AI Grammar Summarizer

AI Grammar Summarizer — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Noom

  Noom is an American privately held digital health company that provides weight management and behavioral health services through a subscription-based mobile application. Founded in 2008, the company combines behavior change psychology with access to weight loss medications and dietary supplements. The platform incorporates elements of cognitive behavioral therapy (CBT) and goal-setting strategies, and its programs are designed to support users in developing healthier habits. In addition to its weight management services, Noom has expanded to offer products related to stress management and general wellness. Noom has received both praise and criticism. Supporters cite its focus on mental and behavioral aspects of health, while critics have raised concerns about the accuracy of its calorie goals, the use of algorithmically determined weight loss targets, and questions about the qualifications of some of its coaching staff. == History == Noom was founded in 2008 by friends Artem Petakov and Saeju Jeong. The company's mobile app officially launched in 2016. In 2025, Noom relocated its headquarters from New York City to Princeton, New Jersey. Petakov, a former software engineer at Google, currently leads Noom Ventures, while Jeong serves as Noom's Chairman. In 2023, Geoff Cook was appointed CEO of Noom. In 2019, Noom partnered with Novo Nordisk to offer patients prescribed the diabetes medication Saxenda one year of free access to the Noom platform. In 2020, Noom reported $400 million in revenue. As of April 2021, the company stated it employed approximately 3,000 people, including 2,700 coaches. == Services == === Noom App === The Noom app is the primary platform through which users engage with the company's services. Upon creating an account, users are prompted to provide physical information such as weight, height, and age, along with experiential data including lifestyle habits, personal goals, and perceived obstacles. Users log their meals and physical activity, and in return, the app delivers feedback through multiple channels: algorithmically generated insights, guidance from a human coach, peer interaction, educational articles, and interactive quizzes. The app has been reviewed by a range of media outlets, including newspapers such as the Chicago Tribune and USA Today; health information sources such as WebMD; and lifestyle magazines including Good Housekeeping. === Other services === In 2024, Noom launched Noom Vibe, a mobile application that encourages users to develop healthy habits by awarding "vibes"—a form of points—for activities such as walking or meeting step goals. That same year, Noom introduced a 3D body scanning feature within its app, designed to help users monitor physical changes and prevent muscle atrophy during weight loss. Also in 2024, Noom began offering a compounded GLP-1 medication as part of its weight management program. The formulation includes the same active ingredient found in the anti-obesity medications Wegovy and Ozempic. == Research == In 2016, a study published in Scientific Reports analyzed data from approximately 36,000 users of the Noom app, of whom 78% were female and 22% male. The data were collected between October 2012 and April 2014. To be included in the analysis, users had to log their weight at least twice per month over a period of six consecutive months. The study found that 78% of participants self-reported weight loss while using the app. The median duration of weight reporting was 267 days (approximately nine months). The frequency of data logging was positively correlated with weight loss. Additionally, male users had a higher average starting BMI and reported greater average weight loss compared to female users. In 2017, the Centers for Disease Control and Prevention (CDC) recognized Noom as a certified diabetes prevention program, making it the first mobile health application to receive such designation. == Criticisms == === Health programs === Noom has been criticized for promoting elements of diet culture in its advertising campaigns. The app has also faced criticism for setting calorie goals that some users and experts have deemed inappropriately low, and for employing coaches who may lack formal qualifications as registered dietitians. Coaching has been described as relying heavily on canned responses. Upon sign-up, users are prompted to complete a questionnaire consisting of over 50 questions, which is used to generate a personalized program. In 2021, the UK-based organization Privacy International alleged that Noom, along with other diet platforms, used such lengthy surveys to attract users but did not always tailor the resulting programs to the collected data. The organization claimed that many users received the same or highly similar programs regardless of their answers. It also raised concerns about the handling of potentially sensitive health data, alleging a lack of transparency regarding the sharing of such data with third parties, including Facebook, potentially in violation of the European General Data Protection Regulation (GDPR). In a follow-up investigation in 2023, Privacy International reported that Noom had made "significant positive changes" to its data handling practices. However, the organization noted that data was still being shared with Facebook and concluded that "there is still room for improvement." === Billing issues lawsuit === In August 2020, the Better Business Bureau (BBB) issued a warning to consumers regarding Noom's subscription practices. The BBB reported that numerous customers had filed complaints about difficulties canceling their subscriptions after the free trial period, as well as challenges in contacting the company to request refunds. In February 2022, Noom agreed to a $62 million settlement in a class-action lawsuit that alleged the company had used deceptive billing practices related to automatic subscription renewals. Qualifying claimants received approximately $167 each. During the case, a former senior software engineer at Noom testified that the cancellation process was intentionally designed to be difficult, with the goal of generating revenue from customers who failed to cancel in time. In response, Noom stated that it had taken steps to improve transparency around its pricing and policies, including the implementation of self-service cancellation tools.

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  Pol.is

  Polis (or Pol.is) is wiki survey software designed for large group collaborations. As a civic technology, Polis allows people to share their opinions and ideas, and its algorithm is intended to elevate ideas that can facilitate better decision-making, especially when there are lots of participants. Polis has been credited for assisting the passage of legislation in Taiwan. Pol.is has been used by governments in the United States, Canada, Singapore, Philippines, Finland, Spain and elsewhere. == History == Pol.is was founded by Colin Megill, Christopher Small, and Michael Bjorkegren after the Occupy Wall Street and Arab Spring movements. In Taiwan, pol.is has been "one of the key parts" of vTaiwan's suite of open-source tools for its citizen engagement efforts arising out of the Sunflower Student Movement. vTaiwan claims that of the 26 national issues related to technology discussed on the platform, 80% led to government action. Pol.is is also utilized by "Join," a national platform for online deliberation run by the Taiwanese government. In 2022, Wired reported that Polis was an influence on the Community Notes project at Twitter. In 2023, Megill advised OpenAI on how to facilitate deliberation at scale in a way that was more efficient than Polis, which still required significant human labor and analysis at the time. He helped to award $1 million in grants to teams working on solving the problem of deliberation at scale. In 2023, Anthropic was also exploring steering model behavior using Polis. In 2025, it helped the county that includes Bowling Green, Kentucky make a 25 year plan by facilitating the collection and review of ideas from thousands of residents, representing 10% of the county. 2,370 of 3,940 unique ideas were agreed-upon by over 80% of survey respondents. Ideas were screened by volunteers if they were redundant to an existing idea, off-topic or obscene. == How it works == Pol.is participants are anonymous and cannot reply directly to others posts, in an effort to avoid personal attacks for users. Its algorithms are designed not for engagement and scrolling, but to find areas of agreement to better understand the nuances of a wide range of opinions. Participants are prompted for ideas and vote on other participants' ideas. == Reception == Andrew Leonard, The Financial Times, and VentureBeat describe Pol.is as a possible antidote to the divisiveness of traditional internet discourse by gamifying consensus. Audrey Tang agreed saying, "Polis is quite well known in that it's a kind of social media that instead of polarizing people to drive so called engagement or addiction or attention, it automatically drives bridge making narratives and statements. So only the ideas that speak to both sides or to multiple sides will gain prominence in Polis." Niall Ferguson argues that the approach to utilize tools like Pol.is and Join in Taiwan empowers ordinary people instead of the elite and protects individual freedoms, providing a contrast to the AI-enhanced panopticon model seen in China. Carl Miller praised the technology as having "gamified finding consensus." Darshana Narayanan, in an op-ed in the Economist, argues that open-source machine-learning-based tools like Polis can help to bypass the influence of special interests or experts. Jamie Susskind cited polis and vTaiwan as a model for democracies, particularly around digital policy issues.

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  Microsoft Office PerformancePoint Server

  Microsoft Office PerformancePoint Server is a business intelligence software product released in 2007 by Microsoft. The product was generally an integration of the acquisitions from ProClarity - the Planning Server and Monitoring Server - into Microsoft's SharePoint server product line. Although discontinued in 2009, the dashboard, scorecard, and analytics capabilities of PerformancePoint Server were incorporated into SharePoint 2010 and later versions. PerformancePoint Server also provided a planning and budgeting component directly integrated with Excel. == History == Microsoft offered preview releases of PerformancePoint Server starting in mid-2006. Previews of the product were formed from Business Scorecard Manager 2005 and the Planning Server component. Acquisitions ProClarity and Great Plains brought additional analytics and planning/reporting capabilities, as well as companion products ProClarity 6.3 and FRx. PerformancePoint Server was officially released in November 2007. Microsoft discontinued PerformancePoint Server as an independent product in 2009 and folded its dashboard, scorecard and analytics capabilities into PerformancePoint Services in SharePoint Server 2010. == Monitoring Server Component == Business monitoring capabilities, including dashboards, scorecards & key performance indicators, navigable reports for deeper analysis, strategy maps, and linked filtering, are provided by PerformancePoint's Monitoring Server component. A Dashboard Designer application that is distributed from Monitoring Server enables business analysts or IT Administrators to: create & test data source connections create views that use those data connections assemble the views into a dashboard deploy the dashboard as a SharePoint page Dashboard Designer saved content and security information back to the Monitoring Server. Data source connections, such as OLAP cubes or relational tables, were also made through Monitoring Server. After a dashboard has been published to the Monitoring Server database, it would be deployed as a SharePoint page and shared with other users as such. When the pages were opened in a web browser, Monitoring Server updated the data in the views by connecting back to the original data sources. == Planning Server Component == PerformancePoint's Planning Server component supported maintenance of logical business models, budget & approval workflows, enterprise data sources, and it followed Generally Accepted Accounting Principles. Planning Server made use of Excel for input and line-of-business reporting, as well as SQL Server for storing and processing business models. == Management Reporter Component == The Management Reporter component was designed to perform financial reporting and can read PerformancePoint Planning models directly. A development kit was also available to allow this component to read other models.

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  Pseudonymization

  Pseudonymization is a data management and de-identification procedure by which personally identifiable information fields within a data record are replaced by one or more artificial identifiers, or pseudonyms. A single pseudonym for each replaced field or collection of replaced fields makes the data record less identifiable while remaining suitable for data analysis and data processing. Pseudonymization (or pseudonymisation, the spelling under European guidelines) is one way to comply with the European Union's General Data Protection Regulation (GDPR) demands for secure data storage of personal information. Pseudonymized data can be restored to its original state with the addition of information which allows individuals to be re-identified. In contrast, anonymization is intended to prevent re-identification of individuals within the dataset. Clause 18, Module Four, footnote 2 of the Adoption by the European Commission of the Implementing Decisions (EU) 2021/914 "requires rendering the data anonymous in such a way that the individual is no longer identifiable by anyone ... and that this process is irreversible." == Impact of Schrems II ruling == The European Data Protection Supervisor (EDPS) on 9 December 2021 highlighted pseudonymization as the top technical supplementary measure for Schrems II compliance. Less than two weeks later, the EU Commission highlighted pseudonymization as an essential element of the equivalency decision for South Korea, which is the status that was lost by the United States under the Schrems II ruling by the Court of Justice of the European Union (CJEU). The importance of GDPR-compliant pseudonymization increased dramatically in June 2021 when the European Data Protection Board (EDPB) and the European Commission highlighted GDPR-compliant pseudonymization as the state-of-the-art technical supplementary measure for the ongoing lawful use of EU personal data when using third country (i.e., non-EU) cloud processors or remote service providers under the "Schrems II" ruling by the CJEU. Under the GDPR and final EDPB Schrems II Guidance, the term pseudonymization requires a new protected "state" of data, producing a protected outcome that: Protects direct, indirect, and quasi-identifiers, together with characteristics and behaviors; Protects at the record and data set level versus only the field level so that the protection travels wherever the data goes, including when it is in use; and Protects against unauthorized re-identification via the mosaic effect by generating high entropy (uncertainty) levels by dynamically assigning different tokens at different times for various purposes. The combination of these protections is necessary to prevent the re-identification of data subjects without the use of additional information kept separately, as required under GDPR Article 4(5) and as further underscored by paragraph 85(4) of the final EDPB Schrems II guidance: Article 4(5) "Definitions" of the GDPR defines pseudonymization as "the processing of personal data in such a manner that the personal data can no longer be attributed to a specific data subject without the use of additional information, provided that such additional information is kept separately and is subject to technical and organisational measures to ensure that the personal data are not attributed to an identified or identifiable natural person." "Use Case 2: Transfer of pseudonymised Data Paragraph 85(4)" of the final EDPB Schrems II Guidance requires that “the controller has established by means of a thorough analysis of the data in question – taking into account any information that the public authorities of the recipient country may be expected to possess and use – that the pseudonymised personal data cannot be attributed to an identified or identifiable natural person even if cross-referenced with such information." GDPR-compliant pseudonymization requires that data is "anonymous" in the strictest EU sense of the word – globally anonymous – but for the additional information held separately and made available under controlled conditions as authorized by the data controller for permitted re-identification of individual data subjects. Clause 18, Module Four, footnote 2 of the Adoption by the European Commission of the Implementing Decision (EU) 2021/914 "requires rendering the data anonymous in such a way that the individual is no longer identifiable by anyone, in line with recital 26 of Regulation (EU) 2016/679, and that this process is irreversible." Before the Schrems II ruling, pseudonymization was a technique used by security experts or government officials to hide personally identifiable information to maintain data structure and privacy of information. Some common examples of sensitive information include postal code, location of individuals, names of individuals, race and gender, etc. After the Schrems II ruling, GDPR-compliant pseudonymization must satisfy the above-noted elements as an "outcome" versus merely a technique. == Data fields == The choice of which data fields are to be pseudonymized is partly subjective. Less selective fields, such as birth date or postal code are often also included because they are usually available from other sources and therefore make a record easier to identify. Pseudonymizing these less identifying fields removes most of their analytic value and is therefore normally accompanied by the introduction of new derived and less identifying forms, such as year of birth or a larger postal code region. Data fields that are less identifying, such as date of attendance, are usually not pseudonymized. This is because too much statistical utility is lost in doing so, not because the data cannot be identified. For example, given prior knowledge of a few attendance dates it is easy to identify someone's data in a pseudonymized dataset by selecting only those people with that pattern of dates. This is an example of an inference attack. The weakness of pre-GDPR pseudonymized data to inference attacks is commonly overlooked. A famous example is the AOL search data scandal. The AOL example of unauthorized re-identification did not require access to separately kept "additional information" that was under the control of the data controller as is now required for GDPR-compliant pseudonymization, outlined below under the section "New Definition for Pseudonymization Under GDPR". Protecting statistically useful pseudonymized data from re-identification requires: a sound information security base controlling the risk that the analysts, researchers or other data workers cause a privacy breach The pseudonym allows tracking back of data to its origins, which distinguishes pseudonymization from anonymization, where all person-related data that could allow backtracking has been purged. Pseudonymization is an issue in, for example, patient-related data that has to be passed on securely between clinical centers. The application of pseudonymization to e-health intends to preserve the patient's privacy and data confidentiality. It allows primary use of medical records by authorized health care providers and privacy preserving secondary use by researchers. In the US, HIPAA provides guidelines on how health care data must be handled and data de-identification or pseudonymization is one way to simplify HIPAA compliance. However, plain pseudonymization for privacy preservation often reaches its limits when genetic data are involved (see also genetic privacy). Due to the identifying nature of genetic data, depersonalization is often not sufficient to hide the corresponding person. Potential solutions are the combination of pseudonymization with fragmentation and encryption. An example of application of pseudonymization procedure is creation of datasets for de-identification research by replacing identifying words with words from the same category (e.g. replacing a name with a random name from the names dictionary), however, in this case it is in general not possible to track data back to its origins. == New definition under GDPR == Effective as of May 25, 2018, the EU General Data Protection Regulation (GDPR) defines pseudonymization for the very first time at the EU level in Article 4(5). Under Article 4(5) definitional requirements, data is pseudonymized if it cannot be attributed to a specific data subject without the use of separately kept "additional information". Pseudonymized data embodies the state of the art in Data Protection by Design and by Default because it requires protection of both direct and indirect identifiers (not just direct). GDPR Data Protection by Design and by Default principles as embodied in pseudonymization require protection of both direct and indirect identifiers so that personal data is not cross-referenceable (or re-identifiable) via the "mosaic effect" without access to "additional information" that is kept separately by the controller. Because access to separately kept "additional information" is required

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  DeepRoute.ai

  DeepRoute.ai (Chinese: 元戎启行) is a Chinese autonomous driving company founded in 2019 and headquartered in Shenzhen, China. The company develops full-stack self-driving solutions including perception, decision-making, and control systems. == History == DeepRoute.ai was founded in February 2019 in Shenzhen, China, by Zhou Guang (周光), who serves as the company's CEO. In September 2019, the company collaborated with Dongfeng for a live-streamed autonomous driving demonstration. In October 2019, during the 7th Military World Games, DeepRoute.ai conducted Robotaxi demonstration operations. In November 2019, it obtained an intelligent connected vehicle road test permit for public roads in Shenzhen. In October 2020, DeepRoute.ai signed an "Autonomous Driving Leadership Project" with Dongfeng to build one of China's largest autonomous fleets. In August 2020, DeepRoute.ai announced its partnership with Cao Cao Mobility, a Geely-backed ride-hailing company, to test Robotaxis in Hangzhou for daily operations, planning to provide Robotaxis during the 2022 Asian Games. In September 2021, DeepRoute.ai secured US$300 million in a Series B funding round led by Alibaba. In December 2021, the company unveiled its DeepRoute-Driver 2.0, an L4-level autonomous driving solution comprising five solid-state lidar sensors, eight cameras, a proprietary computing system and an optional millimeter-wave radar. with a production cost of under US$10,000. In June 2022, it partnered with Deppon Express to provide autonomous light truck freight transfer services. In March 2023, the company launched its high-precision map-free intelligent driving solution, DeepRoute-Driver 3.0. In November 2024, Great Wall Motor announced a $100 million Series C funding round for Deeproute. With this, Deeproute has completed five rounds of financing, raising a cumulative total of over $500 million. Its shareholders include Fosun RZ Capital, Yunqi Partners, Alibaba, Vision Plus Capital, and Dongfeng, among others. In the same month, Deeproute.ai emphasised that they were in "deep cooperation" with Nvidia and spoke on being part of the first batch of companies in China to get a hold of Nvidia's newer Thor chip for cars which will be used in a new system released next year. This new system will help manage more complex driving scenarios through visual cues. == Products == === VLA Model === VLA Model is a Vision–language–action model designed for autonomous driving systems. It integrates visual perception, semantic understanding, and action decision-making into a unified framework, aiming to enhance the safety and adaptability of advanced driver-assistance systems (ADAS) in complex road environments. The model was officially launched on August 26, 2025, as the core of DeepRoute.ai's DeepRoute IO 2.0 platform. The VLA model is characterized by its "visual-language-action" architecture, which incorporates a chain-of-thought (CoT) reasoning capability inspired by large language models. This design is intended to address the "black box" limitations of traditional end-to-end autonomous driving systems by enabling the model to analyze information, infer causality, and make decisions in a more transparent and interpretable manner. === Appliance === The company has partnered with several automakers including Dongfeng Motor Corporation and Geely to develop and test autonomous vehicles.

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  Certifying algorithm

  In theoretical computer science, a certifying algorithm is an algorithm that outputs, together with a solution to the problem it solves, a proof that the solution is correct. A certifying algorithm is said to be efficient if the combined runtime of the algorithm and a proof checker is slower by at most a constant factor than the best known non-certifying algorithm for the same problem. The proof produced by a certifying algorithm should be in some sense simpler than the algorithm itself, for otherwise any algorithm could be considered certifying (with its output verified by running the same algorithm again). Sometimes this is formalized by requiring that a verification of the proof take less time than the original algorithm, while for other problems (in particular those for which the solution can be found in linear time) simplicity of the output proof is considered in a less formal sense. For instance, the validity of the output proof may be more apparent to human users than the correctness of the algorithm, or a checker for the proof may be more amenable to formal verification. Implementations of certifying algorithms that also include a checker for the proof generated by the algorithm may be considered to be more reliable than non-certifying algorithms. For, whenever the algorithm is run, one of three things happens: it produces a correct output (the desired case), it detects a bug in the algorithm or its implication (undesired, but generally preferable to continuing without detecting the bug), or both the algorithm and the checker are faulty in a way that masks the bug and prevents it from being detected (undesired, but unlikely as it depends on the existence of two independent bugs). == Examples == Many examples of problems with checkable algorithms come from graph theory. For instance, a classical algorithm for testing whether a graph is bipartite would simply output a Boolean value: true if the graph is bipartite, false otherwise. In contrast, a certifying algorithm might output a 2-coloring of the graph in the case that it is bipartite, or a cycle of odd length if it is not. Any graph is bipartite if and only if it can be 2-colored, and non-bipartite if and only if it contains an odd cycle. Both checking whether a 2-coloring is valid and checking whether a given odd-length sequence of vertices is a cycle may be performed more simply than testing bipartiteness. Analogously, it is possible to test whether a given directed graph is acyclic by a certifying algorithm that outputs either a topological order or a directed cycle. It is possible to test whether an undirected graph is a chordal graph by a certifying algorithm that outputs either an elimination ordering (an ordering of all vertices such that, for every vertex, the neighbors that are later in the ordering form a clique) or a chordless cycle. And it is possible to test whether a graph is planar by a certifying algorithm that outputs either a planar embedding or a Kuratowski subgraph. The extended Euclidean algorithm for the greatest common divisor of two integers x and y is certifying: it outputs three integers g (the divisor), a, and b, such that ax + by = g. This equation can only be true of multiples of the greatest common divisor, so testing that g is the greatest common divisor may be performed by checking that g divides both x and y and that this equation is correct.

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  XOR swap algorithm

  In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required. The algorithm is primarily a novelty and a way of demonstrating properties of the exclusive or operation. It is sometimes discussed as a program optimization, but there are almost no cases where swapping via exclusive or provides benefit over the standard, obvious technique. == The algorithm == Conventional swapping requires the use of a temporary storage variable. Using the XOR swap algorithm, however, no temporary storage is needed. The algorithm is as follows: Since XOR is a commutative operation, either X XOR Y or Y XOR X can be used interchangeably in any of the foregoing three lines. Note that on some architectures the first operand of the XOR instruction specifies the target location at which the result of the operation is stored, preventing this interchangeability. The algorithm typically corresponds to three machine-code instructions, represented by corresponding pseudocode and assembly instructions in the three rows of the following table: In the above System/370 assembly code sample, R1 and R2 are distinct registers, and each XR operation leaves its result in the register named in the first argument. Using x86 assembly, values X and Y are in registers eax and ebx (respectively), and xor places the result of the operation in the first register (Note: x86 supports XCHG instruction so using triple XOR do not make sense on this architecture). In RISC-V assembly, value X and Y are in registers x10 and x11, and xor places the result of the operation in the first operand. However, in the pseudocode or high-level language version or implementation, the algorithm fails if x and y use the same storage location, since the value stored in that location will be zeroed out by the first XOR instruction, and then remain zero; it will not be "swapped with itself". This is not the same as if x and y have the same values. The trouble only comes when x and y use the same storage location, in which case their values must already be equal. That is, if x and y use the same storage location, then the line: sets x to zero (because x = y so X XOR Y is zero) and sets y to zero (since it uses the same storage location), causing x and y to lose their original values. == Proof of correctness == The binary operation XOR over bit strings of length N {\displaystyle N} exhibits the following properties (where ⊕ {\displaystyle \oplus } denotes XOR): L1. Commutativity: A ⊕ B = B ⊕ A {\displaystyle A\oplus B=B\oplus A} L2. Associativity: ( A ⊕ B ) ⊕ C = A ⊕ ( B ⊕ C ) {\displaystyle (A\oplus B)\oplus C=A\oplus (B\oplus C)} L3. Identity exists: there is a bit string, 0, (of length N) such that A ⊕ 0 = A {\displaystyle A\oplus 0=A} for any A {\displaystyle A} L4. Each element is its own inverse: for each A {\displaystyle A} , A ⊕ A = 0 {\displaystyle A\oplus A=0} . Suppose that we have two distinct registers R1 and R2 as in the table below, with initial values A and B respectively. We perform the operations below in sequence, and reduce our results using the properties listed above. === Linear algebra interpretation === As XOR can be interpreted as binary addition and a pair of bits can be interpreted as a vector in a two-dimensional vector space over the field with two elements, the steps in the algorithm can be interpreted as multiplication by 2×2 matrices over the field with two elements. For simplicity, assume initially that x and y are each single bits, not bit vectors. For example, the step: which also has the implicit: corresponds to the matrix ( 1 1 0 1 ) {\displaystyle \left({\begin{smallmatrix}1&1\\0&1\end{smallmatrix}}\right)} as ( 1 1 0 1 ) ( x y ) = ( x + y y ) . {\displaystyle {\begin{pmatrix}1&1\\0&1\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}={\begin{pmatrix}x+y\\y\end{pmatrix}}.} The sequence of operations is then expressed as: ( 1 1 0 1 ) ( 1 0 1 1 ) ( 1 1 0 1 ) = ( 0 1 1 0 ) {\displaystyle {\begin{pmatrix}1&1\\0&1\end{pmatrix}}{\begin{pmatrix}1&0\\1&1\end{pmatrix}}{\begin{pmatrix}1&1\\0&1\end{pmatrix}}={\begin{pmatrix}0&1\\1&0\end{pmatrix}}} (working with binary values, so 1 + 1 = 0 {\displaystyle 1+1=0} ), which expresses the elementary matrix of switching two rows (or columns) in terms of the transvections (shears) of adding one element to the other. To generalize to where X and Y are not single bits, but instead bit vectors of length n, these 2×2 matrices are replaced by 2n×2n block matrices such as ( I n I n 0 I n ) . {\displaystyle \left({\begin{smallmatrix}I_{n}&I_{n}\\0&I_{n}\end{smallmatrix}}\right).} These matrices are operating on values, not on variables (with storage locations), hence this interpretation abstracts away from issues of storage location and the problem of both variables sharing the same storage location. == Code example == A C function that implements the XOR swap algorithm: The code first checks if the addresses are distinct and uses a guard clause to exit the function early if they are equal. Without that check, if they were equal, the algorithm would fold to a triple x ^= x resulting in zero. == Reasons for avoidance in practice == On modern CPU architectures, the XOR technique can be slower than using a temporary variable to do swapping. At least on recent x86 CPUs, both by AMD and Intel, moving between registers regularly incurs zero latency. (This is called MOV-elimination.) Even if there is not any architectural register available to use, the XCHG instruction will be at least as fast as the three XORs taken together. Another reason is that modern CPUs strive to execute instructions in parallel via instruction pipelines. In the XOR technique, the inputs to each operation depend on the results of the previous operation, so they must be executed in strictly sequential order, negating any benefits of instruction-level parallelism. === Aliasing === The XOR swap is also complicated in practice by aliasing. If an attempt is made to XOR-swap the contents of some location with itself, the result is that the location is zeroed out and its value lost. Therefore, XOR swapping must not be used blindly in a high-level language if aliasing is possible. This issue does not apply if the technique is used in assembly to swap the contents of two registers. Similar problems occur with call by name, as in Jensen's Device, where swapping i and A[i] via a temporary variable yields incorrect results due to the arguments being related: swapping via temp = i; i = A[i]; A[i] = temp changes the value for i in the second statement, which then results in the incorrect i value for A[i] in the third statement. == Variations == The underlying principle of the XOR swap algorithm can be applied to any operation meeting criteria L1 through L4 above. Replacing XOR by addition and subtraction gives various slightly different, but largely equivalent, formulations. For example: Unlike the XOR swap, this variation requires that the underlying processor or programming language uses a method such as modular arithmetic or bignums to guarantee that the computation of X + Y cannot cause an error due to integer overflow. Therefore, it is seen even more rarely in practice than the XOR swap. However, the implementation of AddSwap above in the C programming language always works even in case of integer overflow, since, according to the C standard, addition and subtraction of unsigned integers follow the rules of modular arithmetic, i. e. are done in the cyclic group Z / 2 s Z {\displaystyle \mathbb {Z} /2^{s}\mathbb {Z} } where s {\displaystyle s} is the number of bits of unsigned int. Indeed, the correctness of the algorithm follows from the fact that the formulas ( x + y ) − y = x {\displaystyle (x+y)-y=x} and ( x + y ) − ( ( x + y ) − y ) = y {\displaystyle (x+y)-((x+y)-y)=y} hold in any abelian group. This generalizes the proof for the XOR swap algorithm: XOR is both the addition and subtraction in the abelian group ( Z / 2 Z ) s {\displaystyle (\mathbb {Z} /2\mathbb {Z} )^{s}} (which is the direct sum of s copies of Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ). This doesn't hold when dealing with the signed int type (the default for int). Signed integer overflow is an undefined behavior in C and thus modular arithmetic is not guaranteed by the standard, which may lead to incorrect results. The sequence of operations in AddSwap can be expressed via matrix multiplication as: ( 1 − 1 0 1 ) ( 1 0 1 − 1 ) ( 1 1 0 1 ) = ( 0 1 1 0 ) {\displaystyle {\begin{pmatrix}1&-1\\0&1\end{pmatrix}}{\begin{pmatrix}1&0\\1&-1\end{pmatrix}}{\begin{pmatrix}1&1\\0&1\end{pmatrix}}={\begin{pmatrix}0&1\\1&0\end{pmatrix}}} == Application to register allocation == On architectures lacking a dedicated swap instruction, because it avoids the extra temporary register, the XOR swap algorithm is required for optimal register allocatio

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  Birkhoff algorithm

  Birkhoff's algorithm (also called Birkhoff-von-Neumann algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation matrices. It was published by Garrett Birkhoff in 1946. It has many applications. One such application is for the problem of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose it into a lottery on deterministic allocations. == Terminology == A bistochastic matrix (also called: doubly-stochastic) is a matrix in which all elements are greater than or equal to 0 and the sum of the elements in each row and column equals 1. An example is the following 3-by-3 matrix: ( 0.2 0.3 0.5 0.6 0.2 0.2 0.2 0.5 0.3 ) {\displaystyle {\begin{pmatrix}0.2&0.3&0.5\\0.6&0.2&0.2\\0.2&0.5&0.3\end{pmatrix}}} A permutation matrix is a special case of a bistochastic matrix, in which each element is either 0 or 1 (so there is exactly one "1" in each row and each column). An example is the following 3-by-3 matrix: ( 0 1 0 0 0 1 1 0 0 ) {\displaystyle {\begin{pmatrix}0&1&0\\0&0&1\\1&0&0\end{pmatrix}}} A Birkhoff decomposition (also called: Birkhoff-von-Neumann decomposition) of a bistochastic matrix is a presentation of it as a sum of permutation matrices with non-negative weights. For example, the above matrix can be presented as the following sum: 0.2 ( 0 1 0 0 0 1 1 0 0 ) + 0.2 ( 1 0 0 0 1 0 0 0 1 ) + 0.1 ( 0 1 0 1 0 0 0 0 1 ) + 0.5 ( 0 0 1 1 0 0 0 1 0 ) {\displaystyle 0.2{\begin{pmatrix}0&1&0\\0&0&1\\1&0&0\end{pmatrix}}+0.2{\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}}+0.1{\begin{pmatrix}0&1&0\\1&0&0\\0&0&1\end{pmatrix}}+0.5{\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}}} Birkhoff's algorithm receives as input a bistochastic matrix and returns as output a Birkhoff decomposition. == Tools == A permutation set of an n-by-n matrix X is a set of n entries of X containing exactly one entry from each row and from each column. A theorem by Dénes Kőnig says that: Every bistochastic matrix has a permutation-set in which all entries are positive.The positivity graph of an n-by-n matrix X is a bipartite graph with 2n vertices, in which the vertices on one side are n rows and the vertices on the other side are the n columns, and there is an edge between a row and a column if the entry at that row and column is positive. A permutation set with positive entries is equivalent to a perfect matching in the positivity graph. A perfect matching in a bipartite graph can be found in polynomial time, e.g. using any algorithm for maximum cardinality matching. Kőnig's theorem is equivalent to the following:The positivity graph of any bistochastic matrix admits a perfect matching.A matrix is called scaled-bistochastic if all elements are non-negative, and the sum of each row and column equals c, where c is some positive constant. In other words, it is c times a bistochastic matrix. Since the positivity graph is not affected by scaling:The positivity graph of any scaled-bistochastic matrix admits a perfect matching. == Algorithm == Birkhoff's algorithm is a greedy algorithm: it greedily finds perfect matchings and removes them from the fractional matching. It works as follows. Let i = 1. Construct the positivity graph GX of X. Find a perfect matching in GX, corresponding to a positive permutation set in X. Let z[i] > 0 be the smallest entry in the permutation set. Let P[i] be a permutation matrix with 1 in the positive permutation set. Let X := X − z[i] P[i]. If X contains nonzero elements, Let i = i + 1 and go back to step 2. Otherwise, return the sum: z[1] P[1] + ... + z[2] P[2] + ... + z[i] P[i]. The algorithm is correct because, after step 6, the sum in each row and each column drops by z[i]. Therefore, the matrix X remains scaled-bistochastic. Therefore, in step 3, a perfect matching always exists. == Run-time complexity == By the selection of z[i] in step 4, in each iteration at least one element of X becomes 0. Therefore, the algorithm must end after at most n2 steps. However, the last step must simultaneously make n elements 0, so the algorithm ends after at most n2 − n + 1 steps, which implies O ( n 2 ) {\displaystyle O(n^{2})} . In 1960, Joshnson, Dulmage and Mendelsohn showed that Birkhoff's algorithm actually ends after at most n2 − 2n + 2 steps, which is tight in general (that is, in some cases n2 − 2n + 2 permutation matrices may be required). == Application in fair division == In the fair random assignment problem, there are n objects and n people with different preferences over the objects. It is required to give an object to each person. To attain fairness, the allocation is randomized: for each (person, object) pair, a probability is calculated, such that the sum of probabilities for each person and for each object is 1. The probabilistic-serial procedure can compute the probabilities such that each agent, looking at the matrix of probabilities, prefers his row of probabilities over the rows of all other people (this property is called envy-freeness). This raises the question of how to implement this randomized allocation in practice? One cannot just randomize for each object separately, since this may result in allocations in which some people get many objects while other people get no objects. Here, Birkhoff's algorithm is useful. The matrix of probabilities, calculated by the probabilistic-serial algorithm, is bistochastic. Birkhoff's algorithm can decompose it into a convex combination of permutation matrices. Each permutation matrix represents a deterministic assignment, in which every agent receives exactly one object. The coefficient of each such matrix is interpreted as a probability; based on the calculated probabilities, it is possible to pick one assignment at random and implement it. == Extensions == The problem of computing the Birkhoff decomposition with the minimum number of terms has been shown to be NP-hard, but some heuristics for computing it are known. This theorem can be extended for the general stochastic matrix with deterministic transition matrices. Budish, Che, Kojima and Milgrom generalize Birkhoff's algorithm to non-square matrices, with some constraints on the feasible assignments. They also present a decomposition algorithm that minimizes the variance in the expected values. Vazirani generalizes Birkhoff's algorithm to non-bipartite graphs. Valls et al. showed that it is possible to obtain an ϵ {\displaystyle \epsilon } -approximate decomposition with O ( log ⁡ ( 1 / ϵ 2 ) ) {\displaystyle O(\log(1/\epsilon ^{2}))} permutations.

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  Macromedia FreeHand

  Macromedia FreeHand (formerly Aldus FreeHand) is a discontinued computer application for creating two-dimensional vector graphics oriented primarily to professional illustration, desktop publishing and content creation for the Web. FreeHand was similar in scope, intended market, and functionality to Adobe Illustrator, CorelDRAW and Xara Designer Pro. Because of FreeHand's dedicated page layout and text control features, it also compares to Adobe InDesign and QuarkXPress. Professions using FreeHand include graphic design, illustration, cartography, fashion and textile design, product design, architects, scientific research, and multimedia production. FreeHand was created by Altsys Corporation in 1988 and licensed to Aldus Corporation, which released versions 1 through 4. In 1994, Aldus merged with Adobe Systems and because of the overlapping market with Adobe Illustrator, FreeHand was returned to Altsys by order of the Federal Trade Commission. Altsys was later bought by Macromedia, which released FreeHand versions 5 through 11 (FreeHand MX). In 2005, Adobe Systems acquired Macromedia and its product line which included FreeHand MX, under whose ownership it presently resides. Since 2003, FreeHand development has been discontinued; in the Adobe Systems catalog, FreeHand has been replaced by Adobe Illustrator. FreeHand MX continues to run under Windows 11 and under Mac OS X 10.6 (Snow Leopard) within Rosetta, a PowerPC code emulator, and requires a registration patch supplied by Adobe. FreeHand 10 runs without problems on Mac OS X Snow Leopard with Rosetta enabled, and does not require a registration patch. Later versions of macOS can use a Mac OS X Snow Leopard Server virtual machine to emulate the required PowerPC support. == History == === Altsys and Aldus FreeHand === In 1984, James R. Von Ehr founded Altsys Corporation to develop graphics applications for personal computers. Based in Plano, Texas, the company initially produced font editing and conversion software; Fontastic Plus, Metamorphosis, and the Art Importer. Their premier PostScript font-design package, Fontographer, was released in 1986 and was the first such program on the market. With the PostScript background having been established by Fontographer, Altsys also developed FreeHand (originally called Masterpiece) as a Macintosh Postscript-based illustration program that used Bézier curves for drawing and was similar to Adobe Illustrator. FreeHand was announced as "... a Macintosh graphics program described as having all the features of Adobe's Illustrator plus drawing tools such as those in Mac Paint and Mac Draft and special effects similar to those in Cricket Draw." Seattle's Aldus Corporation acquired a licensing agreement with Altsys Corporation to release FreeHand along with their flagship product, Pagemaker, and Aldus FreeHand 1.0 was released in 1988. FreeHand's product name used intercaps; the F and H were capitalized. The partnership between the two companies continued with Altsys developing FreeHand and with Aldus controlling marketing and sales. After 1988, a competitive exchange between Aldus FreeHand and Adobe Illustrator ensued on the Macintosh platform with each software advancing new tools, achieving better speed, and matching significant features. Windows PC development also allowed Illustrator 2 (aka, Illustrator 88 on the Mac) and FreeHand 3 to release Windows versions to the graphics market. FreeHand 1.0 sold for $495 in 1988. It included the standard drawing tools and features as other draw programs including special effects in fills and screens, text manipulation tools, and full support for CMYK color printing. It was also possible to create and insert PostScript routines anywhere within the program. FreeHand performed in preview mode instead of keyline mode but performance was slower. FreeHand 2.0 sold for $495 in 1989. Besides improving on the features of FreeHand 1.0, FreeHand 2 added faster operation, Pantone colors, stroked text, flexible fill patterns and automatically import graphic assets from other programs. It added accurate control over a color monitor screen display, limited only by its resolution. FreeHand 3.0 sold for $595 in 1991. New features included resizable color, style, and layer panels including an Attributes menu. Also tighter precision of both the existing tools and aligning of objects. FH3 created compound Paths. Text could be converted to paths, applied to an ellipse, or made vertical. Carried over from version 1.0, FreeHand 3 suffered by having text entered into a dialog box instead of directly to the page. In October 1991, a 3.1 upgrade made FreeHand work with System 7 but additionally, it supported pressure-sensitive drawing which offered varying line widths with a users stroke. It improved element manipulation and added more import/export options. FreeHand 4.0 sold for $595 in 1994. Altsys ported FreeHand 3.0 to the NeXT system creating a new program named Virtuoso. Virtuoso continued its development at Altsys and version 2.0 of Virtuoso was feature-equivalent to FreeHand 4 (with the addition of NeXT-specific features such as Services and Display PostScript) and file compatible, with Virtuoso 2 able to open FreeHand 4 files and vice versa. A prominent feature of this version was the ability to type directly into the page and wrap inside or outside any shape. It also included drag-and-drop color imaging, a larger pasteboard, and a user interface that featured floating, rollup panels. The colors palette included a color mixer for adding new colors to the swatch list. Speed increases were made. In the same year of FreeHand 4 release, Adobe Systems announced merger plans with Aldus Corporation for $525 million. Fear about the end of competition between these two leading applications was reported in the media and expressed by customers (Illustrator versus FreeHand and Adobe Photoshop versus Aldus PhotoStyler.) Because of this overlapping of the market, Altsys stepped in by suing Aldus, saying that the merger deal was "a prima facie violation of a non-compete clause within the FreeHand licensing agreement." Altsys CEO Jim Von Ehr explained, "No one loves FreeHand more than we do. We will do whatever it takes to see it survive." The Federal Trade Commission issued a complaint against Adobe Systems on October 18, 1994, ordering a divestiture of FreeHand to "remedy the lessening of competition resulting from the acquisition as alleged in the Commission's complaint," and further, the FTC ordering, "That for a period of ten (10) years from the date on which this order becomes final, respondents shall not, without the prior approval of the Commission, directly or indirectly, through subsidiaries, partnerships, or otherwise .. Acquire any Professional Illustration Software or acquire or enter into any exclusive license to Professional Illustration Software;" (referring to FreeHand.) FreeHand was returned to Altsys with all licensing and marketing rights as well as Aldus FreeHand's customer list. === Macromedia Freehand === By late 1994, Altsys still retained all rights to FreeHand. Despite brief plans to keep it in-house to sell it along with Fontographer and Virtuoso, Altsys reached an agreement with the multimedia software company, Macromedia, to be acquired. This mutual agreement provided FreeHand and Fontographer a new home with ample resources for marketing, sales, and competition against the newly merged Adobe-Aldus company. Altsys would remain in Richardson, Texas, but would be renamed as the Digital Arts Group of Macromedia and was responsible for the continued development of FreeHand. Macromedia received FreeHand's 200,000 customers and expanded its traditional product line of multimedia graphics software to illustration and design graphics software. CEO James Von Ehr became a Macromedia vice-president until 1997 when he left to start another venture. FreeHand 5.0 sold for $595 in 1995. This version featured a more customizable and expanded workspace, multiple views, stronger design and editing tools, a report generator, spell check, paragraph styles, multicolor gradient fills up to 64 colors, speed improvements, and it accepted Illustrator plugins. In September 1995, a 5.5 upgrade added Photoshop plug-in support, PDF import capabilities, the Extract feature, inline graphics to text, improved auto-expanding text containers, the Crop feature, and the Create PICT Image feature. A FreeHand 5.5 upgrade was part of the FreeHand Graphics Studio (a suite that included Fontographer, Macromedia xRes image editing application, and Extreme 3D animation and modeling application). FreeHand 6.0 in 1996. This version only existed in beta. Some Freehand 7 prerelease versions were released under the Freehand 6 tag. FreeHand 7.0 sold for $399 in 1996, or $449 as part of the FreeHand Graphics Studio (see above.) Features included a redesigned user interface that allowed recombining Inspectors, Panel Tabs, Dockable Panels, Smart Cursors,

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  Project workforce management

  Project workforce management is the practice of combining the coordination of all logistic elements of a project through a single software application (or workflow engine). This includes planning and tracking of schedules and mileposts, cost and revenue, resource allocation, as well as overall management of these project elements. Efficiency is improved by eliminating manual processes, like spreadsheet tracking to monitor project progress. It also allows for at-a-glance status updates and ideally integrates with existing legacy applications in order to unify ongoing projects, enterprise resource planning (ERP) and broader organizational goals. There are a lot of logistic elements in a project. Different team members are responsible for managing each element and often, the organisation may have a mechanism to manage some logistic areas as well. By coordinating these various components of project management, workforce management and financials through a single solution, the process of configuring and changing project and workforce details is simplified. == Introduction == A project workforce management system defines project tasks, project positions, and assigns personnel to the project positions. The project tasks and positions are correlated to assign a responsible project position or even multiple positions to complete each project task. Because each project position may be assigned to a specific person, the qualifications and availabilities of that person can be taken into account when determining the assignment. By associating project tasks and project positions, a manager can better control the assignment of the workforce and complete the project more efficiently. When it comes to project workforce management, it is all about managing all the logistic aspects of a project or an organisation through a software application. Usually, this software has a workflow engine defined. Therefore, all the logistic processes take place in the workflow engine. == About == === Technical field === This invention relates to project management systems and methods, more particularly to a software-based system and method for project and workforce management. === Software usage === Due to the software usage, all the project workflow management tasks can be fully automated without leaving many tasks for the project managers. This returns high efficiency to the project management when it comes to project tracking proposes. In addition to different tracking mechanisms, project workforce management software also offer a dashboard for the project team. Through the dashboard, the project team has a glance view of the overall progress of the project elements. Most of the times, project workforce management software can work with the existing legacy software systems such as ERP (enterprise resource planning) systems. This easy integration allows the organisation to use a combination of software systems for management purposes. === Background === Good project management is an important factor for the success of a project. A project may be thought of as a collection of activities and tasks designed to achieve a specific goal of the organisation, with specific performance or quality requirements while meeting any subject time and cost constraints. Project management refers to managing the activities that lead to the successful completion of a project. Furthermore, it focuses on finite deadlines and objectives. A number of tools may be used to assist with this as well as with assessment. Project management may be used when planning personnel resources and capabilities. The project may be linked to the objects in a professional services life cycle and may accompany the objects from the opportunity over quotation, contract, time and expense recording, billing, period-end-activities to the final reporting. Naturally the project gets even more detailed when moving through this cycle. For any given project, several project tasks should be defined. Project tasks describe the activities and phases that have to be performed in the project such as writing of layouts, customising, testing. What is needed is a system that allows project positions to be correlated with project tasks. Project positions describe project roles like project manager, consultant, tester, etc. Project-positions are typically arranged linearly within the project. By correlating project tasks with project positions, the qualifications and availability of personnel assigned to the project positions may be considered. == Benefits of project management == Good project management should: Reduce the chance of a project failing Ensure a minimum level of quality and that results meet requirements and expectations Free up other staff members to get on with their area of work and increase efficiency both on the project and within the business Make things simpler and easier for staff with a single point of contact running the overall project Encourage consistent communications amongst staff and suppliers Keep costs, timeframes and resources to budget == Workflow engine == When it comes to project workforce management, it is all about managing all the logistic aspects of a project or an organisation through a software application. Usually, this software has a workflow engine defined in them. So, all the logistic processes take place in the workflow engine. The regular and most common types of tasks handled by project workforce management software or a similar workflow engine are: === Planning and monitoring project schedules and milestones === Regularly monitoring your project's schedule performance can provide early indications of possible activity-coordination problems, resource conflicts, and possible cost overruns. To monitor schedule performance. Collecting information and evaluating it ensure a project accuracy. The project schedule outlines the intended result of the project and what's required to bring it to completion. In the schedule, we need to include all the resources involved and cost and time constraints through a work breakdown structure (WBS). The WBS outlines all the tasks and breaks them down into specific deliverables. === Tracking the cost and revenue aspects of projects === The importance of tracking actual costs and resource usage in projects depends upon the project situation. Tracking actual costs and resource usage is an essential aspect of the project control function. === Resource utilisation and monitoring === Organisational profitability is directly connected to project management efficiency and optimal resource utilisation. To sum up, organisations that struggle with either or both of these core competencies typically experience cost overruns, schedule delays and unhappy customers. The focus for project management is the analysis of project performance to determine whether a change is needed in the plan for the remaining project activities to achieve the project goals. == Other management aspects of project management == === Project risk management === Risk identification consists of determining which risks are likely to affect the project and documenting the characteristics of each. === Project communication management === Project communication management is about how communication is carried out during the course of the project === Project quality management === It is of no use completing a project within the set time and budget if the final product is of poor quality. The project manager has to ensure that the final product meets the quality expectations of the stakeholders. This is done by good: Quality planning: Identifying what quality standards are relevant to the project and determining how to meet them. Quality assurance: Evaluating overall project performance on a regular basis to provide confidence that the project will satisfy the relevant quality standards. Quality control: Monitoring specific project results to determine if they comply with relevant quality standards and identifying ways to remove causes of poor performance. == Project workforce management vs. traditional management == There are three main differences between Project Workforce Management and traditional project management and workforce management disciplines and solutions: === Workflow-driven === All project and workforce processes are designed, controlled and audited using a built-in graphical workflow engine. Users can design, control and audit the different processes involved in the project. The graphical workflow is quite attractive for the users of the system and allows the users to have a clear idea of the workflow engine. === Organisation and work breakdown structures === Project Workforce Management provides organization and work breakdown structures to create, manage and report on functional and approval hierarchies, and to track information at any level of detail. Users can create, manage, edit and report work breakdown structures. Work breakdown structures have different abstraction

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  Algorithmic game theory

  Algorithmic game theory (AGT) is an interdisciplinary field at the intersection of game theory and computer science, focused on understanding and designing algorithms for environments where multiple strategic agents interact. This research area combines computational thinking with economic principles to address challenges that emerge when algorithmic inputs come from self-interested participants. In traditional algorithm design, inputs are assumed to be fixed and reliable. However, in many real-world applications—such as online auctions, internet routing, digital advertising, and resource allocation systems—inputs are provided by multiple independent agents who may strategically misreport information to manipulate outcomes in their favor. AGT provides frameworks to analyze and design systems that remain effective despite such strategic behavior. The field can be approached from two complementary perspectives: Analysis: Evaluating existing algorithms and systems through game-theoretic tools to understand their strategic properties. This includes calculating and proving properties of Nash equilibria (stable states where no participant can benefit by changing only their own strategy), measuring price of anarchy (efficiency loss due to selfish behavior), and analyzing best-response dynamics (how systems evolve when players sequentially optimize their strategies). Design: Creating mechanisms and algorithms with both desirable computational properties and game-theoretic robustness. This sub-field, known as algorithmic mechanism design, develops systems that incentivize truthful behavior while maintaining computational efficiency. Algorithm designers in this domain must satisfy traditional algorithmic requirements (such as polynomial-time running time and good approximation ratio) while simultaneously addressing incentive constraints that ensure participants act according to the system's intended design. == History == === Nisan-Ronen: a new framework for studying algorithms === In 1999, the seminal paper of Noam Nisan and Amir Ronen drew the attention of the Theoretical Computer Science community to designing algorithms for selfish (strategic) users. As they claim in the abstract: We consider algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. As such participants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents’ interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. In this model the algorithmic solution is adorned with payments to the participants and is termed a mechanism. The payments should be carefully chosen as to motivate all participants to act as the algorithm designer wishes. We apply the standard tools of mechanism design to algorithmic problems and in particular to the shortest path problem. This paper coined the term algorithmic mechanism design and was recognized by the 2012 Gödel Prize committee as one of "three papers laying foundation of growth in Algorithmic Game Theory". === Price of Anarchy === The other two papers cited in the 2012 Gödel Prize for fundamental contributions to Algorithmic Game Theory introduced and developed the concept of "Price of Anarchy". In their 1999 paper "Worst-case Equilibria", Koutsoupias and Papadimitriou proposed a new measure of the degradation of system efficiency due to the selfish behavior of its agents: the ratio of between system efficiency at an optimal configuration, and its efficiency at the worst Nash equilibrium. (The term "Price of Anarchy" only appeared a couple of years later.) === The Internet as a catalyst === The Internet created a new economy—both as a foundation for exchange and commerce, and in its own right. The computational nature of the Internet allowed for the use of computational tools in this new emerging economy. On the other hand, the Internet itself is the outcome of actions of many. This was new to the classic, ‘top-down’ approach to computation that held till then. Thus, game theory is a natural way to view the Internet and interactions within it, both human and mechanical. Game theory studies equilibria (such as the Nash equilibrium). An equilibrium is generally defined as a state in which no player has an incentive to change their strategy. Equilibria are found in several fields related to the Internet, for instance financial interactions and communication load-balancing. Game theory provides tools to analyze equilibria, and a common approach is then to ‘find the game’—that is, to formalize specific Internet interactions as a game, and to derive the associated equilibria. Rephrasing problems in terms of games allows the analysis of Internet-based interactions and the construction of mechanisms to meet specified demands. If equilibria can be shown to exist, a further question must be answered: can an equilibrium be found, and in reasonable time? This leads to the analysis of algorithms for finding equilibria. Of special importance is the complexity class PPAD, which includes many problems in algorithmic game theory. == Areas of research == === Algorithmic mechanism design === Mechanism design is the subarea of economics that deals with optimization under incentive constraints. Algorithmic mechanism design considers the optimization of economic systems under computational efficiency requirements. Typical objectives studied include revenue maximization and social welfare maximization. === Inefficiency of equilibria === The concepts of price of anarchy and price of stability were introduced to capture the loss in performance of a system due to the selfish behavior of its participants. The price of anarchy captures the worst-case performance of the system at equilibrium relative to the optimal performance possible. The price of stability, on the other hand, captures the relative performance of the best equilibrium of the system. These concepts are counterparts to the notion of approximation ratio in algorithm design. === Complexity of finding equilibria === The existence of an equilibrium in a game is typically established using non-constructive fixed point theorems. There are no efficient algorithms known for computing Nash equilibria. The problem is complete for the complexity class PPAD even in 2-player games. In contrast, correlated equilibria can be computed efficiently using linear programming, as well as learned via no-regret strategies. === Computational social choice === Computational social choice studies computational aspects of social choice, the aggregation of individual agents' preferences. Examples include algorithms and computational complexity of voting rules and coalition formation. Other topics include: Algorithms for computing Market equilibria Fair division Multi-agent systems And the area counts with diverse practical applications: Sponsored search auctions Spectrum auctions Cryptocurrencies Prediction markets Reputation systems Sharing economy Matching markets such as kidney exchange and school choice Crowdsourcing and peer grading Economics of the cloud == Journals and newsletters == ACM Transactions on Economics and Computation (TEAC) SIGEcom Exchanges Algorithmic Game Theory papers are often also published in Game Theory journals such as GEB, Economics journals such as Econometrica, and Computer Science journals such as SICOMP.

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  Unrestricted algorithm

  An unrestricted algorithm is an algorithm for the computation of a mathematical function that puts no restrictions on the range of the argument or on the precision that may be demanded in the result. The idea of such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980. In the problem of developing algorithms for computing, as regards the values of a real-valued function of a real variable (e.g., g[x] in "restricted" algorithms), the error that can be tolerated in the result is specified in advance. An interval on the real line would also be specified for values when the values of a function are to be evaluated. Different algorithms may have to be applied for evaluating functions outside the interval. An unrestricted algorithm envisages a situation in which a user may stipulate the value of x and also the precision required in g(x) quite arbitrarily. The algorithm should then produce an acceptable result without failure.

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  Peanut App

  Peanut, a product of Peanut App Ltd. is an online community for women who are planning to become pregnant, women who are pregnant, women who have had children, and women who are experiencing menopause. Profiles of potential friends are displayed to users who can swipe up to show intent to connect. Users can also connect via discussion threads, groups, and live audio conversations. The app allows users to select their stage of life (trying to conceive, pregnancy, motherhood, or menopause), so as to meet women at a similar life stage, and to discover relevant content. Peanut was founded by Michelle Kennedy shortly after she left Bumble, a female-first dating app. She has described Peanut as, "the app she wishes she had when she first became a mother". == History == Peanut was initially launched in 2017 for mothers and pregnant women. The app focuses on helping users find others with shared interests, such as spoken languages, occupations, and hobbies. It also displays a woman's life stage, such as the age of her children, or the stage of pregnancy. In 2018, it launched a community discussion feature that intended to give women an "alternative to other social platforms". In 2019, it started to serve women who are trying to conceive. In April 2021, it integrated live audio, in response to the COVID-19 pandemic, and the restrictions around in-person socializing. in September 2021, it started to include women who are navigating perimenopause, menopause, and postmenopausal. Although it had initially catered for younger women navigating into new families, a large number of users had undergone surgically or chemically induced menopause due to medical conditions. In July 2021, Peanut launched an investment micro fund, Peanut StartHER, focused on investing in women-owned businesses, as well as other historically excluded founders. == Operation == The Peanut app is a social network exclusively for women, focusing on topics of pregnancy, motherhood, fertility, and menopause. It is available on iOS and Android devices. Users must prove their identity, in keeping with the primary function of in-app safety, and then they can create a profile to interact with other users. For pregnant users, the “Bump Buddies” feature helps connect them with other Peanut users who have a similar due date, which aimed to help expecting mothers combat loneliness during the COVID-19 pandemic. Peanut users also have the option to join “Groups” ‒ sub-sections of users focused on specific topics, including (but not limited to) location, life stage, pregnancy due date, and interests or hobbies. The live voice chat feature “Pods”, enables Peanut users to socialize without the pressure of photos or video chat. It offers features such as a muted audience of listeners who need to virtually raise their hand to speak, emoji reactions, and hosts who can moderate the conversations and invite people to speak.

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  Applied Information Science in Economics

  The Applied Information Science in Economics (Russian: Прикладная информатика в Экономике) or Applied Computer Science in Economics is a professional qualification generally awarded in Russian Federation. The degree inherited from the U.S.S.R. education system also known as Specialist degree. The degree is awarded after five years of full-time study and includes several internships, course-works, thesis writing and defense. The degree has similarities with German Magister Artium or Diplom degree. However, due to the Bologna Process number of such degrees are declining. Degree focuses on applying mathematical methods in economics involving maximum information technology. It is very close to applied mathematics, but includes also major part of computer science. == List of specialty codes in the education system == 080801 - Applied computer science in economics 351400 - Applied computer science == Fields of activity == Organization and management; Project design; Experimental research; Marketing; Consulting; Operational and Maintenance. == Major == Information Science and Programming. High Level Methods of Information Science and Programming. Information Technologies in Economics. Computer Systems, Networks and Telecommunications Services. Operational Environments, Systems and Shells. Architecture and Design of Information Systems for Companies. Data Bases. Information security. Information Management. Imitative Simulation.

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  Randomized rounding

  In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. The basic idea of randomized rounding is to convert an optimal solution of a relaxation of the problem into an approximately-optimal solution to the original problem. The resulting algorithm is usually analyzed using the probabilistic method. == Overview == The basic approach has three steps: Formulate the problem to be solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the ILP. Round the fractional solution x {\displaystyle x} of the LP to an integer solution x ′ {\displaystyle x'} of the ILP. (Although the approach is most commonly applied with linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) In the first step, the challenge is to choose a suitable integer linear program. Familiarity with linear programming, in particular modelling using linear programs and integer linear programs, is required. For many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm. In the third step, the fractional solution must be converted into an integer solution (and thus a solution to the original problem). This is called rounding the fractional solution. The resulting integer solution should (provably) have cost not much larger than the cost of the fractional solution. This will ensure that the cost of the integer solution is not much larger than the cost of the optimal integer solution. The main technique used to do the third step (rounding) is to use randomization, and then to use probabilistic arguments to bound the increase in cost due to the rounding (following the probabilistic method from combinatorics). Therein, probabilistic arguments are used to show the existence of discrete structures with desired properties. In this context, one uses such arguments to show the following: Given any fractional solution x {\displaystyle x} of the LP, with positive probability the randomized rounding process produces an integer solution x ′ {\displaystyle x'} that approximates x {\displaystyle x} according to some desired criterion. Finally, to make the third step computationally efficient, one either shows that x ′ {\displaystyle x'} approximates x {\displaystyle x} with high probability (so that the step can remain randomized) or one derandomizes the rounding step, typically using the method of conditional probabilities. The latter method converts the randomized rounding process into an efficient deterministic process that is guaranteed to reach a good outcome. == Example: the set cover problem == The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance ⟨ c , S ⟩ {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} . === Computing the fractional solution === For step 1, let IP be the standard integer linear program for set cover for this instance. For step 2, let LP be the linear programming relaxation of IP, and compute an optimal solution x ∗ {\displaystyle x^{}} to LP using any standard linear programming algorithm. This takes time polynomial in the input size. The feasible solutions to LP are the vectors x {\displaystyle x} that assign each set s ∈ S {\displaystyle s\in {\mathcal {S}}} a non-negative weight x s {\displaystyle x_{s}} , such that, for each element e ∈ U {\displaystyle e\in {\mathcal {U}}} , x ′ {\displaystyle x'} covers e {\displaystyle e} —the total weight assigned to the sets containing e {\displaystyle e} is at least 1, that is, ∑ s ∋ e x s ≥ 1. {\displaystyle \sum _{s\ni e}x_{s}\geq 1.} The optimal solution x ∗ {\displaystyle x^{}} is a feasible solution whose cost ∑ s ∈ S c ( S ) x s ∗ {\displaystyle \sum _{s\in {\mathcal {S}}}c(S)x_{s}^{}} is as small as possible. Note that any set cover C {\displaystyle {\mathcal {C}}} for S {\displaystyle {\mathcal {S}}} gives a feasible solution x {\displaystyle x} (where x s = 1 {\displaystyle x_{s}=1} for s ∈ C {\displaystyle s\in {\mathcal {C}}} , x s = 0 {\displaystyle x_{s}=0} otherwise). The cost of this C {\displaystyle {\mathcal {C}}} equals the cost of x {\displaystyle x} , that is, ∑ s ∈ C c ( s ) = ∑ s ∈ S c ( s ) x s . {\displaystyle \sum _{s\in {\mathcal {C}}}c(s)=\sum _{s\in {\mathcal {S}}}c(s)x_{s}.} In other words, the linear program LP is a relaxation of the given set-cover problem. Since x ∗ {\displaystyle x^{}} has minimum cost among feasible solutions to the LP, the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover. === Randomized rounding step === In step 3, we must convert the minimum-cost fractional set cover x ∗ {\displaystyle x^{}} into a feasible integer solution x ′ {\displaystyle x'} (corresponding to a true set cover). The rounding step should produce an x ′ {\displaystyle x'} that, with positive probability, has cost within a small factor of the cost of x ∗ {\displaystyle x^{}} .Then (since the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover), the cost of x ′ {\displaystyle x'} will be within a small factor of the optimal cost. As a starting point, consider the most natural rounding scheme: For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( 1 , x s ∗ ) {\displaystyle \min(1,x_{s}^{})} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . With this rounding scheme, the expected cost of the chosen sets is at most ∑ s c ( s ) x s ∗ {\displaystyle \sum _{s}c(s)x_{s}^{}} , the cost of the fractional cover. This is good. Unfortunately the coverage is not good. When the variables x s ∗ {\displaystyle x_{s}^{}} are small, the probability that an element e {\displaystyle e} is not covered is about ∏ s ∋ e 1 − x s ∗ ≈ ∏ s ∋ e exp ⁡ ( − x s ∗ ) = exp ⁡ ( − ∑ s ∋ e x s ∗ ) ≈ exp ⁡ ( − 1 ) . {\displaystyle \prod _{s\ni e}1-x_{s}^{}\approx \prod _{s\ni e}\exp(-x_{s}^{})=\exp {\Big (}-\sum _{s\ni e}x_{s}^{}{\Big )}\approx \exp(-1).} So only a constant fraction of the elements will be covered in expectation. To make x ′ {\displaystyle x'} cover every element with high probability, the standard rounding scheme first scales up the rounding probabilities by an appropriate factor λ > 1 {\displaystyle \lambda >1} . Here is the standard rounding scheme: Fix a parameter λ ≥ 1 {\displaystyle \lambda \geq 1} . For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( λ x s ∗ , 1 ) {\displaystyle \min(\lambda x_{s}^{},1)} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . Scaling the probabilities up by λ {\displaystyle \lambda } increases the expected cost by λ {\displaystyle \lambda } , but makes coverage of all elements likely. The idea is to choose λ {\displaystyle \lambda } as small as possible so that all elements are provably covered with non-zero probability. Here is a detailed analysis. ==== Lemma (approximation guarantee for rounding scheme) ==== Fix λ = ln ⁡ ( 2 | U | ) {\displaystyle \lambda =\ln(2|{\mathcal {U}}|)} . With positive probability, the rounding scheme returns a set cover x ′ {\displaystyle x'} of cost at most 2 ln ⁡ ( 2 | U | ) c ⋅ x ∗ {\displaystyle 2\ln(2|{\mathcal {U}}|)c\cdot x^{}} (and thus of cost O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} times the cost of the optimal set cover). (Note: with care the O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} can be reduced to ln ⁡ ( | U | ) + O ( log ⁡ log ⁡ | U | ) {\displaystyle \ln(|{\mathcal {U}}|)+O(\log \log |{\mathcal {U}}|)} .) ==== Proof ==== The output x ′ {\displaystyle x'} of the random rounding scheme has the desired properties as long as none of the following "bad" events occur: the cost c ⋅ x ′ {\displaystyle c\cdot x'} of x ′ {\displaystyle x'} exceeds 2 λ c ⋅ x ∗ {\displaystyle 2\lambda c\cdot x^{}} , or for some element e {\displaystyle e} , x ′ {\displaystyle x'} fails to cover e {\displaystyle e} . The expectation of each x s ′ {\displaystyle x'_{s}} is at most λ x s ∗ {\displaystyle \lambda x_{s

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