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Grammar induction

Grammar induction (or grammatical inference) is the process in machine learning of learning a formal grammar (usually as a collection of re-write rules or productions or alternatively as a finite-state machine or automaton of some kind) from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs. == Grammar classes == Grammatical inference has often been very focused on the problem of learning finite-state machines of various types (see the article Induction of regular languages for details on these approaches), since there have been efficient algorithms for this problem since the 1980s. Since the beginning of the century, these approaches have been extended to the problem of inference of context-free grammars and richer formalisms, such as multiple context-free grammars and parallel multiple context-free grammars. Other classes of grammars for which grammatical inference has been studied are combinatory categorial grammars, stochastic context-free grammars, contextual grammars and pattern languages. == Learning models == The simplest form of learning is where the learning algorithm merely receives a set of examples drawn from the language in question: the aim is to learn the language from examples of it (and, rarely, from counter-examples, that is, example that do not belong to the language). However, other learning models have been studied. One frequently studied alternative is the case where the learner can ask membership queries as in the exact query learning model or minimally adequate teacher model introduced by Angluin. == Methodologies == There is a wide variety of methods for grammatical inference. Two of the classic sources are Fu (1977) and Fu (1982). Duda, Hart & Stork (2001) also devote a brief section to the problem, and cite a number of references. The basic trial-and-error method they present is discussed below. For approaches to infer subclasses of regular languages in particular, see Induction of regular languages. A more recent textbook is de la Higuera (2010), which covers the theory of grammatical inference of regular languages and finite state automata. D'Ulizia, Ferri and Grifoni provide a survey that explores grammatical inference methods for natural languages. === Induction of probabilistic grammars === There are several methods for induction of probabilistic context-free grammars. === Grammatical inference by trial-and-error === The method proposed in Section 8.7 of Duda, Hart & Stork (2001) suggests successively guessing grammar rules (productions) and testing them against positive and negative observations. The rule set is expanded so as to be able to generate each positive example, but if a given rule set also generates a negative example, it must be discarded. This particular approach can be characterized as "hypothesis testing" and bears some similarity to Mitchel's version space algorithm. The Duda, Hart & Stork (2001) text provide a simple example which nicely illustrates the process, but the feasibility of such an unguided trial-and-error approach for more substantial problems is dubious. === Grammatical inference by genetic algorithms === Grammatical induction using evolutionary algorithms is the process of evolving a representation of the grammar of a target language through some evolutionary process. Formal grammars can easily be represented as tree structures of production rules that can be subjected to evolutionary operators. Algorithms of this sort stem from the genetic programming paradigm pioneered by John Koza. Other early work on simple formal languages used the binary string representation of genetic algorithms, but the inherently hierarchical structure of grammars couched in the EBNF language made trees a more flexible approach. Koza represented Lisp programs as trees. He was able to find analogues to the genetic operators within the standard set of tree operators. For example, swapping sub-trees is equivalent to the corresponding process of genetic crossover, where sub-strings of a genetic code are transplanted into an individual of the next generation. Fitness is measured by scoring the output from the functions of the Lisp code. Similar analogues between the tree structured lisp representation and the representation of grammars as trees, made the application of genetic programming techniques possible for grammar induction. In the case of grammar induction, the transplantation of sub-trees corresponds to the swapping of production rules that enable the parsing of phrases from some language. The fitness operator for the grammar is based upon some measure of how well it performed in parsing some group of sentences from the target language. In a tree representation of a grammar, a terminal symbol of a production rule corresponds to a leaf node of the tree. Its parent nodes corresponds to a non-terminal symbol (e.g. a noun phrase or a verb phrase) in the rule set. Ultimately, the root node might correspond to a sentence non-terminal. === Grammatical inference by greedy algorithms === Like all greedy algorithms, greedy grammar inference algorithms make, in iterative manner, decisions that seem to be the best at that stage. The decisions made usually deal with things like the creation of new rules, the removal of existing rules, the choice of a rule to be applied or the merging of some existing rules. Because there are several ways to define 'the stage' and 'the best', there are also several greedy grammar inference algorithms. These context-free grammar generating algorithms make the decision after every read symbol: Lempel-Ziv-Welch algorithm creates a context-free grammar in a deterministic way such that it is necessary to store only the start rule of the generated grammar. Sequitur and its modifications. These context-free grammar generating algorithms first read the whole given symbol-sequence and then start to make decisions: Byte pair encoding and its optimizations. === Distributional learning === A more recent approach is based on distributional learning. Algorithms using these approaches have been applied to learning context-free grammars and mildly context-sensitive languages and have been proven to be correct and efficient for large subclasses of these grammars. === Learning of pattern languages === Angluin defines a pattern to be "a string of constant symbols from Σ and variable symbols from a disjoint set". The language of such a pattern is the set of all its nonempty ground instances i.e. all strings resulting from consistent replacement of its variable symbols by nonempty strings of constant symbols. A pattern is called descriptive for a finite input set of strings if its language is minimal (with respect to set inclusion) among all pattern languages subsuming the input set. Angluin gives a polynomial algorithm to compute, for a given input string set, all descriptive patterns in one variable x. To this end, she builds an automaton representing all possibly relevant patterns; using sophisticated arguments about word lengths, which rely on x being the only variable, the state count can be drastically reduced. Erlebach et al. give a more efficient version of Angluin's pattern learning algorithm, as well as a parallelized version. Arimura et al. show that a language class obtained from limited unions of patterns can be learned in polynomial time. === Pattern theory === Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. In addition to the new algebraic vocabulary, its statistical approach was novel in its aim to: Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was commonplace at the time. Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph. Study the randomness and variability of these graphs. Create the basic classes of stochastic models applied by listing the deformations of the patterns. Synthesize (sample) from the models, not just analyze signals with it. Broad in its mathematical coverage, pattern theory spans algebra and statistics, as well as local topological and global entropic properties. == Applications == The principle of grammar induction has been applied to other aspects of natural language processing, and has been applied (among many other problems) to semantic parsing, natural language understanding, example-based translation, language acquisition, grammar-based compre
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Probabilistic database

Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..." Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly. == Terminology == In a probabilistic database, each tuple is associated with a probability between 0 and 1, with 0 representing that the data is certainly incorrect, and 1 representing that it is certainly correct. === Possible worlds === A probabilistic database could exist in multiple states. For example, if there is uncertainty about the existence of a tuple in the database, then the database could be in two different states with respect to that tuple—the first state contains the tuple, while the second one does not. Similarly, if an attribute can take one of the values x, y or z, then the database can be in three different states with respect to that attribute. Each of these states is called a possible world. Consider the following database: (Here {b3, b3′, b3′′} denotes that the attribute can take any of the values b3, b3′ or b3′′) Assuming that there is uncertainty about the first tuple, certainty about the second tuple, and uncertainty about the value of attribute B in the third tuple. Then the actual state of the database may or may not contain the first tuple (depending on whether it is correct or not). Similarly, the value of the attribute B may be b3, b3′ or b3′′. Consequently, the possible worlds corresponding to the database are as follows: === Types of Uncertainties === There are essentially two kinds of uncertainties that could exist in a probabilistic database, as described in the table below: By assigning values to random variables associated with the data items, different possible worlds can be represented. == History == The first published use of the term "probabilistic database" was probably in the 1987 VLDB conference paper "The theory of probabilistic databases", by Cavallo and Pittarelli. The title (of the 11 page paper) was intended as a bit of a joke, since David Maier's 600 page monograph, The Theory of Relational Databases, would have been familiar at that time to many of the conference participants and readers of the conference proceedings.
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Gundam Build Metaverse

Gundam Build Metaverse (Japanese: ガンダムビルドメタバース, Hepburn: Gandamu Birudo Metabāzu) is a Japanese original net animation anime mini-series produced by Sunrise Beyond, and the fifth series within the Gundam Build Series sub-series. The series celebrates the 10th anniversary of the Gundam Build franchise, including characters from the previous installments. == Plot == The story is set in the same universe of the Gundam Build series in an online metaverse space where users can use avatars to move around and interact with other users, including conducting Gunpla (Gundam plastic model) battles with them. The story centers on Rio Hōjō, a boy who lives in Hawaii, and who learns how to build Gunpla from a local hobbyist named Seria Urutsuki. In the metaverse, a figure known as Mask Lady teaches him the art of Gunpla battling, and he strives to get better at it every day. With his custom Lah Gundam, he seeks out ever stronger opponents. == Characters == === Main characters === Rio Hojo (ホウジョウ・リオ, Hōjō Rio) Voiced by: Chika Anzai A young boy from Hawaii who is an enthusiast of Gunpla Battle and is an apprentice of the mysterious Diver "Mask Lady". Rio's Gunpla is the Lah Gundam, modeled after an entry-grade RX-78-2 Gundam, from the original Mobile Suit Gundam anime series. Seria Urutsuki (ウルツキ・セリア, Urutsuki Seria) / Mask Lady (マスクレディー, Masuku Reidi) Voiced by: Rio Tsuchiya A clerk at a local hobby shop and the instructor at their Gunpla class, Seria becomes Rio's Gunpla mentor using the alias "Mask Lady". Seria's Gunpla is the ZGMF-X20A-PF Gundam Perfect Strike Freedom Rouge, based on both the MBF-02 Strike Rouge and the GAT-X105+AQM/E-YM1 Perfect Strike Gundam from Mobile Suit Gundam Seed and the ZGMF-X20A Strike Freedom Gundam from Mobile Suit Gundam Seed Destiny. === Returning characters === Fumina Hoshino (ホシノ・フミナ, Hoshino Fumina) Voiced by: Yui Makino A veteran Gunpla Battler from the early days of the sport and the Leader of "Team Try Fighters", she works as an advertiser and announcer within the Metaverse realm. Tatsuya Yuuki (ユウキ・タツヤ, Yūki Tatsuya) / Meijin Kawaguchi III (三代目メイジン・カワグチ, Sandaime Meijin Kawaguchi) Voiced by: Takuya Satō A builder and three-times Gunpla Battle world champion who inherited the name of the legendary Meijin Kawaguchi, known as "Meijin Kawaguchi III", and still the current title holder. His newest Gunpla is the Gundam Amazing Barbatos Lupus based on the ASW-G-08 Gundam Barbatos Lupus from Mobile Suit Gundam: Iron-Blooded Orphans. Riku Mikami (ミカミ・リク, Mikami Riku) / Riku (リク) Voiced by: Yūsuke Kobayashi The Founder and former leader of the legendary force, "Build Divers". His Gunpla is the Gundam 00 Diver Arc, the latest version of the original GN-0000DVR Gundam 00 Diver from Gundam Build Divers, incorporating elements from the 00 Gundam from Mobile Suit Gundam 00 and the Gundam AGE-FX from Mobile Suit Gundam AGE. Sarah (サラ, Sara) Voiced by: Haruka Terui An EL-Diver and member of the Build Divers. Momoka Yashiro (ヤシロ・モモカ, Yashiro Momoka) / Momo (モモ) Voiced by: Nene Hieda Member of Build Divers. Her gunpla is the MOMOKAPOOL (R×R), an upgraded version of her PEN-01M Momokapool from Gundam Build Divers Aya Fujisawa (フジサワ・アヤ, Fujisawa Aya) / Ayame (アヤメ) Voiced by: Manami Numakura Member of Build Divers. Her Gunpla is the F-Kunoichi Kai, an SD Gunpla based on the F91 Gundam F91 from Mobile Suit Gundam F91. Sei Iori (イオリ・セイ, Iori Sei) Voiced by: Mikako Komatsu A builder and one time Gunpla Battle World Champion. His current Gunpla is the GAT-X105B/EG Build Strike Exceed Galaxy, the latest version of the original GAT-X105B Build Strike Gundam from Gundam Build Fighters. Aria von Reiji Asuna (アリーア・フォン・レイジ・アスナ, Arīa fon Reiji Asuna) Voiced by: Sachi Kokuryu A prince from the country called Arian that exists within a space colony in another dimension, who became friends with Sei Iori and together won the Gunpla Battle World Championship. He somehow manages to log into the metaverse to reunite with his friend, piloting the SB-011 Star Burning Gundam. Sekai Kamiki (カミキ・セカイ, Kamiki Sekai) Voiced by: Kazumi Togashi A veteran builder and former member of Team Try Fighters. He is currently the Japanese National representative Champion. In the series he develops a rivalry relationship with Hiroto similar to that of Kyoya and Rommel. His current Gunpla is the Shin Burning Gundam, the latest version of the original KMK-B01 Kamiki Burning Gundam from Gundam Build Fighters Try which is based on the Burning Gundam and Master Gundam. Hiroto Kuga (クガ・ヒロト, Kuga Hiroto) / Hiroto (ヒロト, Hiroto) Voiced by: Chiaki Kobayashi A veteran diver, the one responsible for discovering more EL-Divers, and a former member of the legendary force "Avalon", who later joined the unofficial, "BUILD DiVERS" and eventually became the current Force Leader, and as well as the current title holder of "Hero of Gunpla". In the third episode he is the only Build Diver member who participates in the tournament, while his fellow force-mates are in the audience routing for him and Rio. His Gunpla is the Plutine Gundam, which is a combination of his Core Gundam II Plus, upgraded from the Core Gundam II featured in Gundam Build Divers Re:Rise equipped with the Pluto Armor. Magee (マギー, Magī) Voiced by: Taishi Murata A flamboyant veteran Diver who owns a shop in the metaverse and is an acquaintance of Seria's. Freddie (フレディ, Furedi) Voiced by: Ai Kakuma An alien anthropomorphic dog boy from planet Eldora, a support member to both Build Diver teams, who manages to access the metaverse from his home planet along his fellow Eldorans. Ogre (オーガ, Ōga) Voiced by: Wataru Hatano Kyoya Kisugi (キスギ・キョウヤ, Kisugi Kyōya) / Kyoya Kujo (クジョウ・キョウヤ, Kujō Kyōya) Voiced by: Jun Kasama Leader of the legendary force "Avalon" and the reigning and current title holder of "World Champion". He along with Hiroto Kuga, Maria Urutsuki, and Tatsuya Yuuki are currently at the top of the entire gunpla world community. His current gunpla is an recolored version of his AGE-TRYMAG Gundam TRY AGE Magnum from Gundam Build Divers Re:Rise. Susumu Sazaki (サザキ・ススム, Sazaki Susumu) Voiced by: Ryo Hirohashi Kaoruko Sazaki (サザキ・カオルコ, Sazaki Kaoruko) Voiced by: Ryo Hirohashi Mahiru Shigure (シグレ・マヒル, Shigure Mahiru) Voiced by: Rinko Natsuhi Keiko Sano (サノ・ケイコ, Sano Keiko) Voiced by: Ami Naito === Others === Maria Urutsuki (ウルツキ・マリア, Urutsuki Maria) / Mascarilla (マスカリージャ, Masukarīja) Voiced by: Ai Kakuma A mysterious masked woman with a harsh rivalry with Seria and a similar avatar as hers, she is later revealed as Seria's younger sister Maria, who began to loathe her sister after she quit on their dream to fight for the title of Lady Kawaguchi. She later obtains the title, becoming "Lady Kawaguchi VII". Jeff (ジェフさん, Jefu-san) Voiced by: Kenta Miyake A distant relative of Seria and Maria's and owner of the hobby shop where Seria lives. Mellow Neige (メロウ・ネージュ, Merō Nēju) Voiced by: Chikano Ibuki A sentient A.I. who is the current publicity face of the Gunpla Metaverse. == Episodes ==
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Artificial Intelligence Cold War

The Artificial Intelligence Cold War (AI Cold War) is a narrative in which geopolitical tensions between the United States of America (USA) and the People's Republic of China (PRC) could lead to a Second Cold War waged in the area of artificial intelligence technology rather than in the areas of nuclear capabilities or ideology. The context of the AI Cold War narrative is the AI arms race, which involves a build-up of military capabilities using AI technology by the US and China and the usage of increasingly advanced semiconductors which power those capabilities. According to a February 2019 publication by the Center for a New American Security, General Secretary of the Chinese Communist Party Xi Jinping – believes that being at the forefront of AI technology will be critical to the future of China's global military and economic power competition. == Origins of the term == The term AI Cold War first appeared in 2018 in an article in Wired magazine by Nicholas Thompson and Ian Bremmer. The two authors trace the emergence of the AI Cold War narrative to 2017, when China published its AI Development Plan, which included a strategy aimed at becoming the global leader in AI by 2030. While the authors acknowledge the use of AI by China to strengthen its authoritarian (totalitarian) rule, they warn against the perils for the US of engaging in an AI Cold War strategy. Thompson and Bremmer rather advocate for a technological cooperation between the US and China to encourage global standards in privacy and ethical use of AI. Shortly after the publication of the article in Wired magazine, the former U.S. Treasury Secretary Hank Paulson referred to the emergence of an ‘Economic Iron Curtain’ between the US and China, reinforcing the new AI Cold War narrative. == Proponents of the AI Cold War narrative == Politico contributed to reinforcing the AI Cold War narrative. In 2020, the paper argued that because of the increasing AI capabilities of China, the US and other democratic countries have to create an alliance to stay ahead of China. Former Google chief executive Eric Schmidt, together with Graham T. Allison alleged in an article in Project Syndicate that, in the context of the COVID-19 pandemic, the AI capabilities of China are ahead of the US in most critical areas. Scientists who have immigrated to the U.S. play an outsize role in the country's development of AI technology. Many of them were educated in China, prompting debates about national security concerns amid worsening relations between the two countries. Policy and technology experts have pointed to concerns about unethical use of AI which would be primarily associated with China. Ethics would therefore constitute a major ideological divide in the upcoming AI Cold War. Fears around disrupting supply chains and a global semiconductor shortage are linked to Taiwan's critical role in the production of semiconductors. 70% of semiconductors are either produced in Taiwan or transfer through Taiwan, where TSMC, world's largest chipmaker is headquartered. The PRC does not recognize the sovereignty of Taiwan and trade restrictions by the US on companies selling semiconductors to the PRC have disrupted in the past the commercial relationships between TSMC and Huawei. == Reactions to the AI Cold War == === Review of the validity of the AI Cold War narrative === Academics and observers expressed concerns about the validity and soundness of the AI Cold War narrative. Denise Garzia expressed concern in Nature that the AI Cold War narrative will undermine the efforts by the US to establish global rules for AI ethics. Researchers have warned in MIT Technology Review that the breakdown in international collaboration in the area of science because of the threat of the alleged AI Cold War would be detrimental to progress. Additionally, the AI Cold War narrative impacts on many more areas including the planning of supply chains and the proliferation of AI. The dissemination of the AI Cold War narrative could therefore be costly and destructive and exacerbate existing tensions. Joanna Bryson and Helena Malikova have pointed to Big Tech's potential interest in promoting the AI Cold War narrative, as technology companies lobby for less onerous regulation of AI in the US and the EU. A factual assessment of the existing AI capabilities of different countries shows a less binary reality than portrayed by the AI Cold War narrative. The AI Cold War started as a narrative but it could turn into a self-fulfilling prophecy and fuel an arms race, not only because of corporate interests but also because of the existing interests at different national security departments. Regarding cyber power, the International Institute for Strategic Studies published a study in June 2021, which argued that the online capabilities of China have been exaggerated and that Chinese cyber power is at least a decade behind the US, largely due to lingering security issues. === Restrictions to trading with China === US politicians and European industry players have invoked the looming AI Cold War as a reason to ban procurement by public authorities in Europe of Huawei 5G technology due to concerns over the Chinese state-sponsored surveillance industry. In 2019, the Trump administration successfully lobbied the Dutch government into stopping the Netherlands-based company ASML from exporting equipment to China. ASML manufactures a machine called an extreme ultraviolet lithography system used by semiconductor producers, including TSMC and Intel to produce state-of the-art microchips. The Biden administration adopted the same course of action as the Trump administration and requested the Netherlands to restrict sales by ASML to China, invoking national-security concerns. The trade restrictions imposed by the Trump administration affected semiconductors imports from China to the US and raised concerns by the US industry that supply chains will be disrupted in case of an AI Cold War. This prompted US technology companies to develop mitigation strategies including hoarding semiconductors and trying to set up local semiconductor production facilities, with the support of government subsidies. === Industrial policy initiatives === ==== United States ==== In June 2021, the US Senate approved the U.S. Innovation and Competition Act providing around 250 billion US dollars public money support to the US technological and manufacturing industry. The alleged Chinese threat in the area of technology helped secure a strong bipartisan support for the new legislation, amounting to the largest industrial policy move by the US in decades. Chinese authorities reproached to the US that the bill was “full of cold war zero-sum thinking”. The legislative bill is aimed at strengthening capabilities in the area of technology, such as quantum computing and AI specifically to face the competitive threat from China perceived as urgent. Senator Chuck Schumer, the leader of the Senate majority and one of the sponsors of the industrial policy bill invoked the threat of authoritarian regimes that want “grab the mantle of global economic leadership and own the innovations”. In 2022, U.S. Innovation and Competition Act was amended and turned into the Chips and Science Act with planned spending of 280 billion US dollars, 53 billion thereof are allocated directly to subsidies for semiconductors manufacturing. Commentators identified possible positive effects on innovation from the US attempts to compete with China in a perceived rivalry. Among the main beneficiaries of the US CHIPS Act are the semiconductor producers Intel, TSMC and Micron Technology. ==== European Chips Act ==== In February 2022, the European Union introduced its own European Chips Act initiative. The background of the initiative would be the objective of European strategic autonomy. The EU's initiative puts forward subsidies of 30 billion euros to encourage manufacturing of semiconductors in the EU. The US company Intel is one beneficiary of the initiative. The US and European chips acts raise concerns of protectionism and a risk of a subsidies "race to the bottom." === New world order === The AI Cold War heralds a new world order in geopolitics, according to Hemant Taneja and Fareed Zakaria. This new world order is a departure from the unipolar system dominated by the US. It is characterized by existence of two parallel digital ecosystems, ran by China and the US. In order to succeed countries that consider themselves as democracies are to align their technological ecosystems to that of the US, in a process labelled re-globalization.
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Imaging

Imaging is the process of creating visual representations of objects, scenes, or phenomena. The term encompasses both the formation of images through physical processes and the technologies used to capture, store, process, and display them. While traditional imaging relies on visible light, modern imaging systems can visualize information across the electromagnetic spectrum and through other physical phenomena such as sound waves, magnetic fields, and particle emissions, enabling the visualization of subjects invisible to the human eye. Imaging science is the multidisciplinary field concerned with the theoretical foundations and practical applications of image creation and analysis. The field draws on physics, mathematics, electrical engineering, computer science, computer vision, and perceptual psychology to develop systems that generate, collect, duplicate, analyze, modify, and visualize images. == Principles == === The imaging chain === The imaging chain is a conceptual framework describing the interconnected components of any imaging system. Understanding each link in this chain allows engineers and scientists to optimize system performance for specific applications. The chain begins with the subject and its observable properties, typically energy that is emitted, reflected, or transmitted. A light source or other energy source may illuminate the subject to make these properties detectable. The capture device then collects this energy using appropriate sensors: optical systems for electromagnetic radiation, transducers for acoustic waves, or antenna arrays for radio frequencies. In digital systems, a processor converts the captured signals into a format suitable for rendering, applying algorithms for noise reduction, enhancement, or reconstruction. Finally, a display renders the processed information as a visible image on media such as paper, screens, or projection surfaces. Throughout this process, the characteristics of the human visual system inform design decisions, as the ultimate purpose of most imaging systems is to convey information to human observers. === Coherent and non-coherent imaging === Imaging systems are often classified by whether they use coherent or non-coherent illumination. Coherent imaging employs an active source that produces waves with a consistent phase relationship, as in radar, synthetic aperture radar, medical ultrasound, and optical coherence tomography. These systems can capture phase information in addition to amplitude, enabling techniques such as holography and interferometry. Non-coherent imaging systems, including conventional photography, fluorescence microscopy, and telescopes, rely on illumination sources where light waves have random phase relationships. == Methods and applications == Imaging methods span a wide range of physical principles, each suited to particular applications. Optical imaging encompasses photography, cinematography, microscopy, and telescopic observation. These methods capture electromagnetic radiation in or near the visible spectrum and form the basis of most consumer and scientific imaging. Extensions include thermography, which visualizes infrared radiation to reveal temperature distributions, and multispectral imaging, which captures data across multiple wavelength bands for applications in remote sensing and materials analysis. Medical imaging comprises techniques designed to visualize the interior of the human body for diagnostic and therapeutic purposes. Radiography and computed tomography use X-rays to image dense structures such as bone. Magnetic resonance imaging exploits nuclear magnetic properties to produce detailed soft-tissue images without ionizing radiation. Ultrasound imaging uses high-frequency sound waves and is particularly valuable for real-time imaging and fetal monitoring. Nuclear medicine techniques such as positron emission tomography track radioactive tracers to reveal metabolic activity. Emerging modalities include photoacoustic imaging, which combines optical and acoustic principles, and Magneto-acousto-electrical tomography, which maps electrical conductivity in biological tissues. Acoustic imaging uses sound waves to create images. Beyond medical ultrasound, applications include sonar for underwater navigation and mapping, seismic imaging for geological exploration, and industrial non-destructive testing. Radar and microwave imaging employ radio waves to detect and image objects. Synthetic aperture radar produces high-resolution images from aircraft or satellites regardless of weather or lighting conditions, making it essential for Earth observation and reconnaissance. Ground-penetrating radar images subsurface structures for archaeological and engineering applications. Electron and particle imaging use beams of electrons or other particles to achieve resolutions far beyond the diffraction limit of visible light. Electron microscopes can image individual atoms, enabling advances in materials science and structural biology. Chemical imaging combines spectroscopy with spatial imaging to map the chemical composition of samples, with applications in pharmaceutical development, food safety, and forensics. LIDAR (Light Detection and Ranging) measures distances using laser pulses to create three-dimensional representations of surfaces and objects, widely used in autonomous vehicles, topographic mapping, and forestry. Computational and digital imaging encompasses image processing, computer graphics, three-dimensional rendering, and digital image restoration. Computer vision applies algorithmic analysis to extract information from images automatically. == History == Photography and imaging have always been intertwined. When Joseph Nicéphore Niépce created the first permanent photograph using heliography in 1826, and Louis Daguerre refined the process into the daguerreotype a decade later, they weren't just inventing a new art form, they were laying the groundwork for an entire scientific discipline built on silver halide chemistry. For most of the nineteenth century, photography remained the province of specialists. That changed with George Eastman's Kodak camera, introduced in 1888 with the slogan "You press the button, we do the rest." Suddenly, anyone could take pictures. Around the same time, Wilhelm Röntgen stumbled onto X-rays in 1895, an accident that would spawn the entire field of medical imaging. World War II proved to be a turning point. Radar technology, developed frantically on both sides of the conflict, introduced concepts that engineers would later adapt for synthetic aperture radar and medical ultrasound. Then the charge-coupled device came: Willard Boyle and George E. Smith built the first one at Bell Labs in 1969, and within a few decades it had made film nearly obsolete. Magnetic resonance imaging arrived in the 1970s, offering doctors something X-rays never could, detailed views of soft tissue without any radiation. Digital cameras took over fast. By the 2000s, film was already in decline; by the 2010s, smartphones had put a surprisingly capable camera in nearly every pocket. Features that once required real skill, proper exposure, sharp focus, accurate color, became automatic. Today, billions of photos get uploaded to social media every day. As a result, a growing issue is that generative artificial intelligence can fabricate photorealistic images from scratch. What counts as a "real" photograph is no longer necessarily obvious.
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Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960s and 1970s went further by considering issues such as linguistic variables and lattices. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. == Overview == Classical logic only permits conclusions that are either true or false. However, there are also propositions with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. === Applying truth values === A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. Fuzzy set theory provides a means for representing uncertainty. === Linguistic variables === In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. == Fuzzy systems == === Mamdani === The most well-known system is the Mamdani rule-based one. It uses the following rules: Fuzzify all input values into fuzzy membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp" output values. ==== Fuzzification ==== Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner. For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot"; i.e. this temperature has zero membership in the fuzzy set "hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The degree of membership assigned for each fuzzy set is the result of fuzzification. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 (which can have a length of 0 or greater) and a slope where the value is decreasing. They can also be defined using a sigmoid function. One common case is the standard logistic function defined as S ( x ) = 1 1 + e − x {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} which has the following symmetry property S ( x ) + S ( − x ) = 1. {\displaystyle S(x)+S(-x)=1.} From this it follows that ( S ( x ) + S ( − x ) ) ⋅ ( S ( y ) + S ( − y ) ) ⋅ ( S ( z ) + S ( − z ) ) = 1 {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1} ==== Fuzzy logic operators ==== Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators ("gates") AND, OR, NOT must be available. There are several ways to accomplish this. A common replacement is called the Zadeh operators: For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. However, an arbitrary choice table does not always define a fuzzy logic function. In the paper (Zaitsev, et al), a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum. A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area (to the right of the function value in the inequality, including the function value). Another set of AND/OR operators is based on multiplication, where Given any two of AND/OR/NOT, it is possible to derive the third. The generalization of AND is an instance of a t-norm. ==== IF-THEN rules ==== IF-THEN rules map input or computed truth values to desired output truth values. Example: Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable. Should an output variable occur in several THEN parts, the values from the respective IF parts are combined using the OR operator. ==== Defuzzification ==== The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. One has then to decide for a number that matches best the "intention" encoded in the truth value. For example, for several truth values of fan_speed, an actual speed must be found that best fits the computed truth values of the variables 'slow', 'moderate' and so on. There is no single algorithm for this purpose. A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. === Takagi–Sugeno–Kang (TSK) === The Takagi–Sugeno or Takagi–Sugeno–Kang (TSK) system was introduced by Tomohiro Takagi and Michio Sugeno for fuzzy identification of systems and applications to modeling and control. Sugeno and Kang later developed methods for structure identification of such fuzzy models from input-output data. The TSK system is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules. These are also adapted, so that instead the consequent of the rule is represented through a polynomial function, usually constant in a zero-order model or linear in a first-order model. An example of a rule with a constant output would be: In this case, the output will be equal to the constant of the consequent (e.g. 2). In most scenarios we would have an entire rule base, with 2 or more rules. If this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Y
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Agent2Agent

Agent2Agent (A2A) is an open protocol that defines how artificial intelligence agents communicate with each other across different systems. It is intended to allow agents built by different vendors or frameworks to discover one another, exchange messages, and coordinate tasks. == History == The Agent2Agent protocol was announced by Google in April 2025 as an open standard for agent interoperability. In June 2025, Google transferred the protocol, its specification, and related software development kits to the Linux Foundation. The Linux Foundation established the Agent2Agent project to provide vendor-neutral governance. == Design == The A2A protocol supports communication between autonomous software agents operating across different platforms and organizations. It enables agents to discover one another and exchange structured messages without requiring shared internal state or proprietary integrations. A2A uses metadata documents, known as Agent Cards, to describe an agent's capabilities and how it can be accessed. These documents are exchanged using widely adopted web technologies such as HTTP and JSON-based messaging formats. A2A includes support for authentication and authorization to control which agents may participate in workflows. The protocol supports established security technologies including Transport Layer Security (TLS), JSON Web Tokens (JWTs), and OpenID Connect. A2A is often discussed alongside the Model Context Protocol (MCP). MCP focuses on connecting agents to tools and data sources, while A2A focuses on communication between agents themselves. == Adoption == At the time the Linux Foundation adopted the protocol, more than 100 technology companies had announced support for the Agent2Agent project. Microsoft stated that it planned to support the protocol in its AI platforms. == Reception == Technology press coverage has described A2A as an attempt to reduce fragmentation in AI agent ecosystems by providing a shared communication layer. TechRepublic characterized the protocol as part of a broader industry effort to reduce vendor lock-in for enterprise AI systems.
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Probabilistic database

Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..." Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly. == Terminology == In a probabilistic database, each tuple is associated with a probability between 0 and 1, with 0 representing that the data is certainly incorrect, and 1 representing that it is certainly correct. === Possible worlds === A probabilistic database could exist in multiple states. For example, if there is uncertainty about the existence of a tuple in the database, then the database could be in two different states with respect to that tuple—the first state contains the tuple, while the second one does not. Similarly, if an attribute can take one of the values x, y or z, then the database can be in three different states with respect to that attribute. Each of these states is called a possible world. Consider the following database: (Here {b3, b3′, b3′′} denotes that the attribute can take any of the values b3, b3′ or b3′′) Assuming that there is uncertainty about the first tuple, certainty about the second tuple, and uncertainty about the value of attribute B in the third tuple. Then the actual state of the database may or may not contain the first tuple (depending on whether it is correct or not). Similarly, the value of the attribute B may be b3, b3′ or b3′′. Consequently, the possible worlds corresponding to the database are as follows: === Types of Uncertainties === There are essentially two kinds of uncertainties that could exist in a probabilistic database, as described in the table below: By assigning values to random variables associated with the data items, different possible worlds can be represented. == History == The first published use of the term "probabilistic database" was probably in the 1987 VLDB conference paper "The theory of probabilistic databases", by Cavallo and Pittarelli. The title (of the 11 page paper) was intended as a bit of a joke, since David Maier's 600 page monograph, The Theory of Relational Databases, would have been familiar at that time to many of the conference participants and readers of the conference proceedings.
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Machine-learned interatomic potential

Machine-learned interatomic potentials (MLIPs), or simply machine learning potentials (MLPs), are interatomic potentials constructed using machine learning. Beginning in the 1990s, researchers have employed such programs to construct interatomic potentials by mapping atomic structures to their potential energies. These potentials are referred to as MLIPs or MLPs. Such machine learning potentials promised to fill the gap between density functional theory, a highly accurate but computationally intensive modelling method, and empirically derived or intuitively-approximated potentials, which were far lighter computationally but substantially less accurate. Improvements in artificial intelligence technology heightened the accuracy of MLPs while lowering their computational cost, increasing the role of machine learning in fitting potentials. Machine learning potentials began by using neural networks to tackle low-dimensional systems. While promising, these models could not systematically account for interatomic energy interactions; they could be applied to small molecules in a vacuum, or molecules interacting with frozen surfaces, but not much else – and even in these applications, the models often relied on force fields or potentials derived empirically or with simulations. These models thus remained confined to academia. Modern neural networks construct highly accurate and computationally light potentials, as theoretical understanding of materials science was increasingly built into their architectures and preprocessing. Almost all are local, accounting for all interactions between an atom and its neighbor up to some cutoff radius. There exist some nonlocal models, but these have been experimental for almost a decade. For most systems, reasonable cutoff radii enable highly accurate results. Almost all neural networks intake atomic coordinates and output potential energies. For some, these atomic coordinates are converted into atom-centered symmetry functions. From this data, a separate atomic neural network is trained for each element; each atomic network is evaluated whenever that element occurs in the given structure, and then the results are pooled together at the end. This process – in particular, the atom-centered symmetry functions which convey translational, rotational, and permutational invariances – has greatly improved machine learning potentials by significantly constraining the neural network search space. Other models use a similar process but emphasize bonds over atoms, using pair symmetry functions and training one network per atom pair. Other models to learn their own descriptors rather than using predetermined symmetry-dictating functions. These models, called message-passing neural networks (MPNNs), are graph neural networks. Treating molecules as three-dimensional graphs (where atoms are nodes and bonds are edges), the model takes feature vectors describing the atoms as input, and iteratively updates these vectors as information about neighboring atoms is processed through message functions and convolutions. These feature vectors are then used to predict the final potentials. The flexibility of this method often results in stronger, more generalizable models. In 2017, the first-ever MPNN model (a deep tensor neural network) was used to calculate the properties of small organic molecules. == Gaussian Approximation Potential (GAP) == One popular class of machine-learned interatomic potential is the Gaussian Approximation Potential (GAP), which combines compact descriptors of local atomic environments with Gaussian process regression to machine learn the potential energy surface of a given system. To date, the GAP framework has been used to successfully develop a number of MLIPs for various systems, including for elemental systems such as carbon, silicon, phosphorus, and tungsten, as well as for multicomponent systems such as Ge2Sb2Te5 and austenitic stainless steel, Fe7Cr2Ni. == Equivariant graph neural networks == A significant limitation of early MPNNs was that they were not inherently equivariant to rotations and reflections of atomic structures — meaning predictions could change depending on how a molecule was oriented in space. Beginning around 2021, a new class of models addressed this by incorporating equivariance directly into the message-passing layers using spherical harmonics and irreducible representations. Notable examples include NequIP (2021), MACE (2022), and GemNet-OC (2022). These equivariant architectures proved substantially more data-efficient and accurate than their predecessors, and became the dominant paradigm for high-accuracy MLIPs. == Universal MLIPs and large-scale datasets == Early MLIPs were system-specific, trained on a few thousand structures of a single material. A major shift occurred with the creation of large, chemically diverse datasets enabling models that generalize across many elements, bonding environments, and application domains — so-called universal MLIPs. A key driver was the Open Catalyst Project (OC20, OC22), a collaboration between Meta AI (FAIR) and Carnegie Mellon University launched in 2020. OC20 comprises approximately 1.3 million DFT relaxations across 82 elements, designed to accelerate the discovery of catalysts for renewable energy applications. It was among the first datasets large enough to train GNNs that generalize across diverse chemical systems, and established a widely-used benchmark for the field. A subsequent dataset, Open Direct Air Capture (OpenDAC 2023 and OpenDAC 2025), applied the same approach to carbon capture, providing a large computational database of metal-organic frameworks and sorbent candidates evaluated for CO₂ capture, generated using nearly 400 million CPU hours of quantum chemistry calculations in collaboration with Georgia Tech. These datasets revealed a new challenge: the GNN architectures most effective for atomic simulations were memory-intensive, as they model higher-order interactions between triplets or quadruplets of atoms, making it difficult to scale model size. Graph Parallelism, introduced by Sriram et al. (ICLR 2022), addressed this by distributing a single input graph across multiple GPUs — a distinct strategy from data parallelism (which distributes training examples) or model parallelism (which distributes layers). This enabled training GNNs with hundreds of millions to billions of parameters for the first time. Building on these foundations, Meta FAIR released the Universal Model for Atoms (UMA) in 2025, trained on approximately 500 million unique 3D atomic structures spanning molecules, materials, and catalysts — the largest training run to date for an MLIP. UMA introduced a Mixture of Linear Experts (MoLE) architecture, enabling one model to learn from datasets generated by different DFT codes and settings without significant inference overhead. It matches or surpasses specialized models across catalysis, materials, and molecular benchmarks without task-specific fine-tuning, and has been described as marking a "pre/post-UMA" divide in the field. == Applications == Catalyst discovery: MLIPs have significantly accelerated the computational screening of heterogeneous catalysts by replacing expensive DFT relaxations with fast neural network surrogates. The Open Catalyst Project explicitly targets this application, aiming to identify new catalysts for green hydrogen production and other renewable energy reactions. Carbon capture: The OpenDAC project applies universal MLIPs to screening sorbent materials for direct air capture of CO₂, a key technology for climate change mitigation. AI-accelerated screening allows evaluation of orders of magnitude more candidate materials than traditional DFT workflows. Drug discovery and molecular design: MLIPs are increasingly used in pharmaceutical research to model molecular conformations and binding energies. The Open Molecules 2025 (OMol25) dataset, released by Meta FAIR in 2025, provides high-accuracy calculations for a large set of molecular systems to support this use case. Materials discovery: Universal MLIPs enable high-throughput screening of novel inorganic materials, including battery electrolytes, semiconductors, and superconductors, by rapidly estimating stability and properties across large chemical spaces.
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For a Breath I Tarry

"For a Breath I Tarry" is a 1966 post-apocalyptic novelette by American writer Roger Zelazny, which was nominated for the Hugo Award for Best Novelette in 1967. Set in a future long after the self-extinction of humanity, the novelette recounts the tale of Frost, a sentient machine. Although humans have caused their own extinction, the sentient machines that they created continue the work of rebuilding a shattered Earth. Along the way, the story explores the differences between humanity and machines, the former experiencing the world qualitatively, while the latter doing so quantitatively. This difference is illustrated through philosophical conversations between Frost and another machine named Mordel. Frost's goal of becoming human, along with literary allusions, drives the plot and sets the tone of the novelette. These allusions include the first chapter of the Book of Job, in both situation and language, since verses are both quoted directly and paraphrased. In addition, the first three chapters of the Book of Genesis are echoed. Finally, Frost and Mordel enter into a Faustian bargain, though with better results than in the original story. The other major character is the Beta Machine, Frost's peer in the Southern Hemisphere. (Frost controls the Northern Hemisphere.) The novelette hints that though being a machine, Beta has a feminine personality. After Frost has succeeded in his millennium-long quest to become human (via recovered DNA), Beta agrees to join him in becoming human—suggesting the possibility of rebirth for the human race. The novelette has appeared in collections of Zelazny's works and in anthologies. The title is from a phrase in the poet A. E. Housman's collection A Shropshire Lad.
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The Last Question

"The Last Question" is a science fiction short story by American writer Isaac Asimov. It first appeared in the November 1956 issue of Science Fiction Quarterly; and in the anthologies in the collections Nine Tomorrows (1959), The Best of Isaac Asimov (1973), Robot Dreams (1986), The Best Science Fiction of Isaac Asimov (1986), the retrospective Opus 100 (1969), and Isaac Asimov: The Complete Stories, Vol. 1 (1990). While he also considered it one of his best works, "The Last Question" was Asimov's favorite short story of his own authorship, and is one of a loosely connected series of stories concerning a fictional computer called Multivac. Through successive generations, humanity questions Multivac on the subject of entropy. The story blends science fiction, theology, and philosophy. It has been recognized as a counterpoint to Fredric Brown's short short story "Answer", published two years earlier. == History == In conceiving Multivac, Asimov was extrapolating the trend towards centralization that characterized computation technology planning in the 1950s to an ultimate centrally managed global computer. After seeing a planetarium adaptation of his work, Asimov "privately" concluded that the story was his best science fiction yet written. He placed it just higher than "The Ugly Little Boy" (September 1958) and "The Bicentennial Man" (1976). The story asks the question of humanity's fate, and human existence as a whole, highlighting Asimov's focus on important aspects of our future like population growth and environmental issues. "The Last Question" ranks with "Nightfall" (1941) as one of Asimov's best-known and most acclaimed short stories. He wrote in 1973 that he appreciated how easy the story was to write after he had the idea. He was so often approached by fans who remembered the story but not the title, that in one instance he gave the answer, correctly, before the fan had even described the story. == Plot summary == By the year 2061, Multivac, a self-adjusting and self-correcting computer, has allowed mankind to reach beyond the planetary confines of Earth and harness solar energy. Two technicians, Adell and Lupov, celebrate Multivac's role in this development. Over drinks, they discuss that the sun will expire due to the second law of thermodynamics, which states that entropy inevitably increases. When Adell asks Multivac whether this can be reversed, the computer responds that it has insufficient data to answer. In several episodes over ten trillion years, increasingly advanced humans pose the same question to the computers of their time. Each time the computer gives the same response. At the heat death of the universe, the last disembodied consciousness of Man asks the question a final time of a computer that resides in hyperspace before merging with it. After collecting the last data from the dead universe, the computer continues to process it alone and finds an answer to the last question. Having no one to tell it to, it proceeds to demonstrate by saying "LET THERE BE LIGHT!" == Themes == === Philosophy === Although science and religion are frequently presented as having an oppositional relationship, "The Last Question" explores some biblical contexts ("Let there be light"). In Asimov's story, aspects like the great meaning of existence are culminated through both technology and human knowledge. The evolution from Multivac to AC also emulates a sort of cycle of existence. === Dystopian happy ending === Multivac's purpose was conceptualized with a desire for knowledge, promoting the idea that more knowledge will lead to a better and more fruitful future for humanity. However, the computer's answers regarding the future suggest an inevitable exhaustion of the Sun, and this thirst for knowledge becomes an obsession with the future. The story's end displays a dichotomy between annihilation and peace. == Dramatic adaptations == === Planetarium shows === "The Last Question" was first adapted for the Abrams Planetarium at Michigan State University (in 1966), featuring the voice of Leonard Nimoy, as Asimov wrote in his autobiography In Joy Still Felt (1980). It was adapted for the Strasenburgh Planetarium in Rochester, New York (in 1969), under the direction of Ian C. McLennan. It was adapted for the Edmonton Space Sciences Centre in Edmonton, Alberta (early 1970s), under the direction of John Hault. It was adapted for the Gates Planetarium at the Denver Museum of Natural History in 1973 under the direction of Mark B. Peterson It subsequently played at the: Fels Planetarium of the Franklin Institute in Philadelphia in 1973 Planetarium of the Reading School District in Reading, Pennsylvania in 1974 Buhl Planetarium, Pittsburgh in 1974 The Space Transit Planetarium of the Museum of Science in Miami during 1977 Vanderbilt Planetarium in Centerport New York, in 1978, read by singer-songwriter and Long Island resident Harry Chapin. Hansen Planetarium in Salt Lake City, Utah (in 1980 and 1989) A reading of the story was played on BBC Radio 7 in 2008 and 2009. Gates Planetarium in Denver, Colorado (in early 2020) In 1989 Asimov updated the star show adaptation to add in quasars and black holes. The story was adapted as a comic book by Don Thompson and drawn by John Estes in the third issue of ORBiT.
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Oblivion (2013 film)

Oblivion is a 2013 American epic post-apocalyptic science fiction action film produced and directed by Joseph Kosinski from a screenplay by Karl Gajdusek and Michael deBruyn, starring Tom Cruise in the main role alongside Morgan Freeman, Olga Kurylenko, Andrea Riseborough, Nikolaj Coster-Waldau, and Melissa Leo in supporting roles. Based on Kosinski's unpublished Radical Comics graphic novel of the same name, the film pays homage to 1970s sci-fi, and is a "love story" set in 2077 on an Earth desolated by an alien war; a maintenance technician on the verge of completing his mission finds a woman who survived from a space ship crash, leading him to question his purpose and discover the truth about the war. Oblivion premiered in Buenos Aires on March 26, 2013, and was released in theaters by Universal Pictures on April 19. The film grossed $286 million worldwide on a production budget of $120 million and received mixed reviews from critics. == Plot == In 2017, aliens known as Scavengers attack Earth and destroy the Moon, triggering global natural disasters. Although humanity wins the war using nuclear weapons, Earth is left uninhabitable. Sixty years later, the remnants of humanity have relocated to a colony on Saturn's moon Titan, except for Unit 49—technician Jack and his communications officer Victoria—who are scheduled to join them in two weeks. The pair oversee hydro rigs that convert seawater into fusion energy for the Tet, the last remaining human colony ship in orbit. Though Jack and Victoria are romantically involved and have had their memories erased for security reasons, Jack experiences recurring dreams of an unknown woman. He also secretly visits a hidden, verdant valley where he has built a lakeside cabin and collects relics of Earth's past. While investigating a missing drone—autonomous, highly advanced, and heavily armed machines—Jack is nearly captured by Scavengers. Later, he discovers the Scavengers are transmitting a signal into space. A NASA pod crash-lands at the signal's coordinates, carrying five humans in suspended animation, including the woman from Jack's dreams. A drone arrives and destroys four of the pods, but Jack rescues the remaining one and brings the unconscious woman to Unit 49's base. After reviving her, Jack and Victoria learn that the woman, Julia, has been in stasis aboard the Odyssey spaceship since 2017. Julia insists on recovering the ship's flight recorder. However, she and Jack are captured by Scavengers and brought to the Raven Rock Mountain Complex. Their leader, Malcolm, reveals that the Scavengers are actually surviving humans. Malcolm needs Jack to reprogram a captured drone to deliver a nuclear bomb, built from Odyssey's reactor, to the Tet. Jack refuses, so Malcolm releases him and Julia, urging him to seek the truth in the radiation zone, which is supposedly deadly and off-limits. Julia helps Jack recall that she is his wife, and fragments of his memories begin to return. When they arrive back at Unit 49, a devastated Victoria informs Sally, the Tet's mission controller, that she and Jack are no longer an "effective team." A drone activates and kills Victoria. Jack and Julia destroy the drone, but crash their aircraft inside the radiation zone. There, they encounter another version of Jack—"Jack-52"—who arrives to repair the drone. Jack subdues him, but Julia is seriously injured in the fight. Jack impersonates his clone to infiltrate Unit 52, meets Victoria-52, and steals medical supplies for Julia. They rest at his cabin. At Raven Rock, Malcolm reveals the truth: humanity lost the war, and the Tet is an alien machine intelligence harvesting Earth's resources. After the Moon's destruction, the Tet deployed thousands of clones of astronaut Jack Harper—brainwashed into obedience—to exterminate the remaining humans. Malcolm had assumed these clones were inhuman until witnessing Jack show interest in a discarded book, hinting at lingering humanity. Jack reprograms the captured drone, but it is destroyed in a surprise attack by other drones, leaving Malcolm badly wounded. Jack and Julia resolve to deliver the bomb themselves; Julia enters a stasis pod. En route, Jack listens to the Odyssey's flight recorder, which reveals the original Jack Harper and Victoria were astronauts sent to explore Titan before being confronted by the Tet. The pair were captured, but not before Jack ejected the remaining crew—including Julia—in stasis pods to protect them. Jack gains access to the Tet by claiming he is delivering Julia, as previously instructed. However, the stasis pod contains a dying Malcolm. Jack and Malcolm detonate the bomb, destroying the Tet and themselves. Julia later awakens at the cabin. Three years later, Julia lives there and it is revealed she had a daughter with Jack. A group of Raven Rock survivors arrives, alongside Jack-52, who has begun regaining fragments of his own lost identity. == Cast == Tom Cruise as Jack Harper—Tech 49, a technician who works to repair drones on Earth and questions his mission. Originally, he was the American commander of a mission en route to Titan who was captured by the Tet and cloned to fight humanity. Cruise also plays Jack Harper—Tech 52, a clone who seeks out Julia after the destruction of the Tet. Morgan Freeman as Malcolm Beech, an American veteran soldier and leader of a large community of scavengers, the human survivors of the alien Tet's attacks. Olga Kurylenko as Julia Rusakova Harper, Jack's wife and a Russian crew member on the Odyssey, who was sent back towards Earth by her husband to protect her from the initial contact with the Tet. Andrea Riseborough as Victoria "Vika" Olsen, Jack's communications partner and housemate. Originally, she was the British co-pilot of Jack's mission to Titan who was captured and cloned to assist in the Tet's war on humanity. Riseborough also plays a clone of Vika who Jack misleads to obtain medical supplies. Nikolaj Coster-Waldau as Sergeant Sykes, the main military commander of Beech's community of scavengers who is skeptical of Jack at first. Melissa Leo as the Tet, an alien artificial intelligence seeking to acquire Earth's natural resources and wipe out humanity. Leo also plays Sally, the mission director of Jack and Julia's mission to Titan; her likeness was copied by the Tet to serve as its visual and auditory representation. Zoë Bell as Kara, a soldier and member of the scavengers. == Production == === Development === Joseph Kosinski started the movie process by beginning work on a graphic novel called Oblivion featuring his story. While the completion of this would be teased to the public and the concept was used to pitch the movie, it was never finished and Kosinski claims he never intended to, stating it was "just a stage in the project [of film development]". Arvid Nelson was billed as co-writer and Radical Comics was attached as publisher. The novel was never finished; Kosinski explaining: "the partnership with Radical Comics allowed me to continue working on the story by developing a series of images and continuing to refine the story more over a period of years. Then I basically used all that development as a pitch kit to the studio. So even though we really never released it as an illustrated novel the story is being told as a film, which was always the intention." Walt Disney Pictures, which produced Kosinski's previous film Tron: Legacy (2010), acquired the Oblivion film adaptation rights from Radical Comics and Kosinski after a heated auction in August 2010. The film was a directing vehicle for Kosinski, with Barry Levine producing, and Jesse Berger executive producing. Other studios that made bids on the film were Paramount Pictures, 20th Century Fox, and Universal Pictures. Disney subsequently released the rights after realizing the PG-rated film they envisioned, in line with their family-oriented reputation, would require too many story changes. Universal, which had also bid for the original rights, then bought them from Kosinski and Radical and authorized a PG-13 film version. The film's script was originally written by Kosinski and William Monahan and underwent a first rewrite by Karl Gajdusek. When the film passed into Universal's hands, a final rewrite was done by Michael Arndt, under the pen name "Michael deBruyn". Universal was particularly appreciative of the script, saying, "It's one of the most beautiful scripts we've ever come across." The Bubble Ship operated by Cruise's main character, Jack 49, was inspired by the Bell 47 helicopter (often colloquially referred to as a "bubble cockpit" helicopter), a utilitarian 1947 vehicle with a transparent round canopy that Kosinski saw in the lobby of the Museum of Modern Art in Manhattan, and which he likened to a dragonfly. Daniel Simon, who previously worked with Kosinski as the lead vehicle designer on Tron: Legacy, was tasked with creating the Bubble Ship from this basis, incorporating elements evocative of an advanced fighter
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Mastodon (social network)

Mastodon is a free and open-source software platform for decentralized social networking with microblogging features similar to Twitter. It operates as a federated network of independently managed servers that communicate using the ActivityPub protocol, allowing users to connect across different instances within the Fediverse. Each Mastodon instance establishes its own moderation policies and content guidelines, distinguishing it from centrally controlled social media platforms. First released in 2016 by Eugen Rochko, Mastodon has positioned itself as an alternative to mainstream social media, particularly for users seeking decentralized, community-driven spaces. The platform has experienced multiple surges in adoption, most notably following the Twitter acquisition by Elon Musk in 2022, as users sought alternatives to Twitter. It is part of a broader shift toward decentralized social networks, including Bluesky and Lemmy. Mastodon emphasizes user privacy and moderation flexibility, offering features such as granular post visibility controls, content warning options, and local community-driven moderation. The software is written in Ruby on Rails and Node.js, with a web interface built using React and Redux. It is interoperable with other ActivityPub-based platforms, such as Threads, and supports various third-party applications on desktop and mobile devices. == Functionality == Users post short-form status messages, historically known as "toots", for others to see and interact with. On a standard Mastodon instance, these messages can include up to 500 text-based characters, greater than Twitter's 280-character limit. Some instances support even longer messages. Images, audio files, videos or polls can also be added to a message. Users join a specific Mastodon server, rather than a single centralized website or application. The servers are connected as nodes in a network, and each server can administer its own rules, account privileges, and whether to share messages to and from other servers. Users can communicate and follow each other across connected Mastodon servers with usernames similar in format to full email addresses. Since version 2.9.0, Mastodon's web user interface has offered a single-column mode for new users by default. In advanced mode, the interface approximates the microblogging interface of TweetDeck. === Privacy === Mastodon includes a number of specific privacy features. Each message has a variety of privacy options available, and users can choose whether the message is public or private. Messages can display public on a global feed, known as a timeline, or can be shared only to the user's followers. Messages can also be marked as unlisted from timelines or direct between users. Users can also mark their accounts as completely private. In the timeline, messages can display with an optional content warning feature, which requires readers to click on the hidden main body of the message to reveal it. Mastodon servers have used this feature to hide spoilers, trigger warnings, and not safe for work (NSFW) content, though some accounts use the feature to hide links and thoughts others might not want to read. Mastodon aggregates messages in local and federated timelines in real time. The local timeline shows messages from users on a singular server, while the federated timeline shows messages across all participating Mastodon servers. === Content moderation === In early 2017, journalists like Sarah Jeong distinguished Mastodon from Twitter for its approach to combating harassment. Mastodon uses community-based moderation, in which each server can limit or filter out undesirable types of content, while Twitter uses a single, global policy on content moderation. Servers can choose to limit or filter out messages with disparaging content. The founder of Mastodon, Eugen Rochko, believes that small, closely related communities deal with unwanted behavior more effectively than a large company's small safety team. In Move Slowly and Build Bridges, Robert W. Gehl argues that predominantly white participation has shaped Mastodon in ways that affect how reports of racism are received and limit its ability to replicate Black Twitter on Twitter. Users can also block and report others to administrators, much like on Twitter. Instance administrators can block other instances from interacting with their own, an action called defederation. By posting toots hashtagged with #fediblock, some instance administrators and users alert others of issues requiring moderation. === Searching === Mastodon by default allows searching for hashtags and mentioned accounts in the Fediverse. Server administrators can optionally enable Elasticsearch to search the full-text of public posts that have opted in to being indexed. == Versions == In September 2018, with the release of version 2.5 with redesigned public profile pages, Mastodon marked its 100th release. Mastodon 2.6 was released in October 2018, introducing the possibilities of verified profiles and live, in-stream link previews for images and videos. Version 2.7, in January 2019, made it possible to search for multiple hashtags at once, instead of searching for just a single hashtag, with more robust moderation capabilities for server administrators and moderators, while accessibility, such as contrast for users with sight issues, was improved. The ability for users to create and vote in polls, as well as a new invitation system to manage registrations was integrated in April 2019. Mastodon 2.8.1, released in May 2019, made images with content warnings blurred instead of completely hidden. In version 2.9 in June 2019, an optional single-column view was added. This view became the default displayed to new users, with a user "preferences" option to switch to a multiple-column-based view. In August 2020, Mastodon 3.2 was released. It included a redesigned audio player with custom thumbnails and the ability to add personal notes to one's profile. In July 2021, an official client for iOS devices was released. According to the project's then CEO, Eugen Rochko, the release was part of an effort to attract new users. Mastodon 4.0 was released in November 2022, including language support for translating posts, editing posts and following hashtags. Mastodon 4.5 was released in November 2025. Among other features it introduced quote posts, which were previously rejected from being implemented due to concerns about toxicity and harassment. To mitigate these issues Mastodon's quote post feature has been designed in a way that lets users decide if and by whom their posts can be quoted. == Software == Mastodon is published as free and open-source software under the Affero GPL license, allowing anyone to use the software or modify it as they wish. Servers can be run by any individual or organization, and users can join these servers as they wish. The server software itself is powered by Ruby on Rails and Node.js, with its web client being written in React.js and Redux. The only database software supported is PostgreSQL, with Redis being used for job processing and various actions that Mastodon needs to process. The service is interoperable with the fediverse, a collection of social networking services which use the ActivityPub protocol for communication between each other, with previous versions containing support for OStatus. Client apps for interacting with the Mastodon API are available for desktop computer operating systems, including Windows, macOS and the Linux family of operating systems, as well as mobile phones running iOS and Android. The API is open for anyone to utilize, allowing clients to be built for any operating system that can connect to the internet. === Integration with Fediverse === Mastodon uses the ActivityPub protocol for federation; this allows users to communicate between independent Mastodon instances and other ActivityPub compatible services. Thus, Mastodon is generally considered to be a part of the Fediverse. Services utilizing the ActivityPub protocol exist which allow for searching all posts on all instances as long as users opt-in. For similar reasons, only hashtags can appear in a Mastodon instance's trending topics, not arbitrary popular words. Trending topics vary between instances, since individual instances are aware of different subsets of posts from the whole fediverse. === Security concerns === While Mastodon's decentralized structure is one of its most distinctive features, it also poses additional security challenges. Since many Mastodon instances are run by volunteers, some security experts are concerned about data security and responsiveness to new threats and vulnerabilities across the network, considering the difficulty of configuring and maintaining an instance as well as uneven skill levels among administrators. Administrators of an instance also have access to the private information of any users that are either registered with that instance or have federated
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Semantic Scholar

Semantic Scholar is a research tool for scientific literature. It is developed at the Allen Institute for AI and was publicly released in November 2015. Semantic Scholar uses modern techniques in natural language processing to support the research process, for example by providing automatically generated summaries of scholarly papers. The Semantic Scholar team is actively researching the use of artificial intelligence in natural language processing, machine learning, human–computer interaction, and information retrieval. Semantic Scholar began as a database for the topics of computer science, geoscience, and neuroscience. In 2017, the system began including biomedical literature in its corpus. As of September 2022, it includes over 200 million publications from all fields of science. == Technology == Semantic Scholar provides a one-sentence summary of scientific literature. One of its aims was to address the challenge of reading numerous titles and lengthy abstracts on mobile devices. It also seeks to ensure that the three million scientific papers published yearly reach readers, since it is estimated that only half of this literature is ever read. Artificial intelligence is used to capture the essence of a paper, generating it through an "abstractive" technique. The project uses a combination of machine learning, natural language processing, and machine vision to add a layer of semantic analysis to the traditional methods of citation analysis, and to extract relevant figures, tables, entities, and venues from papers. Another key AI-powered feature is Research Feeds, an adaptive research recommender that uses AI to quickly learn what papers users care about reading and recommends the latest research to help scholars stay up to date. It uses a paper embedding model trained using contrastive learning to find papers similar to those in each Library folder. Semantic Scholar also offers Semantic Reader, an augmented reader with the potential to revolutionize scientific reading by making it more accessible and richly contextual. Semantic Reader provides in-line citation cards that allow users to see citations with TLDR (short for Too Long, Didn't Read) automatically generated short summaries as they read and skimming highlights that capture key points of a paper so users can digest faster. In contrast with Google Scholar and PubMed, Semantic Scholar is designed to highlight the most important and influential elements of a paper. The AI technology is designed to identify hidden connections and links between research topics. Like the previously cited search engines, Semantic Scholar also exploits graph structures, which include the Microsoft Academic Knowledge Graph, Springer Nature's SciGraph, and the Semantic Scholar Corpus (originally a 45 million papers corpus in computer science, neuroscience and biomedicine). == Article identifier == Each paper hosted by Semantic Scholar is assigned a unique identifier called the Semantic Scholar Corpus ID (abbreviated S2CID). The following entry is an example: Liu, Ying; Gayle, Albert A; Wilder-Smith, Annelies; Rocklöv, Joacim (March 2020). "The reproductive number of COVID-19 is higher compared to SARS coronavirus". Journal of Travel Medicine. 27 (2). doi:10.1093/jtm/taaa021. PMID 32052846. S2CID 211099356. == Indexing == Semantic Scholar is free to use and unlike similar search engines (e.g., Google Scholar) does not search for material that is behind a paywall. One study compared the index scope of Semantic Scholar to Google Scholar, and found that for the papers cited by secondary studies in computer science, the two indices had comparable coverage, each only missing a handful of the papers. == Number of users and publications == As of January 2018, following a 2017 project that added biomedical papers and topic summaries, the Semantic Scholar corpus included more than 40 million papers from computer science and biomedicine. In March 2018, Doug Raymond, who developed machine learning initiatives for the Amazon Alexa platform, was hired to lead the Semantic Scholar project. As of August 2019, the number of included papers metadata (not the actual PDFs) had grown to more than 173 million after the addition of the Microsoft Academic Graph records. In 2020, a partnership between Semantic Scholar and the University of Chicago Press Journals made all articles published under the University of Chicago Press available in the Semantic Scholar corpus. At the end of 2020, Semantic Scholar had indexed 190 million papers. In 2020, Semantic Scholar reached seven million users per month.
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Fuzzy mathematics

Fuzzy mathematics is a branch of mathematics that extends classical set theory and logic to model reasoning under uncertainty. Initiated by Lotfi Asker Zadeh in 1965 with the introduction of fuzzy sets, the field has since evolved to include fuzzy set theory, fuzzy logic, and various fuzzy analogues of traditional mathematic structures. Unlike classical mathematics, which usually relies on binary membership (an element either belongs to a set or it does not), fuzzy mathematics allows elements to partially belong to a set, with degrees of membership represented by values in the interval [0, 1]. This framework enables more flexible modeling of imprecise or vague concepts. Fuzzy mathematics has found applications in numerous domains, including control theory, artificial intelligence, decision theory, pattern recognition, and linguistics, where the modeling of gradations and uncertainty is essential. == Definition == A fuzzy subset A of a set X is defined by a function A: X → L, where L is typically the interval [0, 1]. This function is called the membership function of the fuzzy subset and assigns to each element x in X a degree of membership A(x) in the fuzzy set A. In classical set theory, a subset of X can be represented by an indicator function (also known as a characteristic function), which maps elements to either 0 or 1, indicating non-membership or full membership, respectively. Fuzzy subsets generalize this concept by allowing any real value between 0 and 1, thereby enabling partial membership. More generally, the codomain L of the membership function can be replaced with any complete lattice, resulting in the broader framework of L-fuzzy sets. == Fuzzification == The development of fuzzification in mathematics can be broadly divided into three historical stages: Initial, straightforward fuzzifications (1960s–1970s), Expansion of generalization techniques (1980s), Standardization, axiomatization, and L-fuzzification (1990s). Fuzzification generally involves extending classical mathematical concepts from binary (crisp) logic, where membership is determined by characteristic functions, to fuzzy logic, where membership is expressed by values in the interval [0, 1] via membership functions. Let A and B be fuzzy subsets of a set X. The fuzzy versions of set-theoretic operations are commonly defined as: ( A ∩ B ) ( x ) = min ( A ( x ) , B ( x ) ) {\displaystyle (A\cap B)(x)=\min(A(x),B(x))} ( A ∪ B ) ( x ) = max ( A ( x ) , B ( x ) ) {\displaystyle (A\cup B)(x)=\max(A(x),B(x))} for all x ∈ X {\displaystyle x\in X} . These operations can be generalized using t-norms and t-conorms, respectively. For example, the minimum operation can be replaced by multiplication: ( A ∩ B ) ( x ) = A ( x ) ⋅ B ( x ) {\displaystyle (A\cap B)(x)=A(x)\cdot B(x)} Fuzzification of algebraic structures often relies on generalizing the closure property. Let ∗ {\displaystyle } be a binary operation on X, and let A be a fuzzy subset of X. Then A is said to satisfy fuzzy closure if: A ( x ∗ y ) ≥ min ( A ( x ) , A ( y ) ) {\displaystyle A(xy)\geq \min(A(x),A(y))} for all x , y ∈ X {\displaystyle x,y\in X} . If ( G , ∗ ) {\displaystyle (G,)} is a group, then a fuzzy subset A of G is a fuzzy subgroup if: A ( x ∗ y − 1 ) ≥ min ( A ( x ) , A ( y − 1 ) ) {\displaystyle A(xy^{-1})\geq \min(A(x),A(y^{-1}))} for all x , y ∈ G {\displaystyle x,y\in G} . Similar generalizations apply to relational properties. For example, for example, for fuzzification of the transitivity property, a fuzzy relation R {\displaystyle R} on X {\displaystyle X} (i.e., a fuzzy subset of X × X {\displaystyle X\times X} ) is said to be fuzzy transitive if: R ( x , z ) ≥ min ( R ( x , y ) , R ( y , z ) ) {\displaystyle R(x,z)\geq \min(R(x,y),R(y,z))} for all x , y , z ∈ X {\displaystyle x,y,z\in X} . == Fuzzy analogues == Fuzzy subgroupoids and fuzzy subgroups were introduced in 1971 by A. Rosenfeld. Analogues of other mathematical subjects have been translated to fuzzy mathematics, such as fuzzy field theory and fuzzy Galois theory, fuzzy topology, fuzzy geometry, fuzzy orderings, and fuzzy graphs.
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