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Structured-light 3D scanner

A structured-light 3D scanner is a device used to capture the three-dimensional shape of an object by projecting light patterns, such as grids or stripes, onto its surface. The deformation of these patterns is recorded by cameras and processed using specialized algorithms to generate a detailed 3D model. Structured-light 3D scanning is widely employed in fields such as industrial design, quality control, cultural heritage preservation, augmented reality gaming, and medical imaging. Compared to laser-based 3D scanning, structured-light scanners use non-coherent light sources, such as LEDs or projectors, which enable faster data acquisition and eliminate potential safety concerns associated with lasers. However, the accuracy of structured-light scanning can be influenced by external factors, including ambient lighting conditions and the reflective properties of the scanned object. == Principle == Projecting a narrow band of light onto a three-dimensional surface creates a line of illumination that appears distorted when viewed from perspectives other than that of the projector. This distortion can be analyzed to reconstruct the geometry of the surface, a technique known as light sectioning. Projecting patterns composed of multiple stripes or arbitrary fringes simultaneously enables the acquisition of numerous data points at once, improving scanning speed. While various structured light projection techniques exist, parallel stripe patterns are among the most commonly used. By analyzing the displacement of these stripes, the three-dimensional coordinates of surface details can be accurately determined. === Generation of light patterns === Two major methods of stripe pattern generation have been established: Laser interference and projection. The laser interference method works with two wide planar laser beam fronts. Their interference results in regular, equidistant line patterns. Different pattern sizes can be obtained by changing the angle between these beams. The method allows for the exact and easy generation of very fine patterns with unlimited depth of field. Disadvantages are high cost of implementation, difficulties providing the ideal beam geometry, and laser typical effects like speckle noise and the possible self interference with beam parts reflected from objects. Typically, there is no means of modulating individual stripes, such as with Gray codes. The projection method uses incoherent light and basically works like a video projector. Patterns are usually generated by passing light through a digital spatial light modulator, typically based on one of the three currently most widespread digital projection technologies, transmissive liquid crystal, reflective liquid crystal on silicon (LCOS) or digital light processing (DLP; moving micro mirror) modulators, which have various comparative advantages and disadvantages for this application. Other methods of projection could be and have been used, however. Patterns generated by digital display projectors have small discontinuities due to the pixel boundaries in the displays. Sufficiently small boundaries however can practically be neglected as they are evened out by the slightest defocus. A typical measuring assembly consists of one projector and at least one camera. For many applications, two cameras on opposite sides of the projector have been established as useful. Invisible (or imperceptible) structured light uses structured light without interfering with other computer vision tasks for which the projected pattern will be confusing. Example methods include the use of infrared light or of extremely high framerates alternating between two exact opposite patterns. === Calibration === Geometric distortions by optics and perspective must be compensated by a calibration of the measuring equipment, using special calibration patterns and surfaces. A mathematical model is used for describing the imaging properties of projector and cameras. Essentially based on the simple geometric properties of a pinhole camera, the model also has to take into account the geometric distortions and optical aberration of projector and camera lenses. The parameters of the camera as well as its orientation in space can be determined by a series of calibration measurements, using photogrammetric bundle adjustment. === Analysis of stripe patterns === There are several depth cues contained in the observed stripe patterns. The displacement of any single stripe can directly be converted into 3D coordinates. For this purpose, the individual stripe has to be identified, which can for example be accomplished by tracing or counting stripes (pattern recognition method). Another common method projects alternating stripe patterns, resulting in binary Gray code sequences identifying the number of each individual stripe hitting the object. An important depth cue also results from the varying stripe widths along the object surface. Stripe width is a function of the steepness of a surface part, i.e. the first derivative of the elevation. Stripe frequency and phase deliver similar cues and can be analyzed by a Fourier transform. Finally, the wavelet transform has recently been discussed for the same purpose. In many practical implementations, series of measurements combining pattern recognition, Gray codes and Fourier transform are obtained for a complete and unambiguous reconstruction of shapes. Another method also belonging to the area of fringe projection has been demonstrated, utilizing the depth of field of the camera. It is also possible to use projected patterns primarily as a means of structure insertion into scenes, for an essentially photogrammetric acquisition. === Precision and range === The optical resolution of fringe projection methods depends on the width of the stripes used and their optical quality. It is also limited by the wavelength of light. An extreme reduction of stripe width proves inefficient due to limitations in depth of field, camera resolution and display resolution. Therefore, the phase shift method has been widely established: A number of at least 3, typically about 10 exposures are taken with slightly shifted stripes. The first theoretical deductions of this method relied on stripes with a sine wave shaped intensity modulation, but the methods work with "rectangular" modulated stripes, as delivered from LCD or DLP displays as well. By phase shifting, surface detail of e.g. 1/10 the stripe pitch can be resolved. Current optical stripe pattern profilometry hence allows for detail resolutions down to the wavelength of light, below 1 micrometer in practice or, with larger stripe patterns, to approx. 1/10 of the stripe width. Concerning level accuracy, interpolating over several pixels of the acquired camera image can yield a reliable height resolution and also accuracy, down to 1/50 pixel. Arbitrarily large objects can be measured with accordingly large stripe patterns and setups. Practical applications are documented involving objects several meters in size. Typical accuracy figures are: Planarity of a 2-foot (0.61 m) wide surface, to 10 micrometres (0.00039 in). Shape of a motor combustion chamber to 2 micrometres (7.9×10−5 in) (elevation), yielding a volume accuracy 10 times better than with volumetric dosing. Shape of an object 2 inches (51 mm) large, to about 1 micrometre (3.9×10−5 in) Radius of a blade edge of e.g. 10 micrometres (0.00039 in), to ±0.4 μm === Navigation === As the method can measure shapes from only one perspective at a time, complete 3D shapes have to be combined from different measurements in different angles. This can be accomplished by attaching marker points to the object and combining perspectives afterwards by matching these markers. The process can be automated, by mounting the object on a motorized turntable on robotic inspection cell, or CNC positioning device. Markers can as well be applied on a positioning device instead of the object itself. The 3D data gathered can be used to retrieve CAD (computer aided design) data and models from existing components (reverse engineering), hand formed samples or sculptures, natural objects or artifacts. === Challenges === As with all optical methods, reflective or transparent surfaces raise difficulties. Reflections cause light to be reflected either away from the camera or right into its optics. In both cases, the dynamic range of the camera can be exceeded. Transparent or semi-transparent surfaces also cause major difficulties. In these cases, coating the surfaces with a thin opaque lacquer just for measuring purposes is a common practice. A recent method handles highly reflective and specular objects by inserting a 1-dimensional diffuser between the light source (e.g., projector) and the object to be scanned. Alternative optical techniques have been proposed for handling perfectly transparent and specular objects. Double reflections and inter-reflections can cause the stripe pattern to be overlaid with unwanted ligh
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AI Copywriting Tools Reviews: What Actually Works in 2026

Shopping for the best AI copywriting tool? An AI copywriting tool 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 copywriting tool 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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Yasuo Matsuyama

Yasuo Matsuyama (born March 23, 1947) is a Japanese researcher in machine learning and human-aware information processing. Matsuyama is a Professor Emeritus and an Honorary Researcher of the Research Institute of Science and Engineering of Waseda University. == Early life and education == Matsuyama received his bachelor’s, master’s and doctoral degrees in electrical engineering from Waseda University in 1969, 1971, and 1974 respectively. The dissertation title for the Doctor of Engineering is Studies on Stochastic Modeling of Neurons. There, he contributed to the spiking neurons with stochastic pulse-frequency modulation. Advisors were Jun’ichi Takagi, Kageo, Akizuki, and Katsuhiko Shirai. Upon the completion of the doctoral work at Waseda University, he was dispatched to the United States as a Japan-U.S. exchange fellow by the joint program of the Japan Society for the Promotion of Science, Fulbright Program, and the Institute of International Education. Through this exchange program, he completed his Ph.D. program at Stanford University in 1978. The dissertation title is Process Distortion Measures and Signal Processing. There, he contributed to the theory of probabilistic distortion measures and its applications to speech encoding with spectral clustering or vector quantization. His advisor was Robert. M. Gray. == Career == From 1977 to 1078, Matsuyama was a research assistant at the Information Systems Laboratory of Stanford University Archived 2018-03-16 at the Wayback Machine. From 1979 to 1996, he was a faculty of Ibaraki University, Japan (the final position was a professor and chairperson of the Information and System Sciences Major). Since 1996, he was a Professor of Waseda University, Department of Computer Science and Engineering. From 2011 to 2013, he was the director of the Media Network Center of Waseda University. At the 2011 Tōhoku earthquake and tsunami of March 11, 2011, he was in charge of the safety inquiry of 65,000 students, staffs and faculties. Since 2017, Matsuyama is a Professor Emeritus and an Honorary Researcher of the Research Institute of Science and Engineering of Waseda University. Since 2018, he serves as an acting president of the Waseda Electrical Engineering Society. == Work == Matsuyama’s works on machine learning and human-aware information processing have dual foundations. Studies on the competitive learning (vector quantization) for his Ph.D. at Stanford University brought about his succeeding works on machine learning contributions. Studies on stochastic spiking neurons for his Dr. Engineering at Waseda University set off applications of biological signals to the machine learning. Thus, his works can be grouped reflecting these dual foundations. Statistical machine learning algorithms: The use of the alpha-logarithmic likelihood ratio in learning cycles generated the alpha-EM algorithm (alpha-Expectation maximization algorithm). Because the alpha-logarithm includes the usual logarithm, the alpha-EM algorithm contains the EM-algorithm (more precisely, the log-EM algorithm). The merit of the speedup by the alpha-EM over the log-EM is due to the ability to utilize the past information. Such a usage of the messages from the past brought about the alpha-HMM estimation algorithm (alpha-hidden Markov model estimation algorithm) that is a generalized and faster version of the hidden Markov model estimation algorithm (HMM estimation algorithm). Competitive learning on empirical data: Starting from the speech compression studies at Stanford, Matsuyama developed generalized competitive learning algorithms; the harmonic competition and the multiple descent cost competition. The former realizes the multiple-object optimization. The latter admits deformable centroids. Both algorithms generalize the batch-mode vector quantization (simply called, vector quantization) and the successive-mode vector quantization (or, called learning vector quantization). A hierarchy from the alpha-EM to the vector quantization: Matsuyama contributed to generate and identify the hierarchy of the above algorithms. Alpha-EM ⊃ log-EM ⊃ basic competitive learning (vector quantization, VQ; or clustering). On the class of the vector quantization and competitive learning, he contributed to generate and identify the hierarchy of VQs. VQ ⇔ {batch mode VQ, and learning VQ} ⊂ {harmonic competition} ⊂ {multiple descent cost competition}. Applications to Human-aware information processing: The dual foundations of his led to the applications to huma-aware information processing. Retrieval systems for similar images and videos. Bipedal humanoid operations via invasive and noninvasive brain signals as well as gestures. Continuous authentication of uses by brain signals. Self-organization and emotional feature injection based on the competitive learning. Decomposition of DNA sequences by the independent component analysis (US Patent: US 8,244,474 B2). Data compression of speech signals by the competitive learning. The above theories and applications work as contributions to IoCT (Internet of Collaborative Things) and IoXT (http://www.asc-events.org/ASC17/Workshop.php Archived 2018-02-06 at the Wayback Machine). == Awards and honors == 2016: e-Teaching Award of Waseda University 2015: Best Textbook Award by the Japanese Society of Information Processing 2014: Fellow of the Japanese Society of Information Processing 2013: IEEE Life Fellow 2008: Y. Dote Memorial Best Paper Award of CSTST 2008 from ACM and IEEE 2006: LSI Intellectual Property Design Award from the LSI IP Committee 2004: Best Paper Award for Application Oriented Research from Asia Pacific Neural Network Assembly 2002: Fellow Award from the Institute of Electronics, Information and Communication Engineers. 2001: Telecommunication System Major Award of the Telecommunications Advancement Foundation 2001: Outstanding Paper Award of IEEE Transactions on Neural Networks Archived 2013-01-17 at the Wayback Machine 1998: Fellow Award from IEEE for contributions to learning algorithms with competition. 1992: Best Paper Award from the Institute of Electronics, Information and Communication Engineers 1989: Telecommunication System Promotion Award of the Telecommunications Advancement Foundation
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AI Code-review Tools Reviews: What Actually Works in 2026

Shopping for the best AI code-review tool? An AI code-review tool 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 code-review tool 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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PCPaint

PCPaint was one of the first IBM PC-based mouse-driven GUI paint programs, released in 1984. It followed after Microsoft Doodle, released in 1983 with the Microsoft Mouse version 1 drivers for DOS, and around the same time as Digital Research’s Draw program. It was developed and created by John Bridges and Doug Wolfgram. It was later developed into Pictor Paint. The hardware manufacturer Mouse Systems bundled PCPaint with millions of computer mice that they sold, making PCPaint one of the best-selling DOS-based paint programs of the mid 1980s. == History == In 1983, Doug Wolfgram bought a Microsoft Mouse and decided to write a drawing program for it. They named it “Mouse Draw”. The interface was primitive but the program functioned well. Wolfgram traveled to SoftCon in New Orleans where he demonstrated the program to Mouse Systems. Mouse Systems was developing an optical mouse and they wanted to bundle a painting program so they agreed to publish Mouse Draw. The original program was written entirely in assembly language with primitive graphics routines developed by Wolfgram. John Bridges worked for an educational software company, Classroom Consortia Media, Inc., developing and writing Apple and IBM graphics libraries for CCM's software. Bridges and Wolfgram were friends who had been connected through a bulletin board system developed and run by Wolfgram. The two collaborated cross country via the BBS, Wolfram in California and Bridges in New York. Mouse Systems wanted the paint program to capture the look and feel of MacPaint. John Bridges and Doug Wolfgram started reworking Mouse Draw into what became PCPaint. The program was completely re-written using Bridge's graphics library and the top-level elements were written in C rather than assembly language. Bridges developed the core graphics code for the first version of PCPaint while Wolfgram worked on the user interface and top-level code. Mouse Systems signed an exclusive agreement with Wolfgram's company, Microtex Industries, Inc., to bundle PCPaint with every mouse they sold. They began publishing PCPaint with their mice in 1984. Microsoft responded in 1985 by bundling a competing product, PC Paintbrush, with version 4 of its DOS drivers for the Microsoft Mouse, replacing its in-house Microsoft Doodle program which it published with version 1 of the DOS drivers in mid-1983. Microsoft’s mouse began to outsell Mouse Systems mouse. In November 1985 Microsoft bundled a cut-down version of PC Paintbrush with Windows 1.0 (called Microsoft Paint), later bundling an updated version of PC Paintbrush with Windows 3.0 (as Paintbrush), impacting PCPaint’s marketshare. In early 1987, Mouse Systems decided that PCPaint wasn't helping to sell mice any longer so they discontinued the bundle deal and returned rights to the code to MicroTex Industries, but retained rights to the name, PCPaint. Wolfgram then combined the paint program with a new animation system he was developing (called GRASP) and Paul Mace Software bought publishing rights to the animation system and PCPaint, which was to be renamed Pictor. Bridges again got involved and took over programming responsibilities for GRASP as well as PCPaint while Wolfgram focused on more of the business details. In creating the first version of PCPaint, Doug had a dual-floppy machine with a Computer Innovations compiler on one disk and source code on the other. John had the "luxury" of a 10MB hard disk in his XT. Data was exchanged daily via 1200, then 2400 baud modems. === Authorship and Ownership === John Bridges and Wolfgram continued to work on PCPaint and GRASP on behalf of Paul Mace Software until 1990. Also in that year, Doug Wolfgram sold his remaining rights to PCPaint (and its animation system, GRASP) to John Bridges. In 1994, GRASP development stopped and so did development of Pictor Paint. John Bridges terminated his GRASP publishing contract with Paul Mace Software, and went off to create GLPro (the next generation of GRASP) with GMEDIA. Along with GLPro, came GLPaint, the successor to PCPaint and Pictor Paint. == Versions == In June 1984, Mouse Systems shipped PCPaint 1.0, the first GUI based Paint program for the IBM PC family of computers. John Bridges and Doug Wolfgram, were the co-authors of PCPaint 1.0. PCPaint 1.0 saved its graphics in a modified BSaved image format with the extension of ".PIC". The release of PCPaint Version 1.5 followed in late 1984, with the additions of graphics image compression for the .PIC format and support for "larger-than-screen" images. PCjr support was also added in this version after overcoming severe memory shortage problems getting PCPaint to run on the 128k PCjr. October 1985 saw the release of PCPaint 2.0. EGA support and publishing features were added to this version. The .PIC format was further refined, offering support for the rapidly expanding graphics capabilities of the PC and efficient image compression. PCPaint 3.1 was released in 1989. Unlike previous versions, it was not bundled with mice but was sold as a stand-alone software product. PCPaint 3.1 offered improved text and image handling, provided 36 types of flood and fill, worked with VGA adapters in hi-res 16-color and 256-color modes, allowed the user to save and retrieve files in a variety of intercompatible formats (.PIC, .GIF, .PCX, .IMG), and printed selected portions of images on color or black-and-white dot matrix, ink jet, and laser printers such as PostScript and HP Laser Jet. PCPaint 3.1 is still in use today by some users of DOS emulation programs like DOSBox and available for free download. Pictor Paint was an improved version, written by John Bridges, and bundled with GRASP GRaphical System for Presentation also written by John Bridges. It was also called "The Painter's Easel". GLPaint, released in 1995, was the last in this series of paint programs written by John Bridges. By 1998 version 7.0 provided support for TrueColor images and the Pictor PIC format was expanded to handle these. == Pictor PIC Image Format == PCPaint 1.0 saved its graphics in a modified BSAVE image format (which was popular at the time) with the file type (extension) of ".PIC". By PCPaint 1.5 this format was extended further to accommodate image compression. With the release of version 2.0 the PICtor PIC image format was developed almost to its present state, with no similarity to the BSAVE format used by earlier versions. Pictor Paint saved its files in a compressed format with the file extension PIC, which was the same format used by PCPaint.
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Language and Computers

Language and Computers: Studies in Practical Linguistics (ISSN 0921-5034) is a book series on corpus linguistics and related areas. As studies in linguistics, volumes in the series have, by definition, their foundations in linguistic theory; however, they are not concerned with theory for theory's sake, but always with a definite direct or indirect interest in the possibilities of practical application in the dynamic area where language and computers meet. The book series was founded in 1988, and is published by Brill|Rodopi. == Editors == Christian Mair Charles F. Meyer == Volumes == Volumes include: # 77. English Corpus Linguistics: Variation in Time, Space and Genre. Selected papers from ICAME 32., Edited by Gisle Andersen and Kristin Bech. ISBN 978-90-420-3679-6 E-ISBN 978-94-012-0940-3 # 76. English Corpus Linguistics: Crossing Paths., Edited by Merja Kytö. ISBN 978-90-420-3518-8 E-ISBN 978-94-012-0793-5 # 75. Corpus Linguistics and Variation in English.Theory and Description., Edited by Joybrato Mukherjee and Magnus Huber. ISBN 978-90-420-3495-2 E-ISBN 978-94-012-0771-3 # 74. English Corpus Linguistics: Looking back, Moving forward. Papers from the 30th International Conference on English Language Research on Computerized Corpora (ICAME 30), Lancaster, UK, 27–31 May 2009., Edited by Sebastian Hoffmann, Paul Rayson and Geoffrey Leech. ISBN 978-90-420-3466-2 E-ISBN 978-94-012-0747-8 #73. Corpus-based Studies in Language Use, Language Learning, and Language Documentation., Edited by John Newman, Harald Baayen and Sally Rice. ISBN 978-90-420-3401-3 E-ISBN 978-94-012-0688-4 #72. The Progressive in Modern English. A Corpus-Based Study of Grammaticalization and Related Changes., by Svenja Kranich. ISBN 978-90-420-3143-2 E-ISBN 978-90-420-3144-9 #71. Corpus-linguistic applications. Current studies, new directions, Edited by Stefan Th. Gries, Stefanie Wulff, and Mark Davies.. ISBN 978-90-420-2800-5 #70. A resource-light approach to morpho-syntactic tagging., by Anna Feldman and Jirka Hana. ISBN 978-90-420-2768-8 #69. Corpus Linguistics. Refinements and Reassessments., Edited by Antoinette Renouf and Andrew Kehoe. ISBN 978-90-420-2597-4 #68. Corpora: Pragmatics and Discourse. Papers from the 29th International Conference on English Language Research on Computerized Corpora (ICAME 29). Ascona, Switzerland, 14–18 May 2008., Edited by Andreas H. Jucker, Daniel Schreier and Marianne Hundt. ISBN 978-90-420-2592-9 #67. Modals and Quasi-modals in English., by Peter Collins. ISBN 978-90-420-2532-5 #66. Linking up contrastive and learner corpus research., Edited by Gaëtanelle Gilquin, Szilvia Papp and María Belén Díez-Bedmar. ISBN 978-90-420-2446-5 #64. Language, People, Numbers. Corpus Linguistics and Society., Edited by Andrea Gerbig and Oliver Mason. ISBN 978-90-420-2350-5 #63. Variation and change in the lexicon. A corpus-based analysis of adjectives in English ending in –ic and –ical. , by Mark Kaunisto. ISBN 978-90-420-2233-1 #62. Corpus Linguistics 25 Years on., Edited by Roberta Facchinetti. ISBN 978-90-420-2195-2 #61. Corpora in the Foreign Language Classroom. Selected papers from the Sixth International Conference on Teaching and Language Corpora (TaLC 6), Edited by Encarnación Hidalgo, Luis Quereda and Juan Santana. ISBN 978-90-420-2142-6 #60. Corpus Linguistics Beyond the Word. Corpus Research from Phrase to Discourse, Edited by Eileen Fitzpatrick. ISBN 978-90-420-2135-8 #59. Corpus Linguistics and the Web., Edited by Marianne Hundt, Nadja Nesselhauf and Carolin Biewer. ISBN 978-90-420-2128-0 #58. English mediopassive constructions. A cognitive, corpus-based study of their origin, spread, and current status, by Marianne Hundt. ISBN 978-90-420-2127-3 / ISBN 90-420-2127-6
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Multiple sequence alignment

Multiple sequence alignment (MSA) is the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. These alignments are used to infer evolutionary relationships via phylogenetic analysis and can highlight homologous features between sequences. Alignments highlight mutation events such as point mutations (single amino acid or nucleotide changes), insertion mutations and deletion mutations, and alignments are used to assess sequence conservation and infer the presence and activity of protein domains, tertiary structures, secondary structures, and individual amino acids or nucleotides. Multiple sequence alignments require more sophisticated methodologies than pairwise alignments, as they are more computationally complex. Most multiple sequence alignment programs use heuristic methods rather than global optimization because identifying the optimal alignment between more than a few sequences of moderate length is prohibitively computationally expensive. However, heuristic methods generally cannot guarantee high-quality solutions and have been shown to fail to yield near-optimal solutions on benchmark test cases. == Problem statement == Given m {\displaystyle m} sequences S i {\displaystyle S_{i}} , i = 1 , ⋯ , m {\displaystyle i=1,\cdots ,m} similar to the form below: S := { S 1 = ( S 11 , S 12 , … , S 1 n 1 ) S 2 = ( S 21 , S 22 , ⋯ , S 2 n 2 ) ⋮ S m = ( S m 1 , S m 2 , … , S m n m ) {\displaystyle S:={\begin{cases}S_{1}=(S_{11},S_{12},\ldots ,S_{1n_{1}})\\S_{2}=(S_{21},S_{22},\cdots ,S_{2n_{2}})\\\,\,\,\,\,\,\,\,\,\,\vdots \\S_{m}=(S_{m1},S_{m2},\ldots ,S_{mn_{m}})\end{cases}}} A multiple sequence alignment is taken of this set of sequences S {\displaystyle S} by inserting any amount of gaps needed into each of the S i {\displaystyle S_{i}} sequences of S {\displaystyle S} until the modified sequences, S i ′ {\displaystyle S'_{i}} , all conform to length L ≥ max { n i ∣ i = 1 , … , m } {\displaystyle L\geq \max\{n_{i}\mid i=1,\ldots ,m\}} and no values in the sequences of S {\displaystyle S} of the same column consists of only gaps. The mathematical form of an MSA of the above sequence set is shown below: S ′ := { S 1 ′ = ( S 11 ′ , S 12 ′ , … , S 1 L ′ ) S 2 ′ = ( S 21 ′ , S 22 ′ , … , S 2 L ′ ) ⋮ S m ′ = ( S m 1 ′ , S m 2 ′ , … , S m L ′ ) {\displaystyle S':={\begin{cases}S'_{1}=(S'_{11},S'_{12},\ldots ,S'_{1L})\\S'_{2}=(S'_{21},S'_{22},\ldots ,S'_{2L})\\\,\,\,\,\,\,\,\,\,\,\vdots \\S'_{m}=(S'_{m1},S'_{m2},\ldots ,S'_{mL})\end{cases}}} To return from each particular sequence S i ′ {\displaystyle S'_{i}} to S i {\displaystyle S_{i}} , remove all gaps. == Graphing approach == A general approach when calculating multiple sequence alignments is to use graphs to identify all of the different alignments. When finding alignments via graph, a complete alignment is created in a weighted graph that contains a set of vertices and a set of edges. Each of the graph edges has a weight based on a certain heuristic that helps to score each alignment or subset of the original graph. === Tracing alignments === When determining the best suited alignments for each MSA, a trace is usually generated. A trace is a set of realized, or corresponding and aligned, vertices that has a specific weight based on the edges that are selected between corresponding vertices. When choosing traces for a set of sequences it is necessary to choose a trace with a maximum weight to get the best alignment of the sequences. == Alignment methods == There are various alignment methods used within multiple sequence to maximize scores and correctness of alignments. Each is usually based on a certain heuristic with an insight into the evolutionary process. Most try to replicate evolution to get the most realistic alignment possible to best predict relations between sequences. === Dynamic programming === A direct method for producing an MSA uses the dynamic programming technique to identify the globally optimal alignment solution. For proteins, this method usually involves two sets of parameters: a gap penalty and a substitution matrix assigning scores or probabilities to the alignment of each possible pair of amino acids based on the similarity of the amino acids' chemical properties and the evolutionary probability of the mutation. For nucleotide sequences, a similar gap penalty is used, but a much simpler substitution matrix, wherein only identical matches and mismatches are considered, is typical. The scores in the substitution matrix may be either all positive or a mix of positive and negative in the case of a global alignment, but must be both positive and negative, in the case of a local alignment. For n individual sequences, the naive method requires constructing the n-dimensional equivalent of the matrix formed in standard pairwise sequence alignment. The search space thus increases exponentially with increasing n and is also strongly dependent on sequence length. Expressed with the big O notation commonly used to measure computational complexity, a naïve MSA takes O(LengthNseqs) time to produce. To find the global optimum for n sequences this way has been shown to be an NP-complete problem. In 1989, based on Carrillo-Lipman Algorithm, Altschul introduced a practical method that uses pairwise alignments to constrain the n-dimensional search space. In this approach pairwise dynamic programming alignments are performed on each pair of sequences in the query set, and only the space near the n-dimensional intersection of these alignments is searched for the n-way alignment. The MSA program optimizes the sum of all of the pairs of characters at each position in the alignment (the so-called sum of pair score) and has been implemented in a software program for constructing multiple sequence alignments. In 2019, Hosseininasab and van Hoeve showed that by using decision diagrams, MSA may be modeled in polynomial space complexity. === Progressive alignment construction === The most widely used approach to multiple sequence alignments uses a heuristic search known as progressive technique (also known as the hierarchical or tree method) developed by Da-Fei Feng and Doolittle in 1987. Progressive alignment builds up a final MSA by combining pairwise alignments beginning with the most similar pair and progressing to the most distantly related. All progressive alignment methods require two stages: a first stage in which the relationships between the sequences are represented as a phylogenetic tree, called a guide tree, and a second step in which the MSA is built by adding the sequences sequentially to the growing MSA according to the guide tree. The initial guide tree is determined by an efficient clustering method such as neighbor-joining or unweighted pair group method with arithmetic mean (UPGMA), and may use distances based on the number of identical two-letter sub-sequences (as in FASTA rather than a dynamic programming alignment). Progressive alignments are not guaranteed to be globally optimal. The primary problem is that when errors are made at any stage in growing the MSA, these errors are then propagated through to the final result. Performance is also particularly bad when all of the sequences in the set are rather distantly related. Most modern progressive methods modify their scoring function with a secondary weighting function that assigns scaling factors to individual members of the query set in a nonlinear fashion based on their phylogenetic distance from their nearest neighbors. This corrects for non-random selection of the sequences given to the alignment program. Progressive alignment methods are efficient enough to implement on a large scale for many (100s to 1000s) sequences. A popular progressive alignment method has been the Clustal family. ClustalW is used extensively for phylogenetic tree construction, in spite of the author's explicit warnings that unedited alignments should not be used in such studies and as input for protein structure prediction by homology modeling. European Bioinformatics Institute (EMBL-EBI) announced that CLustalW2 will expire in August 2015. They recommend Clustal Omega which performs based on seeded guide trees and HMM profile-profile techniques for protein alignments. An alternative tool for progressive DNA alignments is multiple alignment using fast Fourier transform (MAFFT). Another common progressive alignment method named T-Coffee is slower than Clustal and its derivatives but generally produces more accurate alignments for distantly related sequence sets. T-Coffee calculates pairwise alignments by combining the direct alignment of the pair with indirect alignments that aligns each sequence of the pair to a third sequence. It uses the output from Clustal as well as another local alignment program LALIGN, which finds multiple regions of local alignment between two sequences. The resulting alignment and phylogenetic tree are used as a guide to produce new and more accurate w
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Pietro Perona

Pietro Perona (born 3 September 1961) is an Italian-American educator and computer scientist. He is the Allan E. Puckett Professor of Electrical Engineering and Computation and Neural Systems at the California Institute of Technology and director of the National Science Foundation Engineering Research Center in Neuromorphic Systems Engineering. He is known for his research in computer vision and is the director of the Caltech Computational Vision Group. == Academic biography == Perona obtained his D.Eng. in electrical engineering cum laude from the University of Padua in 1985 and completed his Ph.D. at the University of California, Berkeley in 1990. His dissertation was titled Finding Texture and Brightness Boundaries in Images, and his adviser was Jitendra Malik. In 1990, Perona was a postdoctoral fellow at the International Computer Science Institute at Berkeley. From 1990 to 1991, he was a postdoctoral fellow at the Massachusetts Institute of Technology in the Laboratory for Information and Decision Systems. He has been on the faculty of the California Institute of Technology since 1991, and he was named Allan E. Puckett Professor in 2008. == Research == Perona’s research focuses on the computational aspects of vision and learning. He developed the anisotropic diffusion equation, a partial differential equation that reduces noise in images while enhancing region boundaries. He is currently interested in visual recognition and in visual analysis of behavior. Perona and Serge Belongie lead the Visipedia project, which facilitates research on visual knowledge representation, visual search, and human-in-the-loop machine learning systems. Perona pioneered the study of visual categorization (including the publication of the Caltech 101 dataset) for which he was awarded the Longuet-Higgins Prize in 2013. He is also the recipient of the 2010 Koenderink Prize for Fundamental Contributions in Computer Vision, the 2003 Conference on Computer Vision and Pattern Recognition best paper award, and a 1996 NSF Presidential Young Investigator Award. == Media coverage == Perona has been quoted or had his research featured in various national media outlets, including the New York Times, Science Friday, The New Yorker, and the Los Angeles Times. In 2003, Perona and Stephen Nowlin organized the NEURO art exhibition, which brought together contemporary artists and scientists to explore neuromorphic engineering.
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Dave's Redistricting

Dave's Redistricting App (DRA) is an online web app originally created by Dave Bradlee that allows anyone to simulate redistricting a U.S. state's congressional and legislative districts. == Purpose == According to Bradlee, the software was designed to "put power in people's hands," and so that they "can see how the process works, so it's a little less mysterious than it was 10 years ago." Bradlee has noticed that many citizens are taking this process seriously and using his app to create legitimate redistricting maps that could be put in place. Some websites have called Bradlee the pioneer and cause of the rise of do-it-yourself redistricting. States such as Montana in 2021 allowed the general population to use it to submit redistricting proposals following the 2020 United States Census. Dave's Redistricting has frequently been mentioned as a resource that can be used to combat gerrymandering, given that the public has free access to it. Political science firms such as FiveThirtyEight have used the website to draw examples of gerrymandered districts, including on their famous Atlas of Redistricting. Dave Bradlee built the first generation of DRA. DRA 2020 is built by a small team of volunteers—Dave Bradlee, Terry Crowley, Alec Ramsay, and David Rinn—all with a shared passion for technology & democracy and all Microsoft veterans. Their mission is to empower civic organizations and citizen activists to advocate for fair congressional and legislative districts and increased transparency in the redistricting process. == Functions == Users can redraw the congressional and state legislative districts for all 50 states, the District of Columbia, and Puerto Rico using a variety of census and election datasets including Cook PVI. Maps can be optimized for different criteria. DRA 2020 added several major features to the first generation app: Sharing & collaborative editing of maps, like Google Docs Multiple statewide elections for all 50 states including the ability to import your own data Comprehensive analytics for evaluating and comparing maps Custom overlays, and Block-level editing DRA remains free to use. == Versions == 2.2: This uses Bing Maps, an outdated software that projects the districts of a single state onto a map of the United States. 2.5: After Bing Maps announced that it would no longer be updating for the foreseen future, the U.S. Map feature was removed. DRA 2020: At the end of 2018, a beta version of 2020 was released. This version that did not require Microsoft Silverlight and could be used in any web browser. DRA 2020 has been under continuous development since and is built using React (JavaScript library), Mapbox, OpenStreetMap, TypeScript, Node.js, Amazon Web Services, as well as many open source components, tools, and icons.
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Peter Flach

Pieter "Peter" Adriaan Flach (born 8 April 1961, Sneek) is a Dutch computer scientist and a Professor of Artificial Intelligence in the Department of Computer Science at the University of Bristol. He is author of the acclaimed Simply Logical: Intelligent Reasoning by Example (John Wiley, 1994) and Machine Learning: the Art and Science of Algorithms that Make Sense of Data (Cambridge University Press, 2012). == Education == Flach received an MSc Electrical Engineering from Universiteit Twente in 1987 and a PhD in Computer Science from Tilburg University in 1995. == Research == Flach's research interests are in data mining and machine learning.
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Jiaya Jia

Jiaya Jia (Chinese: 贾佳亚) is a Chair Professor of the Department of Computer Science and Engineering at The Hong Kong University of Science and Technology (HKUST). He is an IEEE Fellow, the associate editor-in-chief of one of IEEE’s flagship and premier journals- Transactions on Pattern Analysis and Machine Intelligence (TPAMI), as well as on the editorial board of International Journal of Computer Vision (IJCV). == Early life and education == Jiaya Jia joined CUHK in 2004 as an assistant professor, and was promoted to full professor in 2015. He obtained his PhD degree in computer science jointly from Hong Kong University of Science and Technology and Microsoft Research in 2004. From March 2003 to August 2004, he was a visiting scholar at Microsoft. He conducted collaborative research at Adobe Research in 2007. == Career == Jiaya Jia is a distinguished scientist in the fields of computer vision and artificial intelligence. His research team at HKUST, DV Lab, is one of the largest vision AI research teams in the world and has been making significant contribution to advanced development of computer vision algorithms and technologies with focuses on image/video understanding, detection and segmentation, multi-modal AI, computational imaging, practical optimization, and advanced learning for visual content since 2000. Jiaya Jia has published 200+ top papers and was cited 80,000+ times on Google Scholar with H-Index 110+. 40+ PhDs and fellows from this group are now active in academia and industry, and have become prominent AI tech leaders as professors, directors in major research labs, and founders of several successful startups. Jiaya Jia assumes the position of associate editor-in-chief of IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) since 2021. He is also on the editorial board of International Journal of Computer Vision (IJCV). Jiaya Jia has served as the area chair of ICCV, CVPR, AAAI, ECCV, and several other premium international AI conferences for years. He was on program committees of major conferences in graphics and computational imaging, including ICCP, SIGGRAPH, and SIGGRAPH Asia. == Research == The research areas of Jiaya Jia are computer vision, large X models, and deep learning. Jiaya Jia has made outstanding contributions to computer vision technology, algorithms and engineering, and is among the world's leading experts in the field. His research partners include numerous renowned multinational technology companies, such as Microsoft, Qualcomm, Adobe, Intel, NVIDIA, Amazon, and Lenovo. Jia has cultivated a number of outstanding talents with Master's and PhDs who continue to engage in scientific research and development in computer vision. Many technologies in image analysis and processing developed by Jiaya Jia are still leading in the field worldwide. Wherein, his achievements in image deblurring, filtering, image sparse processing, multi-band image signal fusion and enhancement, large range motion estimation, texture and structure-based layering, etc. have been published in the industry's most influential conferences and publications, and implemented in the real-world applications. These achievements have demonstrated outstanding performance in established systems, and most of which are open source so as to enable wider applications across industries such as aviation, medical imaging, safety management, robotic design, meteorological analysis and many more. == Selected publications == In his over 20 years of research experience, Jiaya Jia has published 200+ top papers that have been cited more than 80,000 times. According to HKUST Website in August 2024, Jiaya Jia has accumulatively published over 200 scientific papers in books, journals and conferences, such as IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), International Journal of Computer Vision (IJCV) "Computer Vision and Pattern Recognition (CVPR)", and "International Conference on Computer Vision (ICCV)". Representative papers include: Jiaya Jia: Mathematical Models and Practical Solvers for Uniform Motion Deblurring (in Motion Deblurring: Algorithms and Systems), Cambridge University Press, ISBN 9781107044364, 2014; Jiaya Jia: “Matte Extraction” Book: Computer Vision - A Reference Guide, Springer, ISBN 9780387307718 Editor-in-chief: Ikeuchi, Katsushi; Jiaya Jia, Chi-Keung Tang：Image Stitching Using Structure Deformation，IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), Vol. 30, No. 4, 2008; Jiaya Jia, Jian Sun, Chi-Keung Tang, Heung-Yeung Shum：Drag-and-Drop Pasting，ACM Transactions on Graphics (also in SIGGRAPH 2006), Vol. 25, No. 3, 2006. Xiaojuan Qi, Zheng zhe Liu, Renjie Liao, Philip HS Torr, Raquel Urtasun, Jiaya Jia：GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimation，IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI). Accepted. == Selected honors and awards == ACM Fellow. 1st Place of WAD Drivable Area Segmentation Challenge 2018; 1st Place of LSUN'17 Instance and Semantic Segmentation Challenges; 1st Place of COCO Instance Segmentation Challenge 2017; 2nd Place in COCO Detection Challenge 2017; 1st Place of ImageNet Scene Parsing Challenge 2016 with the paper PSPNet presented in CVPR 2017.
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Volker Markl

Volker Markl (born 1971) is a German computer scientist and database systems researcher. == Career == In 1999, Markl received his PhD in computer science under the direction of Rudolf Bayer at the Technical University of Munich. His doctoral research led to the development of the UB-Tree. From 1997 to 2000, he was research group leader at FORWISS, the Bavarian research center for knowledge-based systems. From 2001 to 2008, he was project leader at the IBM Almaden Research Center, Silicon Valley. Since 2008, he has been full professor and Chair of the Database Systems and Information Management Group at Technische Universität Berlin. Since 2014, he is head of the Intelligent Analytics for Massive Data Research Department at the German Research Centre for Artificial Intelligence (DFKI), Berlin. From 2014 to 2020, he was director of the Berlin Big Data Center (BBDC). From 2018 to 2020, he was co-director of the Berlin Machine Learning Center (BZML). Together with Klaus-Robert Müller he became director of the new Berlin Institute for the Foundations of Learning and Data (BIFOLD), after both BBDC and the BZML merged into BIFOLD in 2020. From 2010 through 2019, he led the DFG funded Stratosphere project, which led to the establishment of Apache Flink. In 2018, he was elected president of the VLDB Endowment for a six years period that ended in 2024. == Research == Markl’s research interests lie at the intersection of distributed systems, scalable data processing, and machine learning. == Awards and honors == Markl was elected member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2021. Since 2026 he is member of the German National Academy of Sciences Leopoldina. His work was honoured with several awards, including: 2025 ICDE Best Paper Award 2021 ICDE Best Paper Award 2021 BTW Best Paper Award 2020 ACM SIGMOD Best Paper Award 2020 ACM Fellow 2019 EDBT Best Paper Award 2017 BTW Best Paper Award 2017 EDBT Best Demonstration Award 2016 ACM SIGMOD Research Highlight Award 2014 VLDB Best Paper Award 2012 IBM Faculty Award 2012 IBM Shared University Research Grant 2010 Hewlett Packard Open Innovation Award 2005 IBM Outstanding Technological Achievement Award 2005 IBM Pat Goldberg Best Paper Award
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Overcast (app)

Overcast is a podcast app for iOS that was launched in 2014 by founder and operator Marco Arment. == Founder and operator == Arment was also the Chief Technology Officer of Tumblr and founder of Instapaper before founding Overcast, and he had created his own podcasts before launching the app. In March 2023, Arment told The Vergecast how he built and maintains Overcast by himself, and that he uses ad banners promoting podcasts to cover the costs of the free app. == Features and reception == In 2014, Overcast received positive reviews from MacWorld and iMore. In 2015, The Verge and The Sweet Setup each named it the best podcast app for iOS that year. In 2017, Discover Pods gave an endorsement citing the "smart speed" feature, which shortens quiet gaps in a podcast. In April 2019, Overcast introduced a feature that allowed users to share clips from podcasts to social media. In January 2020, Overcast was updated to allow users to skip the intros and outros of podcasts.
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Ω-automaton

In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of a finite automaton that runs on infinite, rather than finite, strings as input. Since ω-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accepting states. ω-automata are useful for specifying behavior of systems that are not expected to terminate, such as hardware, operating systems and control systems. For such systems, one may want to specify a property such as "for every request, an acknowledge eventually follows", or its negation "there is a request that is not followed by an acknowledge". The former is a property of infinite words: one cannot say of a finite sequence that it satisfies this property. Classes of ω-automata include the Büchi automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These classes of ω-automata differ only in terms of acceptance condition. They all recognize precisely the regular ω-languages except for the deterministic Büchi automata, which is strictly weaker than all the others. Although all these types of automata recognize the same set of ω-languages, they nonetheless differ in succinctness of representation for a given ω-language. == Deterministic ω-automata == Formally, a deterministic ω-automaton is a tuple A = ( Q , Σ , δ , q 0 , A a c c ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},A_{acc})} , that consists of the following components: Q {\textstyle Q} , is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } , is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \rightarrow Q} is a function, called the transition function of A {\textstyle A} . Q 0 {\textstyle Q_{0}} is an element of Q {\textstyle Q} , called the initial state. A a c c {\textstyle A_{acc}} is a set of accepting states of A {\textstyle A} , formally a subset of Q ω {\textstyle Q^{\omega }} . An input for A {\textstyle A} is an infinite string over the alphabet Σ {\textstyle \Sigma } , i.e. it is an infinite sequence α = ( a 1 , a 2 , a 3 , … ) {\textstyle \alpha =(a_{1},a_{2},a_{3},\ldots )} . The run of A {\textstyle A} on such an input is an infinite sequence ρ = ( r 0 , r 1 , r 2 , … ) {\textstyle \rho =(r_{0},r_{1},r_{2},\ldots )} of states, defined as follows: r 0 = q 0 {\textstyle r_{0}=q_{0}} . r 1 = δ ( r 0 , a 1 ) {\textstyle r_{1}=\delta (r_{0},a_{1})} . r 2 = δ ( r 1 , a 2 ) {\textstyle r_{2}=\delta (r_{1},a_{2})} . ... that is, for every i {\textstyle i} : r i = δ ( r i − 1 , a i ) {\textstyle r_{i}=\delta (r_{i-1},a_{i})} . The main purpose of an ω-automaton is to define a subset of the set of all inputs: The set of accepted inputs. Whereas in the case of an ordinary finite automaton every run ends with a state r n {\textstyle r_{n}} and the input is accepted if and only if r n {\textstyle r_{n}} is an accepting state, the definition of the set of accepted inputs is more complicated for ω-automata. Here we must look at the entire run ρ {\textstyle \rho } . The input is accepted if the corresponding run is in Acc {\textstyle {\text{Acc}}} . The set of accepted input ω-words is called the recognized ω-language by the automaton, which is denoted as L ( A ) {\textstyle L(A)} . The definition of Acc {\textstyle {\text{Acc}}} as a subset of Q ω {\textstyle Q^{\omega }} is purely formal and not suitable for practice because normally such sets are infinite. The difference between various types of ω-automata (Büchi, Rabin etc.) consists in how they encode certain subsets Acc {\textstyle {\text{Acc}}} of Q ω {\textstyle Q^{\omega }} as finite sets, and therefore in which such subsets they can encode. == Nondeterministic ω-automata == Formally, a nondeterministic ω-automaton is a tuple A = ( Q , Σ , Δ , Q 0 , Acc ) {\textstyle A=(Q,\Sigma ,\Delta ,Q_{0},{\text{Acc}})} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . Δ {\textstyle \Delta } is a subset of Q × Σ × Q {\textstyle Q\times \Sigma \times Q} and is called the transition relation of A {\textstyle A} . Q 0 {\textstyle Q_{0}} is a subset of Q {\textstyle Q} , called the initial set of states. Acc {\textstyle {\text{Acc}}} is the acceptance condition, a subset of Q ω {\textstyle Q^{\omega }} . Unlike a deterministic ω-automaton, which has a transition function δ {\textstyle \delta } , the non-deterministic version has a transition relation Δ {\textstyle \Delta } . Note that Δ {\textstyle \Delta } can be regarded as a function Q × Σ → P ( Q ) {\textstyle Q\times \Sigma \rightarrow {\mathcal {P}}(Q)} from Q × Σ {\textstyle Q\times \Sigma } to the power set P ( Q ) {\textstyle {\mathcal {P}}(Q)} . Thus, given a state q n {\textstyle q_{n}} and a symbol a n {\textstyle a_{n}} , the next state q n + 1 {\textstyle q_{n+1}} is not necessarily determined uniquely, rather there is a set of possible next states. A run of A {\textstyle A} on the input α = ( a 1 , a 2 , a 3 , … ) {\textstyle \alpha =(a_{1},a_{2},a_{3},\ldots )} is any infinite sequence ρ = ( r 0 , r 1 , r 2 , … ) {\textstyle \rho =(r_{0},r_{1},r_{2},\ldots )} of states that satisfies the following conditions: r 0 {\textstyle r_{0}} is an element of Q 0 {\textstyle Q_{0}} . r 1 {\textstyle r_{1}} is an element of Δ ( r 0 , a 1 ) {\textstyle \Delta (r_{0},a_{1})} . r 2 {\textstyle r_{2}} is an element of Δ ( r 1 , a 2 ) {\textstyle \Delta (r_{1},a_{2})} . ... that is, for every i {\textstyle i} : r i {\textstyle r_{i}} is an element of Δ ( r i − 1 , a i ) {\textstyle \Delta (r_{i-1},a_{i})} . A nondeterministic ω-automaton may admit many different runs on any given input, or none at all. The input is accepted if at least one of the possible runs is accepting. Whether a run is accepting depends only on Acc {\textstyle {\text{Acc}}} , as for deterministic ω-automata. Every deterministic ω-automaton can be regarded as a nondeterministic ω-automaton by taking Δ {\textstyle \Delta } to be the graph of δ {\textstyle \delta } . The definitions of runs and acceptance for deterministic ω-automata are then special cases of the nondeterministic cases. == Acceptance conditions == Acceptance conditions may be infinite sets of ω-words. However, people mostly study acceptance conditions that are finitely representable. The following lists a variety of popular acceptance conditions. Before discussing the list, let's make the following observation. In the case of infinitely running systems, one is often interested in whether certain behavior is repeated infinitely often. For example, if a network card receives infinitely many ping requests, then it may fail to respond to some of the requests but should respond to an infinite subset of received ping requests. This motivates the following definition: For any run ρ {\textstyle \rho } , let Inf ( ρ ) {\textstyle {\text{Inf}}(\rho )} be the set of states that occur infinitely often in ρ {\textstyle \rho } . This notion of certain states being visited infinitely often will be helpful in defining the following acceptance conditions. A Büchi automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some subset F {\textstyle F} of Q {\textstyle Q} : Büchi condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } for which Inf ( ρ ) ∩ F ≠ ∅ {\textstyle {\text{Inf}}(\rho )\cap F\neq \emptyset } , i.e. there is an accepting state that occurs infinitely often in ρ {\textstyle \rho } . A Rabin automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some set Ω {\textstyle \Omega } of pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} of sets of states: Rabin condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } for which there exists a pair ( B i , G i ) {\textstyle (B_{i},G_{i})} in Ω {\textstyle \Omega } such that B i ∩ Inf ( ρ ) = ∅ {\textstyle B_{i}\cap {\text{Inf}}(\rho )=\emptyset } and G i ∩ Inf ( ρ ) ≠ ∅ {\textstyle G_{i}\cap {\text{Inf}}(\rho )\neq \emptyset } . A Streett automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some set Ω {\textstyle \Omega } of pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} of sets of states: Streett condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } such that for all pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} in Ω {\textstyle \Omega } , B i ∩ Inf ( ρ ) ≠ ∅ {\textstyle B_{i}\cap {\text{Inf}}(\rho )\neq \emptyset } or G i ∩ Inf ( ρ ) = ∅ {\textstyle G_{i}\cap {\text{Inf}}(\rho )=\emptyset } . A parity automaton is an automaton A {\textstyle A} whose set of states is Q = { 0 , 1 , 2 , … , k } {\textstyle Q=\{0,1,2,\ldots ,k\}} for some natural number k {\textst
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The Best Free AI Bug Finder for Beginners

Shopping for the best AI bug finder? An AI bug finder 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 bug finder 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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