AI Chat On Google

AI Chat On Google — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  DeepSeek (chatbot)

  DeepSeek is a generative artificial intelligence chatbot developed by the Chinese company DeepSeek. Released on 20 January 2025, DeepSeek-R1 surpassed ChatGPT as the most downloaded freeware app on the iOS App Store in the United States by 27 January. DeepSeek's success against larger and more established rivals has been described as "upending AI" and initiating "a global AI space race". DeepSeek's compliance with Chinese government censorship policies and its data collection practices have also raised concerns over privacy and information control in the model, prompting regulatory scrutiny in multiple countries. However, it has also been praised for its open weights and infrastructure code, energy efficiency and contributions to open-source artificial intelligence. == History == On 10 January 2025, DeepSeek released the chatbot, based on the DeepSeek-R1 model, for iOS and Android. By 27 January, DeepSeek-R1 surpassed ChatGPT as the most-downloaded freeware app on the iOS App Store in the United States, which resulted in an 18% drop in Nvidia's share price. And after a "large-scale" cyberattack on the same day disrupted the proper functioning of its servers, DeepSeek had limited its new user registration to phone numbers from mainland China, email addresses, or Google account logins. On 3 April 2025, in collaboration with researchers at Tsinghua University, DeepSeek published a paper unveiling a new model that combines the techniques generative reward modeling (GRM) and self-principled critique tuning (SPCT). The resulting model is referred to as DeepSeek-GRM. The goal of using these techniques is to foster more effective inference-time scaling within their LLM and chatbot services. Notably, DeepSeek has said that these new models will be released and made open source. On 30 April 2025, Deepseek released its math-focused Artificial Intelligence Model named "DeepSeek-Prover-V2-671B". This model is useful for formal theorem proving and mathematical reasoning. On 24 April 2026, DeepSeek released DeepSeek V4 and V4-Pro. == Usage == DeepSeek can answer questions, solve logic problems, and write computer programs on par with other chatbots, according to benchmark tests used by American AI companies. Users can access the chatbot for free through the official DeepSeek website or mobile application, without limitation on the number of queries. DeepSeek only supports user-signup via a global email service, e.g. Gmail, Google or Yahoo. DeepSeek also offers access to the R1 and V3 models that power the chatbot via an API with a usage-based pricing model. This modality is primarily targeted towards developers and businesses. As of February 2025, API usage is priced at approximately $0.28 per million input tokens and $0.42 per million output tokens, making it less expensive than some competing services. Its web version is completely free, with 500 messages per hour cap limit to prevent bots from spamming. == Operation == DeepSeek-V3 uses significantly fewer resources compared to its peers. For example, whereas the world's leading AI companies train their chatbots with supercomputers using as many as 16,000 graphics processing units (GPUs), DeepSeek claims to have needed only about 2,000 GPUs—namely, the H800 series chips from Nvidia. It was trained in around 55 days at a cost of US$5.58 million, which is roughly one-tenth of what tech giant Meta spent building its latest AI technology. == Reactions == DeepSeek's success against larger and more established rivals has been described as "upending AI", constituting "the first shot at what is emerging as a global AI space race", and ushering in "a new era of AI brinkmanship". === Challenge to US AI dominance === DeepSeek's competitive performance at relatively minimal cost has been recognized as potentially challenging the global dominance of American AI models. Various publications and news media, such as The Hill and The Guardian, have described the release of the R1 chatbot as a "Sputnik moment" for American AI, echoing Marc Andreessen's view. OpenAI wrote a letter to the Office of Science and Technology Policy (OSTP), in March 2025, citing issues concerning a possibility that Deepseek could manipulate responses to cause harm. === Chinese perspective === DeepSeek's founder Liang Wenfeng has been compared to OpenAI CEO Sam Altman, with CNN calling him the Sam Altman of China and an evangelist for AI. Chinese state media widely praised DeepSeek as a national asset. On 20 January 2025, Chinese Premier Li Qiang invited Wenfeng to his symposium with experts and asked him to provide opinions and suggestions on a draft for comments of the annual 2024 government work report. On 20 February 2025, Wenfeng met with General Secretary of the Chinese Communist Party Xi Jinping, who encouraged party and state leaders to experiment with DeepSeek. Government officials responded to Xi's approval of the chatbot by reportedly using it to draft legal judgements, propose medical treatment plans, and analyze surveillance videos to search for missing persons. === Performance and success === Leading figures in the American AI sector had mixed reactions to DeepSeek's performance and success. Microsoft CEO Satya Nadella and OpenAI CEO Altman—whose companies are involved in the United States government-backed "Stargate Project" to develop American AI infrastructure—both called DeepSeek "super impressive". Various companies including Amazon Web Services, Toyota, and Stripe are seeking to use the model in their program. When American President Donald Trump announced The Stargate Project, he referred to DeepSeek as a wake-up call and a positive development. Other leaders in the AI field, however—including Scale AI CEO Alexandr Wang, Anthropic cofounder and CEO Dario Amodei, and Elon Musk—have expressed skepticism of the app's performance or of the sustainability of its success. Wang in particularly referred to DeepSeek-V3 as "earth-shattering" and DeepSeek-R1 as "top performing, or roughly on par with the best American models", but speculated that China may possess more AI-powering Nvidia H100 GPUs than thought. === Stock market implications === DeepSeek's optimization of limited resources has highlighted potential limits of United States sanctions on China's AI development, including export restrictions on advanced AI chips to China. The success of the company's AI models consequently "sparked market turmoil" and caused shares in major global technology companies to plunge on 27 January 2025: Nvidia's stock fell by as much as 17–18%, as did the stock of rival Broadcom. Other tech firms also sank, including Microsoft (down 2.5%), Google's owner Alphabet (down over 4%), and Dutch chip equipment maker ASML (down over 7%). A global sell-off of technology stocks on Nasdaq, prompted by the release of the R1 model, led to record losses of about $593 billion in the market capitalizations of AI and computer hardware companies; and by the next day a total of $1 trillion of value was wiped from American stocks. == Concerns == === Distillation === DeepSeek has been reported to sometimes claim that it is ChatGPT. OpenAI said that DeepSeek may have "inappropriately" used outputs from its model as training data in a process called distillation. However, there is currently no method to prove this conclusively. === Censorship === DeepSeek's compliance with Chinese government censorship policies and its data collection practices have raised concerns over information control in the model, prompting regulatory scrutiny in multiple countries. Reports indicate that it applies content moderation in accordance with the government's "public opinion guidance" regulations, limiting responses on topics such as the Tiananmen Square massacre and Taiwan's political status. DeepSeek models that have been uncensored also display a bias towards Chinese government viewpoints on controversial topics such as Xi Jinping's human rights record and Taiwan's political status. However, users who have downloaded the models and hosted them on their own devices and servers have reported successfully removing this censorship. Some sources have observed that the official application programming interface (API) version of R1, which runs from servers located in mainland China, uses censorship mechanisms for topics considered politically sensitive for the government of China. For example, the model may initially generate answers to questions about the 1989 Tiananmen Square massacre, persecution of Uyghurs, comparisons between Xi Jinping and Winnie the Pooh, and human rights in China, but a censorship mechanism deletes the uncensored response afterwards and replaces it with a message such as:"Sorry, that's beyond my current scope. Let's talk about something else." The post hoc censorship mechanisms and restrictions added on top of the model's output can be removed in the open-source version of the R1 model. If the "core Socialist values" defined by the Chinese Internet regul

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  Cellular neural network

  In computer science and machine learning, Cellular Neural Networks (CNN) or Cellular Nonlinear Networks (CNN) are a parallel computing paradigm similar to neural networks, with the difference that communication is allowed between neighbouring units only. Typical applications include image processing, analyzing 3D surfaces, solving partial differential equations, reducing non-visual problems to geometric maps, modelling biological vision and other sensory-motor organs. CNN is not to be confused with convolutional neural networks (also colloquially called CNN). == CNN architecture == Due to their number and variety of architectures, it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of finite, fixed-number, fixed-location, fixed-topology, locally interconnected, multiple-input, single-output, nonlinear processing units. The nonlinear processing units are often referred to as neurons or cells. Mathematically, each cell can be modeled as a dissipative, nonlinear dynamical system where information is encoded via its initial state, inputs and variables used to define its behavior. Dynamics are usually continuous, as in the case of Continuous-Time CNN (CT-CNN) processors, but can be discrete, as in the case of Discrete-Time CNN (DT-CNN) processors. Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically real-valued, but can be complex or even quaternion, i.e. a Multi-Valued CNN (MV-CNN). Most CNN processors, processing units are identical, but there are applications that require non-identical units, which are called Non-Uniform Processor CNN (NUP-CNN) processors, and consist of different types of cells. === Chua-Yang CNN === In the original Chua-Yang CNN (CY-CNN) processor, the state of the cell was a weighted sum of the inputs and the output was a piecewise linear function. However, like the original perceptron-based neural networks, the functions it could perform were limited: specifically, it was incapable of modeling non-linear functions, such as XOR. More complex functions are realizable via Non-Linear CNN (NL-CNN) processors. Cells are defined in a normed gridded space like two-dimensional Euclidean geometry. However, the cells are not limited to two-dimensional spaces; they can be defined in an arbitrary number of dimensions and can be square, triangle, hexagonal, or any other spatially invariant arrangement. Topologically, cells can be arranged on an infinite plane or on a toroidal space. Cell interconnect is local, meaning that all connections between cells are within a specified radius (with distance measured topologically). Connections can also be time-delayed to allow for processing in the temporal domain. Most CNN architectures have cells with the same relative interconnects, but there are applications that require a spatially variant topology, i.e. Multiple-Neighborhood-Size CNN (MNS-CNN) processors. Also, Multiple-Layer CNN (ML-CNN) processors, where all cells on the same layer are identical, can be used to extend the capability of CNN processors. The definition of a system is a collection of independent, interacting entities forming an integrated whole, whose behavior is distinct and qualitatively greater than its entities. Although connections are local, information exchange can happen globally through diffusion. In this sense, CNN processors are systems because their dynamics are derived from the interaction between the processing units and not within processing units. As a result, they exhibit emergent and collective behavior. Mathematically, the relationship between a cell and its neighbors, located within an area of influence, can be defined by a coupling law, and this is what primarily determines the behavior of the processor. When the coupling laws are modeled by fuzzy logic, it is a fuzzy CNN. When these laws are modeled by computational verb logic, it becomes a computational verb CNN. Both fuzzy and verb CNNs are useful for modelling social networks when the local couplings are achieved by linguistic terms. == History == The idea of CNN processors was introduced by Leon Chua and Lin Yang in 1988. In these articles, Chua and Yang outline the underlying mathematics behind CNN processors. They use this mathematical model to demonstrate, for a specific CNN implementation, that if the inputs are static, the processing units will converge, and can be used to perform useful calculations. They then suggest one of the first applications of CNN processors: image processing and pattern recognition (which is still the largest application to date). Leon Chua is still active in CNN research and publishes many of his articles in the International Journal of Bifurcation and Chaos, of which he is an editor. Both IEEE Transactions on Circuits and Systems and the International Journal of Bifurcation also contain a variety of useful articles on CNN processors authored by other knowledgeable researchers. The former tends to focus on new CNN architectures and the latter more on the dynamical aspects of CNN processors. In 1993, Tamas Roska and Leon Chua introduced the first algorithmically programmable analog CNN processor in the world. The multi-national effort was funded by the Office of Naval Research, the National Science Foundation, and the Hungarian Academy of Sciences, and researched by the Hungarian Academy of Sciences and the University of California. This article proved that CNN processors were producible and provided researchers a physical platform to test their CNN theories. After this article, companies started to invest into larger, more capable processors, based on the same basic architecture as the CNN Universal Processor. Tamas Roska is another key contributor to CNNs. His name is often associated with biologically inspired information processing platforms and algorithms, and he has published numerous key articles and has been involved with companies and research institutions developing CNN technology. === Literature === Two references are considered invaluable since they manage to organize the vast amount of CNN literature into a coherent framework: An overview by Valerio Cimagalli and Marco Balsi. The paper provides a concise intro to definitions, CNN types, dynamics, implementations, and applications. "Cellular Neural Networks and Visual Computing Foundations and Applications", written by Leon Chua and Tamas Roska, which provides examples and exercises. The book covers many different aspects of CNN processors and can serve as a textbook for a Masters or Ph.D. course. Other resources include The proceedings of "The International Workshop on Cellular Neural Networks and Their Applications" provide much CNN literature. The proceedings are available online, via IEEE Xplore, for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005 and 2006. There was also a workshop held in Santiago de Composetela, Spain. Topics included theory, design, applications, algorithms, physical implementations and programming and training methods. For an understanding of the analog semiconductor based CNN technology, AnaLogic Computers has their product line, in addition to the published articles available on their homepage and their publication list. They also have information on other CNN technologies such as optical computing. Many of the commonly used functions have already been implemented using CNN processors. A good reference point for some of these can be found in image processing libraries for CNN based visual computers such as Analogic’s CNN-based systems. == Related processing architectures == CNN processors could be thought of as a hybrid between artificial neural network (ANN) and Continuous Automata (CA). === Artificial Neural Networks === The processing units of CNN and NN are similar. In both cases, the processor units are multi-input, dynamical systems, and the behavior of the overall systems is driven primarily through the weights of the processing unit’s linear interconnect. However, in CNN processors, connections are made locally, whereas in ANN, connections are global. For example, neurons in one layer are fully connected to another layer in a feed-forward NN and all the neurons are fully interconnected in Hopfield networks. In ANNs, the weights of interconnections contain information on the processing system’s previous state or feedback. But in CNN processors, the weights are used to determine the dynamics of the system. Furthermore, due to the high inter-connectivity of ANNs, they tend not exploit locality in either the data set or the processing and as a result, they usually are highly redundant systems that allow for robust, fault-tolerant behavior without catastrophic errors. A cross between an ANN and a CNN processor is a Ratio Memory CNN (RMCNN). In RMCNN processors, the cell interconnect is local and topologically invariant, but the weights are used to store

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  KataGo

  KataGo is a free and open-source computer Go program, capable of defeating top-level human players. First released on 27 February 2019, it is developed by David Wu, who also developed the Arimaa playing program bot_Sharp which defeated three top human players to win the Arimaa AI Challenge in 2015. KataGo's first release was trained by David Wu using resources provided by his employer Jane Street Capital, but it is now trained by a distributed effort. Members of the computer Go community provide computing resources by running the client, which generates self-play games and rating games, and submits them to a server. The self-play games are used to train newer networks and the rating games to evaluate the networks' relative strengths. KataGo supports the Go Text Protocol, with various extensions, thus making it compatible with popular GUIs such as Lizzie. As an alternative, it also implements a custom "analysis engine" protocol, which is used by the KaTrain GUI, among others. KataGo is widely used by strong human go players, including the South Korean national team, for training purposes. KataGo is also used as the default analysis engine in the online Go website AI Sensei, as well as OGS (the Online Go Server). == Technology == Based on techniques used by DeepMind's AlphaGo Zero, KataGo implements Monte Carlo tree search with a convolutional neural network providing position evaluation and policy guidance. Compared to AlphaGo, KataGo introduces many refinements that enable it to learn faster and play more strongly. Notable features of KataGo that are absent in many other Go-playing programs include score estimation; support for small boards, rectangular boards, and large boards; arbitrary values of komi and handicaps; and the ability to use various Go rulesets and adjust its play and evaluation for the small differences between them. === Network === The network used in KataGo are ResNets with pre-activation. While AlphaGo Zero has only game board history as input features (as it was designed as a general architecture for board games, subsequently becoming AlphaZero), the input to the network contains additional features designed by hand specifically for playing Go. These features include liberties, komi parity, pass-alive, and ladders. The trunk is essentially the same as in AlphaGo Zero, but with global pooling layers added to allow the network to be conditioned on global context such as ko fights. This is similar to the Squeeze-and-Excitation Network. The network has two heads: a policy head and a value head. The policy and value heads are mostly the same as in AlphaGo Zero, but both heads have auxiliary subheads to provide auxiliary loss signal for faster training: Policy head: predicts policy for the current player's move this turn, and the opponent player's move in the next turn. A policy Each is a logit array of size 19 × 19 + 1 {\displaystyle 19\times 19+1} , representing the logit of making a move in one of the points, plus the logit of passing. Value head: predicts game outcome, expected score difference, expected board ownership, etc. The network is described in detail in Appendix A of the report. The code base switched from using TensorFlow to PyTorch in version 1.12. === Training === Let its trunk have b {\displaystyle b} residual blocks and c {\displaystyle c} channels. During its first training run, multiple networks were trained with increasing ( b , c ) {\displaystyle (b,c)} . It took 19 days using a maximum of 28 Nvidia V100 GPUs at 4.2 million games. After the first training run, training became a distributed project run by volunteers, with increasing network sizes. As of August 2024, it has reached b28c512 (28 blocks, 512 channels). == Adversarial attacks == In 2022, KataGo was used as the target for adversarial attack research, designed to demonstrate the "surprising failure modes" of AI systems. The researchers were able to trick KataGo into ending the game prematurely. Adversarial training improves defense against adversarial attacks, though not perfectly.

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  TasteDive

  TasteDive (formerly named TasteKid) is an entertainment recommendation engine for films, TV shows, music, video games, books, people, places, and brands. It also has elements of a social media site; it allows users to connect with "tastebuds", people with like minded interests. == History == TasteDive was founded in 2008 as TasteKid by brothers Andrei Oghina and Felix Oghina. In 2019, it was acquired by Qloo headquartered in NYC. "Qloo has built for developers and enterprises what TasteDive has built for individuals". == Description == When a user types in the title of a film or TV show, the site's algorithm provides a list of similar content. It provides recommendations for TV shows to watch based on films liked by the user, and vice versa. It also provides recommendations for music, video games, and books, and includes film and TV trailers and music videos. An account is free and is not required to receive recommendations, but recommendations are more accurate for those with an account. The more a user explores the site, the more the site learns about the user's preferences and the better the results become. The site also has a social media aspect where one can see activity and gain recommendations from other users, how many others in the community like or dislike any recommendation, and how popular their tastes are within the TasteDive community. The main competitors of TasteDive are Taste App, Trakt.tv and Tastoid.

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  Gonioreflectometer

  A gonioreflectometer is a device for measuring a bidirectional reflectance distribution function (BRDF). The device consists of a light source illuminating the material to be measured and a sensor that captures light reflected from that material. The light source should be able to illuminate and the sensor should be able to capture data from a hemisphere around the target. The hemispherical rotation dimensions of the sensor and light source are the four dimensions of the BRDF. The 'gonio' part of the word refers to the device's ability to measure at different angles. Several similar devices have been built and used to capture data for similar functions. Most of these devices use a camera instead of the light intensity-measuring sensor to capture a two-dimensional sample of the target. Examples include: a spatial gonioreflectometer for capturing the SBRDF (McAllister, 2002). a camera gantry for capturing the light field (Levoy and Hanrahan, 1996). an unnamed device for capturing the bidirectional texture function (Dana et al., 1999).

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  International Journal of Pattern Recognition and Artificial Intelligence

  The International Journal of Pattern Recognition and Artificial Intelligence was founded in 1987 and is published by World Scientific. The journal covers developments in artificial intelligence, and its sub-field, pattern recognition. This includes articles on image and language processing, robotics and neural networks. == Abstracting and indexing == The journal is abstracted and indexed in: SciSearch ISI Alerting Services CompuMath Citation Index Current Contents/Engineering, Computing & Technology Inspec io-port.net Compendex Computer Abstracts

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  National Security Commission on Artificial Intelligence

  The National Security Commission on Artificial Intelligence (NSCAI) was an independent commission of the United States of America from 2018 to 2021. Its mission was to make recommendations to the President and Congress to "advance the development of artificial intelligence, machine learning, and associated technologies to comprehensively address the national security and defense needs of the United States". The commission's 15 members were nominated by the United States Congress. The NSCAI was dissolved on 1 October 2021. == History and reporting == The NSCAI began working in March 2019 and by November 2019 it had received more than 200 classified and unclassified briefings to help with the creation of its final report due in 2021.On 4 November 2019, the NSCAI shared its interim report with Congress, where it explained the 27 initial judgements to base its ongoing work. In the interim report the commission also agreed on seven principles: Global leadership in AI technology is a national security priority AI adoption is an urgent imperative for national security A shared sense of responsibility for the American peoples security must be created from government officials and private sector leaders. It needs to find local AI talent and use it to attract the world’s best minds Actions used for the protection of America’s AI leadership against foreign threats needs to follow the principles of free enterprise, free inquiry and free flow of ideas. The technical limitations of AI are universally known, however, a strong desire remains for powerful, dependable, and secure AI systems. United States used AI must follow American values including the rule of law Fundamental areas of effort for the preservation of U.S. advantages were also agreed upon in the interim report of 2019. The NSCAI released its first report of recommendations in March 2020, most of which were included in the 2021 National Defense Authorization Act. In July 2020, the commission published the second report to Congress. It identified 35 actions for both Executive and Legislative branches, which were focused on six fundamental areas. This report was available to the public. In January 2021, a draft of the final report was presented at a panel led by Schmidt. The report recommended the US to use AI technology for military use and development. It issued its final report in March 2021, saying that the U.S. is not sufficiently prepared to defend or compete against China in the AI era. It was broken up into two parts, the first titled “Defending America in the AI Era”, and the second “Winning the Technology Competition”. The report spoke about China’s efforts and investments into integration and that it could very well take the lead in AI in the next few years. Additional suggestions were made to concentrate on AI in everything we do and to implement it into US national security on multiple levels, as well as focus on bringing in new talent to develop AI and to introduce it to the working force on both civilian and military levels. Another recommendation of the NSCAI report was to develop and provide China and Russia with alternative models that are based on norms and democratic values. The final report also included a proposed $40 billion budget for government spending. On 14 April 2021, NSCAI executive director Ylli Bajraktari and director of Research and Analysis Justin Lynch participated in an event held by the Center for Security and Emerging Technology (CSET) to discuss the final report findings. In October 2021, NSCAI chair Eric Schmidt founded the bipartisan, non-profit Special Competitive Studies Project (SCSP) through his family led non-profit Eric & Wendy Schmidt Fund for Strategic Innovation in order to carry on the NSCAI’s efforts and expand beyond national security. The Foundation for Defense of Democracies held an event in June 2023, called “Thinking Forward After the NSCAI and CSC: A Discussion on AI and Cyber Policy”, with former members of NSCAI on the moderation panel, including Eric Schmidt and Ylli Bajraktari. == Members == Members of the National Security Commission on Artificial Intelligence: Eric Schmidt (chair), former CEO of Google Robert Work (Vice Chair), former Deputy Secretary of Defense Mignon Clyburn, former Commissioner of the Federal Communications Commission Chris Darby, CEO of In-Q-Tel Kenneth M. Ford, CEO of the Florida Institute for Human and Machine Cognition Jose-Marie Griffiths, President of Dakota State University Eric Horvitz, Technical Fellow at Microsoft Katrina G. McFarland, former Assistant Secretary of Defense for Acquisition Jason Matheny, Director of the Center for Security and Emerging Technology at Georgetown University Gilman Louie, partner at Alsop Louie Partners William Mark, vice president at SRI International Andy Jassy, CEO of Amazon Web Services (AWS) Safra Catz, CEO of Oracle Steve Chien, Technical Fellow at Jet Propulsion Laboratory (JPL) Andrew Moore, Google/Alphabet == Recommendations == The report's recommendations include: Dramatically increasing non-defense federal spending on AI research and development, doubling every year from $2 billion in 2022, to $32 billion in 2026. That would bring it up to a level similar to spending on biomedical research A dramatic increase in undergraduate scholarship and graduate studies fellowships in AI Creation of a Digital Corps to bring skilled tech workers into government Founding of a Digital Service Academy: an accredited university providing subsidized education in exchange for a commitment to work for a time in government Include civil rights and civil liberty reports for new AI systems or major updates to existing systems Expanding allocations of employment-based green cards, and giving them to every AI PhD graduate from an accredited U.S. university Reforming the acquisition management system Department of Defense to make it faster and easier to introduce new technologies == Transparency == In December 2019, a ruling was made under the Freedom of Information Act (FOIA) that the NSCAI must also provide historical documents upon request. The Electronic Privacy Information Center (EPIC) filed the lawsuit against the NSCAI in September 2019 after being refused information about the upcoming meetings and prepared records of the commission under FOIA and the Federal Advisory Committee Act (FACA). The U.S. District Court for the District of Columbia ruled in June 2020 that the NSCAI must comply with FACA and therefore hold open meetings and provide records to the public. The lawsuit was also filed by EPIC.

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  Liveness test

  A liveness test, liveness check or liveness detection is an automated method for determining whether a subject is a real person or part of a spoofing attack. The technique is used as part of know your customer checks in financial services and during facial age estimation. Liveness detection is a cornerstone of digital safety. == Test process == The threat in face spoofing attacks is that "the attacker only needs to find a good face swap library on Github and understand how to inject the model into the camera feed during the KYC process". Fraudsters usually buy stolen IDs on the dark web to start a deepfake attack. An AI-powered generative adversarial network (GAN) can then generate the face swapping model that many online verification services fail to detect. Low level hackers may use face swapping apps such as SwapFace, DeepFaceLive, and Swapstream (increasing interest for those apps in 2023 according to Google Trends). In a video liveness test, users are typically asked to look into a camera and to move, smile or blink, and features of their moving face may then be compared to that of a still image. Artificial intelligence is used to counter presentation attacks such as deepfakes or users wearing hyperrealistic masks, or video injection attacks. Other forms of liveness test include checking for a pulse when using a fingerprint scanner or checking that a person's voice is not a recording or artificially generated during speaker recognition. == Adoption and certification == In a 2022 report published by the security firm Sensity, it was demonstrated that the liveness test of most US banks was easily cheated with new and publicly-available AI-powered techniques. Many of these banks disregarded the results of the report. In the first half of 2023, the security firm iProov detected a 704% increase in face-swap attacks. In 2023, in the UK, many customers of Ryanair were upset to have to go through many ID verification checks, including liveness tests, before boarding, as the airline was using it as a mean to deter customers to buy tickets through third-party websites. In the first half of 2024 iBeta Quality Assurance issued 18 new ISO/IEC 30107-3 Presentation Attack Detection certificates, raising the cumulative total to 85 since 2018. In January 2024, the Department of Homeland Security (DHS) opened applications from vendors to test their Liveness test. Identity frauds peaked during the COVID-19 lockdown, leading government agencies to take reinforced measures to secure their digital applications.

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  Foreign key

  A foreign key is a set of attributes in a table that refers to the primary key of another table, linking these two tables. In the context of relational databases, a foreign key is subject to an inclusion dependency constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S; furthermore that those attributes must also be a candidate key in S. In other words, a foreign key is a set of attributes that references a candidate key. For example, a table called TEAM may have an attribute, MEMBER_NAME, which is a foreign key referencing a candidate key, PERSON_NAME, in the PERSON table. Since MEMBER_NAME is a foreign key, any value existing as the name of a member in TEAM must also exist as a person's name in the PERSON table; in other words, every member of a TEAM is also a PERSON. == Summary == The table containing the foreign key is called the child table, and the table containing the candidate key is called the referenced or parent table. In database relational modeling and implementation, a candidate key is a set of zero or more attributes, the values of which are guaranteed to be unique for each tuple (row) in a relation. The value or combination of values of candidate key attributes for any tuple cannot be duplicated for any other tuple in that relation. Since the purpose of the foreign key is to identify a particular row of referenced table, it is generally required that the foreign key is equal to the candidate key in some row of the primary table, or else have no value (the NULL value.). This rule is called a referential integrity constraint between the two tables. Because violations of these constraints can be the source of many database problems, most database management systems provide mechanisms to ensure that every non-null foreign key corresponds to a row of the referenced table. For example, consider a database with two tables: a CUSTOMER table that includes all customer data and an ORDER table that includes all customer orders. Suppose the business requires that each order must refer to a single customer. To reflect this in the database, a foreign key column is added to the ORDER table (e.g., CUSTOMERID), which references the primary key of CUSTOMER (e.g. ID). Because the primary key of a table must be unique, and because CUSTOMERID only contains values from that primary key field, we may assume that, when it has a value, CUSTOMERID will identify the particular customer which placed the order. However, this can no longer be assumed if the ORDER table is not kept up to date when rows of the CUSTOMER table are deleted or the ID column altered, and working with these tables may become more difficult. Many real world databases work around this problem by 'inactivating' rather than physically deleting master table foreign keys, or by complex update programs that modify all references to a foreign key when a change is needed. Foreign keys play an essential role in database design. One important part of database design is making sure that relationships between real-world entities are reflected in the database by references, using foreign keys to refer from one table to another. Another important part of database design is database normalization, in which tables are broken apart and foreign keys make it possible for them to be reconstructed. Multiple rows in the referencing (or child) table may refer to the same row in the referenced (or parent) table. In this case, the relationship between the two tables is called a one to many relationship between the referencing table and the referenced table. In addition, the child and parent table may, in fact, be the same table, i.e. the foreign key refers back to the same table. Such a foreign key is known in SQL:2003 as a self-referencing or recursive foreign key. In database management systems, this is often accomplished by linking a first and second reference to the same table. A table may have multiple foreign keys, and each foreign key can have a different parent table. Each foreign key is enforced independently by the database system. Therefore, cascading relationships between tables can be established using foreign keys. A foreign key is defined as an attribute or set of attributes in a relation whose values match a primary key in another relation. The syntax to add such a constraint to an existing table is defined in SQL:2003 as shown below. Omitting the column list in the REFERENCES clause implies that the foreign key shall reference the primary key of the referenced table. Likewise, foreign keys can be defined as part of the CREATE TABLE SQL statement. If the foreign key is a single column only, the column can be marked as such using the following syntax: Foreign keys can be defined with a stored procedure statement. child_table: the name of the table or view that contains the foreign key to be defined. parent_table: the name of the table or view that has the primary key to which the foreign key applies. The primary key must already be defined. col3 and col4: the name of the columns that make up the foreign key. The foreign key must have at least one column and at most eight columns. == Referential actions == Because the database management system enforces referential constraints, it must ensure data integrity if rows in a referenced table are to be deleted (or updated). If dependent rows in referencing tables still exist, those references have to be considered. SQL:2003 specifies 5 different referential actions that shall take place in such occurrences: CASCADE RESTRICT NO ACTION SET NULL SET DEFAULT === CASCADE === Whenever rows in the parent (referenced) table are deleted (or updated), the respective rows of the child (referencing) table with a matching foreign key column will be deleted (or updated) as well. This is called a cascade delete (or update). === RESTRICT === A value cannot be updated or deleted when a row exists in a referencing or child table that references the value in the referenced table. Similarly, a row cannot be deleted as long as there is a reference to it from a referencing or child table. To understand RESTRICT (and CASCADE) better, it may be helpful to notice the following difference, which might not be immediately clear. The referential action CASCADE modifies the "behavior" of the (child) table itself where the word CASCADE is used. For example, ON DELETE CASCADE effectively says "When the referenced row is deleted from the other table (master table), then delete also from me". However, the referential action RESTRICT modifies the "behavior" of the master table, not the child table, although the word RESTRICT appears in the child table and not in the master table! So, ON DELETE RESTRICT effectively says: "When someone tries to delete the row from the other table (master table), prevent deletion from that other table (and of course, also don't delete from me, but that's not the main point here)." RESTRICT is not supported by Microsoft SQL 2012 and earlier. === NO ACTION === NO ACTION and RESTRICT are very much alike. The main difference between NO ACTION and RESTRICT is that with NO ACTION the referential integrity check is done after trying to alter the table. RESTRICT does the check before trying to execute the UPDATE or DELETE statement. Both referential actions act the same if the referential integrity check fails: the UPDATE or DELETE statement will result in an error. In other words, when an UPDATE or DELETE statement is executed on the referenced table using the referential action NO ACTION, the DBMS verifies at the end of the statement execution that none of the referential relationships are violated. This is different from RESTRICT, which assumes at the outset that the operation will violate the constraint. Using NO ACTION, the triggers or the semantics of the statement itself may yield an end state in which no foreign key relationships are violated by the time the constraint is finally checked, thus allowing the statement to complete successfully. === SET NULL, SET DEFAULT === In general, the action taken by the DBMS for SET NULL or SET DEFAULT is the same for both ON DELETE or ON UPDATE: the value of the affected referencing attributes is changed to NULL for SET NULL, and to the specified default value for SET DEFAULT. === Triggers === Referential actions are generally implemented as implied triggers (i.e. triggers with system-generated names, often hidden.) As such, they are subject to the same limitations as user-defined triggers, and their order of execution relative to other triggers may need to be considered; in some cases it may become necessary to replace the referential action with its equivalent user-defined trigger to ensure proper execution order, or to work around mutating-table limitations. Another important limitation appears with transaction isolation: your changes to a row may not be able to fully cascade because the row is ref

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  Catholic Church and artificial intelligence

  The Catholic Church views artificial intelligence as a significant technological development that must be governed by strict ethical principles rooted in human dignity and the common good. In January 2025, the Church issued the doctrinal note Antiqua et nova co-issued by the Dicastery for the Doctrine of the Faith and the Dicastery for Culture and Education. It addresses the "relationship between artificial intelligence and human intelligence" and offers reflections on the "anthropological and ethical challenges raised by AI". In August 2025, Time magazine included Pope Leo XIV in its 2025 list of the World’s Most Influential People in Artificial Intelligence. In May 2026, Pope Leo XIV approved the creation of a new Vatican commission on artificial intelligence. He released his first papal encyclical, titled Magnifica humanitas, on the topic later in the month.

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  Plinian Core

  Plinian Core is a set of vocabulary terms that can be used to describe different aspects of biological species information. Under "biological species Information" all kinds of properties or traits related to taxa—biological and non-biological—are included. Thus, for instance, terms pertaining descriptions, legal aspects, conservation, management, demographics, nomenclature, or related resources are incorporated. == Description == The Plinian Core is aimed to facilitate the exchange of information about the species and upper taxa. What is in scope? Species level catalogs of any kind of biological objects or data. Terminology associated with biological collection data. Striving for compatibility with other biodiversity-related standards. Facilitating the addition of components and attributes of biological data. What is not in scope? Data interchange protocols. Non-biodiversity-related data. Occurrence level data. This standard is named after Pliny the Elder, a very influential figure in the study of the biological species. Plinian Core design requirements includes: ease of use, to be self-contained, able to support data integration from multiple databases, and ability to handle different levels of granularity. Core terms can be grouped in its current version as follows: Metadata Base Elements Record Metadata Nomenclature and Classification Taxonomic description Natural history Invasive species Habitat and Distribution Demography and Threats Uses, Management and Conservation associatedParty, MeasurementOrFact, References, AncillaryData == Background == Plinian Core started as a collaborative project between Instituto Nacional de Biodiversidad and GBIF Spain in 2005. A series of iterations in which elements were defined and implanted in different projects resulted in a "Plinian Core Flat" [deprecated]. As a result, a new development was impulse to overcome them in 2012. New formal requirements, additional input and a will to better support the standard and its documentation, as well as to align it with the processes of TDWG, the world reference body for biodiversity information standards. A new version, Plinian Core v3.x.x was defined. This provides more flexibility to fully represent the information of a species in a variety of scenarios. New elements to deal with aspects such as IPR, related resources, referenced, etc. were introduced, and elements already included were better-defined and documented. Partner for the development of Plinian Core in this new phase incorporated the University of Granada (UG, Spain), the Alexander von Humboldt Institute (IAvH, Colombia), the National Commission for the Knowledge and Use of Biodiversity (Conabio, Mexico) and the University of São Paulo (USP, Brazil). A "Plinian Core Task Group" within TDWG "Interest Group on species Information" was constituted and currently working on its development. == Levels of the standard == Plinian Core is presented in to levels: the abstract model and the application profiles. The abstract model (AM), comprising the abstract model schema(xsd) and the terms' URIs, is the normative part. It is all comprehensive, and allows for different levels of granularity in describing species properties. The AM should be taken as a "menu" from which to choose terms and level of detail needed in any specific project. The subsets of the abstract model intended to be implemented in specific projects are the "application profiles" (APs). Besides containing part of the elements of the AM, APs can impose additional specifications on the included elements, such as controlled vocabularies. Some examples of APs in use follow: Application profile CONABIO Application profile INBIO Application profile GBIF.ES Application profile Banco de Datos de la Naturaleza.Spain Application profile SIB-COLOMBIA == Relation to other standards == Plinian incorporates a number of elements already defined by other standards. The following table summarizes these standards and the elements used in Plinian Core:

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  Partial-order planning

  Partial-order planning is an approach to automated planning that maintains a partial ordering between actions and only commits ordering between actions when forced to, that is, ordering of actions is partial. Also this planning doesn't specify which action will come out first when two actions are processed. By contrast, total-order planning maintains a total ordering between all actions at every stage of planning. Given a problem in which some sequence of actions is needed to achieve a goal, a partial-order plan specifies all actions that must be taken, but specifies an ordering between actions only where needed. Consider the following situation: a person must travel from the start to the end of an obstacle course. The course is composed of a bridge, a see-saw, and a swing-set. The bridge must be traversed before the see-saw and swing-set are reachable. Once reachable, the see-saw and swing-set can be traversed in any order, after which the end is reachable. In a partial-order plan, ordering between these obstacles is specified only when needed. The bridge must be traversed first. Second, either the see-saw or swing-set can be traversed. Third, the remaining obstacle can be traversed. Then the end can be traversed. Partial-order planning relies upon the principle of least commitment for its efficiency. == Partial-order plan == A partial-order plan or partial plan is a plan which specifies all actions that must be taken, but only specifies the order between actions when needed. It is the result of a partial-order planner. A partial-order plan consists of four components: A set of actions (also known as operators). A partial order for the actions. It specifies the conditions about the order of some actions. A set of causal links. It specifies which actions meet which preconditions of other actions. Alternatively, a set of bindings between the variables in actions. A set of open preconditions. It specifies which preconditions are not fulfilled by any action in the partial-order plan. To keep the possible orders of the actions as open as possible, the set of order conditions and causal links must be as small as possible. A plan is a solution if the set of open preconditions is empty. A linearization of a partial order plan is a total order plan derived from the particular partial order plan; in other words, both order plans consist of the same actions, with the order in the linearization being a linear extension of the partial order in the original partial order plan. === Example === For example, a plan for baking a cake might start: go to the store get eggs; get flour; get milk pay for all goods go to the kitchen This is a partial plan because the order for finding eggs, flour and milk is not specified, the agent can wander around the store reactively accumulating all the items on its shopping list until the list is complete. == Partial-order planner == A partial-order planner is an algorithm or program which will construct a partial-order plan and search for a solution. The input is the problem description, consisting of descriptions of the initial state, the goal and possible actions. The problem can be interpreted as a search problem where the set of possible partial-order plans is the search space. The initial state would be the plan with the open preconditions equal to the goal conditions. The final state would be any plan with no open preconditions, i.e. a solution. The initial state is the starting conditions, and can be thought of as the preconditions to the task at hand. For a task of setting the table, the initial state could be a clear table. The goal is simply the final action that needs to be accomplished, for example setting the table. The operators of the algorithm are the actions by which the task is accomplished. For this example there may be two operators: lay (tablecloth), and place (glasses, plates, and silverware). === Plan space === The plan space of the algorithm is constrained between its start and finish. The algorithm starts, producing the initial state and finishes when all parts of the goal have been achieved. In the setting a table example, two types of actions exist that must be addressed: the put-out and lay operators. Four unsolved operators also exist: Action 1, lay-tablecloth, Action 2, Put-out (plates), Action 3, Put-out (silverware), and Action 4, Put-out (glasses). However, a threat arises if Action 2, 3, or 4 comes before Action 1. This threat is that the precondition to the start of the algorithm will be unsatisfied as the table will no longer be clear. Thus, constraints exist that must be added to the algorithm that force Actions 2, 3, and 4 to come after Action 1. Once these steps are completed, the algorithm will finish and the goal will have been completed. === Threats === As seen in the algorithm presented above, partial-order planning can encounter certain threats, meaning orderings that threaten to break connected actions, thus potentially destroying the entire plan. There are two ways to resolve threats: Promotion Demotion Promotion orders the possible threat after the connection it threatens. Demotion orders the possible threat before the connection it threatens. Partial-order planning algorithms are known for being both sound and complete, with sound being defined as the total ordering of the algorithm, and complete being defined as the capability to find a solution, given that a solution does in fact exist. == Partial-order vs. total-order planning == Partial-order planning is the opposite of total-order planning, in which actions are sequenced all at once and for the entirety of the task at hand. The question arises when one has two competing processes, which one is better? Anthony Barret and Daniel Weld have argued in their 1993 book, that partial-order planning is superior to total-order planning, as it is faster and thus more efficient. They tested this theory using Korf’s taxonomy of subgoal collections, in which they found that partial-order planning performs better because it produces more trivial serializability than total-order planning. Trivial serializability facilitates a planner’s ability to perform quickly when dealing with goals that contain subgoals. Planners perform more slowly when dealing with laboriously serializable or nonserializable subgoals. The determining factor that makes a subgoal trivially or laboriously serializable is the search space of different plans. They found that partial-order planning is more adept at finding the quickest path, and is therefore the more efficient of these two main types of planning. == The Sussman anomaly == Partial-order plans are known to easily and optimally solve the Sussman anomaly. Using this type of incremental planning system solves this problem quickly and efficiently. This was a result of partial-order planning that solidified its place as an efficient planning system. == Disadvantages to partial-order planning == One drawback of this type of planning system is that it requires a lot more computational power for each node. This higher per-node cost occurs because the algorithm for partial-order planning is more complex than others. This has important artificial intelligence implications. When coding a robot to do a certain task, the creator needs to take into account how much energy is needed. Though a partial-order plan may be quicker it may not be worth the energy cost for the robot. The creator must be aware of and weigh these two options to build an efficient robot.

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  Quantum artificial life

  Quantum artificial life is the application of quantum algorithms with the ability to simulate biological behavior. Quantum computers offer many potential improvements to processes performed on classical computers, including machine learning and artificial intelligence. Artificial intelligence applications are often inspired by the idea of mimicking human brains through closely related biomimicry. This has been implemented to a certain extent on classical computers (using neural networks), but quantum computers offer many advantages in the simulation of artificial life. Artificial life and artificial intelligence are extremely similar, with minor differences; the goal of studying artificial life is to understand living beings better, while the goal of artificial intelligence is to create intelligent beings. In 2016, Alvarez-Rodriguez et al. developed a proposal for a quantum artificial life algorithm with the ability to simulate life and Darwinian evolution. In 2018, the same research team led by Alvarez-Rodriguez performed the proposed algorithm on the IBM ibmqx4 quantum computer, and received optimistic results. The results accurately simulated a system with the ability to undergo self-replication at the quantum scale. == Artificial life on quantum computers == The growing advancement of quantum computers has led researchers to develop quantum algorithms for simulating life processes. Researchers have designed a quantum algorithm that can accurately simulate Darwinian Evolution. Since the complete simulation of artificial life on quantum computers has only been actualized by one group, this section shall focus on the implementation by Alvarez-Rodriguez, Sanz, Lomata, and Solano on an IBM quantum computer. Individuals were realized as two qubits, one representing the genotype of the individual and the other representing the phenotype. The genotype is copied to transmit genetic information through generations, and the phenotype is dependent on the genetic information as well as the individual's interactions with their environment. In order to set up the system, the state of the genotype is instantiated by some rotation of an ancillary state ( | 0 ⟩ ⟨ 0 | {\displaystyle |0\rangle \langle 0|} ). The environment is a two-dimensional spatial grid occupied by individuals and ancillary states. The environment is divided into cells that are able to possess one or more individuals. Individuals move throughout the grid and occupy cells randomly; when two or more individuals occupy the same cell they interact with each other. === Self replication === The ability to self-replicate is critical for simulating life. Self-replication occurs when the genotype of an individual interacts with an ancillary state, creating a genotype for a new individual; this genotype interacts with a different ancillary state in order to create the phenotype. During this interaction, one would like to copy some information about the initial state into the ancillary state, but by the no cloning theorem, it is impossible to copy an arbitrary unknown quantum state. However, physicists have derived different methods for quantum cloning which does not require the exact copying of an unknown state. The method that has been implemented by Alvarez-Rodriguez et al. is one that involves the cloning of the expectation value of some observable. For a unitary U {\displaystyle U} which copies the expectation value of some set of observables X {\displaystyle {\mathsf {X}}} of state ρ {\displaystyle \rho } into a blank state ρ e {\displaystyle \rho _{e}} , the cloning machine is defined by any ( U , ρ e , X ) {\displaystyle (U,\rho _{e},{\mathsf {X}})} that fulfill the following: ∀ ρ ∀ X ∈ X {\displaystyle \forall \rho \forall X\in {\mathsf {X}}} X ¯ = X 1 ¯ = X 2 ¯ {\displaystyle {\bar {X}}={\bar {X_{1}}}={\bar {X_{2}}}} Where X ¯ {\displaystyle {\bar {X}}} is the mean value of the observable in ρ {\displaystyle \rho } before cloning, X 1 ¯ {\displaystyle {\bar {X_{1}}}} is the mean value of the observable in ρ {\displaystyle \rho } after cloning, and X 2 ¯ {\displaystyle {\bar {X_{2}}}} is the mean value of the observable in ρ e {\displaystyle \rho _{e}} after cloning. Note that the cloning machine has no dependence on ρ {\displaystyle \rho } because we want to be able to clone the expectation of the observables for any initial state. It is important to note that cloning the mean value of the observable transmits more information than is allowed classically. The calculation of the mean value is defined naturally as: X ¯ = T r [ ρ X ] {\displaystyle {\bar {X}}=Tr[\rho X]} , X 1 ¯ = T r [ R X ⊗ I ] {\displaystyle {\bar {X_{1}}}=Tr[RX\otimes I]} , X 2 ¯ = T r [ R I ⊗ X ] {\displaystyle {\bar {X_{2}}}=Tr[RI\otimes X]} where R = U ρ ⊗ ρ e U † {\displaystyle R=U\rho \otimes \rho _{e}U^{\dagger }} The simplest cloning machine clones the expectation value of σ z {\displaystyle \sigma _{z}} in arbitrary state ρ = | ψ ⟩ ⟨ ψ | {\displaystyle \rho =|\psi \rangle \langle \psi |} to ρ e = | 0 ⟩ ⟨ 0 | {\displaystyle \rho _{e}=|0\rangle \langle 0|} using U = C N O T {\displaystyle U=CNOT} . This is the cloning machine implemented for self-replication by Alvarez-Rodriguez et al. The self-replication process clearly only requires interactions between two qubits, and therefore this cloning machine is the only one necessary for self replication. === Interactions === Interactions occur between individuals when the two take up the same space on the environmental grid. The presence of interactions between individuals provides an advantage for shorter-lifespan individuals. When two individuals interact, exchanges of information between the two phenotypes may or may not occur based on their existing values. When both individual's control qubits (genotypes) are alike, no information will be exchanged. When the control qubits differ, the target qubits (phenotype) will be exchanged between the two individuals. This procedure produces a constantly changing predator-prey dynamic in the simulation. Therefore, long-living qubits, with a larger genetic makeup in the simulation, are at a disadvantage. Since information is only exchanged when interacting with an individual of different genetic makeup, the short-lived population has the advantage. === Mutation === Mutations exist in the artificial world with limited probability, equivalent to their occurrence in the real world. There are two ways in which the individual can mutate: through random single qubit rotations and by errors in the self-replication process. There are two different operators that act on the individual and cause mutations. The M operation causes a spontaneous mutation within the individual by rotating a single qubit by parameter θ. The parameter θ is random for each mutation, which creates biodiversity within the artificial environment. The M operation is a unitary matrix which can be described as: M = ( cos ⁡ ( θ ) s i n ( θ ) s i n ( θ ) − c o s ( θ ) ) {\displaystyle M={\begin{pmatrix}\cos(\theta )&sin(\theta )\\sin(\theta )&-cos(\theta )\end{pmatrix}}} The other possible way for mutations to occur is due to errors in the replication process. Due to the no-cloning theorem, it is impossible to produce perfect copies of systems that are originally in unknown quantum states. However, quantum cloning machines make it possible to create imperfect copies of quantum states, in other words, the process introduces some degree of error. The error that exists in current quantum cloning machines is the root cause for the second kind of mutations in the artificial life experiment. The imperfect cloning operation can be seen as: U M ( θ ) = I 4 + 1 2 ( 0 0 0 1 ) ⊗ ( − 1 1 1 − 1 ) ( c o s θ + i s i n θ + 1 ) {\displaystyle U_{M}(\theta )=\mathrm {I} _{4}+{\frac {1}{2}}{\begin{pmatrix}0&0\\0&1\end{pmatrix}}\otimes {\begin{pmatrix}-1&1\\1&-1\end{pmatrix}}(cos\theta +isin\theta +1)} The two kinds of mutations affect the individual differently. While the spontaneous M operation does not affect the phenotype of the individual, the self-replicating error mutation, UM, alters both the genotype of the individual, and its associated lifetime. The presence of mutations in the quantum artificial life experiment is critical for providing randomness and biodiversity. The inclusion of mutations helps to increase the accuracy of the quantum algorithm. === Death === At the instant the individual is created (when the genotype is copied into the phenotype), the phenotype interacts with the environment. As time evolves, the interaction of the individual with the environment simulates aging which eventually leads to the death of the individual. The death of an individual occurs when the expectation value of σ z {\displaystyle \sigma _{z}} is within some ϵ {\displaystyle \epsilon } of 1 in the phenotype, or, equivalently, when ρ p = | 0 ⟩ ⟨ 0 | {\displaystyle \rho _{p}=|0\rangle \langle 0|} The Lindbladian describes the interaction of the individual with the environment: ρ

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  Cerebellar model articulation controller

  The cerebellar model arithmetic computer (CMAC) is a type of neural network based on a model of the mammalian cerebellum. It is also known as the cerebellar model articulation controller. It is a type of associative memory. The CMAC was first proposed as a function modeler for robotic controllers by James Albus in 1975 (hence the name), but has been extensively used in reinforcement learning and also as for automated classification in the machine learning community. The CMAC is an extension of the perceptron model. It computes a function for n {\displaystyle n} input dimensions. The input space is divided up into hyper-rectangles, each of which is associated with a memory cell. The contents of the memory cells are the weights, which are adjusted during training. Usually, more than one quantisation of input space is used, so that any point in input space is associated with a number of hyper-rectangles, and therefore with a number of memory cells. The output of a CMAC is the algebraic sum of the weights in all the memory cells activated by the input point. A change of value of the input point results in a change in the set of activated hyper-rectangles, and therefore a change in the set of memory cells participating in the CMAC output. The CMAC output is therefore stored in a distributed fashion, such that the output corresponding to any point in input space is derived from the value stored in a number of memory cells (hence the name associative memory). This provides generalisation. == Building blocks == In the adjacent image, there are two inputs to the CMAC, represented as a 2D space. Two quantising functions have been used to divide this space with two overlapping grids (one shown in heavier lines). A single input is shown near the middle, and this has activated two memory cells, corresponding to the shaded area. If another point occurs close to the one shown, it will share some of the same memory cells, providing generalisation. The CMAC is trained by presenting pairs of input points and output values, and adjusting the weights in the activated cells by a proportion of the error observed at the output. This simple training algorithm has a proof of convergence. It is normal to add a kernel function to the hyper-rectangle, so that points falling towards the edge of a hyper-rectangle have a smaller activation than those falling near the centre. One of the major problems cited in practical use of CMAC is the memory size required, which is directly related to the number of cells used. This is usually ameliorated by using a hash function, and only providing memory storage for the actual cells that are activated by inputs. == One-step convergent algorithm == Initially least mean square (LMS) method is employed to update the weights of CMAC. The convergence of using LMS for training CMAC is sensitive to the learning rate and could lead to divergence. In 2004, a recursive least squares (RLS) algorithm was introduced to train CMAC online. It does not need to tune a learning rate. Its convergence has been proved theoretically and can be guaranteed to converge in one step. The computational complexity of this RLS algorithm is O(N3). == Hardware implementation infrastructure == Based on QR decomposition, an algorithm (QRLS) has been further simplified to have an O(N) complexity. Consequently, this reduces memory usage and time cost significantly. A parallel pipeline array structure on implementing this algorithm has been introduced. Overall by utilizing QRLS algorithm, the CMAC neural network convergence can be guaranteed, and the weights of the nodes can be updated using one step of training. Its parallel pipeline array structure offers its great potential to be implemented in hardware for large-scale industry usage. == Continuous CMAC == Since the rectangular shape of CMAC receptive field functions produce discontinuous staircase function approximation, by integrating CMAC with B-splines functions, continuous CMAC offers the capability of obtaining any order of derivatives of the approximate functions. == Deep CMAC == In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC. == Summary ==

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  Stockfish (chess)

  Stockfish is a free and open-source chess engine, available for various desktop and mobile platforms. It can be used in chess software through the Universal Chess Interface. Stockfish has been one of the strongest chess engines in the world for several years. It has won all main events of the Top Chess Engine Championship (TCEC) and the Chess.com Computer Chess Championship (CCC) since 2020 and, as of May 2026, is the strongest CPU chess engine in the world with an estimated Elo rating of 3653 in a time control of 40/15 (15 minutes to make 40 moves), according to CCRL. The Stockfish engine was developed by Tord Romstad, Marco Costalba, and Joona Kiiski, and was derived from Glaurung, an open-source engine by Tord Romstad released in 2004. It is now being developed and maintained by the Stockfish community. Stockfish historically used only a classical hand-crafted function to evaluate board positions, but with the introduction of the efficiently updatable neural network (NNUE) in August 2020, Stockfish 12 adopted a hybrid evaluation system that primarily used the neural network and occasionally relied on the hand-crafted evaluation. In July 2023, Stockfish removed the hand-crafted evaluation and transitioned to a fully neural network-based approach. == Features == Stockfish uses a tree-search algorithm based on alpha–beta search with several hand-designed heuristics. Stockfish represents positions using bitboards. Stockfish supports Chess960, a feature it inherited from Glaurung. Support for Syzygy tablebases, previously available in a fork maintained by Ronald de Man, was integrated into Stockfish in 2014. In 2018, support for the 7-man Syzygy was added, shortly after the tablebase was made available. Stockfish supports an unlimited number of CPU threads in multiprocessor systems, with a maximum transposition table size of 32 TB. Stockfish has been a very popular engine on various platforms. On desktop, it is the default chess engine bundled with the Internet Chess Club interface programs BlitzIn and Dasher. On mobile, it has been bundled with the Stockfish app, SmallFish and Droidfish. Other Stockfish-compatible graphical user interfaces (GUIs) include Fritz, Arena, Stockfish for Mac, and PyChess. Stockfish can be compiled to WebAssembly or JavaScript, allowing it to run in the browser. Both Chess.com and Lichess provide Stockfish in this form in addition to a server-side program. Release versions and development versions are available as C++ source code and as precompiled versions for Microsoft Windows, macOS, Linux 32-bit/64-bit and Android. == History == The program originated from Glaurung, an open-source chess engine created by Tord Romstad and first released in 2004. Four years later, Marco Costalba forked the project, naming it Stockfish because it was "produced in Norway and cooked in Italy" (Romstad is Norwegian and Costalba is Italian). The first version, Stockfish 1.0, was released in November 2008. For a while, new ideas and code changes were transferred between the two programs in both directions, until Romstad decided to discontinue Glaurung in favor of Stockfish, which was the stronger engine at the time. The last Glaurung version (2.2) was released in December 2008. Around 2011, Romstad decided to abandon his involvement with Stockfish in order to spend more time on his new iOS chess app. On 18 June 2014 Marco Costalba announced that he had "decided to step down as Stockfish maintainer" and asked that the community create a fork of the current version and continue its development. An official repository, managed by a volunteer group of core Stockfish developers, was created soon after and currently manages the development of the project. === Fishtest === Since 2013, Stockfish has been developed using a distributed testing framework named Fishtest, where volunteers can donate CPU time for testing improvements to the program. Changes to game-playing code are accepted or rejected based on results of playing of tens of thousands of games on the framework against an older "reference" version of the program, using sequential probability ratio testing. Tests on the framework are verified using the chi-squared test, and only if the results are statistically significant are they deemed reliable and used to revise the software code. After the inception of Fishtest, Stockfish gained 120 Elo points in 12 months, propelling it to the top of all major rating lists. As of May 2026, the framework has used a total of more than 20,100 years of CPU time to play over 10 billion chess games. === NNUE === In June 2020, Stockfish introduced the efficiently updatable neural network (NNUE) approach, based on earlier work by computer shogi programmers. Instead of using manually designed heuristics to evaluate the board, this approach introduced a neural network trained on millions of positions which could be evaluated quickly on CPU. On 2 September 2020, the twelfth version of Stockfish was released, incorporating NNUE, and reportedly winning ten times more game pairs than it loses when matched against version eleven. In July 2023, the classical evaluation was completely removed in favor of the NNUE evaluation. == Competition results == === Top Chess Engine Championship === Stockfish is a TCEC multiple-time champion and the current leader in trophy count. Ever since TCEC restarted in 2013, Stockfish has finished first or second in every season except one. Stockfish finished second in TCEC Season 4 and 5, with scores of 23–25 first against Houdini 3 and later against Komodo 1142 in the Superfinal event. Season 5 was notable for the winning Komodo team as they accepted the award posthumously for the program's creator Don Dailey, who succumbed to an illness during the final stage of the event. In his honor, the version of Stockfish that was released shortly after that season was named "Stockfish DD". On 30 May 2014, Stockfish 170514 (a development version of Stockfish 5 with tablebase support) convincingly won TCEC Season 6, scoring 35.5–28.5 against Komodo 7x in the Superfinal. Stockfish 5 was released the following day. In TCEC Season 7, Stockfish again made the Superfinal, but lost to Komodo with a score of 30.5–33.5. In TCEC Season 8, despite losses on time caused by buggy code, Stockfish nevertheless qualified once more for the Superfinal, but lost 46.5–53.5 to Komodo. In Season 9, Stockfish defeated Houdini 5 with a score of 54.5–45.5. Stockfish finished third during season 10 of TCEC, the only season since 2013 in which Stockfish had failed to qualify for the superfinal. It did not lose a game but was still eliminated because it was unable to score enough wins against lower-rated engines. After this technical elimination, Stockfish went on a long winning streak, winning seasons 11 (59–41 against Houdini 6.03), 12 (60–40 against Komodo 12.1.1), and 13 (55–45 against Komodo 2155.00) convincingly. In Season 14, Stockfish faced a new challenger in Leela Chess Zero, eking out a win by one point (50.5–49.5). Its winning streak was finally ended in Season 15, when Leela qualified again and won 53.5–46.5, but Stockfish promptly won Season 16, defeating AllieStein 54.5–45.5, after Leela failed to qualify for the Superfinal. In Season 17, Stockfish faced Leela again in the superfinal, losing 52.5–47.5. However, Stockfish has won every Superfinal since: beating Leela 53.5–46.5 in Season 18, 54.5–45.5 in Season 19, 53–47 in Season 20, and 56–44 in Season 21. In Season 22, Komodo Dragon beat out Leela to qualify for the Superfinal, losing to Stockfish by a large margin 59.5–40.5. Stockfish did not lose an opening pair in this match. Leela made the Superfinal in Seasons 23 and 24, but was crushed by Stockfish both times (58.5–41.5 and 58–42). In Season 25, Stockfish once again defeated Leela, but this time by a narrower margin of 52–48. Stockfish also took part in the TCEC cup, winning the first edition, but was surprisingly upset by Houdini in the semifinals of the second edition. Stockfish recovered to beat Komodo in the third-place playoff. In the third edition, Stockfish made it to the finals, but was defeated by Leela Chess Zero after blundering in a 7-man endgame tablebase draw. It turned this result around in the fourth edition, defeating Leela in the final 4.5–3.5. In TCEC Cup 6, Stockfish finished third after losing to AllieStein in the semifinals, the first time it had failed to make the finals. Since then, Stockfish has consistently won the tournament, with the exception of the 11th edition which Leela won 8.5–7.5. === Chess.com Computer Chess Championship === Ever since Chess.com hosted its first Chess.com Computer Chess Championship in 2018, Stockfish has been the most successful engine. It dominated the earlier championships, winning six consecutive titles before finishing second in CCC7. Since then, its dominance has come under threat from the neural-network engines Leelenstein and Leela Chess Zero, but it has continued to perform w

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