AI Art Zeus

AI Art Zeus — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Tessellation (computer graphics)

    Tessellation (computer graphics)

    In computer graphics, tessellation is the dividing of datasets of polygons (sometimes called vertex sets) presenting objects in a scene into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL 4.0 and Direct3D 11. == In graphics rendering == A key advantage of tessellation for realtime graphics is that it allows detail to be dynamically added and subtracted from a 3D polygon mesh and its silhouette edges based on control parameters (often camera distance). In previously leading realtime techniques such as parallax mapping and bump mapping, surface details could be simulated at the pixel level, but silhouette edge detail was fundamentally limited by the quality of the original dataset. In Direct3D 11 pipeline (a part of DirectX 11), the graphics primitive is the patch. The tessellator generates a triangle-based tessellation of the patch according to tessellation parameters such as the TessFactor, which controls the degree of fineness of the mesh. The tessellation, along with shaders such as a Phong shader, allows for producing smoother surfaces than would be generated by the original mesh. By offloading the tessellation process onto the GPU hardware, smoothing can be performed in real time. Tessellation can also be used for implementing subdivision surfaces, level of detail scaling and fine displacement mapping. OpenGL 4.0 uses a similar pipeline, where tessellation into triangles is controlled by the Tessellation Control Shader and a set of four tessellation parameters. == In computer-aided design == In computer-aided design the constructed design is represented by a boundary representation topological model, where analytical 3D surfaces and curves, limited to faces, edges, and vertices, constitute a continuous boundary of a 3D body. Arbitrary 3D bodies are often too complicated to analyze directly. So they are approximated (tessellated) with a mesh of small, easy-to-analyze pieces of 3D volume—usually either irregular tetrahedra, or irregular hexahedra. The mesh is used for finite element analysis. The mesh of a surface is usually generated per individual faces and edges (approximated to polylines) so that original limit vertices are included into mesh. To ensure that approximation of the original surface suits the needs of further processing, three basic parameters are usually defined for the surface mesh generator: The maximum allowed distance between the planar approximation polygon and the surface (known as "sag"). This parameter ensures that mesh is similar enough to the original analytical surface (or the polyline is similar to the original curve). The maximum allowed size of the approximation polygon (for triangulations it can be maximum allowed length of triangle sides). This parameter ensures enough detail for further analysis. The maximum allowed angle between two adjacent approximation polygons (on the same face). This parameter ensures that even very small humps or hollows that can have significant effect to analysis will not disappear in mesh. An algorithm generating a mesh is typically controlled by the above three and other parameters. Some types of computer analysis of a constructed design require an adaptive mesh refinement, which is a mesh made finer (using stronger parameters) in regions where the analysis needs more detail.

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  • P4-metric

    P4-metric

    The P4 metric (also known as FS or Symmetric F ) enables performance evaluation of a binary classifier. The P4 metric is calculated from precision, recall, specificity, and NPV (negative predictive value). The definition of the P4 metric is similar to that of the F1 metric, however the P4 metric definition addresses criticisms leveled against the definition of the F1 metric. The definition of the P4 metric may, therefore, be understood as an extension of the F1 metric. Like the other known metrics, the P4 metric is a function of: TP (true positives), TN (true negatives), FP (false positives), FN (false negatives). == Justification == The key concept of the P4 metric is to leverage the four key conditional probabilities: P ( + ∣ C + ) {\displaystyle P(+\mid C{+})} — the probability that the sample is positive, provided the classifier result was positive. P ( C + ∣ + ) {\displaystyle P(C{+}\mid +)} — the probability that the classifier result will be positive, provided the sample is positive. P ( C − ∣ − ) {\displaystyle P(C{-}\mid -)} — the probability that the classifier result will be negative, provided the sample is negative. P ( − ∣ C − ) {\displaystyle P(-\mid C{-})} — the probability the sample is negative, provided the classifier result was negative. The main assumption behind this metric is that all the probabilities mentioned above are close to 1 for a properly designed binary classifier. Indeed, P 4 = 1 {\displaystyle \mathrm {P} _{4}=1} if, and only if, all of the probabilities above are equal to 1. Another important feature is that P 4 {\displaystyle \mathrm {P} _{4}} tends to zero any of the above probabilities tend to zero. == Definition == P4 is defined as a harmonic mean of four key conditional probabilities: P 4 = 4 1 P ( + ∣ C + ) + 1 P ( C + ∣ + ) + 1 P ( C − ∣ − ) + 1 P ( − ∣ C − ) = 4 1 p r e c i s i o n + 1 r e c a l l + 1 s p e c i f i c i t y + 1 N P V . {\displaystyle \mathrm {P} _{4}={\frac {4}{{\frac {1}{P(+\mid C{+})}}+{\frac {1}{P(C{+}\mid +)}}+{\frac {1}{P(C{-}\mid -)}}+{\frac {1}{P(-\mid C{-})}}}}={\frac {4}{{\frac {1}{\mathit {precision}}}+{\frac {1}{\mathit {recall}}}+{\frac {1}{\mathit {specificity}}}+{\frac {1}{\mathit {NPV}}}}}.} In terms of TP,TN,FP,FN it can be calculated as follows: P 4 = 4 ⋅ T P ⋅ T N 4 ⋅ T P ⋅ T N + ( T P + T N ) ⋅ ( F P + F N ) . {\displaystyle \mathrm {P} _{4}={\frac {4\cdot \mathrm {TP} \cdot \mathrm {TN} }{4\cdot \mathrm {TP} \cdot \mathrm {TN} +(\mathrm {TP} +\mathrm {TN} )\cdot (\mathrm {FP} +\mathrm {FN} )}}.} == Evaluation of the binary classifier performance == Evaluating the performance of binary classifiers is a multidisciplinary concept. It spans from the evaluation of medical tests, psychiatric tests to machine learning classifiers from a variety of fields. Thus, many of the metrics in use exist under several names, some defined independently. == Properties of P4 metric == Symmetry — contrasting to the F1 metric, P4 is symmetrical. It means - it does not change its value when dataset labeling is changed - positives named negatives and negatives named positives. Range: P 4 ∈ [ 0 , 1 ] {\displaystyle \mathrm {P} _{4}\in [0,1]} . Achieving P 4 ≈ 1 {\displaystyle \mathrm {P} _{4}\approx 1} requires all the key four conditional probabilities being close to 1. For P 4 ≈ 0 {\displaystyle \mathrm {P} _{4}\approx 0} it is sufficient that one of the key four conditional probabilities is close to 0. == Examples, comparing with the other metrics == Dependency table for selected metrics ("true" means depends, "false" - does not depend): Metrics that do not depend on a given probability are prone to misrepresentation when the probability approaches 0. === Example 1: Rare disease detection test === Let us consider a medical test used to detect a rare disease. Suppose a population size of 100000 and 0.05% of the population is infected. Further suppose the following test performance: 95% of all positive individuals are classified correctly (TPR=0.95) and 95% of all negative individuals are classified correctly (TNR=0.95). In such a case, due to high population imbalance and in spite of having high test accuracy (0.95), the probability that an individual who has been classified as positive is in fact positive is very low: P ( + ∣ C + ) = 0.0095. {\displaystyle P(+\mid C{+})=0.0095.} We can observe how this low probability is reflected in some of the metrics: P 4 = 0.0370 {\displaystyle \mathrm {P} _{4}=0.0370} , F 1 = 0.0188 {\displaystyle \mathrm {F} _{1}=0.0188} , J = 0.9100 {\displaystyle \mathrm {J} =\mathbf {0.9100} } (Informedness / Youden index), M K = 0.0095 {\displaystyle \mathrm {MK} =0.0095} (Markedness). === Example 2: Image recognition — cats vs dogs === Consider the problem of training a neural network based image classifier with only two types of images: those containing dogs (labeled as 0) and those containing cats (labeled as 1). Thus, the goal is to distinguish between the cats and dogs. Suppose that the classifier overpredicts in favour of cats ("positive" samples): 99.99% of cats are classified correctly and only 1% of dogs are classified correctly. Further, suppose that the image dataset consists of 100000 images, 90% of which are pictures of cats and 10% are pictures of dogs. In this situation, the probability that the picture containing dog will be classified correctly is pretty low: P ( C − | − ) = 0.01. {\displaystyle P(C-|-)=0.01.} Not all metrics are notice this low probability: P 4 = 0.0388 {\displaystyle \mathrm {P} _{4}=0.0388} , F 1 = 0.9478 {\displaystyle \mathrm {F} _{1}=\mathbf {0.9478} } , J = 0.0099 {\displaystyle \mathrm {J} =0.0099} (Informedness / Youden index), M K = 0.8183 {\displaystyle \mathrm {MK} =\mathbf {0.8183} } (Markedness).

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  • Is an Conversational AI Platform Worth It in 2026?

    Is an Conversational AI Platform Worth It in 2026?

    Looking for the best conversational AI platform? An conversational AI platform is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right conversational AI platform slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Is an AI Code Generator Worth It in 2026?

    Is an AI Code Generator Worth It in 2026?

    Comparing the best AI code generator? An AI code generator is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI code generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Automation

    Automation

    Automation describes a wide range of technologies that reduce human intervention in processes, mainly by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines. Automation has been achieved by various means including mechanical, hydraulic, pneumatic, electrical, electronic devices, and computers, usually in combination. Complicated systems, such as modern factories, airplanes, and ships typically use combinations of all of these techniques. The benefits of automation includes labor savings, reducing waste, savings in electricity costs, savings in material costs, and improvements to quality, accuracy, and precision. Automation includes the use of various equipment and control systems such as machinery, processes in factories, boilers, and heat-treating ovens, switching on telephone networks, steering, stabilization of ships, aircraft and other applications and vehicles with reduced human intervention. Examples range from a household thermostat controlling a boiler to a large industrial control system with tens of thousands of input measurements and output control signals. In the simplest type of an automatic control loop, a controller compares a measured value of a process with a desired set value and processes the resulting error signal to change some input to the process, in such a way that the process stays at its set point despite disturbances. This closed-loop control is an application of negative feedback to a system. The mathematical basis of control theory began in the 18th century and advanced rapidly in the 20th. The term automation, inspired by the earlier word automatic (coming from automaton), was not widely used before 1947, when Ford established an automation department. It was during this time that the industry was rapidly adopting feedback controllers, Technological advancements introduced in the 1930s revolutionized various industries significantly. The World Bank's World Development Report of 2019 shows evidence that the new industries and jobs in the technology sector outweigh the economic effects of workers being displaced by automation. Job losses and downward mobility blamed on automation have been cited as one of many factors in the resurgence of nationalist, protectionist and populist politics in the US, UK and France, among other countries since the 2010s. == History == === Early history === It was a preoccupation of the Greeks and Arabs (in the period between about 300 BC and about 1200 AD) to keep an accurate track of time. In Ptolemaic Egypt, about 270 BC, Ctesibius described a float regulator for a water clock, a device not unlike the ball and cock in a modern flush toilet. This was the earliest feedback-controlled mechanism. The appearance of the mechanical clock in the 14th century made the water clock and its feedback control system obsolete. The Persian Banū Mūsā brothers, in their Book of Ingenious Devices (850 AD), described a number of automatic controls. Two-step level controls for fluids, a form of discontinuous variable structure controls, were developed by the Banu Musa brothers. They also described a feedback controller. The design of feedback control systems up through the Industrial Revolution was by trial-and-error, together with a great deal of engineering intuition. It was not until the mid-19th century that the stability of feedback control systems was analyzed using mathematics, the formal language of automatic control theory. The centrifugal governor was invented by Christiaan Huygens in the seventeenth century, and used to adjust the gap between millstones. === Industrial Revolution in Western Europe === The introduction of prime movers, or self-driven machines advanced grain mills, furnaces, boilers, and the steam engine created a new requirement for automatic control systems including temperature regulators (invented in 1624; see Cornelius Drebbel), pressure regulators (1681), float regulators (1700) and speed control devices. Another control mechanism was used to tent the sails of windmills. It was patented by Edmund Lee in 1745. Also in 1745, Jacques de Vaucanson invented the first automated loom. Around 1800, Joseph Marie Jacquard created a punch-card system to program looms. In 1771 Richard Arkwright invented the first fully automated spinning mill driven by water power, known at the time as the water frame. An automatic flour mill was developed by Oliver Evans in 1785, making it the first completely automated industrial process. A centrifugal governor was used by Mr. Bunce of England in 1784 as part of a model steam crane. The centrifugal governor was adopted by James Watt for use on a steam engine in 1788 after Watt's partner Boulton saw one at a flour mill Boulton & Watt were building. The governor could not actually hold a set speed; the engine would assume a new constant speed in response to load changes. The governor was able to handle smaller variations such as those caused by fluctuating heat load to the boiler. Also, there was a tendency for oscillation whenever there was a speed change. As a consequence, engines equipped with this governor were not suitable for operations requiring constant speed, such as cotton spinning. Several improvements to the governor, plus improvements to valve cut-off timing on the steam engine, made the engine suitable for most industrial uses before the end of the 19th century. Advances in the steam engine stayed well ahead of science, both thermodynamics and control theory. The governor received relatively little scientific attention until James Clerk Maxwell published a paper that established the beginning of a theoretical basis for understanding control theory. === 20th century === Relay logic was introduced with factory electrification, which underwent rapid adaptation from 1900 through the 1920s. Central electric power stations were also undergoing rapid growth and the operation of new high-pressure boilers, steam turbines and electrical substations created a great demand for instruments and controls. Central control rooms became common in the 1920s, but as late as the early 1930s, most process controls were on-off. Operators typically monitored charts drawn by recorders that plotted data from instruments. To make corrections, operators manually opened or closed valves or turned switches on or off. Control rooms also used color-coded lights to send signals to workers in the plant to manually make certain changes. The development of the electronic amplifier during the 1920s, which was important for long-distance telephony, required a higher signal-to-noise ratio, which was solved by negative feedback noise cancellation. This and other telephony applications contributed to the control theory. In the 1940s and 1950s, German mathematician Irmgard Flügge-Lotz developed the theory of discontinuous automatic controls, which found military applications during the Second World War to fire control systems and aircraft navigation systems. Controllers, which were able to make calculated changes in response to deviations from a set point rather than on-off control, began being introduced in the 1930s. Controllers allowed manufacturing to continue showing productivity gains to offset the declining influence of factory electrification. Factory productivity was greatly increased by electrification in the 1920s. U.S. manufacturing productivity growth fell from 5.2%/yr 1919–29 to 2.76%/yr 1929–41. Alexander Field notes that spending on non-medical instruments increased significantly from 1929 to 1933 and remained strong thereafter. The First and Second World Wars saw major advancements in the field of mass communication and signal processing. Other key advances in automatic controls include differential equations, stability theory and system theory (1938), frequency domain analysis (1940), ship control (1950), and stochastic analysis (1941). Starting in 1958, various systems based on solid-state digital logic modules for hard-wired programmed logic controllers (the predecessors of programmable logic controllers [PLC]) emerged to replace electro-mechanical relay logic in industrial control systems for process control and automation, including early Telefunken/AEG Logistat, Siemens Simatic, Philips/Mullard/Valvo Norbit, BBC Sigmatronic, ACEC Logacec, Akkord Estacord, Krone Mibakron, Bistat, Datapac, Norlog, SSR, or Procontic systems. In 1959 Texaco's Port Arthur Refinery became the first chemical plant to use digital control. Conversion of factories to digital control began to spread rapidly in the 1970s as the price of computer hardware fell. === Significant applications === The automatic telephone switchboard was introduced in 1892 along with dial telephones. By 1929, 31.9% of the Bell system was automatic. Automatic telephone switching originally used vacuum tube amplifiers and electro-mechanical switches, which consumed a large amount of electricity. Call volume eve

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  • Translation unit

    Translation unit

    In the field of translation, a translation unit is a segment of a text which the translator treats as a single cognitive unit for the purposes of establishing an equivalence. It may be a single word, a phrase, one or more sentences, or even a larger unit. When a translator segments a text into translation units, the larger these units are, the better chance there is of obtaining an idiomatic translation. This is true not only of human translation, but also where human translators use computer-assisted translation, such as translation memories, and when translations are performed by machine translation systems. == Perceptions on the concept of unit == Vinay and Darbelnet took to Saussure's original concepts of the linguistic sign when beginning to discuss the idea of a single word as a translation unit. According to Saussure, the sign is naturally arbitrary, so it can only derive meaning from contrast in other signs in that same system. However, Russian scholar Leonid Barkhudarov stated that, limiting it to poetry, for instance, a translation unit can take the form of a complete text. This seems to relate to his conception that a translation unit is the smallest unit in the source language with an equivalent in the target one, and when its parts are taken individually, they become untranslatable; these parts can be as small as phonemes or morphemes, or as large as entire texts. Susan Bassnett widened Barkhudarov's poetry perception to include prose, adding that in this type of translation text is the prime unit, including the idea that sentence-by-sentence translation could cause loss of important structural features. Swiss linguist Werner Koller connected Barkhudarov's idea of unit sizing to the difference between the two languages involved, by stating that the more different or unrelated these languages were, the larger the unit would be. One final perception on the idea of unit came from linguist Eugene Nida. To him, translation units have a tendency to be small groups of language building up into sentences, thus forming what he called meaningful mouthfuls of language. == Points of view towards translation units == === Process-oriented POV === According to this point of view, a translation unit is a stretch of text on which attention is focused to be represented as a whole in the target language. In this point of view we can consider the concept of the think-aloud protocol, supported by German linguist Wolfgang Lörscher: isolating units using self-reports by translating subjects. It also relates to how experienced the translator in question is: language learners take a word as a translation unit, whereas experienced translators isolate and translate units of meaning in the form of phrases, clauses or sentences. Since 1996 and 2005 keylogging and eyetracking technologies were introduced in Translation Process Research. These more advanced and non-invasive research methods made it possible to elaborate a finer-grained assessment of translation units as loops of (source or target text) reading and target text typing. Loops of translation units are thought to be the basic units by which translations are produced. Thus, Malmkjaer, for instance, defines process oriented translation units as a “stretch of the source text that the translator keeps in mind at any one time, in order to produce translation equivalents in the text he or she is creating” (p. 286). Records of keystrokes and eye movements allow to investigate these mental constructs through their physical (observable) behavioral traces in the translation process data. Empirical Translation Process Research has deployed numerous theories to explain and models the behavioral traces of these assumed mental units. === Product-oriented POV === Here, the target-text unit can be mapped into an equivalent source-text unit. A case study on this matter was reported by Gideon Toury, in which 27 English-Hebrew student-produced translations were mapped onto a source text. Those students that were less experienced had larger numbers of small units at word and morpheme level in their translations, while one student with translation experience had approximately half of those units, mostly at phrase or clause level.

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  • Node2vec

    Node2vec

    node2vec is an algorithm to generate vector representations of nodes on a graph. The node2vec framework learns low-dimensional representations for nodes in a graph through the use of random walks through a graph starting at a target node. It is useful for a variety of machine learning applications. node2vec follows the intuition that random walks through a graph can be treated like sentences in a corpus. Each node in a graph is treated like an individual word, and a random walk is treated as a sentence. By feeding these "sentences" into a skip-gram, or by using the continuous bag of words model, paths found by random walks can be treated as sentences, and traditional data-mining techniques for documents can be used. The algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and argues that the added flexibility in exploring neighborhoods is the key to learning richer representations of nodes in graphs. The algorithm is considered one of the best graph classifiers.

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  • Is an AI Humanizer Worth It in 2026?

    Is an AI Humanizer Worth It in 2026?

    Shopping for the best AI humanizer? An AI humanizer is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI humanizer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Procreate (software)

    Procreate (software)

    Procreate is a raster graphics editor app for digital painting developed and published by the Australian company Savage Interactive for iOS and iPadOS. It was launched on the App Store in 2011. == Versions == === Procreate === Procreate for iPad was first released in 2011 by the Tasmanian software company Savage Interactive. In June 2013, Savage launched Procreate 2 in conjunction with iOS 7, adding new features such as higher resolution capabilities and more brush options. In 2016, Procreate became one of the top ten best-selling iPad apps on the App Store. In 2018, Procreate became the overall best selling iPad app. With iOS 26, Procreate adapted Liquid Glass into its software. As of March 2026, the most recent version of Procreate for the iPad is 5.4.9. === Procreate Pocket === Procreate Pocket was released to the App Store in December 2014. In 2018, Savage launched Procreate Pocket 2.0 to the App Store. In December 2018, Procreate Pocket received Apple's "App of the Year" award. As of September 2025, the most recent version of Procreate Pocket (for the iPhone) is 4.0.15. === Procreate Dreams === Procreate Dreams, their more recent app focused on 2D animation, was released on the App Store on November 22, 2023. While the application is commended for its intuitive interface and accessibility, some reviewers have noted that it may lack some key animations features, such as reference layers. In June 2024, Procreate Dreams received the 2024 Apple Design Award for Innovation. In December 2025, Savage Interactive released Procreate Dreams 2, a long awaited update and redesign to Procreate Dreams. == Features == The current versions of Procreate use Valkyrie, a proprietary graphics engine to allow customisable brush options and importing brushes from Adobe Photoshop. Procreate offers known features like layers, masks, and blending mode. Its biggest standout compared to other professional drawing software is its simple UI and comparatively easy learning curve. The app also allows for animation. Savage expanded upon Procreate's animation features with a companion app dedicated to 2D animation called Procreate Dreams, released in November 2023. On August 2024, Procreate announced that it would not be incorporating generative artificial intelligence into its software. Savage offers a free internet forum called Procreate Discussions in which users can ask for help, suggest ideas, and share user-generated content on the marketplace or the resources board. == Notable users == Concept artist Doug Chiang creates robot, vehicle, and creature designs for Star Wars in Procreate. Professional artists have also used Procreate to create the posters for Stranger Things, Logan, and Blade Runner 2049, as well as several covers for The New Yorker. It has also been professionally adopted at Marvel Comics, DC Comics, Disney Animation, and Pixar.

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  • Permutation automaton

    Permutation automaton

    In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q0, F), where Q is the set of states of the automaton, Σ is the set of input symbols, δ is the transition function that takes a state q and an input symbol x to a new state δ(q,x), q0 is the initial state of the automaton, and F is the set of accepting states (also: final states) of the automaton. A is a permutation automaton if and only if, for every two distinct states qi and qj in Q and every input symbol x in Σ, δ(qi,x) ≠ δ(qj,x). A formal language is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. For example, the set of strings of even length forms a p-regular language: it may be accepted by a permutation automaton with two states in which every transition replaces one state by the other. == Applications == The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be computable. Another mathematical problem on regular languages is the separating words problem, which asks for the size of a smallest deterministic finite automaton that distinguishes between two given words of length at most n – by accepting one word and rejecting the other. The known upper bound in the general case is O ( n 2 / 5 ( log ⁡ n ) 3 / 5 ) {\displaystyle O(n^{2/5}(\log n)^{3/5})} . The problem was later studied for the restriction to permutation automata. In this case, the known upper bound changes to O ( n 1 / 2 ) {\displaystyle O(n^{1/2})} .

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  • Is an AI Logo Maker Worth It in 2026?

    Is an AI Logo Maker Worth It in 2026?

    Looking for the best AI logo maker? An AI logo maker is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI logo maker slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Best AI Copywriting Tools in 2026

    Best AI Copywriting Tools in 2026

    Looking for the best AI copywriting tool? An AI copywriting tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI copywriting tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Inductive probability

    Inductive probability

    Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem. Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements. Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct. == History == Probability and statistics was focused on probability distributions and tests of significance. Probability was formal, well defined, but limited in scope. In particular its application was limited to situations that could be defined as an experiment or trial, with a well defined population. Bayes's theorem is named after Rev. Thomas Bayes 1701–1761. Bayesian inference broadened the application of probability to many situations where a population was not well defined. But Bayes' theorem always depended on prior probabilities, to generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer programs, that give shorter representations of the data circa 1964. Chris Wallace and D. M. Boulton developed minimum message length circa 1968. Later Jorma Rissanen developed the minimum description length circa 1978. These methods allow information theory to be related to probability, in a way that can be compared to the application of Bayes' theorem, but which give a source and explanation for the role of prior probabilities. Marcus Hutter combined decision theory with the work of Ray Solomonoff and Andrey Kolmogorov to give a theory for the Pareto optimal behavior for an Intelligent agent, circa 1998. === Minimum description/message length === The program with the shortest length that matches the data is the most likely to predict future data. This is the thesis behind the minimum message length and minimum description length methods. At first sight Bayes' theorem appears different from the minimimum message/description length principle. At closer inspection it turns out to be the same. Bayes' theorem is about conditional probabilities, and states the probability that event B happens if firstly event A happens: P ( A ∧ B ) = P ( B ) ⋅ P ( A | B ) = P ( A ) ⋅ P ( B | A ) {\displaystyle P(A\land B)=P(B)\cdot P(A|B)=P(A)\cdot P(B|A)} becomes in terms of message length L, L ( A ∧ B ) = L ( B ) + L ( A | B ) = L ( A ) + L ( B | A ) . {\displaystyle L(A\land B)=L(B)+L(A|B)=L(A)+L(B|A).} This means that if all the information is given describing an event then the length of the information may be used to give the raw probability of the event. So if the information describing the occurrence of A is given, along with the information describing B given A, then all the information describing A and B has been given. ==== Overfitting ==== Overfitting occurs when the model matches the random noise and not the pattern in the data. For example, take the situation where a curve is fitted to a set of points. If a polynomial with many terms is fitted then it can more closely represent the data. Then the fit will be better, and the information needed to describe the deviations from the fitted curve will be smaller. Smaller information length means higher probability. However, the information needed to describe the curve must also be considered. The total information for a curve with many terms may be greater than for a curve with fewer terms, that has not as good a fit, but needs less information to describe the polynomial. === Inference based on program complexity === Solomonoff's theory of inductive inference is also inductive inference. A bit string x is observed. Then consider all programs that generate strings starting with x. Cast in the form of inductive inference, the programs are theories that imply the observation of the bit string x. The method used here to give probabilities for inductive inference is based on Solomonoff's theory of inductive inference. ==== Detecting patterns in the data ==== If all the bits are 1, then people infer that there is a bias in the coin and that it is more likely also that the next bit is 1 also. This is described as learning from, or detecting a pattern in the data. Such a pattern may be represented by a computer program. A short computer program may be written that produces a series of bits which are all 1. If the length of the program K is L ( K ) {\displaystyle L(K)} bits then its prior probability is, P ( K ) = 2 − L ( K ) {\displaystyle P(K)=2^{-L(K)}} The length of the shortest program that represents the string of bits is called the Kolmogorov complexity. Kolmogorov complexity is not computable. This is related to the halting problem. When searching for the shortest program some programs may go into an infinite loop. ==== Considering all theories ==== The Greek philosopher Epicurus is quoted as saying "If more than one theory is consistent with the observations, keep all theories". As in a crime novel all theories must be considered in determining the likely murderer, so with inductive probability all programs must be considered in determining the likely future bits arising from the stream of bits. Programs that are already longer than n have no predictive power. The raw (or prior) probability that the pattern of bits is random (has no pattern) is 2 − n {\displaystyle 2^{-n}} . Each program that produces the sequence of bits, but is shorter than the n is a theory/pattern about the bits with a probability of 2 − k {\displaystyle 2^{-k}} where k is the length of the program. The probability of receiving a sequence of bits y after receiving a series of bits x is then the conditional probability of receiving y given x, which is the probability of x with y appended, divided by the probability of x. ==== Universal priors ==== The programming language affects the predictions of the next bit in the string. The language acts as a prior probability. This is particularly a problem where the programming language codes for numbers and other data types. Intuitively we think that 0 and 1 are simple numbers, and that prime numbers are somehow more complex than numbers that may be composite. Using the Kolmogorov complexity gives an unbiased estimate (a universal prior) of the prior probability of a number. As a thought experiment an intelligent agent may be fitted with a data input device giving a series of numbers, after applying some transformation function to the raw numbers. Another agent might have the same input device with a different transformation function. The agents do not see or know about these transformation functions. Then there appears no rational basis for preferring one function over another. A universal prior insures that although two agents may have different initial probability distributions for the data input, the difference will be bounded by a constant. So universal priors do not eliminate an initial bias, but they reduce and limit it. Whenever we describe an event in a language, either using a natural language or other, the language has encoded in it our prior expectations. So some reliance on prior probabilities are inevitable. A problem arises where an intelligent agent's prior expectations interact with the environment to form a self reinforcing feed back loop. This is the problem of bias or prejudice. Universal priors reduce but do not eliminate this problem. === Universal artificial intelligence === The theory of universal artificial intelligence applies decision theory to inductive probabilities. The theory shows how the best actions to optimize a reward function may be chosen. The result is a theoretical model of intelligence. It is a fundamental theory of intelligence, which optimizes the agents behavior in, Exploring the environment; performing actions to get responses that broaden the agents knowledge. Competing or co-operating with another agent; games. Balancing short and long term rewards. In general no agent will always provi

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  • Alexander Gammerman

    Alexander Gammerman

    Alexander Gammerman (born 2 November 1944) is a British computer scientist, and professor at Royal Holloway University of London. He is the co-inventor of conformal prediction. He is the founding director of the Centre for Machine Learning at Royal Holloway, University of London, and a Fellow of the Royal Statistical Society. == Career == Gammerman's academic career has been pursued in the Soviet Union and the United Kingdom. He started working as a Research Fellow in the Agrophysical Research Institute, St. Petersburg. In 1983, he emigrated to the United Kingdom and was appointed as a lecturer in the Computer Science Department at Heriot-Watt University, Edinburgh. Together with Roger Thatcher, Gammerman published several articles on Bayesian inference. In 1993, he was appointed to the established chair in Computer Science at University of London tenable at Royal Holloway and Bedford New College, where he served as the Head of Computer Science department from 1995 to 2005. In 1998, the Centre for Reliable Machine Learning was established, and Gammerman became the first director of the centre. Gammerman has written 7 books. == Honours and awards == In 1996, Gammerman received the P.W. Allen Award from the Forensic Science Society. In 2006, he became an Honorary Professor, at University College London. In 2009, he became a Distinguished Professor at Complutense University of Madrid, Spain. In 2019, he received a research grant funded by the energy company Centrica about predicting the time to the next failure of equipment. In 2020, he received the Amazon Research Award for the project titled Conformal Martingales for Change-Point Detection == Selected books == Measures of Complexity (2016), Springer, ISBN 3319357786. Algorithmic Learning in a Random World (2005), Springer, ISBN 0387001522. Causal Models and Intelligent Data Management (1999), Springer, ISBN 978-3-642-58648-4. Probabilistic Reasoning and Bayesian Belief Networks (1998), Nelson Thornes Ltd, ISBN 1872474268. Computational Learning and Probabilistic Reasoning (1996), Wiley, ISBN 0471962791.

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  • Interacting particle system

    Interacting particle system

    In probability theory, an interacting particle system (IPS) is a stochastic process ( X ( t ) ) t ∈ R + {\displaystyle (X(t))_{t\in \mathbb {R} ^{+}}} on some configuration space Ω = S G {\displaystyle \Omega =S^{G}} given by a site space, a countably-infinite-order graph G {\displaystyle G} and a local state space, a compact metric space S {\displaystyle S} . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model. IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c Λ ( η , ξ ) > 0 {\displaystyle c_{\Lambda }(\eta ,\xi )>0} where Λ ⊂ G {\displaystyle \Lambda \subset G} is a finite set of sites and η , ξ ∈ Ω {\displaystyle \eta ,\xi \in \Omega } with η i = ξ i {\displaystyle \eta _{i}=\xi _{i}} for all i ∉ Λ {\displaystyle i\notin \Lambda } . The rates describe exponential waiting times of the process to jump from configuration η {\displaystyle \eta } into configuration ξ {\displaystyle \xi } . More generally the transition rates are given in form of a finite measure c Λ ( η , d ξ ) {\displaystyle c_{\Lambda }(\eta ,d\xi )} on S Λ {\displaystyle S^{\Lambda }} . The generator L {\displaystyle L} of an IPS has the following form. First, the domain of L {\displaystyle L} is a subset of the space of "observables", that is, the set of real valued continuous functions on the configuration space Ω {\displaystyle \Omega } . Then for any observable f {\displaystyle f} in the domain of L {\displaystyle L} , one has L f ( η ) = ∑ Λ ∫ ξ : ξ Λ c = η Λ c c Λ ( η , d ξ ) [ f ( ξ ) − f ( η ) ] {\displaystyle Lf(\eta )=\sum _{\Lambda }\int _{\xi :\xi _{\Lambda ^{c}}=\eta _{\Lambda ^{c}}}c_{\Lambda }(\eta ,d\xi )[f(\xi )-f(\eta )]} . For example, for the stochastic Ising model we have G = Z d {\displaystyle G=\mathbb {Z} ^{d}} , S = { − 1 , + 1 } {\displaystyle S=\{-1,+1\}} , c Λ = 0 {\displaystyle c_{\Lambda }=0} if Λ ≠ { i } {\displaystyle \Lambda \neq \{i\}} for some i ∈ G {\displaystyle i\in G} and c i ( η , η i ) = exp ⁡ [ − β ∑ j : | j − i | = 1 η i η j ] {\displaystyle c_{i}(\eta ,\eta ^{i})=\exp[-\beta \sum _{j:|j-i|=1}\eta _{i}\eta _{j}]} where η i {\displaystyle \eta ^{i}} is the configuration equal to η {\displaystyle \eta } except it is flipped at site i {\displaystyle i} . β {\displaystyle \beta } is a new parameter modeling the inverse temperature. == The Voter model == The voter model (usually in continuous time, but there are discrete versions as well) is a process similar to the contact process. In this process η ( x ) {\displaystyle \eta (x)} is taken to represent a voter's attitude on a particular topic. Voters reconsider their opinions at times distributed according to independent exponential random variables (this gives a Poisson process locally – note that there are in general infinitely many voters so no global Poisson process can be used). At times of reconsideration, a voter chooses one neighbor uniformly from amongst all neighbors and takes that neighbor's opinion. One can generalize the process by allowing the picking of neighbors to be something other than uniform. === Discrete time process === In the discrete time voter model in one dimension, ξ t ( x ) : Z → { 0 , 1 } {\displaystyle \xi _{t}(x):\mathbb {Z} \to \{0,1\}} represents the state of particle x {\displaystyle x} at time t {\displaystyle t} . Informally each individual is arranged on a line and can "see" other individuals that are within a radius, r {\displaystyle r} . If more than a certain proportion, θ {\displaystyle \theta } of these people disagree then the individual changes her attitude, otherwise she keeps it the same. Durrett and Steif (1993) and Steif (1994) show that for large radii there is a critical value θ c {\displaystyle \theta _{c}} such that if θ > θ c {\displaystyle \theta >\theta _{c}} most individuals never change, and for θ ∈ ( 1 / 2 , θ c ) {\displaystyle \theta \in (1/2,\theta _{c})} in the limit most sites agree. (Both of these results assume the probability of ξ 0 ( x ) = 1 {\displaystyle \xi _{0}(x)=1} is one half.) This process has a natural generalization to more dimensions, some results for this are discussed in Durrett and Steif (1993). === Continuous time process === The continuous time process is similar in that it imagines each individual has a belief at a time and changes it based on the attitudes of its neighbors. The process is described informally by Liggett (1985, 226), "Periodically (i.e., at independent exponential times), an individual reassesses his view in a rather simple way: he chooses a 'friend' at random with certain probabilities and adopts his position." A model was constructed with this interpretation by Holley and Liggett (1975). This process is equivalent to a process first suggested by Clifford and Sudbury (1973) where animals are in conflict over territory and are equally matched. A site is selected to be invaded by a neighbor at a given time.

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