AI And Analytics

AI And Analytics — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Wadhwani Institute for Artificial Intelligence

    Wadhwani Institute for Artificial Intelligence

    Wadhwani AI, based in Mumbai, Maharashtra, is an independent, non-profit institute. Founded in 2018, it is dedicated to developing Artificial intelligence solutions for social good. Their mission is to build AI-based innovations and solutions for underserved communities in developing countries, for a wide range of domains including agriculture, education, financial inclusion, healthcare, and infrastructure. == History and funding == The institute was founded with a $30 million philanthropic effort by the Wadhwani brothers, Romesh Wadhwani and Sunil Wadhwani. The institute was inaugurated and dedicated to the nation by Narendra Modi, the 14th Prime Minister of India. In 2019, the institute received a $2 million grant from Google.org to create technologies to help reduce crop losses in cotton farming, through integrated pest management. The United States Agency for International Development awarded $2 million to the institute in 2020 to develop tools, using mathematical modeling techniques and digital technologies such as artificial intelligence and machine learning, to forecast COVID-19 disease patterns, estimate resources needed, and plan interventions. == Collaboration == With assistance from Google, the Ministry of Agriculture and Farmers' Welfare and the Wadhwani AI developed Krishi 24/7, the first AI-powered automated agricultural news monitoring and analysis tool. Through better decision-making, Krishi 24/7 will support the identification of valuable news, provide timely notifications, and respond quickly to safeguard farmers' interests and advance sustainable agricultural growth. The application converts news articles into English after scanning them in several languages. It ensures that the ministry is informed in a timely manner about pertinent occurrences that are published online by extracting key information from news items, including the headline, crop name, event type, date, location, severity, summary, and source link. The National Center for Disease Control has effectively implemented a comparable automated surveillance and analysis tool for disease outbreaks.

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  • Payment tokenization

    Payment tokenization

    Payment tokenization is a data security process that replaces sensitive payment information, such as credit card numbers, with a unique identifier or "token." This token can be used in place of actual data during transactions but has no exploitable value if breached, thereby reducing the risk of data theft and fraud. == Overview == Payment tokenization is generally categorized into two types: security tokens and payment tokens. Security tokens, also known as post-authorization tokens, are used to replace sensitive information like Primary Account Numbers (PANs), such as credit card numbers either after a payment is authorized or for storing data securely (data-at-rest), such as in merchant databases. These models have been in use since the mid-2000s, following the introduction of the Payment Card Industry Data Security Standard in 2004, which established standards for safeguarding cardholder data. The Payment Card Industry Security Standards Council's 2011 Tokenization Guidelines and the proposed American National Standards Institute X9 standards emphasize using tokens primarily to secure sensitive information, not as replacements for payment credentials processed over financial networks. Traditionally, merchants stored PANs to support backend operations such as settlements, reconciliations, chargebacks, loyalty programs, and customer service. However, with the adoption of security tokenization, merchants can substitute PANs with tokens in their systems. This not only reduces their exposure to fraud but also helps minimize the scope and cost of PCI-DSS compliance, offering a more secure and efficient way to manage cardholder data. == Applications == Payment tokenization is widely used by mobile wallets such as Apple Pay, Google Pay, and Samsung Pay use tokenization to safely store card data on devices. E-commerce platforms rely on it to securely retain customer payment details for recurring purchases. At the physical point of sale, EMV-enabled systems use tokenization to protect card information during in-store transactions. Also, subscription billing services implement tokenization to manage and safeguard payment credentials for ongoing charges.

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  • Experimental SAGE Subsector

    Experimental SAGE Subsector

    The Experimental Semi-Automatic Ground Environment (SAGE) Sector (ESS, Experimental SAGE Subsector until planned Sectors/Subsectors were renamed NORAD Regions, Divisions, and Sectors) was a prototype Cold War Air Defense Sector for developing the Semi Automatic Ground Environment. The Lincoln Laboratory control center in a new building was at Lexington, Massachusetts. == ESS Computer System == The network's Direction Center was completed in a new 1954 building (Building F, 42°27′37″N 071°16′04″W) with prototype peripherals and a single IBM XD-1 computer, a successor to Lincoln Lab's Whirlwind I computer (WWI). In 1955, Air Force personnel began IBM training at the Kingston, New York, prototype facility, and the "4620th Air Defense Wing (experimental SAGE) was established at Lincoln Laboratory"—its "primary mission was computer programming". ESS had a capacity of 48 tracks and used a pre-SAGE ground environment in a "prototype intercept monitor room [at] MIT's Barta building" with "track situation displays, which geographically showed Air Defense Identification Zone lines and antiaircraft circles [and] each console also had a 5-inch CRT for digital information display. Audible alert signals were used, with a different signal for each symbol on a situation display." == Radar stations == Initial service test models of the Burroughs AN/FST-2 Coordinate Data Transmitting Set were placed with radars at South Truro and West Bath, Maine; followed by Texas Tower#2 (TT2) in the Atlantic Ocean, which provided a "triangular pattern with overlap" radar coverage (TT2 later had a connection from the XD-1 via the GE G/A Data Link Output Subsystem through North Truro Air Force Station.) By August 1955, 13 radar stations were networked by the subsector, e.g.: Chatham Clinton, Massachusetts with gap-filler radar Great Boars Head Halibut Point Killingly, Connecticut (41.865734°N 71.820958°W / 41.865734; -71.820958).with gap-filler radar Rockport Air Force Station Scituate, Massachusetts South Truro West Bath, Maine (43°54′7″N 69°50′43″W) with AN/FPS-31 on Jug Handle Hill: ("Lincoln Laboratories experimental radar station") Required by 21 November 1955 were 44 consoles: 38 for the operations floor, 3 on the computer floor for display maintenance, and 3 near the maintenance console (program checkout). WWI was connected to the Experimental SAGE Subsector to verify crosstelling (collateral communication) with the ESS DC, and WWI was also used for a Ground-to-Air (G/A) experiment using a transmitter of the GE G/A Data Link Output Subsystem on Prospect Hill, Waltham, MA sending data to simulated airborne equipment at Lexington. Transmissions from the WWI SAGE Evaluation (WISE) computer system to XD-1 and back were without error by December 1955 when operational software specifications were frozen. Operating procedures for the ESS external sites were complete in March 1956, and == System Operation Testing == From November 15, 1955, to November 7, 1956, three System Operation Tests were conducted which used voice "Ground-to-Air" communication from the Barta control room to aircraft outfitted with SAGE receivers (F-86 interceptors modified to F-86L models in "Project FOLLOW-ON".) Test teams included employees of Bell Telephone Laboratories, Western Electric-ADES, IBM, the RAND Corporation, and Lincoln Labs' Division 6, Division 3, & Division 2 (Division 6 had been created for ESS support.) The North Truro P-10 AN/FST-2 was moved to Almaden Air Force Station (M-96)c. 1957-8 and on August 7, 1958, control of an airborne BOMARC missile that had malfunctioned transferred from the "Experimental SAGE Sector" to a Westinghouse AN/GPA-35 Ground Environment system and the missile crashed into the Atlantic Ocean. By December 31, 1958, ADC Manual 55-28 described the Model 3 SAGE System. == 1959 Experimental Testing == "To prove out the revised SAGE computer program" for Automatic Targeting and Battery Evaluation and ADDC-AADCP crosstelling, a "SAGE/Missile Master" test was conducted beginning in September 1959 with communications between the ESS XD-1 and Martin AN/FSG-1 Antiaircraft Defense System equipment at Fort Banks planned for the CONAD Joint Control Center at Fort Heath—a "SAGE ATABE Simulation Study" (SASS) was also completed 1959–60 by MITRE Corporation.

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  • Data refuge

    Data refuge

    Data Refuge is a public and collaborative project designed to address concerns about federal climate and environmental data that is in danger of being lost. In particular, the initiative addresses five main concerns: What are the best ways to safeguard data? How do federal agencies play a crucial role in collecting, managing, and distributing data? How do government priorities impact data's accessibility? Which projects and research fields depend on federal data? Which data sets are of value to research and local communities, and why? Data Refuge began as a grassroots organization in opposition to government data on climate change and the environment not being archived systemically. Data Refuge's main goal is to collect and allocate data in multiple safe locations to create a sustainable way of archiving old and new data. Data Refuge was initiated in 2016 to protect federal climate and environmental data that is vulnerable under an administration that denies climate change. The system aims to make public research-quality copies of federal climate and environmental data. Data Refuge is supported by the National Geographic Foundation, private donors, Libraries+ Network, Preserving Electronic Governance Initiative (PEGI), the Union of Concerned Scientists (USC), and the Penn Program in Environmental Humanities (PPEH). == Types of data == Data Refuge collects public federal data on the climate and environment in the form of satellite imagery, PDFs, and stories. The data are stored in multiple trusted locations as they are less vulnerable if in only one location, and to ensure accessibility for researchers. Through the Data Rescue events, Data Refuge has accumulated 4 terabytes of data, 30,000 URLs, and 800 participants. === Storytelling === Data Refuge collects stories on vulnerable federal climate and environmental data through: surveys, oral history, photo essays, maps, video shorts, and animations. The stories are archived in a public bank that showcase how federal environmental data support health and safety in communities. Data Stories are collected at Data Rescue events, which are partnered with universities, city and town halls, and advocacy groups. Data stories are collected and used to emphasize the importance of Data Refuge, in how the data on climate change and the environment are being used by people in the United States and across the world for meaningful practices.

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  • Automated Mathematician

    Automated Mathematician

    The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. == Controversy == Lenat claimed that the system was composed of hundreds of data structures called "concepts", together with hundreds of "heuristic rules" and a simple flow of control: "AM repeatedly selects the top task from the agenda and tries to carry it out. This is the whole control structure!" Yet the heuristic rules were not always represented as separate data structures; some had to be intertwined with the control flow logic. Some rules had preconditions that depended on the history, or otherwise could not be represented in the framework of the explicit rules. What's more, the published versions of the rules often involve vague terms that are not defined further, such as "If two expressions are structurally similar, ..." (Rule 218) or "... replace the value obtained by some other (very similar) value..." (Rule 129). Another source of information is the user, via Rule 2: "If the user has recently referred to X, then boost the priority of any tasks involving X." Thus, it appears quite possible that much of the real discovery work is buried in unexplained procedures. Lenat claimed that the system had rediscovered both Goldbach's conjecture and the fundamental theorem of arithmetic. Later critics accused Lenat of over-interpreting the output of AM. In his paper Why AM and Eurisko appear to work, Lenat conceded that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. However, he argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful. == Successor == This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.

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  • Social media intelligence

    Social media intelligence

    Social media intelligence (SMI or SOCMINT) comprises the collective tools and solutions that allow organizations to analyze conversations, respond to synchronize social signals, and synthesize social data points into meaningful trends and analysis, based on the user's needs. Social media intelligence allows one to utilize intelligence gathering from social media sites, using both intrusive or non-intrusive means, from open and closed social networks. This type of intelligence gathering is one element of OSINT (Open- Source Intelligence). To support both the sensing and seizing of social signals at scale, organisations increasingly rely on dedicated audience intelligence platforms which combine data aggregation, NLP-driven analysis, and cross-platform monitoring. The term 'Social Media Intelligence' was coined in a 2012 paper written by Sir David Omand, Jamie Bartlett and Carl Miller for the Centre for the Analysis of Social Media, at the London-based think tank, Demos. The authors argued that social media is now an important part of intelligence and security work, but that technological, analytical, and regulatory changes are needed before it can be considered a powerful new form of intelligence, including amendments to the United Kingdom Regulation of Investigatory Powers Act 2000. Given the dynamic evolution of social media and social media monitoring, our current understanding of how social media monitoring can help organizations create business value is inadequate. As a result, there is a need to study how organizations can (a) extract and analyze social media data related to their business (Sensing), and (b) utilize external intelligence gained from social media monitoring for specific business initiatives (Seizing). == Governmental use == In Thailand, the Technology Crime Suppression Division not only employs a 30-person team to scrutinize social media for content deemed disrespectful to the monarchy, known as lèse-majesté but also encourages citizens to report such content. Particularly targeting the youth, they run a "Cyber Scout" program where participants are rewarded for reporting individuals posting material perceived as detrimental to the monarchy. Instances in Israel involve the arrest of Palestinians by the police for their social media posts. An example includes a 15-year-old girl who posted a Facebook status with the words "forgive me," raising suspicions among Israeli authorities that she might be planning an attack. In Egypt, a leaked 2014 call for tender from the Ministry of Interior reveals efforts to procure a social media monitoring system to identify leading figures and prevent protests before they occur. In the United States, ZeroFOX faced criticism for sharing a report with Baltimore officials showcasing how their social media monitoring tool could track riots following Freddie Gray's funeral. The report labeled 19 individuals, including two prominent figures from the #BlackLivesMatter movement, as "threat actors." In the UK, the Association of Chief Police Officers of England, Wales, and Northern Ireland emphasized the significance of social media in intelligence gathering during anti-fracking protests in 2011. Social media analysis closely monitored protests against the badger cull in 2013, with a 2013 report revealing a team of 17 officers in the National Domestic Extremism Unit scanning public tweets, YouTube videos, Facebook profiles, and other online content from UK citizens. == Effects on political opinion == During the 2016 United States presidential election, the Senate Intelligence Committee released reports containing information about Russia’s use of troll farms to mislead black voters about voting. Also, German researchers in 2010 analyzed Twitter messages regarding the German federal election concluding that Twitter played a role in leading users to a specific political opinion. In a broad sense, social media refers to a conversational, distributed mode of content generation, dissemination, and communication among communities. Different from broadcast-based traditional and industrial media, social media has torn down the boundaries between authorship and readership, while the information consumption and dissemination process is becoming intrinsically intertwined with the process of generating and sharing information. An example of how SOCMINT is used to affect political opinions is the Cambridge Analytica Scandal. Cambridge Analytica was a company that purchased data from Facebook about its users without the consent or knowledge of Americans. They used this data to build a "psychological warfare tool" to persuade US voters to elect Donald Trump as president in the 2016 election. Christopher Wylie, the whistleblower, reported that personal information was taken in early 2014, and used to build a system that could target US voters with personalized pollical advertisements. More than 50 million individuals' data was exploited and manipulated. == Law enforcement == In September of 2023, the Philadelphia Police Department began using social media to track and stay one step ahead of criminal activity to stop meetups and potential robberies. This new approach has made officers utilize another tool in their field by being able to find new information as quickly as possible. Law enforcement agencies worldwide are increasingly employing social media intelligence to enhance their capabilities in both crime prevention and investigation. By analyzing publicly available data from social platforms such as Facebook, Twitter, and Instagram, police can track criminal activities, identify suspects, and even prevent potential crimes before they occur. For instance, the FBI utilizes SOCMINT to monitor threats and investigate criminal activities, including analyzing posts, images, and videos that might signal illegal activities or security concerns. == Marketing == SOCMINT collects data from both organizations and people on an individual level. It has a variety of different purposes, and though its main goal is to improve national security advancements, there are several other benefits as well. This intelligence can identify patterns, predict trends, gather information in current time, etc. In addition, these aspects have allowed for both improvement within businesses and help for law enforcement. Artificial Social Networking Intelligence (ASNI) refers to the application of artificial intelligence within social networking services and social media platforms. It encompasses various technologies and techniques used to automate, personalize, enhance, improve, and synchronize user's interactions and experiences within social networks. ASNI is expected to evolve rapidly, influencing how we interact online and shaping their digital experiences. Transparency, ethical considerations, media influence bias, and user control over data will be crucial to ensure responsible development and positive impact. Google provides many free services and has built an entire media brand with its vast variety of products. Along with data collection, Google also owns two advertising services, Google Ads, and Google AdSense. Surprisingly, most of its revenue comes from advertising, not direct sales of its services or products. Google makes money by selling advertising services to advertisers. They provide ad space to websites on Google, and target ads to consumers of Google services and products. Google can market ads using SOCMINT to collect data from its users and generate revenue. Research shows that various social media platforms on the Internet such as Twitter, Tumblr (micro-blogging websites), Facebook (a popular social networking website), YouTube (largest video sharing and hosting website), Blogs and discussion forums are being misused by extremist groups for spreading their beliefs and ideologies, promoting radicalization, recruiting members and creating online virtual communities sharing a common agenda. Popular microblogging websites such as Twitter are being used as a real-time platform for information sharing and communication during the planning and mobilization of civil unrest-related events.

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  • Talim (textiles)

    Talim (textiles)

    Talim (Kashmiri: تعليم, Kashmiri pronunciation: [t̪əːliːm], Urdu: تَعْلِیم, Arabic: تعليم, pronounced [taʕ.liːm] ) in textiles is a symbolic code and system of notation that facilitates the creation of intricate patterns in fabrics, such as shawls and carpets, and the written coded plans that include colour schemes and weaving instructions. The term is used in traditional hand-weaving in the Indian subcontinent. Talim was initially used to create certain types of patterns in Kashmiri shawls, and later came to be applied in the production of carpets. == Etymology and origin == The term talim, which refers to a symbolic code and system of notation used by shawl and carpet artisans in their weaving processes, came to the Urdu language from the Arabic noun taʻlim (تعليم), which means "authoritative instruction", "teaching", or "edification". It means the same in Urdu and Kashmiri. The Arabic noun originated from the second form of the Arabic root verb ʻalima (علم), which means "to know". According to a local belief in Kashmir, talim was introduced to them by Persian scholar and Sufi Muslim saint Mir Sayyid Ali Hamadani. The belief notwithstanding, talim might have originated from Kashmir; Amritsar was the only place outside of Srinagar where talim was used, by migrated Kashmiri artisans. == Technique == Whereas carpets are generally woven horizontally, providing weavers with a clear view of the progress they are making in creating designs, in Kashmir, carpets are woven vertically, so the weaver is reliant on the talim. The talim technique forms fabrics by passing the weft thread as per a given script that has design codes. Weavers use talim to weave the desired pattern with planned colours. Talim involves teamwork when applying the technique, as the process of creating intricate fabric designs in weaving begins with the Naqash (designer, who designs using pencils on graphs) meticulously crafting the design on a blank sheet of paper called a naska, and the master, Talim guru, making the colour codes and symbols for weft yarns that would interlace the warp to construct the desired design. He writes on a long strip of paper, in specific symbols, the colour codes, and the number of knots to be woven with each colour. Taraha guru collaborates with talim guru and is known as the artisan responsible for determining the colours. Talim uthana is a process or the act of "picking the codes" from the graph. A clerk called the Talim Navis would record the step-by-step instructions for these numbers and colours, and thousands of low-paid and interchangeable weavers would read or recite the record to carry out the design. Afterward, a talim copyist makes copies, which are needed when multiple looms weave the same product. The script, which has been encoded, is deciphered and translated according to the specific guidelines of weavers in order to incorporate the design that is included within it. Talim has been compared to "hieroglyphics" or as a "notational-cum-cryptographic system", as it is challenging to decipher and is unique to the shawls of Kashmir, which requires expertise to comprehend. According to researcher Gagan Deep Kaur, "The talim is widely held to be a trade secret of the community and has always been fiercely guarded by the owners." Those who use talim for shawl-making do not assign important tasks to women, because of the fear that the technique and knowledge may be divulged to other communities when the women are sent there to be married. The coded cards known as talim in the Kashmiri language were used for creating certain types of patterns in shawl weaving. The talim technique is employed in the creation of kani shawls, which originated from the Kanihama region of the Kashmir valley. Carpet weaving adapted the technique from shawl making. When Kashmiri artisans started to create carpets, they chose to continue using the talim rather than switching to a different method. The resurgence of the carpet industry in Amritsar during the last century resulted in the prevalent use of the talim technique among the local weavers, a majority of whom hailed from the region of Kashmir. === Recitation of codes === Talim was also communicated through recitation accompanied by a melodic chant or song. In traditional weaving practices, the use of chanting was common. The movement of the shuttles was synchronised with the song of the weaver, adding a musical rhythm to the instructions represented through hieroglyphics. The weaver's chant, "Two blue, one red, three yellow, two blue," served as a guide as they wove and replicated the designated pattern. == Usage == The first factories established in Amritsar around 1860 utilised Bokhara designs. However, Kashmiri weavers maintained their traditional techniques and employed the talim, instead of a cartoon, for tying knots. As a result, Amritsar became the second location in the Indian subcontinent to use the talim. The traditional weaving practices are still carried out in some parts of the Indian subcontinent. The exact date when talim was last used in the subcontinent varies depending on the region and the specific weaving community. Indian textile historian Jasleen Dhamija wrote in her 1989 book Handwoven Fabrics of India that there were still some weavers in the Kashmiri village of Kanihama who applied talim in weaving shawls. As of 2022, the carpet weavers in Kashmir were the only remaining users of talim in carpets, according to Zubair Ahmed, director of the Indian Institute of Carpet Technology. The institute aims to preserve traditional Kashmiri carpet designs by digitising talim and training weavers in the technique. == Gallery ==

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  • Data room

    Data room

    Data rooms are secure spaces used for housing data, usually of a privileged or confidential nature. They can be physical data rooms, virtual data rooms (VDRs), or data centers. They are primarily used for a variety of corporate purposes, including data storage, document exchange, file sharing, financial transactions, and legal proceedings. Today, data rooms are central to workflows in mergers and acquisitions, venture capital, and corporate restructuring, increasingly utilizing artificial intelligence to securely manage and review large datasets. Historically, data rooms were strictly physical locations heavily guarded and monitored. Today, the vast majority of corporate data rooms are hosted virtually on secure cloud platforms, though physical rooms are still occasionally used for highly sensitive government or proprietary intelligence. == Physical Data Rooms == In mergers and acquisitions (M&A), the traditional data room genuinely consists of a physically secured and continually monitored room, normally in the vendor's offices or those of their legal counsel. Bidders and their advisers visit this room in order to inspect and report on various documents, legal contracts, and financial statements made available during the due diligence process. Historically, physical data rooms presented significant logistical challenges. Often, only one bidder at a time was allowed to enter to maintain document integrity and confidentiality. If new documents or new versions of documents were required, they had to be brought in by courier as hardcopies. Teams involved in large due diligence processes typically had to be flown in from many regions or countries and remain available throughout the process. Because these teams comprised a number of experts in different fields—such as legal counsel, forensic accountants, and industry specialists—the overall cost of keeping such groups on call near the physical data room was often extremely high. == Virtual Data Rooms (VDRs) == To address the costs and logistical bottlenecks of physical data rooms, virtual data rooms (VDRs) were developed to provide secure, online dissemination of confidential information. A VDR is essentially a secure cloud repository with strictly controlled access. Access is managed through secure log-ons supplied by the vendor or authority, which can be disabled at any time if a bidder withdraws from a transaction. Because much of the information released during corporate transactions is highly confidential, VDRs utilize digital rights management (DRM) to control information. Restrictions are applied to the viewers' ability to release data to third parties by disabling forwarding, copying, or printing capabilities. Modern VDRs also employ dynamic watermarking and detailed auditing capabilities. Detailed auditing is required for legal reasons so that a precise digital footprint is kept of who has viewed which version of each document, and for how long. Furthermore, modern VDR platforms are typically built to comply with stringent information security standards such as ISO 27001 and SOC 2. Transitioning from sequential physical data rooms to parallel virtual data rooms has been shown to significantly reduce the duration of M&A transactions while allowing sellers to field multiple bidders simultaneously. == Key Applications == Data rooms are commonly used by legal, accounting, investment banking, and private equity firms. Primary applications include: Mergers and Acquisitions (M&A): VDRs are central to the sell-side M&A process. After potential buyers sign a Non-Disclosure Agreement (NDA) and review a Confidential Information Memorandum (CIM), they are granted data room access to perform deep financial due diligence, such as Quality of Earnings (QoE) analysis and legal liability assessments. Venture Capital and Startups: Startups use data rooms as a centralized location for key operational data, capitalization tables, and financial projections to streamline due diligence for angel investors and venture capital firms during fundraising rounds. Initial Public Offerings (IPOs): Taking a company public requires intense regulatory scrutiny. Data rooms are used to securely share company histories and financial audits with investment bankers, legal teams, and regulatory bodies. Corporate Restructuring and Insolvency: During bankruptcies or corporate carve-outs, data rooms are used to organize outstanding debt profiles, creditor agreements, and operational liabilities. == Emerging Technologies == In recent years, the management of virtual data rooms has increasingly incorporated Artificial Intelligence (AI) and Machine Learning (ML). Generative AI and Natural Language Processing (NLP) tools are now integrated into VDRs to automatically index thousands of documents, perform auto-redaction of personally identifiable information (PII), and assist buy-side analysts in identifying hidden liabilities within unstructured text data during the due diligence phase. Modern AI algorithms can extract line items from financial statements to instantly populate structured databases.

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  • Lawbot

    Lawbot

    Lawbots are a broad class of customer-facing legal AI applications that are used to automate specific legal tasks, such as document automation and legal research. The terms robot lawyer and lawyer bot are used as synonyms to lawbot. A robot lawyer or a robo-lawyer refers to a legal AI application that can perform tasks that are typically done by paralegals or young associates at law firms. However, there is some debate on the correctness of the term. Some commentators say that legal AI is technically speaking neither a lawyer nor a robot and should not be referred to as such. Other commentators believe that the term can be misleading and note that the robot lawyer of the future will not be one all-encompassing application but a collection of specialized bots for various tasks. Lawbots use various artificial intelligence techniques or other intelligent systems to limit humans' direct ongoing involvement in certain steps of a legal matter. The user interfaces on lawbots vary from smart searches and step-by-step forms to chatbots. Consumer and enterprise-facing lawbot solutions often do not require direct supervision from a legal professional. Depending on the task, some client-facing solutions used at law firms operate under an attorney supervision. == Levels of autonomy == The following levels of autonomy (LoA) are suggested for automated AI legal reasoning: Level 0 (LoA0): No automation for AI legal reasoning Level 1 (LoA1): Simple assistance automation Level 2 (LoA2): Advanced assistance automation Level 3 (LoA3): Semi-autonomous automation Level 4 (LoA4): Domain automation Level 5 (LoA5): Fully-autonomous automation Level 6 (LoA6): Superhuman automation == Examples == Some legal AI solutions are developed and marketed directly to the customers or consumers, whereas other applications are tools for the attorneys at law firms. There are already hundreds of legal AI solutions that operate in multitude of ways varying in sophistication and dependence on scripted algorithms. One notable legal technology chatbot application is DoNotPay. It had started off as an app for contesting parking tickets, but has since expanded to include features that help users with many different types of legal issues, ranging from consumer protection to immigration rights and other social issues. == Impact on the legal industry == In the 2016 report, Deloitte estimated that more than 110,000 law jobs in just the United Kingdom alone could disappear within the next twenty years due to automation. This change could result in the creation of more highly skilled jobs and in the reduction of paralegal and temporary positions. Deloitte's report asserts that "there is significant potential for high-skilled roles that involve repetitive processes to be automated by smart and self-learning algorithms". According to Lawyers to Engage, between 22% of a lawyer’s work and 35% of a legal assistant’s work can be automated in the US. Top law schools like Harvard have already begun to integrate Artificial Intelligence into the curriculum. Legal tech start-up companies have begun developing applications that assist law firms with completing low-risk legal processes. These applications can enable lawyers to focus on more work that requires their specific expertise. The automation of processes like contract reviewing, enforcement of negotiations (smart contracts) and client intake (expert systems) allows law firms to streamline their procedures and improve efficiency. In addition, automation benefits small-to-medium law firms that do not have the resources to utilize junior talent on such routine tasks. The increase of law firms utilizing automated applications could result into legal tech becoming a necessity in the industry. Digital Reason CEO, Tim Estes, stated that those who refuse the opportunity to integrate AI in their workflow are “most at risk.” In 2018, Forbes reported a 713% increase in investments in legal tech. This rapid growth is reflective of law firms beginning to “cede business to… new model legal providers… that meld technological, business and legal expertise.” == Access to law and justice == It has been widely estimated for at least the last generation that all the programs and resources devoted to ensuring access to justice address only 20% of the civil legal needs of low-income people in the United States. Drawing on this experience, in late 2011, the U.S. government-funded Legal Services Corporation decided to convene a summit of leaders to explore how best to use technology in the access-to-justice community. The group adopted a mission for The Summit on the Use of Technology to Expand Access to Justice (Summit) consistent with the magnitude of the challenge: "to explore the potential of technology to move the United States toward providing some form of effective assistance to 100% of persons otherwise unable to afford an attorney for dealing with essential civil legal needs". In April 2017, joined by Microsoft and Pro Bono Net, the Legal Services Corporation (LSC) announced a pilot program to develop online, statewide legal portals to direct individuals with civil legal needs to the most appropriate forms of assistance. == Technological limitations == Current research in subjects such as computational privacy, explainable machine learning, Bayesian deep learning, knowledge-intensive machine learning, and transfer learning reveals that we do not yet have the technology to enable Level 4 to 6 AI lawbots. In 2023, OpenLaw began developing a model called Law Bot, which interacts in a conversational way as an attorney. The dialogue format makes it possible for Law Bot to answer follow-up questions, challenge incorrect premises, and reject inappropriate requests. Currently, they try to ensure it is in full compliance with all laws and regulations while conducting further beta testing before releasing it to the general public.

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  • Kruskal count

    Kruskal count

    The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift coupling) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coupling effects and rediscovered as a card trick by the American mathematician Martin David Kruskal in the early 1970s as a side-product while working on another problem. It was published by Kruskal's friend Martin Gardner and magician Karl Fulves in 1975. This is related to a similar trick published by magician Alexander F. Kraus in 1957 as Sum total and later called Kraus principle. Besides uses as a card trick, the underlying phenomenon has applications in cryptography, code breaking, software tamper protection, code self-synchronization, control-flow resynchronization, design of variable-length codes and variable-length instruction sets, web navigation, object alignment, and others. == Card trick == The trick is performed with cards, but is more a magical-looking effect than a conventional magic trick. The magician has no access to the cards, which are manipulated by members of the audience. Thus sleight of hand is not possible. Rather the effect is based on the mathematical fact that the output of a Markov chain, under certain conditions, is typically independent of the input. A simplified version using the hands of a clock performed by David Copperfield is as follows. A volunteer picks a number from one to twelve and does not reveal it to the magician. The volunteer is instructed to start from 12 on the clock and move clockwise by a number of spaces equal to the number of letters that the chosen number has when spelled out. This is then repeated, moving by the number of letters in the new number. The output after three or more moves does not depend on the initially chosen number and therefore the magician can predict it.

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  • Myrinet

    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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  • Link encryption

    Link encryption

    Link encryption is an approach to communications security that encrypts and decrypts all network traffic at each network routing point (e.g. network switch, or node through which it passes) until arrival at its final destination. This repeated decryption and encryption is necessary to allow the routing information contained in each transmission to be read and employed further to direct the transmission toward its destination, before which it is re-encrypted. This contrasts with end-to-end encryption where internal information, but not the header/routing information, is encrypted by the sender at the point of origin and only decrypted by the intended recipient. Link encryption offers two main advantages: encryption is automatic so there is less opportunity for human error. if the communications link operates continuously and carries an unvarying level of traffic, link encryption defeats traffic analysis. On the other hand, end-to-end encryption ensures only the intended recipient has access to the plaintext. Link encryption can be used with end-to-end systems by superencrypting the messages. Bulk encryption refers to encrypting a large number of circuits at once, after they have been multiplexed.

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  • Micro stuttering

    Micro stuttering

    Micro stuttering is a visual artifact in real-time computer graphics in which the time intervals between consecutively displayed frames are uneven, even though the average frame rate reported by benchmarking software appears adequate. Tools such as 3DMark typically compute frame rates over intervals of one second or more, which can conceal momentary drops in the instantaneous frame rate that the viewer perceives as hitching or jerking of on-screen motion. At low frame rates the effect is visible as a stutter in moving images, degrading the experience in interactive applications such as video games. In severe cases a lower but more consistent frame rate can appear smoother than a higher but more erratic one. The term gained prominence in the late 2000s in discussions of multi-GPU rendering (see History), but micro stuttering also affects single-GPU systems. Common causes on modern hardware include real-time shader compilation, asset streaming from storage, VRAM exhaustion, and driver bugs. == Causes == === Shader compilation === A common cause of micro stuttering on modern PCs is real-time shader compilation. Shaders are small programs that instruct the GPU on how to render visual effects such as lighting, shadows, and reflections. On consoles, developers can pre-compile all shaders for the known, fixed hardware. On PCs, the variety of GPU architectures means shaders must often be compiled at run time, either when the game launches or during gameplay itself. When the rendering engine encounters a shader that has not yet been compiled, the CPU must finish the compilation before the GPU can draw the affected object. This causes a spike in frame time that the player perceives as a hitch. The problem has been particularly associated with games built on Unreal Engine 4 running under DirectX 12, because DX12 shifts more shader management responsibility to the application. Several techniques exist to reduce shader compilation stutter. Pipeline State Object (PSO) pre-caching records the shader permutations used at runtime so that they can be compiled in advance on subsequent launches. Asynchronous shader compilation moves the work to background CPU threads to avoid blocking the main rendering thread. Platform-level services such as Steam's shader pre-caching distribute previously compiled shaders to users with matching GPU hardware. The Steam Deck, which contains a single fixed GPU, benefits from pre-compiled shader caches because all units share the same hardware configuration. === Other causes === Micro stuttering on single-GPU systems can have several additional causes. CPU bottlenecks or scheduling interruptions from background tasks can prevent the processor from preparing frames at regular intervals. Asset streaming during gameplay (loading textures, geometry, or audio from storage) can produce hitches sometimes called traversal stutter; the use of solid-state drives and technologies such as DirectStorage has reduced but not eliminated this. VRAM exhaustion forces data to be swapped between video memory and system memory over the PCI Express bus, which is slower. Graphics driver bugs can also introduce stutter; Nvidia released hotfix driver 551.46 in February 2024 to correct intermittent micro stuttering when V-Sync was enabled. == Measurement == Micro stuttering drew attention to the limitations of average frame rate as a performance metric. In 2013, Scott Wasson at The Tech Report published a series of articles advocating frame time analysis, in which the delivery time of every individual frame is recorded and plotted rather than collapsed into a single frames-per-second figure. This approach was adopted by other hardware review publications in the following years. GPU reviews now routinely report 1% low and 0.1% low frame rates alongside the average. The 1% low is the average frame rate of the slowest 1% of frames in a sample; it serves as an indicator of worst-case smoothness. A large gap between the average and the 1% low suggests poor frame pacing. Tools for capturing per-frame timing data include FRAPS, PresentMon, OCAT, CapFrameX, and MSI Afterburner with RivaTuner Statistics Server. == Mitigation == === Frame pacing === Frame pacing is a software technique that regulates the timing of frame delivery to produce even intervals between displayed frames. Game engines, GPU drivers, and platform libraries all implement frame pacing strategies to varying degrees. On mobile platforms, Google provides the Android Frame Pacing library (Swappy) as part of the Android Game Development Kit. In December 2025, the Khronos Group published the VK_EXT_present_timing Vulkan extension, giving developers explicit control over presentation timing in a cross-platform graphics API for the first time. === Variable refresh rate === Variable refresh rate (VRR) display technologies allow a monitor's refresh rate to change to match the GPU's frame output. Implementations include Nvidia G-Sync (2013), AMD FreeSync (2015), and the VESA Adaptive-Sync standard built into DisplayPort 1.2a and later. VRR eliminates the screen tearing that results from a mismatch between frame rate and refresh rate, and avoids the frame-holding behaviour of V-Sync that can itself cause stutter. It is effective at smoothing moderate frame rate fluctuations but cannot compensate for large sudden spikes in frame time such as those caused by shader compilation or heavy asset streaming. VRR support has become standard in gaming monitors, televisions (via HDMI 2.1), and the Xbox Series X/S and PlayStation 5 consoles. === Frame generation === Beginning with DLSS 3 on the GeForce RTX 40 series in 2022, Nvidia introduced AI-based frame generation, which uses dedicated optical flow hardware and a neural network to create new frames between traditionally rendered ones. AMD followed with FSR 3 in 2023, using an algorithmic approach, and the AI-based FSR 4 for the Radeon RX 9000 series in 2025. DLSS 4, released in January 2025 for the GeForce RTX 50 series, can generate up to three frames per rendered frame using a technique called Multi Frame Generation. Frame generation increases the displayed frame rate but introduces its own frame pacing concerns. If the underlying rendered frames are unevenly timed, the interpolated frames can make the unevenness more apparent rather than less. DLSS 4 addresses this with hardware-level flip metering on the GPU's display engine, which controls the timing of frame presentation more precisely than the CPU-based pacing used in DLSS 3. Both vendors pair frame generation with latency-reduction features (Nvidia Reflex and AMD Anti-Lag+) to offset the additional input latency that results from inserting synthetic frames into the pipeline. === Frame rate limiters === Capping the frame rate below the display's maximum refresh rate, using tools such as RivaTuner Statistics Server, in-game limiters, or driver-level settings, is a common way to improve frame pacing. Preventing the GPU from running ahead of the display reduces variability in frame delivery times and can produce a smoother result than an uncapped but more irregular frame rate. == History == === Multi-GPU configurations === Micro stuttering was first widely documented in the late 2000s as a side effect of multi-GPU configurations using Alternate Frame Rendering (AFR), in which consecutive frames are assigned to alternating GPUs. Because each GPU may take a different amount of time to complete its assigned frame — due to varying scene complexity, driver scheduling, or inter-GPU communication overhead — the resulting frame delivery is irregular even when the average frame rate is high. Both Nvidia SLI and AMD CrossFireX were affected, with dual-GPU setups exhibiting the worst frame pacing irregularities. In 2012 benchmarks using Battlefield 3, dual Radeon HD 7970 cards in CrossFire showed 85% variation in frame delivery times compared with 7% for a single card, while dual GeForce GTX 680 cards in SLI showed only 7% variation compared with 5% for a single card. Multi-GPU micro stuttering became a significant factor in the eventual decline and discontinuation of consumer multi-GPU gaming. Nvidia restricted SLI to a handful of enthusiast-class cards from the GeForce 10 series onward, then replaced it with NVLink on the GeForce RTX 20 series, which saw limited gaming adoption. AMD ceased active CrossFire development around 2017. By the mid-2020s, neither vendor's current consumer GPUs support multi-GPU rendering for games. Other factors that contributed to the decline include DirectX 12 placing multi-GPU support in the hands of game developers rather than driver authors, the incompatibility of temporal anti-aliasing and other temporal rendering techniques with AFR, and the increasing size, power draw, and cost of individual GPUs. The third-party utility RadeonPro could reduce CrossFire micro stuttering through dynamic V-Sync and frame pacing adjustments, and AMD later introduced a driver-level frame paci

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  • Upworthy

    Upworthy

    Upworthy is a media brand that focuses on positive storytelling. It was started in March 2012 by Eli Pariser, the former executive director of MoveOn, and Peter Koechley, the former managing editor of The Onion. One of Facebook's co-founders, Chris Hughes, was an early investor. At its peak between 2012 and 2014, it reached up to 100 million people a month. In 2017, the company was acquired by Good Worldwide. == History == Upworthy was launched in 2012 with a focus on aggregating positive content, which aligned with Facebook's algorithm. Originally, Upworthy curators searched the internet for existing content to feature on the site. Once selected as an option, curators brainstormed different headlines and shareable images for the content, and tested it with a small sample of Upworthy's visitors before sharing it on the site. The site popularized a clickbait style of two-phrase headlines. The company simplifies issues that are controversial by nature, which are presented from a politically liberal point of view and are heavily fact-checked for accuracy. In June 2013, an article in Fast Company called Upworthy "the fastest growing media site of all time". It had 8.7 million unique monthly visitors in the first six months, and in November 2013, had a high of 87 million unique visitors in a single month. In 2013, Facebook changed its algorithm, leading to a significant decline in readers from that platform. Upworthy fired one round of writers in 2015, and another in 2016, after an unionization effort by some of the staff. The union involved, the Writers Guild of America, East, has organized several online "viral" news publishers. In January 2017, Upworthy was acquired by media company GOOD Worldwide. The newsrooms of the two organizations would merge as part of the acquisition. About 20 staffers were laid off as part of the merger. In March 2020, Upworthy saw a 65% increase in Instagram followers and a 47% increased interest in positive content on-site page views as a result of increased interest in positive content during the COVID-19 pandemic. In January 2023, National Geographic Books bought Good People: Stories From the Best of Humanity from Upworthy, with a publication date of September 3, 2024. The book is described as "a heartwarming collection of first-person tales that will provide comfort and inspiration to anyone who could use a little dose of joy right now". It was created by two senior Upworthy team members, Gabriel Reilich and Lucia Knell, and features 101 stories from Upworthy's audience. The co-creators encouraged Upworthy followers to connect with the brand through questions on their posts, opening the door for organic and personal stories to be shared in the comment sections. The book debuted on The New York Times nonfiction bestseller list on September 22, 2024, and remained on the list for two weeks. The book is seen in the top 10 on Publishers Weekly Fall 2024 Adult Preview: Lifestyle and on The Washington Post's "5 feel-good books".

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  • Cryptographic multilinear map

    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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