tři ceny, včetně Německé herecké ceny pro nejlepší herečku. Ve stejném roce měl na 72. ročníku Filmového festivalu v Cannes premiéru film Na prahu války, kde rovněž ztvárnila hlavní roli. Server IndieWire označil její výkon za jeden z nejlepších hereckých výkonů roku 2019. V roce 2021 si zahrála Matu Hari v akčním snímku Kingsman: První mise.
Filmografie
Film
Televize
Odkazy
Reference
Externí odkazy
Rakouské herečky
Narození v roce 1987
Narození 26. června
Narození ve Welsu
Žijící lidé
Ženy | {
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filed: April 13, 2013 • California
Locals fear desert land will feed city's energy needs
Credit: By Courtney Vaughn, Hi-Desert Star | April 12, 2013 | www.hidesertstar.com ~~
YUCCA VALLEY – As the state rushes to expand its use of renewable energy, the Morongo Basin could be a prime target for solar and wind development.
Conservation groups, residents and local and county leaders met in Yucca Valley's community center Thursday, April 11, to discuss the Desert Renewable Energy Conservation Plan for the first time.
The plan, being developed by state and federal agencies, identifies locations throughout the state that would be most appropriate for renewable energy development in the next 30 years.
So far, the plan encompasses 22.5 million acres of land and color codes areas that could be used for solar, wind or geothermal energy plants.
"The goal for the DRECP is to plan for renewable energy on both public and private land," April Sall, spokeswoman for the California Desert Coalition, explained.
Sall said in the more than two-year planning process, one key thing has been missing from the conservation plan: citizen input.
"They don't make it particularly friendly for citizens and residents to go to the few public meetings they have and engage and make comments," Sall said. "We have to engage and make sure our voices are heard and make sure that our county board of supervisors and our elected officials are educated and following this process as well. … They're doing this plan with or without us."
In the past three years, the Morongo Basin has seen at least four proposals for solar development and one proposed wind energy project, mostly in unincorporated areas.
Supporters argue that solar and wind development should be embraced as a way to reduce the country's reliance on fossil fuels.
Residents at Thursday's meeting voiced concern over the number of utility-scale solar developers buying private land for energy development, often next to rural, residential neighborhoods.
Chris Carrillo, deputy chief of staff for 3rd District County Supervisor James Ramos, referred to the conservation plan as the "mega planning process" in the state and federal government's attempt to conserve land and habitat, but also encourage renewable energy development.
"We have arrived at a historic moment in the desert," Carrillo told the audience. "I think it's hard for people to believe that these huge, utility-scale energy developments are going to be coming to their backyard, but they're coming. Some of them are already here."
Carrillo encouraged those at the meeting to contact each of the county representatives. He said the county has jurisdiction over development on private land in unincorporated areas.
A key concern among meeting attendees was how government agencies notify homeowners when energy developers move into neighborhoods.
One woman said she was informed by a land surveyor that a solar project is already being planned near her neighborhood in north Joshua Tree. Another woman said the Lucerne Valley property her family has owned for 60 years is close to the development phase. She fears it's too late to have a say in the project.
Sall said energy projects in rural neighborhoods will drive down home and property values. She said the county can play a vital role in the planning process.
"It is the county's responsibility to protect regional property values," she said Friday.
Source: By Courtney Vaughn, Hi-Desert Star | April 12, 2013 | www.hidesertstar.com | {
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N. Korea sends back six South Korean men
By 윤민식
One of the South Korean citizens that had been held in North Korea since early 2010 returns from the communist state via the inter-Korean border village of Panmunjeom. (Yonhap News)
North Korea on Friday returned home six South Koreans, who had been held in the reclusive state apparently since early 2010, via the inter-Korean border village of Panmunjeom.
The six men, aged between 27 and 67, walked past the military demarcation line running through the village at around 4:50 p.m., some 20 minutes later than they were set to return here.
They are presumed to have been caught crossing the border between the North and China, Seoul officials believe.
Investigators from the military, police and National Intelligence Service are expected to question them to find out how, when and why they entered the North. Should they be found to have voluntarily entered the North, they could be punished for violating the National Security Law.
After their abrupt release, suspicions were raised over Pyongyang's true intentions.
Analysts said the release appeared aimed at mitigating international criticism for its recent breach of the inter-Korean agreement to hold reunions of separated families and abject human rights conditions concerning kidnapped foreigners and returned refugees.
Some others said the release might be part of efforts by the cash-strapped North to get more support from Seoul including for the resumed operation of the joint industrial park in the North's border city of Gaeseong.
The announcement of the release came on the same day the North accepted a request by South Korean lawmakers to visit the Gaeseong complex, a crucial source of foreign currency. The complex was reopened recently after a five-month suspension.
In recent months, inter-Korean ties have continued to worsen with Pyongyang breaking the accord to hold family reunions and issuing a series of public statements denouncing the Park Geun-hye government for what it calls "hostile" policy toward it.
By Song Sang-ho
([email protected]) | {
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<h2 title="Uses of Interface javax.swing.tree.TreeNode" class="title">Uses of Interface<br>javax.swing.tree.TreeNode</h2>
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<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing packages, and an explanation">
<caption><span>Packages that use <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Package</th>
<th class="colLast" scope="col">Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><a href="#javax.swing">javax.swing</a></td>
<td class="colLast">
<div class="block">Provides a set of "lightweight"
(all-Java language) components that,
to the maximum degree possible, work the same on all platforms.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><a href="#javax.swing.text">javax.swing.text</a></td>
<td class="colLast">
<div class="block">Provides classes and interfaces that deal with editable
and noneditable text components.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><a href="#javax.swing.text.html">javax.swing.text.html</a></td>
<td class="colLast">
<div class="block">Provides the class <code>HTMLEditorKit</code> and supporting classes
for creating HTML text editors.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><a href="#javax.swing.tree">javax.swing.tree</a></td>
<td class="colLast">
<div class="block">Provides classes and interfaces for dealing with
<code>javax.swing.JTree</code>.</div>
</td>
</tr>
</tbody>
</table>
</li>
<li class="blockList">
<ul class="blockList">
<li class="blockList"><a name="javax.swing">
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<h3>Uses of <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> in <a href="../../../../javax/swing/package-summary.html">javax.swing</a></h3>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing classes, and an explanation">
<caption><span>Classes in <a href="../../../../javax/swing/package-summary.html">javax.swing</a> that implement <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Class and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>static class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/JTree.DynamicUtilTreeNode.html" title="class in javax.swing">JTree.DynamicUtilTreeNode</a></strong></code>
<div class="block"><code>DynamicUtilTreeNode</code> can wrap
vectors/hashtables/arrays/strings and
create the appropriate children tree nodes as necessary.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing methods, and an explanation">
<caption><span>Methods in <a href="../../../../javax/swing/package-summary.html">javax.swing</a> that return <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">JTree.DynamicUtilTreeNode.</span><code><strong><a href="../../../../javax/swing/JTree.DynamicUtilTreeNode.html#getChildAt(int)">getChildAt</a></strong>(int index)</code>
<div class="block">Subclassed to load the children, if necessary.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing constructors, and an explanation">
<caption><span>Constructors in <a href="../../../../javax/swing/package-summary.html">javax.swing</a> with parameters of type <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colOne" scope="col">Constructor and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colLast"><code><strong><a href="../../../../javax/swing/JTree.html#JTree(javax.swing.tree.TreeNode)">JTree</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> root)</code>
<div class="block">Returns a <code>JTree</code> with the specified
<code>TreeNode</code> as its root,
which displays the root node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colLast"><code><strong><a href="../../../../javax/swing/JTree.html#JTree(javax.swing.tree.TreeNode,%20boolean)">JTree</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> root,
boolean asksAllowsChildren)</code>
<div class="block">Returns a <code>JTree</code> with the specified <code>TreeNode</code>
as its root, which
displays the root node and which decides whether a node is a
leaf node in the specified manner.</div>
</td>
</tr>
</tbody>
</table>
</li>
<li class="blockList"><a name="javax.swing.text">
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</a>
<h3>Uses of <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> in <a href="../../../../javax/swing/text/package-summary.html">javax.swing.text</a></h3>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing classes, and an explanation">
<caption><span>Classes in <a href="../../../../javax/swing/text/package-summary.html">javax.swing.text</a> that implement <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Class and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/text/AbstractDocument.AbstractElement.html" title="class in javax.swing.text">AbstractDocument.AbstractElement</a></strong></code>
<div class="block">Implements the abstract part of an element.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/text/AbstractDocument.BranchElement.html" title="class in javax.swing.text">AbstractDocument.BranchElement</a></strong></code>
<div class="block">Implements a composite element that contains other elements.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/text/AbstractDocument.LeafElement.html" title="class in javax.swing.text">AbstractDocument.LeafElement</a></strong></code>
<div class="block">Implements an element that directly represents content of
some kind.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/text/DefaultStyledDocument.SectionElement.html" title="class in javax.swing.text">DefaultStyledDocument.SectionElement</a></strong></code>
<div class="block">Default root element for a document...</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing methods, and an explanation">
<caption><span>Methods in <a href="../../../../javax/swing/text/package-summary.html">javax.swing.text</a> that return <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">AbstractDocument.AbstractElement.</span><code><strong><a href="../../../../javax/swing/text/AbstractDocument.AbstractElement.html#getChildAt(int)">getChildAt</a></strong>(int childIndex)</code>
<div class="block">Returns the child <code>TreeNode</code> at index
<code>childIndex</code>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">AbstractDocument.AbstractElement.</span><code><strong><a href="../../../../javax/swing/text/AbstractDocument.AbstractElement.html#getParent()">getParent</a></strong>()</code>
<div class="block">Returns the parent <code>TreeNode</code> of the receiver.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing methods, and an explanation">
<caption><span>Methods in <a href="../../../../javax/swing/text/package-summary.html">javax.swing.text</a> with parameters of type <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><span class="strong">AbstractDocument.AbstractElement.</span><code><strong><a href="../../../../javax/swing/text/AbstractDocument.AbstractElement.html#getIndex(javax.swing.tree.TreeNode)">getIndex</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node)</code>
<div class="block">Returns the index of <code>node</code> in the receivers children.</div>
</td>
</tr>
</tbody>
</table>
</li>
<li class="blockList"><a name="javax.swing.text.html">
<!-- -->
</a>
<h3>Uses of <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> in <a href="../../../../javax/swing/text/html/package-summary.html">javax.swing.text.html</a></h3>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing classes, and an explanation">
<caption><span>Classes in <a href="../../../../javax/swing/text/html/package-summary.html">javax.swing.text.html</a> that implement <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Class and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/text/html/HTMLDocument.BlockElement.html" title="class in javax.swing.text.html">HTMLDocument.BlockElement</a></strong></code>
<div class="block">An element that represents a structural <em>block</em> of
HTML.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/text/html/HTMLDocument.RunElement.html" title="class in javax.swing.text.html">HTMLDocument.RunElement</a></strong></code>
<div class="block">An element that represents a chunk of text that has
a set of HTML character level attributes assigned to
it.</div>
</td>
</tr>
</tbody>
</table>
</li>
<li class="blockList"><a name="javax.swing.tree">
<!-- -->
</a>
<h3>Uses of <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a></h3>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing subinterfaces, and an explanation">
<caption><span>Subinterfaces of <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Interface and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>interface </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/tree/MutableTreeNode.html" title="interface in javax.swing.tree">MutableTreeNode</a></strong></code>
<div class="block">Defines the requirements for a tree node object that can change --
by adding or removing child nodes, or by changing the contents
of a user object stored in the node.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing classes, and an explanation">
<caption><span>Classes in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a> that implement <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Class and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>class </code></td>
<td class="colLast"><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html" title="class in javax.swing.tree">DefaultMutableTreeNode</a></strong></code>
<div class="block">A <code>DefaultMutableTreeNode</code> is a general-purpose node in a tree data
structure.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing fields, and an explanation">
<caption><span>Fields in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a> declared as <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>protected <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#root">root</a></strong></code>
<div class="block">Root of the tree.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing fields, and an explanation">
<caption><span>Fields in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a> with type parameters of type <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../java/util/Enumeration.html" title="interface in java.util">Enumeration</a><<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#EMPTY_ENUMERATION">EMPTY_ENUMERATION</a></strong></code>
<div class="block">An enumeration that is always empty.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing methods, and an explanation">
<caption><span>Methods in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a> that return <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getChildAfter(javax.swing.tree.TreeNode)">getChildAfter</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aChild)</code>
<div class="block">Returns the child in this node's child array that immediately
follows <code>aChild</code>, which must be a child of this node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">TreeNode.</span><code><strong><a href="../../../../javax/swing/tree/TreeNode.html#getChildAt(int)">getChildAt</a></strong>(int childIndex)</code>
<div class="block">Returns the child <code>TreeNode</code> at index
<code>childIndex</code>.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getChildAt(int)">getChildAt</a></strong>(int index)</code>
<div class="block">Returns the child at the specified index in this node's child array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getChildBefore(javax.swing.tree.TreeNode)">getChildBefore</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aChild)</code>
<div class="block">Returns the child in this node's child array that immediately
precedes <code>aChild</code>, which must be a child of this node.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getFirstChild()">getFirstChild</a></strong>()</code>
<div class="block">Returns this node's first child.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getLastChild()">getLastChild</a></strong>()</code>
<div class="block">Returns this node's last child.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">TreeNode.</span><code><strong><a href="../../../../javax/swing/tree/TreeNode.html#getParent()">getParent</a></strong>()</code>
<div class="block">Returns the parent <code>TreeNode</code> of the receiver.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getParent()">getParent</a></strong>()</code>
<div class="block">Returns this node's parent or null if this node has no parent.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getPath()">getPath</a></strong>()</code>
<div class="block">Returns the path from the root, to get to this node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#getPathToRoot(javax.swing.tree.TreeNode)">getPathToRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode)</code>
<div class="block">Builds the parents of node up to and including the root node,
where the original node is the last element in the returned array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#getPathToRoot(javax.swing.tree.TreeNode,%20int)">getPathToRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode,
int depth)</code>
<div class="block">Builds the parents of node up to and including the root node,
where the original node is the last element in the returned array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getPathToRoot(javax.swing.tree.TreeNode,%20int)">getPathToRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode,
int depth)</code>
<div class="block">Builds the parents of node up to and including the root node,
where the original node is the last element in the returned array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getRoot()">getRoot</a></strong>()</code>
<div class="block">Returns the root of the tree that contains this node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getSharedAncestor(javax.swing.tree.DefaultMutableTreeNode)">getSharedAncestor</a></strong>(<a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html" title="class in javax.swing.tree">DefaultMutableTreeNode</a> aNode)</code>
<div class="block">Returns the nearest common ancestor to this node and <code>aNode</code>.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing methods, and an explanation">
<caption><span>Methods in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a> with parameters of type <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getChildAfter(javax.swing.tree.TreeNode)">getChildAfter</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aChild)</code>
<div class="block">Returns the child in this node's child array that immediately
follows <code>aChild</code>, which must be a child of this node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getChildBefore(javax.swing.tree.TreeNode)">getChildBefore</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aChild)</code>
<div class="block">Returns the child in this node's child array that immediately
precedes <code>aChild</code>, which must be a child of this node.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><span class="strong">TreeNode.</span><code><strong><a href="../../../../javax/swing/tree/TreeNode.html#getIndex(javax.swing.tree.TreeNode)">getIndex</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node)</code>
<div class="block">Returns the index of <code>node</code> in the receivers children.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getIndex(javax.swing.tree.TreeNode)">getIndex</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aChild)</code>
<div class="block">Returns the index of the specified child in this node's child array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#getPathToRoot(javax.swing.tree.TreeNode)">getPathToRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode)</code>
<div class="block">Builds the parents of node up to and including the root node,
where the original node is the last element in the returned array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#getPathToRoot(javax.swing.tree.TreeNode,%20int)">getPathToRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode,
int depth)</code>
<div class="block">Builds the parents of node up to and including the root node,
where the original node is the last element in the returned array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a>[]</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#getPathToRoot(javax.swing.tree.TreeNode,%20int)">getPathToRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode,
int depth)</code>
<div class="block">Builds the parents of node up to and including the root node,
where the original node is the last element in the returned array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#isNodeAncestor(javax.swing.tree.TreeNode)">isNodeAncestor</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> anotherNode)</code>
<div class="block">Returns true if <code>anotherNode</code> is an ancestor of this node
-- if it is this node, this node's parent, or an ancestor of this
node's parent.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#isNodeChild(javax.swing.tree.TreeNode)">isNodeChild</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> aNode)</code>
<div class="block">Returns true if <code>aNode</code> is a child of this node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#isNodeSibling(javax.swing.tree.TreeNode)">isNodeSibling</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> anotherNode)</code>
<div class="block">Returns true if <code>anotherNode</code> is a sibling of (has the
same parent as) this node.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#nodeChanged(javax.swing.tree.TreeNode)">nodeChanged</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node)</code>
<div class="block">Invoke this method after you've changed how node is to be
represented in the tree.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#nodesChanged(javax.swing.tree.TreeNode,%20int[])">nodesChanged</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node,
int[] childIndices)</code>
<div class="block">Invoke this method after you've changed how the children identified by
childIndicies are to be represented in the tree.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#nodeStructureChanged(javax.swing.tree.TreeNode)">nodeStructureChanged</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node)</code>
<div class="block">Invoke this method if you've totally changed the children of
node and its childrens children...</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#nodesWereInserted(javax.swing.tree.TreeNode,%20int[])">nodesWereInserted</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node,
int[] childIndices)</code>
<div class="block">Invoke this method after you've inserted some TreeNodes into
node.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#nodesWereRemoved(javax.swing.tree.TreeNode,%20int[],%20java.lang.Object[])">nodesWereRemoved</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node,
int[] childIndices,
<a href="../../../../java/lang/Object.html" title="class in java.lang">Object</a>[] removedChildren)</code>
<div class="block">Invoke this method after you've removed some TreeNodes from
node.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../java/util/Enumeration.html" title="interface in java.util">Enumeration</a></code></td>
<td class="colLast"><span class="strong">DefaultMutableTreeNode.</span><code><strong><a href="../../../../javax/swing/tree/DefaultMutableTreeNode.html#pathFromAncestorEnumeration(javax.swing.tree.TreeNode)">pathFromAncestorEnumeration</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> ancestor)</code>
<div class="block">Creates and returns an enumeration that follows the path from
<code>ancestor</code> to this node.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#reload(javax.swing.tree.TreeNode)">reload</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> node)</code>
<div class="block">Invoke this method if you've modified the <code>TreeNode</code>s upon which
this model depends.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><span class="strong">DefaultTreeModel.</span><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#setRoot(javax.swing.tree.TreeNode)">setRoot</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> root)</code>
<div class="block">Sets the root to <code>root</code>.</div>
</td>
</tr>
</tbody>
</table>
<table border="0" cellpadding="3" cellspacing="0" summary="Use table, listing constructors, and an explanation">
<caption><span>Constructors in <a href="../../../../javax/swing/tree/package-summary.html">javax.swing.tree</a> with parameters of type <a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a></span><span class="tabEnd"> </span></caption>
<tr>
<th class="colOne" scope="col">Constructor and Description</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colLast"><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#DefaultTreeModel(javax.swing.tree.TreeNode)">DefaultTreeModel</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> root)</code>
<div class="block">Creates a tree in which any node can have children.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colLast"><code><strong><a href="../../../../javax/swing/tree/DefaultTreeModel.html#DefaultTreeModel(javax.swing.tree.TreeNode,%20boolean)">DefaultTreeModel</a></strong>(<a href="../../../../javax/swing/tree/TreeNode.html" title="interface in javax.swing.tree">TreeNode</a> root,
boolean asksAllowsChildren)</code>
<div class="block">Creates a tree specifying whether any node can have children,
or whether only certain nodes can have children.</div>
</td>
</tr>
</tbody>
</table>
</li>
</ul>
</li>
</ul>
</div>
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Q: How to parse JSON string in php I'm getting below JSON response:
[{"startDate":"2012-07-12 11:21:38 +0530","totalTime":0},{"startDate":"2012-07-11 11:27:33 +0530","totalTime":0},{"startDate":"2012-07-16 18:38:37 +0530","totalTime":0},{"startDate":"2012-07-17 14:18:32 +0530","totalTime":0}]
i want make array of start date and totalTime, i have used these two lines but it wont work $obj, please suggest..
$obj = json_decode($dateTimeArr);
$dateAr = $obj->{'startDate'};
A: It is very easy:
$Arr = json_decode($JSON, true);
A: As everyone said, and you did - use json_decode.
$dateArrays = json_decode($dateTimeArr, true); // decode JSON to associative array
foreach($dateArrays as $dateArr){
echo $dateArr['startDate'];
echo $dateArr['totalTime'];
}
In future, if you are unsure what type or structure of data is in the variable, do var_dump($var) and it will print type of variable and its content.
A: json_decode() will give you nested PHP types you can then descend to retrieve your data.
A: use json_decode($json_response,true) to convert json to Array
A: Guess what you are looking for is json_decode()
Check out http://php.net/manual/en/function.json-decode.php for the inner workings
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You are here: Home1 / Charity2 / Giving Back Projects3 / 2% of KC employees' income tax went to NGOs
2% of KC employees' income tax went to NGOs
April 17, 2014 /in Giving Back Projects, Social Support
By choosing to redirect 2% of their income tax to NGOs, KeepCalling employees confirm the support that the company constantly offers to local and international organizations. One thing is sure. KeepCalling and the NGOs receiving the 2% contribution have common aims: to support health care and to boost the early education of poor children with the final aim of social integration.
Due to its business orientation towards ethnic groups worldwide, KeepCalling's personality encourages the support of smaller communities through humanitarian actions.
In 2014, KeepCalling encouraged its employees to donate 2% of their income tax to good causes again. Two of the favored organizations were also found on last year's list, while the other two are brand new entries among KeepCalling employees' preferences.
The NGO which received the most donations is SMURD, Romania's most popular emergency rescue service, followed by Animal Life, a local NGO dedicated to helping stray animals. SMURD was also a top favorite in 2013, while Animal Life makes a new entry this year. SMURD and Animal Life were followed by OvidiuRo, also present on last year's list, and AIESEC, marking its premiere among KeepCalling's most appreciated NGOs.
Animal Life is an organization whose volunteers are united by their love for animals and the wish to help them. It was founded in 2006 and its main purposes are finding homes for stray animals and offering medical assistance to animals in danger. Animal Life also promotes the idea of international animal adoptions.
AIESEC is the most popular student organization in the world. It is active in over 114 countries and comprises a number of 83,000 members. AIESEC members are interested in leadership, management, and global issues. The NGO's vision statement is `Peace and fulfilment of humankind's potential`.
This year, KeepCalling team in Romania chose to transfer 2% of their income tax to several national wide NGOs. Three of the top preferences were the Red Cross, SMURD (a popular emergency rescue service) and OvidiuRo, the humanitarian organization whose mission is to support early education. The 2% income tax "donation" is a citizen's simplest way to support a cause.
The initiative taken by KeepCalling employees is part of a complex program aiming to support NGOs that bring real value and generous benefits, regarding formal or informal education, environmental protection, health care or sports. The involvement of the company and its members in social and educational actions is closely bound to KeepCalling's motto: "Give something back to the community."
Top of the NGO list was SMURD. The organization is independent and highly active, plus it is politically neutral, three aspects which match an ideal way of doing things. Moreover, the importance and impact of such a public service are extraordinary. The constant need to have it active in the community is confirmed on daily basis.
As for the Red Cross in Romania, it was KeepCalling members' turn to support it now, after the company had contributed in 2010 to the effort of the international Red Cross team in helping the victims of the earthquake in Haiti.
KeepCalling team also turned their attention towards OvidiuRo. The connection with this early education supporter has already been established in 2012 by the company itself, when KeepCalling contributed to the program "Every child in preschool" ("Fiecare copil in gradinita") by donating $3000.
3D secure – an additional layer of security on all KeepCalling websit... New KeepCalling app version for iOS users | {
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Patients Collaborating with Teams (PaCT) is a partnership between Alberta Health Services (AHS) and the Alberta Medical Association - Toward Optimized Practice (AMA TOP) supported by patient representatives, the Health Quality Council of Alberta (HQCA) and the Alberta Cancer Prevention Legacy Fund (ACPLF).
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If you have questions, would like to get involved or just want to learn more, visit PaCT on the TOP website. | {
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AVCWare Total Video Converter Plus Version 6.0.8.0806 Download - AVCWare Total Video Converter Plus is capable of converting nearly all popular videos formats like AVI, MPEG, WMV, DivX, MP4, RM, MOV, XviD, 3GP and audio MP3, WMA, WAV, RA, M4A, AAC, AC3, OGG between each other.
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As children, we are masters at the art—or at least the attempt of—circumvention. Simply put, kids are in the business of getting what they want. Parents in the business of running block against some of those (often ill-planned) things that children want.
Enter the Art of Circumvention.
The child will either bypass the more "difficult" (translation: more likely to say "no") parent in favor of the more lenient parent; or the child will simply find a way to get around having to ask permission at all. Often it's the latter.
Usually, the parents catch wind and the kid gets caught.
What happens in those cases where the kid doesn't get caught? To their sheer delight, the child revels in the fact that he or she was able to pull a fast one on the 'rents. But in the end—it's the kid who ends up losing . . . because so often a decision to circumvent the authority figures in our lives (Mom, Dad, grandparents, etc.) gets us into trouble. Think dangerous places, dangerous crowds, etc. Parents stand as the gatekeepers of their child's decisions, attempting to field out the dangerous ones and protect the young one.
Most things in life work this way. Our lives are surrounded by rules meant to keep us from going a step too far. Our government is no different.
When our Founding Fathers crafted the structure of our unique system, they knew first-hand what living under the rule of a leader exempt from the rules was like. England, like most places in Europe, had lived under the thumb of a string of monarchs who had near god-like power. Take the infamous Henry VIII, who broke with Rome and created his own church just so he could divorce his first wife, Catherine, and marry the much younger and more attractive Anne Boleyn. Or consider his daughter Queen Mary I who—deeply Catholic, and deeply slighted by her father's rejection of her Catholic Spanish mother—earned the grim moniker "Bloody Mary" for the way that she persecuted non-Catholics during her reign. The examples are many. They could do virtually whatever they wanted, and they did.
Despite some initial desires to create a brand new American monarchy, the Founders instead wisely divided the government into three branches—the legislative, judicial, and executive branches that we have today, limiting the power each branch could wield over the American people they serve. Parameters were put into place to curb our natural human tendency to circumvent the rules in search of the path of least resistance; the easiest path to whatever it is we all want.
So, what does President Barack Obama want?
We all know he wanted the Affordable Care Act. So much so that it was jammed through Congress by his supporters without so much as one vote from the opposing party.
Barack Obama got what he wanted, and on March 23rd, 2010 he signed the Affordable Care Act into law. Signed, sealed, and delivered.
Despite having achieved passage of his signature piece of legislation, this law has never enjoyed majority support. In fact, its numbers have never been spectacular . . . and when the particulars of the law began trickling down into Main Street U.S.A., the numbers did nothing but nose-dive.
So, again, what does President Obama want?
There's an election coming up in 2014. Not unlike any other president in his position, President Obama wants to keep the Senate, and take back the House. With his own job approval numbers hitting epic new lows and Congressional job approval hovering shamefully in a deep, deep hole, the President knows he can't afford to take any more flack from the Obamacare "horror stories" that seem to surface anew each day—despite Senator Harry Reid's claim that they're all lies.
Circumvent the law . . . again . . . and the inevitable negative impact becomes somebody else's problem down the road.
Much to the contrary of what is quickly becoming "popular belief," the president has zero power to draft, change, or bypass legislation.
Yet, this isn't the first time. The administration has now (including this most recent change) arbitrarily changed the health care law 11 times. (It's 28 times if you include the times when Congress and the Supreme Court got involved.) This is just one law, however, and this certainly isn't the administration's first rodeo. From its order to the Department of Justice to cease upholding the federal Defense of Marriage Act in court, to issuing immigration law by fiat, this administration has long been in the practice of refusing to abide by the laws and constraints in place.
It's really irrelevant whether or not Congress is cooperating with the President. The fact of the matter is that we have laws and we have Constitution, and operating by anything less is simply dictatorial. What else do you call a leader who doesn't follow his nation's laws? Indeed, what separates our President from, for example, Vladamir Putin, who simply decided to take Crimea for his own? After all, it could be said that had Putin waited around for the Russian population in Crimea to work with the Ukrainian government to legally separate themselves from Ukraine, it never would have happened . . . and after all, Putin needs that port in the Black Sea now. So, it's ok, right?
Responding to a condemned Jesus, Roman leader Pontius Pilate once famously asked, "What is a truth?" Such a flippant worldview invites disorder . . . after all, if there is no truth, there is no way to establish order.
Similarly, without a Constitution and without rule of law, there can be no order—only the whim of the leader in power. If such a thought doesn't particularly bother you, I ask you to imagine the current situation reversed. Consider a person or party you oppose wielding the very same power, except this time shredding our nation's laws in favor of what you oppose. It's dangerous, no matter what party is in power.
The world is full of places led by a single person, or a single party—Venezuela comes to mind at present—and such dictatorial rule eventually necessitates suppression to quiet those who refuse to cooperate. After generations as the world's bastion for freedom, do we really want to join such ranks?
We understand that Obama has circumvented many laws, but looking at all the regulations we're under we haven't been free in a long time. The question that I have been asking is how can we circumvent the laws and become free again?
It is refreshing to read such concise, articulate writing. I look forward to reading more of your work. | {
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Q: Why I have this error? ArrayIndexOutOfBoundsException I'm creating a android application. When I tested in Emulator, Samsung S8 Plus and General Mobile GM8, I haven't any error but play console always gives me some crushes.
Code is:
int count = getItemCount() >= 30 ? 30 : getItemCount();
if (count == 0)
return new long[] {0};
long[] result = new long[count];
for (int i = 0; i < count; i++)
result[i] = users.get(i).getPk();
return result;
Error message:
ArrayIndexOutOfBoundsException
How I can fix it I really do not know.
A: remove the "=" sign in the condition it will work properly :
int count = getItemCount() > 30 ? 30 : getItemCount();
if (count == 0)
return new long[] {0};
long[] result = new long[count];
for (int i = 0; i < count; i++)
result[i] = users.get(i).getPk();
return result;
A: For eg. if count is 4 and users list have only 3 data or less than count then it will throw ArrayIndexOutOfBoundsException
To avoid ArrayIndexOutOfBoundsException try below approach
int count = getItemCount() >= 30 ? 30 : getItemCount();
if (count == 0)
return new long[] {0};
long[] result = new long[count];
if(users != null && users.size() > 0){
for (int i = 0; i < count; i++){
if(i >= users.size()){
break;
}
result[i] = users.get(i).getPk();
}
}
return result;
A: If what you want is an array with size equal to the size of the users list with maximum 30 items and minimum 1 element, then change count to the users list size if this size is less than 30:
int count = getItemCount() >= 30 ? 30 : getItemCount();
if (count > users.size())
count = users.size();
if (count == 0)
return new long[] {0};
long[] result = new long[count];
for (int i = 0; i < count; i++)
result[i] = users.get(i).getPk();
return result;
A: It can happen because of out of index.
Let me make it simple if array have 4 indexes so
a=[0,1,2,3]//eg:
SO that if you want to print a[0] then
o/p=
0
But for a[5]:
you will have ArrayOutofBoundsExeption
Here in your example you have not specified your user field How it is generated so after making some assumptions..
Im telling you
result[i] = users.get(i).getPk();
here the problem is occured in users.get(i)
where user field is not that contains value but it may be dynamic:
so my solution will be
You should use
Try exception and just pass it ArrayIndexOutOfBoundsException
and raise exception your program should work fine!
I hope it will help you!
A: It seems the size of users list does not equal to counts and it is smaller. so to prevent ArrayIndexOutOfBoundsException, I suggest to edit your code in this way:
int count = getItemCount() >= 30 ? 30 : getItemCount();
count = count > users.size() ? users.size() : count;
if (count == 0)
return new long[] {0};
long[] result = new long[count];
for (int i = 0; i < count; i++)
result[i] = users.get(i).getPk();
return result;
by modifying your code like that, in situations that users list is greater than counts, you will not have any controls on the items at the end of users list.
| {
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Welcome to the Website of Lisa Taitel and Solid Source!
A Short Video about me can be found Here.
Here you will find a wide variety of useful information and resources designed to help you buy or sell a home in the Reno/Sparks areas. From information on the local community, to advice about finding a mortgage or preparing your home to sell, it's all available here on my web site. You can also search for your ideal home by viewing current listings with detailed descriptions and photos; or you can get help determining the value of your home by requesting a report that includes the prices of similar homes that recently sold or are currently for sale.
So whether you are a first time buyer or an experienced investor, feel free to contact me at 775.829.8299 and I will be happy to help you with all your real estate needs.
Thank you for visiting my online real estate source. Please mark this site for future reference and use, and most of all, enjoy! | {
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Gradido account
About Gradido
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"If everyone looks forward together, success will come naturally."
Do you also wish that as soon as possible the things of daily use are available for Gradido and the dream of worldwide prosperity and peace for the human family becomes reality?
But instead of worldwide prosperity and peace, just the opposite seems to be going on. Even here in Central Europe, more and more people are slipping into poverty, and mass bankruptcies are imminent - not to mention the many other problems. Can we 'little people' still counteract in time and effectively to create a future worth living in appreciation, gratitude and love for each other? We owe it to ourselves, our children and all the children of the world to undertake this with all the means at our disposal.
'Undertake' the future
Speaking of 'companies': it is often the self-employed and entrepreneurs who use their competence and know-how, as well as the necessary means, to positively shape the future with their heart and soul. More and more are recognizing the signs of the times and are networking. Recently Bernd was invited by a local group of an entrepreneur network to present Gradido. Afterwards, he answered quite a few questions - to the full satisfaction of the 30 or so listeners present, as the host told us.
The greater the crisis, the greater the opportunity
Now that the fatal consequences of the debt money system are becoming obvious, more and more people are waking up and starting to form alternative structures. In the communities that are emerging in this way, we have the historic opportunity to create a new monetary system together that is based on appreciation, gratitude and love. Gradido is created decentrally by us people for us people in networked communities. Every person can contribute to the common good with his or her very special gifts and thus create his or her Active Basic Income. The Gradidos created in this way are then available for exchange among each other.
As you know, our earth can feed a multiple of the world's population in high quality organic food. But there are no financial means available for this, because in the old system the money flows to the 0.01% unimaginable super rich, who follow their own agenda.
With this, the solution is clear:
With Gradido, we the people are building a new financial system from below that makes the old system obsolete.
Together we are successful
Initially isolated, then in more and more places, and suddenly everywhere, Gradido communities are sprouting up like mushroom crops. The numerous communities are decentrally networked and can no longer be stopped. Together we can produce everything we need for a fulfilled life. We then no longer need the money of the super-rich: "Imagine they have all the money in the world, but no one wants it!" - Then we are free!
A thousand thanks for your support!
At this point we thank all of you from the bottom of our hearts who contribute to the great common goal: the liberation of the human family in prosperity and peace and harmony with nature. You are the true heroes of the future, because you know: it is all about the whole.
Thanks to your generous sponsorship contributions, we can continue to fund the development of the decentralized and scalable Gradido account, so that when the time comes, it will be available to all people - including the poorest - free of charge.
Of course, you are welcome to join us even if you cannot or do not want to provide financial support, because everyone has their own special gifts. Some have time, some have money. Others have other resources, still others a little bit of everything. Everyone can contribute - including you!
You don't have a free Gradido account yet?
>>>Register it today!
You are interested in our support program and would like to receive more than 18 times GradidoTransform as a thank you?
>>>Inform yourself here!
The collapse of the second largest crypto exchange 'FTX', whose customers were relieved of several billions, recently showed once again that BitCoin & Co are no solution.
"When everyone looks forward together, success comes naturally," said Henry Ford. By joining forces, we will create a future worth living for everyone. Misery, hunger, environmental destruction and wars will then come to an end, and no one will have to flee their homeland. Our beautiful earth will once again become the paradise it was presumably once intended to be - for ourselves, our children and all the children of the world.
Thank you a thousand times for being with us and co-creating the livable future!
Margret Baier and Bernd Hückstädt
Gradido founder and developer
PS: Because of the great success, we repeat the gratitude action on December 22. In addition to the multiple GradidoTransform for your funding contribution, we will increase all GDT account balances by 22% on December 22, 2022.
Market+Community
Contact+Support
© 2023 Gradido Academy - | {
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We offer SCARA3 Lysates for use in common research applications: Western Blot. Each SCARA3 Lysate is fully covered by our Guarantee+, to give you complete peace of mind and the support when you need it. Our SCARA3 Lysates can be used in a variety of model species. Use the list below to choose the SCARA3 Lysate which is most appropriate for your research; you can click on each one to view full technical details, images, references, reviews and related products. Choose from our SCARA3 Lysates. | {
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I routinely download books from my public library to my Kindle reader before I leave on a cruise. I never buy any Kindle books. I just borrow them. The problem is that you can only borrow them from the library for 21 days and I have several longer cruises coming up with a number of sea days. I hate sea days and the only thing that keeps me sane on sea days is having something to read.
I wonder if anyone has ever downloaded library books to a Kindle using the ship WiFi. I know that ship WiFi is slow but I am unlimited internet time so a slow download time is not a problem.
1) I link my Kindle to the address of the ship WiFi. This might present a problem if the link to the ship WiFi is not possible or a password is necessary.
2) I log onto the library site on pick the book(s) to download. I would make a list of books to download in advance as browsing the library site is slow.
3) I select a book to download and the library sends the book to my account on Amazon. This would essentially require that I am linked to 2 places on the internet - my library and to Amazon.
4) The book is then transferred to my Amazon account and is then transferred wirelessly to my Kindle.
Does any of this make any sense? Is it possible? Is anyone who goes on cruises doing this? If this would not work does anyone have any other suggestions.
I know that I could buy the books from Amazon but I don't want to buy them. I want to borrow them and return them when I am done reading them.
There are literally thousands of FREE Kindle books that you can download from Amazon. Why not just do that?
Good thought. I had not thought of that. Thanks.
I have downloaded books on my kindle before while on the ship. It's slow and frustrating, but do-able. I got frustrated, because sometimes it will drop the signal when the book is 1/2 downloaded, so you have to reconnect before you can finish downloading the book. I have since just started putting some paperbacks in my luggage. I still like a good book, in book form. But to answer your question - if you have the patience for it, yes, it can be done!
I believe if you download all of your books and then put your Kindle in airplane mode you should be fine.
While it is possible to find a good free kindle book from Amazon, my experience is if you want a popular good best seller, you will have to buy. On my cruise I was able to download an eBook from the library, but not without some frustration and effort. My advise would be to just spend a few bucks and buy some good books from Amazon before the cruise if you will be gone for more than 21 days. | {
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Shakespeare: The fault, dear Brutus, is not in our stars/ but in ourselves.
I have been anticipating this book for a while now. Not just because it's by John Green who is an amazing writer. But also because of the story's premise.
A dying sixteen year old girl named Hazel Grace meets Augustus Waters, a gorgeous boy who also happens to have cancer. He falls for her fast. But Hazel, knowing her death is near, pulls back.
Both are quick witted with very deep thoughts about everything, including a particular book written by a recluse, Peter Van Houten. So Gus decides to use his one WISH (basically a wish granted as a gift by The Genie Foundation specifically for very sick children) to take Hazel to Amsterdam to meet the author.
The trip turns out to be good and bad. Bad because Houten is a drunk loser who tells them nothing they want to know. And Good because finally Hazel relents to loving Gus back. But just when happiness seems possible for the two, Gus finds out his cancer has spread. Now it's just a matter of time before one of them dies.
The first few chapters were hard to process. It felt like I was watching Joey and Dawson in the 90's TV show Dawson's creek in the way they talked to each other. As if existentialism is a part of their daily discussion. But slowly I fell in love with Hazel and Gus. So much so that I almost bawled at the pre-eulogy. But that's getting ahead of the book.
One thing about both is that they are brave, they fight to live and to love. Gus is a sweetheart. His sunny disposition and love for Hazel breaks down her walls. But the tables are turned past half of the book. And you'll see Hazel come into her own for Gus. To help him accept the hand they've been dealt.
This is a great book that will squeeze you dry of tears. Your heart will break. And you will be devastated. But you will also appreciate that life is a gift, and that loving, no matter how short it may be, is always worth the eventual heartbreak.
Looks like a good tearjerker :) Thanks for the review!
This book is (in my opinion) John's best book yet. At one point I was literary laughing out loud only to turn the page and start sobbing (Like Hazel's dad, I'm a bit of a crier). I have never been so emotionally moved by a book and the writing style and dialog is fantastic. Everything was natural and fluid. I would recommend this book to anyone from the cynical to the hopeless romantics. | {
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Q: How to reset checked checkboxes on button click? (vue.js) I am working on a custom search filter, where you can tick off checkboxes to better fit what you're looking for. (Working with Vue.js)
I also want to add a "clear" button, that gets rid of your all the ticks you made previously in the checkboxes. I have this for the button:
<button @click="clear">
<span class="letterspace">クリアする</span>
</button>
and I'm not so sure how to define the method but I wrote it like so:
methods: {
clear() {
(this.selectLocations = []), (this.selectItems = []);
}
}
this is the code I have for the checkboxes:
<div class="checkboxArea" v-show="showItem">
<div id="checkboxes" v-for="(value, index) in items" :key="index">
<label for="select" id="one">
<input type="checkbox" :value="value" v-model="selectItems[index]" />
{{ value }}
</label>
</div>
</div>
where selectItems is defined as an empty array in the data property:
data() {
return {
selectItems: []
};
},
Can somebody please help me figure this out?
A: I don't know where this.selectLocations comes from because I don't see it in the template, but your function cannot work like that.
To reset your selectItems, you'd need to say:
clear() {
this.selectItems = [];
}
This will empty the selected items and deselect all checkboxes again.
A: This is better approach imo.
<template>
<div>
<button @click="clear()">Clear</button>
<div v-for="(item, index) in items" :key="index">
<label>{{ item.label }}</label>
<input v-model="item.selected" type="checkbox" />
</div>
</div>
</template>
<script>
export default {
data() {
return {
items: [
{
label: 'Select 1',
selected: false,
},
{
label: 'Select 2',
selected: false,
},
],
clear: () => {
this.items.forEach((item) => (item.selected = false));
},
};
},
};
</script>
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"Life is a bridge. Don't build a house on it"
Someone called Nizar asked me about this quote today:
"Life is a bridge. Don't build a house on it."
This is often just called an "Indian proverb," but several books, including "Human Life and the Teachings of Buddha" (1988), by Mandar Nath Pathak, attribute this to the Buddha. In "Buddha and the Rasava" (1958), Kumaraswamiji offers an extended version, which he also attributes to the Buddha:
Life is a bridge, build no house upon it; it is a river, cling not to its banks; it is a gymnasium, use it to develop the mind on the apparatus of circumstance; it is a journey, take it and walk on.
A version of this saying ("Life is a bridge. Cross over it, but don't build a house on it.") is attributed to the late Sri Sathya Sai Baba.
It should be pretty obvious to anyone familiar with the Buddhist scriptures that this is not a canonical quotation. The directness of the metaphor and the wording are completely off.
The earliest use of this maxim that I've found so far is in "The Bridge-Builders, and Other Poems" (1908), by H. Harrold Johnson:
"Life is a bridge: pass over it, but build not houses upon it."—Old saying.
No further reference is given.
The English Buddhist writer Christmas Humphreys used essentially the same quote in several of his books. For example in "Studies in the Middle Way: Being Thoughts on Buddhism Applied" (1940), he has
"Life is a bridge: pass over it, but build no houses on it."
This he attributes to Akbar — presumably Akbar the Great, or Akbar I, who was Mughal Emperor from 1556 until his death in 1605. But elsewhere Humphreys says this is an old Chinese proverb.
In the biographical work, "Clendon Daukes, Servant of Empire" (1951), written by Lady Dorothy Maynard Lavington Evans Daukes, we read:
We also visited Fatehpur Sikri, that deserted city of a byegone age, built of red sandstone by the Emperor Akbar. We mused over the Arabic inscription on the great gateway: "Life is a bridge, a bridge that you shall pass over. You shall not build your house upon it."
According to the Wikipedia entry on Buland Darwaza, the Persian inscription says:
Isa (Jesus), son of Mary said: 'The world is a bridge, pass over it, but build no houses upon it. He who hopes for a day, may hope for eternity; but the world endures but an hour. Spend it in prayer for the rest is unseen.'
So Akbar was not the author, but was passing on a quotation, although where it's from, I don't know.
The Buddha did use metaphors regarding bridges: sometimes emphasizing their fragility, as in when he talked of blotting out the conceit "I am" as the wind demolishes a fragile bamboo bridge, and sometimes emphasizing their utility, as when he talked of crossing "the flood" by means of a bridge while others scrambled to get frail rafts together.
Posted on October 31, 2014 November 7, 2022 Author BodhipaksaCategories Fake Buddha Quotes
7 thoughts on ""Life is a bridge. Don't build a house on it""
starnutoditopo says:
I recently visited Taj Mahal and I've been told one of the inscriptions to be exactly this phrase. So it could be attributed to Akbar's grandson. But it could be a quotation from Coran. To be checked…
Al Lockett says:
2. Teaching in Sidon
In entering Sidon, Jesus and his associates passed over a bridge, the first one many of them had ever seen. As they walked over this bridge, Jesus, among other things, said: "This world is only a bridge; you may pass over it, but you should not think to build a dwelling place upon it."
This is a quote from the Urantia Book, section lV: Life and Teachings of Jesus.
Bodhipaksa says:
More information on the Urantia Book, in case anyone is interested.
JMB says:
Found this one. Mahayana Buddhist. This saying seems tied to North India.
You are like a traveler in this life. So don't build a castle where you are just passing by.
~ Padampa Sangye
Thanks. Where's that from? I've found the following attributed to Patrul Rinpoche, but not in many places: "You are a traveler in this life, don't make a castle wherever you are resting for a while."
Eric Sanburg says:
The Gospel of Thomas logion 42 simply says, Yeshua said, "Be passersby".
Previous Previous post: "Your days pass like rainbows, like a flash of lightning, like a star at dawn. Your life is short. How can you quarrel?"
Next Next post: "Compassion is that which makes the heart of the good move at the pain of others." | {
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A friend and I had drawn up a basic design for a lamp with constellations that we wanted to make using a laser cutter. Over the summer I finally had the time to build the structure in a CAD program, and create the constellation art so that it can be built. After a couple versions of the lamp, I've come up with a pretty good process for constructing it.
I bought most of these parts in semi bulk, but the rough estimate that I would give for the cost of building this lamp was around $20.
I've added links to the parts I purchased to give you an example of what the parts look like.
I designed the lamp so that the beam angle (120 degrees) will allow the light to directly hit all parts of the constellations. If you choose a bulb with a smaller beam angle, not all of the holes will be directly lit; this will result in a slightly dimmer glow (after testing, I found this was that big a deal). Also, it is ideal if you can find a bulb that only has one LED/light source on it. This would allow the lamp to cast accurate shadows of the constellations on a wall. I was only able to find MR11 bulbs that had multiple LED lights on each bulb.
If you get a socket base with a diameter that is different than the one that I used (17mm), you are going to want to adjust the corresponding diameter to the part that the socket glues to in the laser cutter file. You want a snug fit, because the socket glues directly on to the piece.
The super glue needs to be quick drying because you need to hold pieces in place. Other glues I used but are optional are a tacky glue to seal cracks in joints to keep too much light from leaking from them, and an expanding glue to help hold the socket base in place.
I built this assembly in Rhino, so I included the original file type here, but also exported it to ai and dxf. Make sure the imported file matches the first picture in this step. Let me know if you have trouble importing the file, and I'll see if I can fix it on my end.
To check and make sure the scale is correct when you import it, the length of the top right piece in the assembly should be about 3 in/7.68 cm (picture 2).
Once you have the file correctly imported, laser cut the assembly. The part file is made to fit an 18x24 inch piece of birch plywood.
The order I recommend for the lamp is staining the pieces --> assembling the lamp --> applying the wood finish. I recommend this order because I found that if you assemble the lamp first, the glue can keep the stain from soaking in the wood, which can result in a splotchy stain.
After laser cutting the pieces, you may want to sand all of the pieces you intend to stain using a reasonably fine sand paper (I used 220 grit), which will help smooth the birch plywood.
Next, apply the stain to the outside pieces of the lamp, using 2-3 coats (I used 3).
Then glue the socket base to it's corresponding piece by laying it onto a flat surface (so the socket will dry level), and gluing around the edges. If you want to use an expanding glue at this point, you can apply it around the edges now too.
I found that wax paper works reasonably well for gluing on, as it doesn't stick to the glue too readily.
Note I'm using disposable latex gloves here; I found out from first-hand experience that the super glue will gladly stick to your fingers, and peeling your fingers off the wood isn't particularly enjoyable.
Also, I will be using the word "joint" throughout the Instructable, which is referring to the edges and slots of many of the pieces that allows them to mesh together.
Start by gluing on the 4 pieces with long bent arms to the base, and make sure you do the two that go on the bottom first. I put super glue in all of the joints that meshed the pieces.
Note: Make sure that the side with the hole in it is in line with the other hole in the bottom assembly.
Next, glue the sides on. When gluing the sides, make sure you push the side down and against the base so that each piece is sitting correctly before the glue dries. Also, the 4 side pieces have two different types of joints mesh, so make sure that the two sides mesh together before applying the super glue and trying to stick them together.
Next, put together the top assembly. Do this by gluing the inner and outer triangular pieces together (first 4 pics). There should be 3 lines on the 3 sides of the inner triangle that were etched in when they were laser cut; these correspond to where the inside edges of the outer triangle go when you glue the pieces together. Once you glue them together, make sure to wipe off any residual glue (3rd pic), because you don't want that drying where the constellation panels are going to go (else they won't sit right).
Then glue the combined triangular pieces together by putting glue in the joint and holding the two pieces together perpendicular to each other until the glue is dried. Do this for all four pieces, and once that is done, glue the piece with a crescent moon to the top.
Now join the top and bottom assemblies of the lamp. When doing this, try to make sure that the glue is on all of the sides of the joints, because it is important to maximize the surface area that is glued.
Next apply wood finish to the lamp if you plan on using finish. I used two coatings on the lamp structure, and just one on the constellation panels. I only did one on the panels because I had to use a toothpick to make sure that the finish wasn't getting into the holes and lines that were a part of the constellation pattern (this would dim the light, which I didn't want). Also make sure to wipe up any wood finish that pools up on the inside edges of the lamp (pic 3).
Attach the wires from the socket base to the adapter, and then glue the adapter into place in the hole on the side. This might be another place where using a glue with a thicker viscosity (like tacky or expanding glue) would help setting the piece in place.
Finally, you will want to put the constellation panels onto the lamp. I used magnets to hold the panels in place, because I wanted to leave the option open for making different types of panels that I could put into the lamp later. However, if you only plan on using these ones, I would recommend gluing the panels on (with the possible exception of one of the panels, so you can access the inside). | {
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Gibbsia carstenszensis är en nässelväxtart som beskrevs av Alfred Barton Rendle. Gibbsia carstenszensis ingår i släktet Gibbsia och familjen nässelväxter. Inga underarter finns listade i Catalogue of Life.
Källor
Nässelväxter
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The desolate wasteland calls once again, its weird and wonderful characters ready to share banter while merciless creatures wait in the shadows for their chance to spill blood; welcome to Fallout 4.
Bethesda's latest offering from the long-standing post-apocalyptic series arrives in Boston, Massachusetts, sharing many of the city's landmarks and customs to great effect; the developer clearly doing their homework. A difference from previous installments is the chance to play the game before the world turns to mush, enjoying life in a suburban neighborhood as a father, husband, and retired soldier.
Things take a turn for the worst just after entering Vault 111, frozen in time and awoken 200 years later only to see your son kidnapped by some shifty looking figures, thus beginning a journey through the wasteland to track him down. The connection to the main narrative is a real let down on Bethesda's part by not keeping the character invested in the welfare of his son. Instead of asking every living soul he meets if they know his whereabouts, you're too busy building settlements and killing Radroaches. This is a common diet for open-world RPGs we know, but on this occasion it really seems like lazy storytelling on the developer's part.
The characters you meet do have their own identity but fail to really grab the moment with any emotion. The dialogue doesn't help either, mostly the main character's sentences will be short and to the point, making you feel more like a cardboard box than a hero. However, the companions available to you do have some personality, Mr. Codsworth one of the more upbeat characters you'll meet. Amazingly the most emotion spilling character is Dogmeat, your canine friend. Even though he can not speak you can grasp his mood, be it playing with a teddy bear or leaving off a small whimper in dismay. Speaking negatively about your fellow companions, they can be a huge pain most of the time and nearly always get in your way when following you.
Continuing with a sequel will always mean improvement from what came before. In Fallout 4 Bethesda added a new feature that allows you to create a settlement from scratch for you and other wasteland survivors. The level of customization is amazing and makes every settlement different, also depending heavily on what location you set up shop. You'll be able to create and place a variant of walls, roofs, and floors for the foundation, then add beds and other furniture to give it a more homely look. Food power, water, and defensive items are also a must, all coming together to keep your settlers happy and most importantly safe.
The workshop menu can be annoying to use at times, most notably the cancel button which is also the button needed to remove an object. This means at times you need to look away from objects completely to just go back to the main workshop menu to be pick another item, a button layout error that could have been avoided Bethesda! To build a settlement resources are needed and the objects you collect around the world will feed the construction machine; wood and steel the most common. Finding resources such as crystal and copper(guide on how to find it) give you a reason to explore the wasteland if you needed one anyway.
Bethesda decided to tinker with Power Armor in Fallout 4 and not only limit how much you can use it but also let you heavily modify it. Power Armor needs Fusion Cores to run, and once it goes empty the suit becomes somewhat useless. Finding scrap and other items to modify it will heighten its stats and make it more enjoyable to run around in, but at the beginning it's a chore to equip.
Gameplay wise not much has changed, everything works the same as previous installments. V.A.T.S(Vault-Tec Assisted Targeting System) returns once again and how each weapon works while using it stying the same, including the Action Points that determine how many times it can be used. One new addition is the "execute critical" option that can be used to land a critical hit once a bar just is filled through attacking enemies. The perk chart hasn't changed much since Fallout 3 and once again offers a plethora of different abilities with the same unlock progression, one star every time you rank up a level which you can add to whatever perk you like.
The heart of combat in Fallout 4 is the weapons, and like previous iterations there's a fine selection on offer. Many have that makeshift look and unlike Fallout 3 and New Vegas, weapon damage doesn't factor, meaning you never have to repair a weapon you create or acquire. On the downside, they have removed the ability to create ammo which was something I enjoyed while playing New Vegas. You have your usual modern-day weapons such as pistols, assault rifles, shotguns, and future weapons likes laser pistols and freezing guns. If you're an avid collector and want the best on offer then searching the wasteland will produce some legendary gear and weapons that perform better than the rest but are always protected by their dangerous keeper.
Fallout 4 is a beautiful looking game that delivers another healthy dose of post-apocalyptic madness. While it has it current issues with game-crashing bugs and glitches, it doesn't damper the enjoyability of running through the wasteland wasting raiders or building a settlement for your league of followers. It may not have the same positive impact as Fallout 3 or New Vegas, but Fallout 4 is a solid release that deserves every piece of praise it gets.
Have you picked up Fallout 4 yet? Let us know in the comments below and make sure to follow us on Facebook for more of today's gaming news. | {
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Села:
Солов'ївка — Автономна Республіка Крим, Сімферопольський район
Солов'ївка — Дніпропетровська область, Верхньодніпровський район
Солов'ївка — Запорізька область, Михайлівський район
Солов'ївка — Кіровоградська область, Олександрійський район
Залізниця:
Солов'ївка — зупинний пункт Знам'янської дирекції Одеської залізниці
Солов'ївка — село, Мінська область, Логойський район | {
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Paris Saint-Germain is struggling to finish the job in Ligue 1. Remaining on two games without a win in the league, the club has missed the mark on the lawn of his dolphin Lille bowing heavily (5- 1). The men of Thomas Tuchel will therefore play this week their day late against FC Nantes to hope to be champion. Possessing 17 lengths in advance, the PSG could not be caught again in case of success on the ground of Nantes. Despite absences, the capital club will try to revive. Teammates Kylian Mbappé should do everything to take the three points during this game. If FC Nantes has won against Lyon (2-1), the Canaries have still lost four of their last five games.
PSG will be keen to end this series of two games without a win.
FC Nantes have only won one of their last four matches.
PSG can ensure the title of champion if successful.
FC Nantes are among the worst-placed teams in the league in the last five days.
PSG have won their last 17 encounters against FC Nantes.
FC Nantes have been doing quite well at PSG in recent seasons. The men of Thomas Tuchel should therefore not be asked to ensure their title of champion of France. | {
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Q: Perl one-liner if else logic I'm evaluating whether or not certain variables match expected values. The variables are set in memory by a certain program, the values of which can be access from the shell with a custom program.
I'm piping the output of the shell command to awk to get the specific field I want and then I want to run it through perl to see if it matches the expected value. For example,
ysgrp autostart | awk -F\: '{print $1}' | perl -e 'print {"True"} else {print "False"} if /on/'
However, I'm getting complaints from perl about compilation errors near "} else". How does one handle if/then/else logic in a perl one-liner?
A: This part:
awk -F\: '{print $1}' | perl -e 'print {"True"} else {print "False"} if /on/'
can be handled in perl (if I remember awk correctly):
perl -F/:/ -lane 'print $F[0] =~ /on/ ? "True" : "False"'
Note the use of the -n switch, without which your perl one-liner will not work. Also note the -l switch, which adds a newline to your print, which is something I assume you want. Otherwise your output will be something like:
TrueTrueTrueFalseTrueFalse
A: You can't use an else condition in a postfix conditional. You can either use a ternary conditional operator like this:
perl -e 'print /on/ ? "True" : "False"'
Or use explicit blocks like this:
perl -e 'if ( /on/ ) { print "True" } else { print "False" }'
A: One does not, except by using the ternary ?: operator; the foo if bar syntax does not support else.
A: You could do:
... | perl -ne 'print /on/ ? "True" : "False"'
but please don't! You'd be better off doing:
... | grep -qF on && echo True || echo False
| {
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Dr. Shyam Sunder Tantia, the Founder Chairman of the Tantia Group was a great visionary & philanthropist with super organizing ability, simplicity and humbleness. By virtue of his initiative, perseverance, resourcefulness and tenacity to overcome, he became a living icon in his lifetime. His ability to translate his dreams into reality elevated him to the stature of a visionary.
He established Tantia Hospital in the year 1982 by taking up psychiatric treatment and proceeded to provide high level patient care and welfare services to the society. Also a pioneer in Sri Ganganagar district & approaching areas of Punjab and Haryana with establishment of radio diagnosis centre in 1994 and C.T.Scan unit in year 2000.Gradually,it has expanded to provide all and best modern diagnostic facilities in whole region.
Then he ventured into the world of education by imparting quality education under the esteemed name of Tantia Higher Education Institutes. The campus comprises of 13 colleges, running medical, para-medical and technical education in this region for past 13 years. The development of various institutions of education and health care thereafter is a saga of perseverance and dedicated work of our beloved Founder.
As of 2013, aforesaid colleges have been merged into one forming part as constituent colleges, a stronger than ever organization came to known as Tantia University. (Established by Rajasthan Govt Act No 32 of 2013 u/s 2(f)of UGC Act 1956.) Getting the University status was the crowning glory for Dr. Shyam Sunder Tantia in his efforts to build centres of excellence.
The heights gained by the Tantia Group bear testimony to his tireless efforts, indomitable will, and strong sense of commitment to his ideals and goals. Our presence in the education sector is an humble tribute to his quintessential existence. | {
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IT staff at Alliance Boots are among those at risk after the company announced it was cutting 900 back office jobs.
The high street pharmacy chain said the cuts would all take place at its head office in Nottingham, hitting IT and other infrastructure and support roles in its Health & Beauty division. At this stage there are no plans to offshore any roles.
Boots aims to cut £57 million from annual costs. Three years ago, the company was bought by private equity firm Kohlberg Kravis Roberts for £11 billion.
In spite of the IT cuts being made, systems will be at the heart of the company's planned transformation. In a statement, Boots said the programme focuses on "optimising end-to-end business processes", including moving to "a leaner central support organisation, supported by new systems" and optimised supply chain and manufacturing.
The cuts represent around 10 percent of the company's support staff, Boots said.
Alex Gourlay, chief executive of the Health & Beauty division at Boots, insisted that the changes were geared at giving the company "a stronger and more agile support infrastructure". | {
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'Hong Kong is becoming like the mainland', author Bi Feiyu says
Bi Feiyu, one of China's leading authors, urged Hong Kong residents to take the lead in preserving the city's culture during an interview with SCMP. Bi said he'd observed "subtle changes" in Hong Kong that he believes will affect the quality of the city and the people within it over time, adding that while good habits can take hundred of years to develop, they can be lost in an instant.
Here's some highlights:
"Unlike my previous stay in 2009, people here no longer say 'excuse me' or 'I'm sorry' when there is bodily contact as they used to. I did a small test on the MTR with my shoulder at one point, but the contacted party did not respond," said Bi, who is spending a month in the city as writer-in-residence at Baptist University.
"I see that as an early sign that Hong Kong is becoming like the mainland. If these sort of things keep happening, it will affect the quality of the city and the people in it," said the 50-year-old novelist, whose Three Sisterswon the Man Asian Literary Prize in 2010. […]
"Good habits take hundreds of years to develop, but losing them could happen very quickly. Hong Kong people should be proud of their culture and etiquette. Safeguard it and don't let it fade away," he said, acknowledging the effect that Hong Kong's colonial past had had in shaping the territory.
"Colonisation is bad, but the diverse culture that comes out of it is good."
Bi is a writer from Nanjing who's known for his open discussion of sensitive social issues, such as the treatment of disabled people. His works are also praised for their portrayal of the "female psyche", and one of his best-known novels, Three Sisters won the 2010 Man Asian Literary Prize.
While talking with the Post, Bi also stressed the importance of hygiene and cleanliness in culture, and called for Hongkongers to "be more tolerant towards the mainland people, who, for their part, should enhance their code of conduct".
Bi's comments edge in nicely to the current riff between mainlanders and Hong Kong residents that began when a family from the mainland allowed their child to pee on the Streets of Hong Kong, eventually leading to a couple of unfortunate protests in the form of bodily functions.
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eehhh,...'The Boat Race'
I have to confess that my left eyebrow shivered a little when I read the news that the annual Oxford and Cambridge University Boat Race – commonly known as 'The Boat Race' – the other day changed its name to The Xchanging Boat Race!
Xchanging, which is a global business processing company, became involved with 'The Boat Race' five years ago as a sponsor. In 2008, the company renewed its sponsorship for five more years. And then the other day, Xchanging became a so called title sponsor for 'The Boat Race'.
Nowadays, it is quite an ordinary thing that sport teams, sport arenas, and sport events sell themselves (and might I add, their souls) to larger business companies. I am sad that the organizers of the 'The Boat Race' and Oxford and Cambridge have felt that they should do so, too. Especially, to a company that I cannot even pronounce correctly.
Of course, just as the Oxford and Cambridge University Boat Race has been called 'The Boat Race', The Xchanging Boat Race can in the future be known as – 'The Boat Race'.
Posted by HTBS editor Göran R Buckhorn at 7:02 PM 2 comments:
Labels: Cambridge, Oxford, The Boat Race
Pocock's Doggett Coat On Display
Last week, rowing historians Bill Miller and Hart Perry (the latter Executive Director of the National Rowing Foundation), and yours truly managed to put together a base and a cover for Dick Pocock's Thomas Doggett's coat and cap (see previous entries on 10 and 11 October) at the rowing exhibit "Let Her Run" at the National Rowing Hall of Fame. Miller had built the base, while a company in Massachusetts had built the cover. It took a couple of hours to put together, but now Pocock's beautiful coat is on display for everyone to admire. It's a wonderful addition to the rowing exhibit, and the showcase is right under Dick's brother George's single scull, hanging from the ceiling (see also entry 23 June).
Labels: Rowing Hall of Fame, The Pocock Brothers, Thomas Doggett Coat and Badge Race
Rowing Myth Busters
So, you ask yourself, can you actually water ski behind a racing shell? Chris Partridge, who is running the eminent blog Rowing for Pleasure, posted the other day a Myth Buster episode showing just that! Enjoy!
Labels: Rowing oddities
Rowing In Japanese
Earlier this month rowing historian Bill Miller announced on his great site Rowinghistory.net that Chris Dodd's brilliant book The Story of World Rowing, published in 1992, has now been translated into Japanese by Akihiro Sakakibara. The Japanese version is published by Tohoku University Press.
Coincidentally, I received an e-mail from Hélène in France, one of the loyal readers of this blog (whom I have mentioned before – again, thank you, Hélène) where she points me in the direction of the Japanese magazines/comics called manga. The author Hidenori Hara has published series called Regatta [Japanese title: Regatta Kimi to Ita Eien]. The Japanese TV has also dramatized Regatta, and you can read more about it by clicking here.
Labels: Manga, Rowing Books, Rowing Films
The Philadelphia Challenge Cup
At the 1920 Olympic rowing event, John "Jack" B. Kelly of Vesper Boat Club, Philadelphia, won the single scull race defeating Jack Beresford Jr., of Thames Rowing Club, London with one second. To celebrate the first American to take an Olympic gold medal in the single sculls, a group lead by J. Elliot Newlin, the Commodore of the Schuylkill Navy, raised $2,500 among the rowing community of Philadelphia to establish a prize, the Philadelphia Challenge Cup. The Schuylkill Navy wanted the Cup, which sometimes has also been referred to as the Philadelphia Gold Cup, to be regarded as the Amateur Single Sculling Championship of the World, and the first sculler being awarded the title was Jack Kelly.
For the years in between the Olympic single sculling races, the Schuylkill Navy would authorize a challenger to race the champion for the title. This happened in 1922, when Walter M. Hoover, of the Undine Barge Club, won a match race for the Cup in Philadelphia, overpowering Paul V. Costello of Vesper BC. Costello was Kelly's cousin and they had won the gold in the double sculls in the 1920 Olympics (and they would do so again in 1924).
The year after, in 1923, W.E. Garrett Gilmore of the Bachelors Barge Club, beat Hoover, now of Duluth Boat Club, at Duluth, Michigan. Back on the Schuylkill River, on 26 May 1924, Costello defeated Gilmore in a race for the Cup. Later that year, at the Olympic rowing races at the Argenteuil, Paris on 17 July, Jack Beresford became the holder of the Cup by beating Gilmore in the final of the single sculls. The following year, on 13 July 1925, there was a challenge race on the River Thames between Putney and Hammersmith where Beresford successfully defended the Cup by easily overcoming Hoover.
By clicking on the following link, you will be able to watch one and a half minutes of this race on the Thames. Please click here.
Later in July 1925, Beresford returned the Cup to the Schuylkill Navy as he did not want to defend it. After that the world's top scullers have been holders of the Philadelphia Challenge Cup, the last one being the Russian sculler Vladimir Ivanov in 1964. Thereafter, the Cup mysteriously disappeared, but was found in June 1996 in an antique store in Philadelphia. You can read the story about the Philadelphia Challenge Cup, its disappearing and re-surfacing, on the following link, please click here (there you will also find a list of all the holders of the Cup).
The photograph above, showing Beresford and Hoover, is from the Thomas E. Weil Collection of the National Rowing Foundation. It is now on display at the rowing exhibit "Let Her Run" at Mystic Seaport Museum. Below the photograph is Beresford's famous saying: "There is no disgrace in being beaten when you are trying to win."
Labels: Jack Beresford, Jack Kelly, Olympic Rowing, Philadelphia Challenge Cup, Rowing Films, Rowing Trophy
New Rowing Film
One of the loyal readers of this blog, Hélène in France, sent an e-mail earlier today, telling me about an upcoming rowing film, La Régate [The Regatta]. The film is about the fifteen year old boy, Alex, who lives alone with his aggressive father. To escape the violence, Alex takes to the oar and decides, at all costs, to win the rowing Championships of Belgium.
The film is directed by the Belgian Bernard Bellefroid, who was born in 1978. He graduated in 2003 from the National Film School of Belgium (INSAS) and has previously made documentary films. La Régate is Bellefroid's first longer feature film, which is produced by Jean-Pierre and Luc Dardenne. It will be released in France in February 2010. However, I find it unlikely that the film will find it's way to the U.S., which is a pity.
If you would like to get more information about this film, click here (information in French!). Many thanks to Hélène!
Labels: La Régate, Rowing Films, Youth Rowing
Maine Built Whitehall
One blog I enjoy reading is Chris Partridge's Rowing for Pleasure. On 5 November, Chris had a great entry about a new Whitehall boat built by Maine based company Shaw and Tenney, who has crafted wooden oars and paddles since 1858. The extravagant version of the Whitehall is $19,000, while there is a cheaper version, too. Read Chris's entry about Shaw and Tenney by clicking here.
Labels: Boat building, wooden boats
The Life-Boat
When I was working in the publishing business in Sweden, I regularly had to travel to Stockholm for meetings. At that time (this was in the 1990s), Stockholm had a lot of good antiquarian booksellers, so I always made certain that I had the time to browse around in some of them. Of course, I looked for rowing books, but it was rare to find something I did not already have.
But then one time, I saw in the window of a bookseller on Drottninggatan a copy of Sir John Cameron Lamb's book The Life-Boat And Its Work, published in 1911 by William Clowes and Sons Ltd in London. I went inside to take a closer look. The book condition was very good +. It was a nice clean tight copy, with no inscriptions, and it still had both the appeal and bequest forms in the back. It was not cheap, but I decided to buy it anyway.
It is really a very nice little book, which gives the story of lifeboats and how it all began – that special boats were built to rescue passengers and crews from shipwrecked vessels. There are several inventors and boat builders that claim to be the ones to have built the first lifeboat. Already in 1765, a Monsieur Bernières of France invented an unsinkable boat for nine people, but according to Lamb's book, Bernières's invention was never set to practical use.
Gentlemen from Tyneside and the Thames created models to suit the newly founded "Tyne Life-Boat Society" and the Royal National Life-Boat Institution. The most famous names were Lionel Lukin, William Wouldhave, and Henry Greathead. The illustration above shows a drawing made from a model presented by Greathead to the Admiralty around the year 1800.
Lamb's book has a lot of black & white photographs and drawings, and around ten different copies are now available to buy on AbeBooks.com.
Labels: Boat building, Collecting Rowing Books, Life-Boats
Next Rowing History Forum
Last Saturday, the River and Rowing Museum in Henley-on-Thames, England was hosting a Rowing History Forum (read more about it in my entry on 8 September). Sadly, I missed it.
The other day, Bill Miller announced on the rowing history site Friends of Rowing History (www.rowinghistory.net) that the next Forum will be on Sunday, 21 March 2010 in Mystic, Connecticut. As usual, this event will be organized by the Friends of Rowing History, the National Rowing Foundation (NRF), and Mystic Seaport Museum. Special guest speaker will be Kent Mitchell, U.S. Olympic oarsman 1960 and 1964. Miller promised to post more information on his site soon.
That weekend will also be a celebration in honour of the up to 20 inductees for the NRF's National Rowing Hall of Fame. There will be a dinner at the Seamen's Inne in Mystic on the eve of 20 March for the inductees and everyone else who would like to mark this very special occasion.
So jot down the 20 and 21 March 2010 in your calendars. These are events that I for sure will not miss.
Finally, I also would like to share the information about the honour that has been bestowed upon me. The Directors of the Friends of Rowing History have very kindly asked me to join their ranks, which I very gladly and humbly accepted.
Labels: NRF, Rowing Event, Rowing Hall of Fame, Rowing History Forum
A 1954 Oxford Rowing Footnote
In the 1954 Boat Race, which was the hundredth in the series, Oxford won with four and a half boat lengths. Being that year's winner, the Oxford crew was invited to row in Sweden at one of the longest river races in Europe, Göta Älvrodden. The previous year, the race had been organized for the first time for eights, and was a 20,000-metre long race on a fairly straight course on the river Göta Älv between the town of Kungälv and the city of Göteborg (Gothenburg).
In the beginning of the 1950s, the Swedes wanted to create a long race to promote the sport of rowing. There was a race on Göta Älv in 1952 for coxed inrigger fours, but glancing towards London, the oarsmen in 'Lilla London' ['Little London'] – as the people in Gothenburg sometimes refer to their city – desired something more like the Boat Race between Oxford and Cambridge. One of the organizers, Reinhold Bråkenhielm, talked to the head of the Gothenburg Sport Federation's rowing section, Bertil Göransson, to get his blessing to invite 1954 winners of the Boat Race. Göransson, who was active as a coxswain and would actually steer the Swedish eight who reached the final in the Grand at Henley in 1955 and the Olympic final the following year, was of course very positive to bring Oxford over to Sweden.
In the spring 1954, Bråkenhielm was working in London for a Swedish company. He contacted ARA's Chairman Gully Nickalls, who arranged a meeting between the Swede and Oxford's famous coach H.R.A. 'Jumbo' Edwards and one member of the crew, Jim Gobbo of Australia. In the beginning of the talk, Bråkenhielm did not want to bring up the length of the course as it was three times as long as the course between Putney and Mortlake, being afraid that it would scare off the Brit and the Australian, but when he eventually did, both Edwards and Gobbo thought it was fine. If you can row almost 7,000 metres on the Thames, you can row 20,000 metres on a Swedish river they seemed to think, Bråkenhielm once said in an interview published in a Swedish rowing magazine.
In September, a week before the race, Oxford arrived at Gothenburg, together with Jumbo Edwards. The local newspaper Göteborgs-Posten paid for the accommodations at the hotel Fars Hatt. When it was time for the race, the Oxford crew had rowed the course several times. When they heard that last year's winner, the local rowing club Kungälvs Roddklubb, had taken 57 minutes, 25 seconds to complete the race, the Oxfordians joked and said that the Swedish crew probably stayed somewhere along the course to have tea.
Well, first crossing the finish line in the 1954 race was Oxford. The winning time was 1 hour, 2 minutes and 29 seconds – if they stayed along the course for tea, no one knows. Due to different weather and current conditions, it is of course impossible to compare the times from one year to another. The race was followed by around 80,000 spectators, and became an enormous success for the sport of rowing on the west coast of Sweden. Edwards never mentions the trip to Sweden in his The Way of a Man with a Blade (1963), nor has it found its way into books about the history of Oxford rowing. This is quite understandable. After all, this is only a little footnote in the history of the Boat Race.
Labels: Jumbo Edwards, Oxford, The Boat Race, The Göta Älv Race | {
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Congratulations to Julia and Bill. They had a beautiful wedding at Diamond Banquet Hall in Markham. We were there to provide Wedding DJ services including speakers and lighting to make the party super fun.
Our playlist was a mix of Chinese wedding songs and modern English songs – with an emphasis on 60s and 70s rock during the cocktail hour. This is all part of ensuring we're able to fuse traditional Chinese wedding elements with western ones.
The reception started at 7:00 pm when we introduced the Bridal Party to the tune of Hello by Martin Solveig and Dragonette. Dinner was a generous 12 course Chinese banquet. Wow… we were all stuffed afterwards.
We eventually kicked off the First Dance after the food, speeches, games and Bouquet/Garter tosses were out of the way. There's something about Only You by the Platters that gets you into a romantic mood. Anyway, it was such an awesome wedding.
Preparing the head table. This is a view of where the main action will take place. The dance floor and the head table on the stage.
We'll be giving these centre pieces away later.
A tower of glasses in preparation for the champagne toast.
Another tower. This time it's made of cup cakes. These types of wedding cakes are very practical and easy to consume.
We also had a beautiful ice sculptured swan. Nice touch.
Julia and Bill's first dance.
We were graced with couples among the guests. Kicking the party off with a slow dance was a great idea. | {
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Most of the time I play indoor pickleball and use the Head Extreme Tour paddle.
The Head Extreme Tour paddle is lightweight and, as such, allows me to swing faster, something that comes in handy when you are using the softer indoor balls. I have also found that I can put a lot of side spin on the ball when I want to, sometimes letting me get some aces on serves.
I also use the Extreme Tour outdoors when the wind is not an option. In fact, I used it in October at the Horseshoe Bay tournament and won gold in Men's 4.0 doubles.
This past week I was playing in a tournament in Port St. Lucie, Florida, where the wind was howling. The picture below gives an indication of how strong the wind was – note the temporary nets lying on their sides.
The firsts match I played was men's "Skinny Singles." Essentially, in Skinny Singles you use only use half the court. You can use either diagonal courts and change each serve, or use half court directly across from each other. I prefer the first method, but in this tournament, we used the "straight across from each other" method. FYI – I no longer have the mobility to play regular singles, so I like Skinny Singles. Skinny Singles also puts the dink game back in play, whereas ingles on full court is not a dink game – it is more like tennis singles. Finally, Skinny Singles can really help your doubles play as it makes you focus on placement of the ball.
Anyway, I signed up for Skinny Singles in the 65-99 bracket. Originally it seemed like there would be a lot of players, but ultimately it came down to just three with no age delimiters. That meant I had to play men younger than me, in one case more than 20 years younger than me. I started off with my Extreme Tour paddle and tried my "down the middle" ace. What happened was the wind took the ball about three feet outside of the service box. Time for a new strategy.
I switched to my Head Radical Tour paddle.
The Radical Tour is heavier than the Extreme Tour and, because of that, I can drive the ball lower and overcome the effects of the wind. Even after losing the first match (to the youngest player) I wound up winning silver. I was happy with that.
My next match was men's doubles. Again, I signed up for 4.0 in the 65-99 bracket. What happened was that the actual bracket was "Men's Doubles Age Groups 4.0 and 4.5: 6-39,40-49,50-59,60-99." (The 6-year-old failed to show up). So, not only were my partner an I going to play men younger than us (in one case almost 40 years younger than me), but we were going to play against some 4.5 players.
Shockingly, and I mean shockingly, my partner and I took silver. Once again, I used my Radical Tour to defeat the wind. By the way, no one came close to beating the gold medal winners, so I was pretty happy with the results.
My partner was Chris Mitchell of Pickleball England. Go to their website – it is quite a program.
Pickleball England Home Page
Here we are getting our medals.
Anyway, I am a firm believer that you really should have different paddles for different situations. | {
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Rachel and Tom decided to hold their wedding day at the Leeds Club in the centre of town. Going for an urban wedding is always great fun, especially when everything is held in one location. You might have seen them on the blog before for their legal ceremony at Leeds Town Hall, as unfortunately Leeds Club didn't have a ceremony licence so they opted for a humanist ceremony. This allowed them to put their stamp on the service. Rachel even surprised Tom with her own vows that she had written.
Rachel picked a gorgeous bespoke bias-cut silk dress from Glory Days Vintage. With Tom opting for a 60's style three piece suit. They wanted flowers that had the wow factor that matched the dress, Rachel picked amnesia roses with lilac calla lilies in a 1940's style bouquet from Adrienne Florist in Farsley.
The beautiful cake, you'd have never guessed but was gluten free made by 2 Oxford Place, each of the three tiers a different flavour, finished off with the simple yet elegant styling.
What a way to end the wedding celebrations, they had Magic Al performing in the bar. While Tom Rocks and the Replicants played in the main room, with Tom jumping in on vocals on a tune as well. | {
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The Gaslight Tavern features live bands, live music gigs most nights featuring some of Adelaide's top muso's along with good value pub meals in our brand new CRACKLIN' ROSIE DINER.
Come spend a night with us first in our new CRACKLIN' ROSIE DINER, then stay on to enjoy great live music gigs featuring local Adelaide and interstate bands.
Live bands & live music most nights covering diverse styles of music with some of Adelaide's top muso's at The Gaslight Tavern. | {
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It's very possible, and sadly far from infrequent, for us humans to have horrible experiences. The spectrum of these far-from-satisfactory encounters is broad; from cringe-worthy embarrassment, to extreme physical torture. Although the term 'Hell' literally originates from the traditional Christian worldview (or perhaps even the Semitic worldview), it is also commonally taken to refer to a particularly unpleasant combination of mental and physical distress that is often prolonged and therefore insidious.
When we, or at least certainly myself, worry about things, about the potential horrors that we could find ourselves in, we most often depict a scenario worthy of an on-screen drama; the details are tangible and in a strange way entertaining and juicy. To go back to the classic Christian depictions of hell; fire, sharp stones, physical suffering, blood, severed limbs and all in eternity -- now that's what you want from a hell!
Yet perhaps true hell is not so obvious and not so easy to see. Hell, in its most 'refined' form, I suspect, is a lot less hollywood but no less unplesant; it is the ambiguous, bearly perceivable, yet incessant threats that pervade our everyday minds. That which fails to grab the centre of our attention, due to the more immediate concerns of work, food, paying the bills, washing, getting enough sleep, etc is, by the token of its peripheral status, able to make demands that, in the light of the day, would otherwise be seen as utterly unreasonable. We only receive vague indications of these demands through the blur of more pressing concerns and whilst these vague indications are enough to register on such a level as to set the body-mind's various coping mechanisms on alert, they are not in the forefront enough for us to coherently decipher them and deal with them pragmatically. Surely this is a worse kind of hell, where we are unconsciously taken hostage by unconfirmed threats that sap our resources yet fail to resolve.
In my experience, life, at its most fundamental level, is entirely manageable; given a clear overview of the problem and a measured response, anything can be overcome. In fact, we may even question the very concept of a 'problem' --in the existential sense at least-- for it so heavily depends on this facade of the apparently insurmountable obstacle. A threat is a threat, it is a possibility, just that, something that could potentially happen, it is not certain. It is simply unreasonable to be expected to fight a robber when they haven't even got into our house yet. Yet for some reason that's what we try and do, my body tenses as, in my mind, I struggle to push the robber to the floor, get to the front door, run away and call the police. And for as long as my mind struggles through this scenario the 'problem', the threat, is not overcome, it remains unresolved.
It's obvious when we realise what we're doing, but we don't always realise what we're doing. The only tool we have to manage all this is our mind, as it is now. It is only this moment we are being asked to engage with, anything we need to know is here, decipherable from this vantage point and perspective. Truly, the taste of a threat or the whiff of an ambiguous demand is enough to sound the alarm bells; to remember that Rome wasn't built in a day and that a journey can only be made one step at a time. | {
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At a time of unprecedented legal freedom, individual Americans feel less free to speak than any time in recent history. Online shame campaigns, economic boycotts, firings, and even physical threats are destroying the culture of free speech. National Review senior writer David French will explain that these threats have emerged before, and robust protections for individual rights – including anonymous speech – have turned them away. David will detail the legal and cultural threats to the safety and privacy of American citizens and outline a strategy for preserving the culture that makes us free.
Come to the North Carolina State Bar Building on December 11th to hear David French speak on free speech and donor privacy.
This event is free and open to the public. Lunch will be provided. Please register so we can get an accurate count for food. | {
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Pictured from left to right: (front row) Jann Lowder, Vice-Chair, State Board of Community Colleges and Stanly County Commissioner | Joe Morton | Bryan Morton | Jack Morton | Dr. John Enamait | Nadine Bowers | The Honorable Justin P. Burr, North Carolina House of Representatives (District 67) | Robin McCree | and Tony Dennis, SCC Foundation Board Member and Stanly County Commissioner.
Back row: Bill Lawhon, Vice Chairman, Stanly County Commissioner | Chris Bramlett, Vice-Chair, SCC Board of Trustees and City of Albemarle Councilmember | Scott Efird, Chairman, Stanly County Commissioner | G.R. "Ronnie" Michael, Mayor of Albemarle | The Honorable Tom McInnis, North Carolina Senate (District 25) | and Peter Asciutto, Stanly County Commissioner.
Stanly Community College (SCC) Board of Trustees, SCC Foundation Board, faculty and staff, Stanly County Officials, City of Albemarle Officials, as well as community members, gathered to celebrate the dedication and open house for the Morton-Moffitt Cosmetology Center on Monday, October 17, 2016. Nearly two-hundred people gathered outside the Center for the dedication and ceremony. The ribbon was cut by members of the Morton-Moffitt family. A reception and tours of the new facility concluded the ceremony.
The naming of the new Center is in memory of Claude and Bethie Morton and Jerrie Sue Moffitt-Morton, parents and late wife of Mr. Jack Morton.
SCC Board of Trustees Chair Nadine Bowers welcomed the guests and thanked everyone for attending. She acknowledged many individuals who were instrumental in bringing the Center to fruition and expressed a special thank you to SCC Board member Tom Hearne and former SCC Board member Jim Nance for their commitment and direction during the planning stages of the new Morton-Moffitt Cosmetology Center.
SCC Executive Vice President of Educational Services Robin McCree talked about the Morton-Moffitt family legacy and how fortunate SCC is to have the family's support and generosity. "From the humble beginnings of a three-room schoolhouse to pursuits of higher education, the legacy of bettering oneself through education is one that the Morton-Moffitt family has carried throughout generations," she explained.
David Smith, SCC Cosmetology Program Head, who graduated from SCC's Cosmetology program in 1998, stated, "We encourage you to visit us to witness firsthand the state-of-the-art equipment that the students will be learning with." Mr. Smith announced the Jerrie Sue Moffitt-Morton Award that will be given annually. The recipient for this award will personify the spirit of the award's namesake and will demonstrate an ability to overcome adversity, maintain integrity, and keep clients' needs as their priority. Furthermore, the chosen recipient will exude a charismatic personality, always making others feel at ease and welcome. The recipient will be known for putting others before self while also possessing a fighting spirit when faced with life's negative circumstances. Mrs. Jerrie Sue Moffitt-Morton leaves behind an enormous legacy, and this recipient's qualities will resonate with the aforementioned attributes that set Mrs. Moffitt-Morton apart from others.
Dr. John Enamait, President of Stanly Community College, gave closing remarks and thanked all who attended the dedication. "This is a momentous day for the College, Stanly County, students and prospective students. The Morton-Moffitt Cosmetology Center will benefit students and their families for many years to come," he noted. Dr. Enamait added that the North Carolina State Board of Cosmetic Art Examiners awarded the facility a score of 100. All salons and schools are graded using the Board's System of Grading Beauty Establishments.
Christy Bogle, Executive Director for the SCC Foundation, said, "The Stanly Community College Foundation is grateful for the generosity of Jack Morton and his brother, Joe Morton. Over the years, the Morton family has contributed to the College and our students in multiple avenues of support including providing scholarships. Today, we celebrate with Jack Morton and are honored and appreciative that he has invested in Stanly Community College in such a significant manner."
According to a recent study from the Centralina Council of Governments, Personal Care Services is expected to grow in Stanly County by 17.4%. The 12,000 square foot Center will sustain the College's ability to train the next generation of personal care and cosmetic arts workers in Stanly County. The Center is comprised of three main classrooms equipped with smart boards, a 16-station manicuring clinic with state-of-the-art Pedi spas, a main clinic area that is furnished with 49-stations, a private facial room, a reception area, laundry room, chemical dispensary, conference room, faculty/staff offices, and a large student lounge.
Program options include: Associate in Applied Science degree, diploma, and certificate; Cosmetology Instructor certificate, Manicuring Instructor certificate, and Manicurist Technician courses. Continuing Education courses are taught throughout the year. SCC also offers a high-school pathway for all Stanly County high-school students that is tuition-free and taught at West Stanly High School. Registration for Spring 2017 classes is now open and classes start on January 10, 2017.
The Morton-Moffitt Cosmetology Center is open for business. For a complete list of operational hours, prices and services, visit https://www.stanly.edu/future-students/educational-offerings/cosmetology. For more information regarding the Stanly Community College Foundation, contact Christy Bogle, at (704) 991-0370 or [email protected]. For a complete photo gallery of the dedication and open house event, visit https://www.stanly.edu/morton-moffitt-cosmetology-center-slideshow. | {
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How to use the new respirator for the new season: The new cartridge is a great way to stay safe!
The NHLPA is working with the league on a new respirators, and it has some great tips for using the new cartridges, according to NHLPA VP and General Manager Jim Rutherford.
Here are some of the highlights.
How to use a respirator cartridge in the new series: If you are already a player and would like to wear a respirators with your regular regular pads, you will need to purchase a new cartridge, Rutherford said.
The NHL has a store that will carry the new cartridge.
If you don't have the store in your area, you can buy one from the NHL store, Rutherford told reporters in a conference call.
The new cartridges are designed to provide a better seal against bacteria.
They come in two sizes, and the new model comes in two flavors, the "sport-like" and the "high-tech" versions.
The Sport-like cartridge has a larger opening that helps it breathe more efficiently and is a better fit for players who wear pads, Rutherford added.
The high-tech version has a wider opening, and is easier to breathe through.
The new models are designed for players with longer arms and legs.
Both cartridges are made of the same material, he said.
Rutherford said players who are currently wearing a helmet should wear one with the Sport-esque cartridge.
They will also be able to wear one without it, Rutherford continued.
There is no cap on the Sport/High-tech cartridges.
Players wearing a mask will be able wear both cartridges, he added.
The caps are not designed to be worn on the inside of the helmet.
Players who don't wear helmets should wear either one of the new products, Rutherford explained.
If a player is a regular-season NHLer and wears a respirating mask, he can still wear the Sport cartridges in that game, Rutherford noted.
But, he explained, "If you have a mask, you have to put it over your face, or it won't fit.
So we would suggest that players wear a helmet."
Rutherford also told reporters that the NHL will provide a free mask for players in their regular pads when the new sets come out.
Players can get a free MaskPass when the league launches the new product, but not the regular-year masks, he noted.
The NHLPA has also given the league permission to distribute new masks to players who have used their regular masks for the past six weeks.
If a player has used a mask for the previous six weeks, the league will provide them with a free new mask, Rutherford clarified.
The latest NHLPA respirators have a capacity of 10,000 breaths per minute, Rutherford stated.
Players will have to wear the new masks for a full two minutes of play.
Players will also need to wear an approved mask for their new season when the respirators come out, Rutherford indicated.
Players wearing masks will not need to use an approved respirator in the preseason, but can still participate in the regular season when they wear a mask.
Rhodes said the NHLPA will work with the NHL to make sure that players who need a respirated environment during games wear their masks and get their respirator.
The respirator will also work on any players who donned protective gear during the preseason.
Next: What is the real deal with the new cricut cartridges?
Next: Which is the best marijuana cartridge for your marijuana needs?
KRT: We'll give you the best-selling ink cartridges, cartridges, and cookies in the US for 2019
How to buy a marijuana cartridge with weed
When to use a preloaded cartridge: A look at what you need to know
How to get the best possible ink cartridge for your smartphone | {
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Epson EH-TW5000 Printer issues like "Windows fails to recognize the new hardware" are not uncommon, especially anytime you are trying to deploy your new Epson and also connect it to your laptop. It is likely that your Epson printer driver was setup incorrectly in such a case, & for this reason Windows is unable to recognize the device.
Fortunately, printer driver troubles are easy to resolve. Read on to learn more about printer drivers, what causes the more common printer driver problems, & how you can troubleshoot printer driver errors.
A personal computer printer does not work until you setup the included driver & software. While you have forget the disc for your printer, you can download the driver for your printer & use the driver to setup your printer.
What is Epson EH-TW5000 printer driver?
Printer driver are software programs, and their main job is to convert the data you command to print from to the form that is specific to the installed printer. Every printer should come with the software used to deploy a printer in Microsoft Windows or your operating system.
Download & locate the correct driver that is most compatible with your Epson EH-TW5000 printer before going further.
Before get Epson EH-TW5000 printer driver, you must understand what is your Operating system version.
Now you must go to your desktop and click "Computer" or "My computer". Right Click in Computer folder, then click "Properties" and review the system os type and name. By doing this, you will probably obtain the driver your system usually requires.
When you need get and setup Epson printer driver?
How to setup Epson EH-TW5000 printer driver? | {
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Screaming Lord Sutch
Official Monster Raving Loony Party
The seventh of May 1987 was an historic landmark in British politics. It was the day that the first representative of the Monster Raving Loony Party took a seat as an elected councillor.
The party's Chairman Mr Alan Hope, landlord of the Golden Lion public house in Ashburton Devon, Annual Conference Centre for the Official Loonies, was elected unopposed as one of 12 residents nominated for the 12 posts of Councillor.
In 1985 the deposit required by anyone wishing to stand as a Parliamentary candidate was raised from £150 to £500.
This was returned if the candidate received more than 5% of the votes cast.
It was a concession to the increase in deposit which before 1985 required that candidates would forfeit their deposit if they received less than 12.5% of the total votes cast.
This was to stop the increase in frivolous candidates and those standing just to gain some publicity. It had no bearing at all on the major parties who rarely lost a deposit. It was acutely embarrassing episode if a candidate from any major party did so.
David Sutch aka Screaming Lord Sutch
Many people in this country saw that as no barrier at all. Thankfully, for otherwise there would have been no Screaming Lord Sutch.
He was born David Edward Sutch on 10 November 1940 and became a rock musician during the early 1960's.
He changed his name to Screaming Lord Sutch as a tribute to Screamin' Jay Hawkins.
He was not a Lord either.
But he was a expert stage performer, appearing out of coffins, wearing blazing headgear and pre-dating acts such as Alice Cooper and Arthur Brown.
He entered politics in 1963 representing the National Teenage Party. In 1983 he formed the National Monster Raving Loony Party and stood at the infamous Bermondsey By-Election. Personal attacks on the openly gay Peter Tatchell cost Labour the previous safe seat and ushered in Simon Hughes who still represents that constituency as a Liberal MP.
In the same year he stood in Margaret Thatcher's Enfield constituency. He invariable lost his deposit but often polled a decent number of votes. Many of his election manifestos were a matter of humour with the major parties and general public such as turning the butter mountain into giant ski slopes and using joggers to turn huge treadmills to power London.
Amongst other measures he promoted were votes at 18 and radio licenses for commercial stations.
In his later life he suffered from depression and hanged himself on 16 June 1999.
Harry Greenway, Tory MP for Ealing North, described him as "the man who brought gaiety to politics and who pricked the pomposity of politicians"
Conservative MP Nigel Evans: "I fought the Ribble Valley by-election in 1991 and Lord Sutch entered the race. He brought a sense of fun and ridicule to what for the rest of the main candidates was cut throat. He was the original and clearly the best. You felt you hadn't really fought a by-election unless Lord Sutch was on the ballot. MPs of all parties will miss him."
This page and more in a similar vein comes from a collection in my eBook An echo from the Green Fields . | {
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Thoughts from the Beanpot luncheon
January 31, 2017 January 31, 2017 by Tyler Lay
The 65th annual Beanpot Tournament is less than a week away. Tickets are selling, fans are rejoicing and the teams are preparing. The Boston Hockey Blog got thoughts from head coach David Quinn and senior players about the Feb. 6 faceoff between No. 3 Boston University and No. 6 Boston College.
Senior forward Nick Roberto said his biggest fear going into the tournament is beating BC a third time, as the Terriers already defeated them twice this season.
NR: "Beating them a third time is going to be extremely hard. Hopefully we're focused for that game, and come out and work hard just like we did the first two games."
"Oettinger for sure," Roberto immediately answered when asked what he considered his teams secret weapon. "Ah no, secret weapon … I think our compete level is probably our secret weapon. When we out compete teams, we're very good. When we play down to teams or let teams hang in with us it's a close game."
Senior Captain Doyle Somerby wants his team to have fun with it, but knows how difficult the game will be on Monday.
DS: "I don't think you realize how special [the Beanpot] is until you actually take the ice for it. Local guys understand it because they grew up coming to it but when you're not from around here it definitely takes the first 10 minutes or so of the game to grasp the full concept of it. It's really unique and special because no one else has this."
What do you tell your team to get them in the right mindset for such a big game?
DS: "Honestly, just have fun with it as much as you can. If you grip the stick too tight, you're too nervous and thinking too much about it, it's going to be a long night. Especially playing BC. We already have that rivalry. People comprehend that and understand how special that is to play against them. They just need to enjoy it as much as they can on Monday night."
This could be one of the last big games of your college hockey career. What's going through your head as your senior season winds down?
DS: "Just trying to enjoy it as much as I can. Being a local kid – I'm about 35 minutes away – so this is something I grew up coming too every single year since I was 4 or 5. With this one you just need to enjoy it. This might be the last time I ever play BC, so on top of the big games you got your last rivalry game. I'm just trying to have fun with it, hoping to come out on top and play for the championship the next Monday."
How hard will it be to beat BC a third time this season?
DS: "It's really hard. When you play a rival like that it doesn't matter what the stat sheet says. It doesn't matter what your record is. Especially in the Beanpot. It's going to be a one-goal game no matter what. It's going to be a lot of fun to play them but it's also going to be pretty interesting. It's going to be a tight game."
Head coach David Quinn agrees it's going to be a close game.
DQ: "Obviously anytime BU and BC get together, in any situation it's an exciting game. It draws a little extra attention from both fan bases, and usually the college hockey world pays a little extra attention to it. But when you put that game in the Beanpot it's even more special. Usually you get great competitive games. Someone has a goalie pulled at the end of the game. Both teams have talent. Both teams compete hard. Both teams are at the top of the league and in the national rankings. It's going to make for an exciting Beanpot, as it usually does."
DQ: "It's always hard to beat BC. I don't care whether you've beaten twice or not. I've got an awful lot of respect for them. It's been such a great rivalry for so long. We still understand what's ahead of us. We're not thinking about the two games that happened three weeks ago. We're going to focus on Monday night."
Quinn, Somerby and Roberto all agree that although the Terriers are the youngest team in college hockey, they won't appear to be on the ice.
NR: "Maybe for the first five minutes the crowd will get into it, the atmosphere will be good. We've played in some hostile environments out in Denver, Michigan and at BC, so [the freshman] will be all set. And a lot of them played in the World Juniors as well. Especially USA-Canada. That was a loud game for them."
DS: "I think Christmas break definitely helped [the freshman], playing in the World Juniors. Playing in Canada against Canada is a pretty chaotic place to play. They definitely learned a lot from there. We learned a couple lessons last week. Definitely I'll just tell them to enjoy as much as they can because you don't get this experience too often."
DQ: "We've been fortunate this year, whether it be at Denver or Michigan or up in Vermont or up in Maine, we've played in some very very big atmospheres. The guys who played at the World Juniors certainly played for 20,000 people up in Canada so we can draw from experiences. I don't think nerves will be an issue for us."
Categories BeanpotTags Beanpot, Boston College, David Quinn, Doyle Somerby, Nick Roberto, World Juniors
Pluses and Minuses: BC prevails over BU in overtime, claims Beanpot championship
Jordan Greenway. PHOTO BY MADDIE MALHOTRA/DAILY FREE PRESS STAFF
None from the current crop of players on the No. 7 Boston University men's hockey team was on the 2012 BU team that lost to Boston College in the Beanpot championship in overtime.
This year's seniors were still a few months removed from Commonwealth Avenue when BC forward Bill Arnold scored the game-winning goal at TD Garden.
But four years later, this year's team is pretty engrained in the Beanpot tradition, and now well acquainted with a similar heartbreak.
A scoreless, physical game throughout Monday night, No. 3 BC finally broke through 1:57 into overtime when Alex Tuch wristed home the first and only goal, defeating BU 1-0 in the Beanpot title game.
BC (20-4-4, 11-1-4 Hockey East) has now won the Beanpot five times in the last six years.
"Certainly an exciting game for everybody in the stands, and the last two periods it was a competitive hockey game," said BU head coach David Quinn. "That's what people expect when they see BU and BC play, and up-and-down action, both teams had great chances in the second and the third, they certainly had a majority of the chances in the first and we felt very fortunate to get out 0-0 after one."
It was scoreless for almost 62 minutes, but that's not to say there isn't a lot to talk about. We'll break this one down in this Beanpot championship Pluses and Minuses.
Minuses
Untimely screen
Senior netminder Sean Maguire was on his game throughout the title game and really the entire Beanpot Tournament. BC had a good deal of chances throughout the first three periods of the game, but Maguire stood on his head just about every time.
One of the few times Maguire didn't see the puck, though, things went wrong for BU (16-8-4, 9-4-3 Hockey East). After both teams tried to get their legs back at the beginning of overtime, the Eagles got the first real opportunity about two minutes in and made it count.
As Tuch skated into the high slot area, BU's defense tried to contain him before he could shoot, but the bodies standing in front of Maguire caused an unintentional screen, setting up an unpleasant result.
"I think if I saw all of it I would've stopped it," Maguire said after the game. "But he [Tuch] made a great shot, and the shot crossed body post in. That's a pro-level shot."
Slog of a start
Against a rival like BC, and in a game of importance such as this one, it's generally pertinent to get things started in the first period on the right foot. The Terriers, however, did not have one of their better opening periods on Monday night.
One thing that stands out right away on the shot chart is the fact that BC not only attempted 32 shots in the opening stanza, but a majority of them came in the slot and home plate area. Life was not easy for Maguire, to say the least.
BU was mostly kept to the outside of the faceoff circles and did not really kick things into gear until the second period.
Sloppy play, Greenway to the box
For anyone who's watched a BU-BC, you know it can get chippy and downright nasty during and after the play. This one was no different, especially on the BU end of things.
Freshman forward Jordan Greenway seemed to be in the middle of it all on Monday, drawing the ire from a lot of the BC contingent in the arena.
Greenway was involved in a play in the third period in which BC goalie Thatcher Demko was knocked down for a few minutes, and he also drew three penalties during one scrum in the second period, including a 10-minute misconduct. BU killed off all of the penalty time, but was without Greenway's presence until early in the third period.
"Well certainly missed him, but I thought we continued to play a pretty good second period," Quinn said. "…But any time you're missing a guy who's 6 foot 5, 230 pounds against that team with the big, strong D corps that they have for an extended period of time, it's not going to help you, that's for sure, but I don't think that had anything to do with the outcome of the game."
BU's offense could not muster a goal in what turned to be Demko's ninth shutout of the season (a new single-season BC record), but the real issue tonight was the lighting at TD Garden.
With 8:53 to play in the first period, the main lights above the ice slowly dimmed and then turned out. The teams skated around the ice to stay loose, but were eventually sent back to their respective dressing rooms. The situation was finally resolved after nearly 30 minutes, but it took longer than a normal intermission to get the lights up and running.
BC head coach Jerry York said after the game said both teams were offered the chance to play a 29-minute second period instead of finishing the first, but York said he and Quinn declined the opportunity.
Pluses
Maguire nearly perfect
We've mentioned it in this article a few times already, but Maguire was good in this one — really good.
He kept BU in the game with 23-first period saves and finished with 41 stops on 42 chances. Maguire, for the tournament, saved 65 shots on 67 opportunities for a .970 save percentage. He wouldn't carry the Beanpot trophy, but he did earn Beanpot MVP and the Eberly Award for the highest save percentage in the tournament.
The only two goaltenders to have a higher single-tournament save percentage than Maguire were former BU netminders John Curry (.985) and Rick DiPietro (.981).
Sarah will have more on Maguire's stellar performance in her sidebar.
Mid-game adjustments
The first period was not one BU will be writing home about anytime soon. The rest of the game, especially from a defensive standpoint, the Terriers did a much better job in their own end.
BU pushed the Eagles to the perimeter and limited the number of "Grade-A" opportunities they could get on net. By game's end, the total shot attempts were closer than the first period may have indicated, with BC holding a slight 68-62 edge.
"…I thought in the second and third period we did a much better job of being decisive and just making a decision and doing it with conviction," Quinn said, "and that made everybody else's job easier and that's why you saw the dramatic drop in shots and scoring chances and made it a hockey game."
Categories Beanpot, Pluses and MinusesTags Alex Tuch, Beanpot, Boston College, David Quinn, Eberly Award, Jerry York, John Curry, Jordan Greenway, Rick DiPietro, Sean Maguire, TD Garden, Thatcher Demko57 Comments
Video: Players, coaches discuss BC's Beanpot title win over BU
BU head coach David Quinn and goaltender Sean Maguire
BC head coach Jerry York, goaltender Thatcher Demko and forwards Alex Tuch and Teddy Doherty
Categories Beanpot, Sean Maguire, VideoTags Alex Tuch, Beanpot, Boston College, David Quinn, Jerry York, Sean Maguire, TD Garden, Teddy Doherty, Thatcher Demko
Pluses and Minuses: No. 4 BC nets late goal, No. 10 Terriers settle for tie
PHOTO BY MADDIE MALHOTRA/DAILY FREE PRESS STAFF
David Quinn said it was typical of a Boston University-Boston College game. Jerry York said it capped off a "good college hockey weekend."
The standings will say it was a tie.
In about as evenly matched a game as you'll see, No. 10 BU and No. 4 BC skated to a 1-1 tie in the second game of a home-and-home series.
The Terriers gained a lead midway through the second period with a goal from senior captain Matt Grzelcyk and looked poised to come away with a win, but BC forward Ryan Fitzgerald knotted things up with a bar-down strike with 2:05 left in the third period.
Back-and-forth action with a lot of chippy play made this one a fun and exciting one to watch. We'll break down the 65 minutes in this Pluses and Minuses.
Oh captain my captain
Injuries have limited Grzelcyk to just 10 games this year — less than half of BU's total number.
But that's been really the only thing getting in the way of BU's (11-7-4, 5-4-3 Hockey East) captain, because when he's been on the ice, he's been a solid force at the blue line.
With the game scoreless on Saturday night, Grzelcyk was in perfect position to redirect a shot from senior assistant captain Danny O'Regan past Thatcher Demko. It was Grzelcyk's seventh goal of the season and 12th point in his 10 games played.
He played well on the defensive side, too, staying on his assignments and closing any gaps. Now that Grzelcyk's getting healthier and more playing time, Quinn said he'll continue to be a force on both ends of the ice.
"I think he's the best defenseman in college hockey," Quinn said, "and when you add that to your lineup, you have a whole different look and I don't know what our record is with him but I bet it's a lot better than without him so he makes everybody on that D corps better, he makes everybody up front better and we're just glad to have him."
Maguire stands tall
Not much separated senior goaltender Sean Maguire from a shutout, but a well-placed BC (15-4-3, 8-1-3, Hockey East) screen and shot ended any chance of that. But that's not to say Maguire didn't play well.
The senior was in good position all night, making a few terrific saves to stop BC odd-man rushes. In all, Maguire finished with 38 saves. Sarah will have more on his game in her sidebar.
Penalty kill comes through
Less than 22 hours after a power-play goal decided Friday night's fate, the Terriers got a chance to right the ship on the penalty kill.
Freshman forward Jordan Greenway and sophomore defenseman John MacLeod were called for successive penalties halfway through the first period, and BU was forced to kill of an extended 5-on-3. The penalty-unit came up big, as it did the other three times on the night, going 5-for-5.
It wasn't as if BC didn't have chances on goal (eight power-play shots), but the Terriers limited grade-A shots, and the ones that were good opportunities, Maguire was generally there to make the stops.
"I liked the fact that we backchecked a lot," Quinn said, "we did a better job coming back and they didn't get as much out of it as last night so baby steps and they're a fast team, that's the strength of their team, their speed up front and they work hard so we're a work in progress and I thought we did a lot of good things tonight."
Making it tough on Maguire
As noted before, Maguire was on his game from start to finish. However, his defense didn't make his life easy. BC had numerous odd-man rushes — like the 2-on-1 in the second period that forward Colin White nearly scored on — and 39 total shots.
There were sequences in the game, which York even said afterward, where both teams sort of lost their way and let the opposition get good shots at the net. It wasn't as if this happened the whole game, but if Maguire hadn't been playing so well, the score might have been different.
0-fer on the power play
BU's penalty kill was good and BC's matched up just as well.
Like the Eagles, BU had five opportunities with the man advantage but could not convert. The first two opportunities for the Terriers looked good, though they didn't score. The problems came after those first two tries, as the Eagles made life tough in the neutral zone on BU entries.
The power play wasn't awful, but a goal with a man up could have gone a long way.
Fortunato to the box… again
For 60 games, sophomore defenseman Brandon Fortunato never once sat in the penalty box. In back-to-back games against BC, Fortunato became much more acquainted with the sin bin.
Fortunato took his second penalty of his collegiate career on Saturday with a holding call in the second period.
"Yeah, he probably won't dress next Friday," Quinn said jokingly after the game. "I don't know … the penalty he took tonight, that was a strange call, but we all make mistakes."
Categories Pluses and MinusesTags Boston College, Brandon Fortunato, David Quinn, Jerry York, Matt Grzelcyk, Sean Maguire12 Comments
Pluses and Minuses: BU struggles in transition, hampered by penalties in loss to BC
(Judy Cohen also helped write this.)
CHESTNUT HILL — After a back-and-forth matchup (My recap of the game is here), the Boston University men's hockey team eventually fell to Boston College by a score of 5-3.
We anticipated it would be, as always, an entertaining game — and we certainly got that. There were a whole lot of takeaways from that game, too, and we've spelled out just some of the things we liked and didn't like below.
While the game was relatively even for the most part when the sides weren't utilizing their special teams units, there were elements to BU's game that did give BC an advantage. For one thing, the Eagles had a pretty easy time in transition, skating through the neutral zone with relative ease and, at times, on odd-man rushes.
The defense was tight in the first period, said senior assistant captain Matt Lane, when things like that weren't occurring. But as the game progressed, the Terriers got "sloppy."
"We didn't close the gap, we gave them too much space," Lane added. "Offensively and defensively, there was just too much space in between our forecheck and our two defenders and they were just kinda airmailing pucks there and getting some odd-man rushes."
Quinn said that the Eagles' success in that area during the game came from the Terriers' "poor puck management, puck-watching and being lazy."
Lane said BU would take measures to eliminate that from its game heading into Saturday's contest, beginning with skating more.
"When you skate, it usually takes care of all of those things, so if our D and our forwards are skating, we'll have better gaps," he continued. "We'll come up and down the ice five as a unit, and we'll eliminate those odd-man rushes."
One step closer to 1,000
A couple months ago, the three of us here at the Boston Hockey Blog joked about Jerry York getting his 1,000th career win against BU. How fitting would that be?
At the time, we assumed he'd have passed 1,000 wins by the time this rivalry series rolled around, but after a 1-3-1 record in December, it became pretty clear that York would have a pretty good shot at 1,000 against the Terriers.
And he got just that much closer with his 999th win on Friday. If BC wins Saturday at Agganis Arena, then that'll do it.
York insisted after Friday's game that the win total was just a number and that he wasn't paying particular attention to the accolade, but it's not like it's an insignificant accomplishment. It makes the stakes in Saturday's game just that much higher, and while a sweep would be bad for BU anyway, this adds that much more pressure.
While it proved to be pretty insignificant in the grand scheme of the game, sophomore defenseman Brandon Fortunato did something Friday he hadn't done in a college game before: He took a penalty.
Yep, after going an entire season last year, and 20 games this year, without recording a penalty, he ended that streak with a tripping call 9:50 into the first period. All good things must come to an end, I guess.
Penalties and special teams in general, sort of
BU was able to capitalize on three different power plays for goals, and special teams were basically the story of the evening. Judy has more about that in her sidebar.
Ahti's 100th
Though there were a bunch of things to dislike about the loss, one of the brighter spots was senior forward Ahti Oksanen getting his 100th collegiate point. The winger had 98 points coming into Friday night on 46 goals and 52 assists through 131 games.
In his 132nd, Oksanen recorded an assist on freshman center Jakob Forsbacka Karlsson's first-period power-play goal for his 99th point and then got a power-play tally of his own in the second for his 100th.
"He's a goal-scorer, always has been, always will be," Lane said. "He shoots the puck, some guys like to say a little too much, but that's his job. And I always tell him to keep shooting, and he knows he's going to keep shooting, and that's why he scores goals, and that's why he's got 100 points."
As has become typical this season, Forsbacka Karlsson impressed during Friday night's game. The freshman was one of three Terriers with multi-point efforts (the others being Oksanen and senior assistant captain Danny O'Regan), registering a goal in the first period and an assist in the second.
He also blocked a pair of shots and was, as usual, a large part of BU's penalty kill. But his traits that don't necessarily appear on the scoresheet were in full view as well, like his neutral-zone stick-lifts and overall play-making abilities.
He accounted for six of BU's 49 total shot attempts and drew a penalty as well.
The BC and Conte Forum Experience
As some of our readers know already, we like to give props where props are due, especially when it comes to off-ice entertainment and accomplishments. And BC's crew goes all out with its graphics and marketing. You can check out a lot of their .gifs and other graphics on their Twitter account. We especially liked this .gif with the team's lineup.
BC's intro video was as good as we've seen all year, and the mid-game hype videos were on point (anytime "Hotline Bling" is involved, we're happy). On top of that, TD Garden organist Ron Poster was on hand at Conte for some live music to add to the experience. Overall, regardless of rooting interests, you can't say that BC doesn't know how to provide some great entertainment.
Categories Pluses and MinusesTags Ahti Oksanen, Boston College, David Quinn, Jerry York, Matt Lane11 Comments
VIDEO: David Quinn, Jerry York discuss BC win over BU
BU head coach David Quinn
BC head coach Jerry York and defenseman Ian McCoshen
Categories VideoTags BC, Boston College, David Quinn, Ian McCoshen, Jerry York
Charlie Coyle happy to be back at BU for Comm Ave Charity Classic
It's been three-and-a-half years since Charlie Coyle left the Boston University men's hockey team midseason to pursue his professional career, but it doesn't change how much his time at BU meant to him.
"Everyone has their own path, the way they want to go," he said. "That's the path I chose, and I enjoyed my time here. It was awesome, it was my dream school to come here, and the toughest thing I've ever had to do was to leave here."
Growing up in Weymouth, Coyle watched a few games at Walter Brown Arena and dreamed of suiting up for the Terriers. He never hit the ice in the historic rink for a game during his collegiate career, but he got the chance to in the first annual Comm Ave Charity Classic to benefit Compassionate Care ALS on Friday night.
Coyle, along with 17 other BU alums, 18 Boston College alums and a few special guests, took part in a game that pitted old rivals against each other to help raise awareness and over $55,000 for amyotrophic lateral sclerosis.
"You want to help out as much as you can, so I think when every guy got the text, they wanted to play today, kind of jumped at the opportunity and they're happy to do it," Coyle said.
The Minnesota Wild forward netted a hat trick in the process and guided BU to a 7-5 win over the Eagles. And though the game was just for fun, Coyle said the intensity of the BC-BU rivalry never wanes.
"I think it goes as long as you live," Coyle said. "You see those guys wherever you go in life, and you always come back to BC-BU … Everyone kind of knows each other, but once you're on the ice and you're playing, BC-BU, it's a whole different story and it's just a huge rivalry. It's competitive, and that's what makes it such a cool tradition, so I was fortunate to be a part of it and be part of it again tonight."
He also reiterated just how much being a member of the Terriers contributed to him becoming the player and professional he is today.
"Coming to BU helped me tremendously," Coyle said. "Like I said, it's where I wanted to go, where I wanted to come my whole life and being here, being coached by Jack Parker and playing with some of these guys behind me, it was awesome. I made a lot of friends, became a better player and it's helped me at the professional level. Work outs … everything, everything, the school, just everything."
Scott Young feels not so young
For BU, roster spots on Friday night weren't as readily filled with current NHL talent as those of its BC counterparts. Some had a prior commitment, as former Terrier Brandon Yip's wedding is this weekend.
But what the scarlet and white lacked in that area, they made up for with veteran talent, including the likes of former BU standout and ex-NHLer Scott Young.
Currently the Director of Hockey Operations for the Terriers, Young won the Stanley Cup on two occasions — once with the Pittsburgh Penguins in 1991 and again with the Colorado Avalanche in 1996. He also donned the red, white and blue for Team USA in three Olympic Games and served as the head coach of St. Marks School in Southborough from 2010 until he returned to BU in 2014. The forward has collected various other accolades in his hockey career, including Hockey East Rookie of the Year in 1986, and racked up 756 career points in 1,186 NHL games.
It seems even after all this time, Young's still got it.
"Young was the best guy on the ice," said former BU goaltender Anthony Moccia after his team's win. "He was talking before, about all, 'oh, I'm out of shape' — yeah, right, Coach!"
At one point in the game Friday, Young was exiting the defensive zone and a teammate tried to get the puck up to him to start a rush.
"He tried to lob it over my shoulder, and I ducked so it could land in front of me and I could skate into it," Young said. "It landed on my shoulder, and kind of hung there for a little bit. It was kind of awkward."
Categories NotebookTags ALS, Anthony Moccia, Boston College, Charlie Coyle, Comm Ave Charity Classic, Minnesota Wild, Scott Young14 Comments
Pluses and Minuses: Freshman defensemen show inexperience in loss to No. 17 Eagles
January 17, 2015 January 17, 2015 by
PHOTO BY DANIEL GUAN/DAILY FREE PRESS STAFF
Losses have been hard to come by for both No. 2/3 Boston University and No. 17 Boston College entering into Friday night's tilt between the archrivals at Agganis Arena.
With both squads posting a combined record of 8-0-5 since the start of December, something had to give.
Unfortunately for the Terriers, a seven-game unbeaten streak was not in the cards against their Chestnut Hill foe, as the Eagles skated off the ice at Jack Parker Rink with a 4-2 victory.
As with any game, there were both positives and negatives to take away from the 267th meeting between the Terriers and Eagles.
Minuses:
BU's blueliners reveal their youth
For perhaps the first time all season, BU's young defenseman corps — which have supplied the Terriers with sound play, keen decision making and a consistent output of offense from the blue line — proved to be the team's Achilles' heel.
Throughout the game, BC's forwards used their size and skill to consistently put BU's defensemen on their heels, specifically the Terriers' four freshman blueliners in John MacLeod, Brandon Hickey, Brandon Fortunato and Brien Diffley.
For BU coach David Quinn, it was his team's inability to challenge the Eagles on transition proved to be the prime culprit for his team's struggles, as maroon and gold skaters were constantly left unchecked before breaking into the Terriers' zone.
"Our gap was horrific," Quinn said. "It was the number-one problem for us all night long. Our D just did not hold the offensive blue line long enough. BC's fast, we made them look a lot faster by just backing off.
"Like I said, we looked like we had four freshmen D tonight, and that hasn't happened very often this year, so frustrating, because it's not how we've been playing, but it was the case tonight."
Penalties prove costly
Before Friday night's contest got underway, the opening faceoff was disrupted for a few fleeting moments after BU senior assistant captain Evan Rodrigues became tangled up with a BC skater and tumbled down near center ice.
It was a telling sign for what was set to transpire.
As has been the case throughout the almost century-long discord between BU and BC, Friday night's game was marked by physical play, post-whistle extracurricular activities and penalties abound.
Both teams combined for 17 penalties in the match — including 12 in the first period — paving the way for multiple special-team chances throughout.
In the end, the Eagles were able to capitalize off of the Terrier's undisciplined slip-ups, notching two 5-on-3 goals and one 4-on-4 tally to jump out to a commanding 3-0 lead after two periods.
While BU managed to light the lamp with an extra skater in the third — the fifth straight game in which the Terriers have scored on the man advantage — it was "too little, too late" for the scarlet and white.
"Dumb penalties in the first period set us back, Quinn said. "We had a power play and we take an offensive-zone penalty which you just can't have and then we take two stupid penalties right after that which we really haven't done all year. They get a 5-on-3 goal, they get a 4-on-4 goal and then they get another 5-on-3 goal and we're down 3-0."
A quick start …. And a strong finish
The Eagles might have entered into the first intermission with a 2-0 advantage, but based off of the opening five minutes of play, it seemed as if the Terriers were primed to establish themselves on the scoresheet thanks to a few scoring chances generated against BC netminder Thatcher Demko.
Ultimately, BU's undisciplined play ended up putting an end to the team's impressive opening display.
"I thought that we actually got off to a pretty good start," Quinn said. "I liked our first five minutes and then the penalties."
BU only managed to compile nine shots against Demko over the final 20 minutes of play, but made its chances count, finding the back of the net twice — thanks to goals from junior forwards Danny O'Regan and Matt Lane — to give the Terriers new life after entering the period staring at a 3-0 BC lead.
The Sasquatch Effect
Down by two goals with a little over five minutes remaining in the game, the Terriers and Agganis Arena crowd seemed to receive a shot in the arm with the arrival of BU superfan "Sasquatch."
No more than 20 seconds after the bewhiskered BU backer made his presence felt in the BU student section, Lane tipped a rebound offering past Demko to cut the Terriers' deficit to one and send Agganis into a frenzy.
Was there a direct correlation? Likely not. But a Sasquatch sighting is always a plus in my book.
Categories Pluses and MinusesTags Boston College, Boston University, Conor Ryan, David Quinn, Pluses and Minuses26 Comments
VIDEO: Postgame reaction to BC's victory over BU
BC head coach Jerry York and forward Alex Tuch
Categories VideoTags Alex Tuch, BC, Boston College, David Quinn, Jerry York, postgame, video
Odds and Ends: Day after BU defeats Maine
November 15, 2014 November 15, 2014 by
The No. 3 Boston University men's hockey team recovered from a slow to start to defeat the University of Maine, 3-1, on the road Friday night.
BU's (6-1-1, 4-1-1 Hockey East) first line contributed all three goals and tallied five combined points. Freshman forward Jack Eichel extended his point streak to eight games when he assisted on junior forward Danny O'Regan's shorthanded goal at the end of the second period.
In case you missed it, here are a few links from our coverage of the game :
— Here's the game recap from Friday's win over the Black Bears
— Conor took a deeper look into what went right and wrong for the Terriers in Pluses and Minuses.
— Coach David Quinn's postgame remarks.
Other Notes From Around College Hockey
— No. 8 Boston College held off Michigan State University, 3-2.
— No. 10 Vermont was shut out by goaltender Jon Gillies and No. 16 Providence College.
— Northeastern University fell to 0-8-1 with a loss to the University of New Hampshire.
— No. 1 University of Minnesota lost to rival University of Minnesota-Duluth Friday night.
Categories Odds and EndsTags Boston College, Danny O'Regan, Jack Eichel, Odds and Ends, University of Maine10 Comments | {
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Scottish teenager Rory Skinner has bounced back form disappointment in his first Red Bull Rookies Cup of 2016 to take a podium finish in his second outing of the year at the Dutch TT.
Unlucky in his first race of the year after colliding with a falling rider, Skinner was nonetheless able to capitalise on a good grid position to get into the battle for the lead in the second outing of the weekend, running with the top trio for the entire battle in treacherous circumstances at Assen.
MotoGP: Jack Miller wins the Dutch TT!
Sitting comfortably in the race until the closing stages, he was able to make the most of race leader Walid Soppe sliding off on the last lap to move into the final podium spot behind double race winner Raúl Fernández and Ayumu Sasaki.
"I got a good start and was happy to go with the other two. I made a couple of mistakes and was finding it hard to stay with them but then the others caught up and we all bunched up together again. I'd been missing out coming out of the chicane, a bit too cautious early on but I got better by the end of the race and the last few laps were great fun."
The podium means Skinner now gets his first points of the season on the board after missing the opening round at Jerez, leaving him fifteenth in the 24-rider field.
The one-makes series returns at Saschenring in three weeks time, but Skinner will be busy in the meantime as he heads to Spain's Albacete this weekend to ride in the Junior World Championship Moto3 class. | {
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Mens hair restoration is completely an interesting topic for any men with hair loss. Even you can find thousands of hair loss products available in the market, mens hair restoration is a final solution for your hair loss. Hair loss is actually unstoppable and has no permanent cure. What you can find in the market is something that can slow or settle down the hair loss at a certain point so you can take mens hair restoration in the end.
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Oh, sweet Summer time. The sounds of bees buzzing around the yard and the laughter of children fill the air, the grass is warm on your toes and you are ready to plant some flowers, but aren't sure what to plant to be different from every other garden on your block.
The tipsy pot planter is a great Do It Yourself project anyone can do, with just a few supplies and a bit of a green thumb.
Using these simple steps below, you can create your own primitive tipsy pot planter!
Project Supplies: Flowers, Potting soil, Primitive pots, 1/2″ steel conduit |Project Tools: Drill, 1″ hole saw.
1.) Pick the location where you want your tipsy pot planter. I chose to place mine in a place where the grass has never really grown well, right near my main entrance, which makes a great way to greet guests as they come for a visit.
2.) Drill holes into the bottom of each pot. If you are using the 1/2″ conduit, you will need to drill a 1″ hole in each pot. This is what allows the pots to tip from side to side.
I used a drill with a 1″ hole saw attached.
3.) Place your first, larger pot in the location you desire.
4.) Push your conduit into the ground, through the hole you drilled in the larger pot & fill your pot with potting soil.
5.) Continue stacking your pots, tipping them as you go, along the way. Fill them with dirt and whatever flowers your little heart desires. I mainly use flowers that will grow and eventually drape over the edge of the buckets (ivy, vinca vine, petunias, Calibrachoa etc).
Your steel conduit should be even or below the top tipsy pot, if needed, give it a few good pounds to push it down into the ground farther.
Pack your soil nice and tight into the first pot, as the rest of your pots will be resting right in the larger of all the pots.
The more rust your bucket has, the easier it will be to drill through.
*You can also read this blog post in the June issue of Queen of the Castle Magazine online , or pick up a copy at a local business.
Categories: Antiquing/Thrifting, Design, DIY, Gardening/Yard work, Home Design/Decor, Primitives | Tags: DIY, DIY tipsy pot planter, garden decor, how to make a tipsy pot planter, How to upcycle old metal buckets, primitive garden decor, primitive tipsy pot planters, Tipsy Pot planter, tipsy pots, unique flower planters, unique garden ideas, Upcycling, yard decor | Permalink.
Well, as if a move & family doesn't keep you busy enough…..look at this wonderful project!
Thanks Kari!!:) T minus 19 days until we move out of this house!! Then the real adventure begins!
Wow there is an after life for leaking buckets. Best planter I have ever seen. Great job. Bet this could even work for Strawberry plants.
Thanks D 🙂 What a great idea-the strawberry plants, I will have to remember that and try it someday soon! 🙂 Thanks for reading!
I was going to do this with clay pots but yours is much much nicer – must go find me some old pots now! beautiful job!!
luv this idea…have some chippy white enamel pots just waiting to become tipsy!!!!
Thanks Rhonda! Have fun creating your own tipsy pot planter! Find The Pink Hammer on facebook and make sure to post photos of yours when complete-Id love to see!
Thank you for sharing your whimsical planter with us……it is rather delightful.
That is just a fun and creative idea! I love a little whimsy in the garden!
love it, can't wait to make one of my own.
Hi Jamie! Thanks so much for reading, enjoy creating your own tipsy pot planter-they are so fun to create!
Just popped over from Inspred by Charm, and I am loving this!!! You've made this project look so easy to put together. I'm keeping my eyes peeled for old metal vessels to create one of my own. Thanks for sharing this great project. I look forward to checking out more of your projects.
Amazing! I've got a base, just need to keep my eyes open for more galvanized goodies! Thanks for an amazing project.
Oh goodness… you have no idea how much I LOVE this! I hope you don't mind me sharing you on my FB page. Found this through Michael!
Found you through Michael at Inspired by Charm. And this planter is absolutely charming! Yard sales here I come a lookin' for the perfect vessels. Now to read through the rest of your blog!
Stumbled upon this and love it!!! I had been collecting old pails for years. They sat in my basement just waiting for the perfect project! I completed mine yesterday. LOVE it!!! Even my husband and son were thrilled with the look.
Hi Kelly, love this! Do you drill the holes in the center on ALL buckets…or to one side or the other?
Drill the holes in the center of each bucket.
Love this so much, I couldn't wait to find rusty buckets. I actually found one, but I bought the tub and another bucket at a farm supply store. For the top I wanted to use a metal watering can and I found one at a flea market that had flowers painted on it and I tipped that to make it look like it was watering the planter. It turned out perfect. Thanks for an awesome inspiration.
Jill, any way you can post a pic? Your's sounds great!
I love, love, love your pretty planters and I'm collecting tins like yours to make my own! I do hope they turn out as lovely as yours are! I've got this linked to my planters post as well today, for inspiration!
I love this planter. I particularly like the idea of several containers in a vertical space rather than horizontal. Fantastic!
Great Idea! I'm lovin' this tower idea for my old rusty bucket collection…..might start with strawberries.
Oh ! how wonderful your new creation is !!!
I love this, and am so glad the "Two Women with a Hoe" shared it on Facebook!! I'm going to try making one, though perhaps not till next year, as everything is burning up here in Kansas this summer!
Reblogged this on The Adventures of Thrive Farm.
Love this idea. I am doing this for sure next spring. Being a rusty old lady I have lost of rusty old buckets to make it and a rusty old husband to help me. I like the idea to put a watering can on top and I just happen to have one of those laying around. Thanks again for the idea and the instructions on how to do it. I never could have figured that out. Learn something new every day.
This is such a fun and beautiful project. Thanks so much for sharing your tutorial!
Just fantastic. Can't wait til spring.
Rustic garden decor. � The Pink Hammer Blog" was in fact superb.
Oh my! I can't wait to try! I was wondering if a good long stick of bamboo or other wood might work instead of the rebar? I have a neurological condition leaving me permanently disabled. I have to steer clear from heavy metals and wonder if the metal in the rebar might be a problem if I grew edibles in it. Just wondering if the bamboo would be strong enough to hold if far enough into ground?
Hello! Yes I absolutely think something like bamboo or a wood dowel would work, just make sure it is far enough in the ground to hold strong.
Love these pots! Thank you!
I personally needed to present this particular blog, "Primitive tipsy pot planters | DIY Rustic garden decor.
| The Pink Hammer Blog" skidki-goroda together with my own buddies on twitter.
I actuallysimply just needed to distribute your very good publishing!
Adorable idea!!!! You are so clever!!!!
Thank you so much for the instructions on the Tipsy Pot…they were flawless! I made mine yesterday and it came great, I am so proud of it! It took some searching around the Antiques Fair for buckets, a piece of rebar from the hardware store and beautiful flowers from Home Depot! Viola!
Hello, I just acquired quite a collection of older galvanized buckets and small troughs. I really like your version of the topsy turvy pots planter. I do not have a drill to make the larger holes that you used. Perhaps, I could use a large mail to pound a hole into them. I just do not want to damage the already weak bottoms. What would you suggest?
What is a 1/2″ conduit?
Pingback: 17 Rad Ideas for Container Gardening | Stewart Landing Co.
Thank you for the great instructions on the tipsy pot. I just moved into a new place and I want to enhance the front. This is a great idea.
Thank you!!! 🙂 Enjoy creating them!
Can someone please tell me where to go to get these pots?
Hi Darleen! Check your local Junk/antique stores, flea markets , garage sales, etc IF you can no find any no matter where you look, you may purchase them from me (for the cost of pots + shipping from Wisconsin) Thanks! | {
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Widespread pensions ignorance can stop reforms from working, study finds
By Rachel Fixsen2021-10-01T15:04:00+01:00
New research from Sweden's Umeå University has concluded that if a country's pension system is not generally understood by individuals, then the economic effects it is designed – and reformed – to produce, may simply not happen.
Johan Gustafsson, the economist behind the study at Umeå University, said: "The economic mechanisms that are built into the system risk becoming ineffective if people do not understand them."
As evidence of such a lack of understanding, he said in his paper, entitled "Implications of Pension Illiteracy for Labor Supply and Redistribution", that the Swedish Pensions Agency claimed a common misconception among individuals was that their actions had no effect on their future retirement benefits.
"This is remarkable since the Swedish pension system is largely earnings-based, with a highly predictable link between individual contributions and entitled pension income following the introduction of notional pension accounts in the 1990s," he said.
He said a previous study, from Sweden's Institute for Labour Market and Education Policy Evaluation, had already found that two in three Swedes said they lacked sufficient knowledge to understand how their own choices affected their future pension.
"In my research, I want to understand more about the consequences of this ignorance," Gustafsson said.
During the 1990s, he said, the Swedish pension system had been reformed with the aim of increasing the correlation between pension contributions and realised pension income, warning, in other words, 'the longer you work, the higher your pension'.
"If people miss that connection, the reform risks failing to increase labour market participation," the academic said.
The university said in its release about the new research that ignorance about the pension system was also detrimental to individual employees' long-term finances.
"We can see that people underestimate the effect that continued work will have on the future pension, and that because of this, they retire earlier than they would have done if they had been aware of how the pension system works," said Gustafsson.
In turn, this could lead to individual workers receiving a lower pension and thus a lower material standard of living, he said.
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Sweden's third largest pension fund buys 10% of shares of electric motorcycle firm Cake | {
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The 50 Most Popular Biblical Baby Names
Ellen DeWitt
Ellen DeWitt Updated: March 21, 2021
Photo by Garrett Jackson on Unsplash
What's in a name? Well, when it comes to biblical names, the answer is: plenty.
Names from the Bible have been popular as long as the Good Book has existed, and many have grown steadily in usage in recent years.
A few biblical characters made names for themselves performing miracles, like Aaron, who transformed his walking staff into a serpent and showed that he could bring on plagues of blood, frogs, and lice. Isaiah predicted the virgin birth of Christ, and Gabriel was the archangel who told the Virgin Mary the news of the Annunciation. Elijah performed miracles and upon his death was taken to heaven in a horse-drawn chariot of fire.
Some of the most intriguing namesakes are the stars of stories told generation after generation. Jonah was swallowed by a whale and sat in its belly for three days before he was hurled onto dry land. Delilah cut off her strong lover Samson's hair, rendering him powerless. Joseph was given a brightly colored coat by his father, making his brothers so jealous that they sold him into slavery and faked his death. Daniel was thrown into a den of lions, who did not eat him alive because an angel sent by God intervened.
Some names were popular in the Middle Ages, adopted by royalty and powerful popes. Others fell into disuse for centuries before they were brought back. Many have found their way into popular culture, as in the hit song "Hey Jude," the classic novel "Silas Marner," and the unstoppable Princess Leia of "Star Wars."
LOOK: The most popular biblical baby names
To determine the most popular biblical baby names, Stacker consulted the name origin site Behind the Name and the Social Security Administration's baby names database then ranked the top 50 names from Behind the Name's Biblical Names origins list of 564 names, based on how many babies had been given these names in 2019. Click through to find out which biblical names have stood the test of time.
Source: The 50 Most Popular Biblical Baby Names
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Wyoming prohibits its sale
Wynne Dinwiddie 2 weeks ago 3 min read
For months now, there has been talk of stopping the sale of diesel and petrol cars in Europe starting from 2035, a decision still full of doubts by many players in the car market, but we will slowly see the developments. Meanwhile, Europe is in favor of that, so we need to understand what steps it will take in this regard.
In this scenario, there is a country that today suffers from the exact opposite: He hates electric cars and wants to ban their sale from 2035. The situation seems almost cynical, but it is true. We are talking about Wyoming, America.
There are states like New York and California, that are aligning with the decisions made here, abroad, and are moving to eliminate cars with internal combustion engines. Then there is Wyoming who goes against the grain of the whole, actually choosing the exact opposite direction.
Why Wyoming wants to ban electric cars
It seems strange to read such a headline, especially in an era when there is no talk of anything other than the benefits that the total circulation of 100% electric vehicles should bring to the environment and consumption by the users themselves.
True, even in Europe – e In Italy in particular, as Prime Minister Giorgia Meloni said – At the moment there are still many doubts. But even Banning the sale of electric cars seems like an incredible decisionbut that's exactly what Wyoming wants to do.
The United States has introduced legislation to phase out the sale of electric cars until 2035 with a complete ban. Even the date is contradictory: the same date when zero-emission cars are likely to be sold only in Europe (although… The date seems very close at the moment).
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However, we cannot talk about a legal obligation, but it is certainly a proposal to ban the sale of electric cars. Senator Jim Anderson initiated this initiative, but many other representatives from the Wyoming House and Senate supported it.
The senator himself declared that the goal was to protect local economic interests.
Why the energy transition threatens Wyoming
Among the states of America, Wyoming is by far the least populated, but still A major oil producer, the eighth largest. There is a reason for wanting to ban electric cars, clearly not a pointless "whim".
The "oil and gas" industry, as stated in the proposal, employs thousands of people. Then the energy transmission It would undermine the employment of many employees in the sector And it could really become a very serious problem for Wyoming, but also for other states that rely heavily on the extraction and refining of petroleum products.
It is clear that the transition to 100% electric mobility will lead to a decrease in the demand for petroleum products and thus Many jobs will be at risk. However, it does not seem possible to propose a real law that would completely ban the sale of electric cars, and it does not seem to be the solution anyway.
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Next Europe is approaching recovery, and is betting on curbing the European Central Bank. Milan returned to pre-war levels | {
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DJ Khaled Unveils All-Star 'Grateful' Tracklist (Video)
DJ Khaled unveils his all-star "Grateful" tracklisting with features from the biggest names in music. Get the scoop.
Xaviera Bryant June 9, 2017
NO STRINGS ATTACHED: Nicki Minaj, Michael Phelps, Amber Rose, Young M.A., & More Star In New Beats By Dre Ad (Video)
Nicki Minaj, Michael Phelps, Amber Rose, Young M.A., and more star in Beats By Dre's new "No Strings Attached" ad campaign. Watch now.
Xaviera Bryant October 17, 2016
VIDEO: PARTYNEXTDOOR – 'Come And See Me' (Starring Kylie Jenner)
PARTYNEXTDOOR releases the official music video for "Come and See Me" featuring his rumored girlfriend, Kylie Jenner, as his leading lady.
Kehlani Deletes Her Instagram Page After Kyrie Irving Fans Swoop Down On Her
Kehlani deactivated her Instagram page on Sunday night when Kyrie Irving fans swooped down on her after he won the NBA championship. Get the scoop.
Chris Brown Slams Kehlani – 'There Is No Attempting Suicide…Stop Flexing For The Gram'
Chris Brown publicly slams Kehlani for allegedly cheating on Kyrie Irving and accuses her of faking her suicide attempt for attention and sympathy.
Xaviera Bryant March 30, 2016
Kyrie Irving's Girlfriend Kehlani Back In Bed With PARTYNEXTDOOR (Pics)
It looks like Kyrie Irving's love affair with R&B singer Kehlani is a wrap after her ex, PARTYNEXTDOOR, posted a photo of them in bed together. | {
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LatinaLista — Aside from the fight against terrorism, the only other battle that has united countries to pool resources and research to find a solution, or in this case a cure, is the fight against AIDS.
In our interconnected world these days, it's not hard for diseases of any kind to bypass customs or border checkpoints and slip into countries as stowaways in a person's lungs or blood. The global trail of AIDS has been tracked for over the last decade and while there are certain countries that suffer disproportionately from the disease, every country is impacted by it.
In the run-up to December 1, World Aids Day, a Spanish-English global campaign was launched asking everyone to be a hero by helping to raise $1 million by December 1.
Announced this week in New York City by Spanish singer Miguel Bose, the campaign is being coordinated by two organizations on different sides of the Atlantic — in New York through AID FOR AIDS (AFA), and in Barcelona, through the Fight Against AIDS Foundation," (FLS, for its Catalan acronym).
The monies raised will be spent on research and development of an AIDS vaccine. People are asked to text the words "LIFE" or "VIDA" to 41010 or go to the website and donate online.
"This agreement is essential in the fight against AIDS and the request we are making, both here and in Barcelona is for all to raise our voices as one," Bose said. | {
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Cheaper to own this 2 bedroom/2 bath condo than it is to rent!! This spacious unit with private entrance faces open field. Great townhouse style condo with 2 bedrooms up and a finished basement with family room, 3/4 bath and laundry room. Slider off dinette to private patio. Steps to your garage. All appliances included.
For more information about 272 Circlegate, New Lenox, IL 60451 contact Urban Real Estate. | {
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Carroll Walter Ringwalt (December 15, 1907 – June 26, 1990) was an American football player.
Ringwalt was born in 1907 in Bedford, Indiana. He played college football as a center for Indiana University from 1927 to 1929.
He then played professional football in the National Football League (NFL) as a center and guard for the Portsmouth Spartans in 1930 and Frankford Yellow Jackets in 1931. He appeared in ten NFL games, four as a starter.
Ringwalt was married to Frances Jane Curran. They had two children. After retiring from football, Ringwalt worked in finance for almost 40 years in Indianapolis. He also served in the Army during World War II. He retired in 1980. He died in 1990 at his home in Indianapolis.
References
1907 births
1990 deaths
Indiana Hoosiers football players
Portsmouth Spartans players
Frankford Yellow Jackets players
Players of American football from Indiana | {
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Best of Waste – biofuel to power United Airlines Jets
United Airlines is planning to power their jets with biofuel and increase their environment friendly quotient. Fulcrum BioEnergy plans to have a new plant in Gary, Indiana, that will create 33 million gallons of fuel from 700,000 tons …
United Airlines Expands Partnership With Copa and Avianca
United Airlines today announced it has reached an agreement with Compañía Panameña de Aviación S.A. (Copa), Aerovías del Continente Americano S.A. (Avianca) and many of Avianca's affiliates, for a joint business agreement (JBA) that, pending government approval, is expected to …
United Airlines all set to provide flights from Santa Rosa to Denver
From coming March 8, United Airlines will provide daily flights from the Charles M. Schulz-Sonoma County Airport to Denver International Airport, an important Colorado travel hub. The Santa Rosa airport, which conducted important flights to Denver for about eight years, …
With Help from United Airlines, Special Olympics Athletes Tee It Up with PGA TOUR Pros
Yesterday, United Airlines, the Official Airline of the PGA TOUR, PGA TOUR Champions and Web.com Tour, flew nine top Special Olympics golfers to THE NORTHERN TRUST for an inside-the-ropes, VIP experience with three PGA TOUR players: Rafa Cabrera Bello, James …
United Airlines Names Gerry Laderman Chief Financial Officer
United Airlines (UAL) today announced Gerry Laderman, a 30-year United veteran, has been named executive vice president and chief financial officer. UAL conducted an internal and external search to fill the role; Laderman had been serving as acting chief financial …
St. Kitts Welcomes Wednesday Peak Season Service from United Airlines
For the first time in the island's history, United Airlines will fly a second weekly nonstop flight from its New York hub at Newark Liberty International Airport (EWR) to St. Kitts, complementing the carrier's existing Saturday service. "The addition …
United Airlines celebrates 50 years on Guam
Celebrating half a century, United Airlines CEO Oscar Munoz was on Guam over the weekend. In a wide ranging interview, the head of the country's third largest airline has mentioned that they have no plans to compete with Korean …
United Airlines MileagePlus Voted Favorite Frequent-Flyer Program in Trazee Awards
Published on : Friday, January 4, 2019
United Airlines' MileagePlus loyalty program was awarded Favorite Frequent-Flyer program at the fourth-annual Trazee Awards last night at a special awards event at the Global Business Travel Association convention in San Diego. "We are extremely proud that our customers …
United Airlines computer glitch strands hundreds of passengers at Newark Airport
United Airlines had experienced a computer glitch on Saturday evening that stranded hundreds of people at Newark Airport. Live at Newark Airport, KUSI's own John Soderman gave an eyewitness account of the situation. Soderman's flight was postponed multiple …
United Airlines ready to welcome new planes for regional flights
United Airlines made an announcement mentioning that it is ready to add new planes to its regional routes offering added comfort and new amenities to its short-haul flights. It is about to purchase 25 new Embraer E-175 aircraft that …
United Airlines Launches Inaugural Flight Between San Francisco and Tahitie
Published on : Thursday, January 3, 2019
United Airlines today started the only nonstop service by a U.S. carrier to the Islands of Tahiti. The airline launched its first flight between San Francisco and Pape'ete, the capital of Tahiti. As part of its inaugural celebration, United also …
United Airlines Names Jake Cefolia Senior Vice President, Worldwide Sales
United Airlines today announced Jake Cefolia has been promoted to senior vice president of Worldwide Sales. A veteran sales leader, he will be responsible for directing the efforts of a team of 725 sales professionals who manage sales programs, services, …
United Airlines Announces New Nonstop Service Between Washington, D.C. and Tel Aviv
United Airlines today announced it will begin its 20th year of service to Israel with a new nonstop flight between its hub at Washington Dulles International Airport and Tel Aviv's Ben Gurion International Airport starting May 22, 2019 – subject to government approval. The new flight will …
United Airlines flight makes an emergency landing at SFO
A United Airlines flight 863 made a safe emergency landing at 12:35 a.m. It was headed to Sydney when it had to turn around and come back to SFO. The passengers say one of the engines caught fire …
United Airlines Announces $1 Million Grant To Help California Foster Youth Succeed
Today, United Airlines announced a $1 million grant to First Place for Youth in support of their My First Place program. The four-year investment will enable First Place to expand wraparound support services to 50 percent more foster youth in the region. …
United Airlines' Redesigned Homepage Takes Off
Today, United Airlines (UAL) announced the redesigned united.com homepage, featuring a more personalized digital experience for each customer and an updated, more modern, user-friendly design. The new homepage was created to better tailor the experience for customers, while also improving …
U.S. airlines are designing smaller bathrooms to enlarge passenger space
U.S. airlines are increasingly diminishing the size of bathrooms to expand passenger space. As labor costs rise and fuel prices surge, most of the airlines are taking advantage of robust travel demand to squeeze as many passengers as …
United Airlines Earns Top Marks on Disability Equality Index
Announced today, United Airlines (UAL) achieved the top score of 100 percent on the 2018 Disability Equality Index, a prominent benchmarking metric that rates U.S. companies on their disability inclusion policies and practices. This designation also earns United a place …
United Airlines, American Airlines top scorers on 'Disability Equality'
United Airlines and American Airlines have scored top marks on Monday for their disability inclusion attempts on the 2018 Disability Equality Index (DEI) that represents a benchmarking metric rating the U.S. companies on their disability inclusion policies. United Airlines … | {
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Turbie twist towels are the best in market to dry your hairs after shower. Best thing about these towels are they take very less time compared to blow drying and one size fits all. It is super absorbent and You can wash in machine also. These come in Cotton and Microfiber.
For Some People Microfiber is best and for some people Cotton is Best.
Definitely 100 % Cotton is best for me which is more Thick & Plush. | {
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Die Sprögnitz ist ein rechter Zufluss zum Kamp bei Waldhausen in Niederösterreich.
Die im Ortsgebiet von Sprögnitz entspringende Sprögnitz fließt nach Nordosten ab und sammelt mehrere kleine Zubringer auf, bis sie zum rechtsseitig einfließenden Nondorfer Bach gelangt, ihrem größten Zufluss. Dieser entspringt bei Obernondorf, durchfließt Niedernondorf, wo der Fuchsenlochgraben einfließt und ergießt sich im Ortsgebiet von Niederwaltenreith in die Sprögnitz. Nach der Aufnahme des aus Wiesenreith kommenden Wiesenreithbaches und des den Ort Brand entwässernden Brandbaches strebt die Sprögnitz nach Norden auf den Stausee Ottenstein zu und nimmt dabei noch den Wolfsberggraben auf, der aus Wolfsberg abfließt. Hier bildet sie auch die Gemeindegrenze zwischen Zwettl und Waldhausen, die sich im Stausee fortsetzt. Ihr Einzugsgebiet umfasst 25,1 km² in teilweise offener Landschaft.
Früher mündete die Sprögnitz nicht in den Stausee, sondern in den Friedersbach, der sich knapp danach in den Purzelkamp ergoss.
Einzelnachweise
Gewässer im Bezirk Zwettl
Großgöttfritz
Waldhausen (Niederösterreich)
Zwettl-Niederösterreich | {
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Families Against Cult Teachings (F.A.C.T.): Shop on Amazon and Help FACT at the same time!
Shop on Amazon and Help FACT at the same time!
If you are a regular shopper on Amazon and would like to support us at the same time, please click the link below to select FACT as your charity of choice. Though we receive only a small percentage per sale, if enough people join in it could really add up! Plus, it is easy to do and no cost to you.
Thank you, we really appreciate your support!
F.A.C.T will be a part of #GivingTuesday! | {
"redpajama_set_name": "RedPajamaC4"
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23:24: Blinds up! More updates on the next level's page.
23:23: Chico makes it 45k from the Button and gets 2 calls: Hamid in the SB and Marc in the BB. Flop AsKs6c. Chico c-bets 52k when checked to. Hamid shoves all in and both opponents fold.
23:19: Folds to Chris Thomson in the SB and he shoves his 115k stack all in. Chico looks him up with 8s4s and gets there with a Flush vs the T7o. Down to 8 now. Chris Thomson 9th for £1,000.
23:17: Bruno shoves all in from middle position. Chris calls! Bruno has AK and 188k. He gets a double up through Chris with A2. Chris now crippled with about 115k.
23:16: Turns out it's Hamid's birthday on 3rd February! Hopefully he's still in at Midnight.
23:15: Barry shoves all in from the Hijack (105k). He gets it through! Conor showed the 32o in the bb.
23:11: Chico opens for 47.5k. Mohamed calls from the bb. Flop As6c2h. Check/check. Turn Kh. Mohmed bets about 120k and takes it down. He said afterwards it was a misclick and he meant to be just 70k.
23:10: Hamid open shoves from the cut-off and takes the pot down.
23:09: John takes a hand off, folding UTG. Chris Thomson makes it 52k. Marc Leishman calls from the Button. Heads up. Flop 9c8d5d. Chris check/folds to Marc's bet.
23:07: Barry now in the bb and short. John Angus shoves all in in second position. All folds and John puts a nice two hand combo together.
23:05: All in from Barry McQueen UTG (258k) and John Angus is all in (113k) behind him. All others fold and it's Barry's As6s vs John's QQ. The Queens hold and they pretty much swap stack sizes.
23:03: Folded to Chico in the SB and he shoved all in on Hamid. After thinking it over Hamid made the call with A5 and his 285k stack. Chico showed the old 72 suited and couldn't find a suckout Double up for Hamid!
23:00: A few hands later an another one for Chico. This time he check-raised the 753 flop after Conor had bet and Chris called. He took it down.
22:54: Chico opens for 47k. Takes it down.
22:53: Chico opens for 47.5k. Takes it down.
22:52: Shortest stack John Angus in the big blind this hand. He only has about 85k behind! And he gets a walk!
22:51: Mohamed opens for 45k again but takes it down this time with no contest.
22:47: Mohamed opens to 45k from middle position. Chico calls. We have some new 50k white chips in play btw. Flop Ks5s3h and check/check. Turn 3h and Chico bets 68k when checked to. Mohamed calls. River Jd. Mohamed checks and Chico checks back. Mohamed immediately declares "Set" and shows 55 for a flopped set. Looks like he was trying to set a trap for Chico there.
22:46: Bruno open-shoves all in from early position. Gets it through! With blinds at 10k/20k and a 2k ante that's another 39k on his stack.
22:43: Nothing too existing first few hands.
Great blog Martin, well done and thanks for your dedication. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,056 | [
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