AI Assistant Zalando

AI Assistant Zalando — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Stairstep interpolation

In the field of image processing, stairstep interpolation is a widely employed method technique for interpolating pixels after enlarging an image. The fundamental concept is to interpolate multiple times, in small increments, using any interpolation algorithm that is better than nearest-neighbor interpolation such as; bilinear interpolation, and bicubic interpolation. A common scenario is to interpolate an image by using a bicubic interpolation which increases the image size by no more than 10% (110% of the original size) at a time until the desired size is reached. Fred Miranda, a developer, popularized this method by creating and developing several Photoshop plug-ins that incorporate this technique. == Example ==
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The Best Free AI Essay Writer for Beginners

In search of the best AI essay writer? An AI essay writer 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 essay writer 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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Marilyn Walker

Marilyn A. Walker is an American computer scientist. She is professor of computer science and head of the Natural Language and Dialogue Systems Lab at the University of California, Santa Cruz (UCSC). Her research includes work on computational models of dialogue interaction and conversational agents, analysis of affect, sarcasm and other social phenomena in social media dialogue, acquiring causal knowledge from text, conversational summarization, interactive story and narrative generation, and statistical methods for training the dialogue manager and the language generation engine for dialogue systems. == Biography == Walker received an M.S. in Computer Science from Stanford University in 1987, and a Ph.D. in Computer and Information Science and an M.A in linguistics from the University of Pennsylvania in 1993. Walker was awarded a Royal Society Wolfson Research Fellowship at the University of Sheffield from 2003 to 2009. She was inducted as a Fellow of the Association for Computational Linguistics (ACL) in December 2016 for "fundamental contributions to statistical methods for dialog optimization, to centering theory, and to expressive generation for dialog". She served as the general chair of the 2018 North American Association for Computational Linguistics (NAACL-2018) conference. Walker pioneered the use of statistical methods for dialog optimization at AT&T Bell Labs Research where she conducted some of the first experiments on reinforcement learning for optimizing dialogue systems. Her research on Centering Theory is taught in standard textbooks on NLP. She also pioneered the use of statistical NLP methods for Natural Language Generation with the development of the first statistical sentence planner for dialogue systems in 2001. She is well known for her work with François Mairesse on recognizing Big Five personality from text as well as using statistical methods for stylistic Natural Language Generation to express a particular Big Five personality type. An extension of this work learns how to manifest the linguistic style of a particular character in a film. She has published over 300 papers and is the holder of 10 U.S. patents. Her work on the evaluation of dialogue systems conducted at AT&T Bell Labs Research (PARADISE: A framework for evaluating spoken dialogue agents) is a classic, has been cited more than 1100 times. At UCSC, her lab focuses on computational modeling of dialogue and user-generated content in social media such as weblogs, including spoken dialogue systems and interactive stories. She led the Athena team, which was selected as a contender in the Alexa Prize SocialBot Challenge for 5 challenges between 2018 and 2023.
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AI Voice Assistants Reviews: What Actually Works in 2026

In search of the best AI voice assistant? An AI voice assistant 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 voice assistant 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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Online service provider

An online service provider (OSP) can, for example, be an Internet service provider, an email provider, a news provider (press), an entertainment provider (music, movies), a search engine, an e-commerce site, an online banking site, a health site, an official government site, social media, a wiki, or a Usenet newsgroup. In its original more limited definition, it referred only to a commercial computer communication service in which paid members could dial via a computer modem the service's private computer network and access various services and information resources such as bulletin board systems, downloadable files and programs, news articles, chat rooms, and electronic mail services. The term "online service" was also used in references to these dial-up services. The traditional dial-up online service differed from the modern Internet service provider in that they provided a large degree of content that was only accessible by those who subscribed to the online service, while ISP mostly serves to provide access to the Internet and generally provides little if any exclusive content of its own. In the U.S., the Online Copyright Infringement Liability Limitation Act (OCILLA) portion of the U.S. Digital Millennium Copyright Act has expanded the legal definition of online service in two different ways for different portions of the law. It states in section 512(k)(1): (A) As used in subsection (a), the term "service provider" means an entity offering the transmission, routing, or providing of connections for digital online communications, between or among points specified by a user, of material of the user's choosing, without modification to the content of the material as sent or received. (B) As used in this section, other than subsection (a), the term "service provider" means a provider of online services or network access, or the operator of facilities therefore, and includes an entity described in subparagraph (A). These broad definitions make it possible for numerous web businesses to benefit from the OCILLA. == History == The first commercial online services went live in 1969. CompuServe (owned in the 1980s and 1990s by H&R Block) and The Source (for a time owned by The Reader's Digest) are considered the first major online services created to serve the market of personal computer users. Utilizing text-based interfaces and menus, these services allowed anyone with a modem and communications software to use email, chat, news, financial and stock information, bulletin boards, special interest groups (SIGs), forums and general information. Subscribers could exchange email only with other subscribers of the same service. (For a time a service called DASnet carried mail among several online services, and CompuServe, MCI Mail, and other services experimented with X.400 protocols to exchange email until the Internet rendered these outmoded.) Other text-based online services followed such as Delphi, GEnie and MCI Mail. The 1980s also saw the rise of independent Computer Bulletin Boards, or BBSes. (Online services are not BBSes. An online service may contain an electronic bulletin board, but the term "BBS" is reserved for independent dialup, microcomputer-based services that are usually single-user systems.) The commercial services used pre-existing packet-switched (X.25) data communications networks, or the services' own networks (as with CompuServe). In either case, users dialed into local access points and were connected to remote computer centers where information and services were located. As with telephone service, subscribers paid by the minute, with separate day-time and evening/weekend rates. As the use of computers that supported color and graphics, such the Atari 8-bit computers, Commodore 64, TI-99/4A, Apple II, and early IBM PC compatibles, increased, online services gradually developed framed or partially graphical information displays. Early services such as CompuServe added increasingly sophisticated graphics-based front end software to present their information, though they continued to offer text-based access for those who needed or preferred it. In 1985 Viewtron, which began as a Videotex service requiring a dedicated terminal, introduced software allowing home computer owners access. Beginning in the mid-1980s graphics based online services such as PlayNET, Prodigy, and Quantum Link (aka Q-Link) were developed. Quantum Link, which was based on Commodore-only Playnet software, later developed AppleLink Personal Edition, PC-Link (based on Tandy's DeskMate), and Promenade (for IBM), all of which (including Q-Link) were later combined as America Online. These online services presaged the web browser that would change global online life 10 years later. Before Quantum Link, Apple computer had developed its own service, called AppleLink, which was mostly a support network targeted at Apple dealers and developers. Later, Apple offered the short-lived eWorld, targeted at Mac consumers and based on the Mac version of the America Online software. Beginning in 1992, the Internet, which had previously been limited to government, academic, and corporate research settings, was opened to commercial entities. The first online service to offer Internet access was DELPHI, which had developed TCP/IP access much earlier, in connection with an environmental group that rated Internet access. The explosion of popularity of the World Wide Web in 1994 accelerated the development of the Internet as an information and communication resource for consumers and businesses. The sudden availability of low- to no-cost email and appearance of free independent web sites broke the business model that had supported the rise of the early online service industry. CompuServe, BIX, AOL, DELPHI, and Prodigy gradually added access to Internet e-mail, Usenet newsgroups, ftp, and to web sites. At the same time, they moved from usage-based billing to monthly subscriptions. Similarly, companies that paid to have AOL host their information or early online stores began to develop their own web sites, putting further stress on the economics of the online industry. Only the largest services like AOL (which later acquired CompuServe, just as CompuServe acquired The Source) were able to make the transition to the Internet-centric world. A new class of online service provider arose to provide access to the Internet, the internet service provider or ISP. Internet-only service providers like UUNET, The Pipeline, Panix, Netcom, the World, EarthLink, and MindSpring provided no content of their own, concentrating their efforts on making it easy for nontechnical users to install the various software required to "get online" before consumer operating systems came internet-enabled out of the box. In contrast to the online services' multitiered per-minute or per-hour rates, many ISPs offered flat-fee, unlimited access plans. Independent companies sprang up to offer access and packages to compete with the big networks (eg, the-wire.com, 1994 in Toronto and bway.net 1995 in New York). These providers first offered access through telephone and modem, just as did the early online services providers. By the early 2000s, these independent ISPs had largely been supplanted by high speed and broadband access through cable and phone companies, as well as wireless access. The importance of the online services industry was vital in "paving the road" for the information superhighway. When Mosaic and Netscape were released in 1994, they had a ready audience of more than 10 million people who were able to download their first web browser through an online service. Though ISPs quickly began offering software packages with setup to their customers, this brief period gave many users their first online experience. Two online services in particular, Prodigy and AOL, are often confused with the Internet, or the origins of the Internet. Prodigy's Chief Technical Officer said in 1999: "Eleven years ago, the Internet was just an intangible dream that Prodigy brought to life. Now it is a force to be reckoned with." Despite that statement, neither service provided the back bone for the Internet, nor did either start the Internet. == Online service interfaces == The first online service used a simple text-based interface in which content was largely text only and users made choices via a command prompt. This allowed just about any computer with a modem and terminal communications program the ability to access these text-based online services. CompuServe would later offer, with the advent of the Apple Macintosh and Microsoft Windows-based PCs, a GUI interface program for their service. This provided a very rudimentary GUI interface. CompuServe continued to offer text-only access for those needing it. Online services like Prodigy and AOL developed their online service around a GUI and thus unlike CompuServe's early GUI-based software, these online services provided a more robust GUI interface. Early GUI-base
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AI Art Generators: Free vs Paid (2026)

In search of the best AI art generator? An AI art generator 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 art generator 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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Raymond J. Mooney

Raymond J. Mooney is an American computer scientist, professor of computer science, and director of the Artificial Intelligence laboratory at the University of Texas at Austin. His research focuses on machine learning and natural language processing. He was educated at O'Fallon Township High School in O'Fallon, Illinois and earned a BS, MS, and Ph.D. in computer science at the University of Illinois at Urbana-Champaign, where he was advised by Gerald DeJong. He is a fellow of the Association for Computing Machinery (ACM), Association for Computational Linguistics (ACL), and Association for the Advancement of Artificial Intelligence (AAAI).
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The Best Free AI Headshot Generator for Beginners

Shopping for the best AI headshot generator? An AI headshot generator 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 headshot generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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VSCO

VSCO ( ), formerly known as VSCO Cam, is a photography mobile app available for iOS and Android devices. The app was created by Joel Flory and Greg Lutze. The VSCO app allows users to capture photos in the app and edit them, using preset filters and editing tools. == History == Visual Supply Company was founded by Joel Flory and Greg Lutze in California, in 2011. VSCO was launched in 2012. It raised $40 million from investors in May 2014. In 2017, VSCO launched a subscription model. As of 2018, Visual Supply Company has $90 million in funding from investors and over 2 million paying members. In 2019, VSCO acquired Rylo, a video editing startup founded by the original developer of Instagram’s Hyperlapse. Visual Supply Company has locations in Oakland, California, where it is headquartered, and Chicago, Illinois. In December 2020 VSCO acquired AI-powered video editing app Trash. In April 2018, VSCO reached over 30 million users. In September 2023, Eric Wittman was appointed as the new CEO and co-founder Joel Flory became executive chairman. == Usage == Users must register an account to use the app. Photos can be taken or imported from the camera roll, as well as short videos or animated GIFs (known in the app as DSCO; iOS only). The user can edit their photos through various preset filters, or through the "toolkit" feature which allows finer adjustments to fade, clarity, skin tone, tint, sharpness, saturation, contrast, temperature, exposure, and other properties. Users have the option of posting their photos to their profile, where they can also add captions and hashtags. Photos can also be exported back into the camera roll or shared with other social networking services. The users also have an option to edit their own videos from their camera roll with the VSCO yearly membership, but they are not able to post camera roll as VSCO Film X videos to their account on VSCO. JPEG and raw image files can be used. Research on image based social media platforms has found that engagement with posting, editing, and interacting with images can influence users' mood, self esteem, and body satisfaction. Studies also suggest that greater emotional investment in social media content is associated with increased negative psychological outcomes including stress and depressive symptoms. == In popular culture == VSCO's Oakland headquarters was a key filming location for Boots Riley's 2018 film Sorry to Bother You.
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Is an AI Copywriting Tool Worth It in 2026?

Looking for the best AI copywriting tool? An AI copywriting tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI copywriting tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Ronald J. Williams

Ronald James Williams (1945 – February 16, 2024) was an American mathematician and computer scientist who spent the majority of his career at Northeastern University. He is considered one of the pioneers of neural networks. In 1986, he co-authored the seminal paper in Nature on the backpropagation algorithm along with David Rumelhart and Geoffrey Hinton, which triggered a boom in neural network research. == Education and career == Williams was born in Southern California. He studied at California Institute of Technology as a undergraduate student and received a B.S. in mathematics there in 1966. He received his M.A. and Ph.D. in mathematics, both at University of California, San Diego (UCSD) in 1972 and 1975, respectively. His Ph.D. thesis was supervised by Donald Werner Anderson. He worked for a defense contractor for some time after graduation. From 1983 to 1986, Williams was a member of the Parallel Distributed Processing research group headed by David Rumelhart at the Institute for Cognitive Science at UCSD. In 1986, Williams accepted a professorship in computer science at Northeastern University in Boston, where he remained afterwards. In addition to the backpropagation paper, Williams made fundamental contributions to the fields of recurrent neural networks, where he, along with David Zipser, invented the teacher forcing algorithm and made important contributions to backpropagation through time. In reinforcement learning, Williams introduced the REINFORCE algorithm in 1992, which became the first policy gradient method. Besides his works on neural networks, Williams, together with Wenxu Tong and Mary Jo Ondrechen, developed Partial Order Optimum Likelihood (POOL), a machine learning method used in the prediction of active amino acids in protein structures. POOL is a maximum likelihood method with a monotonicity constraint and is a general predictor of properties that depend monotonically on the input features.
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Optical braille recognition

Optical braille recognition is technology to capture and process images of braille characters into natural language characters. It is used to convert braille documents for people who cannot read them into text, and for preservation and reproduction of the documents. == History == In 1984, a group of researchers at the Delft University of Technology designed a braille reading tablet, in which a reading head with photosensitive cells was moved along set of rulers to capture braille text line-by-line. In 1988, a group of French researchers at the Lille University of Science and Technology developed an algorithm, called Lectobraille, which converted braille documents into plain text. The system photographed the braille text with a low-resolution CCD camera, and used spatial filtering techniques, median filtering, erosion, and dilation to extract the braille. The braille characters were then converted to natural language using adaptive recognition. The Lectobraille technique had an error rate of 1%, and took an average processing time of seven seconds per line. In 1993, a group of researchers from the Katholieke Universiteit Leuven developed a system to recognize braille that had been scanned with a commercially available scanner. The system, however, was unable to handle deformities in the braille grid, so well-formed braille documents were required. In 1999, a group at the Hong Kong Polytechnic University implemented an optical braille recognition technique using edge detection to translate braille into English or Chinese text. In 2001, Murray and Dais created a handheld recognition system, that scanned small sections of a document at once. Because of the small area scanned at once, grid deformation was less of an issue, and a simpler, more efficient algorithm was employed. In 2003, Morgavi and Morando designed a system to recognize braille characters using artificial neural networks. This system was noted for its ability to handle image degradation more successfully than other approaches. == Challenges == Many of the challenges to successfully processing braille text arise from the nature of braille documents. Braille is generally printed on solid-color paper, with no ink to produce contrast between the raised characters and the background paper. However, imperfections in the page can appear in a scan or image of the page. Many documents are printed inter-point, meaning they are double-sided. As such, the depressions of the braille of one side appear interlaid with the protruding braille of the other side. == Techniques == Some optical braille recognition techniques attempt to use oblique lighting and a camera to reveal the shadows of the depressions and protrusions of the braille. Others make use of commercially available document scanners.
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Commitment ordering

Commitment ordering (CO) is a class of interoperable serializability techniques in concurrency control of databases, transaction processing, and related applications. It allows optimistic (non-blocking) implementations. With the proliferation of multi-core processors, CO has also been increasingly utilized in concurrent programming, transactional memory, and software transactional memory (STM) to achieve serializability optimistically. CO is also the name of the resulting transaction schedule (history) property, defined in 1988 with the name dynamic atomicity. In a CO compliant schedule, the chronological order of commitment events of transactions is compatible with the precedence order of the respective transactions. CO is a broad special case of conflict serializability and effective means (reliable, high-performance, distributed, and scalable) to achieve global serializability (modular serializability) across any collection of database systems that possibly use different concurrency control mechanisms (CO also makes each system serializability compliant, if not already). Each not-CO-compliant database system is augmented with a CO component (the commitment order coordinator—COCO) which orders the commitment events for CO compliance, with neither data-access nor any other transaction operation interference. As such, CO provides a low overhead, general solution for global serializability (and distributed serializability), instrumental for global concurrency control (and distributed concurrency control) of multi-database systems and other transactional objects, possibly highly distributed (e.g., within cloud computing, grid computing, and networks of smartphones). An atomic commitment protocol (ACP; of any type) is a fundamental part of the solution, utilized to break global cycles in the conflict (precedence, serializability) graph. CO is the most general property (a necessary condition) that guarantees global serializability, if the database systems involved do not share concurrency control information beyond atomic commitment protocol (unmodified) messages and have no knowledge of whether transactions are global or local (the database systems are autonomous). Thus CO (with its variants) is the only general technique that does not require the typically costly distribution of local concurrency control information (e.g., local precedence relations, locks, timestamps, or tickets). It generalizes the popular strong strict two-phase locking (SS2PL) property, which in conjunction with the two-phase commit protocol (2PC), is the de facto standard to achieve global serializability across (SS2PL based) database systems. As a result, CO compliant database systems (with any different concurrency control types) can transparently join such SS2PL based solutions for global serializability. In addition, locking based global deadlocks are resolved automatically in a CO based multi-database environment, a vital side-benefit (including the special case of a completely SS2PL based environment; a previously unnoticed fact for SS2PL). Furthermore, strict commitment ordering (SCO; Raz 1991c), the intersection of Strictness and CO, provides better performance (shorter average transaction completion time and resulting in better transaction throughput) than SS2PL whenever read-write conflicts are present (identical blocking behavior for write-read and write-write conflicts; comparable locking overhead). The advantage of SCO is especially during lock contention. Strictness allows both SS2PL and SCO to use the same effective database recovery mechanisms. Two major generalizing variants of CO exist, extended CO (ECO; Raz 1993a) and multi-version CO (MVCO; Raz 1993b). They also provide global serializability without local concurrency control information distribution, can be combined with any relevant concurrency control, and allow optimistic (non-blocking) implementations. Both use additional information for relaxing CO constraints and achieving better concurrency and performance. Vote ordering (VO or Generalized CO (GCO); Raz 2009) is a container schedule set (property) and technique for CO and all its variants. Local VO is necessary for guaranteeing global serializability if the atomic commitment protocol (ACP) participants do not share concurrency control information (have the generalized autonomy property). CO and its variants inter-operate transparently, guaranteeing global serializability and automatic global deadlock resolution together in a mixed, heterogeneous environment with different variants. == Overview == The Commitment ordering (CO; Raz 1990, 1992, 1994, 2009) schedule property has been referred to also as Dynamic atomicity (since 1988), commit ordering, commit order serializability, and strong recoverability (since 1991). The latter is a misleading name since CO is incomparable with recoverability, and the term "strong" implies a special case. This means that a substantial recoverability property does not necessarily have the CO property and vice versa. In 2009 CO has been characterized as a major concurrency control method, together with the previously known (since the 1980s) three major methods: Locking, Time-stamp ordering, and Serialization graph testing, and as an enabler for the interoperability of systems using different concurrency control mechanisms. In a federated database system or any other more loosely defined multidatabase system, which are typically distributed in a communication network, transactions span multiple and possibly Distributed databases. Enforcing global serializability in such system is problematic. Even if every local schedule of a single database is still serializable, the global schedule of a whole system is not necessarily serializable. The massive communication exchanges of conflict information needed between databases to reach conflict serializability would lead to unacceptable performance, primarily due to computer and communication latency. The problem of achieving global serializability effectively had been characterized as open until the public disclosure of CO in 1991 by its inventor Yoav Raz (Raz 1991a; see also Global serializability). Enforcing CO is an effective way to enforce conflict serializability globally in a distributed system since enforcing CO locally in each database (or other transactional objects) also enforces it globally. Each database may use any, possibly different, type of concurrency control mechanism. With a local mechanism that already provides conflict serializability, enforcing CO locally does not cause any other aborts, since enforcing CO locally does not affect the data access scheduling strategy of the mechanism (this scheduling determines the serializability related aborts; such a mechanism typically does not consider the commitment events or their order). The CO solution requires no communication overhead since it uses (unmodified) atomic commitment protocol messages only, already needed by each distributed transaction to reach atomicity. An atomic commitment protocol plays a central role in the distributed CO algorithm, which enforces CO globally by breaking global cycles (cycles that span two or more databases) in the global conflict graph. CO, its special cases, and its generalizations are interoperable and achieve global serializability while transparently being utilized together in a single heterogeneous distributed environment comprising objects with possibly different concurrency control mechanisms. As such, Commitment ordering, including its special cases, and together with its generalizations (see CO variants below), provides a general, high performance, fully distributed solution (no central processing component or central data structure are needed) for guaranteeing global serializability in heterogeneous environments of multidatabase systems and other multiple transactional objects (objects with states accessed and modified only by transactions; e.g., in the framework of transactional processes, and within Cloud computing and Grid computing). The CO solution scales up with network size and the number of databases without any negative impact on performance (assuming the statistics of a single distributed transaction, e.g., the average number of databases involved with a single transaction, are unchanged). With the proliferation of Multi-core processors, Optimistic CO (OCO) has also been increasingly utilized to achieve serializability in software transactional memory, and numerous STM articles and patents utilizing "commit order" have already been published (e.g., Zhang et al. 2006). == The commitment ordering solution for global serializability == === General characterization of CO === Commitment ordering (CO) is a special case of conflict serializability. CO can be enforced with non-blocking mechanisms (each transaction can complete its task without having its data-access blocked, which allows optimistic concurrency control; however, commitment could be blo
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Top 10 Conversational AI Platforms Compared (2026)

In search of the best conversational AI platform? An conversational AI platform 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 conversational AI platform 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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Andrei Knyazev (mathematician)

Andrew Knyazev is an American mathematician. He graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University under the supervision of Evgenii Georgievich D'yakonov (Russian: Евгений Георгиевич Дьяконов) in 1981 and obtained his PhD in Numerical Mathematics at the Russian Academy of Sciences under the supervision of Vyacheslav Ivanovich Lebedev (Russian: Вячеслав Иванович Лебедев) in 1985. He worked at the Kurchatov Institute between 1981–1983, and then to 1992 at the Marchuk Institute of Numerical Mathematics (Russian: ru:Институт вычислительной математики имени Г. И. Марчука РАН) of the Russian Academy of Sciences, headed by Gury Marchuk (Russian: Гурий Иванович Марчук). From 1993–1994, Knyazev held a visiting position at the Courant Institute of Mathematical Sciences of New York University, collaborating with Olof B. Widlund. From 1994 until retirement in 2014, he was a Professor of Mathematics at the University of Colorado Denver, supported by the National Science Foundation and United States Department of Energy grants. He was a recipient of the 2008 Excellence in Research Award, the 2000 college Teaching Excellence Award, and a finalist of the CU President's Faculty Excellence Award for Advancing Teaching and Learning through Technology in 1999. He was awarded the title of Professor Emeritus at the University of Colorado Denver and named the SIAM Fellow Class of 2016 and AMS Fellow Class of 2019. From 2012–2018, Knyazev worked at the Mitsubishi Electric Research Laboratories on algorithms for image and video processing, data sciences, optimal control, and material sciences, resulting in dozens of publications and 13 patent applications. Since 2018, he contributed to numerical techniques in quantum computing at Zapata Computing, real-time embedded anomaly detection in automotive data, and algorithms for silicon photonics-based hardware. Knyazev is mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly preconditioning and the iterative method LOBPCG. Knyazev's implementation of LOBPCG is available in many open source software packages, e.g., BLOPEX, SciPy, and ABINIT. Knyazev collaborated with John Osborn on the theory of the Ritz method in the finite element method context and with Nikolai Sergeevich Bakhvalov (Russian: Николай Серге́евич Бахвалов) (Erdős number 3 via Leonid Kantorovich) on numerical solution of elliptic partial differential equations with large jumps in the main coefficients. Jointly with his Ph.D. students, Knyazev pioneered using majorization for bounds in the Rayleigh–Ritz method (see and references there) and contributed to the theory of angles between flats.
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