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List of Fortran software and tools

This is a list of Fortran software and tools, including IDEs, compilers, libraries, debugging tools, numerical and scientific computing tools, and related projects. == Fortran compilers == Absoft Pro Fortran — Absoft Pro Fortran is discontinued and ran on Linux and macOS AOCC — from AMD Classic Flang — part of the LLVM Project LLVM Flang — part of the LLVM Project Fortran 77 — Fortran 77 was developed by Digital Equipment Corporation, it is discontinued. G95 – portable open-source Fortran 95 compiler GCC (GNU Fortran) PGI compilers – NVIDIA developed compilers after acquiring The Portland Group IBM XL Fortran — IBM XL Fortran is current and runs on Linux (Power/AIX) and integrates with Eclipse Intel Fortran Compiler – part of Intel OneAPI HPC toolkit LFortran — LFortran is current, cross-platform, and has IDE support. MinGW – cross compiler and forked into Mingw-w64 nAG Fortran Compiler - from nAG Open64 — Open64 is an open-source compiler that has been terminated and ran on Linux Open Watcom — Open Watcom is current, runs on MS-DOS and OS/2, and has IDE support. Oracle Fortran — Oracle Fortran is discontinued, ran on Linux and Solaris. ROSE — source-to-source compiler framework developed at Lawrence Livermore National Laboratory Silverfrost FTN95 — FTN95 from Silverfrost is current, runs on Windows, and has IDE support. == Integrated development environments (IDEs) and editors == Code::Blocks — supports Fortran with plugins Eclipse IDE — with Fortran support via Photran Emacs — extensible text editor with built-in Fortran modes and support for modern tooling via language servers Geany — lightweight cross-platform IDE based on GTK IntelliJ IDEA — cross-platform IDE by JetBrains with Fortran pluggin KDevelop — KDE-based IDE NetBeans — Apache software foundation IDE with Fortran configuration OpenWatcom — IDE and compiler suite for C, C++, and Fortran Simply Fortran — standalone Fortran IDE for Windows, Linux, and macOS Vim — modal text editor with native Fortran syntax support and extensive plugin-based development features Visual Studio — with Intel Fortran integration Visual Studio Code — supports Fortran via extensions == Mathematical libraries == == Scientific libraries == ABINIT — software suite to calculate optical, mechanical, vibrational, and other observable properties of materials Cantera — chemical kinetics, thermodynamics, and transport tool suite CERN Program Library — collection of Fortran libraries for physics applications from CERN CP2K — quantum chemistry and solid-state physics software package for atomistic simulations Dalton — molecular electronic structure program FFTPACK — subroutines for the fast Fourier transform Kinetic PreProcessor – open-source software tool used in atmospheric chemistry MESA — Modules for Experiments in Stellar Astrophysics Nek5000 — MPI parallel higher-order spectral element CFD solver NWChem — open-source high-performance computational chemistry software Octopus — real-space Time-Dependent Density Functional Theory code MODTRAN – model atmospheric propagation of electromagnetic radiation MOLCAS — quantum chemistry software package for multiconfigurational electronic structure calculations NOVAS – software library for astrometry-related numerical computations Physics Analysis Workstation – data analysis and graphical presentation in high-energy physics Quantum ESPRESSO — integrated suite for electronic-structure calculations and materials modeling SIESTA — first-principles materials simulation code using density functional theory Tinker — software tools for molecular design == Debugging and performance tools == GDB — GNU Debugger with Fortran support Valgrind — memory debugging and profiling tool VTune Profiler — performance analysis tool Allinea Forge — debugger and profiler for HPC applications == Build and package management == Autotools — build system supporting Fortran projects CMake — cross-platform build system supporting Fortran Make — build automation tool Spack — package manager for HPC software including Fortran libraries == Machine learning and AI libraries == Athena Fiats (Functional Inference And Training for Surrogates) FNN (Fortran Neural Network) FortNN Fortran-TF-lib (Fortran interface to TensorFlow) FTorch (Fortran interface to PyTorch) MlFortran RoseNNa == Parallel and high-performance computing tools == MPI Fortran bindings — standard interface for distributed-memory parallelism OpenMP — shared-memory parallel programming support through compiler directives Coarray Fortran — parallel programming model introduced in Fortran 2008 ScaLAPACK — parallel linear algebra package built on top of LAPACK == Testing frameworks == FUnit — open-source unit testing framework developed at NASA’s Langley Research Center, for Fortran 90, 95, and 2003. pFUnit — unit testing framework for Fortran, modeled after JUnit == Documentation and code analysis tools == FORD — automatic documentation generator for modern Fortran projects SQuORE — software quality and management platform with code analysis support Understand — static analysis and code comprehension tool for large Fortran projects
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Pachinko allocation

In machine learning and natural language processing, the pachinko allocation model (PAM) is a topic model. Topic models are a suite of algorithms to uncover the hidden thematic structure of a collection of documents. The algorithm improves upon earlier topic models such as latent Dirichlet allocation (LDA) by modeling correlations between topics in addition to the word correlations which constitute topics. PAM provides more flexibility and greater expressive power than latent Dirichlet allocation. While first described and implemented in the context of natural language processing, the algorithm may have applications in other fields such as bioinformatics. The model is named for pachinko machines—a game popular in Japan, in which metal balls bounce down around a complex collection of pins until they land in various bins at the bottom. == History == Pachinko allocation was first described by Wei Li and Andrew McCallum in 2006. The idea was extended with hierarchical Pachinko allocation by Li, McCallum, and David Mimno in 2007. In 2007, McCallum and his colleagues proposed a nonparametric Bayesian prior for PAM based on a variant of the hierarchical Dirichlet process (HDP). The algorithm has been implemented in the MALLET software package published by McCallum's group at the University of Massachusetts Amherst. == Model == PAM connects words in V and topics in T with an arbitrary directed acyclic graph (DAG), where topic nodes occupy the interior levels and the leaves are words. The probability of generating a whole corpus is the product of the probabilities for every document: P ( D | α ) = ∏ d P ( d | α ) {\displaystyle P(\mathbf {D} |\alpha )=\prod _{d}P(d|\alpha )}
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Aravind Joshi

Aravind Krishna Joshi (August 5, 1929 – December 31, 2017) was the Henry Salvatori Professor of Computer and Cognitive Science in the computer science department of the University of Pennsylvania. Joshi defined the tree-adjoining grammar formalism which is often used in computational linguistics and natural language processing. Joshi studied at Pune University and the Indian Institute of Science, where he was awarded a BE in electrical engineering and a DIISc in communication engineering respectively. Joshi's graduate work was done in the electrical engineering department at the University of Pennsylvania, and he was awarded his PhD in 1960. He became a professor at Penn and was the co-founder and co-director of the Institute for Research in Cognitive Science. == Awards and recognitions == Guggenheim fellow, 1971–72 Fellow of the Institute of Electrical and Electronics Engineers (IEEE), 1976 Best Paper Award at the National Conference on Artificial Intelligence, 1987 Founding Fellow of the American Association for Artificial Intelligence (AAAI), 1990 IJCAI Award for Research Excellence, 1997 Fellow of the Association for Computing Machinery, 1998 Elected to the National Academy of Engineering, 1999 First to be awarded the Association for Computational Linguistics Lifetime Achievement Award at the 40th anniversary meeting of the ACL, 2002 Awarded the Rumelhart Prize, 2003 Benjamin Franklin Medal in Computer and Cognitive Science, 2005 Doctor honoris causa of mathematical and physical sciences, Charles University in Prague, October 30, 2013 S.-Y. Kuroda Prize of the SIG Mathematics of Language of the ACL, 2013 === Awarded history === On April 21, 2005, Joshi was awarded the Franklin Institute's Benjamin Franklin Medal in Computer and Cognitive Science. The Franklin Institute citation states that he was awarded the medal "for his fundamental contributions to our understanding of how language is represented in the mind, and for developing techniques that enable computers to process efficiently the wide range of human languages. These advances have led to new methods for computer translation."
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James Curran (educator)

James R. Curran is an Australian computational linguist. He is the former CEO of Grok Academy and previously a senior lecturer at the University of Sydney. He holds a PhD in Informatics from the University of Edinburgh. == Research == Curran's research focuses on natural language processing (NLP), more specifically combinatory categorial grammar and question answering systems. In addition to his contributions to NLP, Curran has produced a paper on the development of search engines to assist in driving problem based learning. == Works == Curran has co-authored software packages such as C&C tools, a CCG parser (with Stephen Clark). == Educational work == In addition to his work as a University of Sydney lecturer, Curran directed the National Computer Science School, an annual summer school for technologically talented high school students. In 2013, based on their work with NCSS, he, Tara Murphy, Nicky Ringland and Tim Dawborn founded Grok Learning. In 2013 he was one of the authors of the Digital Technologies section of the Australian Curriculum - its first appearance in the national curriculum. Additionally, he acted as an advocate for digital literacy among Australian students. He was the academic director of the Australian Computing Academy, a not-for-profit within the University of Sydney until its merger with Grok Learning in 2021 to form Grok Academy. In 2022, Grok Academy under Curran secured a significant amount of funding from Richard White, founder of WiseTech, with the aim of developing new courses and encouraging other large technology companies to donate likewise. In 2024 Curran cohosted an unreleased children's reality TV show called Future Fixers, which Grok was co-producing. The show was abandoned after other producers learned of pre-existing harassment claims against him. == Sexual harassment allegations == In October 2024, he resigned from his position as CEO and board member of Grok Academy after multiple allegations of harassment were substantiated by an independent investigator. It was reported that over a 10-year span there were nine women, including six who were in high school at the time, that allege Curran sent them inappropriate messages. Additionally, it was revealed that a 2019 University of Sydney investigation found 35 cases of harassment, after which he received a warning and a 2024 University of New South Wales investigation was referred to the NSW police, who took no action as they found no criminal wrongdoing by Curran, in part because the students were over 16 at the time of the alleged harassment. In December 2024, Curran said he was “deeply sorry” for his actions.
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Schema-agnostic databases

Schema-agnostic databases or vocabulary-independent databases aim at supporting users to be abstracted from the representation of the data, supporting the automatic semantic matching between queries and databases. Schema-agnosticism is the property of a database of mapping a query issued with the user terminology and structure, automatically mapping it to the dataset vocabulary. The increase in the size and in the semantic heterogeneity of database schemas bring new requirements for users querying and searching structured data. At this scale it can become unfeasible for data consumers to be familiar with the representation of the data in order to query it. At the center of this discussion is the semantic gap between users and databases, which becomes more central as the scale and complexity of the data grows. == Description == The evolution of data environments towards the consumption of data from multiple data sources and the growth in the schema size, complexity, dynamicity and decentralisation (SCoDD) of schemas increases the complexity of contemporary data management. The SCoDD trend emerges as a central data management concern in Big Data scenarios, where users and applications have a demand for more complete data, produced by independent data sources, under different semantic assumptions and contexts of use, which is the typical scenario for Semantic Web Data applications. The evolution of databases in the direction of heterogeneous data environments strongly impacts the usability, semiotics and semantic assumptions behind existing data accessibility methods such as structured queries, keyword-based search and visual query systems. With schema-less databases containing potentially millions of dynamically changing attributes, it becomes unfeasible for some users to become aware of the 'schema' or vocabulary in order to query the database. At this scale, the effort in understanding the schema in order to build a structured query can become prohibitive. == Schema-agnostic queries == Schema-agnostic queries can be defined as query approaches over structured databases which allow users satisfying complex information needs without the understanding of the representation (schema) of the database. Similarly, Tran et al. defines it as "search approaches, which do not require users to know the schema underlying the data". Approaches such as keyword-based search over databases allow users to query databases without employing structured queries. However, as discussed by Tran et al.: "From these points, users however have to do further navigation and exploration to address complex information needs. Unlike keyword search used on the Web, which focuses on simple needs, the keyword search elaborated here is used to obtain more complex results. Instead of a single set of resources, the goal is to compute complex sets of resources and their relations." The development of approaches to support natural language interfaces (NLI) over databases have aimed towards the goal of schema-agnostic queries. Complementarily, some approaches based on keyword search have targeted keyword-based queries which express more complex information needs. Other approaches have explored the construction of structured queries over databases where schema constraints can be relaxed. All these approaches (natural language, keyword-based search and structured queries) have targeted different degrees of sophistication in addressing the problem of supporting a flexible semantic matching between queries and data, which vary from the completely absence of the semantic concern to more principled semantic models. While the demand for schema-agnosticism has been an implicit requirement across semantic search and natural language query systems over structured data, it is not sufficiently individuated as a concept and as a necessary requirement for contemporary database management systems. Recent works have started to define and model the semantic aspects involved on schema-agnostic queries. === Schema-agnostic structured queries === Consist of schema-agnostic queries following the syntax of a structured standard (for example SQL, SPARQL). The syntax and semantics of operators are maintained, while different terminologies are used. ==== Example 1 ==== SELECT ?y { BillClinton hasDaughter ?x . ?x marriedTo ?y . } which maps to the following SPARQL query in the dataset vocabulary: ==== Example 2 ==== which maps to the following SPARQL query in the dataset vocabulary: === Schema-agnostic keyword queries === Consist of schema-agnostic queries using keyword queries. In this case the syntax and semantics of operators are different from the structured query syntax. ==== Example ==== "Bill Clinton daughter married to" "Books by William Goldman with more than 300 pages" == Semantic complexity == As of 2016 the concept of schema-agnostic queries has been developed primarily in academia. Most of schema-agnostic query systems have been investigated in the context of Natural Language Interfaces over databases or over the Semantic Web. These works explore the application of semantic parsing techniques over large, heterogeneous and schema-less databases. More recently, the individuation of the concept of schema-agnostic query systems and databases have appeared more explicitly within the literature. Freitas et al. provide a probabilistic model on the semantic complexity of mapping schema-agnostic queries.
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How to Choose an AI Chatbot

Looking for the best AI chatbot? An AI chatbot 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 chatbot slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Irwin King

Irwin King is a Hong Kong computer scientist known for his contributions to machine learning, social computing, and recommender systems. == Career == King is a professor in the Department of Computer Science and Engineering at the Chinese University of Hong Kong. His research focuses on machine learning and social computing, including work on social recommendation, trust-aware recommender systems, and graph-based learning. King has served as editor-in-chief of the journal ACM Transactions on Intelligent Systems and Technology (TIST). == Awards == ACM Fellow (2024) IEEE Fellow (2019) INNS Fellow (2021) AAIA Fellow (2022) HKIE Fellow ACM WSDM Test of Time Award (2022) ACM SIGIR Test of Time Award (2020) ACM CIKM Test of Time Award (2019) 2021 INNS Dennis Gabor Award for work in Neural Engineering for Social Computing 2020 APNNS Outstanding Achievement Award
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Lin-Shan Lee

Lin-Shan Lee (Chinese: 李琳山; born 23 September 1952) is a Taiwanese computer scientist. == Education and career == Lee earned a bachelor's degree in electrical engineering from National Taiwan University in 1974, and pursued a doctorate in the same subject at Stanford University, graduating in 1977. He subsequently returned to Taiwan and joined the NTU faculty in 1982. Lee is a 1993 fellow of the Institute of Electrical and Electronics Engineers, recognized "[f]or contributions to computer voice input/output techniques for Mandarin Chinese and to engineering education." The International Speech Communication Association elevated him to fellow status in 2010 "[f]or his contributions to Chinese spoken language processing and speech information retrieval, and his service to the speech language community." In 2016, Lee was elected a member of Academia Sinica.
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Photometric stereo

Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions (photometry). It is based on the fact that the amount of light reflected by a surface is dependent on the orientation of the surface in relation to the light source and the observer. By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited. Given enough light sources from different angles, the surface orientation may be constrained to a single orientation or even overconstrained. The technique was originally introduced by Woodham in 1980. The special case where the data is a single image is known as shape from shading, and was analyzed by B. K. P. Horn in 1989. Photometric stereo has since been generalized to many other situations, including extended light sources and non-Lambertian surface finishes. Current research aims to make the method work in the presence of projected shadows, highlights, and non-uniform lighting. Photometric stereo is widely used in various fields, including archaeology, cultural heritage conservation, and quality control. It is now integrated into widely used open-source software, such as Meshroom. == Basic method == Under Woodham's original assumptions — Lambertian reflectance, known point-like distant light sources, and uniform albedo — the problem can be solved by inverting the linear equation I = L ⋅ n {\displaystyle I=L\cdot n} , where I {\displaystyle I} is a (known) vector of m {\displaystyle m} observed intensities, n {\displaystyle n} is the (unknown) surface normal, and L {\displaystyle L} is a (known) 3 × m {\displaystyle 3\times m} matrix of normalized light directions. This model can easily be extended to surfaces with non-uniform albedo, while keeping the problem linear. Taking an albedo reflectivity of k {\displaystyle k} , the formula for the reflected light intensity becomes I = k ( L ⋅ n ) . {\displaystyle I=k(L\cdot n).} If L {\displaystyle L} is square (there are exactly 3 lights) and non-singular, it can be inverted, giving L − 1 I = k n . {\displaystyle L^{-1}I=kn.} Since the normal vector is known to have length 1, k {\displaystyle k} must be the length of the vector k n {\displaystyle kn} , and n {\displaystyle n} is the normalised direction of that vector. If L {\displaystyle L} is not square (there are more than 3 lights), a generalisation of the inverse can be obtained using the Moore–Penrose pseudoinverse, by simply multiplying both sides with L T {\displaystyle L^{T}} , giving L T I = L T k ( L ⋅ n ) , {\displaystyle L^{T}I=L^{T}k(L\cdot n),} ( L T L ) − 1 L T I = k n , {\displaystyle (L^{T}L)^{-1}L^{T}I=kn,} after which the normal vector and albedo can be solved as described above. == Non-Lambertian surfaces == The classical photometric stereo problem concerns itself only with Lambertian surfaces, with perfectly diffuse reflection. This is unrealistic for many types of materials, especially metals, glass and smooth plastics, and will lead to aberrations in the resulting normal vectors. Many methods have been developed to lift this assumption. In this section, a few of these are listed. === Specular reflections === Historically, in computer graphics, the commonly used model to render surfaces started with Lambertian surfaces and progressed first to include simple specular reflections. Computer vision followed a similar course with photometric stereo. Specular reflections were among the first deviations from the Lambertian model. These are a few adaptations that have been developed. Many techniques ultimately rely on modelling the reflectance function of the surface, that is, how much light is reflected in each direction. This reflectance function has to be invertible. The reflected light intensities towards the camera is measured, and the inverse reflectance function is fit onto the measured intensities, resulting in a unique solution for the normal vector. === General BRDFs and beyond === According to the Bidirectional reflectance distribution function (BRDF) model, a surface may distribute the amount of light it receives in any outward direction. This is the most general known model for opaque surfaces. Some techniques have been developed to model (almost) general BRDFs. In practice, all of these require many light sources to obtain reliable data. These are methods in which surfaces with general BRDFs can be measured. Determine the explicit BRDF prior to scanning. To do this, a different surface is required that has the same or a very similar BRDF, of which the actual geometry (or at least the normal vectors for many points on the surface) is already known. The lights are then individually shone upon the known surface, and the amount of reflection into the camera is measured. Using this information, a look-up table can be created that maps reflected intensities for each light source to a list of possible normal vectors. This puts constraints on the possible normal vectors the surface may have, and reduces the photometric stereo problem to an interpolation between measurements. Typical known surfaces to calibrate the look-up table with are spheres for their wide variety of surface orientations. Restricting the BRDF to be symmetrical. If the BRDF is symmetrical, the direction of the light can be restricted to a cone about the direction to the camera. Which cone this is depends on the BRDF itself, the normal vector of the surface, and the measured intensity. Given enough measured intensities and the resulting light directions, these cones can be approximated and therefore the normal vectors of the surface. Some progress has been made towards modelling an even more general surfaces, such as Spatially Varying Bidirectional Distribution Functions (SVBRDF), Bidirectional surface scattering reflectance distribution functions (BSSRDF), and accounting for interreflections. However, such methods are still fairly restrictive in photometric stereo. Better results have been achieved with structured light. == Uncalibrated photometric stereo == Uncalibrated Photometric Stereo is an approach in photometric stereo that aims to reconstruct the 3D shape of an object from images captured under unknown lighting conditions. Unlike classical methods, which often assume controlled or known lighting setups, this approach removes these constraints, making it adaptable to diverse and real-world environments. The advent of deep learning has revolutionized universal PS by replacing handcrafted assumptions with data-driven models. Recent approaches leverage Transformer-based architectures and multi-scale encoder–decoder networks to directly estimate surface normals from input images. Uncalibrated Photometric Stereo is inherently an ill-posed problem, as it attempts to recover 3D shape and lighting conditions simultaneously from images alone. This leads to fundamental ambiguities in the reconstruction process, which manifest as systematic errors in the recovered geometry, including global distortions in the object's overall shape, and misinterpretation of surface orientation, where concave regions may appear convex and vice versa. To address the challenges of uncalibrated photometric stereo, hybrid methods have emerged that combine multi-view stereo and photometric stereo. These approaches leverage the strengths of both techniques, including geometric reliability and resolution.
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Additive smoothing

In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts x = ⟨ x 1 , x 2 , … , x d ⟩ {\displaystyle \mathbf {x} =\langle x_{1},x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts gives the estimator θ ^ i = x i + α N + α d ( i = 1 , … , d ) , {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\alpha }{N+\alpha d}}\qquad (i=1,\ldots ,d),} where the smoothed count x ^ i = N θ ^ i {\displaystyle {\hat {x}}_{i}=N{\hat {\theta }}_{i}} , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) x i / N {\displaystyle x_{i}/N} and the uniform probability 1 / d . {\displaystyle 1/d.} Common choices for α are 0 (no smoothing), +1⁄2 (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empirically based on the observed data. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution. == History == Laplace came up with this smoothing technique when he tried to estimate the chance that the sun will rise tomorrow. His rationale was that even given a large sample of days with the rising sun, we still can not be completely sure that the sun will still rise tomorrow (known as the sunrise problem). == Pseudocount == A pseudocount is an amount (not generally an integer, despite its name) added to the number of observed cases in order to change the expected probability in a model of those data, when not known to be zero. It is so named because, roughly speaking, a pseudo-count of value α {\displaystyle \alpha } weighs into the posterior distribution similarly to each category having an additional count of α {\displaystyle \alpha } . If the number of occurrences of each item i {\displaystyle i} is x i {\displaystyle x_{i}} out of N {\displaystyle N} samples, the empirical probability of event i {\displaystyle i} is p i , empirical = x i N , {\displaystyle p_{i,{\text{empirical}}}={\frac {x_{i}}{N}},} but the posterior probability when additively smoothed is p i , α -smoothed = x i + α N + α d , {\displaystyle p_{i,\alpha {\text{-smoothed}}}={\frac {x_{i}+\alpha }{N+\alpha d}},} as if to increase each count x i {\displaystyle x_{i}} by α {\displaystyle \alpha } a priori. Depending on the prior knowledge, which is sometimes a subjective value, a pseudocount may have any non-negative finite value. It may only be zero (or the possibility ignored) if impossible by definition, such as the possibility of a decimal digit of π being a letter, or a physical possibility that would be rejected and so not counted, such as a computer printing a letter when a valid program for π is run, or excluded and not counted because of no interest, such as if only interested in the zeros and ones. Generally, there is also a possibility that no value may be computable or observable in a finite time (see the halting problem). But at least one possibility must have a non-zero pseudocount, otherwise no prediction could be computed before the first observation. The relative values of pseudocounts represent the relative prior expected probabilities of their possibilities. The sum of the pseudocounts, which may be very large, represents the estimated weight of the prior knowledge compared with all the actual observations (one for each) when determining the expected probability. In any observed data set or sample there is the possibility, especially with low-probability events and with small data sets, of a possible event not occurring. Its observed frequency is therefore zero, apparently implying a probability of zero. This oversimplification is inaccurate and often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. By artificially adjusting the probability of rare (but not impossible) events so those probabilities are not exactly zero, zero-frequency problems are avoided. Also see Cromwell's rule. === Choice of pseudocount === ==== Weakly informative prior ==== One common approach is to add 1 to each observed number of events, including the zero-count possibilities. This is sometimes called Laplace's rule of succession. This approach is equivalent to assuming a uniform prior distribution over the probabilities for each possible event (spanning the simplex where each probability is between 0 and 1, and they all sum to 1). Using the Jeffreys prior approach, a pseudocount of one half should be added to each possible outcome. Pseudocounts should be set to one or one-half only when there is no prior knowledge at all – see the principle of indifference. However, given appropriate prior knowledge, the sum should be adjusted in proportion to the expectation that the prior probabilities should be considered correct, despite evidence to the contrary – see further analysis. Higher values are appropriate inasmuch as there is prior knowledge of the true values (for a mint-condition coin, say); lower values inasmuch as there is prior knowledge that there is probable bias, but of unknown degree (for a bent coin, say). ==== Frequentist interval ==== One way to motivate pseudocounts, particularly for binomial data, is via a formula for the midpoint of an interval estimate, particularly a binomial proportion confidence interval. The best-known is due to Edwin Bidwell Wilson, in Wilson (1927): the midpoint of the Wilson score interval corresponding to ⁠ z {\displaystyle z} ⁠ standard deviations on either side is n S + z n + 2 z {\displaystyle {\frac {n_{S}+z}{n+2z}}} Taking z = 2 {\displaystyle z=2} standard deviations to approximate a 95% confidence interval (⁠ z ≈ 1.96 {\displaystyle z\approx 1.96} ⁠) yields pseudocount of 2 for each outcome, so 4 in total, colloquially known as the "plus four rule": n S + 2 n + 4 {\displaystyle {\frac {n_{S}+2}{n+4}}} This is also the midpoint of the Agresti–Coull interval (Agresti & Coull 1998). ==== Known incidence rates ==== Often the bias of an unknown trial population is tested against a control population with known parameters (incidence rates) μ = ⟨ μ 1 , μ 2 , … , μ d ⟩ . {\displaystyle {\boldsymbol {\mu }}=\langle \mu _{1},\mu _{2},\ldots ,\mu _{d}\rangle .} In this case the uniform probability 1 / d {\displaystyle 1/d} should be replaced by the known incidence rate of the control population μ i {\displaystyle \mu _{i}} to calculate the smoothed estimator: θ ^ i = x i + μ i α d N + α d ( i = 1 , … , d ) . {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\mu _{i}\alpha d}{N+\alpha d}}\qquad (i=1,\ldots ,d).} As a consistency check, if the empirical estimator happens to equal the incidence rate, i.e. μ i = x i / N , {\displaystyle \mu _{i}=x_{i}/N,} the smoothed estimator is independent of α {\displaystyle \alpha } and also equals the incidence rate. == Applications == === Classification === Additive smoothing is commonly a component of naive Bayes classifiers. === Statistical language modelling === In a bag of words model of natural language processing and information retrieval, the data consists of the number of occurrences of each word in a document. Additive smoothing allows the assignment of non-zero probabilities to words which do not occur in the sample. Studies have shown that additive smoothing is more effective than other probability smoothing methods in several retrieval tasks such as language-model-based pseudo-relevance feedback and recommender systems.
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Extended affix grammar

In computer science, extended affix grammars (EAGs) are a formal grammar formalism for describing the context free and context sensitive syntax of language, both natural language and programming languages. EAGs are a member of the family of two-level grammars; more specifically, a restriction of Van Wijngaarden grammars with the specific purpose of making parsing feasible. Like Van Wijngaarden grammars, EAGs have hyperrules that form a context-free grammar except in that their nonterminals may have arguments, known as affixes, the possible values of which are supplied by another context-free grammar, the metarules. EAGs were introduced and studied by D.A. Watt in 1974; recognizers were developed at the University of Nijmegen between 1985 and 1995. The EAG compiler developed there will generate either a recogniser, a transducer, a translator, or a syntax directed editor for a language described in the EAG formalism. The formalism is quite similar to Prolog, to the extent that it borrowed its cut operator. EAGs have been used to write grammars of natural languages such as English, Spanish, and Hungarian. The aim was to verify the grammars by making them parse corpora of text (corpus linguistics); hence, parsing had to be sufficiently practical. However, the parse tree explosion problem that ambiguities in natural language tend to produce in this type of approach is worsened for EAGs because each choice of affix value may produce a separate parse, even when several different values are equivalent. The remedy proposed was to switch to the much simpler Affix Grammar over a Finite Lattice (AGFL) instead, in which metagrammars can only produce simple finite languages.
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Phraselator

The Phraselator is a weatherproof handheld language translation device developed by Applied Data Systems and VoxTec, a former division of the military contractor Marine Acoustics, located in Annapolis, Maryland, USA. It was designed to serve as a handheld computer device that translates English into one of 40 different languages. == The device == The Phraselator is a small speech translation PDA-sized device designed to aid in interpretation. The device does not produce synthesized speech like that utilized by Stephen Hawking; instead, it plays pre-recorded foreign language MP3 files. Users can select the phrase they wish to convey from an English list on the screen or speak into the device. It then uses speech recognition technology called DynaSpeak, developed by SRI International, to play the proper sound file. The accuracy of the speech recognition software is over 70 percent according to software developer Jack Buchanan. The device can also record replies for translation later. Pre-recorded phrases are stored on Secure Digital flash memory cards. A 128 MB card can hold up to 12,000 phrases in four or five languages. Users can download phrase modules from the official website, which contained over 300,000 phrases as of March 2005. Users can also construct their own custom phrase modules. Earlier devices were known to have run on an SA-1110 Strong Arm 206 MHz CPU with 32MB SDRAM and 32MB onboard Flash RAM. A newer model, the P2, was released in 2004 and developed according to feedback from U.S. soldiers. It translates one way from English to approximately 60 other languages. It has a directional microphone, a larger library of phrases and a longer battery life. The 2004 release was created by and utilizes a computer board manufactured by InHand Electronics, Inc. In the future, the device will be able to display pictures so users can ask questions such as "Have you seen this person?" Developer Ace Sarich notes that the device is inferior to human interpreter. Conclusions derived from a Nepal field test conducted by U.S. and Nepal based NGO Himalayan Aid in 2004 seemed to confirm Sarich's comparisons: The very concept of using a machine as a communication point between individuals seemed to actually encourage a more limited form of interaction between tester and respondent. Usually, when limited language skills are present between parties, the genuine struggle and desire to communicate acts as a display of good will – we openly display our weakness in this regard – and the result is a more relaxed and human encounter. This was not necessarily present with the Phraselator as all parties abandoned learning about each other and instead focused on learning how to work with the device. As a tool for bridging any cultural differences or communicating effectively at any length, the Phraselator would not be recommended. This device, at least in the form tested, would best be used in large-scale operations where there is no time for language training and there is a need to communicate fixed ideas, quickly, over the greatest distance by employing large amounts of unskilled users. Large humanitarian or natural disasters in remote areas of third-world countries might be an effective example. == Origin == The original idea for the device came from Lee Morin, a Navy doctor in Operation Desert Storm. To communicate with patients, he played Arabic audio files from his laptop. He informed Ace Sarich, the vice president of VoxTec, about the idea. VoxTec won a DARPA Small Business Innovation Research grant in early 2001 to develop a military-grade handheld phrase translator. During its development, the Phraselator was tested and evaluated by scientists from the Army Research Laboratory. The device was first field tested in Afghanistan in 2001. By 2002, about 500 Phraselators were built for soldiers around the world with another 250 ordered by the U.S. Special Forces. The device cost $2000 to develop and could convert spoken English into one of 200,000 recorded commands and questions in 30 languages. However, the device could only translate one-way. At the time, the only existing two-way voice translator that could convert speech back and forth between languages was the Audio Voice Translation Guide System, or TONGUES, which was developed by Carnegie Mellon University for Lockheed Martin. As part of a DARPA program known as the Spoken Language Communication and Translation System for Tactical Use, SRI International has further developed two-way translation software for use in Iraq called IraqComm in 2006 which contains a vocabulary of 40,000 English words and 50,000 words in Iraqi Arabic. == Notable users == The handheld translator was recently used by U.S. troops while providing relief to tsunami victims in early 2005. About 500 prototypes of the device were provided to U.S. military forces in Operation Enduring Freedom. Units loaded with Haitian dialects have been provided to U.S. troops in Haiti. Army military police have used it in Kandahar to communicate with POWs. In late 2004, the U.S. Navy began to augment some ships with a version of the device attached to large speakers in order to broadcast clear voice instructions up to 400 yards (370 m) away. Corrections officers and law enforcement in Oneida County, New York, have tested the device. Hospital emergency rooms and health departments have also evaluated it. Several Native American tribes such as the Choctaw Nation, the Ponca, and the Comanche Nation have also used the device to preserve their dying languages. Various law enforcement agencies, such as the Los Angeles Police Department, also use the phraselator in their patrol cars. == Awards == In March 2004, DARPA director Dr. Tony Tether presented the Small Business Innovative Research Award to the VoxTec division of Marine Acoustics at DARPATech 2004 in Anaheim, CA. The device was recently listed as one of "Ten Emerging Technologies That Will Change Your World" in MIT's Technology Review. == Pop culture == Software developer Jack Buchanan believes that building a device similar to the fictional universal translator seen in Star Trek would be harder than building the Enterprise. The device was mentioned in a list of "Top 10 Star Trek Tech" on Space.com.
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Mix automation

In music recording, mix automation allows the mixing console to remember the mixing engineer's dynamic adjustment of faders during a musical piece in the post-production editing process. A timecode is necessary for the synchronization of automation. Modern mixing consoles and digital audio workstations use comprehensive mix automation. The need for automated mixing originated from the late 1970s transition form 8-track to 16-track and then 24-track multitrack recording, as mixing could be laborious and require multiple people and hands, and the results could be almost impossible to reproduce. With 48-track recording - synchronized twin 24-track recorders (for a net 46 audio tracks, with one on each machine for SMPTE timecode) - came larger recording and mixing consoles with even more channel faders to manage during mixdown. Manufacturers, such as Neve Electronics (now AMS Neve) and Solid State Logic (SSL), both English companies, developed systems that enabled one engineer to oversee every detail of a complex mix, although the computers required to power these desks remained a rarity into the late 1970s. According to record producer Roy Thomas Baker, Queen's 1975 single "Bohemian Rhapsody" was one of the first mixes to be done with automation. == Types == Voltage Controlled Automation fader levels are regulated by voltage-controlled amplifiers (VCA). VCAs control the audio level and not the actual fader. Moving Fader Automation a motor is attached to the fader, which then can be controlled by the console, digital audio workstation (DAW), or user. Software Controlled Automation the software can be internal to the console, or external as part of a DAW. The virtual fader can be adjusted in the software by the user. MIDI Automation the communications protocol MIDI can be used to send messages to the console to control automation. == Modes == Auto Write used the first time automation is created or when writing over existing automation Auto Touch writes automation data only while a fader is touched/faders return to any previously automated position after release Auto Latch starts writing automation data when a fader is touched/stays in position after release Auto Read digital Audio Workstation performs the written automation Auto Off automation is temporarily disabled All of these include the mute button. If mute is pressed during writing of automation, the audio track will be muted during playback of that automation. Depending on software, other parameters such as panning, sends, and plug-in controls can be automated as well. In some cases, automation can be written using a digital potentiometer instead of a fader.
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Is an AI Clip Maker Worth It in 2026?

Trying to pick the best AI clip maker? An AI clip maker is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI clip 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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Regular language

In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. == Formal definition == The collection of regular languages over an alphabet Σ is defined recursively as follows: The empty language ∅ is a regular language. For each a ∈ Σ (a belongs to Σ), the singleton language {a} is a regular language. If A is a regular language, A (Kleene star) is a regular language. Due to this, the empty string language {ε} is also regular. If A and B are regular languages, then A ∪ B (union) and A • B (concatenation) are regular languages. No other languages over Σ are regular. See Regular expression § Formal language theory for syntax and semantics of regular expressions. == Examples == All finite languages are regular; in particular the empty string language {ε} = ∅ is regular. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs. A simple example of a language that is not regular is the set of strings {anbn | n ≥ 0}. Intuitively, it cannot be recognized with a finite automaton, since a finite automaton has finite memory and it cannot remember the exact number of a's. Techniques to prove this fact rigorously are given below. == Equivalent formalisms == A regular language satisfies the following equivalent properties: it is the language of a regular expression (by the above definition) it is the language accepted by a nondeterministic finite automaton (NFA) it is the language accepted by a deterministic finite automaton (DFA) it can be generated by a regular grammar it is the language accepted by an alternating finite automaton it is the language accepted by a two-way finite automaton it can be generated by a prefix grammar it can be accepted by a read-only Turing machine it can be defined in monadic second-order logic (Büchi–Elgot–Trakhtenbrot theorem) it is recognized by some finite syntactic monoid M, meaning it is the preimage {w ∈ Σ | f(w) ∈ S} of a subset S of a finite monoid M under a monoid homomorphism f : Σ → M from the free monoid on its alphabet the number of equivalence classes of its syntactic congruence is finite. (This number equals the number of states of the minimal deterministic finite automaton accepting L.) Properties 10. and 11. are purely algebraic approaches to define regular languages; a similar set of statements can be formulated for a monoid M ⊆ Σ. In this case, equivalence over M leads to the concept of a recognizable language. Some authors use one of the above properties different from "1." as an alternative definition of regular languages. Some of the equivalences above, particularly those among the first four formalisms, are called Kleene's theorem in textbooks. Precisely which one (or which subset) is called such varies between authors. One textbook calls the equivalence of regular expressions and NFAs ("1." and "2." above) "Kleene's theorem". Another textbook calls the equivalence of regular expressions and DFAs ("1." and "3." above) "Kleene's theorem". Two other textbooks first prove the expressive equivalence of NFAs and DFAs ("2." and "3.") and then state "Kleene's theorem" as the equivalence between regular expressions and finite automata (the latter said to describe "recognizable languages"). A linguistically oriented text first equates regular grammars ("4." above) with DFAs and NFAs, calls the languages generated by (any of) these "regular", after which it introduces regular expressions which it terms to describe "rational languages", and finally states "Kleene's theorem" as the coincidence of regular and rational languages. Other authors simply define "rational expression" and "regular expressions" as synonymous and do the same with "rational languages" and "regular languages". Apparently, the term regular originates from a 1951 technical report where Kleene introduced regular events and explicitly welcomed "any suggestions as to a more descriptive term". Noam Chomsky, in his 1959 seminal article, used the term regular in a different meaning at first (referring to what is called Chomsky normal form today), but noticed that his finite state languages were equivalent to Kleene's regular events. == Closure properties == The regular languages are closed under various operations, that is, if the languages K and L are regular, so is the result of the following operations: the set-theoretic Boolean operations: union K ∪ L, intersection K ∩ L, and complement L, hence also relative complement K − L. the regular operations: K ∪ L, concatenation ⁠ K ∘ L {\displaystyle K\circ L} ⁠, and Kleene star L. the trio operations: string homomorphism, inverse string homomorphism, and intersection with regular languages. As a consequence they are closed under arbitrary finite state transductions, like quotient K / L with a regular language. Even more, regular languages are closed under quotients with arbitrary languages: If L is regular then L / K is regular for any K. the reverse (or mirror image) LR. Given a nondeterministic finite automaton to recognize L, an automaton for LR can be obtained by reversing all transitions and interchanging starting and finishing states. This may result in multiple starting states; ε-transitions can be used to join them. == Decidability properties == Given two deterministic finite automata A and B, it is decidable whether they accept the same language. As a consequence, using the above closure properties, the following problems are also decidable for arbitrarily given deterministic finite automata A and B, with accepted languages LA and LB, respectively: Containment: is LA ⊆ LB ? Disjointness: is LA ∩ LB = {} ? Emptiness: is LA = {} ? Universality: is LA = Σ ? Membership: given a ∈ Σ, is a ∈ LB ? For regular expressions, the universality problem is NP-complete already for a singleton alphabet. For larger alphabets, that problem is PSPACE-complete. If regular expressions are extended to allow also a squaring operator, with "A2" denoting the same as "AA", still just regular languages can be described, but the universality problem has an exponential space lower bound, and is in fact complete for exponential space with respect to polynomial-time reduction. For a fixed finite alphabet, the theory of the set of all languages – together with strings, membership of a string in a language, and for each character, a function to append the character to a string (and no other operations) – is decidable, and its minimal elementary substructure consists precisely of regular languages. For a binary alphabet, the theory is called S2S. == Complexity results == In computational complexity theory, the complexity class of all regular languages is sometimes referred to as REGULAR or REG and equals DSPACE(O(1)), the decision problems that can be solved in constant space (the space used is independent of the input size). REGULAR ≠ AC0, since it (trivially) contains the parity problem of determining whether the number of 1 bits in the input is even or odd and this problem is not in AC0. On the other hand, REGULAR does not contain AC0, because the nonregular language of palindromes, or the nonregular language { 0 n 1 n : n ∈ N } {\displaystyle \{0^{n}1^{n}:n\in \mathbb {N} \}} can both be recognized in AC0. If a language is not regular, it requires a machine with at least Ω(log log n) space to recognize (where n is the input size). In other words, DSPACE(o(log log n)) equals the class of regular languages. In practice, most nonregular problems are studied in a setting with at least logarithmic space, as this is the amount of space required to store a pointer into the input tape. == Location in the Chomsky hierarchy == To locate the regular languages in the Chomsky hierarchy, one notices that every regular language is context-free. The converse is not true: for example, the language consisting of all strings having the same number of as as bs is context-free but not regular. To prove that a language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma. Other approaches include using the closure properties of regular languages or quantifying Kolmogorov complexity. Important subclasses of regular languages include: Finite languages, those containing only a finite number of words. These are regular la
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