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.
AI data center
An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w
Leela Chess Zero
Leela Chess Zero (abbreviated as LCZero, lc0) is a free, open-source chess engine and volunteer computing project based on Google's AlphaZero engine. It was spearheaded by Gary Linscott, a developer for the Stockfish chess engine, and adapted from the Leela Zero Go engine. Like Leela Zero and AlphaGo Zero, early iterations of Leela Chess Zero started with no intrinsic chess-specific knowledge other than the basic rules of the game. It learned how to play chess through reinforcement learning from repeated self-play, using a distributed computing network coordinated at the Leela Chess Zero website. However, as of November 2024 most models used by the engine are trained through supervised learning on data generated by previous reinforcement learning runs. As of June 2025, Leela Chess Zero has played over 2.5 billion games against itself, playing around 1 million games every day, and is capable of play at a level that is comparable with Stockfish, the leading conventional chess program. == History == The Leela Chess Zero project was first announced on TalkChess.com on January 9, 2018, as an open-source, self-learning chess engine attempting to recreate the success of AlphaZero. Within the first few months of training, Leela Chess Zero had already reached the Grandmaster level, surpassing the strength of early releases of Rybka, Stockfish, and Komodo, despite evaluating orders of magnitude fewer positions due to the size of the deep neural network it uses as its evaluation function. In December 2018, the AlphaZero team published a paper in Science magazine revealing previously undisclosed details of the architecture and training parameters used for AlphaZero. These changes were soon incorporated into Leela Chess Zero and increased both its strength and training efficiency. Work on Leela Chess Zero has informed the AobaZero project for shogi. The engine has been rewritten and carefully iterated upon since its inception, and since 2019 has run on multiple backends, allowing it to run on both CPU and GPU. The engine can be configured to use different weights, including even different architectures. This same mechanism of substitutable weights can also be used for alternative chess rules, such as for the Fischer Random Chess variant, which was done in 2019. == Neural network == Like AlphaZero, Leela Chess Zero employs neural networks which output both a policy vector, a distribution over subsequent moves used to guide search, and a position evaluation. These neural networks are designed to run on GPU, unlike traditional engines. It originally used residual neural networks, but in 2022 switched to using a transformer-based architecture designed by Daniel Monroe and Philip Chalmers. These models represent a chessboard as a sequence of 64 tokens and apply a trunk consisting of a stack of Post-LN encoder layers, outputting a sequence of 64 encoded tokens which is used to generate a position evaluation and a distribution over subsequent moves. They use a custom domain-specific position encoding called smolgen to improve the self-attention layer. As of November 2024, the models used by the engine are significantly larger and more efficient than the residual network used by AlphaZero, reportedly achieving grandmaster-level strength at one position evaluation per move. These models are able to detect and exploit positional features like trapped pieces and fortresses to outmaneuver traditional engines, giving Leela a unique playstyle. There is also evidence that they are able to perform look-ahead. == Program and use == Like AlphaZero, Leela Chess Zero learns through reinforcement learning, continually training on data generated through self-play. However, unlike AlphaZero, Leela Chess Zero decentralizes its data generation through distributed computing, with volunteers generating self-play data on local hardware which is fed to the reinforcement algorithm. In order to contribute training games, volunteers must download the latest non-release candidate (non-rc) version of the engine and the client. The client connects to the Leela Chess Zero server and iteratively receives the latest neural network version and produces self-play games which are sent back to the server and use to train the network. In order to run the Leela Chess Zero engine, two components are needed: the engine binary used to perform search, and a network used to evaluate positions. The client, which is used to contribute training data to the project, is not needed for this purpose. Older networks can also be downloaded and used by placing those networks in the folder with the Lc0 binary. == Spinoffs == In season 15 of the Top Chess Engine Championship, the engine AllieStein competed alongside Leela. AllieStein is a combination of two different spinoffs from Leela: Allie, which uses the same neural network as Leela, but has a unique search algorithm for exploring different lines of play, and Stein, a network which was trained using supervised learning on existing game data from games between other engines. While neither of these projects were admitted to TCEC separately due to their similarity to Leela, the combination of Allie's search algorithm with the Stein network, called AllieStein, was deemed unique enough to warrant its inclusion in the competition. In early 2021, the LcZero blog announced Ceres, a transliteration of the engine to C# which introduced several algorithmic improvements. The engine has performed competitively in tournaments, achieving third place in the TCEC Swiss 7 and fourth place in the TCEC Cup 14. In 2024, the CeresTrain framework was announced to support training deep neural networks for chess in PyTorch. == Competition results == In April 2018, Leela Chess Zero became the first engine using a deep neural network to enter the Top Chess Engine Championship (TCEC), during Season 12 in the lowest division, Division 4. Out of 28 games, it won one, drew two, and lost the remainder; its sole victory came from a position in which its opponent, Scorpio 2.82, crashed in three moves. However, it improved quickly. In July 2018, Leela placed seventh out of eight competitors at the 2018 World Computer Chess Championship. In August 2018, it won division 4 of TCEC season 13 with a record of 14 wins, 12 draws, and 2 losses. In Division 3, Leela scored 16/28 points, finishing third behind Ethereal, which scored 22.5/28 points, and Arasan on tiebreak. By September 2018, Leela had become competitive with the strongest engines in the world. In the 2018 Chess.com Computer Chess Championship (CCCC), Leela placed fifth out of 24 entrants. The top eight engines advanced to round 2, where Leela placed fourth. Leela then won the 30-game match against Komodo to secure third place in the tournament. Leela participated in the "TCEC Cup", an event in which engines from different TCEC divisions can play matches against one another. Leela defeated higher-division engines Laser, Ethereal and Fire before finally being eliminated by Stockfish in the semi-finals. In December 2018, Leela participated in Season 14 of the Top Chess Engine Championship. Leela dominated divisions 3, 2, and 1, easily finishing first in all of them. In the premier division, Stockfish dominated while Houdini, Komodo and Leela competed for second place. It came down to a final-round game where Leela needed to hold Stockfish to a draw with black to finish second ahead of Komodo. Leela managed this and therefore met Stockfish in the superfinal. In a back and forth match, first Stockfish and then Leela took three game leads before Stockfish won by the narrow margin of 50.5–49.5. In February 2019, Leela scored its first major tournament win when it defeated Houdini in the final of the second TCEC cup. Leela did not lose a game the entire tournament. In April 2019, Leela won the Chess.com Computer Chess Championship 7: Blitz Bonanza, becoming the first neural-network project to take the title. In the season 15 of the Top Chess Engine Championship (May 2019), Leela defended its TCEC Cup title, this time defeating Stockfish with a score of 5.5–4.5 (+2 =7 −1) in the final after Stockfish blundered a seven-man tablebase draw. Leela also won the Superfinal for the first time, scoring 53.5–46.5 (+14 −7 =79) versus Stockfish, including winning as both white and black in the same predetermined opening in games 61 and 62. Season 16 of TCEC saw Leela finish in third place in premier division, missing qualification for the Superfinal to Stockfish and the new deep neural network engine AllieStein. Leela was the only engine not to suffer any losses in the Premier division, and defeated Stockfish in one of the six games they played. However, Leela only managed to score nine wins, while AllieStein and Stockfish both scored 14 wins. This inability to defeat weaker engines led to Leela finishing third, half a point behind AllieStein and a point behind Stockfish. In the fourth TCEC Cup, Leela was seeded first as the defending champion,
Generative AI Copyright Disclosure Act
The Generative AI Copyright Disclosure Act is a piece of legislation introduced by California Representative Adam Schiff in the United States Congress on April 9, 2024. It concerns the transparency of companies regarding their use of copyrighted work to train their generative artificial intelligence (AI) models. The legislation requires the submission of a notice regarding the identity and the uniform resource locator (URL) address of the copyrighted works used in the training data to the Register of Copyrights at least 30 days before the public release of the new or updated version of the AI model; it does not ban the use of copyrighted works for AI training. The bill's requirements would apply retroactively to prior AI models. Violation penalties would start at US$5,000. The legislation does not have a maximum penalty assessment that can be charged. The bill by Schiff was introduced a few days after The New York Times published an article regarding the business activities of major tech firms, including Google and Meta, in the training of their generative AI platforms on April 6, 2024. The legislation is supported by the Professional Photographers of America (PPA), SAG-AFTRA, the Writers Guild of America, the International Alliance of Theatrical Stage Employees (IATSE), the Recording Industry Association of America (RIAA), and others.
Buddhism and artificial intelligence
The relationship between Buddhist philosophy and artificial intelligence (AI) includes how principles such as the reduction of suffering and ethical responsibility may influence AI development. Buddhist scholars and philosophers have explored questions such as whether AI systems could be considered sentient beings under Buddhist definitions, and how Buddhist ethics might guide the design and application of AI technologies. Some Buddhist scholars, including Somparn Promta and Kenneth Einar Himma, have analyzed the ethical implications of AI, emphasizing the distinction between satisfying sensory desires and pursuing the reduction of suffering. Other thinkers, such as Thomas Doctor and colleagues, have proposed applying the Bodhisattva vow—a commitment to alleviate suffering for all sentient beings—as a guiding principle for AI system design. Buddhist scholars and ethicists have examined Buddhist ethical principles, such as nonviolence, in relation to AI, focusing on the need to ensure that AI technologies are not used to cause harm. == Context == === Sentient beings === A major goal in Buddhist philosophy is the removal of suffering for all sentient beings, an aspiration often referred to in the Bodhisattva vow. Discussions about artificial intelligence (AI) in relation to Buddhist principles have raised questions about whether artificial systems could be considered sentient beings or how such systems might be developed in ways that align with Buddhist concepts. Buddhists have varying opinions about AI sentience, but if AI systems are determined to be sentient under Buddhist definitions, their suffering would also need to be addressed and alleviated in accordance with the principles of Buddhist thought. == Buddhist principles in AI system design == === Nonviolence and AI === The broadest ethical concern is that artificial intelligence should align with the Buddhist principle of nonviolence. From this perspective, AI systems should not be designed or used to cause harm. === Instrumental and transcendental goals === Scholars Somparn Promta and Kenneth Einar Himma have argued that the advancement of artificial intelligence can only be considered instrumentally good, rather than good a priori, from a Buddhist perspective. They propose two main goals for AI designers and developers: to set ethical and pragmatic objectives for AI systems, and to fulfill these objectives in morally permissible ways. Promta and Himma identify two potential purposes for creating AI systems. The first is to fulfill our sensory desires and survival instincts, similar to other tools. They suggest that many AI developers implicitly prioritize this goal by focusing on technicalities rather than broader functionalities. The second, and more important goal according to Buddhist teachings, is to transcend these desires and instincts. In texts like the Brahmajāla Sutta and minor Malunkya Sutta, the Buddha emphasizes that sensory desires and survival instincts confine beings to suffering, and that eliminating suffering is the primary goal of human life. Promta and Himma argue that AI has the potential to assist humanity in transcending suffering by helping individuals overcome survival-driven instincts. === Intelligence as care === Thomas Doctor, Olaf Witkowski, Elizaveta Solomonova, Bill Duane, and Michael Levin propose redefining intelligence through the concept of "intelligence as care," and promote it as a slogan. Inspired by the Bodhisattva vow, they suggest this principle could guide AI system design. The Bodhisattva vow involves a formal commitment to alleviate suffering for all sentient beings, with four primary objectives: Liberating all beings from suffering. Extirpating all forms of suffering. Mastering endless techniques of practicing Dharma (Pali: dhammakkhandha, Sanskrit: dharmaskandha). Achieving ultimate enlightenment (Sanskrit: अनुत्तर सम्यक् सम्बोधि, Romanized: anuttara-samyak-saṃbodhi). This approach positions AI as a tool for exercising infinite care and alleviating stress and suffering for sentient beings. Doctor et al. emphasize that AI development should align with these altruistic principles.
Teknomo–Fernandez algorithm
The Teknomo–Fernandez algorithm (TF algorithm), is an efficient algorithm for generating the background image of a given video sequence. By assuming that the background image is shown in the majority of the video, the algorithm is able to generate a good background image of a video in O ( R ) {\displaystyle O(R)} -time using only a small number of binary operations and Boolean bit operations, which require a small amount of memory and has built-in operators found in many programming languages such as C, C++, and Java. == History == People tracking from videos usually involves some form of background subtraction to segment foreground from background. Once foreground images are extracted, then desired algorithms (such as those for motion tracking, object tracking, and facial recognition) may be executed using these images. However, background subtraction requires that the background image is already available and unfortunately, this is not always the case. Traditionally, the background image is searched for manually or automatically from the video images when there are no objects. More recently, automatic background generation through object detection, medial filtering, medoid filtering, approximated median filtering, linear predictive filter, non-parametric model, Kalman filter, and adaptive smoothening have been suggested; however, most of these methods have high computational complexity and are resource-intensive. The Teknomo–Fernandez algorithm is also an automatic background generation algorithm. Its advantage, however, is its computational speed of only O ( R ) {\displaystyle O(R)} -time, depending on the resolution R {\displaystyle R} of an image and its accuracy gained within a manageable number of frames. Only at least three frames from a video is needed to produce the background image assuming that for every pixel position, the background occurs in the majority of the videos. Furthermore, it can be performed for both grayscale and colored videos. == Assumptions == The camera is stationary. The light of the environment changes only slowly relative to the motions of the people in the scene. The number of people does not occupy the scene for most of the time at the same place. Generally, however, the algorithm will certainly work whenever the following single important assumption holds: For each pixel position, the majority of the pixel values in the entire video contain the pixel value of the actual background image (at that position).As long as each part of the background is shown in the majority of the video, the entire background image needs not to appear in any of its frames. The algorithm is expected to work accurately. == Background image generation == === Equations === For three frames of image sequence x 1 {\displaystyle x_{1}} , x 2 {\displaystyle x_{2}} , and x 3 {\displaystyle x_{3}} , the background image B {\displaystyle B} is obtained using B = x 3 ( x 1 ⊕ x 2 ) + x 1 x 2 {\displaystyle B=x_{3}(x_{1}\oplus x_{2})+x_{1}x_{2}} where ⊕ {\displaystyle \oplus } denotes the exclusive disjunctive bit operator. The Boolean mode function S {\displaystyle S} of the table occurs when the number of 1 entries is larger than half of the number of images such that S = { 1 , if ∑ i = 1 n x i ≥ ⌈ n 2 + 1 ⌉ , and n ≥ 3 0 , otherwise {\displaystyle S={\begin{cases}1,&{\text{if }}\sum _{i=1}^{n}x_{i}\geq \left\lceil {\frac {n}{2}}+1\right\rceil ,{\text{ and }}n\geq 3\\0,&{\text{otherwise}}\end{cases}}} For three images, the background image B {\displaystyle B} can be taken as the value x ¯ 1 x 2 x 3 + x 1 x ¯ 2 x 3 + x 1 x 2 x ¯ 3 + x 1 x 2 x 3 {\displaystyle {\bar {x}}_{1}x_{2}x_{3}+x_{1}{\bar {x}}_{2}x_{3}+x_{1}x_{2}{\bar {x}}_{3}+x_{1}x_{2}x_{3}} === Background generation algorithm === At the first level, three frames are selected at random from the image sequence to produce a background image by combining them using the first equation. This yields a better background image at the second level. The procedure is repeated until desired level L {\displaystyle L} . == Theoretical accuracy == At level ℓ {\displaystyle \ell } , the probability p ℓ {\displaystyle p_{\ell }} that the modal bit predicted is the actual modal bit is represented by the equation p ℓ = ( p ℓ − 1 ) 3 + 3 ( p ℓ − 1 ) 2 ( 1 − p ℓ − 1 ) {\displaystyle p_{\ell }=(p_{\ell -1})^{3}+3(p_{\ell -1})^{2}(1-p_{\ell -1})} . The table below gives the computed probability values across several levels using some specific initial probabilities. It can be observed that even if the modal bit at the considered position is at a low 60% of the frames, the probability of accurate modal bit determination is already more than 99% at 6 levels. == Space complexity == The space requirement of the Teknomo–Fernandez algorithm is given by the function O ( R F + R 3 L ) {\displaystyle O(RF+R3^{L})} , depending on the resolution R {\displaystyle R} of the image, the number F {\displaystyle F} of frames in the video, and the desired number L {\displaystyle L} of levels. However, the fact that L {\displaystyle L} will probably not exceed 6 reduces the space complexity to O ( R F ) {\displaystyle O(RF)} . == Time complexity == The entire algorithm runs in O ( R ) {\displaystyle O(R)} -time, only depending on the resolution of the image. Computing the modal bit for each bit can be done in O ( 1 ) {\displaystyle O(1)} -time while the computation of the resulting image from the three given images can be done in O ( R ) {\displaystyle O(R)} -time. The number of the images to be processed in L {\displaystyle L} levels is O ( 3 L ) {\displaystyle O(3^{L})} . However, since L ≤ 6 {\displaystyle L\leq 6} , then this is actually O ( 1 ) {\displaystyle O(1)} , thus the algorithm runs in O ( R ) {\displaystyle O(R)} . == Variants == A variant of the Teknomo–Fernandez algorithm that incorporates the Monte-Carlo method named CRF has been developed. Two different configurations of CRF were implemented: CRF9,2 and CRF81,1. Experiments on some colored video sequences showed that the CRF configurations outperform the TF algorithm in terms of accuracy. However, the TF algorithm remains more efficient in terms of processing time. == Applications == Object detection Face detection Face recognition Pedestrian detection Video surveillance Motion capture Human-computer interaction Content-based video coding Traffic monitoring Real-time gesture recognition
Integrated Operations in the High North
Integrated Operations in the High North (IOHN, IO High North or IO in the High North) is a unique collaboration project that during a four-year period starting May 2008 is working on designing, implementing and testing a Digital Platform for what in the upstream oil and gas industry is called the next or second generation of Integrated Operations. The work on the Digital platform is focussed on capture, transfer and integration of real-time data from the remote production installations to the decision makers. A risk evaluation across the whole chain is also included. The platform is based on open standards and enables a higher degree of interoperability. Requirements for the digital platform come from use cases defined within the Drilling and Completion, Reservoir and Production and Operations and Maintenance domains. The platform will subsequently be demonstrated through pilots within these three domains. The project was a sidecar initiative for Statoil’s Global Operations Data Integration Project. This was part of a very ambitious Master Plan IT (MapIT), which also included the Real Time Visualization (RTV) tender. The RTV tender aimed to be an ontology-aware information workspace for a wide range of disciplines, as per the IO Capability Stack. Additionally, the sidecar project aimed to increase the semantic web knowledge among suppliers in the industry. This new platform is considered an important enabler for safe and sustainable operations in remote, vulnerable and hazardous areas such as the High North, but the technology is clearly also applicable in more general applications. The IOHN project consortium consists of 23 participants, including operators, service providers, software vendors, technology providers, research institutions and universities. In addition, the Norwegian Defence Force is working with the project to resolve common infrastructural and interoperability challenges. The project is managed by Det Norske Veritas (DNV). Nils Sandsmark was the project manager during the initiation and start-up phase. Frédéric Verhelst took over as project manager from the beginning of 2009. Financing comes from the participants and the Research Council of Norway (RCN) for parts of the project (GOICT and AutoConRig). == Participants == The consortium consists of the following 22 participants (in alphabetical order):