AI Analytical Thinking

AI Analytical Thinking — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Microscope image processing

    Microscope image processing

    Microscope image processing is a broad term that covers the use of digital image processing techniques to process, analyze and present images obtained from a microscope. Such processing is now commonplace in a number of diverse fields such as medicine, biological research, cancer research, drug testing, metallurgy, etc. A number of manufacturers of microscopes now specifically design in features that allow the microscopes to interface to an image processing system. == Image acquisition == Until the early 1990s, most image acquisition in video microscopy applications was typically done with an analog video camera, often simply closed circuit TV cameras. While this required the use of a frame grabber to digitize the images, video cameras provided images at full video frame rate (25-30 frames per second) allowing live video recording and processing. While the advent of solid state detectors yielded several advantages, the real-time video camera was actually superior in many respects. Today, acquisition is usually done using a CCD camera mounted in the optical path of the microscope. The camera may be full colour or monochrome. Very often, very high resolution cameras are employed to gain as much direct information as possible. Cryogenic cooling is also common, to minimise noise. Often digital cameras used for this application provide pixel intensity data to a resolution of 12-16 bits, much higher than is used in consumer imaging products. Ironically, in recent years, much effort has been put into acquiring data at video rates, or higher (25-30 frames per second or higher). What was once easy with off-the-shelf video cameras now requires special, high speed electronics to handle the vast digital data bandwidth. Higher speed acquisition allows dynamic processes to be observed in real time, or stored for later playback and analysis. Combined with the high image resolution, this approach can generate vast quantities of raw data, which can be a challenge to deal with, even with a modern computer system. While current CCD detectors allow very high image resolution, often this involves a trade-off because, for a given chip size, as the pixel count increases, the pixel size decreases. As the pixels get smaller, their well depth decreases, reducing the number of electrons that can be stored. In turn, this results in a poorer signal-to-noise ratio. For best results, one must select an appropriate sensor for a given application. Because microscope images have an intrinsic limiting resolution, it often makes little sense to use a noisy, high resolution detector for image acquisition. A more modest detector, with larger pixels, can often produce much higher quality images because of reduced noise. This is especially important in low-light applications such as fluorescence microscopy. Moreover, one must also consider the temporal resolution requirements of the application. A lower resolution detector will often have a significantly higher acquisition rate, permitting the observation of faster events. Conversely, if the observed object is motionless, one may wish to acquire images at the highest possible spatial resolution without regard to the time required to acquire a single image. == 2D image techniques == Image processing for microscopy application begins with fundamental techniques intended to most accurately reproduce the information contained in the microscopic sample. This might include adjusting the brightness and contrast of the image, averaging images to reduce image noise and correcting for illumination non-uniformities. Such processing involves only basic arithmetic operations between images (i.e. addition, subtraction, multiplication and division). The vast majority of processing done on microscope image is of this nature. Another class of common 2D operations called image convolution are often used to reduce or enhance image details. Such "blurring" and "sharpening" algorithms in most programs work by altering a pixel's value based on a weighted sum of that and the surrounding pixels (a more detailed description of kernel based convolution deserves an entry for itself) or by altering the frequency domain function of the image using Fourier Transform. Most image processing techniques are performed in the Frequency domain. Other basic two dimensional techniques include operations such as image rotation, warping, color balancing etc. At times, advanced techniques are employed with the goal of "undoing" the distortion of the optical path of the microscope, thus eliminating distortions and blurring caused by the instrumentation. This process is called deconvolution, and a variety of algorithms have been developed, some of great mathematical complexity. The end result is an image far sharper and clearer than could be obtained in the optical domain alone. This is typically a 3-dimensional operation, that analyzes a volumetric image (i.e. images taken at a variety of focal planes through the sample) and uses this data to reconstruct a more accurate 3-dimensional image. == 3D image techniques == Another common requirement is to take a series of images at a fixed position, but at different focal depths. Since most microscopic samples are essentially transparent, and the depth of field of the focused sample is exceptionally narrow, it is possible to capture images "through" a three-dimensional object using 2D equipment like confocal microscopes. Software is then able to reconstruct a 3D model of the original sample which may be manipulated appropriately. The processing turns a 2D instrument into a 3D instrument, which would not otherwise exist. In recent times this technique has led to a number of scientific discoveries in cell biology. == Analysis == Analysis of images will vary considerably according to application. Typical analysis includes determining where the edges of an object are, counting similar objects, calculating the area, perimeter length and other useful measurements of each object. A common approach is to create an image mask which only includes pixels that match certain criteria, then perform simpler scanning operations on the resulting mask. It is also possible to label objects and track their motion over a series of frames in a video sequence.

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  • PROMT

    PROMT

    ProMT is a lead Russian developer of language translation software for businesses and private users since 1991. The company provides on-premises software based on neural technologies. == History == On March 6, 1998, ProMT launched a free online translation services, which is now known as PROMT.One. In 1997, ProMT and the French company Softissimo developed a line of products for the European company Reverso. == Technology == Historically, ProMT systems used rule-based machine translation (RBMT) technology. In 2011 a hybrid approach which combined rule-based and statistical MT was implemented. In 2019, ProMT introduced its new neural technology and flagship solution - PROMT Neural Translation Server. Since then all MT systems developed by ProMT are based on neural machine translation. The software can run on Microsoft Windows, Linux, MacOS, iOS and Android and works in offline mode providing secure machine translation. As of 2025, it translates 62 languages from and to English, German, and Russian.

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  • Diane Litman

    Diane Litman

    Diane Litman is an American professor of computer science at the University of Pittsburgh. She also jointly holds the positions of senior scientist with the Learning Research and Development Center and faculty with the Intelligent Systems department. Litman is noted for her work in the areas of artificial intelligence, computational linguistics, knowledge representation and reasoning, natural language processing, and user modeling. == Education == Litman did her undergraduate studies at the College of William and Mary and her master's and PhD degrees at the University of Rochester. == Career == Before joining the University of Pittsburgh, she was an assistant professor at Columbia University. She additionally held the position of a research scientist in the Artificial Intelligence Principles Research Department Laboratory at AT&T Labs. Litman has held the position of Chair of the North American Chapter of the Association for Computational Linguistics two times, elected twice for the position, whose tenure lasts four years. She is also a distinguished member of the executive committee of the Association for Computational Linguistics, and a member of the editorial boards of Computational Linguistics and User Modeling and User-Adapted Interaction. She has also held the position of Leverhulme Professor at the University of Edinburgh. Litman was the keynote speaker at the Speech and Language Technology in Education 2013 symposium, the 2006 SIGdial Meeting on Discourse and Dialogue, and at the 2008 Symposium of the Annual Meeting of the Society for the Study of Artificial Intelligence and Simulation of Behaviour. She also sits on the board of the several interest groups, including the International Speech Communication Association's Special Interest Group on Speech and Language Technology in Education. Litman has served as chair, organizer, and a senior member of numerous committees of peer-reviewed scientific journals. == Awards and recognition == She has also co-authored numerous award-winning papers and was awarded senior member status by the Association for the Advancement of Artificial Intelligence in 2011, an award designed to honor those who have "achieved significant accomplishments within the field of artificial intelligence."

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  • Abeba Birhane

    Abeba Birhane

    Abeba Birhane is an Ethiopian-born cognitive scientist who works at the intersection of complex adaptive systems, machine learning, algorithmic bias, and critical race studies. Birhane's work with Vinay Prabhu uncovered that large-scale image datasets commonly used to develop AI systems, including ImageNet and 80 Million Tiny Images, carried racist and misogynistic labels and offensive images. She has been recognized by VentureBeat as a top innovator in computer vision and named as one of the 100 most influential persons in AI 2023 by TIME magazine. == Early life and education == Birhane was born in Ethiopia. She received her Bachelors of Science in Psychology and a Bachelors of Arts in Philosophy from The Open University. In 2015, she completed her Master of Science in Cognitive Science and, in 2021, her Ph.D. at the Complex Software Lab in the School of Computer Science at University College Dublin. == Career and research == Birhane studied the impacts of emerging AI technologies and how they shape individuals and local communities. She found that AI algorithms tend to disproportionately impact vulnerable groups such as older workers, trans people, immigrants, and children. Her research on relational ethics won the best paper award at NeurIPS’s Black in AI workshop in 2019. She has also studied and written about algorithmic colonization driven by corporate agendas. Her work in decolonizing computational sciences addressed the inherited oppressions in current systems especially towards women of color. In 2020, Birhane and Vinay Prabhu, principal machine learning scientist at UnifyID, published a paper examining the problematic data collection, labelling, classification, and consequences of large image datasets. These datasets, including ImageNet and MIT's 80 Million Tiny Images, have been used to develop thousands of AI algorithms and systems. Birhane and Prabhu found that they contained many racist and misogynistic labels and slurs as well as offensive images. This resulted in MIT voluntarily and formally taking down the 80 Million Tiny Images dataset. More recently, Birhane has worked with Rediet Abebe, George Obaido, and Sekou Remy on researching the barriers to data sharing in Africa. They found that power imbalances are significant in the data sharing process, even when the data comes from Africa. Their research was published at the ACM Conference on Fairness, Accountability, and Transparency. In 2024, Birhane established the AI Accountability Lab research group at Trinity College Dublin. == Selected awards == 2019 NeurIPS Black in AI Workshop Best Paper Award 2020 Venture Beat AI Innovations Award in the category Computer Vision Innovation (received with Vinay Prabhu) 2021 100 Brilliant Women in AI Ethics Hall of Fame Honoree 2022 Lero Director’s Prize for PhD/PostDoctoral Contribution. 2023 100 Most Influential People in AI by TIME magazine

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  • Actionstep

    Actionstep

    Actionstep is a cloud-based legal practice management software for law firms and compliance-focused businesses. Actionstep is built to be a comprehensive practice management software with features for workflow automation as well as automatic document generation == History == Actionstep was created by Ted Jordan, CEO of Actionstep, in 2004. It was first used commercially in 2005 by a New Zealand construction franchise as well as a law firm. Actionstep soon expanded into central government and a wider range of small business users (mainly in New Zealand and Australia). After a few years the expanse of their legal client base prompted the company to add key legal specific features to the product with the aim of further expanding their legal market. Through Actionstep's tenure as a practice management software they have gradually expanded from their headquarters in New Zealand and offices located in the United Kingdom and the United States of America. In October 2020, private equity firm Serent Capital Partners purchased 84.25% stake in Actionstep. In April 2022, the company announced unlimited annual leave to its staff == Product == The premise of Actionstep is that it saves companies from having to purchase software tailored to their work flow and instead allows companies to modify the program without additional coding.{{Citation needed}} The founder and CEO Ted Jordan used cloud technology to allow the software to be continuously updated without the need to purchase or redesign new software. This theoretically allows businesses to remain current all the time and cut external I.T. costs.{{Citation needed}} Actionstep also integrates with software from other companies, such as Xero accounting, Microsoft Office & Office 365, Gmail, Google Drive, Dropbox, NetDocuments, QuickBooks, LawPay, BundleDocs, Box, HotDocs, Infotrack, GlobalX, PEXA, JOSEF and Zapier. Actionstep contains workflow automation features aimed at increasing office efficiency. These automated processes include automatic task assignment, information collection, document generation & automation, cataloguing, and matter generation. == Awards == Actionstep was named First International Best of SaaS Showplace Award Winner in 2009. Actionstep has also been a finalist in the ComputerWorld Excellence Awards (2007), and the Vero Excellence in Business Support (2010).

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  • Jian Ma (computational biologist)

    Jian Ma (computational biologist)

    Jian Ma (Chinese: 马坚) is an American computer scientist and computational biologist. He is the Ray and Stephanie Lane Professor of Computational Biology in the School of Computer Science at Carnegie Mellon University. He is a faculty member in the Ray and Stephanie Lane Computational Biology Department. His lab develops AI/ML methods to study the structure and function of the human genome and cellular organization and their implications for health and disease. During his Ph.D. and postdoc training, he developed algorithms to reconstruct the ancestral mammalian genome and evolutionary history. His research group has recently pioneered a series of new machine learning solutions for 3D genome organization, single-cell epigenomics, spatial omics, and complex molecular interactions. His lab also explores large language models to uncover gene regulatory mechanisms and the intricate connections among cellular components, with the aim of driving discovery and guiding experimentation. He received an NSF CAREER award in 2011. In 2020, he was awarded a Guggenheim Fellowship in Computer Science. He received the Allen Newell Award for Research Excellence (2025). He is an elected Fellow of the American Association for the Advancement of Science, the American Institute for Medical and Biological Engineering, the International Society for Computational Biology, and the Association for Computing Machinery. He leads an NIH 4D Nucleome Center to develop machine learning algorithms to better understand the cell nucleus. He served as the Program Chair for RECOMB 2024. He is also a member of the Scientific Advisory Board of the Chan Zuckerberg Biohub Chicago (CZ Biohub Chicago) and the RECOMB Steering Committee. In 2024, he launched the Center for AI-Driven Biomedical Research (AI4BIO) at CMU, which will be a catalyst for innovations at the intersection of AI and biomedicine across the School of Computer Science and campus. == Selected Recent Publications == Chen V#, Yang M#, Cui W, Kim JS, Talwalkar A, and Ma J. Applying interpretable machine learning in computational biology - pitfalls, recommendations and opportunities for new developments. Nature Methods, 21(8):1454-1461, 2024. Xiong K#, Zhang R#, and Ma J. scGHOST: Identifying single-cell 3D genome subcompartments. Nature Methods, 21(5):814-822, 2024. Zhou T, Zhang R, Jia D, Doty RT, Munday AD, Gao D, Xin L, Abkowitz JL, Duan Z, and Ma J. GAGE-seq concurrently profiles multiscale 3D genome organization and gene expression in single cells. Nature Genetics, 56(8):1701-1711, 2024. Zhang Y, Boninsegna L, Yang M, Misteli T, Alber F, and Ma J. Computational methods for analysing multiscale 3D genome organization. Nature Reviews Genetics, 5(2):123-141, 2024. Chidester B#, Zhou T#, Alam S, and Ma J. SPICEMIX enables integrative single-cell spatial modeling of cell identity. Nature Genetics, 55(1):78-88, 2023. [Cover Article] Zhang R#, Zhou T#, and Ma J. Ultrafast and interpretable single-cell 3D genome analysis with Fast-Higashi. Cell Systems, 13(10):P798-807.E6, 2022. [Cover Article] Zhu X#, Zhang Y#, Wang Y, Tian D, Belmont AS, Swedlow JR, and Ma J. Nucleome Browser: An integrative and multimodal data navigation platform for 4D Nucleome. Nature Methods, 19(8):911-913, 2022. Zhang R, Zhou T, and Ma J. Multiscale and integrative single-cell Hi-C analysis with Higashi. Nature Biotechnology, 40:254–261, 2022.

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  • Chris Callison-Burch

    Chris Callison-Burch

    Chris Callison-Burch is an American computer scientist and professor of computer and information science at the University of Pennsylvania (Penn), specializing in natural language processing (NLP), artificial intelligence (AI), and crowdsourcing. He is recognised for his contributions to machine translation, paraphrase generation, and the application of large language models (LLMs) to AI challenges, with over 200 publications cited more than 33,000 times. Callison-Burch has influenced public policy on AI and copyright, testifying before the U.S. Congress in 2023 on generative AI’s implications. He serves as the faculty director for Penn’s Online Master of Science in Engineering in AI program. == Education == Callison-Burch earned his PhD in Computer Science from the University of Edinburgh in 2008, focusing on machine translation and paraphrasing techniques. His doctoral research developed statistical methods for generating paraphrases in machine translation systems, laying the foundation for his later NLP work. Prior to his PhD, he studied at Stanford University, where he developed an interest in computational linguistics. == Career == After his PhD, Callison-Burch joined the Centre for Language and Speech Processing at Johns Hopkins University as a research faculty member from 2008 to 2013, working on NLP projects, including machine translation and crowdsourcing for creating training data. In 2013, he joined the University of Pennsylvania as an assistant professor in the Department of Computer and Information Science and was promoted to associate professor in 2017, and to full professor in 2024. At Penn, Callison-Burch teaches courses on AI and NLP, including CIS 5300 (Natural Language Processing) and CIS 5210 (Artificial Intelligence), which attract over 500 students annually. He directs Penn’s Online Master of Science in Engineering in AI program, launched in 2025. He teaches AI and NLP courses on Coursera, reaching thousands of global learners. Callison-Burch was a part-time visiting researcher at Google in 2019 and 2020, where he collaborated on applying Google's LLM to Dungeons & Dragons dialogues. In 2023, he took a sabbatical at the Allen Institute for AI (AI2), where he contributed to vision-language models. == Research == Callison-Burch’s research focuses on NLP, AI, and crowdsourcing, with significant contributions to machine translation, paraphrase generation, and LLMs for tasks like text simplification and bias detection. His early work developed crowdsourcing methods for machine translation, leveraging non-expert annotators for paraphrase-based evaluation, influencing platforms like Amazon Mechanical Turk. Recent projects have included several notable works. Molmo and PixMo (2025) are open-weight vision-language models developed with AI2, achieving state-of-the-art multimodal performance and earning a Best Paper Honourable Mention at CVPR 2025. Also in 2025, his work on Calibrating Large Language Models with Sample Consistency improves LLM reliability via sample-based calibration, presented at NAACL 2025. The Media Bias Detector (2025) is a real-time tool analysing selection and framing bias in news, using LLMs to detect persuasive language differences (e.g., Russian vs. English Wikipedia). Holodeck (2024) is a language-guided system for generating 3D embodied AI environments, presented at CVPR 2024. BORDIRLINES (2024) is a dataset for cross-lingual retrieval-augmented generation, focusing on culturally sensitive tasks. He has co-authored over 200 publications, featured at conferences like ACL, EMNLP, and CVPR. == Awards and recognition == Callison-Burch has received numerous awards: Best Paper Honourable Mention at CVPR 2025 for "Molmo and PixMo". Best Paper Award at the Workshop on Cognitive Modelling and Computational Linguistics (CMCL) 2024 for "Evaluating Vision-Language Models on Bistable Images". Best Paper Award at STARSEM 2016 for "So-Called Non-Subsective Adjectives". Best Paper Award at the Workshop on Sense, Concept and Entity Representations 2017 for "Word Sense Filtering Improves Embedding-Based Lexical Substitution". Honourable Mention Award at CHI 2018 for "A Data-Driven Analysis of Workers’ Earnings on Amazon Mechanical Turk". Google Faculty Research Award (2013) for crowdsourcing in NLP. Sloan Research Fellowship (2014). He has received research funding from Google, Microsoft, Amazon, Facebook, Roblox, DARPA, IARPA, and NSF. His h-index is 72, with over 33,000 citations. He served as General Chair of ACL 2017 and as the Program Co-Chair EMNLP 2015. == Public policy and testimony == On May 17, 2023, Callison-Burch testified before the U.S. House Subcommittee on Courts, Intellectual Property, and the Internet on AI and copyright law. His testimony emphasised generative AI’s role in creative industries and the need for balanced copyright frameworks. He has appeared on Fox News to discuss AI’s societal impact, and discussed its impact with other print news sources. He contributes to AI ethics discussions, including workshops on AI’s effects on writing and creative professions.

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  • Markov switching multifractal

    Markov switching multifractal

    In financial econometrics (the application of statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fisher that incorporates stochastic volatility components of heterogeneous durations. MSM captures the outliers, log-memory-like volatility persistence and power variation of financial returns. In currency and equity series, MSM compares favorably with standard volatility models such as GARCH(1,1) and FIGARCH both in- and out-of-sample. MSM is used by practitioners in the financial industry for different types of forecasts. == MSM specification == The MSM model can be specified in both discrete time and continuous time. === Discrete time === Let P t {\displaystyle P_{t}} denote the price of a financial asset, and let r t = ln ⁡ ( P t / P t − 1 ) {\displaystyle r_{t}=\ln(P_{t}/P_{t-1})} denote the return over two consecutive periods. In MSM, returns are specified as r t = μ + σ ¯ ( M 1 , t M 2 , t . . . M k ¯ , t ) 1 / 2 ϵ t , {\displaystyle r_{t}=\mu +{\bar {\sigma }}(M_{1,t}M_{2,t}...M_{{\bar {k}},t})^{1/2}\epsilon _{t},} where μ {\displaystyle \mu } and σ {\displaystyle \sigma } are constants and { ϵ t {\displaystyle \epsilon _{t}} } are independent standard Gaussians. Volatility is driven by the first-order latent Markov state vector: M t = ( M 1 , t M 2 , t … M k ¯ , t ) ∈ R + k ¯ . {\displaystyle M_{t}=(M_{1,t}M_{2,t}\dots M_{{\bar {k}},t})\in R_{+}^{\bar {k}}.} Given the volatility state M t {\displaystyle M_{t}} , the next-period multiplier M k , t + 1 {\displaystyle M_{k,t+1}} is drawn from a fixed distribution M with probability γ k {\displaystyle \gamma _{k}} , and is otherwise left unchanged. The transition probabilities are specified by γ k = 1 − ( 1 − γ 1 ) ( b k − 1 ) {\displaystyle \gamma _{k}=1-(1-\gamma _{1})^{(b^{k-1})}} . The sequence γ k {\displaystyle \gamma _{k}} is approximately geometric γ k ≈ γ 1 b k − 1 {\displaystyle \gamma _{k}\approx \gamma _{1}b^{k-1}} at low frequency. The marginal distribution M has a unit mean, has a positive support, and is independent of k. ==== Binomial MSM ==== In empirical applications, the distribution M is often a discrete distribution that can take the values m 0 {\displaystyle m_{0}} or 2 − m 0 {\displaystyle 2-m_{0}} with equal probability. The return process r t {\displaystyle r_{t}} is then specified by the parameters θ = ( m 0 , μ , σ ¯ , b , γ 1 ) {\displaystyle \theta =(m_{0},\mu ,{\bar {\sigma }},b,\gamma _{1})} . Note that the number of parameters is the same for all k ¯ > 1 {\displaystyle {\bar {k}}>1} . === Continuous time === MSM is similarly defined in continuous time. The price process follows the diffusion: d P t P t = μ d t + σ ( M t ) d W t , {\displaystyle {\frac {dP_{t}}{P_{t}}}=\mu dt+\sigma (M_{t})\,dW_{t},} where σ ( M t ) = σ ¯ ( M 1 , t … M k ¯ , t ) 1 / 2 {\displaystyle \sigma (M_{t})={\bar {\sigma }}(M_{1,t}\dots M_{{\bar {k}},t})^{1/2}} , W t {\displaystyle W_{t}} is a standard Brownian motion, and μ {\displaystyle \mu } and σ ¯ {\displaystyle {\bar {\sigma }}} are constants. Each component follows the dynamics: The intensities vary geometrically with k: γ k = γ 1 b k − 1 . {\displaystyle \gamma _{k}=\gamma _{1}b^{k-1}.} When the number of components k ¯ {\displaystyle {\bar {k}}} goes to infinity, continuous-time MSM converges to a multifractal diffusion, whose sample paths take a continuum of local Hölder exponents on any finite time interval. == Inference and closed-form likelihood == When M {\displaystyle M} has a discrete distribution, the Markov state vector M t {\displaystyle M_{t}} takes finitely many values m 1 , . . . , m d ∈ R + k ¯ {\displaystyle m^{1},...,m^{d}\in R_{+}^{\bar {k}}} . For instance, there are d = 2 k ¯ {\displaystyle d=2^{\bar {k}}} possible states in binomial MSM. The Markov dynamics are characterized by the transition matrix A = ( a i , j ) 1 ≤ i , j ≤ d {\displaystyle A=(a_{i,j})_{1\leq i,j\leq d}} with components a i , j = P ( M t + 1 = m j | M t = m i ) {\displaystyle a_{i,j}=P\left(M_{t+1}=m^{j}|M_{t}=m^{i}\right)} . Conditional on the volatility state, the return r t {\displaystyle r_{t}} has Gaussian density f ( r t | M t = m i ) = 1 2 π σ 2 ( m i ) exp ⁡ [ − ( r t − μ ) 2 2 σ 2 ( m i ) ] . {\displaystyle f(r_{t}|M_{t}=m^{i})={\frac {1}{\sqrt {2\pi \sigma ^{2}(m^{i})}}}\exp \left[-{\frac {(r_{t}-\mu )^{2}}{2\sigma ^{2}(m^{i})}}\right].} === Conditional distribution === === Closed-form Likelihood === The log likelihood function has the following analytical expression: ln ⁡ L ( r 1 , … , r T ; θ ) = ∑ t = 1 T ln ⁡ [ ω ( r t ) . ( Π t − 1 A ) ] . {\displaystyle \ln L(r_{1},\dots ,r_{T};\theta )=\sum _{t=1}^{T}\ln[\omega (r_{t}).(\Pi _{t-1}A)].} Maximum likelihood provides reasonably precise estimates in finite samples. === Other estimation methods === When M {\displaystyle M} has a continuous distribution, estimation can proceed by simulated method of moments, or simulated likelihood via a particle filter. == Forecasting == Given r 1 , … , r t {\displaystyle r_{1},\dots ,r_{t}} , the conditional distribution of the latent state vector at date t + n {\displaystyle t+n} is given by: Π ^ t , n = Π t A n . {\displaystyle {\hat {\Pi }}_{t,n}=\Pi _{t}A^{n}.\,} MSM often provides better volatility forecasts than some of the best traditional models both in and out of sample. Calvet and Fisher report considerable gains in exchange rate volatility forecasts at horizons of 10 to 50 days as compared with GARCH(1,1), Markov-Switching GARCH, and Fractionally Integrated GARCH. Lux obtains similar results using linear predictions. == Applications == === Multiple assets and value-at-risk === Extensions of MSM to multiple assets provide reliable estimates of the value-at-risk in a portfolio of securities. === Asset pricing === In financial economics, MSM has been used to analyze the pricing implications of multifrequency risk. The models have had some success in explaining the excess volatility of stock returns compared to fundamentals and the negative skewness of equity returns. They have also been used to generate multifractal jump-diffusions. == Related approaches == MSM is a stochastic volatility model with arbitrarily many frequencies. MSM builds on the convenience of regime-switching models, which were advanced in economics and finance by James D. Hamilton. MSM is closely related to the Multifractal Model of Asset Returns. MSM improves on the MMAR's combinatorial construction by randomizing arrival times, guaranteeing a strictly stationary process. MSM provides a pure regime-switching formulation of multifractal measures, which were pioneered by Benoit Mandelbrot.

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  • Skipper (computer software)

    Skipper (computer software)

    Skipper is a visualization tool and code/schema generator for PHP ORM frameworks like Doctrine2, Doctrine, Propel, and CakePHP, which are used to create database abstraction layer. Skipper is developed by Czech company Inventic, s.r.o. based in Brno, and was known as ORM Designer prior to rebranding in 2014. == Overview == Generates visual model from the schema definition files Repetitive import/export of schema definitions in supported formats (XML, YML, PHP annotations) Schema definition files are automatically generated from the visual model Visual representation uses ER diagram extended by concepts of inheritance and many-to-many Supports customization using .xml configuration files and JavaScript Does not support direct connections to the database Crude and simplistic visual representation and menus == Architecture == Skipper was built on the Qt framework. Import/export of the schema definitions uses XSL transformations powered by LibXslt library. Imported source files are first converted to XML format: no conversion for XML, simple conversion for YML, creating the Abstract Syntax Tree and its subsequent conversion to XML for PHP annotations. The import/export scripts are configured in JavaScript and can be freely customized. == Supported ORM frameworks == Frameworks supported for visual model and schema files generation: Doctrine2 Doctrine CakePHP == History == Skipper was created as an internal tool for the web applications developed by Inventic. It was first published as a commercial tool under the name ORM Designer in 2009. Application was reworked and optimized in January 2013, and released as ORM Designer 2. In May 2013 ORM Designer became part of the South Moravian Innovation Center Incubator program (support program for innovative technological startups). In June 2014, ORM Designer version 3 was released and rebranded under the name of Skipper

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  • The Best Free AI Virtual Assistant for Beginners

    The Best Free AI Virtual Assistant for Beginners

    Comparing the best AI virtual assistant? An AI virtual assistant is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI virtual assistant 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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  • Co-Büchi automaton

    Co-Büchi automaton

    In automata theory, a co-Büchi automaton is a variant of Büchi automaton. The only difference is the accepting condition: a Co-Büchi automaton accepts an infinite word w {\displaystyle w} if there exists a run, such that all the states occurring infinitely often in the run are in the final state set F {\displaystyle F} . In contrast, a Büchi automaton accepts a word w {\displaystyle w} if there exists a run, such that at least one state occurring infinitely often in the final state set F {\displaystyle F} . (Deterministic) Co-Büchi automata are strictly weaker than (nondeterministic) Büchi automata. == Formal definition == Formally, a deterministic co-Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\delta ,q_{0},F)} that consists of the following components: Q {\displaystyle Q} is a finite set. The elements of Q {\displaystyle Q} are called the states of A {\displaystyle {\mathcal {A}}} . Σ {\displaystyle \Sigma } is a finite set called the alphabet of A {\displaystyle {\mathcal {A}}} . δ : Q × Σ → Q {\displaystyle \delta :Q\times \Sigma \rightarrow Q} is the transition function of A {\displaystyle {\mathcal {A}}} . q 0 {\displaystyle q_{0}} is an element of Q {\displaystyle Q} , called the initial state. F ⊆ Q {\displaystyle F\subseteq Q} is the final state set. A {\displaystyle {\mathcal {A}}} accepts exactly those words w {\displaystyle w} with the run ρ ( w ) {\displaystyle \rho (w)} , in which all of the infinitely often occurring states in ρ ( w ) {\displaystyle \rho (w)} are in F {\displaystyle F} . In a non-deterministic co-Büchi automaton, the transition function δ {\displaystyle \delta } is replaced with a transition relation Δ {\displaystyle \Delta } . The initial state q 0 {\displaystyle q_{0}} is replaced with an initial state set Q 0 {\displaystyle Q_{0}} . Generally, the term co-Büchi automaton refers to the non-deterministic co-Büchi automaton. For more comprehensive formalism see also ω-automaton. == Acceptance Condition == The acceptance condition of a co-Büchi automaton is formally ∃ i ∀ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \exists i\forall j:\;j\geq i\quad \rho (w_{j})\in F.} The Büchi acceptance condition is the complement of the co-Büchi acceptance condition: ∀ i ∃ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \forall i\exists j:\;j\geq i\quad \rho (w_{j})\in F.} == Properties == Co-Büchi automata are closed under union, intersection, projection and determinization.

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  • Comparison of machine translation applications

    Comparison of machine translation applications

    Machine translation is an algorithm which attempts to translate text or speech from one natural language to another. == General information == Basic general information for popular machine translation applications. == Languages features comparison == The following table compares the number of languages which the following machine translation programs can translate between. (Moses and Moses for Mere Mortals allow you to train translation models for any language pair, though collections of translated texts (parallel corpus) need to be provided by the user. The Moses site provides links to training corpora.) This is not an all-encompassing list. Some applications have many more language pairs than those listed below. This is a general comparison of key languages only. A full and accurate list of language pairs supported by each product should be found on each of the product's websites. === Multi-pair translations === === Paired translations ===

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  • StatCrunch

    StatCrunch

    StatCrunch is a web-based statistical software application from Pearson Education. StatCrunch was originally created for use in college statistics courses. As a full-featured statistics package, it is now also used for research and for other statistical analysis purposes. == History == American statistics professor Webster West created StatCrunch in 1997. Over the next 19 years West assisted by others added many more statistical procedures and graphing capabilities, and made user interface improvements. In 2005, West received two awards for StatCrunch: the CAUSEweb Resource of the Year Award and the MERLOT Classics Award. In 2013, the StatCrunch Java code was rewritten in JavaScript in order to avoid Java browser security problems, and so that it would run on iOS and Android. In 2015, new ways of importing data were added, including importing multi-page data directly from Wikipedia tables and other Web sources, and also importing with drag-and-drop for various data formats. In 2016, StatCrunch was acquired by Pearson Education, which had already been serving as the primary distributor of StatCrunch for several years. == Software == A StatCrunch license is included with many of Pearson's statistical textbooks. Because StatCrunch is a web application, it works on multiple platforms, including Windows, macOS, iOS, and Android. Data in StatCrunch is represented in a "data table" view, which is similar to a spreadsheet view, but unlike spreadsheets, the cells in a data table can only contain numbers or text. Formulas cannot be stored in these cells. There are many ways to import data into StatCrunch. Data can be typed directly into cells in the data table. Entire blocks of data may be cut-and-pasted into the data table. Text files (.csv, .txt, etc.) and Microsoft Excel files (.xls and .xlsx) can be drag-and-dropped into the data table. Data can be pulled into StatCrunch directly from Wikipedia tables or other Web tables, including multi-page tables. Data can be loaded directly from Google Drive and Dropbox. Shared data sets saved by other StatCrunch community users can be searched for by title or keyword and opened in a data table. Graphs, results, and reports created by StatCrunch can be shared with other users, in addition to the sharing of data sets. StatCrunch has a library of data transformation functions. StatCrunch can also recode and reorganize data. All data is stored in memory, and all processing happens on the client, so response is fast, even with large data sets. StatCrunch can interact with multiple graphs simultaneously. If a user selects a data point on one graph, then that same data point is highlighted on all other displayed graphs. In addition to standard statistical and graphing procedures, StatCrunch has a collection of about forty "applets" which illustrate statistical concepts interactively.

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  • Interlingual machine translation

    Interlingual machine translation

    Interlingual machine translation is one of the classic approaches to machine translation. In this approach, the source language, i.e. the text to be translated is transformed into an interlingua, i.e., an abstract language-independent representation. The target language is then generated from the interlingua. Within the rule-based machine translation paradigm, the interlingual approach is an alternative to the direct approach and the transfer approach. In the direct approach, words are translated directly without passing through an additional representation. In the transfer approach the source language is transformed into an abstract, less language-specific representation. Linguistic rules which are specific to the language pair then transform the source language representation into an abstract target language representation and from this the target sentence is generated. The interlingual approach to machine translation has advantages and disadvantages. The advantages are that it requires fewer components in order to relate each source language to each target language, it takes fewer components to add a new language, it supports paraphrases of the input in the original language, it allows both the analysers and generators to be written by monolingual system developers, and it handles languages that are very different from each other (e.g. English and Arabic). The obvious disadvantage is that the definition of an interlingua is difficult and maybe even impossible for a wider domain. The ideal context for interlingual machine translation is thus multilingual machine translation in a very specific domain. For example, Interlingua has been used as a pivot language in international conferences and has been proposed as a pivot language for the European Union. == History == The first ideas about interlingual machine translation appeared in the 17th century with Descartes and Leibniz, who came up with theories of how to create dictionaries using universal numerical codes, not unlike numerical tokens used by large language models nowadays. Others, such as Cave Beck, Athanasius Kircher and Johann Joachim Becher worked on developing an unambiguous universal language based on the principles of logic and iconographs. In 1668, John Wilkins described his interlingua in his "Essay towards a Real Character and a Philosophical Language". In the 18th and 19th centuries many proposals for "universal" international languages were developed, the most well known being Esperanto. That said, applying the idea of a universal language to machine translation did not appear in any of the first significant approaches. Instead, work started on pairs of languages. However, during the 1950s and 60s, researchers in Cambridge headed by Margaret Masterman, in Leningrad headed by Nikolai Andreev and in Milan by Silvio Ceccato started work in this area. The idea was discussed extensively by the Israeli philosopher Yehoshua Bar-Hillel in 1969. During the 1970s, noteworthy research was done in Grenoble by researchers attempting to translate physics and mathematical texts from Russian to French, and in Texas a similar project (METAL) was ongoing for Russian to English. Early interlingual MT systems were also built at Stanford in the 1970s by Roger Schank and Yorick Wilks; the former became the basis of a commercial system for the transfer of funds, and the latter's code is preserved at The Computer Museum at Boston as the first interlingual machine translation system. In the 1980s, renewed relevance was given to interlingua-based, and knowledge-based approaches to machine translation in general, with much research going on in the field. The uniting factor in this research was that high-quality translation required abandoning the idea of requiring total comprehension of the text. Instead, the translation should be based on linguistic knowledge and the specific domain in which the system would be used. The most important research of this era was done in distributed language translation (DLT) in Utrecht, which worked with a modified version of Esperanto, and the Fujitsu system in Japan. In 2016, Google Neural Machine Translation achieved "zero-shot translation", that is it directly translates one language into another. For example, it might be trained just for Japanese-English and Korean-English translation, but can perform Japanese-Korean translation. The system appears to have learned to produce a language-independent intermediate representation of language (an "interlingua"), which allows it to perform zero-shot translation by converting from and to the interlingua. == Outline == In this method of translation, the interlingua can be thought of as a way of describing the analysis of a text written in a source language such that it is possible to convert its morphological, syntactic, semantic (and even pragmatic) characteristics, that is "meaning" into a target language. This interlingua is able to describe all of the characteristics of all of the languages which are to be translated, instead of simply translating from one language to another. Sometimes two interlinguas are used in translation. It is possible that one of the two covers more of the characteristics of the source language, and the other possess more of the characteristics of the target language. The translation then proceeds by converting sentences from the first language into sentences closer to the target language through two stages. The system may also be set up such that the second interlingua uses a more specific vocabulary that is closer, or more aligned with the target language, and this could improve the translation quality. The above-mentioned system is based on the idea of using linguistic proximity to improve the translation quality from a text in one original language to many other structurally similar languages from only one original analysis. This principle is also used in pivot machine translation, where a natural language is used as a "bridge" between two more distant languages. For example, in the case of translating to English from Ukrainian using Russian as an intermediate language. == Translation process == In interlingual machine translation systems, there are two monolingual components: the analysis of the source language and the interlingual, and the generation of the interlingua and the target language. It is however necessary to distinguish between interlingual systems using only syntactic methods (for example the systems developed in the 1970s at the universities of Grenoble and Texas) and those based on artificial intelligence (from 1987 in Japan and the research at the universities of Southern California and Carnegie Mellon). The first type of system corresponds to that outlined in Figure 1. while the other types would be approximated by the diagram in Figure 4. The following resources are necessary to an interlingual machine translation system: Dictionaries (or lexicons) for analysis and generation (specific to the domain and the languages involved). A conceptual lexicon (specific to the domain), which is the knowledge base about events and entities known in the domain. A set of projection rules (specific to the domain and the languages). Grammars for the analysis and generation of the languages involved. One of the problems of knowledge-based machine translation systems is that it becomes impossible to create databases for domains larger than very specific areas. Another is that processing these databases is very computationally expensive. == Efficacy == One of the main advantages of this strategy is that it provides an economical way to make multilingual translation systems. With an interlingua it becomes unnecessary to make a translation pair between each pair of languages in the system. So instead of creating n ( n − 1 ) {\displaystyle n(n-1)} language pairs, where n {\displaystyle n} is the number of languages in the system, it is only necessary to make 2 n {\displaystyle 2n} pairs between the n {\displaystyle n} languages and the interlingua. The main disadvantage of this strategy is the difficulty of creating an adequate interlingua. It should be both abstract and independent of the source and target languages. The more languages added to the translation system, and the more different they are, the more potent the interlingua must be to express all possible translation directions. Another problem is that it is difficult to extract meaning from texts in the original languages to create the intermediate representation. == Existing interlingual machine translation systems == Calliope-Aero Carabao Linguistic Virtual Machine Grammatical Framework Number Translator Google Translate use English internally as a pivot language for some language pairs such as Chinese and Japanese, and more generally those with "higher quality" neural-network translators with English but not between each other.

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  • AI Copywriting Tools Reviews: What Actually Works in 2026

    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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