AI App How To Use

AI App How To Use — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Foodsi

  Foodsi is a Polish mobile application that connects customers with restaurants, convenience stores, bakeries and cafes that have a surplus of food, allowing its users to buy the surplus at a reduced price. The service launched in 2019 in Warsaw and has expanded to other major cities in Poland. In 2023, a new feature was introduced in the app, allowing users to buy packages not only with self-pickup but also with delivery. The products range has also been expanded to include unsold magazines, cosmetics or plants. == History == The company was created in 2019 in Poland by Mateusz Kowalczyk and Jakub Fryszczyn. During studies in their home country and abroad, when they made a living working in restaurants and bakeries, they recognized the problem and the scale of food waste. They launched the application by themselves, having previously raised PLN 100,000 on their own for the purpose. Initially, Foodsi was an Android-only app, but over time, an IOS version was developed. In 2022, the startup raised PLN 6 million in a seed round from VC companies including CofounderZone and Status Starter, as well as private investors such as founders of Pyszne.pl. As of December 2023, it claimed more than 5000 businesses, serving over 1,5 million users, have saved nearly 3 million bags of food. == Purpose == Foodsi aims to significantly reduce food waste, which contributes to the Sustainable Development Goals. The application bridges the gap between the customers who are looking for shopping deals and the companies that want to reduce surplus products but are unable to sell them at a normal price. This allows the customers to buy unsold products for as little as 30% of the normal price. The company claims that every 4 out of 5 packages are sold on average. As of 2019 Foodsi employed more than 30 people. By 2024 it was more than 50. For now, Foodsi operates in major Polish cities such as Warsaw, Kraków, Trójmiasto, Wrocław, Poznań etc. However, in the upcoming years, Foodsi plans to expand to other countries. == Use == To start selling surplus, a company must leave Foodsi its contact information to register in the system. Registration in the app is completely free of charge. Then, companies offer available packages anticipating what won’t be sold and post them in the app along with the price so that users can buy them and pick them up. Companies can put their packages in the app at any time during the day. Users can pick up packages from bakeries, grocery stores, restaurants, but also florists and beauty stores. Foodsi charges a small commission on each package from the cooperating companies. If a user wants to start ordering packages from Foodsi, he or she needs to install the app on their mobile phone (Android or IOS) and register an account. The app displays a list of restaurants and other venues available in a specific region set by the user's location. Customers can see the price, address, distance and time range for package pickup. Packages are usually in the form of so-called 'surprise-packages', meaning that customers do not know specifically what kind of food/product will be inside. Some restaurants offer a choice of different package sizes. Prices are up to 70% lower than those of the original products. Customers have to show up at the restaurant to pick up the package using their phone at a time specified in the app. == Awards == Auler All-Stars 2025 - 3rd place Deloitte Technology Fast 50 - 2025 Central Europe Executive Club - Innowacja Roku: Żywność i Rolnictwo - Wyróżnienie (2025) Stena Circular Economy Award - Lider Gospodarki Obiegu Zamkniętego (2025) - wyróżnienie w kategorii start-up wdrażający GOZ na rynku polskim 255th place in the international poll FoodTech 500 2025 Finalist for the EY Entrepreneur Of The Year™ 2025 Wpływowi 2024 - Laureat w kategorii “Zrównoważony rozwój” Supplier of the Year 2024 - XXII Food & Business Forum Supplier of the Year 2024 - VII Sweets & Coffee Forum Innovative Leader 2024 - Leader in Food / Food-Tech Category - Executive Summit “Orzeł Innowacji - Start-up z potencjałem Polska-Świat” (Rzeczpospolita, 2024) 102nd place in the international poll FoodTech 500 2024 Auler 2023 Startup of the Year 2023 according to money.pl Start(up) w zrównoważoną przyszłość Kongresu Kompas ESG 2023 Marka Godna Zaufania according to My Company Polska 2023 184th place in the international poll FoodTech 500 2023 In 2023, Foodsi co-founder Mateusz Kowalczyk was recognized by Forbes magazine and included in its "30 before 30" list.

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  Social media use in hiring

  Social media use in hiring refers to the examination by employers of job applicants' (public) social media profiles as part of the hiring assessment. For example, the vast majority of Fortune 500 companies use social media as a tool to screen prospective employees and as a tool for talent acquisition. This practice raises ethical questions. Employers and recruiters note that they have access only to information that applicants choose to make public. Many Western-European countries restrict employer's use of social media in the workplace. States including Arkansas, California, Colorado, Illinois, Maryland, Michigan, Nevada, New Jersey, New Mexico, Utah, Washington, and Wisconsin protect applicants and employees from surrendering usernames and passwords for social media accounts. Use of social media has caused significant problems for some applicants who are active on social media. A 2013 survey of 17,000 young people in six countries found that one in ten people aged 16 to 34 claimed to have been rejected for a job because of social media activity. Social media services have been reported to affect deception in resumes. While these services do not affect deception frequency, it does increase deception about interests and hobbies. == Ethical implications == This issue raises many ethical questions that some consider an employer's right and others consider discrimination. As of 2016, except in the states of California, Maryland, and Illinois, there are no laws that prohibit employers from using social media profiles as a basis of whether or not someone should be hired. Title VII also prohibits discrimination during any aspect of employment including hiring or firing, recruitment, or testing. Social media has been integrating into the workplace, and this has led to conflicts within employees and employers.[107] Particularly, Facebook has been seen as a popular platform for employers to investigate in order to learn more about potential employees. This conflict first started in Maryland when an employer requested and received an employee's Facebook username and password. State lawmakers first introduced legislation in 2012 to prohibit employers from requesting passwords to personal social accounts in order to get a job or to keep a job. This led to Canada, Germany, the U.S. Congress and 11 U.S. states to pass or propose legislation that prevents employers' access to private social accounts of employees.[108] Many Western European countries have already implemented laws that restrict the regulation of social media in the workplace. States including Arkansas, California, Colorado, Illinois, Maryland, Michigan, Nevada, New Jersey, New Mexico, Utah, Washington, and Wisconsin have passed legislation that protects potential employees and current employees from employers that demand them to give forth their username or password for a social media account. Laws that forbid employers from disciplining an employee based on activity off the job on social media sites have also been put into act in states including California, Colorado, Connecticut, North Dakota, and New York. Several states have similar laws that protect students in colleges and universities from having to grant access to their social media accounts. Eight states have passed the law that prohibits post secondary institutions from demanding social media login information from any prospective or current students and privacy legislation has been introduced or is pending in at least 36 states as of July 2013. As of May 2014, legislation has been introduced and is in the process of pending in at least 28 states and has been enacted in Maine and Wisconsin. In addition, the National Labor Relations Board has been devoting a lot of their attention to attacking employer policies regarding social media that can discipline employees who seek to speak and post freely on social media sites. Use of social media by young people has caused significant problems for some applicants who are active on social media when they try to enter the job market. A survey of 17,000 young people in six countries in 2013 found that 1 in 10 people aged 16 to 34 have been rejected for a job because of online comments they made on social media websites. A 2014 survey of recruiters found that 93% of them check candidates' social media postings. Moreover, professor Stijn Baert of Ghent University conducted a field experiment in which fictitious job candidates applied for real job vacancies in Belgium. They were identical except in one respect: their Facebook profile photos. It was found that candidates with the most wholesome photos were a lot more likely to receive invitations for job interviews than those with the more controversial photos. In addition, Facebook profile photos had a greater impact on hiring decisions when candidates were highly educated. These cases have created some privacy implications as to whether or not companies should have the right to look at employee's Facebook profiles. In March 2012, Facebook decided they might take legal action against employers for gaining access to employee's profiles through their passwords. According to Facebook Chief Privacy Officer for policy, Erin Egan, the company has worked hard to give its users the tools to control who sees their information. He also said users shouldn't be forced to share private information and communications just to get a job. According to the network's Statement of Rights and Responsibilities, sharing or soliciting a password is a violation of Facebook policy. Employees may still give their password information out to get a job, but according to Erin Egan, Facebook will continue to do their part to protect the privacy and security of their users. == Impacts == Use of social media by young people has caused significant problems for some applicants who are active on social media when they try to enter the job market. A survey of 17,000 young people in six countries in 2013 found that 1 in 10 people aged 16 to 34 have been rejected for a job because of online comments they made on social media websites. A 2014 survey of recruiters found that 93% of them check candidates' social media postings. Moreover, in 2015 professor Stijn Baert of Ghent University conducted a field experiment in which fictitious job candidates applied for real job vacancies in Belgium. They were identical except in one respect: their Facebook profile photos. It was found that candidates with the most wholesome photos were a lot more likely to receive invitations for job interviews than those with the more controversial photos. In addition, Facebook profile photos had a greater impact on hiring decisions when candidates were highly educated. These cases have created some privacy implications as to whether or not companies should have the right to look at employee's Facebook profiles. In March 2012, Facebook decided they might take legal action against employers for gaining access to employee's profiles through their passwords. According to Facebook Chief Privacy Officer for policy, Erin Egan, the company has worked hard to give its users the tools to control who sees their information. He also said users shouldn't be forced to share private information and communications just to get a job. According to the network's Statement of Rights and Responsibilities, sharing or soliciting a password is a violation of Facebook policy. Employees may still give their password information out to get a job, but according to Erin Egan, Facebook will continue to do their part to protect the privacy and security of their users. == Policy Responses == 26 US states now have laws against an employer requiring a current or potential employee to give the employer their username and password.

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  SFINKS

  Sfinks (Polish for "Sphynx") was also the initial name of the Janusz A. Zajdel Award In cryptography, SFINKS is a stream cypher algorithm developed by An Braeken, Joseph Lano, Nele Mentens, Bart Preneel, and Ingrid Verbauwhede. It includes a message authentication code. It has been submitted to the eSTREAM Project of the eCRYPT network. In 2005, Nicolas T. Courtois noted that, while the cipher is elegant and secure against some simple algebraic attacks, it is vulnerable to more elaborate known attacks.

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  Social media as a news source

  Social media as a news source is defined as the use of online social media platforms such as Instagram, TikTok, and Facebook rather than the use of traditional media platforms like the newspaper or live TV to obtain news. Television had just begun to turn a nation of people who once listened to media content into watchers of media content between the 1950s and the 1980s when the popularity of social media had also begun creating a nation of media content creators. Almost half of Americans use social media as a news source, according to the Pew Research Center. As social media's role in news consumption grows, questions have emerged about its impact on knowledge, the formation of echo chambers, and the effectiveness of fact-checking efforts in combating misinformation. Social media platforms allow user-generated content and sharing content within one's own virtual network. Using social media as a news source allows users to engage with news in a variety of ways including: Consuming and discovering news Sharing or reposting news Posting one's own photos, videos, or reports of news (i.e., engage in citizen or participatory journalism) Commenting on news posts Using social media as a news source has become an increasingly popular way for people of all age groups to obtain current and important information. Just like many other new forms of technology there are going to be pros and cons. There are ways that social media positively affects the world of news and journalism but it is important to acknowledge that there are also ways in which social media has a negative effect on the news. With this accessibility, people now have more ways to consume false news, biased news, and even disturbing content. In 2019, the Pew Research Center created a poll that reported Americans are wary about the ways that social media sites share news and certain content. This wariness of accuracy grew as awareness that social media sites could be exploited by bad actors who concoct false narratives and fake news. == Relationship to traditional news sources == Unlike traditional news platforms such as newspapers and news shows, social media platforms allow people without professional journalistic backgrounds to create news and cover events that news agencies might not cover. Social media users may read a set of news that differs slightly from what newspaper editors prioritize in the print press. A 2019 study found that Facebook and Twitter users are more likely to share politics, public affairs, and visual media news. Typically social media users circulate more towards posting about negative news. A study of tweets found that while optimistic-sounding and neutral-sounding tweets were equally likely to express certainty or uncertainty, the pessimistic tweets were nearly twice as likely to appear certain of an outcome than uncertain. These results could imply that posts of a more pessimistic nature that are also written with an air of certainty are more likely to be shared or otherwise permeate groups on Twitter. A similar bias towards negativity has developed on Facebook, where internal memos revealed that an algorithm built to promote "meaningful social interaction" actually incentivized publishers to promote negative and sensational news. Biases towards negativity need to be considered when the utility of new media is addressed, as the potential for human opinion to overemphasize any particular news story is greater despite general improvement. In order to compete in this rapidly changing technological environment, there has been an upheaval of traditional news sources onto online spaces. The production and circulation of newspaper prints have continued to globally decline in accordance with the increasing presence of news outlets on social media. Prominent platforms such as Twitter and Facebook have been key in engaging users through the integration of journalistic news into their newsfeeds. This feature has now become a foundational part of these apps' interfaces. Social media incentivizes both legacy news brands and individual professional journalists to share their reporting and interact with audiences on social platforms to boost engagement. However, most people who consume news on social media report that accessing news is not their main motivation for being on social media, but rather, they see and consume news incidentally. Nonetheless, informational interviews reveal that these consumers rely on being informed through social media. Some news consumers attest that a news brand's participation in social media does not improve their trust in the brand and that more in-depth reporting and more transparency about biases would improve trust instead. == Use as a news source == Globally, data from 2020 shows that over 70% of adult participants from Kenya, South Africa, Chile, Bulgaria, Greece, and Argentina utilized social media for news while those from France, the UK, the Netherlands, Germany, and Japan were reportedly less than 40 percent. According to the Pew Research Center, 20% of adults in the United States in 2018 said they get their news from social media "often," compared to 16% who said they often get news from print newspapers, 26% who often get it from the radio, 33% who often get it from news websites, and 49% who often get it from TV. The same survey found that social media was the most popular way for American adults age 18–29 to get news, the second-to-last most popular way for Americans age 20–49 to get news, and the least popular way for American adults age 50-64 and 65+ to get the news. In 2019, the Pew Research Center found that over half of Americans (54%) either got their news "sometimes" or "often" from social media, and Facebook was the most popular social media site where American adults got their news. However, at least 50% off all respondents reported that the following were either a "very big problem" or a "moderately big problem" for getting news on social media: One-sided news (83%) Inaccurate news (81%) Censorship of the news (69%) Uncivil discussions about the news (69%) Harassment of journalists (57%) News organizations or personalities being banned (53%) Violent or disturbing news images or videos (51%) In a later survey from the same year, the Pew Research Center reported that 18% of American adults reported that the most common way they get news about politics and the election was from social media. Additional source information shows that from politics and the United States presidential election in 2016, the popularity of fake news had grown to global attention. With this information, the study explains that more than 60 percent of adults receive their news from social media, the most popular being Facebook. With the increase of fake news, and the large amount of adult participation on these social media sites, it made it much harder for those who were searching for news to find a source that they could find credible. Another study found that adult participants found their own friends on Facebook to be a more reliable source of information online compared to a professional news organization. Although, when news was posted by a news organization online, they were then found more reliable compared to when they are shared by their online friends. Showing that adult participants found that the news that was only posted on Facebook and social media was much more credible to them than compared to other forms of information spreading. The study further states that these outcomes have the potential explanation that the topic of the news article played a part in the ways they were affected. This could have affected the way adult participants interacted with the different news sources, such as their online friends compared to a news organization, prominently because depending on the story, they want to have the correct information about the news from the most credible source. === By young people === Social media platforms are some of the most easily accessible forms of news and with the growing generations, the technology is only going to grow. With that, the use of social media in younger generations is also going to grow alongside it. Technology in the hands of young kids can be a concern moving into the future. Globally, there is evidence that through social media, youth have become more directly involved in protests, social campaigns and generally, in the sharing of news across multiple platforms. The number of people who use social media platforms such as Twitter, Facebook, Instagram, or Snapchat as ways to seek information has increased significantly in recent years especially for people who are part of the younger generation.TikTok is a rapidly expanding platform that young adults can use to find news content on social media. TikTok is one of the sites that young adults and teens utilize to get news about trending themes and controversial topics. The younger generation accepts without hesitation the information that thei

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  Once (dating platform)

  Once is an online dating platform founded in 2015. The platform offers users one selected match per day for more meaningful connections. == History == Once was established in 2015, the founders included dating industry entrepreneur Jean Meyer, who became a CEO of the company, as well as Guillaume Sempe and Guilhem Duche. It focused on providing a single daily match to its users. On its early stages Once secured a $3.5 million seed round from Partech Ventures and some private investors. The same year, it opened offices in Paris, and London. By 2016, it reached 1 million users. In 2020, the company was acquired by Dating Group for $18 million. Following the acquisition, Once underwent rebranding. Alexandra Beaumont took over leadership of the brand in 2021, driving growth, rebranding, and innovation. == Overview == Once provides an online dating service with a focus on thoughtful connections. Users receive one selected match per day, which encourages meaningful interactions. The platform operates primarily in the United States, the United Kingdom, Canada, France, and Spain. The platform is supported by Android, iOS, and Apple Watch OS.

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  Myrinet

  Myrinet, ANSI/VITA 26-1998, is a high-speed local area networking system designed by the company Myricom to be used as an interconnect between multiple machines to form computer clusters. == Description == Myrinet was promoted as having lower protocol overhead than standards such as Ethernet, and therefore better throughput, less interference, and lower latency while using the host CPU. Although it can be used as a traditional networking system, Myrinet is often used directly by programs that "know" about it, thereby bypassing a call into the operating system. Earlier versions of Myrinet used a variety of media and connectors: Generation 2 used copper media with DC-37 (Myrinet-LAN, M2L- controllers and switches) or microribbon (Myrinet-SAN, M2M-) connectors. Generation 3 used copper media with HSSDC (Myrinet-Serial, M3S-) or microribbon (Myrinet-SAN, M3M-) connectors, or fiber with LC-connectors (Myrinet-Fiber, M3F-). The later versions of Myrinet physically consist of two fibre optic cables, upstream and downstream, connected to the host computers with a single connector. Machines are connected via low-overhead routers and switches, as opposed to connecting one machine directly to another. Myrinet includes a number of fault-tolerance features, mostly backed by the switches. These include flow control, error control, and "heartbeat" monitoring on every link. The "fourth-generation" Myrinet, called Myri-10G, supported a 10 Gbit/s data rate and can use 10 Gigabit Ethernet on PHY, the physical layer (cables, connectors, distances, signaling). Myri-10G started shipping at the end of 2005. Myrinet was approved in 1998 by the American National Standards Institute for use on the VMEbus as ANSI/VITA 26-1998. One of the earliest publications on Myrinet is a 1995 IEEE article. === Performance === Myrinet is a lightweight protocol with little overhead that allows it to operate with throughput close to the basic signaling speed of the physical layer. For supercomputing, the low latency of Myrinet is even more important than its throughput performance, since, according to Amdahl's law, a high-performance parallel system tends to be bottlenecked by its slowest sequential process, which in all but the most embarrassingly parallel supercomputer workloads is often the latency of message transmission across the network. === Deployment === According to Myricom, 141 (28.2%) of the June 2005 TOP500 supercomputers used Myrinet technology. In the November 2005 TOP500, the number of supercomputers using Myrinet was down to 101 computers, or 20.2%, in November 2006, 79 (15.8%), and by November 2007, 18 (3.6%), a long way behind gigabit Ethernet at 54% and InfiniBand at 24.2%. In the June 2014 TOP500 list, the number of supercomputers using Myrinet interconnect was 1 (0.2%). In November 2013, the assets of Myricom (including the Myrinet technology) were acquired by CSP Inc. In 2016, it was reported that Google had also offered to buy the company.

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  Social commerce

  Social commerce is a subset of electronic commerce that involves social media and online media that supports social interaction, and user contributions to assist online buying and selling of products and services. More succinctly, social commerce is the use of social network(s), and user-generated content in the context of e-commerce transactions. The term social commerce was introduced by Yahoo! in November 2005 which describes a set of online collaborative shopping tools such as shared pick lists, user ratings and other user-generated content of online product information and advice. The concept of social commerce was developed by David Beisel to denote user-generated advertorial content on e-commerce sites, and by Steve Rubel to include collaborative e-commerce tools that enable shoppers "to get advice from trusted individuals, find goods and services and then purchase them". The social networks that spread this advice have been found to increase the customer's trust in one retailer over another. Social commerce may assist companies in achieving the following purposes: Firstly, social commerce helps companies engage customers with their brands according to the customers' social behaviors. Secondly, it provides an incentive for customers to return to their website. Thirdly, it provides customers with a platform to talk about their brand on their website. Fourthly, it provides all the information customers need to research, compare, and ultimately choose you over your competitor, thus purchasing from you and not others. In these days, the range of social commerce has been expanded to include social media tools and content used in the context of e-commerce, especially in the fashion industry. Examples of social commerce include customer ratings and reviews, user recommendations and referrals, social shopping tools (sharing the act of shopping online), forums and communities, social media optimization, social applications and social advertising. Technologies such as augmented reality have also been integrated with social commerce, allowing shoppers to visualize apparel items on themselves and solicit feedback through social media tools. Some academics have sought to distinguish "social commerce" from "social shopping", with the former being referred to as collaborative networks of online vendors; the latter, the collaborative activity of online shoppers. == Timeline == 2005: The term "social commerce" was first introduced on Yahoo! in 2005. 2021: The Global Web Index associated one's use of social media to his/her eagerness to buy. Social media with its entertaining and inspirational content can increase a product's profitability. This explains why Instagram expanded its Checkout feature to similar content like IG Stories, IGTV, and Reels. == Elements == The attraction and effectiveness of Social Commerce can be understood in terms of Robert Cialdini's Principles of InfluenceInfluence: Science and Practice": Reciprocity – When a company gives a person something for free, that person will feel the need to return the favor, whether by buying again or giving good recommendations for the company. Community – When people find an individual or a group that shares the same values, likes, beliefs, etc., they find community. People are more committed to a community that they feel accepted within. When this commitment happens, they tend to follow the same trends as a group and when one member introduces a new idea or product, it is accepted more readily based on the previous trust that has been established. It would be beneficial for companies to develop partnerships with social media sites to engage social communities with their products. Social proof – To receive positive feedback, a company needs to be willing to accept social feedback and to show proof that other people are buying, and like, the same things that I like. This can be seen in a lot of online companies such as eBay and Amazon, that allow public feedback of products and when a purchase is made, they immediately generate a list showing purchases that other people have made in relation to my recent purchase. It is beneficial to encourage open recommendation and feedback. This creates trust for you as a seller. 55% of buyers turn to social media when they're looking for information. Authority – Many people need proof that a product is of good quality. This proof can be based on the recommendations of others who have bought the same product. If there are many user reviews about a product, then a consumer will be more willing to trust their own decision to buy this item. Liking – People trust based on the recommendations of others. If there are a lot of "likes" of a particular product, then the consumer will feel more confident and justified in making this purchase. Scarcity – As part of supply and demand, a greater value is assigned to products that are regarded as either being in high demand or are seen as being in a shortage. Therefore, if a person is convinced that they are purchasing something that is unique, special, or not easy to acquire, they will have more of a willingness to make a purchase. If there is trust established from the seller, they will want to buy these items immediately. This can be seen in the cases of Zara and Apple Inc. who create demand for their products by convincing the public that there is a possibility of missing out on being able to purchase them. == Types == === Onsite === Onsite social commerce refers to retailers including social sharing and other social functionality on their website. Some notable examples include Zazzle which enables users to share their purchases, Macy's which allows users to create a poll to find the right product, and Fab.com which shows a live feed of what other shoppers are buying. Onsite user reviews are also considered a part of social commerce. This approach has been successful in improving customer engagement, conversion and word-of-mouth branding according to several industry sources. === Offsite === Offsite social commerce includes activities that happen outside of the retailers' website. This may include posting products on social networks such as Facebook, X, and TikTok. It may also include advertising on shopping forums such as SlickDeals, Red Flag Deals, and LatestDeals.co.uk. == Measurements == Social commerce can be measured by any of the principle ways to measure social media. Return on Investment: measures the effect or action of social media on sales. Reputation: indices measure the influence of social media investment in terms of changes to online reputation – made up of the volume and valence of social media mentions. Reach: metrics use traditional media advertising metrics to measure the exposure rates and levels of an audience with social media. == Business applications == This category is based on individuals' shopping, selling, recommending behaviors. Social network-driven sales (Soldsie) – Facebook commerce and Twitter commerce belong to this part. Sales take place on established social network sites. Peer-to-peer sales platforms (eBay, Etsy, Amazon) – In these websites, users can directly communicate and sell products to other users. Group buying (Groupon, LivingSocial) – Users can buy products or services at a lower price when enough users agree to make this purchase. Peer recommendations and reviews (Amazon, Yelp, Bazaarvoice) – Users can see recommendations and reviews from other users. User-curated shopping (The Fancy, Lyst) – Users create and share lists of products and services for others to shop from. Participatory commerce (Betabrand, Threadless, Kickstarter) – Users can get involved in the production process. Social shopping (Squadded) – Allowing e-commerce to provide their users live chat sessions and shared shopping lists so they can communicate with their friends or other shoppers for advice. == Business examples == Here are some notable business examples of Social Commerce: Betabrand: an online brand using participatory design to release new, community-created ideas every week. Cafepress: an online retailer of stock and user-customized on demand products. Etsy: an e-commerce website focused on handmade or vintage items and supplies, as well as unique factory-manufactured items under Etsy's new guidelines. Eventbrite: an online ticketing service that allows event organizers to plan, set up ticket sales and promote events (event management) and publish them across Facebook, Twitter and other social-networking tools directly from the site's interface. Groupon: a deal-of-the-day website that features discounted gift certificates usable at local or national companies. Houzz: a web site and online community about architecture, interior design and decorating, landscape design and home improvement. LivingSocial: an online marketplace that allows clients to buy and share things to do in their city. Lockerz: an international social commerce website based in Seattle, Washington. OpenSky: is a r

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  MDS matrix

  An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography. Technically, an m × n {\displaystyle m\times n} matrix A {\displaystyle A} over a finite field K {\displaystyle K} is an MDS matrix if it is the transformation matrix of a linear transformation f ( x ) = A x {\displaystyle f(x)=Ax} from K n {\displaystyle K^{n}} to K m {\displaystyle K^{m}} such that no two different ( m + n ) {\displaystyle (m+n)} -tuples of the form ( x , f ( x ) ) {\displaystyle (x,f(x))} coincide in n {\displaystyle n} or more components. Equivalently, the set of all ( m + n ) {\displaystyle (m+n)} -tuples ( x , f ( x ) ) {\displaystyle (x,f(x))} is an MDS code, i.e., a linear code that reaches the Singleton bound. Let A ~ = ( I n A ) {\displaystyle {\tilde {A}}={\begin{pmatrix}\mathrm {I} _{n}\\\hline \mathrm {A} \end{pmatrix}}} be the matrix obtained by joining the identity matrix I n {\displaystyle \mathrm {I} _{n}} to A {\displaystyle A} . Then a necessary and sufficient condition for a matrix A {\displaystyle A} to be MDS is that every possible n × n {\displaystyle n\times n} submatrix obtained by removing m {\displaystyle m} rows from A ~ {\displaystyle {\tilde {A}}} is non-singular. This is also equivalent to the following: all the sub-determinants of the matrix A {\displaystyle A} are non-zero. Then a binary matrix A {\displaystyle A} (namely over the field with two elements) is never MDS unless it has only one row or only one column with all components 1 {\displaystyle 1} . Reed–Solomon codes have the MDS property and are frequently used to obtain the MDS matrices used in cryptographic algorithms. Serge Vaudenay suggested using MDS matrices in cryptographic primitives to produce what he called multipermutations, not-necessarily linear functions with this same property. These functions have what he called perfect diffusion: changing t {\displaystyle t} of the inputs changes at least m − t + 1 {\displaystyle m-t+1} of the outputs. He showed how to exploit imperfect diffusion to cryptanalyze functions that are not multipermutations. MDS matrices are used for diffusion in such block ciphers as AES, SHARK, Square, Twofish, Anubis, KHAZAD, Manta, Hierocrypt, Kalyna, Camellia and HADESMiMC, and in the stream cipher MUGI and the cryptographic hash function Whirlpool, Poseidon.

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  ROCm

  ROCm is an Advanced Micro Devices (AMD) software stack for graphics processing unit (GPU) programming. ROCm spans several domains, including general-purpose computing on graphics processing units (GPGPU), high performance computing (HPC), and heterogeneous computing. It offers several programming models: HIP (GPU-kernel-based programming), OpenMP (directive-based programming), and OpenCL. ROCm is free, libre and open-source software (except the GPU firmware blobs), and it is distributed under various licenses. The name initially stood for Radeon Open Compute platform; however, due to Open Compute being a registered trademark, the name no longer functions as an acronym. == Background == The first GPGPU software stack from ATI/AMD was Close to Metal, which became Stream. ROCm was launched around 2016 with the Boltzmann Initiative. ROCm stack builds upon previous AMD GPU stacks; some tools trace back to GPUOpen and others to the Heterogeneous System Architecture (HSA). === Heterogeneous System Architecture Intermediate Language === HSAIL was aimed at producing a middle-level, hardware-agnostic intermediate representation that could be JIT-compiled to the eventual hardware (GPU, FPGA...) using the appropriate finalizer. This approach was dropped for ROCm: now it builds only GPU code, using LLVM, and its AMDGPU backend that was upstreamed, although there is still research on such enhanced modularity with LLVM MLIR. == Programming abilities == ROCm as a stack ranges from the kernel driver to the end-user applications. AMD has introductory videos about AMD GCN hardware, and ROCm programming via its learning portal. One of the best technical introductions about the stack and ROCm/HIP programming, remains, to date, to be found on Reddit. == Hardware support == ROCm is primarily targeted at discrete professional GPUs, but consumer GPUs and APUs of the same architecture as a supported professional GPU are known to work with ROCm. For example, all professional GPUs of the RDNA 2 architecture are officially supported by ROCm 5.x; users report that Consumer RDNA2 units such as the Radeon 6800M APU and the Radeon 6700XT GPU also work. === Professional-grade GPUs === === Consumer-grade GPUs === == Software ecosystem == === Machine learning === Various deep learning frameworks have a ROCm backend: PyTorch TensorFlow ONNX MXNet CuPy MIOpen Caffe Iree (which uses LLVM Multi-Level Intermediate Representation (MLIR)) llama.cpp === Supercomputing === ROCm is gaining significant traction in the top 500. ROCm is used with the Exascale supercomputers El Capitan and Frontier. Some related software is to be found at AMD Infinity hub. === Other acceleration & graphics interoperation === As of version 3.0, Blender can now use HIP compute kernels for its renderer cycles. === Other languages === ==== Julia ==== Julia has the AMDGPU.jl package, which integrates with LLVM and selects components of the ROCm stack. Instead of compiling code through HIP, AMDGPU.jl uses Julia's compiler to generate LLVM IR directly, which is later consumed by LLVM to generate native device code. AMDGPU.jl uses ROCr's HSA implementation to upload native code onto the device and execute it, similar to how HIP loads its own generated device code. AMDGPU.jl also supports integration with ROCm's rocBLAS (for BLAS), rocRAND (for random number generation), and rocFFT (for FFTs). Future integration with rocALUTION, rocSOLVER, MIOpen, and certain other ROCm libraries is planned. === Software distribution === ==== Official ==== Installation instructions are provided for Linux and Windows in the official AMD ROCm documentation. ROCm software is currently spread across several public GitHub repositories. Within the main public meta-repository, there is an XML manifest for each official release: using git-repo, a version control tool built on top of Git, is the recommended way to synchronize with the stack locally. AMD starts distributing containerized applications for ROCm, notably scientific research applications gathered under AMD Infinity Hub. AMD distributes itself packages tailored to various Linux distributions. ==== Third-party ==== There is a growing third-party ecosystem packaging ROCm. Linux distributions are officially packaging (natively) ROCm, with various degrees of advancement: Arch Linux, Gentoo, Debian, Fedora , GNU Guix, and NixOS. There are Spack packages. == Components == There is one kernel-space component, ROCk, and the rest - there is roughly a hundred components in the stack - is made of user-space modules. The unofficial typographic policy is to use: uppercase ROC lowercase following for low-level libraries, i.e. ROCt, and the contrary for user-facing libraries, i.e. rocBLAS. AMD is active developing with the LLVM community, but upstreaming is not instantaneous, and as of January 2022, is still lagging. AMD still officially packages various LLVM forks for parts that are not yet upstreamed – compiler optimizations destined to remain proprietary, debug support, OpenMP offloading, etc. === Low-level === ==== ROCk – Kernel driver ==== ==== ROCm – Device libraries ==== Support libraries implemented as LLVM bitcode. These provide various utilities and functions for math operations, atomics, queries for launch parameters, on-device kernel launch, etc. ==== ROCt – Thunk ==== The thunk is responsible for all the thinking and queuing that goes into the stack. ==== ROCr – Runtime ==== The ROC runtime is a set of APIs/libraries that allows the launch of compute kernels by host applications. It is AMD's implementation of the HSA runtime API. It is different from the ROC Common Language Runtime. ==== ROCm – CompilerSupport ==== ROCm code object manager is in charge of interacting with LLVM intermediate representation. === Mid-level === ==== ROCclr Common Language Runtime ==== The common language runtime is an indirection layer adapting calls to ROCr on Linux and PAL on windows. It used to be able to route between different compilers, like the HSAIL-compiler. It is now being absorbed by the upper indirection layers (HIP and OpenCL). ==== OpenCL ==== ROCm ships its installable client driver (ICD) loader and an OpenCL implementation bundled together. As of January 2022, ROCm 4.5.2 ships OpenCL 2.2, and is lagging behind competition. ==== HIP – Heterogeneous Interface for Portability ==== The AMD implementation for its GPUs is called HIPAMD. There is also a CPU implementation mostly for demonstration purposes. ==== HIPCC ==== HIP builds a `HIPCC` compiler that either wraps Clang and compiles with LLVM open AMDGPU backend, or redirects to the NVIDIA compiler. ==== HIPIFY ==== HIPIFY is a source-to-source compiling tool. It translates CUDA to HIP and reverse, either using a Clang-based tool, or a sed-like Perl script. ==== GPUFORT ==== Like HIPIFY, GPUFORT is a tool compiling source code into other third-generation-language sources, allowing users to migrate from CUDA Fortran to HIP Fortran. It is also in the repertoire of research projects, even more so. === High-level === ROCm high-level libraries are usually consumed directly by application software, such as machine learning frameworks. Most of the following libraries are in the General Matrix Multiply (GEMM) category, which GPU architecture excels at. The majority of these user-facing libraries comes in dual-form: hip for the indirection layer that can route to Nvidia hardware, and roc for the AMD implementation. ==== rocBLAS / hipBLAS ==== rocBLAS and hipBLAS are central in high-level libraries, it is the AMD implementation for Basic Linear Algebra Subprograms. It uses the library Tensile privately. ==== rocSOLVER / hipSOLVER ==== This pair of libraries constitutes the LAPACK implementation for ROCm and is strongly coupled to rocBLAS. === Utilities === ROCm developer tools: Debug, tracer, profiler, System Management Interface, Validation suite, Cluster management. GPUOpen tools: GPU analyzer, memory visualizer... External tools: radeontop (TUI overview) == Comparison with competitors == ROCm competes with other GPU computing stacks: Nvidia CUDA and Intel OneAPI. === Nvidia CUDA === Nvidia's CUDA is closed-source, whereas AMD ROCm is open source. There is open-source software built on top of the closed-source CUDA, for instance RAPIDS. CUDA is able to run on consumer GPUs, whereas ROCm support is mostly offered for professional hardware such as AMD Instinct and AMD Radeon Pro. Nvidia provides a C/C++-centered frontend and its Parallel Thread Execution (PTX) LLVM GPU backend as the Nvidia CUDA Compiler (NVCC). === Intel OneAPI === All the oneAPI corresponding libraries are published on its GitHub Page. ==== Unified Acceleration Foundation (UXL) ==== Unified Acceleration Foundation (UXL) is a new technology consortium that are working on the continuation of the OneAPI initiative, with the goal to create a new open standard accelerator software ecosystem, related open standards and specification projects through Working Groups and Specia

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  Undeniable signature

  An undeniable signature is a digital signature scheme which allows the signer to be selective to whom they allow to verify signatures. The scheme adds explicit signature repudiation, preventing a signer later refusing to verify a signature by omission; a situation that would devalue the signature in the eyes of the verifier. It was invented by David Chaum and Hans van Antwerpen in 1989. == Overview == In this scheme, a signer possessing a private key can publish a signature of a message. However, the signature reveals nothing to a recipient/verifier of the message and signature without taking part in either of two interactive protocols: Confirmation protocol, which confirms that a candidate is a valid signature of the message issued by the signer, identified by the public key. Disavowal protocol, which confirms that a candidate is not a valid signature of the message issued by the signer. The motivation for the scheme is to allow the signer to choose to whom signatures are verified. However, that the signer might claim the signature is invalid at any later point, by refusing to take part in verification, would devalue signatures to verifiers. The disavowal protocol distinguishes these cases removing the signer's plausible deniability. It is important that the confirmation and disavowal exchanges are not transferable. They achieve this by having the property of zero-knowledge; both parties can create transcripts of both confirmation and disavowal that are indistinguishable, to a third-party, of correct exchanges. The designated verifier signature scheme improves upon deniable signatures by allowing, for each signature, the interactive portion of the scheme to be offloaded onto another party, a designated verifier, reducing the burden on the signer. == Zero-knowledge protocol == The following protocol was suggested by David Chaum. A group, G, is chosen in which the discrete logarithm problem is intractable, and all operation in the scheme take place in this group. Commonly, this will be the finite cyclic group of order p contained in Z/nZ, with p being a large prime number; this group is equipped with the group operation of integer multiplication modulo n. An arbitrary primitive element (or generator), g, of G is chosen; computed powers of g then combine obeying fixed axioms. Alice generates a key pair, randomly chooses a private key, x, and then derives and publishes the public key, y = gx. === Message signing === Alice signs the message, m, by computing and publishing the signature, z = mx. === Confirmation (i.e., avowal) protocol === Bob wishes to verify the signature, z, of m by Alice under the key, y. Bob picks two random numbers: a and b, and uses them to blind the message, sending to Alice: c = magb. Alice picks a random number, q, uses it to blind, c, and then signing this using her private key, x, sending to Bob: s1 = cgq ands2 = s1x. Note that s1x = (cgq)x = (magb)xgqx = (mx)a(gx)b+q = zayb+q. Bob reveals a and b. Alice verifies that a and b are the correct blind values, then, if so, reveals q. Revealing these blinds makes the exchange zero knowledge. Bob verifies s1 = cgq, proving q has not been chosen dishonestly, and s2 = zayb+q, proving z is valid signature issued by Alice's key. Note that zayb+q = (mx)a(gx)b+q. Alice can cheat at step 2 by attempting to randomly guess s2. === Disavowal protocol === Alice wishes to convince Bob that z is not a valid signature of m under the key, gx; i.e., z ≠ mx. Alice and Bob have agreed an integer, k, which sets the computational burden on Alice and the likelihood that she should succeed by chance. Bob picks random values, s ∈ {0, 1, ..., k} and a, and sends: v1 = msga and v2 = zsya, where exponentiating by a is used to blind the sent values. Note that v2 = zsya = (mx)s(gx)a = v1x. Alice, using her private key, computes v1x and then the quotient, v1xv2−1 = (msga)x(zsgxa)−1 = msxz−s = (mxz−1)s. Thus, v1xv2−1 = 1, unless z ≠ mx. Alice then tests v1xv2−1 for equality against the values: (mxz−1)i for i ∈ {0, 1, …, k}; which are calculated by repeated multiplication of mxz−1 (rather than exponentiating for each i). If the test succeeds, Alice conjectures the relevant i to be s; otherwise, she conjectures random value. Where z = mx, (mxz−1)i = v1xv2−1 = 1 for all i, s is unrecoverable. Alice commits to i: she picks a random r and sends hash(r, i) to Bob. Bob reveals a. Alice confirms that a is the correct blind (i.e., v1 and v2 can be generated using it), then, if so, reveals r. Revealing these blinds makes the exchange zero knowledge. Bob checks hash(r, i) = hash(r, s), proving Alice knows s, hence z ≠ mx. If Alice attempts to cheat at step 3 by guessing s at random, the probability of succeeding is 1/(k + 1). So, if k = 1023 and the protocol is conducted ten times, her chances are 1 to 2100.

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  Data lineage

  Data lineage refers to the process of tracking how data is generated, transformed, transmitted and used across systems over time. It documents data's origins, transformations and movements, providing detailed visibility into its life cycle. This process simplifies the identification of errors in data analytics workflows, by enabling users to trace issues back to their root causes. Data lineage facilitates the ability to replay specific segments or inputs of the dataflow. This can be used in debugging or regenerating lost outputs. In database systems, this concept is closely related to data provenance, which involves maintaining records of inputs, entities, systems and processes that influence data. Data provenance provides a historical record of data origins and transformations. It supports forensic activities such as data-dependency analysis, error/compromise detection, recovery, auditing and compliance analysis: "Lineage is a simple type of why provenance." Data governance plays a critical role in managing metadata by establishing guidelines, strategies and policies. Enhancing data lineage with data quality measures and master data management adds business value. Although data lineage is typically represented through a graphical user interface (GUI), the methods for gathering and exposing metadata to this interface can vary. Based on the metadata collection approach, data lineage can be categorized into three types: Those involving software packages for structured data, programming languages and Big data systems. Data lineage information includes technical metadata about data transformations. Enriched data lineage may include additional elements such as data quality test results, reference data, data models, business terminology, data stewardship information, program management details and enterprise systems associated with data points and transformations. Data lineage visualization tools often include masking features that allow users to focus on information relevant to specific use cases. To unify representations across disparate systems, metadata normalization or standardization may be required. == Representation of data lineage == Representation broadly depends on the scope of the metadata management and reference point of interest. Data lineage provides sources of the data and intermediate data flow hops from the reference point with backward data lineage, leading to the final destination's data points and its intermediate data flows with forward data lineage. These views can be combined with end-to-end lineage for a reference point that provides a complete audit trail of that data point of interest from sources to their final destinations. As the data points or hops increase, the complexity of such representation becomes incomprehensible. Thus, the best feature of the data lineage view is the ability to simplify the view by temporarily masking unwanted peripheral data points. Tools with the masking feature enable scalability of the view and enhance analysis with the best user experience for both technical and business users. Data lineage also enables companies to trace sources of specific business data to track errors, implement changes in processes and implementing system migrations to save significant amounts of time and resources. Data lineage can improve efficiency in business intelligence BI processes. Data lineage can be represented visually to discover the data flow and movement from its source to destination via various changes and hops on its way in the enterprise environment. This includes how the data is transformed along the way, how the representation and parameters change and how the data splits or converges after each hop. A simple representation of the Data Lineage can be shown with dots and lines, where dots represent data containers for data points, and lines connecting them represent transformations the data undergoes between the data containers. Data lineage can be visualized at various levels based on the granularity of the view. At a very high-level, data lineage is visualized as systems that the data interacts with before it reaches its destination. At its most granular, visualizations at the data point level can provide the details of the data point and its historical behavior, attribute properties and trends and data quality of the data passed through that specific data point in the data lineage. The scope of the data lineage determines the volume of metadata required to represent its data lineage. Usually, data governance and data management of an organization determine the scope of the data lineage based on their regulations, enterprise data management strategy, data impact, reporting attributes and critical data elements of the organization. == Rationale == Distributed systems like Google Map Reduce, Microsoft Dryad, Apache Hadoop (an open-source project) and Google Pregel provide such platforms for businesses and users. However, even with these systems, Big Data analytics can take several hours, days or weeks to run, simply due to the data volumes involved. For example, a ratings prediction algorithm for the Netflix Prize challenge took nearly 20 hours to execute on 50 cores, and a large-scale image processing task to estimate geographic information took 3 days to complete using 400 cores. "The Large Synoptic Survey Telescope is expected to generate terabytes of data every night and eventually store more than 50 petabytes, while in the bioinformatics sector, the 12 largest genome sequencing houses in the world now store petabytes of data apiece. It is very difficult for a data scientist to trace an unknown or an unanticipated result. === Big data debugging === Big data analytics is the process of examining large data sets to uncover hidden patterns, unknown correlations, market trends, customer preferences and other useful business information. Machine learning, among other algorithms, is used to transform and analyze the data. Due to the large size of the data, there could be unknown features in the data. The massive scale and unstructured nature of data, the complexity of these analytics pipelines, and long runtimes pose significant manageability and debugging challenges. Even a single error in these analytics can be extremely difficult to identify and remove. While one may debug them by re-running the entire analytics through a debugger for stepwise debugging, this can be expensive due to the amount of time and resources needed. Auditing and data validation are other major problems due to the growing ease of access to relevant data sources for use in experiments, the sharing of data between scientific communities and use of third-party data in business enterprises. As such, more cost-efficient ways of analyzing data intensive scale-able computing (DISC) are crucial to their continued effective use. === Challenges in Big Data debugging === ==== Massive scale ==== According to an EMC/IDC study, 2.8 ZB of data were created and replicated in 2012. Furthermore, the same study states that the digital universe will double every two years between now and 2020, and that there will be approximately 5.2 TB of data for every person in 2020. Based on current technology, the storage of this much data will mean greater energy usage by data centers. ==== Unstructured data ==== Unstructured data usually refers to information that doesn't reside in a traditional row-column database. Unstructured data files often include text and multimedia content, such as e-mail messages, word processing documents, videos, photos, audio files, presentations, web pages and many other kinds of business documents. While these types of files may have an internal structure, they are still considered "unstructured" because the data they contain doesn't fit neatly into a database. The amount of unstructured data in enterprises is growing many times faster than structured databases are growing. Big data can include both structured and unstructured data, but IDC estimates that 90 percent of Big Data is unstructured data. The fundamental challenge of unstructured data sources is that they are difficult for non-technical business users and data analysts alike to unbox, understand and prepare for analytic use. Beyond issues of structure, the sheer volume of this type of data contributes to such difficulty. Because of this, current data mining techniques often leave out valuable information and make analyzing unstructured data laborious and expensive. In today's competitive business environment, companies have to find and analyze the relevant data they need quickly. The challenge is going through the volumes of data and accessing the level of detail needed, all at a high speed. The challenge only grows as the degree of granularity increases. One possible solution is hardware. Some vendors are using increased memory and parallel processing to crunch large volumes of data quickly. Another method is putting data in-memory but using a grid

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  Back-Up Interceptor Control

  Backup Interceptor Control (BUIC, ) was the Electronic Systems Division 416M System to backup the SAGE 416L System in the United States and Canada. BUIC deployed Cold War command, control, and coordination systems to SAGE radar stations to create dispersed NORAD Control Centers. == Background == Prior to the SAGE Direction Centers becoming operational, the USAF deployed data link systems at NORAD Control Centers with ground computers for controlling crewed interceptors. After SAGE IBM AN/FSQ-7 Combat Direction Centrals became operational and the Super Combat Centers with improved (digital) computers were cancelled, a backup to SAGE was planned in the event the above-ground SAGE Air Defense Direction Center failed. == General Electric AN/GPA-37 Course Directing Group == BUIC began with deployment of General Electric AN/GPA-37 Course Directing Groups to several Long Range Radar stations. Units designated included the "U.S. Air Force 858th Air Defense Group (BUIC) [which became] a permanent operating facility" at Naval Air Station Fallon in Nevada. == BUIC II == BUIC II was used to command and control sites using the Burroughs AN/GSA-51 Radar Course Directing Group. North Truro AFS became the first ADC installation configured for BUIC II. == BUIC III == The AN/GYK-19 (initially AN/GSA-51A) was an upgraded version of the BUIC II system designated AN/GSA-51A and required a larger building than the AN/GSA-51. The first BUIC III site was Fort Fisher AFS, and Air Defense Command's was first installed at Fort Fisher Air Force Station, North Carolina. Although more advanced systems were contemplated, the final design of the BUIC III system was an upgraded version of the BUIC II with around twice the performance. == Closure and upgrade == In 1972, the USAF decided to shut down most of the BUIC sites; most of the sites mothballed by 1974, except for the BUIC III site at Tyndall Air Force Base. In Canada the BUIC site at Senneterre was shut down, but St Margarets remained open. The remaining sites were closed between 1983-1984 when SAGE was replaced by the Joint Surveillance System. The AN/FYQ-47 Common Digitizer for the Joint Surveillance System, and the Radar Video Data Processor (RVDP) was a combined system for the Air Force and Federal Aviation Administration (FAA), it replaced the SAGE Burroughs AN/FST-2 Coordinate Data Transmitting Sets.

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  Convolutional layer

  In artificial neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of the primary building blocks of convolutional neural networks (CNNs), a class of neural network most commonly applied to images, video, audio, and other data that have the property of uniform translational symmetry. The convolution operation in a convolutional layer involves sliding a small window (called a kernel or filter) across the input data and computing the dot product between the values in the kernel and the input at each position. This process creates a feature map that represents detected features in the input. == Concepts == === Kernel === Kernels, also known as filters, are small matrices of weights that are learned during the training process. Each kernel is responsible for detecting a specific feature in the input data. The size of the kernel is a hyperparameter that affects the network's behavior. === Convolution === For a 2D input x {\displaystyle x} and a 2D kernel w {\displaystyle w} , the 2D convolution operation can be expressed as: y [ i , j ] = ∑ m = 0 k h − 1 ∑ n = 0 k w − 1 x [ i + m , j + n ] ⋅ w [ m , n ] {\displaystyle y[i,j]=\sum _{m=0}^{k_{h}-1}\sum _{n=0}^{k_{w}-1}x[i+m,j+n]\cdot w[m,n]} where k h {\displaystyle k_{h}} and k w {\displaystyle k_{w}} are the height and width of the kernel, respectively. This generalizes immediately to nD convolutions. Commonly used convolutions are 1D (for audio and text), 2D (for images), and 3D (for spatial objects, and videos). === Stride === Stride determines how the kernel moves across the input data. A stride of 1 means the kernel shifts by one pixel at a time, while a larger stride (e.g., 2 or 3) results in less overlap between convolutions and produces smaller output feature maps. === Padding === Padding involves adding extra pixels around the edges of the input data. It serves two main purposes: Preserving spatial dimensions: Without padding, each convolution reduces the size of the feature map. Handling border pixels: Padding ensures that border pixels are given equal importance in the convolution process. Common padding strategies include: No padding/valid padding. This strategy typically causes the output to shrink. Same padding: Any method that ensures the output size same as input size is a same padding strategy. Full padding: Any method that ensures each input entry is convolved over for the same number of times is a full padding strategy. Common padding algorithms include: Zero padding: Add zero entries to the borders of input. Mirror/reflect/symmetric padding: Reflect the input array on the border. Circular padding: Cycle the input array back to the opposite border, like a torus. The exact numbers used in convolutions is complicated, for which we refer to (Dumoulin and Visin, 2018) for details. == Variants == === Standard === The basic form of convolution as described above, where each kernel is applied to the entire input volume. === Depthwise separable === Depthwise separable convolution separates the standard convolution into two steps: depthwise convolution and pointwise convolution. The depthwise separable convolution decomposes a single standard convolution into two convolutions: a depthwise convolution that filters each input channel independently and a pointwise convolution ( 1 × 1 {\displaystyle 1\times 1} convolution) that combines the outputs of the depthwise convolution. This factorization significantly reduces computational cost. It was first developed by Laurent Sifre during an internship at Google Brain in 2013 as an architectural variation on AlexNet to improve convergence speed and model size. === Dilated === Dilated convolution, or atrous convolution, introduces gaps between kernel elements, allowing the network to capture a larger receptive field without increasing the kernel size. === Transposed === Transposed convolution, also known as deconvolution, fractionally strided convolution, and upsampling convolution, is a convolution where the output tensor is larger than its input tensor. It's often used in encoder-decoder architectures for upsampling. It's used in image generation, semantic segmentation, and super-resolution tasks. == History == The concept of convolution in neural networks was inspired by the visual cortex in biological brains. Early work by Hubel and Wiesel in the 1960s on the cat's visual system laid the groundwork for artificial convolution networks. An early convolution neural network was developed by Kunihiko Fukushima in 1969. It had mostly hand-designed kernels inspired by convolutions in mammalian vision. In 1979 he improved it to the Neocognitron, which learns all convolutional kernels by unsupervised learning (in his terminology, "self-organized by 'learning without a teacher'"). During the 1988 to 1998 period, a series of CNN were introduced by Yann LeCun et al., ending with LeNet-5 in 1998. It was an early influential CNN architecture for handwritten digit recognition, trained on the MNIST dataset, and was used in ATM. (Olshausen & Field, 1996) discovered that simple cells in the mammalian primary visual cortex implement localized, oriented, bandpass receptive fields, which could be recreated by fitting sparse linear codes for natural scenes. This was later found to also occur in the lowest-level kernels of trained CNNs. The field saw a resurgence in the 2010s with the development of deeper architectures and the availability of large datasets and powerful GPUs. AlexNet, developed by Alex Krizhevsky et al. in 2012, was a catalytic event in modern deep learning. In that year’s ImageNet competition, the AlexNet model achieved a 16% top-five error rate, significantly outperforming the next best entry, which had a 26% error rate. The network used eight trainable layers, approximately 650,000 neurons, and around 60 million parameters, highlighting the impact of deeper architectures and GPU acceleration on image recognition performance. From the 2013 ImageNet competition, most entries adopted deep convolutional neural networks, building on the success of AlexNet. Over the following years, performance steadily improved, with the top-five error rate falling from 16% in 2012 and 12% in 2013 to below 3% by 2017, as networks grew increasingly deep.

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  Cryptographic multilinear map

  A cryptographic n {\displaystyle n} -multilinear map is a kind of multilinear map, that is, a function e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times \cdots \times G_{n}\rightarrow G_{T}} such that for any integers a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} and elements g i ∈ G i {\displaystyle g_{i}\in G_{i}} , e ( g 1 a 1 , … , g n a n ) = e ( g 1 , … , g n ) ∏ i = 1 n a i {\displaystyle e(g_{1}^{a_{1}},\ldots ,g_{n}^{a_{n}})=e(g_{1},\ldots ,g_{n})^{\prod _{i=1}^{n}a_{i}}} , and which in addition is efficiently computable and satisfies some security properties. It has several applications on cryptography, as key exchange protocols, identity-based encryption, and broadcast encryption. There exist constructions of cryptographic 2-multilinear maps, known as bilinear maps, however, the problem of constructing such multilinear maps for n > 2 {\displaystyle n>2} seems much more difficult and the security of the proposed candidates is still unclear. == Definition == === For n = 2 === In this case, multilinear maps are mostly known as bilinear maps or pairings, and they are usually defined as follows: Let G 1 , G 2 {\displaystyle G_{1},G_{2}} be two additive cyclic groups of prime order q {\displaystyle q} , and G T {\displaystyle G_{T}} another cyclic group of order q {\displaystyle q} written multiplicatively. A pairing is a map: e : G 1 × G 2 → G T {\displaystyle e:G_{1}\times G_{2}\rightarrow G_{T}} , which satisfies the following properties: Bilinearity ∀ a , b ∈ F q ∗ , ∀ P ∈ G 1 , Q ∈ G 2 : e ( a P , b Q ) = e ( P , Q ) a b {\displaystyle \forall a,b\in F_{q}^{},\ \forall P\in G_{1},Q\in G_{2}:\ e(aP,bQ)=e(P,Q)^{ab}} Non-degeneracy If g 1 {\displaystyle g_{1}} and g 2 {\displaystyle g_{2}} are generators of G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} , respectively, then e ( g 1 , g 2 ) {\displaystyle e(g_{1},g_{2})} is a generator of G T {\displaystyle G_{T}} . Computability There exists an efficient algorithm to compute e {\displaystyle e} . In addition, for security purposes, the discrete logarithm problem is required to be hard in both G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} . === General case (for any n) === We say that a map e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times \cdots \times G_{n}\rightarrow G_{T}} is an n {\displaystyle n} -multilinear map if it satisfies the following properties: All G i {\displaystyle G_{i}} (for 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} ) and G T {\displaystyle G_{T}} are groups of same order; if a 1 , … , a n ∈ Z {\displaystyle a_{1},\ldots ,a_{n}\in \mathbb {Z} } and ( g 1 , … , g n ) ∈ G 1 × ⋯ × G n {\displaystyle (g_{1},\ldots ,g_{n})\in G_{1}\times \cdots \times G_{n}} , then e ( g 1 a 1 , … , g n a n ) = e ( g 1 , … , g n ) ∏ i = 1 n a i {\displaystyle e(g_{1}^{a_{1}},\ldots ,g_{n}^{a_{n}})=e(g_{1},\ldots ,g_{n})^{\prod _{i=1}^{n}a_{i}}} ; the map is non-degenerate in the sense that if g 1 , … , g n {\displaystyle g_{1},\ldots ,g_{n}} are generators of G 1 , … , G n {\displaystyle G_{1},\ldots ,G_{n}} , respectively, then e ( g 1 , … , g n ) {\displaystyle e(g_{1},\ldots ,g_{n})} is a generator of G T {\displaystyle G_{T}} There exists an efficient algorithm to compute e {\displaystyle e} . In addition, for security purposes, the discrete logarithm problem is required to be hard in G 1 , … , G n {\displaystyle G_{1},\ldots ,G_{n}} . === Candidates === All the candidates multilinear maps are actually slightly generalizations of multilinear maps known as graded-encoding systems, since they allow the map e {\displaystyle e} to be applied partially: instead of being applied in all the n {\displaystyle n} values at once, which would produce a value in the target set G T {\displaystyle G_{T}} , it is possible to apply e {\displaystyle e} to some values, which generates values in intermediate target sets. For example, for n = 3 {\displaystyle n=3} , it is possible to do y = e ( g 2 , g 3 ) ∈ G T 2 {\displaystyle y=e(g_{2},g_{3})\in G_{T_{2}}} then e ( g 1 , y ) ∈ G T {\displaystyle e(g_{1},y)\in G_{T}} . The three main candidates are GGH13, which is based on ideals of polynomial rings; CLT13, which is based approximate GCD problem and works over integers, hence, it is supposed to be easier to understand than GGH13 multilinear map; and GGH15, which is based on graphs.

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  Backup

  In information technology, a backup, or data backup is a copy of computer data taken and stored elsewhere so that it may be used to restore the original after a data loss event. The verb form, referring to the process of doing so, is "back up", whereas the noun and adjective form is "backup". Backups can be used to recover data after its loss from data deletion or corruption, or to recover data from an earlier time. Backups provide a simple form of IT disaster recovery; however not all backup systems are able to reconstitute a computer system or other complex configuration such as a computer cluster, active directory server, or database server. A backup system contains at least one copy of all data considered worth saving. The data storage requirements can be large. An information repository model may be used to provide structure to this storage. There are different types of data storage devices used for copying backups of data that is already in secondary storage onto archive files. There are also different ways these devices can be arranged to provide geographic dispersion, data security, and portability. Data is selected, extracted, and manipulated for storage. The process can include methods for dealing with live data, including open files, as well as compression, encryption, and de-duplication. Additional techniques apply to enterprise client-server backup. Backup schemes may include dry runs that validate the reliability of the data being backed up. There are limitations and human factors involved in any backup scheme. == Storage == A backup strategy requires an information repository, "a secondary storage space for data" that aggregates backups of data "sources". The repository could be as simple as a list of all backup media (DVDs, etc.) and the dates produced, or could include a computerized index, catalog, or relational database. === 3-2-1 Backup Rule === The backup data needs to be stored, requiring a backup rotation scheme, which is a system of backing up data to computer media that limits the number of backups of different dates retained separately, by appropriate re-use of the data storage media by overwriting of backups no longer needed. The scheme determines how and when each piece of removable storage is used for a backup operation and how long it is retained once it has backup data stored on it. The 3-2-1 rule can aid in the backup process. It states that there should be at least 3 copies of the data, stored on 2 different types of storage media, and one copy should be kept offsite, in a remote location (this can include cloud storage). 2 or more different media should be used to eliminate data loss due to similar reasons (for example, optical discs may tolerate being underwater while LTO tapes may not, and SSDs cannot fail due to head crashes or damaged spindle motors since they do not have any moving parts, unlike hard drives). An offsite copy protects against fire, theft of physical media (such as tapes or discs) and natural disasters like floods and earthquakes. Physically protected hard drives are an alternative to an offsite copy, but they have limitations like only being able to resist fire for a limited period of time, so an offsite copy still remains as the ideal choice. Because there is no perfect storage, many backup experts recommend maintaining a second copy on a local physical device, even if the data is also backed up offsite. === Backup methods === ==== Unstructured ==== An unstructured repository may simply be a stack of tapes, DVD-Rs or external HDDs with minimal information about what was backed up and when. This method is the easiest to implement, but unlikely to achieve a high level of recoverability as it lacks automation. ==== Full only/System imaging ==== A repository using this backup method contains complete source data copies taken at one or more specific points in time. Copying system images, this method is frequently used by computer technicians to record known good configurations. However, imaging is generally more useful as a way of deploying a standard configuration to many systems rather than as a tool for making ongoing backups of diverse systems. ==== Incremental ==== An incremental backup stores data changed since a reference point in time. Duplicate copies of unchanged data are not copied. Typically a full backup of all files is made once or at infrequent intervals, serving as the reference point for an incremental repository. Subsequently, a number of incremental backups are made after successive time periods. Restores begin with the last full backup and then apply the incrementals. Some backup systems can create a synthetic full backup from a series of incrementals, thus providing the equivalent of frequently doing a full backup. When done to modify a single archive file, this speeds restores of recent versions of files. ==== Near-CDP ==== Continuous Data Protection (CDP) refers to a backup that instantly saves a copy of every change made to the data. This allows restoration of data to any point in time and is the most comprehensive and advanced data protection. Near-CDP backup applications—often marketed as "CDP"—automatically take incremental backups at a specific interval, for example every 15 minutes, one hour, or 24 hours. They can therefore only allow restores to an interval boundary. Near-CDP backup applications use journaling and are typically based on periodic "snapshots", read-only copies of the data frozen at a particular point in time. Near-CDP (except for Apple Time Machine) intent-logs every change on the host system, often by saving byte or block-level differences rather than file-level differences. This backup method differs from simple disk mirroring in that it enables a roll-back of the log and thus a restoration of old images of data. Intent-logging allows precautions for the consistency of live data, protecting self-consistent files but requiring applications "be quiesced and made ready for backup." Near-CDP is more practicable for ordinary personal backup applications, as opposed to true CDP, which must be run in conjunction with a virtual machine or equivalent and is therefore generally used in enterprise client-server backups. Software may create copies of individual files such as written documents, multimedia projects, or user preferences, to prevent failed write events caused by power outages, operating system crashes, or exhausted disk space, from causing data loss. A common implementation is an appended ".bak" extension to the file name. ==== Reverse incremental ==== A Reverse incremental backup method stores a recent archive file "mirror" of the source data and a series of differences between the "mirror" in its current state and its previous states. A reverse incremental backup method starts with a non-image full backup. After the full backup is performed, the system periodically synchronizes the full backup with the live copy, while storing the data necessary to reconstruct older versions. This can either be done using hard links—as Apple Time Machine does, or using binary diffs. ==== Differential ==== A differential backup saves only the data that has changed since the last full backup. This means a maximum of two backups from the repository are used to restore the data. However, as time from the last full backup (and thus the accumulated changes in data) increases, so does the time to perform the differential backup. Restoring an entire system requires starting from the most recent full backup and then applying just the last differential backup. A differential backup copies files that have been created or changed since the last full backup, regardless of whether any other differential backups have been made since, whereas an incremental backup copies files that have been created or changed since the most recent backup of any type (full or incremental). Changes in files may be detected through a more recent date/time of last modification file attribute, and/or changes in file size. Other variations of incremental backup include multi-level incrementals and block-level incrementals that compare parts of files instead of just entire files. === Storage media === Regardless of the repository model that is used, the data has to be copied onto an archive file data storage medium. The medium used is also referred to as the type of backup destination. ==== Magnetic tape ==== Magnetic tape was for a long time the most commonly used medium for bulk data storage, backup, archiving, and interchange. It was previously a less expensive option, but this is no longer the case for smaller amounts of data. Tape is a sequential access medium, so the rate of continuously writing or reading data can be very fast. While tape media itself has a low cost per space, tape drives are typically dozens of times as expensive as hard disk drives and optical drives. Tape media are generally rotated on a schedule so at least one set is off-site in case something should happe

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