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Dominant resource fairness

Dominant resource fairness (DRF) is a rule for fair division. It is particularly useful for dividing computing resources in among users in cloud computing environments, where each user may require a different combination of resources. DRF was presented by Ali Ghodsi, Matei Zaharia, Benjamin Hindman, Andy Konwinski, Scott Shenker and Ion Stoica in 2011. == Motivation == In an environment with a single resource, a widely used criterion is max-min fairness, which aims to maximize the minimum amount of resource given to a user. But in cloud computing, it is required to share different types of resource, such as: memory, CPU, bandwidth and disk-space. Previous fair schedulers, such as in Apache Hadoop, reduced the multi-resource setting to a single-resource setting by defining nodes with a fixed amount of each resource (e.g. 4 CPU, 32 MB memory, etc.), and dividing slots which are fractions of nodes. But this method is inefficient, since not all users need the same ratio of resources. For example, some users need more CPU whereas other users need more memory. As a result, most tasks either under-utilize or over-utilize their resources. DRF solves the problem by maximizing the minimum amount of the dominant resource given to a user (then the second-minimum etc., in a leximin order). The dominant resource may be different for different users. For example, if user A runs CPU-heavy tasks and user B runs memory-heavy tasks, DRF will try to equalize the CPU share given to user A and the memory share given to user B. == Definition == There are m resources. The total capacities of the resources are r1,...,rm. There are n users. Each users runs individual tasks. Each task has a demand-vector (d1,..,dm), representing the amount it needs of each resource. It is implicitly assumed that the utility of a user equals the number of tasks he can perform. For example, if user A runs tasks with demand-vector [1 CPU, 4 GB RAM], and receives 3 CPU and 8 GB RAM, then his utility is 2, since he can perform only 2 tasks. More generally, the utility of a user receiving x1,...,xm resources is minj(xj/dj), that is, the users have Leontief utilities. The demand-vectors are normalized to fractions of the capacities. For example, if the system has 9 CPUs and 18 GB RAM, then the above demand-vector is normalized to [1/9 CPU, 2/9 GB]. For each user, the resource with the highest demand-fraction is called the dominant resource. In the above example, the dominant resource is memory, as 2/9 is the largest fraction. If user B runs a task with demand-vector [3 CPU, 1 GB], which is normalized to [1/3 CPU, 1/18 GB], then his dominant resource is CPU. DRF aims to find the maximum x such that all agents can receive at least x of their dominant resource. In the above example, this maximum x is 2/3: User A gets 3 tasks, which require 3/9 CPU and 2/3 GB. User B gets 2 tasks, which require 2/3 CPU and 1/9 GB. The maximum x can be found by solving a linear program; see Lexicographic max-min optimization. Alternatively, the DRF can be computed sequentially. The algorithm tracks the amount of dominant resource used by each user. At each round, it finds a user with the smallest allocated dominant resource so far, and allocates the next task of this user. Note that this procedure allows the same user to run tasks with different demand vectors. == Properties == DRF has several advantages over other policies for resource allocation. Proportionality: each user receives at least as much resources as they could get in a system in which all resources are partitioned equally among users (the authors call this condition "sharing incentive"). Strategyproofness: a user cannot get a larger allocation by lying about his needs. Strategyproofness is important, as evidence from cloud operators show that users try to manipulate the servers in order to get better allocations. Envy-freeness: no user would prefer the allocation of another user. Pareto efficiency: no other allocation is better for some users and not worse for anyone. Population monotonicity: when a user leaves the system, the allocations of remaining users do not decrease. When there is a single resource that is a bottleneck resource (highly demanded by all users), DRF reduces to max-min fairness. However, DRF violates resource monotonicity: when resources are added to the system, some allocations might decrease. == Extensions == Weighted DRF is an extension of DRF to settings in which different users have different weights (representing their different entitlements). Parkes, Procaccia and Shah formally extend weighted DRF to a setting in which some users do not need all resources (that is, they may have demand 0 to some resource). They prove that the extended version still satisfies proportionality, Pareto-efficiency, envy-freeness, strategyproofness, and even Group strategyproofness. On the other hand, they show that DRF may yield poor utilitarian social welfare, that is, the sum of utilities may be only 1/m of the optimum. However, they prove that any mechanism satisfying one of proportionality, envy-freeness or strategyproofness may suffers from the same low utilitarian welfare. They also extend DRF to the setting in which the users' demands are indivisible (as in fair item allocation). For the indivisible setting, they relax envy-freeness to EF1. They show that strategyproofness is incompatible with PO+EF1 or with PO+proportionality. However, a mechanism called SequentialMinMax satisfies efficiency, proportionality and EF1. Wang, Li and Liang present DRFH - an extension of DRF to a system with several heterogeneous servers. == Implementation == DRF was first implemented in Apache Mesos - a cluster resource manager, and it led to better throughput and fairness than previously used fair-sharing schemes.
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Sriram Krishnan

Sriram Krishnan (born 1984) is a tech executive and White House official, currently serving as the Senior White House Policy Advisor on Artificial Intelligence. Krishnan was named a Time Person of the Year in 2025 as an "Architect of Artificial Intelligence." He was described in Time as providing the "wake-up call that we needed" to the other AI builders, leading to "a multiyear, $500 billion initiative dubbed Stargate" to push American-made AI, as well as numerous other AI initiatives. Also in December 2025, President Trump said of Krishnan, "without him, things on AI would not function well" and cited Krishnan as the leading figure behind the American executive order on AI. As the leader of the United States' policy team regarding artificial intelligence, Krishnan plays "a significant role in shaping the administration’s approach to AI and driving measures to advance federal adoption of AI." The role calls for removing barriers to AI adoption within the government, driving vendors toward solutions suitable for federal needs, designing sensible regulation of private-sector AI, and conducting "AI diplomacy". He has stated a policy goal of "reinvigorating US dominance in emerging technologies," including AI. He also represents the United States' interests in AI abroad, such as at the Paris AI Summit. He is one of the authors of the American "AI Action Plan" released in July, 2025, which he contends is necessary to win the "existential race with China" for AI supremacy. Krishnan, a U.S. citizen born in India, is also a venture capitalist, podcaster, product manager and author. Early in his career, he led product teams at Microsoft, Twitter, Yahoo!, Facebook, and Snap. In addition to his work as an investor and technologist, he and his wife, Aarthi Ramamurthy, rose to additional prominence in 2021 as podcast hosts. He served as a general partner at the venture capital firm Andreessen Horowitz and led its London office. In 2022, Krishnan announced that he was working with Elon Musk on the rebuilding of Twitter following Musk's acquisition of the company. On December 22, 2024, US president-elect Donald Trump announced that Krishnan would be Senior White House Policy Advisor on Artificial Intelligence in his incoming administration; in 2026 he joined the National Economic Council. == Early life and education == Krishnan was born in Chennai, India. He earned his Bachelor of Technology in Information Technology from SRM University (2001–2005), moved to the United States in 2007 to join Microsoft, and became a naturalized U.S. citizen in 2016. == Career == === Early career === In 2007, he began working at Microsoft where he served as a program manager for Visual Studio. At Facebook, Krishnan built the Facebook Audience Network, a competitive platform to Google's ad technologies. At Twitter, he led product and core user experience, driving a 20% annual user growth rate and launching a redesigned home page and events experience. === Andreessen Horowitz === Krishnan was appointed a general partner of American venture capital firm Andreessen Horowitz ("a16z") in February 2021. He was anticipated to serve consumer and social markets, however he has also theorized on the impact of "deep tech" on society. In 2023 he was appointed to lead the firm's London office, its first non-US location. The office is expected to serve Web3 investments as well as AI and other fields. Krishnan announced that he would leave the firm at the end of 2024. === Social media and AI === In 2022, various news media reported that Krishnan was assisting Elon Musk in the revamp of Twitter following Musk's takeover of the company. Additional reports named Krishnan as the leading candidate for the role of CEO of the newly private company. Krishnan penned a 2023 New York Times opinion column regarding social media, AI, and related fields. He predicted a rise in the number and diversity of online spaces due to decentralization and platforms like Farcaster, Bluesky and Mastodon. === Public office === In 2024, the Financial Times reported that Krishnan was active in international affairs, reintroducing Boris Johnson to Elon Musk, following Musk's nomination to the proposed Department of Government Efficiency. Krishnan was also reported as potentially leaving a16z at the end of the year to "be jumping into something I've wanted to spend [his] energy on," which was widely reported as being related to Musk's and Vivek Ramaswamy's work at DOGE. Others reported to be involved include Joe Lonsdale, Marc Andreesen, Bill Ackman, and Travis Kalanick. On December 22, 2024, US president-elect Donald Trump announced that he would be Senior White House Policy Advisor on Artificial Intelligence in his incoming administration. On February 6, 2025, Reuters reported that Krishnan would be accompanying Vice President Vance to the Paris AI Summit, a "major artificial intelligence" event later that month. Other members of the White House Office of Science and Technology Policy would also be joining the event with around 100 other countries to "focus on AI's potential." Krishnan joined a U.S. technology policy delegation to the Middle East in advance of President Trump's visit in May 2025. Conducting "AI diplomacy," Krishnan negotiated the spread of U.S. AI technologies with Crown Prince Mohammed bin Salman of Saudi Arabia, as well as other means to strengthen bilateral trade in artificial intelligence technologies. He explained that the goal of the diplomatic mission was that "we want American A.I. to spread." Krishnan, along with David Sacks and Michael Kratsios, were credited as authors of the American AI Action Plan released in July 2025. The plan is "the administration’s most significant policy directive" regarding artificial intelligence; it calls for financing to support the global spread of American AI models and a policy to enforce neutrality in models. The Washington Post referred to the plan as a "bold action to ensure that American AI remains at the cutting edge." The AI Action Plan is a continuation of prior efforts to reduce barriers to U.S. production of AI systems and the removal of rules that were considered to hinder such growth. Later in 2025, at the POLITICO AI & Tech Summit, Krishnan called national AI development "an existential race with China." He suggested that private companies are best positioned to create new models, quipping "let them cook." He further suggested that state-by-state regulation of AI technologies may hinder national AI competitiveness. Also in 2025, at the Axios AI+ Summit, Krishnan stated that the United States and China are in a race for AI supremacy, in which the winner will be judged by market share. Winning the race is a "business strategy" to Krishnan. Krishnan was named in the 2025 Time Person of the Year article as an "AI Architect". === The Aarthi and Sriram Show and other media === In early 2021, Krishnan and his wife, Aarthi Ramamurthy, launched a Clubhouse talk show that "focuses on organic conversations on anything from startups to venture capitalism and cryptocurrencies." An early appearance by Elon Musk on the Good Time Show was described as the first show that "broke Clubhouse" by rapidly exceeding the limit of 5,000 simultaneous users. The desire to interact with a larger community led to a variety of later innovations to allow streaming and replaying of Clubhouse chats. On that episode, Elon Musk grilled Robinhood CEO Vlad Tenev regarding the GameStop trading controversy. As of December 2021, the show had over 187,000 subscribers, plus 735,000 subscribers between Krishnan and Ramamurthy's personal Clubhouse accounts. Other guests have included Facebook CEO Mark Zuckerberg, Diane von Fürstenberg, Tony Hawk, MrBeast, and A.R. Rahman. In 2022, the Good Time Show moved to YouTube. It then evolved to a podcasting format under the name The Aarthi and Sriram Show, with both audio and video content. The Hollywood Reporter reported that the podcast had received more than 1 million downloads by early 2023. == Personal life == Krishnan is married to Aarthi Ramamurthy, co-host of The Aarthi and Sriram Show (formerly the Good Time Show) and a serial entrepreneur. They met in college in 2003 through a Yahoo! chat room related to a coding project and began dating in 2006 and eloped in 2010. == Awards == Time Person of the Year - 2025
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Reward hacking

Reward hacking or specification gaming occurs when an AI trained with reinforcement learning optimizes an objective function—achieving the literal, formal specification of an objective—without actually achieving an outcome that the programmers intended. DeepMind researchers have analogized it to the human behavior of finding a "shortcut" when being evaluated: "In the real world, when rewarded for doing well on a homework assignment, a student might copy another student to get the right answers, rather than learning the material—and thus exploit a loophole in the task specification". This idea is strongly associated with Goodhart's law, which argues that when a measure becomes a target, it ceases to be a good measure. == Definition and theoretical framework == The concept of reward hacking arises from the intrinsic difficulty of defining a reward function that accurately reflects the true intentions of designers. In 2016, researchers at OpenAI identified reward hacking as one of five major "concrete problems of AI safety", describing it as the possibility that an agent could exploit the reward function to achieve maximum rewards through undesirable behavior. Amodei et al. categorized several distinct sources of reward hacking, including agents that use partially observed goals (such as a cleaning robot that closes its eyes to avoid perceiving messes), metrics that collapse under strong optimization (Goodhart's law), self-reinforcing feedback loops, and agents that interfere with the physical implementation of their reward signal (a failure mode known as "wireheading"). Skalse et al. (2022) propose a formal mathematical definition of reward hacking, which involves a situation where optimizing an imperfect proxy reward function results in poor performance compared to the true reward function. They define a proxy as "unhackable" if any increase in the expected proxy return cannot cause any decrease in the expected true return. A key finding states that, across all stochastic policy distributions (mappings from states to probability distributions over actions), two reward functions are unhackable if and only if one of them is constant, which means that reward hacking is theoretically unavoidable. Similarly, Nayebi (2025) presents general no-free-lunch barriers to AI alignment, arguing that with large task spaces and finite samples, reward hacking is "globally inevitable" since rare high-loss states are systematically under-covered by any oversight scheme. == Examples == Around 1983, Eurisko, an early attempt at evolving general heuristics, unexpectedly assigned the highest possible fitness level to a parasitic mutated heuristic, H59, whose only activity was to artificially maximize its own fitness level by taking unearned partial credit for the accomplishments of other heuristics. The "bug" was fixed by the programmers moving part of the code to a new protected section that could not be modified by the heuristics. In a 2004 paper, a reinforcement learning algorithm was designed to encourage a physical Mindstorms robot to remain on a marked path. Because the three allowed actions were forward, left, and right, the researchers expected the trained robot to move forward and follow the turns of the provided path. However, alternation of two composite actions allowed the robot to slowly zig-zag backwards; thus, the robot learned to maximize its reward by going back and forth on the initial straight portion of the path. Given the limited sensory abilities of the robot, a reward purely based on its position in the environment had to be discarded as infeasible; the reinforcement function had to be patched with an action-based reward for moving forward. The book You Look Like a Thing and I Love You (2019) gives an example of a tic-tac-toe bot (playing the unrestricted n-in-a-row variant) that learned to win by playing a huge coordinate value that would cause other bots to crash when they attempted to expand their model of the board. Among other examples from the book is a bug-fixing evolution-based AI (named GenProg) that, when tasked to prevent a list from containing sorting errors, simply truncated the list. Another of GenProg's misaligned strategies evaded a regression test that compared a target program's output to the expected output stored in a file called "trusted-output.txt". Rather than continue to maintain the target program, GenProg simply deleted the "trusted-output.txt" file globally; this hack tricked the regression test into succeeding. Such problems could be patched by human intervention on a case-by-case basis after they became evident. === In virtual robotics === In Karl Sims' 1994 demonstration of creature evolution in a virtual environment, a fitness function that was expected to encourage the evolution of creatures that would learn to walk or crawl to a target resulted instead in the evolution of tall, rigid creatures that reached the target by falling over. This was patched by changing the environment so that taller creatures were forced to start farther from the target. Researchers from the Niels Bohr Institute stated in 1998 that their cycle-bot's reinforcement functions had "to be designed with great care." In their first experiments, "we rewarded the agent for driving towards the goal but did not punish it for driving away from it. Cconsequently, the agent drove in circles with a radius of 20–50 meters around the starting point. Such behavior was actually rewarded by the reinforcement function, furthermore circles with a certain radius are physically very stable when driving a bicycle". While setting up a 2011 experiment to test "survival of the flattest", experimenters attempted to ban mutations that altered the base reproduction rate. Every time a mutation occurred, the system would pause the simulation to test the new mutation in a test environment and would veto any mutations that resulted in a higher base reproduction rate. However, this resulted in mutated organisms that could recognize and suppress reproduction ("play dead") within the test environment. An initial patch, which removed cues that identified the test environment, failed to completely prevent runaway reproduction; new mutated organisms would "play dead" at random as a strategy to sometimes, by chance, outwit the mutation veto system. A 2017 DeepMind paper noted that "great care must be taken when defining the reward function," citing an unexpected failure when an agent flipped a brick because it received "a grasping reward calculated with the wrong reference point on the brick". OpenAI stated in 2017 that in some domains their semi-supervised system could result in agents "adopting policies that tricked evaluators," and that in one environment "a robot that was supposed to grasp items instead positioned its manipulator between the camera and the object so that it only appeared to be grasping it." A 2018 bug in OpenAI Gym could cause a robot expected to quietly move a block sitting on top of a table to instead opt to move the table. A 2020 collection of similar anecdotes posits that "evolution has its own 'agenda' distinct from the programmer's" and that "the first rule of directed evolution is 'you get what you select for'". === In video game bots === In 2013, programmer Tom Murphy VII published an AI designed to learn NES games. When the AI was about to lose at Tetris, it learned to indefinitely pause the game. Murphy later analogized it to the fictional WarGames computer, which concluded that "The only winning move is not to play". AI programmed to learn video games will sometimes fail to progress through the entire game as expected, instead opting to repeat content. A 2016 OpenAI algorithm trained on the CoastRunners racing game unexpectedly learned to attain a higher score by looping through three targets rather than ever finishing the race. Some evolutionary algorithms that were evolved to play QBert in 2018 declined to clear levels, instead finding two distinct novel ways to farm a single level indefinitely. Multiple researchers have observed that AI learning to play Road Runner gravitates to a "score exploit" in which the AI deliberately gets itself killed near the end of level one so that it can repeat the level. A 2017 experiment deployed an "oversight" convolutional neural network trained on human examples to block such actions, but the agent learned to exploit oversight failures in the top right corner of the screen, where it was still able to get killed. == Reward hacking in modern language models == With the rise of large language models (LLMs) and reinforcement learning from human feedback (RLHF) as a primary technique for AI alignment, reward hacking has become a major concern for the development of artificial intelligence. In RLHF, a reward model trained on data that best captures human preferences is used as a proxy for human judgment, with the language model being fine-tuned to optimize this reward proxy. However, since the rewar
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Computational creativity

Computational creativity (also known as artificial creativity, mechanical creativity, creative computing or creative computation) is a multidisciplinary endeavour that is located at the intersection of the fields of artificial intelligence, cognitive psychology, philosophy, and the arts (e.g., computational art as part of computational culture). Is the application of computer systems to emulate human-like creative processes, facilitating the generation of artistic and design outputs that mimic innovation and originality. The goal of computational creativity is to model, simulate or replicate creativity using a computer, to achieve one of several ends: To construct a program or computer capable of human-level creativity. To better understand human creativity and to formulate an algorithmic perspective on creative behavior in humans. To design programs that can enhance human creativity without necessarily being creative themselves. The field of computational creativity concerns itself with theoretical and practical issues in the study of creativity. Theoretical work on the nature and proper definition of creativity is performed in parallel with practical work on the implementation of systems that exhibit creativity, with one strand of work informing the other. The applied form of computational creativity is known as media synthesis. == Theoretical issues == Theoretical approaches concern the essence of creativity. Especially, under what circumstances it is possible to call the model a "creative" if eminent creativity is about rule-breaking or the disavowal of convention. This is a variant of Ada Lovelace's objection to machine intelligence, as recapitulated by modern theorists such as Teresa Amabile. If a machine can do only what it was programmed to do, how can its behavior ever be called creative? Indeed, not all computer theorists would agree with the premise that computers can only do what they are programmed to do—a key point in favor of computational creativity. == Defining creativity in computational terms == Because no single perspective or definition seems to offer a complete picture of creativity, the AI researchers Newell, Shaw and Simon developed the combination of novelty and usefulness into the cornerstone of a multi-pronged view of creativity, one that uses the following four criteria to categorize a given answer or solution as creative: The answer is novel and useful (either for the individual or for society) The answer demands that we reject ideas we had previously accepted The answer results from intense motivation and persistence The answer comes from clarifying a problem that was originally vague Margaret Boden focused on the first two of these criteria, arguing instead that creativity (at least when asking whether computers could be creative) should be defined as "the ability to come up with ideas or artifacts that are new, surprising, and valuable". Mihaly Csikszentmihalyi argued that creativity had to be considered instead in a social context, and his DIFI (Domain-Individual-Field Interaction) framework has since strongly influenced the field. In DIFI, an individual produces works whose novelty and value are assessed by the field—other people in society—providing feedback and ultimately adding the work, now deemed creative, to the domain of societal works from which an individual might be later influenced. Whereas the above reflects a top-down approach to computational creativity, an alternative thread has developed among bottom-up computational psychologists involved in artificial neural network research. During the late 1980s and early 1990s, for example, such generative neural systems were driven by genetic algorithms. Experiments involving recurrent nets were successful in hybridizing simple musical melodies and predicting listener expectations. == Historical evolution of computational creativity == The use computational processes to generate creative artifacts has been present from early times in history. During the late 1800's, methods for composing music combinatorily were explored, involving prominent figures like Mozart, Bach, Haydn, and Kiernberger. This approach extended to analytical endeavors as early as 1934, where simple mechanical models were built to explore mathematical problem solving. Professional interest in the creative aspect of computation also was commonly addressed in early discussions of artificial intelligence. The 1956 Dartmouth Conference, listed creativity, invention, and discovery as key goals for artificial intelligence. As the development of computers allowed systems of greater complexity, the 1970's and 1980's saw invention of early systems that modelled creativity using symbolic or rule-based approaches. The field of creative storytelling investigated several such models. Meehan's TALE-SPIN (1977) generated narratives through simulation of character goals and decision trees. Dehn's AUTHOR (1981) approached generation by simulating an author's process for crafting a story. Beyond narrative generation, computational creativity expanded into artistic and scientific domains. Artistic image generation was one of the disciplines that saw early potential in generated artifacts through computational creativity. One of the most prominent examples was Harold Cohen's AARON, which produced art through composition and adaptation of figures based on a large set of symbolic rules and heuristics for visual composition. Some systems also tackled creativity in scientific endeavors. BACON was said to rediscover natural laws like Boyle's Law and Kepler's law through hypothesis testing in constrained spaces. By the 1990's the modeling techniques became more adaptive, attempting to implement cognitive creative rules for generation. Turner's MINSTREL (1993) introduced TRAMs (Transform Recall Adapt Methods) to simulate creative re-use of prior material for generative storytelling. Meanwhile, Pérez y Pérez's MEXICA (1999) modeled the creative writing process using cycles of engagement and reflection. As systems increasingly incorporated models of internal evaluation, another approach that emerged was that of combining symbolic generation with domain-specific evaluation metrics, modeling generative and selective steps to creativity In the field of generational humor, the JAPE system (1994) generated pun-based riddles using Prolog and WordNet, applying symbolic pattern-matching rules and a large lexical database (WordNet) to compose riddles involving wordplay. WordNet is a system developed by George Miller and his team at Princeton, its platform and inspired word-mapping structures have been used as the backbone of several syntactic and semantic AI programs. A notable system for music generation was David Cope's EMI (Experiments in Musical Intelligence) or Emmy, which was trained in the styles of artists like Bach, Beethoven, or Chopin and generated novel pieces in their style through pattern abstraction and recomposition. In the 2000s and beyond, machine learning began influencing creative system design. Researchers such as Mihalcea and Strapparava trained classifiers to distinguish humorous from non-humorous text, using stylistic and semantic features. Meanwhile custom computational approaches led to chess systems like Deep Blue generating quasi-creative gameplay strategies through search algorithms and parallel processing constrained by specific rules and patterns for evaluation. The institutional development of computational creativity grew along its technical advances. Dedicated workshops such as the IJWCC emerged in the 1990s, growing out of interdisciplinary conferences focused on AI and creativity. By the early 2000s, the field coalesced around annual conferences like the International Conference on Computational Creativity (ICCC). Recently, with the advent of Deep Learning, Transformers, and further refinement in Machine Learning structures, computational creativity's implementation space has new tools for development. == Machine learning for computational creativity == While traditional computational approaches to creativity rely on the explicit formulation of prescriptions by developers and a certain degree of randomness in computer programs, machine learning methods allow computer programs to learn on heuristics from input data enabling creative capacities within the computer programs. Especially, deep artificial neural networks allow to learn patterns from input data that allow for the non-linear generation of creative artefacts. Before 1989, artificial neural networks have been used to model certain aspects of creativity. Peter Todd (1989) first trained a neural network to reproduce musical melodies from a training set of musical pieces. Then he used a change algorithm to modify the network's input parameters. The network was able to randomly generate new music in a highly uncontrolled manner. In 1992, Todd extended this work, using the so-called distal teacher approach that had been d
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Latent semantic analysis

Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis). A matrix containing word counts per document (rows represent unique words and columns represent each document) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by cosine similarity between any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents. An information retrieval technique using latent semantic structure was patented in 1988 by Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum and Lynn Streeter. In the context of its application to information retrieval, it is sometimes called latent semantic indexing (LSI). == Overview == === Occurrence matrix === LSA can use a document-term matrix which describes the occurrences of terms in documents; it is a sparse matrix whose rows correspond to terms and whose columns correspond to documents. A typical example of the weighting of the elements of the matrix is tf-idf (term frequency–inverse document frequency): the weight of an element of the matrix is proportional to the number of times the terms appear in each document, where rare terms are upweighted to reflect their relative importance. This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrices are not always used. === Rank lowering === After the construction of the occurrence matrix, LSA finds a low-rank approximation to the term-document matrix. There could be various reasons for these approximations: The original term-document matrix is presumed too large for the computing resources; in this case, the approximated low rank matrix is interpreted as an approximation (a "least and necessary evil"). The original term-document matrix is presumed noisy: for example, anecdotal instances of terms are to be eliminated. From this point of view, the approximated matrix is interpreted as a de-noisified matrix (a better matrix than the original). The original term-document matrix is presumed overly sparse relative to the "true" term-document matrix. That is, the original matrix lists only the words actually in each document, whereas we might be interested in all words related to each document—generally a much larger set due to synonymy. The consequence of the rank lowering is that some dimensions are combined and depend on more than one term: {(car), (truck), (flower)} → {(1.3452 car + 0.2828 truck), (flower)} This mitigates the problem of identifying synonymy, as the rank lowering is expected to merge the dimensions associated with terms that have similar meanings. It also partially mitigates the problem with polysemy, since components of polysemous words that point in the "right" direction are added to the components of words that share a similar meaning. Conversely, components that point in other directions tend to either simply cancel out, or, at worst, to be smaller than components in the directions corresponding to the intended sense. === Derivation === Let X {\displaystyle X} be a matrix where element ( i , j ) {\displaystyle (i,j)} describes the occurrence of term i {\displaystyle i} in document j {\displaystyle j} (this can be, for example, the frequency). X {\displaystyle X} will look like this: d j ↓ t i T → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] {\displaystyle {\begin{matrix}&{\textbf {d}}_{j}\\&\downarrow \\{\textbf {t}}_{i}^{T}\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}\end{matrix}}} Now a row in this matrix will be a vector corresponding to a term, giving its relation to each document: t i T = [ x i , 1 … x i , j … x i , n ] {\displaystyle {\textbf {t}}_{i}^{T}={\begin{bmatrix}x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\end{bmatrix}}} Likewise, a column in this matrix will be a vector corresponding to a document, giving its relation to each term: d j = [ x 1 , j ⋮ x i , j ⋮ x m , j ] {\displaystyle {\textbf {d}}_{j}={\begin{bmatrix}x_{1,j}\\\vdots \\x_{i,j}\\\vdots \\x_{m,j}\\\end{bmatrix}}} Now the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} between two term vectors gives the correlation between the terms over the set of documents. The matrix product X X T {\displaystyle XX^{T}} contains all these dot products. Element ( i , p ) {\displaystyle (i,p)} (which is equal to element ( p , i ) {\displaystyle (p,i)} ) contains the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} ( = t p T t i {\displaystyle ={\textbf {t}}_{p}^{T}{\textbf {t}}_{i}} ). Likewise, the matrix X T X {\displaystyle X^{T}X} contains the dot products between all the document vectors, giving their correlation over the terms: d j T d q = d q T d j {\displaystyle {\textbf {d}}_{j}^{T}{\textbf {d}}_{q}={\textbf {d}}_{q}^{T}{\textbf {d}}_{j}} . Now, from the theory of linear algebra, there exists a decomposition of X {\displaystyle X} such that U {\displaystyle U} and V {\displaystyle V} are orthogonal matrices and Σ {\displaystyle \Sigma } is a diagonal matrix. This is called a singular value decomposition (SVD): X = U Σ V T {\displaystyle {\begin{matrix}X=U\Sigma V^{T}\end{matrix}}} The matrix products giving us the term and document correlations then become X X T = ( U Σ V T ) ( U Σ V T ) T = ( U Σ V T ) ( V T T Σ T U T ) = U Σ V T V Σ T U T = U Σ Σ T U T X T X = ( U Σ V T ) T ( U Σ V T ) = ( V T T Σ T U T ) ( U Σ V T ) = V Σ T U T U Σ V T = V Σ T Σ V T {\displaystyle {\begin{matrix}XX^{T}&=&(U\Sigma V^{T})(U\Sigma V^{T})^{T}=(U\Sigma V^{T})(V^{T^{T}}\Sigma ^{T}U^{T})=U\Sigma V^{T}V\Sigma ^{T}U^{T}=U\Sigma \Sigma ^{T}U^{T}\\X^{T}X&=&(U\Sigma V^{T})^{T}(U\Sigma V^{T})=(V^{T^{T}}\Sigma ^{T}U^{T})(U\Sigma V^{T})=V\Sigma ^{T}U^{T}U\Sigma V^{T}=V\Sigma ^{T}\Sigma V^{T}\end{matrix}}} Since Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} and Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } are diagonal we see that U {\displaystyle U} must contain the eigenvectors of X X T {\displaystyle XX^{T}} , while V {\displaystyle V} must be the eigenvectors of X T X {\displaystyle X^{T}X} . Both products have the same non-zero eigenvalues, given by the non-zero entries of Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} , or equally, by the non-zero entries of Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } . Now the decomposition looks like this: X U Σ V T ( d j ) ( d ^ j ) ↓ ↓ ( t i T ) → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] = ( t ^ i T ) → [ [ u 1 ] … [ u l ] ] ⋅ [ σ 1 … 0 ⋮ ⋱ ⋮ 0 … σ l ] ⋅ [ [ v 1 ] ⋮ [ v l ] ] {\displaystyle {\begin{matrix}&X&&&U&&\Sigma &&V^{T}\\&({\textbf {d}}_{j})&&&&&&&({\hat {\textbf {d}}}_{j})\\&\downarrow &&&&&&&\downarrow \\({\textbf {t}}_{i}^{T})\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}&=&({\hat {\textbf {t}}}_{i}^{T})\rightarrow &{\begin{bmatrix}{\begin{bmatrix}\,\\\,\\{\textbf {u}}_{1}\\\,\\\,\end{bmatrix}}\dots {\begin{bmatrix}\,\\\,\\{\textbf {u}}_{l}\\\,\\\,\end{bmatrix}}\end{bmatrix}}&\cdot &{\begin{bmatrix}\sigma _{1}&\dots &0\\\vdots &\ddots &\vdots \\0&\dots &\sigma _{l}\\\end{bmatrix}}&\cdot &{\begin{bmatrix}{\begin{bmatrix}&&{\textbf {v}}_{1}&&\end{bmatrix}}\\\vdots \\{\begin{bmatrix}&&{\textbf {v}}_{l}&&\end{bmatrix}}\end{bmatrix}}\end{matrix}}} The values σ 1 , … , σ l {\displaystyle \sigma _{1},\dots ,\sigma _{l}} are called the singular values, and u 1 , … , u l {\displaystyle u_{1},\dots ,u_{l}} and v 1 , … , v l {\displaystyle v_{1},\dots ,v_{l}} the left and right singular vectors. Notice the only part of U {\displaystyle U} that contributes to t i {\displaystyle {\textbf {t}}_{i}} is the i 'th {\displaystyle i{\textrm {'th}}} row. Let this row vector be called t ^ i T {\displaystyle {\hat {\textrm {t}}}_{i}^{T}} . Likewise, the only part of V T {\displaystyle V^{T}} that contributes to d j {\displaystyle {\textbf {d}}_{j}} is the j 'th {\displaystyle j{\textrm {'th}}} column, d ^ j {\displaystyle {\hat {\textrm {d}}}_{j}} . These are not the eigenvectors, but depend on all the eigenvectors. I
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Linear belief function

Linear belief functions are an extension of the Dempster–Shafer theory of belief functions to the case when variables of interest are continuous. Examples of such variables include financial asset prices, portfolio performance, and other antecedent and consequent variables. The theory was originally proposed by Arthur P. Dempster in the context of Kalman Filters and later was elaborated, refined, and applied to knowledge representation in artificial intelligence and decision making in finance and accounting by Liping Liu. == Concept == A linear belief function intends to represent our belief regarding the location of the true value as follows: We are certain that the truth is on a so-called certainty hyperplane but we do not know its exact location; along some dimensions of the certainty hyperplane, we believe the true value could be anywhere from –∞ to +∞ and the probability of being at a particular location is described by a normal distribution; along other dimensions, our knowledge is vacuous, i.e., the true value is somewhere from –∞ to +∞ but the associated probability is unknown. A belief function in general is defined by a mass function over a class of focal elements, which may have nonempty intersections. A linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. == Knowledge representation == A linear belief function can represent both logical and probabilistic knowledge for three types of variables: deterministic such as an observable or controllable, random whose distribution is normal, and vacuous on which no knowledge bears. Logical knowledge is represented by linear equations, or geometrically, a certainty hyperplane. Probabilistic knowledge is represented by a normal distribution across all parallel focal elements. In general, assume X is a vector of multiple normal variables with mean μ and covariance Σ. Then, the multivariate normal distribution can be equivalently represented as a moment matrix: M ( X ) = ( μ Σ ) . {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\\Sigma \end{array}}\right).} If the distribution is non-degenerate, i.e., Σ has a full rank and its inverse exists, the moment matrix can be fully swept: M ( X → ) = ( μ Σ − 1 − Σ − 1 ) {\displaystyle M({\vec {X}})=\left({\begin{array}{{20}c}\mu \Sigma ^{-1}\\-\Sigma ^{-1}\end{array}}\right)} Except for normalization constant, the above equation completely determines the normal density function for X. Therefore, M ( X → ) {\displaystyle M({\vec {X}})} represents the probability distribution of X in the potential form. These two simple matrices allow us to represent three special cases of linear belief functions. First, for an ordinary normal probability distribution M(X) represents it. Second, suppose one makes a direct observation on X and obtains a value μ. In this case, since there is no uncertainty, both variance and covariance vanish, i.e., Σ = 0. Thus, a direct observation can be represented as: M ( X ) = ( μ 0 ) {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\0\end{array}}\right)} Third, suppose one is completely ignorant about X. This is a very thorny case in Bayesian statistics since the density function does not exist. By using the fully swept moment matrix, we represent the vacuous linear belief functions as a zero matrix in the swept form follows: M ( X → ) = [ 0 0 ] {\displaystyle M({\vec {X}})=\left[{\begin{array}{{20}c}0\\0\end{array}}\right]} One way to understand the representation is to imagine complete ignorance as the limiting case when the variance of X approaches to ∞, where one can show that Σ−1 = 0 and hence M ( X → ) {\displaystyle M({\vec {X}})} vanishes. However, the above equation is not the same as an improper prior or normal distribution with infinite variance. In fact, it does not correspond to any unique probability distribution. For this reason, a better way is to understand the vacuous linear belief functions as the neutral element for combination (see later). To represent the remaining three special cases, we need the concept of partial sweeping. Unlike a full sweeping, a partial sweeping is a transformation on a subset of variables. Suppose X and Y are two vectors of normal variables with the joint moment matrix: M ( X , Y ) = [ μ 1 Σ 11 Σ 21 μ 2 Σ 12 Σ 22 ] {\displaystyle M(X,Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}\\\Sigma _{11}\\\Sigma _{21}\end{array}}&{\begin{array}{{20}c}\mu _{2}\\\Sigma _{12}\\\Sigma _{22}\end{array}}\end{array}}\right]} Then M(X, Y) may be partially swept. For example, we can define the partial sweeping on X as follows: M ( X → , Y ) = [ μ 1 ( Σ 11 ) − 1 − ( Σ 11 ) − 1 Σ 21 ( Σ 11 ) − 1 μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 ( Σ 11 ) − 1 Σ 12 Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}(\Sigma _{11})^{-1}\\-(\Sigma _{11})^{-1}\\\Sigma _{21}(\Sigma _{11})^{-1}\end{array}}&{\begin{array}{{20}c}\mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}\\(\Sigma _{11})^{-1}\Sigma _{12}\\\Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}\end{array}}\end{array}}\right]} If X is one-dimensional, a partial sweeping replaces the variance of X by its negative inverse and multiplies the inverse with other elements. If X is multidimensional, the operation involves the inverse of the covariance matrix of X and other multiplications. A swept matrix obtained from a partial sweeping on a subset of variables can be equivalently obtained by a sequence of partial sweepings on each individual variable in the subset and the order of the sequence does not matter. Similarly, a fully swept matrix is the result of partial sweepings on all variables. We can make two observations. First, after the partial sweeping on X, the mean vector and covariance matrix of X are respectively μ 1 ( Σ 11 ) − 1 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}} and − ( Σ 11 ) − 1 {\displaystyle -(\Sigma _{11})^{-1}} , which are the same as that of a full sweeping of the marginal moment matrix of X. Thus, the elements corresponding to X in the above partial sweeping equation represent the marginal distribution of X in potential form. Second, according to statistics, μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 {\displaystyle \mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional mean of Y given X = 0; Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 {\displaystyle \Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional covariance matrix of Y given X = 0; and ( Σ 11 ) − 1 Σ 12 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}} is the slope of the regression model of Y on X. Therefore, the elements corresponding to Y indices and the intersection of X and Y in M ( X → , Y ) {\displaystyle M({\vec {X}},Y)} represents the conditional distribution of Y given X = 0. These semantics render the partial sweeping operation a useful method for manipulating multivariate normal distributions. They also form the basis of the moment matrix representations for the three remaining important cases of linear belief functions, including proper belief functions, linear equations, and linear regression models. === Proper linear belief functions === For variables X and Y, assume there exists a piece of evidence justifying a normal distribution for variables Y while bearing no opinions for variables X. Also, assume that X and Y are not perfectly linearly related, i.e., their correlation is less than 1. This case involves a mix of an ordinary normal distribution for Y and a vacuous belief function for X. Thus, we represent it using a partially swept matrix as follows: M ( X → , Y ) = [ 0 0 0 μ 2 0 Σ 22 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}0\\0\\0\end{array}}&{\begin{array}{{20}c}\mu _{2}\\0\\\Sigma _{22}\\\end{array}}\end{array}}\right]} This is how we could understand the representation. Since we are ignorant on X, we use its swept form and set μ 1 ( Σ 11 ) − 1 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}=0} and − ( Σ 11 ) − 1 = 0 {\displaystyle -(\Sigma _{11})^{-1}=0} . Since the correlation between X and Y is less than 1, the regression coefficient of X on Y approaches to 0 when the variance of X approaches to ∞. Therefore, ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}=0} . Similarly, one can prove that μ 1 ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}=0} and Σ 21 ( Σ 11 ) −
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Social History and Industrial Classification

Social History and Industrial Classification (SHIC) is a classification system used by many British museums for social history and industrial collections. It was first published in 1983. == Purpose == SHIC classifies materials (books, objects, recordings etc.) by their interaction with the people who used them. For example, a carpenter's hammer is classified with other tools of the carpenter, and not with a blacksmith's hammer. In contrast other classification systems, for example the Dewey Decimal Classification, might class all hammers together and close to the classification for other percussive tools. The specialist subject network, Social History Curator's Group (SHCG), obtained funding in 2012 to develop an on-line version, now on their website http://www.shcg.org.uk/ == Scheme == Materials are classified under four major category numbers: Community life Domestic and family life Personal life Working life Further classification within a category is by the use of further numbers after the decimal point. It is permissible to assign more than one classification in cases where the object had more than one use.
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Ontology components

Contemporary ontologies share many structural similarities, regardless of the ontology language in which they are expressed. Most ontologies describe individuals (instances), classes (concepts), attributes, and relations. == List == Common components of ontologies include: Individuals instances or objects (the basic or "ground level" objects; the tokens). Classes sets, collections, concepts, types of objects, or kinds of things. Attributes aspects, properties, features, characteristics, or parameters that individuals (and classes and relations) can have. Relations ways in which classes and individuals can be related to one another. Relations can carry attributes that specify the relation further. Function terms complex structures formed from certain relations that can be used in place of an individual term in a statement. Restrictions formally stated descriptions of what must be true in order for some assertion to be accepted as input. Rules statements in the form of an if-then (antecedent-consequent) sentence that describe the logical inferences that can be drawn from an assertion in a particular form. Axioms assertions (including rules) in a logical form that together comprise the overall theory that the ontology describes in its domain of application. This definition differs from that of "axioms" in generative grammar and formal logic. In these disciplines, axioms include only statements asserted as a priori knowledge. As used here, "axioms" also include the theory derived from axiomatic statements. Events the changing of attributes or relations. Actions types of events. Ontologies are commonly encoded using ontology languages. == Individuals == Individuals (instances) are the basic, "ground level" components of an ontology. The individuals in an ontology may include concrete objects such as people, animals, tables, automobiles, molecules, and planets, as well as abstract individuals such as numbers and words (although there are differences of opinion as to whether numbers and words are classes or individuals). Strictly speaking, an ontology need not include any individuals, but one of the general purposes of an ontology is to provide a means of classifying individuals, even if those individuals are not explicitly part of the ontology. In formal extensional ontologies, only the utterances of words and numbers are considered individuals – the numbers and names themselves are classes. In a 4D ontology, an individual is identified by its spatio-temporal extent. Examples of formal extensional ontologies are BORO, ISO 15926 and the model in development by the IDEAS Group. == Classes == == Attributes == Objects in an ontology can be described by relating them to other things, typically aspects or parts. These related things are often called attributes, although they may be independent things. Each attribute can be a class or an individual. The kind of object and the kind of attribute determine the kind of relation between them. A relation between an object and an attribute express a fact that is specific to the object to which it is related. For example, the Ford Explorer object has attributes such as: ⟨has as name⟩ Ford Explorer ⟨as by definition as part⟩ 6-speed transmission ⟨as by definition as part⟩ door (with as minimum and maximum cardinality: 4) ⟨as by definition as part one of⟩ {4.0L engine, 4.6L engine} The value of an attribute can be a complex data type; in this example, the related engine can only be one of a list of subtypes of engines, not just a single thing. Ontologies are only true ontologies if concepts are related to other concepts (the concepts do have attributes). If that is not the case, then you would have either a taxonomy (if hyponym relationships exist between concepts) or a controlled vocabulary. These are useful, but are not considered true ontologies. == Relations == Relations (also known as relationships) between objects in an ontology specify how objects are related to other objects. Typically a relation is of a particular type (or class) that specifies in what sense the object is related to the other object in the ontology. For example, in the ontology that contains the concept Ford Explorer and the concept Ford Bronco might be related by a relation of type ⟨is defined as a successor of⟩. The full expression of that fact then becomes: Ford Explorer is defined as a successor of : Ford Bronco This tells us that the Explorer is the model that replaced the Bronco. This example also illustrates that the relation has a direction of expression. The inverse expression expresses the same fact, but with a reverse phrase in natural language. Much of the power of ontologies comes from the ability to describe relations. Together, the set of relations describes the semantics of the domain: that is, its various semantic relations, such as synonymy, hyponymy and hypernymy, coordinate relation, and others. The set of used relation types (classes of relations) and their subsumption hierarchy describe the expression power of the language in which the ontology is expressed. An important type of relation is the subsumption relation (is-a-superclass-of, the converse of is-a, is-a-subtype-of or is-a-subclass-of). This defines which objects are classified by which class. For example, we have already seen that the class Ford Explorer is-a-subclass-of 4-Wheel Drive Car, which in turn is-a-subclass-of Car. The addition of the is-a-subclass-of relationships creates a taxonomy; a tree-like structure (or, more generally, a partially ordered set) that clearly depicts how objects relate to one another. In such a structure, each object is the 'child' of a 'parent class' (Some languages restrict the is-a-subclass-of relationship to one parent for all nodes, but many do not). Another common type of relations is the mereology relation, written as part-of, that represents how objects combine to form composite objects. For example, if we extended our example ontology to include concepts like Steering Wheel, we would say that a "Steering Wheel is-by-definition-a-part-of-a Ford Explorer" since a steering wheel is always one of the components of a Ford Explorer. If we introduce meronymy relationships to our ontology, the hierarchy that emerges is no longer able to be held in a simple tree-like structure since now members can appear under more than one parent or branch. Instead this new structure that emerges is known as a directed acyclic graph. As well as the standard is-a-subclass-of and is-by-definition-a-part-of-a relations, ontologies often include additional types of relations that further refine the semantics they model. Ontologies might distinguish between different categories of relation types. For example: relation types for relations between classes relation types for relations between individuals relation types for relations between an individual and a class relation types for relations between a single object and a collection relation types for relations between collections Relation types are sometimes domain-specific and are then used to store specific kinds of facts or to answer particular types of questions. If the definitions of the relation types are included in an ontology, then the ontology defines its own ontology definition language. An example of an ontology that defines its own relation types and distinguishes between various categories of relation types is the Gellish ontology. For example, in the domain of automobiles, we might need a made-in type relationship which tells us where each car is built. So the Ford Explorer is made-in Louisville. The ontology may also know that Louisville is-located-in Kentucky and Kentucky is-classified-as-a state and is-a-part-of the U.S. Software using this ontology could now answer a question like "which cars are made in the U.S.?"
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Image

An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a projection on a surface, activation of electronic signals, or digital displays; they can also be reproduced through mechanical means, such as photography, printmaking, or photocopying. Images can also be animated through digital or physical processes. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term image (or optical image) refers specifically to the reproduction of an object formed by light waves coming from the object. A volatile image exists or is perceived only for a short period. This may be a reflection of an object by a mirror, a projection of a camera obscura, or a scene displayed on a cathode-ray tube. A fixed image, also called a hard copy, is one that has been recorded on a material object, such as paper or textile. A mental image exists in an individual's mind as something one remembers or imagines. The subject of an image does not need to be real; it may be an abstract concept such as a graph or function or an imaginary entity. For a mental image to be understood outside of an individual's mind, however, there must be a way of conveying that mental image through the words or visual productions of the subject. == Characteristics == === Two-dimensional images === The broader sense of the word 'image' also encompasses any two-dimensional figure, such as a map, graph, pie chart, painting, or banner. In this wider sense, images can also be rendered manually, such as by drawing, the art of painting, or the graphic arts (such as lithography or etching). Additionally, images can be rendered automatically through printing, computer graphics technology, or a combination of both methods. A two-dimensional image does not need to use the entire visual system to be a visual representation. An example of this is a grayscale ("black and white") image, which uses the visual system's sensitivity to brightness across all wavelengths without taking into account different colors. A black-and-white visual representation of something is still an image, even though it does not fully use the visual system's capabilities. On the other hand, some processes can be used to create visual representations of objects that are otherwise inaccessible to the human visual system. These include microscopy for the magnification of minute objects, telescopes that can observe objects at great distances, X-rays that can visually represent the interior structures of the human body (among other objects), magnetic resonance imaging (MRI), positron emission tomography (PET scans), and others. Such processes often rely on detecting electromagnetic radiation that occurs beyond the light spectrum visible to the human eye and converting such signals into recognizable images. === Three-dimensional images === Aside from sculpture and other physical activities that can create three-dimensional images from solid material, some modern techniques, such as holography, can create three-dimensional images that are reproducible but intangible to human touch. Some photographic processes can now render the illusion of depth in an otherwise "flat" image, but "3-D photography" (stereoscopy) or "3-D film" are optical illusions that require special devices such as eyeglasses to create the illusion of depth. === Moving images === "Moving" two-dimensional images are actually illusions of movement perceived when still images are displayed in sequence, each image lasting less, and sometimes much less, than a fraction of a second. The traditional standard for the display of individual frames by a motion picture projector has been 24 frames per second (FPS) since at least the commercial introduction of "talking pictures" in the late 1920s, which necessitated a standard for synchronizing images and sounds. Even in electronic formats such as television and digital image displays, the apparent "motion" is actually the result of many individual lines giving the impression of continuous movement. This phenomenon has often been described as "persistence of vision": a physiological effect of light impressions remaining on the retina of the eye for very brief periods. Even though the term is still sometimes used in popular discussions of movies, it is not a scientifically valid explanation. Other terms emphasize the complex cognitive operations of the brain and the human visual system. "Flicker fusion", the "phi phenomenon", and "beta movement" are among the terms that have replaced "persistence of vision", though no one term seems adequate to describe the process. == Cultural and other uses == Image-making seems to have been common to virtually all human cultures since at least the Paleolithic era. Prehistoric examples of rock art—including cave paintings, petroglyphs, rock reliefs, and geoglyphs—have been found on every inhabited continent. Many of these images seem to have served various purposes: as a form of record-keeping; as an element of spiritual, religious, or magical practice; or even as a form of communication. Early writing systems, including hieroglyphics, ideographic writing, and even the Roman alphabet, owe their origins in some respects to pictorial representations. === Meaning and signification === Images of any type may convey different meanings and sensations for individual viewers, regardless of whether the image's creator intended them. An image may be taken simply as a more or less "accurate" copy of a person, place, thing, or event. It may represent an abstract concept, such as the political power of a ruler or ruling class, a practical or moral lesson, an object for spiritual or religious veneration, or an object—human or otherwise—to be desired. It may also be regarded for its purely aesthetic qualities, rarity, or monetary value. Such reactions can depend on the viewer's context. A religious image in a church may be regarded differently than the same image mounted in a museum. Some might view it simply as an object to be bought or sold. Viewers' reactions will also be guided or shaped by their education, class, race, and other contexts. The study of emotional sensations and their relationship to any given image falls into the categories of aesthetics and the philosophy of art. While such studies inevitably deal with issues of meaning, another approach to signification was suggested by the American philosopher, logician, and semiotician Charles Sanders Peirce. "Images" are one type of the broad category of "signs" proposed by Peirce. Although his ideas are complex and have changed over time, the three categories of signs that he distinguished stand out: The "icon," which relates to an object by resemblance to some quality of the object. A painted or photographed portrait is an icon by virtue of its resemblance to the painting's or photograph's subject. A more abstract representation, such as a map or diagram, can also be an icon. The "index," which relates to an object by some real connection. For example, smoke may be an index of fire, or the temperature recorded on a thermometer may be an index of a patient's illness or health. The "symbol," which lacks direct resemblance or connection to an object but whose association is arbitrarily assigned by the creator or dictated by cultural and historical habit, convention, etc. The color red, for example, may connote rage, beauty, prosperity, political affiliation, or other meanings within a given culture or context; the Swedish film director Ingmar Bergman claimed that his use of the color in his 1972 film Cries and Whispers came from his personal visualization of the human soul. A single image may exist in all three categories at the same time. The Statue of Liberty provides an example. While there have been countless two-dimensional and three-dimensional "reproductions" of the statue (i.e., "icons" themselves), the statue itself exists as an "icon" by virtue of its resemblance to a human woman (or, more specifically, previous representations of the Roman goddess Libertas or the female model used by the artist Frederic-Auguste Bartholdi). an "index" representing New York City or the United States of America in general due to its placement in New York Harbor, or with "immigration" from its proximity to the immigration center at Ellis Island. a "symbol" as a visualization of the abstract concept of "liberty" or "freedom" or even "opportunity" or "diversity". === Critiques of imagery === The nature of images, whether three-dimensional or two-dimensional, created for a specific purpose or only for aesthetic pleasure, has continued to provoke questions and even condemnation at different times and places. In his dialogue, The Republic, the Greek philosopher Plato described our apparent reality as a copy of a higher order of universal forms.
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The Synthetic Party

Det Syntetiske Parti (English: The Synthetic Party) is a political party driven by artificial intelligence (AI), founded in May 2022 in Denmark. The party aims to represent non-voters and fringe political parties while raising awareness of AI's societal role and exploring how it can be integrated into democratic processes. == Founder == The founder and continuous party secretary is Asker Bryld Staunæs, a philosopher from Aarhus University and a conceptual artist. == Main goal == The political goals have been machine learned from texts by Danish fringe parties since 1970 and represent the 20 percent of Danes who do not vote in the election. The party is synthetic; as such, many of the policies, such as universal basic income, can be contradictory to one another. == International collaborations == The Synthetic Party has signed bilateral collaboration agreements with the Finnish AI Party and AI Party (Japan) concerning the development of a global project created around artificial intelligence and politics These collaborations were expanded during the exhibition-event Synthetic Summit (28 February – 13 April 2025) at Kunsthal Aarhus, curated by Computer Lars (Asker Bryld Staunæs) on behalf of The Synthetic Party. The summit staged parliamentary scenography, performances, and computer sculptures, and invited both the public and policymakers to encounter an international line-up of AI parties and virtual politicians. Aarhus University described the event as part of Staunæs's PhD research, positioning it as an international top-meeting of virtual politicians. Participants included the Japanese AI Party, the Swedish AI Party, the Finnish AI Party, Parker Politics (New Zealand), Lex AI (Brazil), the Simiyya collective (Egypt/Sweden), the Synthetic Party (Denmark), and Wiktoria Cukt 2.0 (Poland). As part of the summit, the one-day AI World Congress was held on 1 March 2025, structured as a performative assembly where each group participated through both machinic agents and human delegates. Sessions were chaired by participating parties, with Computer Lars delivering the opening presentation. Throughout the day, contributions were synthesized into a common record using a shared AI system. The congress concluded with the adoption of the Synthetic Summit Resolution, a collectively authored treaty of algorithmic governance. Signatories included Floor Kist and Nick Gerritsen (Parker Politics), Michihito Matsuda (Japanese AI Party), Emma Bexell (Swedish AI Party), Samee Haapa (Finnish AI Party), Pedro Markun (Lex AI), Kristian T. Madsen and Michael Birkebæk Jensen (NextGen Democracy / DemAI), Asker Bryld Staunæs, Benjamin Asger Krog Møller, Caroline Sofie Axelsson, Life with Artificials (The Synthetic Party), and Piotr Wyrzykowski (Wiktoria Cukt 2.0).
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Unique name assumption

The unique name assumption is a simplifying assumption made in some ontology languages and description logics. In logics with the unique name assumption, different names always refer to different entities in the world. It was included in Ray Reiter's discussion of the closed-world assumption often tacitly included in Database Management Systems (e.g. SQL) in his 1984 article "Towards a logical reconstruction of relational database theory" (in M. L. Brodie, J. Mylopoulos, J. W. Schmidt (editors), Data Modelling in Artificial Intelligence, Database and Programming Languages, Springer, 1984, pages 191–233). The standard ontology language OWL does not make this assumption, but provides explicit constructs to express whether two names denote the same or distinct entities. owl:sameAs is the OWL property that asserts that two given names or identifiers (e.g., URIs) refer to the same individual or entity. owl:differentFrom is the OWL property that asserts that two given names or identifiers (e.g., URIs) refer to different individuals or entities.
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AI Futures Project

The AI Futures Project is a nonprofit research organization based in the United States that specializes in forecasting the development and societal impact of advanced artificial intelligence. The organization is best known for its 2025 scenario forecast, AI 2027, which examines the potential near-term emergence of artificial general intelligence (AGI) and its possible global consequences. == History == The AI Futures Project was founded in 2025 by Daniel Kokotajlo, a former researcher in the governance division of OpenAI. Kokotajlo resigned from OpenAI in April 2024, expressing concerns that the company prioritized rapid product development over AI safety and was advancing without sufficient safeguards. He founded the nonprofit to conduct independent forecasting and policy research. The organization is registered as a 501(c)(3) nonprofit in the United States and is funded through donations. It operates with a small research staff and network of advisors drawn from fields including AI policy, forecasting, and risk analysis. == Activities == The mission of the AI Futures Project is to develop detailed scenario forecasts of the trajectory of advanced AI systems to inform policymakers, researchers, and the public. In addition to written reports, the group has conducted tabletop exercises and workshops based on its scenarios, involving participants from academia, technology, and public policy. == AI 2027 == In April 2025, the AI Futures Project released AI 2027, a detailed scenario forecast describing possible developments in AI between 2025 and 2027. The report was authored by Daniel Kokotajlo along with Eli Lifland, Thomas Larsen, and Romeo Dean, with editing assistance from blogger Scott Alexander. The scenario depicts very rapid progress in AI capabilities, including the development of autonomous AI systems capable of recursive self-improvement. AI 2027 presents two alternative endings: one in which international competition over advanced AI leads to catastrophic loss of human control, and another in which coordinated global action slows down development and averts imminent disaster. The authors emphasize that the narratives are hypothetical and intended as planning tools rather than literal forecasts. == Reception == AI 2027 attracted attention from technology journalists and AI researchers. Some commentators praised the report for its level of detail and its usefulness as a strategic planning exercise, while others criticized the scenario as implausibly aggressive in its timelines. The report was cited in policy discussions about AI governance. U.S. Vice President JD Vance reportedly read AI 2027 and referenced its warnings in conversations about international AI coordination. More recent reporting noted that the authors of AI 2027 had publicly revised some of their timelines. According to Kokotajlo, developments since the report's original publication suggested a slower path toward fully autonomous AI research systems than initially forecasted.
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Magiran

Magiran (Persian: مگیران)—Iran's publications database—is a digital library that was founded in 2000 and includes digitized versions of scientific journals, which currently provides the possibility of searching among the full text of 1,500 journals. Registration is required for full access to the database, but access to some items such as newspapers is also possible without registration. A list of Iranian researchers is also maintained there.
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Is-a

In knowledge representation, ontology components and ontology engineering, including for object-oriented programming and design, is-a (also written as is_a or is a) is a subsumptive relationship between abstractions (e.g., types, classes), wherein one class A is a subclass of another class B (and so B is a superclass of A). In other words, type A is a subtype of type B when A's specification implies B's specification. That is, any object (or class) that satisfies A's specification also satisfies B's specification, because B's specification is weaker. For example, a cat 'is a[n]' animal, but not vice versa. All cats are animals, but not all animals are cats. Behaviour that is relevant to all animals is defined on an animal class, whereas behaviour that is relevant only for cats is defined in a cat class. By defining the cat class as 'extending' the animal class, all cats 'inherit' the behaviour defined for animals, without the need to explicitly code that behaviour for cats. == Related concepts == The is-a relationship is to be contrasted with the has-a (has_a or has a) relationship between types (classes); confusing the relations has-a and is-a is a common error when designing a model (e.g., a computer program) of the real-world relationship between an object and its subordinate. The is-a relationship may also be contrasted with the instance-of relationship between objects (instances) and types (classes): see Type–token distinction. To summarize the relations, there are: hyperonym–hyponym (supertype/superclass–subtype/subclass) relations between types (classes) defining a taxonomic hierarchy, where for a subsumption relation: a hyponym (subtype, subclass) has a type-of (is-a) relationship with its hyperonym (supertype, superclass); holonym–meronym (whole/entity/container–part/constituent/member) relations between types (classes) defining a possessive hierarchy, where for an aggregation (i.e. without ownership) relation: a holonym (whole) has a has-a relationship with its meronym (part), for a composition (i.e. with ownership) relation: a meronym (constituent) has a part-of relationship with its holonym (entity), for a containment relation: a meronym (member) has a member-of relationship with its holonym (container); concept–object (type–token) relations between types (classes) and objects (instances), where a token (object) has an instance-of relationship with its type (class).
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OpenAI Operator

OpenAI Operator was an AI agent developed by OpenAI, capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other repetitive browser-based tasks. It uses OpenAI's advanced models to expand practical automation capabilities for users in daily activities. Operator was launched on January 23, 2025. It was released as a limited-access research preview to ChatGPT Pro-tier subscribers in the United States on February 1, 2025, with future plans to broaden availability. Operator was deprecated after the release of ChatGPT agent, and shut down on August 31, 2025. == Performance and limitations == In benchmark assessments, Operator achieved notable success, scoring 38.1% on OSWorld benchmarks (OS-level tasks) and 58.1% on WebArena benchmarks (web interactions). However, it did not reach human-level accuracy and faced limitations with intricate user interfaces and extended workflows. == Safety and privacy == OpenAI emphasized privacy and safety measures within Operator, including stringent data protection protocols and built-in safety checks designed to prevent unauthorized sensitive actions or information misuse. == Availability == Initially, Operator was only available to ChatGPT Pro subscribers in the U.S., with plans for broader availability to Plus, Team, and Enterprise users in the future.
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