AI Writing Generator

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Test data

Test data are sets of inputs or information used to verify the correctness, performance, and reliability of software systems. Test data encompass various types, such as positive and negative scenarios, edge cases, and realistic user scenarios, and aims to exercise different aspects of the software to uncover bugs and validate its behavior. Test data is also used in regression testing to verify that new code changes or enhancements do not introduce unintended side effects or break existing functionalities. == Background == Test data may be used to verify that a given set of inputs to a function produces an expected result. Alternatively, data can be used to challenge the program's ability to handle unusual, extreme, exceptional, or unexpected inputs. Test data can be produced in a focused or systematic manner, as is typically the case in domain testing, or through less focused approaches, such as high-volume randomized automated tests. Test data can be generated by the tester or by a program or function that assists the tester. It can be recorded for reuse or used only once. Test data may be created manually, using data generation tools (often based on randomness), or retrieved from an existing production environment. The data set may consist of synthetic (fake) data, but ideally, it should include representative (real) data. == Limitations == Due to privacy regulations such as GDPR, PCI, and the HIPAA, the use of privacy-sensitive personal data for testing is restricted. However, anonymized (and preferably subsetted) production data may be used as representative data for testing and development. Programmers may also choose to generate synthetic data as an alternative to using real or anonymized data. While synthetic data can offer significant advantages, such as enhanced privacy and flexibility, it also comes with limitations. For instance, generating synthetic data that accurately reflects real-world complexity can be challenging. There is also a risk of synthetic data not fully capturing the nuances of real data, potentially leading to gaps in test coverage. == Domain testing == Domain testing is a set of techniques focusing on test data. This includes identifying critical inputs, values at the boundaries between equivalence classes, and combinations of inputs that drive the system toward specific outputs. Domain testing helps ensure that various scenarios are effectively tested, including edge cases and unusual conditions.
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Cobham's theorem

Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. == Definitions == Let n > 0 {\displaystyle n>0} be an integer. The representation of a natural number n {\textstyle n} in base b {\textstyle b} is the sequence of digits n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} such that n = n 0 + n 1 b + ⋯ + n h b h {\displaystyle n=n_{0}+n_{1}b+\cdots +n_{h}b^{h}} where 0 ≤ n 0 , n 1 , … , n h < b {\displaystyle 0\leq n_{0},n_{1},\ldots ,n_{h} 0 {\displaystyle n_{h}>0} . The word n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} is often denoted ⟨ n ⟩ b {\displaystyle \langle n\rangle _{b}} , or more simply, n b {\displaystyle n_{b}} . A set of natural numbers S is recognisable in base b {\textstyle b} or more simply b {\textstyle b} -recognisable or b {\textstyle b} -automatic if the set { n b ∣ n ∈ S } {\displaystyle \{n_{b}\mid n\in S\}} of the representations of its elements in base b {\displaystyle b} is a language recognisable by a finite automaton on the alphabet { 0 , 1 , … , b − 1 } {\displaystyle \{0,1,\ldots ,b-1\}} . Two positive integers k {\displaystyle k} and ℓ {\displaystyle \ell } are multiplicatively independent if there are no non-negative integers p {\displaystyle p} and q {\displaystyle q} such that k p = ℓ q {\displaystyle k^{p}=\ell ^{q}} . For example, 2 and 3 are multiplicatively independent, but 8 and 16 are not since 8 4 = 16 3 {\displaystyle 8^{4}=16^{3}} . Two integers are multiplicatively dependent if and only if they are powers of a same third integer. == Problem statements == === Original problem statement === More equivalent statements of the theorem have been given. The original version by Cobham is the following: Another way to state the theorem is by using automatic sequences. Cobham himself calls them "uniform tag sequences." The following form is found in Allouche and Shallit's book:We can show that the characteristic sequence of a set of natural numbers S recognisable by finite automata in base k is a k-automatic sequence and that conversely, for all k-automatic sequences u {\displaystyle u} and all integers 0 ≤ i < k {\displaystyle 0\leq i 1 {\displaystyle \alpha >1} is the dominant eigenvalue of the matrix of morphism f {\displaystyle f} , namely, the matrix M ( f ) = ( m x , y ) x ∈ B , y ∈ A {\displaystyle M(f)=(m_{x,y})_{x\in B,y\in A}} , where m x , y {\displaystyle m_{x,y}} is the number of occurrences of the letter x {\displaystyle x} in the word f ( y ) {\displaystyle f(y)} . A set S of natural numbers is α {\displaystyle \alpha } -recognisable if its characteristic sequence s {\displaystyle s} is α {\displaystyle \alpha } -substitutive. A last definition: a Perron number is an algebraic number z > 1 {\displaystyle z>1} such that all its conjugates belong to the disc { z ′ ∈ C , | z ′ | < z } {\displaystyle \{z'\in \mathbb {C} ,|z'| Read more →
Sequential minimal optimization

Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM). It was invented by John Platt in 1998 at Microsoft Research. SMO is widely used for training support vector machines and is implemented by the popular LIBSVM tool. The publication of the SMO algorithm in 1998 has generated a lot of excitement in the SVM community, as previously available methods for SVM training were much more complex and required expensive third-party QP solvers. == Optimization problem == Consider a binary classification problem with a dataset (x1, y1), ..., (xn, yn), where xi is an input vector and yi ∈ {-1, +1} is a binary label corresponding to it. A soft-margin support vector machine is trained by solving a quadratic programming problem, which is expressed in the dual form as follows: max α ∑ i = 1 n α i − 1 2 ∑ i = 1 n ∑ j = 1 n y i y j K ( x i , x j ) α i α j , {\displaystyle \max _{\alpha }\sum _{i=1}^{n}\alpha _{i}-{\frac {1}{2}}\sum _{i=1}^{n}\sum _{j=1}^{n}y_{i}y_{j}K(x_{i},x_{j})\alpha _{i}\alpha _{j},} subject to: 0 ≤ α i ≤ C , for i = 1 , 2 , … , n , {\displaystyle 0\leq \alpha _{i}\leq C,\quad {\mbox{ for }}i=1,2,\ldots ,n,} ∑ i = 1 n y i α i = 0 {\displaystyle \sum _{i=1}^{n}y_{i}\alpha _{i}=0} where C is an SVM hyperparameter and K(xi, xj) is the kernel function, both supplied by the user; and the variables α i {\displaystyle \alpha _{i}} are Lagrange multipliers. == Algorithm == SMO is an iterative algorithm for solving the optimization problem described above. SMO breaks this problem into a series of smallest possible sub-problems, which are then solved analytically. Because of the linear equality constraint involving the Lagrange multipliers α i {\displaystyle \alpha _{i}} , the smallest possible problem involves two such multipliers. Then, for any two multipliers α 1 {\displaystyle \alpha _{1}} and α 2 {\displaystyle \alpha _{2}} , the constraints are reduced to: 0 ≤ α 1 , α 2 ≤ C , {\displaystyle 0\leq \alpha _{1},\alpha _{2}\leq C,} y 1 α 1 + y 2 α 2 = k , {\displaystyle y_{1}\alpha _{1}+y_{2}\alpha _{2}=k,} and this reduced problem can be solved analytically: one needs to find a minimum of a one-dimensional quadratic function. k {\displaystyle k} is the negative of the sum over the rest of terms in the equality constraint, which is fixed in each iteration. The algorithm proceeds as follows: Find a Lagrange multiplier α 1 {\displaystyle \alpha _{1}} that violates the Karush–Kuhn–Tucker (KKT) conditions for the optimization problem. Pick a second multiplier α 2 {\displaystyle \alpha _{2}} and optimize the pair ( α 1 , α 2 ) {\displaystyle (\alpha _{1},\alpha _{2})} . Repeat steps 1 and 2 until convergence. When all the Lagrange multipliers satisfy the KKT conditions (within a user-defined tolerance), the problem has been solved. Although this algorithm is guaranteed to converge, heuristics are used to choose the pair of multipliers so as to accelerate the rate of convergence. This is critical for large data sets since there are n ( n − 1 ) / 2 {\displaystyle n(n-1)/2} possible choices for α i {\displaystyle \alpha _{i}} and α j {\displaystyle \alpha _{j}} . == Related work == The first approach to splitting large SVM learning problems into a series of smaller optimization tasks was proposed by Bernhard Boser, Isabelle Guyon, and Vladimir Vapnik. It is known as the "chunking algorithm". The algorithm starts with a random subset of the data, solves this problem, and iteratively adds examples which violate the optimality conditions. One disadvantage of this algorithm is that it is necessary to solve QP-problems scaling with the number of SVs. On real world sparse data sets, SMO can be more than 1000 times faster than the chunking algorithm. In 1997, E. Osuna, R. Freund, and F. Girosi proved a theorem which suggests a whole new set of QP algorithms for SVMs. By the virtue of this theorem a large QP problem can be broken down into a series of smaller QP sub-problems. A sequence of QP sub-problems that always add at least one violator of the Karush–Kuhn–Tucker (KKT) conditions is guaranteed to converge. The chunking algorithm obeys the conditions of the theorem, and hence will converge. The SMO algorithm can be considered a special case of the Osuna algorithm, where the size of the optimization is two and both Lagrange multipliers are replaced at every step with new multipliers that are chosen via good heuristics. The SMO algorithm is closely related to a family of optimization algorithms called Bregman methods or row-action methods. These methods solve convex programming problems with linear constraints. They are iterative methods where each step projects the current primal point onto each constraint.
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Heikki Mannila

Heikki Olavi Mannila (born 4 January 1960 in Espoo) is a Finnish computer scientist, the president of the Academy of Finland. Mannila earned his Ph.D. in 1985 from the University of Helsinki under the supervision of Esko Ukkonen and for many years he was a professor at the University of Helsinki himself. From 2004 to 2008 he was Academy Professor at the Academy of Finland. He became Vice President for Academic Affairs at Aalto University in 2009, and was appointed by the Finnish government as president of the Academy of Finland for a term lasting from 2012 to 2017. The appointment was renewed for the period 2017–2022. Mannila is known for his research in data mining, and has published highly cited papers on association rule learning and sequence mining. With David Hand and Padhraic Smyth, he is the co-author of the book Principles of Data Mining (MIT Press, 2001). Heikki Mannila is son to the professor Elina Haavio-Mannila.
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Split screen (computing)

Split screen is a display technique in computer graphics that consists of dividing graphics and/or text into non-overlapping adjacent parts, typically as two or four rectangular areas. This allows for the simultaneous presentation of (usually) related graphical and textual information on a computer display. TV sports adopted this presentation methodology in the 1960s for instant replay. Non-dynamic split screens differ from windowing systems in that the latter allowed overlapping and freely movable parts of the screen (the "windows") to present both related and unrelated application data to the user. In contrast, split-screen views are strictly limited to fixed positions. The split screen technique can also be used to run two instances of an application, potentially allowing another user to interact with the second instance. == In operating systems == Split screen modes are used by mobile operating systems to enable computer multitasking similar to the window interface present in desktop operating systems. Android supports split screen view of two apps natively on all devices, while certain devices, such as Samsung Galaxy Z TriFold, support three sumultaneous views. Split screen functionality is not supported on iOS, but a similar feature called Split View is present in iPadOS, first introduced in 2015 with the first generation of iPad Pro. == In video games == The split screen feature is commonly used in non-networked, also known as couch co-op, video games with multiplayer options. In its most easily understood form, a split screen for a multiplayer video game is an audiovisual output device (usually a standard television for video game consoles) where the display has been divided into 2-4 equally sized areas (depending on number of players) so that the players can explore different areas simultaneously without being close to each other. This has historically been remarkably popular on consoles, which until the 2000s did not have access to the Internet or any other network and is less common today with modern support for networked console-to-console multiplayer. In competitive split-screen games, it is customarily considered cheating to look at another player's screen section to gain an advantage. === History === Split screen gaming dates back to at least the 1970s, with games such Drag Race (1977) from Kee Games in the arcades being presented in this format. It has always been a common feature of two or more player home console and computer games too, with notable titles being Kikstart II for 8-bit systems, a number of 16-bit racing games (such as Lotus Esprit Turbo Challenge and Road Rash II), and action/strategy games (such as Toejam & Earl and Lemmings), all employing a vertical or horizontal screen split for two player games. Xenophobe is notable as a three-way split screen arcade title, although on home platforms it was reduced to one or two screens. The addition of four controller ports on home consoles also ushered in more four-way split screen games, with Mario Kart 64 and Goldeneye 007 on the Nintendo 64 being two well known examples. In arcades, machines tended to move towards having a whole screen for each player, or multiple connected machines, for multiplayer. On home machines, especially in the first and third person shooter genres, multiplayer is now more common over a network or the internet rather than locally with split screen. Starting from the late 2000s, the presence of split screen multiplayer has largely been declining due to the increasing prevalence of online multiplayer, though TechRadar reported a resurgence of split screen due to support from independent studios and increased interest from the players.
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Is an AI Text-to-video Tool Worth It in 2026?

In search of the best AI text-to-video tool? An AI text-to-video tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI text-to-video 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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Bidyut Baran Chaudhuri

Bidyut Baran Chaudhuri (B. B. Chauduri) is a senior computer scientist and an emeritus professor of Techno India University in West Bengal, India. He is also adjuncted to Indian Statistical Institute, where he was a professor for about three decades. He was the founding Head of Computer Vision and Pattern Recognition Unit (which was established in 1994) of ISI. Moreover, he was a J.C. Bose Fellow and Indian National Academy of Engineering Distinguished Professor at ISI. He was the vice-president of the Society for Natural Language Technology Research (SNLTR). His primary research contributes to the fields of computer vision, image processing and pattern recognition. He is a pioneer of "Indian language script OCR". == Education == Chaudhuri received his BSc (Hons.), BTech and MTech degrees from University of Calcutta, India in 1969, 1972 and 1974, respectively and PhD Degree from Indian Institute of Technology Kanpur in 1980. He did his post-doc work during 1981-1982 from Queen's University, U.K, through Leverhulme Overseas Fellowship. He also worked as a visiting faculty at Tech University, Hannover during 1986-87 as well as at GSF Institute of Radiation Protection (now Leibnitz Institute), Munich in 1990 and 1992. == Awards and recognition == Chaudhuri has been elected as a Life Fellow of IEEE "for contributions to pattern recognition, especially Indian language script OCR, document processing and natural language processing". He has become a Fellow of International Association for Pattern Recognition (IAPR) "for contributions to character recognition and speech synthesis in Indian language". He is also Fellow of The World Academy of Sciences (TWAS), Indian National Science Academy (INSA), Indian National Academy of Engineering (INAE), National Academy of Sciences (NASI), and Institute of Electronics and Telecommunication Engineering (IETE). In 2011, Chaudhuri received the Om Prakash Bhasin Award for his contribution in the field of electronics and information technology. Chaudhuri's interview on some of his works has been reported in Indian newspaper as well. He is within world's top 2% scientists and top-10 Indian AI scientists according to a study conducted by Stanford University. He has also been featured as top-10 machine learning researcher from India.
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How to Choose an AI Bug Finder

Comparing the best AI bug finder? An AI bug finder 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 bug finder 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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Knowledge assessment methodology

The knowledge assessment methodology (KAM) is "an interactive benchmarking tool created by the World Bank's Knowledge for Development Program to help countries identify the challenges and opportunities they face in making the transition to the knowledge-based economy." KAM does so by providing information on knowledge economy indicators for 146 countries. Its products include the Knowledge Economy Index and the Knowledge Index.
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Cognitive Technologies

Cognitive Technologies is a Russian software corporation that develops corporate business applications, AI-based advanced driver assistance systems. Founded in 1993 in Moscow (Russia), the company has offices in Eastern Europe, with R&D Centers in Russia. == History == Cognitive Technologies was founded in 1993 by Olga Uskova and Vladimir Arlazarov. The first employees previously worked in the team that developed the first world computer chess champion "Kaissa". The first programs developed by Cognitive Technologies were optical image and character recognition software – Tiger and CuneiForm. In February 2015 Cognitive Technologies and Kamaz, Russian Dakar Rally-winning truck manufacturer, started working on the self-driving Kamaz truck project. The first field tests took place in June 2015. In 2015 Andrey Chernogorov was appointed CEO of the company. == Products == Cognitive Technologies develops business application software and self-driving vehicle artificial intelligence. The main products are: C-pilot, AI-based ADAS E1 Evfrat – electronic workflow system CognitiveLot – e-purchasing systems == Cooperation with global companies == Under the contract signed between Cognitive Technologies and Hewlett-Packard, all scanners sold in Russia had text recognition software developed by Cognitive Technologies. It was the first contract with HP for an Eastern European company. Afterwards, Cognitive Technologies signed OEM contracts and business agreements with several global IT-companies, including IBM, Canon, Corel, Samsung, Xerox, Brother, Epson, and Olivetti. In 1998 Cognitive Technologies became the first company in Eastern Europe to get the Oracle Complementary Software Provider status. In 2001 Cognitive Technologies sold its Russian language speech corpus to Intel. In 2010 Cognitive Technologies sold its text parsing module to Yandex. The company also signed an agreement with NVIDIA join efforts in the development of intelligent document recognition technologies. == Self-driving car project == The system developed by Cognitive Technologies does not require building smart cities and smart roads equipped with multiple sensors – it works the opposite way, trying to understand the situation on the road like humans do. The system uses a video camera like a driver who uses his eyes, analyzing the information and focusing on the relevant data. For this purpose the system uses a special type of computer vision – foveal computer vision. Only 5–7% of the data gathered by the video cameras and sensors is processed by the system as relevant. The prototype is being tested in Russia on rough roads, on roads without marking, with the goal to prepare the system for work in difficult situations and on bad roads all around the world. == C-Pilot ADAS project == In August 2016 Cognitive Technologies started its own ADAS development project C-Pilot for ground transport control automation. == Self-driving tractors and harvesters project == The experts from Cognitive Technologies claim that the system will track stones, poles, and other obstacles that might be dangerous for the vehicles. This data will enable the engineers to develop an interactive field map, with GPS coordinates for stones and other obstacles. Eventually, this will result in an alteration of the harvester's movement pattern preventing it from running into stones or other objects that may inflict damage. Harvesters will work autonomously on the field, on the territory that is narrowed by radio beacons. == Present international activities == In 2016 Cognitive Technologies has joined the international community OpenPower Foundation, a consortium of open source solutions to developers based on POWER technology from IBM, which includes the world's leading IT map of Google, NVidia, Mellanox, etc. Within the consortium Cognitive Technologies is the initiator of forming of an international working group to develop a single software standard for the self-driving vehicle control. == Awards == In 2016, the leading Russian business newspaper Kommersant, announced that Cognitive Technologies is the TOP-2 Russian software company. TOP-6 Russian software company in 2015 according to Russoft TOP-500 biggest Russian companies according to RBC TOP-2 company of the Russian EDMS market in 2014 according to IDC TOP-20 Russian biggest IT-companies in 2013 according to Cnews Analytics
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The Best Free AI Resume Builder for Beginners

Curious about the best AI resume builder? An AI resume builder is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI resume builder slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Xu Li (computer scientist)

Xu Li is a Chinese computer scientist and co-founder and current CEO of SenseTime, an artificial intelligence (AI) company. Xu has led SenseTime since the company's incorporation and helped it independently develop its proprietary deep learning platform. == Education and research == Xu obtained both his bachelor's and master's degrees in computer science from Shanghai Jiao Tong University. He received his doctorate in computer science from the Chinese University of Hong Kong. Xu has published more than 50 papers at international conferences and in journals in the field of computer vision and won the Best Paper Award at the international conference on Non-Photorealistic Rendering and Animation (NPAR) 2012 and the Best Reviewer Award at the international conferences Asian Conference on Computer Vision ACCV 2012 and International Conference on Computer Vision (ICCV) 2015. He has three algorithms that have been included into the visual open-source platform OpenCV, and his "L0 Smoothing" algorithm garnered the most citations in research papers over a span of five years (2011–2015) within the ACM Transactions on Graphics (TOG), a scientific journal that Thomson Reuters InCites has placed first among software engineering journals. == Career == Previously, Xu worked at Lenovo Corporate Research & Development. He was also a visiting researcher at Motorola China R&D Institute, Omron Research Institute, and Microsoft Research. == Selected publications == Jimmy Ren, Xiaohao Chen, Jianbo Liu, Wenxiu Sun, Li Xu, Jiahao Pang, Qiong Yan, Yu-wing Tai, "Accurate Single Stage Detector Using Recurrent Rolling Convolution", (CVPR), 2017. Jimmy SJ. Ren, Yongtao Hu, Yu-Wing Tai, Chuan Wang, Li Xu, Wenxiu Sun, Qiong Yan, "Look, Listen and Learn – A Multimodal LSTM for Speaker Identification", The 30th AAAI Conference on Artificial Intelligence (AAAI), 2016 Jimmy SJ. Ren, Li Xu, Qiong Yan, Wenxiu Sun, "Shepard Convolutional Neural Networks" Advances in Neural Information Processing Systems (NIPS), 2015. Xiaoyong Shen, Chao Zhou, Li Xu, Jiaya Jia, "Mutual-Structure for Joint Filtering" International Conference on Computer Vision (ICCV), (oral presentation), 2015. Jianping Shi, Qiong Yan, Li Xu, Jiaya Jia, "Hierarchical Image Saliency Detection on Extended CSSD" IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2015. Jianping Shi, Xin Tao, Li Xu, Jiaya Jia, "Break Ames Room Illusion: Depth from General Single Images" ACM Transactions on Graphics (TOG), (Proc. ACM SIGGRAPH ASIA2015). Yongtao Hu, Jimmy SJ. Ren, Jingwen Dai, Chang Yuan, Li Xu, Wenping Wang, "Deep Multimodal Speaker Naming" ACM International Conference on Multimedia (MM), 2015. Li Xu, Jimmy SJ. Ren, Qiong Yan, Renjie Liao, Jiaya Jia "Deep Edge-Aware Filters" International Conference on Machine Learning (ICML), 2015. Jianping Shi, Li Xu, Jiaya Jia "Just Noticeable Defocus Blur Detection and Estimation" IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015. Ziyang Ma, Renjie Liao, Xin Tao, Li Xu, Jiaya Jia, Enhua Wu "Handling Motion Blur in Multi-Frame Super-Resolution" IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015. Xiaoyong Shen, Qiong Yan, Li Xu, Lizhuang Ma, Jiaya Jia"Multispectral Joint Image Restoration via Optimizing a Scale Map" IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2015. Jimmy SJ. Ren, Li Xu, "On Vectorization of Deep Convolutional Neural Networks for Vision Tasks" AAAI Conference on Artificial Intelligence (AAAI), 2015. == Awards and honors == Xu was ranked 7th in Fortune magazine's 2018 edition of its 40 Under 40. He was also named "China's Outstanding AI Industry Leader" by The Economic Observer, received the "Innovative Business Leader" Award under NetEase's "Future Technology Talent Awards", and was honored as Sina's "2017 Top Ten Economic Figures". In 2018, Xu was named EY's "Entrepreneur of the Year China" in the Technology category.
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Structural similarity index measure

The structural similarity index measure (SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. It is also used for measuring the similarity between two images. The SSIM index is a full reference metric; in other words, the measurement or prediction of image quality is based on an initial uncompressed or distortion-free image as reference. SSIM is a perception-based model that considers image degradation as perceived change in structural information, while also incorporating important perceptual phenomena, including both luminance masking and contrast masking terms. This distinguishes from other techniques such as mean squared error (MSE) or peak signal-to-noise ratio (PSNR) that instead estimate absolute errors. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important information about the structure of the objects in the visual scene. Luminance masking is a phenomenon whereby image distortions (in this context) tend to be less visible in bright regions, while contrast masking is a phenomenon whereby distortions become less visible where there is significant activity or "texture" in the image. == History == The predecessor of SSIM was called Universal Quality Index (UQI), or Wang–Bovik index, which was developed by Zhou Wang and Alan Bovik in 2001. This evolved, through their collaboration with Hamid Sheikh and Eero Simoncelli, into the current version of SSIM, which was published in April 2004 in the IEEE Transactions on Image Processing. In addition to defining the SSIM quality index, the paper provides a general context for developing and evaluating perceptual quality measures, including connections to human visual neurobiology and perception, and direct validation of the index against human subject ratings. The basic model was developed in the Laboratory for Image and Video Engineering (LIVE) at The University of Texas at Austin and further developed jointly with the Laboratory for Computational Vision (LCV) at New York University. Further variants of the model have been developed in the Image and Visual Computing Laboratory at University of Waterloo and have been commercially marketed. SSIM subsequently found strong adoption in the image processing community and in the television and social media industries. The 2004 SSIM paper has been cited over 50,000 times according to Google Scholar, making it one of the highest cited papers in the image processing and video engineering fields. It was recognized with the IEEE Signal Processing Society Best Paper Award for 2009. It also received the IEEE Signal Processing Society Sustained Impact Award for 2016, indicative of a paper having an unusually high impact for at least 10 years following its publication. Because of its high adoption by the television industry, the authors of the original SSIM paper were each accorded a Primetime Engineering Emmy Award in 2015 by the Television Academy. == Algorithm == The SSIM index is calculated between two windows of pixel values x {\displaystyle x} and y {\displaystyle y} of common size, from corresponding locations in two images to be compared. These SSIM values can be aggregated across the full images by averaging or other variations. === Special-case formula === In one simple special case, further explained in the next section, the SSIM measure between x {\displaystyle x} and y {\displaystyle y} is: SSIM ( x , y ) = ( 2 μ x μ y + c 1 ) ( 2 σ x y + c 2 ) ( μ x 2 + μ y 2 + c 1 ) ( σ x 2 + σ y 2 + c 2 ) {\displaystyle {\hbox{SSIM}}(x,y)={\frac {(2\mu _{x}\mu _{y}+c_{1})(2\sigma _{xy}+c_{2})}{(\mu _{x}^{2}+\mu _{y}^{2}+c_{1})(\sigma _{x}^{2}+\sigma _{y}^{2}+c_{2})}}} with: μ x {\displaystyle \mu _{x}} the pixel sample mean of x {\displaystyle x} ; μ y {\displaystyle \mu _{y}} the pixel sample mean of y {\displaystyle y} ; σ x 2 {\displaystyle \sigma _{x}^{2}} the sample variance of x {\displaystyle x} ; σ y 2 {\displaystyle \sigma _{y}^{2}} the sample variance of y {\displaystyle y} ; σ x y {\displaystyle \sigma _{xy}} the sample covariance of x {\displaystyle x} and y {\displaystyle y} ; c 1 = ( k 1 L ) 2 {\displaystyle c_{1}=(k_{1}L)^{2}} , c 2 = ( k 2 L ) 2 {\displaystyle c_{2}=(k_{2}L)^{2}} two variables to stabilize the division with weak denominator; L {\displaystyle L} the dynamic range of the pixel-values (typically this is 2 # b i t s p e r p i x e l − 1 {\displaystyle 2^{\#bits\ per\ pixel}-1} ); k 1 = 0.01 {\displaystyle k_{1}=0.01} and k 2 = 0.03 {\displaystyle k_{2}=0.03} by default. === General formula and components === The SSIM formula is based on three comparison measurements between the samples of x {\displaystyle x} and y {\displaystyle y} : luminance ( l {\displaystyle l} ), contrast ( c {\displaystyle c} ), and structure ( s {\displaystyle s} ). The individual comparison functions are: l ( x , y ) = 2 μ x μ y + c 1 μ x 2 + μ y 2 + c 1 {\displaystyle l(x,y)={\frac {2\mu _{x}\mu _{y}+c_{1}}{\mu _{x}^{2}+\mu _{y}^{2}+c_{1}}}} c ( x , y ) = 2 σ x σ y + c 2 σ x 2 + σ y 2 + c 2 {\displaystyle c(x,y)={\frac {2\sigma _{x}\sigma _{y}+c_{2}}{\sigma _{x}^{2}+\sigma _{y}^{2}+c_{2}}}} s ( x , y ) = σ x y + c 3 σ x σ y + c 3 {\displaystyle s(x,y)={\frac {\sigma _{xy}+c_{3}}{\sigma _{x}\sigma _{y}+c_{3}}}} The SSIM for each block is then a weighted combination of those comparative measures: SSIM ( x , y ) = l ( x , y ) α ⋅ c ( x , y ) β ⋅ s ( x , y ) γ {\displaystyle {\text{SSIM}}(x,y)=l(x,y)^{\alpha }\cdot c(x,y)^{\beta }\cdot s(x,y)^{\gamma }} Choosing the third denominator stabilizing constant as: c 3 = c 2 / 2 {\displaystyle c_{3}=c_{2}/2} leads to a simplification when combining the c and s components with equal exponents ( β = γ {\displaystyle \beta =\gamma } ), as the numerator of c is then twice the denominator of s, leading to a cancellation leaving just a 2. Setting the weights (exponents) α , β , γ {\displaystyle \alpha ,\beta ,\gamma } to 1, the formula can then be reduced to the special case shown above. === Mathematical properties === SSIM satisfies the identity of indiscernibles, and symmetry properties, but not the triangle inequality or non-negativity, and thus is not a distance function. However, under certain conditions, SSIM may be converted to a normalized root MSE measure, which is a distance function. The square of such a function is not convex, but is locally convex and quasiconvex, making SSIM a feasible target for optimization. === Application of the formula === In order to evaluate the image quality, this formula is usually applied only on luma, although it may also be applied on color (e.g., RGB) values or chromatic (e.g. YCbCr) values. The resultant SSIM index is a decimal value between -1 and 1, where 1 indicates perfect similarity, 0 indicates no similarity, and -1 indicates perfect anti-correlation. For an image, it is typically calculated using a sliding Gaussian window of size 11×11 or a block window of size 8×8. The window can be displaced pixel-by-pixel on the image to create an SSIM quality map of the image. In the case of video quality assessment, the authors propose to use only a subgroup of the possible windows to reduce the complexity of the calculation. === Variants === ==== Multi-scale SSIM ==== A more advanced form of SSIM, called Multiscale SSIM (MS-SSIM) is conducted over multiple scales through a process of multiple stages of sub-sampling, reminiscent of multiscale processing in the early vision system. It has been shown to perform equally well or better than SSIM on different subjective image and video databases. ==== Multi-component SSIM ==== Three-component SSIM (3-SSIM) is a form of SSIM that takes into account the fact that the human eye can see differences more precisely on textured or edge regions than on smooth regions. The resulting metric is calculated as a weighted average of SSIM for three categories of regions: edges, textures, and smooth regions. The proposed weighting is 0.5 for edges, 0.25 for the textured and smooth regions. The authors mention that a 1/0/0 weighting (ignoring anything but edge distortions) leads to results that are closer to subjective ratings. This suggests that edge regions play a dominant role in image quality perception. The authors of 3-SSIM have also extended the model into four-component SSIM (4-SSIM). The edge types are further subdivided into preserved and changed edges by their distortion status. The proposed weighting is 0.25 for all four components. ==== Structural dissimilarity ==== Structural dissimilarity (DSSIM) may be derived from SSIM, though it does not constitute a distance function as the triangle inequality is not necessarily satisfied. DSSIM ( x , y ) = 1 − SSIM ( x , y ) 2 {\displaystyle {\hbox{DSSIM}}(x,y)={\frac {1-{\hbox{SSIM}}(x,y)}{2}}} ==== Video quality metrics and temporal variants ==== It is worth noting that the original vers
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AI Blog Writers: Free vs Paid (2026)

Shopping for the best AI blog writer? An AI blog writer 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 blog writer 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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Ancient text corpora

Ancient text corpora are the entire collection of texts from the period of ancient history, defined in this article as the period from the beginning of writing up to 300 AD. These corpora are important for the study of literature, history, linguistics, and other fields, and are a fundamental component of the world's cultural heritage. Chinese, Latin, and Greek are examples of ancient languages with significant text corpora, although much of these corpora are known to us via transmission (frequently via medieval manuscript copies) rather than in their original form. These texts – both transmitted and original – provide valuable insights into the history and culture of different regions of the world, and have been studied for centuries by scholars and researchers. Other ancient texts – particularly stone inscriptions and papyrus scrolls – have been published following archaeological research, notably the cuneiform corpus of c.10 million words and the c.5 million words in ancient Egyptian. Through advances in technology and digitization, ancient text corpora are more accessible than ever before. Tools such as the Perseus Digital Library and the Digital Corpus of Sanskrit have made it easier for researchers to access and analyze these texts. == Quantifying the corpora == Two types of ancient texts are known to modern scholars – those that have only survived in younger manuscripts, but whose great age is undisputed (this applies to the bulk of the Chinese, Brahmi, Greek, Latin, Hebrew and Avestan tradition), and those known from original inscriptions, papyri and other manuscripts. Counting of the words in each corpus presents significant methodological challenges – in principle, every single occurrence of a word in the text is counted separately, but in the case of parallel transmission of literary texts, only a single transmission is taken into account. Just as the Book of the Dead and the coffin texts are only included once in the number given for the Egyptian, the Greek and Latin literary works should only be counted according to one manuscript. If, on the other hand, tombs, royal inscriptions or economic documents of certain ancient languages often show a more or less identical form, this is not evaluated as a purely "parallel tradition". Attached prepositions are counted as separate words, except in the case of the definite article in Hebrew, Aramaic and Greek since it has no equivalent in most languages, so its frequency would significantly affect the comparability of numbers. === Languages with known size estimates === === South Asian === Sanskrit (Vedic Sanskrit and Classical Sanskrit) Indus script (3,800 items, c.20,000 characters) Brahmi script Old Tamil Early Indian epigraphy and Indian epic poetry Kharosthi Pali literature List of historic Indian texts === Mesoamerican === Olmec hieroglyphs Maya script === East Asian === Old Chinese Chinese classics The pre-Qin corpus: a collection of ancient Chinese texts written before the Qin dynasty (221 BCE). The corpus includes texts from Confucianism, Taoism, Legalism, and other schools of thought. The pre-Han corpus: a collection of ancient Chinese texts written before the Han dynasty (202 BCE). The corpus includes texts from Confucianism, Taoism, Legalism, and other schools of thought. See the Chinese Text Project Chinese bronze inscriptions, Oracle bone script, Seal script, Clerical script === Central Iranian languages === Prior to 300 AD, the Central Iranian languages are mainly in the form of Sassanid stone inscriptions in the two closely related idioms Middle Persian (Pahlavi scripts and Inscriptional Parthian), there are 5000 for the corpus of Middle Persian (mostly 3rd, but also 4th/5th centuries) and for the corpus of Parthian (3rd century) 3000 words. To what extent some of the Manichaean Middle Persian literary texts may date back to the 3rd century is difficult to estimate; Mani is said to have personally written the Shabuhragan totaling about 5000 words. In any case, if we combine Middle Persian and Parthian, we come to over 10,000 words. === Proto-Sinaitic === Proto-Sinaitic script has no more than about 400 letters (number of words is unknown since the script has not been fully interpreted). To a similar extent, there are probably approximately contemporaneous Proto-Canaanite inscriptions (ibid.). === Anatolian === Luwian cuneiform, approx. 3000 words the Palaic language few hundred words. Hieroglyphic Luwian the Lycian alphabet (the best attested Anatolian successor language written in alphabetic script) with about 5000 words The Lydian alphabet 109 inscriptions comprising about 1500 words The Phrygian alphabet the in-tomb inscriptions from the 2nd and 3rd centuries AD (approx. 1000 words) and in the so-called "old Phrygian" inscriptions less than 300 words The Carian alphabets whose texts, mainly from Egypt, contain around 600 words. === Old Italic === the Umbrian language attested essentially by the sacrificial instructions of the Iguvinian Tables with 5000 words the Oscan language (ibid.) with 2000 words the Messapic language with probably a good 1000 words (the estimate is difficult because most texts in this hardly understandable language do not use word separators) the Venetic language a few hundred words the Faliscan language a few hundred words Cisalpine Celtic inscriptions amount to approximately 2000 words, to which are added a number of glosses by classical authors === Iberia === Iberian scripts, more rarely written in Greek or Latin script, approx. 2500 words Celtiberian script, which refers to Celtic language testimonies in Iberian, but also in Latin script from Spain (approx. 1000 words) Southwest Paleohispanic script, 78 inscriptions, a few hundred words Lusitanian language, three monuments in Latin script, approx. 60 words === Germanic Northern Europe === Runic inscriptions dated before the 4th century amount to about 30 pieces, which contain no more than 50 words in total === Africa === Geʽez script: comparatively few inscriptions with a total of around 1,000 words before 300 AD. Following Christianization in the 4th century, more extensive texts are known. Libyco-Berber alphabet: over 1,000 inscriptions from the Maghreb, which are dated to Roman times. Most texts do not use a word separator; Peust estimates that the total number of words could be around 5,000 Meroitic script (Ancient Nubian): about 900 texts are known, which Peust estimates may contain approximately 10,000 words, albeit with uncertainty from the fact that the word separator is not used consistently in the Meroitic script. === Aegean === The Cretan Linear A inscriptions that have not yet been deciphered are available in about 2500 texts, which contain a total of around 20,000 characters. The total number of words can hardly be determined; Peust tentatively put it in the same order of magnitude as in Meroitic. In addition to the Linear A texts, there are also inscriptions Cretan hieroglyphs of a few hundred characters and texts written in the Greek alphabet, but not in Greek, with a few dozen words Cypriot syllabary in the first millennium BC, in which mostly Greek texts were recorded. The relevant texts comprise around 100 to 200 words. === Micro corpora === There are a significant number of ancient micro-corpus languages. Estimating the total number of attested ancient languages may be as difficult as estimating their corpus size. For example, Greek and Latin sources hand down an enormous amount of foreign-language glosses, the seriousness of which is not always certain. == Preservation and curation == Historic preservation and maintaining ancient text corpora presents several challenges, including issues with preservation, translation, and digitization. Many ancient texts have been lost over time, and those that survive may be damaged or fragmented. Translating ancient languages and scripts requires specialized expertise, and digitizing texts can be time-consuming and resource-intensive. == Corpus linguistics == The field of corpus linguistics studies language as expressed in text corpora. This includes the analysis of word frequency, collocations, grammar, and semantics. Ancient text corpora provide a valuable resource for corpus linguistics research, enabling scholars to explore the evolution of language and culture over time.
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