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List of Fortran software and tools

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

András Kornai (born 1957 in Budapest) is a mathematical linguist. == Education == Kornai is the son of economist János Kornai. He earned two PhDs with the first being in mathematics in 1983 from Eötvös Loránd University in Budapest, where his advisor was Miklós Ajtai. His second was in linguistics in 1991 from Stanford University, where his advisor was Paul Kiparsky. == Career == He is a professor in the Department of Algebra at the Budapest Institute of Technology, where he works on an open source Hungarian morphological analyzer. He was Chief Scientist at MetaCarta, where he worked on information extraction before the company was acquired by Nokia. Prior to MetaCarta, he was Chief Scientist at Northern Light. He is on the board of the journal Grammars and YourAmigo PLC. His research interests include all mathematical aspects of natural language processing, speech recognition, and OCR. As area editor he was responsible for the Mathematical Linguistics area of the Oxford International Encyclopedia of Linguistics, and his joint work with Geoffrey Pullum, "The X-bar Theory of Phrase Structure", formally reconstructed that then-popular linguistic theory. == Awards and honors == 2009: ACM Distinguished Member == Monographs == Semantics. Springer Nature, 2020. ISBN 978-3-319-65644-1 Mathematical Linguistics. Springer Verlag, in the series Advanced Information and Knowledge Processing, November 2007. ISBN 978-1-84628-985-9 Hardbound, approximately 300 pages. See description. Formal Phonology. In the series Outstanding Dissertations in Linguistics, Garland Publishing, 1994, ISBN 0-8153-1730-1, hardbound, 240 pages Contents, Preface, Introduction (20 pages) On Hungarian Morphology. In the series Linguistica, Hungarian Academy of Sciences, 1994, ISBN 963-8461-73-X, paperbound, 174 pages Contents, Preface, Introduction (10 pages) == Books edited == Oxford International Encyclopedia of Linguistics (Mathematical Linguistics Area Editor under Editor in Chief William Frawley). 4 volumes, Oxford University Press, 2003, ISBN 978-0-19-513977-8. Proceedings of the HLT-NAACL Workshop on the Analysis of Geographic References. Jointly with Beth Sundheim. Association for Computational Linguistics, 2003, ISBN 1-932432-04-3 (WS9), paperbound, vi+81 pages. See related material. Extended Finite State Models of Language (editor). In the series Studies in Natural Language Processing, Cambridge University Press, 1999, ISBN 0-521-63198-X, hardbound, x+278 pages Contents, Introduction (7 pages). == Selected papers == Digital Language Death. PLoS ONE 8(10): e77056, 2012. [1] Hunmorph: open source word analysis (Jointly with V. Tron, Gy. Gyepesi, P. Halacsy, L. Nemeth, and D. Varga). In Proc. ACL 2005 Software Workshop 77-85 [2] Leveraging the open source ispell codebase for minority language analysis (Jointly with P. Halacsy, L. Nemeth, A. Rung, I. Szakadat, and V. Tron). In J. Carson-Berndsen (ed): Proc. SALTMIL 2004 56-59 [3] Explicit Finitism, International Journal of Theoretical Physics 2003/2 301-307 [4] Mathematical Linguistics (Jointly with G.K. Pullum) In W. Frawley (ed): Oxford International Encyclopedia of Linguistics, Oxford University Press 2003, v3 17-20 [5] Optical Character Recognition, In W. Frawley (ed): Oxford International Encyclopedia of Linguistics, Oxford University Press 2003, v3 33-34 [6] How many words are there? Glottometrics 2002/4 61-86 [7] Zipf's law outside the middle range Proc. Sixth Meeting on Mathematics of Language University of Central Florida, 1999 347-356 [8] A Robust, Language-Independent OCR System. (Jointly with Z. Lu, I. Bazzi, J. Makhoul, P. Natarajan, and R. Schwartz) In: Robert J. Mericsko (ed): Proc. 27th AIPR Workshop: Advances in Computer-Assisted Recognition SPIE Proceedings 3584 1999 [9] Quantitative Comparison of Languages. Grammars 1998/2 155-165 [10] The generative power of feature geometry. Annals of Mathematics and Artificial Intelligence 8 1993 37-46 [11] The X-bar Theory of Phrase Structure. (Jointly with G.K. Pullum) Language 66 1990 24-50 [12]
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Ziad Obermeyer

Ziad Obermeyer (Arabic: زياد أوبرماير) is a Lebanese American physician and researcher whose work focuses on machine learning, health policy, and clinical decision-making in medicine. He is the Blue Cross of California Distinguished Associate Professor at the UC Berkeley School of Public Health, a Chan Zuckerberg Biohub investigator, and a research associate at the National Bureau of Economic Research. He is known for his research on racial bias in health care algorithms and the use of artificial intelligence in health care. == Early life and education == Obermeyer was born in Beirut, Lebanon, and raised in Cambridge, Massachusetts. He earned a Bachelor of Arts degree from Harvard College and a Master of Philosophy (M.Phil.) in History and Science from the University of Cambridge. He received his Doctor of Medicine (M.D.) from Harvard Medical School in 2008. Before pursuing medicine, Obermeyer worked as a consultant at McKinsey & Company, advising pharmaceutical and global health clients in New Jersey, Geneva, and Tokyo. After completing his medical degree, he trained as an emergency physician at Mass General Brigham (MGB) in Boston, Massachusetts. He later continued practicing emergency medicine at the Fort Defiance Indian Hospital on the Navajo Nation in Arizona. == Academic career == Obermeyer served as an Assistant Professor at Harvard Medical School from 2014 to 2020. In 2020, he joined the University of California, Berkeley as an Associate Professor and the Blue Cross of California Distinguished Professor at the School of Public Health. == Research focus == === Algorithmic racial bias in healthcare === In 2019, Obermeyer and economist Sendhil Mullainathan examined a commercial healthcare algorithm by UnitedHealth Group, used in hospitals and by insurers to identify patients with complex health needs. The study found that the algorithm underestimated the health needs of Black patients compared to white patients with similar conditions and that reformulating it would reduce racial bias. In 2020, Obermeyer analyzed an algorithm used to allocate CARE Act relief funding to hospitals. The study identified allocation patterns that favored hospitals with higher revenues over hospitals serving larger numbers of COVID-19 patients who are predominantly Black. === Clinical decision-making === In 2021, Obermeyer and colleagues examined physician decision-making in cardiac care using machine learning models. The study found that physicians misdiagnose cases when they rely on symptoms representative of a heart attack, such as chest pain, over other symptoms. === Pain assessment === Obermeyer developed a deep learning approach to investigate the severity of osteoarthritis in underserved communities. == Policy and regulatory work == Following the publication of the 2019 algorithmic racial bias study, the New York Department of Financial Services and Department of Health launched an investigation into UnitedHealth Group's algorithm, requesting that the company cease using it, citing discriminatory business practices. Also related to this study, in December 2019, Democratic Senators Cory Booker and Ron Wyden released letters to the Federal Trade Commission and Centers for Medicare and Medicaid Services asking to investigate potential discrimination in decision-making algorithms against marginalized communities in healthcare. The senators also wrote to major healthcare companies, including Aetna and Blue Cross Blue Shield, about their internal safeguards against racial bias in their technology. In 2021, Obermeyer and colleagues at the University of Chicago Booth School of Business released the Algorithmic Bias Playbook, a resource for policymakers and technical teams working in healthcare on how to measure and mitigate algorithmic racial bias. Obermeyer testified before the U.S. Senate Financial Committee in February 2024 on artificial intelligence in healthcare, recommending transparency requirements for AI developers and independent algorithm evaluations. In December 2025, he testified before the United States House Committee on Oversight and Government Reform on the role of AI in affordable healthcare and the impact of its integration on the workforce. == Organizations == In 2021, Obermeyer cofounded Nightingale Open Science, a non-profit that creates new medical imaging datasets available for research, and Dandelion Health, a health data analytics company. In June 2023, the company launched a program to audit and evaluate the performance of algorithms to identify potential racial, ethnic, and geographic bias, funded by the Gordon and Betty Moore Foundation and the SCAN Foundation. Dandelion Health partnered with the American Heart Association in 2025 to power an AI assessment lab for cardiovascular algorithms. Obermeyer is a founding faculty member of the University of California, Berkeley–University of California, San Francisco joint program in computational precision health. == Recognition == TIME magazine named Obermeyer one of the 100 most influential people in artificial intelligence in 2023. He has served as a Chan Zuckerberg Biohub Investigator since 2022, and as a Research Associate at the National Bureau of Economic Research since 2023. He was designated an Emerging Leader by the National Academy of Medicine in 2020. Obermeyer's racial bias study received the Willard G. Manning Memorial Award for the Best Research in Health Econometrics from the American Society of Health Economists (ASHEcon) in 2021 and the Responsible Business Education Award from the Financial Times in 2022.
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Two-way finite automaton

In computer science, in particular in automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. == Two-way deterministic finite automaton == A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value indicating whether the machine will move its position in the input to the left, right, or stay at the same position. Equivalently, 2DFAs can be seen as read-only Turing machines with no work tape, only a read-only input tape. 2DFAs were introduced in a seminal 1959 paper by Rabin and Scott, who proved them to have equivalent power to one-way DFAs. That is, any formal language which can be recognized by a 2DFA can be recognized by a DFA which only examines and consumes each character in order. Since DFAs are obviously a special case of 2DFAs, this implies that both kinds of machines recognize precisely the class of regular languages. However, the equivalent DFA for a 2DFA may require exponentially many states, making 2DFAs a much more practical representation for algorithms for some common problems. 2DFAs are also equivalent to read-only Turing machines that use only a constant amount of space on their work tape, since any constant amount of information can be incorporated into the finite control state via a product construction (a state for each combination of work tape state and control state). == Formal description == Formally, a two-way deterministic finite automaton can be described by the following 8-tuple: M = ( Q , Σ , L , R , δ , s , t , r ) {\displaystyle M=(Q,\Sigma ,L,R,\delta ,s,t,r)} where Q {\displaystyle Q} is the finite, non-empty set of states Σ {\displaystyle \Sigma } is the finite, non-empty set of input symbols L {\displaystyle L} is the left endmarker R {\displaystyle R} is the right endmarker δ : Q × ( Σ ∪ { L , R } ) → Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow Q\times \{\mathrm {left,right} \}} s {\displaystyle s} is the start state t {\displaystyle t} is the end state r {\displaystyle r} is the reject state In addition, the following two conditions must also be satisfied: For all q ∈ Q {\displaystyle q\in Q} δ ( q , L ) = ( q ′ , r i g h t ) {\displaystyle \delta (q,L)=(q^{\prime },\mathrm {right} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} δ ( q , R ) = ( q ′ , l e f t ) {\displaystyle \delta (q,R)=(q^{\prime },\mathrm {left} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} It says that there must be some transition possible when the pointer reaches either end of the input word. For all symbols σ ∈ Σ ∪ { L } {\displaystyle \sigma \in \Sigma \cup \{L\}} δ ( t , σ ) = ( t , R ) {\displaystyle \delta (t,\sigma )=(t,R)} δ ( r , σ ) = ( r , R ) {\displaystyle \delta (r,\sigma )=(r,R)} δ ( t , R ) = ( t , L ) {\displaystyle \delta (t,R)=(t,L)} δ ( r , R ) = ( r , L ) {\displaystyle \delta (r,R)=(r,L)} It says that once the automaton reaches the accept or reject state, it stays in there forever and the pointer goes to the right most symbol and cycles there infinitely. == Two-way nondeterministic finite automaton == A two-way nondeterministic finite automaton (2NFA) may have multiple transitions defined in the same configuration. Its transition function is δ : Q × ( Σ ∪ { L , R } ) → 2 Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow 2^{Q\times \{\mathrm {left,right} \}}} . Like a standard one-way NFA, a 2NFA accepts a string if at least one of the possible computations is accepting. Like the 2DFAs, the 2NFAs also accept only regular languages. == Two-way alternating finite automaton == A two-way alternating finite automaton (2AFA) is a two-way extension of an alternating finite automaton (AFA). Its state set is Q = Q ∃ ∪ Q ∀ {\displaystyle Q=Q_{\exists }\cup Q_{\forall }} where Q ∃ ∩ Q ∀ = ∅ {\displaystyle Q_{\exists }\cap Q_{\forall }=\emptyset } . States in Q ∃ {\displaystyle Q_{\exists }} and Q ∀ {\displaystyle Q_{\forall }} are called existential resp. universal. In an existential state a 2AFA nondeterministically chooses the next state like an NFA, and accepts if at least one of the resulting computations accepts. In a universal state 2AFA moves to all next states, and accepts if all the resulting computations accept. == State complexity tradeoffs == Two-way and one-way finite automata, deterministic and nondeterministic and alternating, accept the same class of regular languages. However, transforming an automaton of one type to an equivalent automaton of another type incurs a blow-up in the number of states. Christos Kapoutsis determined that transforming an n {\displaystyle n} -state 2DFA to an equivalent DFA requires n ( n n − ( n − 1 ) n ) {\displaystyle n(n^{n}-(n-1)^{n})} states in the worst case. If an n {\displaystyle n} -state 2DFA or a 2NFA is transformed to an NFA, the worst-case number of states required is ( 2 n n + 1 ) = O ( 4 n n ) {\displaystyle {\binom {2n}{n+1}}=O\left({\frac {4^{n}}{\sqrt {n}}}\right)} . Ladner, Lipton and Stockmeyer. proved that an n {\displaystyle n} -state 2AFA can be converted to a DFA with 2 n 2 n {\displaystyle 2^{n2^{n}}} states. The 2AFA to NFA conversion requires 2 Θ ( n log ⁡ n ) {\displaystyle 2^{\Theta (n\log n)}} states in the worst case, see Geffert and Okhotin. It is an open problem whether every 2NFA can be converted to a 2DFA with only a polynomial increase in the number of states. The problem was raised by Sakoda and Sipser, who compared it to the P vs. NP problem in the computational complexity theory. Berman and Lingas discovered a formal relation between this problem and the L vs. NL open problem, see Kapoutsis for a precise relation. == Sweeping automata == Sweeping automata are 2DFAs of a special kind that process the input string by making alternating left-to-right and right-to-left sweeps, turning only at the endmarkers. Sipser constructed a sequence of languages, each accepted by an n-state NFA, yet which is not accepted by any sweeping automata with fewer than 2 n {\displaystyle 2^{n}} states. == Two-way quantum finite automaton == The concept of 2DFAs was in 1997 generalized to quantum computing by John Watrous's "On the Power of 2-Way Quantum Finite State Automata", in which he demonstrates that these machines can recognize nonregular languages and so are more powerful than DFAs. == Two-way pushdown automaton == A pushdown automaton that is allowed to move either way on its input tape is called two-way pushdown automaton (2PDA); it has been studied by Hartmanis, Lewis, and Stearns (1965). Aho, Hopcroft, Ullman (1968) and Cook (1971) characterized the class of languages recognizable by deterministic (2DPDA) and non-deterministic (2NPDA) two-way pushdown automata; Gray, Harrison, and Ibarra (1967) investigated the closure properties of these languages.
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Comparison of vector graphics editors

A number of vector graphics editors exist for various platforms. Potential users of these editors will make comparisons based on factors such as the availability for the user's platform, the software license, the feature set, the merits of the user interface (UI) and the focus of the program. Some programs are more suitable for artistic work while others are better for technical drawings. Another important factor is the application's support of various vector and bitmap image formats for import and export. The tables in this article compare general and technical information for a number of vector graphics editors. See the article on each editor for further information. This article is neither all-inclusive nor necessarily up-to-date. == Some editors in detail == Adobe Fireworks (formerly Macromedia Fireworks) is a vector editor with bitmap editing capabilities with its main purpose being the creation of graphics for Web and screen. Fireworks supports RGB color scheme and has no CMYK support. This means it is mostly used for screen design. The native Fireworks file format is editable PNG (FWPNG or PNG). Adobe Fireworks has a competitive price, but its features can seem limited in comparison with other products. It is easier to learn than other products and can produce complex vector artwork. The Fireworks editable PNG file format is not supported by other Adobe products. Fireworks can manage the PSD and AI file formats which enables it to be integrated with other Adobe apps. Fireworks can also open FWPNG/PNG, PSD, AI, EPS, JPG, GIF, BMP, TIFF file formats, and save/export to FWPNG/PNG, PSD, AI (v.8), FXG (v.2.0), JPG, GIF, PDF, SWF and some others. Some support for exporting to SVG is available via a free Export extension. On May 6, 2013, Adobe announced that Fireworks would be phased out. Adobe Flash (formerly a Macromedia product) has straightforward vector editing tools that make it easier for designers and illustrators to use. The most important of these tools are vector lines and fills with bitmap-like selectable areas, simple modification of curves via the "selection" or the control points/handles through "direct selection" tools. Flash uses Actionscript for OOP, and has full XML functionality through E4X support. Adobe FreeHand (formerly Macromedia Freehand and Aldus Freehand) is mainly used by professional graphic designers. The functionality of FreeHand includes the flexibility of the application in the wide design environment, catering to the output needs of both traditional image reproduction methods and to contemporary print and digital media with its page-layout capabilities and text attribute controls. Specific functions of FreeHand include a superior image-tracing operation for vector editing, page layout features within multiple-page documents, and embedding custom print-settings (such as variable halftone-screen specifications within a single graphic, etc.) to each document independent of auxiliary printer-drivers. User-operation is considered to be more suited for designers with an artistic background compared to designers with a technical background. When being marketed, FreeHand lacked the promotional backing, development and PR support in comparison to other similar products. FreeHand was transferred to the classic print group after Macromedia was purchased by Adobe in 2005. On May 16, 2007, Adobe announced that no further updates to Freehand would be developed but continues to sell FreeHand MX as a Macromedia product. FreeHand continues to run on Mac OS X Snow Leopard (using an Adobe fix) and on Windows 7. For macOS, Affinity Designer is able to open version 10 & MX Freehand files. Adobe Illustrator is a commonly used editor because of Adobe's market dominance, but is more expensive than other similar products. It is primarily developed consistently in line with other Adobe products and is best integrated with Adobe's Creative Suite packages. The ai file format is proprietary, but some vector editors can open and save in that format. Illustrator imports over two dozen formats, including PSD, PDF and SVG, and exports AI, PDF, SVG, SVGZ, GIF, JPG, PNG, WBMP, and SWF. However, the user must be aware of unchecking the "Preserve Illustrator Editing Capabilities" option if generating interoperable SVG files is desired. Affinity Designer by Serif Europe (the successor to their previous product, DrawPlus) is non-subscription-based software that is often described as an alternative to Adobe Illustrator. The application can open Portable Document Format (PDF), Adobe Photoshop, and Adobe Illustrator files, as well as export to those formats and to the Scalable Vector Graphics (SVG) and Encapsulated PostScript (EPS) formats. It also supports import from some Adobe Freehand files (specifically versions 10 & MX). Apache OpenOffice Draw is the vector graphics editor of the Apache OpenOffice open source office suite. It supports many import and export file formats and is available for multiple desktop operating systems. Boxy SVG is a chromium-based vector graphics editor for creating illustrations, as well as logos, icons, and other elements of graphic design. It is primarily focused on editing drawings in the SVG file format. The program is available as both a web app and a desktop application for Windows, macOS, ChromeOS, and Linux-based operating systems. Collabora Online Draw is the vector graphics editor of the Collabora Online open source office suite. It supports many import and export file formats and is accessible via any modern web browser, it also supports desktop editing features, Collabora Office is available for desktop and mobile operating systems, it is the enterprise ready version of LibreOffice. ConceptDraw PRO is a business diagramming tool and vector graphics editor available for both Windows and macOS. It supports multi-page documents, and includes an integrated presentation mode. ConceptDraw PRO supports imports and exports several formats, including Microsoft Visio and Microsoft PowerPoint. Corel Designer (originally Micrografx Designer) is one of the earliest vector-based graphics editors for the Microsoft Windows platform. The product is mainly used for the creation of engineering drawings and is shipped with extensive libraries for the needs of engineers. It is also flexible enough for most vector graphics design applications. CorelDRAW is an editor used in the graphic design, sign making and fashion design industries. CorelDRAW is capable of limited interoperation by reading file formats from Adobe Illustrator. CorelDRAW has over 50 import and export filters, on-screen and dialog box editing and the ability to create multi-page documents. It can also generate TrueType and Type 1 fonts, although refined typographic control is better suited to a more specific application. Some other features of CorelDRAW include the creation and execution of VBA macros, viewing of colour separations in print preview mode and integrated professional imposing options. Dia is a free and open-source diagramming and vector graphics editor available for Windows, Linux and other Unix-based computer operating systems. Dia has a modular design and several shape packages for flowcharting, network diagrams and circuit diagrams. Its design was inspired by Microsoft Visio, although it uses a Single Document Interface similar to other GNOME software (such as GIMP). DrawPlus, first built for the Windows platform in 1993, has matured into a full featured vector graphics editor for home and professional users. Also available as a feature-limited free 'starter edition': DrawPlus SE. DrawPlus developers, Serif Europe, have now ceased its development in order to focus on its successor, Affinity Designer. Edraw Max is a cross-platform diagram software and vector graphics editor available for Windows, Mac and Linux. It supports kinds of diagram types. It supports imports and exports SVG, PDF, HTML, Multiple page TIFF, Microsoft Visio and Microsoft PowerPoint. Embroidermodder is a free machine embroidery software tool that supports a variety of formats and allows the user to add custom modifications to their embroidery designs. Fatpaint is a free, light-weight, browser-based graphic design application with built-in vector drawing tools. It can be accessed through any browser with Flash 9 installed. Its integration with Zazzle makes it particularly suitable for people who want to create graphics for custom printed products such as T-shirts, mugs, iPhone cases, flyers and other promotional products. Figma is a collaborative web-based online vector graphics editor, used primarily for UX design and prototyping. GIMP, which works mainly with raster images, offers a limited set of features to create and record SVG files. It can also load and handle SVG files created with other software like Inkscape. Inkscape is a free and open-source vector editor with the primary native format being SVG. Inkscape is available for Linux, Windows, Mac OS X, and
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Structured support vector machine

The structured supportvector machine is a machine learning algorithm that generalizes the support vector machine (SVM) classifier. Whereas the SVM classifier supports binary classification, multiclass classification and regression, the structured SVM allows training of a classifier for general structured output labels. As an example, a sample instance might be a natural language sentence, and the output label is an annotated parse tree. Training a classifier consists of showing pairs of correct sample and output label pairs. After training, the structured SVM model allows one to predict for new sample instances the corresponding output label; that is, given a natural language sentence, the classifier can produce the most likely parse tree. == Training == For a set of n {\displaystyle n} training instances ( x i , y i ) ∈ X × Y {\displaystyle ({\boldsymbol {x}}_{i},y_{i})\in {\mathcal {X}}\times {\mathcal {Y}}} , i = 1 , … , n {\displaystyle i=1,\dots ,n} from a sample space X {\displaystyle {\mathcal {X}}} and label space Y {\displaystyle {\mathcal {Y}}} , the structured SVM minimizes the following regularized risk function. min w ‖ w ‖ 2 + C ∑ i = 1 n max y ∈ Y ( 0 , Δ ( y i , y ) + ⟨ w , Ψ ( x i , y ) ⟩ − ⟨ w , Ψ ( x i , y i ) ⟩ ) {\displaystyle {\underset {\boldsymbol {w}}{\min }}\quad \|{\boldsymbol {w}}\|^{2}+C\sum _{i=1}^{n}{\underset {y\in {\mathcal {Y}}}{\max }}\left(0,\Delta (y_{i},y)+\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y)\rangle -\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y_{i})\rangle \right)} The function is convex in w {\displaystyle {\boldsymbol {w}}} because the maximum of a set of affine functions is convex. The function Δ : Y × Y → R + {\displaystyle \Delta :{\mathcal {Y}}\times {\mathcal {Y}}\to \mathbb {R} _{+}} measures a distance in label space and is an arbitrary function (not necessarily a metric) satisfying Δ ( y , z ) ≥ 0 {\displaystyle \Delta (y,z)\geq 0} and Δ ( y , y ) = 0 ∀ y , z ∈ Y {\displaystyle \Delta (y,y)=0\;\;\forall y,z\in {\mathcal {Y}}} . The function Ψ : X × Y → R d {\displaystyle \Psi :{\mathcal {X}}\times {\mathcal {Y}}\to \mathbb {R} ^{d}} is a feature function, extracting some feature vector from a given sample and label. The design of this function depends very much on the application. Because the regularized risk function above is non-differentiable, it is often reformulated in terms of a quadratic program by introducing one slack variable ξ i {\displaystyle \xi _{i}} for each sample, each representing the value of the maximum. The standard structured SVM primal formulation is given as follows. min w , ξ ‖ w ‖ 2 + C ∑ i = 1 n ξ i s.t. ⟨ w , Ψ ( x i , y i ) ⟩ − ⟨ w , Ψ ( x i , y ) ⟩ + ξ i ≥ Δ ( y i , y ) , i = 1 , … , n , ∀ y ∈ Y {\displaystyle {\begin{array}{cl}{\underset {{\boldsymbol {w}},{\boldsymbol {\xi }}}{\min }}&\|{\boldsymbol {w}}\|^{2}+C\sum _{i=1}^{n}\xi _{i}\\{\textrm {s.t.}}&\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y_{i})\rangle -\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y)\rangle +\xi _{i}\geq \Delta (y_{i},y),\qquad i=1,\dots ,n,\quad \forall y\in {\mathcal {Y}}\end{array}}} == Inference == At test time, only a sample x ∈ X {\displaystyle {\boldsymbol {x}}\in {\mathcal {X}}} is known, and a prediction function f : X → Y {\displaystyle f:{\mathcal {X}}\to {\mathcal {Y}}} maps it to a predicted label from the label space Y {\displaystyle {\mathcal {Y}}} . For structured SVMs, given the vector w {\displaystyle {\boldsymbol {w}}} obtained from training, the prediction function is the following. f ( x ) = argmax y ∈ Y ⟨ w , Ψ ( x , y ) ⟩ {\displaystyle f({\boldsymbol {x}})={\underset {y\in {\mathcal {Y}}}{\textrm {argmax}}}\quad \langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}},y)\rangle } Therefore, the maximizer over the label space is the predicted label. Solving for this maximizer is the so-called inference problem and similar to making a maximum a-posteriori (MAP) prediction in probabilistic models. Depending on the structure of the function Ψ {\displaystyle \Psi } , solving for the maximizer can be a hard problem. == Separation == The above quadratic program involves a very large, possibly infinite number of linear inequality constraints. In general, the number of inequalities is too large to be optimized over explicitly. Instead the problem is solved by using delayed constraint generation where only a finite and small subset of the constraints is used. Optimizing over a subset of the constraints enlarges the feasible set and will yield a solution that provides a lower bound on the objective. To test whether the solution w {\displaystyle {\boldsymbol {w}}} violates constraints of the complete set inequalities, a separation problem needs to be solved. As the inequalities decompose over the samples, for each sample ( x i , y i ) {\displaystyle ({\boldsymbol {x}}_{i},y_{i})} the following problem needs to be solved. y n ∗ = argmax y ∈ Y ( Δ ( y i , y ) + ⟨ w , Ψ ( x i , y ) ⟩ − ⟨ w , Ψ ( x i , y i ) ⟩ − ξ i ) {\displaystyle y_{n}^{}={\underset {y\in {\mathcal {Y}}}{\textrm {argmax}}}\left(\Delta (y_{i},y)+\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y)\rangle -\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y_{i})\rangle -\xi _{i}\right)} The right hand side objective to be maximized is composed of the constant − ⟨ w , Ψ ( x i , y i ) ⟩ − ξ i {\displaystyle -\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y_{i})\rangle -\xi _{i}} and a term dependent on the variables optimized over, namely Δ ( y i , y ) + ⟨ w , Ψ ( x i , y ) ⟩ {\displaystyle \Delta (y_{i},y)+\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y)\rangle } . If the achieved right hand side objective is smaller or equal to zero, no violated constraints for this sample exist. If it is strictly larger than zero, the most violated constraint with respect to this sample has been identified. The problem is enlarged by this constraint and resolved. The process continues until no violated inequalities can be identified. If the constants are dropped from the above problem, we obtain the following problem to be solved. y i ∗ = argmax y ∈ Y ( Δ ( y i , y ) + ⟨ w , Ψ ( x i , y ) ⟩ ) {\displaystyle y_{i}^{}={\underset {y\in {\mathcal {Y}}}{\textrm {argmax}}}\left(\Delta (y_{i},y)+\langle {\boldsymbol {w}},\Psi ({\boldsymbol {x}}_{i},y)\rangle \right)} This problem looks very similar to the inference problem. The only difference is the addition of the term Δ ( y i , y ) {\displaystyle \Delta (y_{i},y)} . Most often, it is chosen such that it has a natural decomposition in label space. In that case, the influence of Δ {\displaystyle \Delta } can be encoded into the inference problem and solving for the most violating constraint is equivalent to solving the inference problem.
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Hartmut Neven

Hartmut Neven (born 1964) is a German American scientist working in quantum computing, computer vision, robotics and computational neuroscience. He is best known for his work in face and object recognition and his contributions to quantum machine learning. He is currently Vice President of Engineering at Google where he leads the Quantum Artificial Intelligence Lab, which he founded in 2012. == Education == Hartmut Neven studied Physics and Economics in Brazil, Köln, Paris, Tübingen and Jerusalem. He wrote his Master thesis on a neuronal model of object recognition at the Max Planck Institute for Biological Cybernetics under Valentino Braitenberg. In 1996 he received his Ph.D. in Physics from the Institute for Neuroinformatics at the Ruhr University in Bochum, Germany, for a thesis on "Dynamics for vision-guided autonomous mobile robots" written under the tutelage of Christoph von der Malsburg. He received a scholarship from the Studienstiftung des Deutschen Volkes, Germany's most prestigious scholarship foundation. == Work == In 1998 Neven became research professor of computer science at the University of Southern California at the Laboratory for Biological and Computational Vision. In 2003 he returned as the head of the Laboratory for Human-Machine Interfaces at USC's Information Sciences Institute. === Face recognition, avatars and face filters === Neven co-founded two companies, Eyematic for which he served as CTO and Neven Vision which he initially led as CEO. At Eyematic he developed face recognition technology and real-time facial feature analysis for avatar animation. Teams led by Neven have repeatedly won top scores in government sponsored tests designed to determine the most accurate face recognition software. Face filters, now ubiquitous on mobile phones, were launched for the first time by Neven Vision on the networks of NTT DoCoMo and Vodafone Japan in 2003. Neven Vision also pioneered mobile visual search for camera phones. Neven Vision was acquired by Google in 2006. === Object recognition and adversarial images === At Google he managed teams responsible for advancing Google's visual search technologies. His team launched Google Goggles now Google Lens. The concept of adversarial patterns originated in his group when he tasked Christian Szegedy with a project to modify the pixel inputs of a deep neural network to lower the activity of select output nodes. The motivation was to use this technique for object localization which did not work out. But the idea gave rise to the fields of adversarial learning and DeepDream art. In 2013 his optical character recognition team won the ICDAR Robust Reading Competition by a wide margin and in 2014 the object recognition team won the ImageNet challenge. === Google Glass === Neven was a co-founder of the Google Glass project. His team completed the first prototype, codenamed Ant, in 2011. === Quantum Artificial Intelligence === In 2006 Neven started to explore the application of quantum computing to hard combinatorial problems arising in machine learning. In collaboration with D-Wave Systems he developed the first image recognition system based on quantum algorithms. It was demonstrated at SuperComputing07. At NIPS 2009 his team demonstrated the first binary classifier trained on a quantum processor. In 2012 together with Pete Worden at NASA Ames he founded the Quantum Artificial Intelligence Laboratory. In 2014 he invited John M. Martinis and his group at UC Santa Barbara to join the lab to start a fabrication facility for superconducting quantum processors. The Quantum Artificial Intelligence team performed the first experimental demonstration of a scalable simulation of a molecule. In 2016 the team formulated an experiment to demonstrate quantum supremacy. Quantum supremacy was then declared by Google in October 2019. In 2023 Quantum AI researchers demonstrated that quantum error correction works in practice by showing for the first time that the error of a logical qubit decreases when increasing the number of physical qubits it is composed of. Google's quantum processors have been used to study the physics of quantum many body states that otherwise are challenging to prepare in a laboratory such as time crystals, traversable wormholes and non-Abelian anyons. ==== Neven's law ==== Neven's law states that the performance of quantum computers improves at a doubly exponential rate.
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Claire Cardie

Claire Cardie is an American computer scientist specializing in natural language processing. Since 2006, she has been a professor of computer science and information science at Cornell University, and from 2010 to 2011 she was the first Charles and Barbara Weiss Chair of Information Science at Cornell. Her research interests include coreference resolution and sentiment analysis. == Education and career == Cardie is a 1982 graduate of Yale University, majoring in computer science. After working for several companies as a computer programmer, she returned to graduate study in the late 1980s and completed her Ph.D. at the University of Massachusetts Amherst in 1994. Her dissertation, Domain-Specific Knowledge Acquisition for Conceptual Sentence Analysis, was supervised by Wendy Lehnert. She has been on the Cornell University faculty since 1994, initially in computer science and since 2005 also in information science. She was an assistant professor (1994–2000) and associate professor (2000–06), before being promoted to a full professorship in 2006. In 2007 she founded a start-up company, Appinions, and she was its chief scientist until 2015. Her doctoral students at Cornell have included Amit Singhal and Kiri Wagstaff. == Recognition == Cardie became a Fellow of the Association for Computational Linguistics in 2016. She was elected as an ACM Fellow in 2019 "for contributions to natural language processing, including coreference resolution, information and opinion extraction". She was named to the 2021 class of Fellows of the American Association for the Advancement of Science.
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IT operations analytics

In the fields of information technology (IT) and systems management, IT operations analytics (ITOA) is an approach or method to retrieve, analyze, and report data for IT operations. ITOA may apply big data analytics to large datasets to produce business insights. In 2014, Gartner predicted its use might increase revenue or reduce costs. By 2017, it predicted that 15% of enterprises will use IT operations analytics technologies. == Definition == IT operations analytics (ITOA) (also known as advanced operational analytics, or IT data analytics) technologies are primarily used to discover complex patterns in high volumes of often "noisy" IT system availability and performance data. Forrester Research defined IT analytics as "The use of mathematical algorithms and other innovations to extract meaningful information from the sea of raw data collected by management and monitoring technologies." Note, ITOA is different than AIOps, which focuses on applying artificial intelligence and machine learning to the applications of ITOA. == History == Operations research as a discipline emerged from the Second World War to improve military efficiency and decision-making on the battlefield. However, only with the emergence of machine learning tech in the early 2000s could an artificially intelligent operational analytics platform actually begin to engage in the high-level pattern recognition that could adequately serve business needs. A critical catalyst towards ITOA development was the rise of Google, which pioneered a predictive analytics model that represented the first attempt to read into patterns of human behavior on the Internet. IT specialists then applied predictive analytics to the IT Industry, coming forward with platforms that can sift through data to generate insights without the need for human intervention. Due to the mainstream embrace of cloud computing and the increasing desire for businesses to adopt more big data practices, the ITOA industry has grown significantly since 2010. A 2016 ExtraHop survey of large and mid-size corporations indicates that 65 percent of the businesses surveyed will seek to integrate their data silos either this year or the next. The current goals of ITOA platforms are to improve the accuracy of their APM services, facilitate better integration with the data, and to enhance their predictive analytics capabilities. == Applications == ITOA systems tend to be used by IT operations teams, and Gartner describes seven applications of ITOA systems: Root cause analysis: The models, structures and pattern descriptions of IT infrastructure or application stack being monitored can help users pinpoint fine-grained and previously unknown root causes of overall system behavior pathologies. Proactive control of service performance and availability: Predicts future system states and the impact of those states on performance. Problem assignment: Determines how problems may be resolved or, at least, direct the results of inferences to the most appropriate individuals, or communities in the enterprise for problem resolution. Service impact analysis: When multiple root causes are known, the analytics system's output is used to determine and rank the relative impact, so that resources can be devoted to correcting the fault in the most timely and cost-effective way possible. Complement best-of-breed technology: The models, structures and pattern descriptions of IT infrastructure or application stack being monitored are used to correct or extend the outputs of other discovery-oriented tools to improve the fidelity of information used in operational tasks (e.g., service dependency maps, application runtime architecture topologies, network topologies). Real time application behavior learning: Learns & correlates the behavior of Application based on user pattern and underlying Infrastructure on various application patterns, create metrics of such correlated patterns and store it for further analysis. Dynamically baselines threshold: Learns behavior of Infrastructure on various application user patterns and determines the Optimal behavior of the Infra and technological components, bench marks and baselines the low and high water mark for the specific environments and dynamically changes the bench mark baselines with the changing infra and user patterns without any manual intervention. == Types == In their Data Growth Demands a Single, Architected IT Operations Analytics Platform, Gartner Research describes five types of analytics technologies: Log analysis Unstructured text indexing, search and inference (UTISI) Topological analysis (TA) Multidimensional database search and analysis (MDSA) Complex operations event processing (COEP) Statistical pattern discovery and recognition (SPDR) == Tools and ITOA platforms == A number of vendors operate in the ITOA space:
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Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it, i.e. the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too high dimensional to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. == General explanation == Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to evaluate an integral over that variable, as its expected value or variance. Practically, an ensemble of chains is generally developed, starting from a set of points arbitrarily chosen and sufficiently distant from each other. These chains are stochastic processes of "walkers" which move around randomly according to an algorithm that looks for places with a reasonably high contribution to the integral to move into next, assigning them higher probabilities. Random walk Monte Carlo methods are a kind of random simulation or Monte Carlo method. However, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC are autocorrelated. Correlations of samples introduces the need to use the Markov chain central limit theorem when estimating the error of mean values. These algorithms create Markov chains such that they have an equilibrium distribution which is proportional to the function given. == History == The development of MCMC methods is deeply rooted in the early exploration of Monte Carlo (MC) techniques in the mid-20th century, particularly in physics. These developments were marked by the Metropolis algorithm proposed by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall Rosenbluth, Augusta H. Teller, and Edward Teller in 1953, which was designed to tackle high-dimensional integration problems using early computers. Then in 1970, W. K. Hastings generalized this algorithm and inadvertently introduced the component-wise updating idea, later known as Gibbs sampling. Simultaneously, the theoretical foundations for Gibbs sampling were being developed, such as the Hammersley–Clifford theorem from Julian Besag's 1974 paper. Although the seeds of MCMC were sown earlier, including the formal naming of Gibbs sampling in image processing by Stuart Geman and Donald Geman (1984) and the data augmentation method by Martin A. Tanner and Wing Hung Wong (1987), its "revolution" in mainstream statistics largely followed demonstrations of the universality and ease of implementation of sampling methods (especially Gibbs sampling) for complex statistical (particularly Bayesian) problems, spurred by increasing computational power and software like BUGS. This transformation was accompanied by significant theoretical advancements, such as Luke Tierney's (1994) rigorous treatment of MCMC convergence, and Jun S. Liu, Wong, and Augustine Kong's (1994, 1995) analysis of Gibbs sampler structure. Subsequent developments further expanded the MCMC toolkit, including particle filters (Sequential Monte Carlo) for sequential problems, Perfect sampling aiming for exact simulation (Jim Propp and David B. Wilson, 1996), RJMCMC (Peter J. Green, 1995) for handling variable-dimension models, and deeper investigations into convergence diagnostics and the central limit theorem. Overall, the evolution of MCMC represents a paradigm shift in statistical computation, enabling the analysis of numerous previously intractable complex models and continually expanding the scope and impact of statistics. == Mathematical setting == Suppose (Xn) is a Markov Chain in the general state space X {\displaystyle {\mathcal {X}}} with specific properties. We are interested in the limiting behavior of the partial sums: S n ( h ) = 1 n ∑ i = 1 n h ( X i ) {\displaystyle S_{n}(h)={\dfrac {1}{n}}\sum _{i=1}^{n}h(X_{i})} as n goes to infinity. Particularly, we hope to establish the Law of Large Numbers and the Central Limit Theorem for MCMC. In the following, we state some definitions and theorems necessary for the important convergence results. In short, we need the existence of invariant measure and Harris recurrent to establish the Law of Large Numbers of MCMC (Ergodic Theorem). And we need aperiodicity, irreducibility and extra conditions such as reversibility to ensure the Central Limit Theorem holds in MCMC. === Irreducibility and aperiodicity === Recall that in the discrete setting, a Markov chain is said to be irreducible if it is possible to reach any state from any other state in a finite number of steps with positive probability. However, in the continuous setting, point-to-point transitions have zero probability. In this case, φ-irreducibility generalizes irreducibility by using a reference measure φ on the measurable space ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} . Definition (φ-irreducibility) Given a measure φ {\displaystyle \varphi } defined on ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} , the Markov chain ( X n ) {\displaystyle (X_{n})} with transition kernel K ( x , y ) {\displaystyle K(x,y)} is φ-irreducible if, for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} with φ ( A ) > 0 {\displaystyle \varphi (A)>0} , there exists n {\displaystyle n} such that K n ( x , A ) > 0 {\displaystyle K^{n}(x,A)>0} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} (Equivalently, P x ( τ A < ∞ ) > 0 {\displaystyle P_{x}(\tau _{A}<\infty )>0} , here τ A = inf { n ≥ 1 ; X n ∈ A } {\displaystyle \tau _{A}=\inf\{n\geq 1;X_{n}\in A\}} is the first n {\displaystyle n} for which the chain enters the set A {\displaystyle A} ). This is a more general definition for irreducibility of a Markov chain in non-discrete state space. In the discrete case, an irreducible Markov chain is said to be aperiodic if it has period 1. Formally, the period of a state ω ∈ X {\displaystyle \omega \in {\mathcal {X}}} is defined as: d ( ω ) := g c d { m ≥ 1 ; K m ( ω , ω ) > 0 } {\displaystyle d(\omega ):=\mathrm {gcd} \{m\geq 1\,;\,K^{m}(\omega ,\omega )>0\}} For the general (non-discrete) case, we define aperiodicity in terms of small sets: Definition (Cycle length and small sets) A φ-irreducible Markov chain ( X n ) {\displaystyle (X_{n})} has a cycle of length d if there exists a small set C {\displaystyle C} , an associated integer M {\displaystyle M} , and a probability distribution ν M {\displaystyle \nu _{M}} such that d is the greatest common divisor of: { m ≥ 1 ; ∃ δ m > 0 such that C is small for ν m ≥ δ m ν M } . {\displaystyle \{m\geq 1\,;\,\exists \,\delta _{m}>0{\text{ such that }}C{\text{ is small for }}\nu _{m}\geq \delta _{m}\nu _{M}\}.} A set C {\displaystyle C} is called small if there exists m ∈ N ∗ {\displaystyle m\in \mathbb {N} ^{}} and a nonzero measure ν m {\displaystyle \nu _{m}} such that: K m ( x , A ) ≥ ν m ( A ) , ∀ x ∈ C , ∀ A ∈ B ( X ) . {\displaystyle K^{m}(x,A)\geq \nu _{m}(A),\quad \forall x\in C,\,\forall A\in {\mathcal {B}}({\mathcal {X}}).} === Harris recurrent === Definition (Harris recurrence) A set A {\displaystyle A} is Harris recurrent if P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ A {\displaystyle x\in A} , where η A = ∑ n = 1 ∞ I A ( X n ) {\displaystyle \eta _{A}=\sum _{n=1}^{\infty }\mathbb {I} _{A}(X_{n})} is the number of visits of the chain ( X n ) {\displaystyle (X_{n})} to the set A {\displaystyle A} . The chain ( X n ) {\displaystyle (X_{n})} is said to be Harris recurrent if there exists a measure ψ {\displaystyle \psi } such that the chain is ψ {\displaystyle \psi } -irreducible and every measurable set A {\displaystyle A} with ψ ( A ) > 0 {\displaystyle \psi (A)>0} is Harris recurrent. A useful criterion for verifying Harris recurrence is the following: Proposition If for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} , we have P x ( τ A < ∞ ) = 1 {\displaystyle P_{x}(\tau _{A}<\infty )=1} for every x ∈ A {\displaystyle x\in A} , then P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} , and the chain ( X n ) {\displaystyle (X_{n})} is Harris recurrent. This definition is only needed when the state space X {\displaystyle {\mathcal {X}}} is uncountable. In the countable case, recurrence corresponds to E x [ η x ] = ∞ {\displaystyle \mathbb {E} _{x}[\eta _{x}]=\infty } , which is equivalent to P x ( τ x < ∞ ) = 1 {\displaystyle P_{x}(\tau _{x}<\infty )=1} for all x ∈ X {\displaystyle x\i
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Timo Honkela

Timo Untamo Honkela (August 4, 1962 – May 9, 2020) was a computer scientist at the University of Helsinki, Aalto University School of Science and Aalto University School of Art, Design and Architecture. He holds a PhD from Helsinki University of Technology. From 2014 until 2018 he held a fixed-term professorship at the University of Helsinki. Before joining the University of Helsinki he worked as a non-tenured professor in two Schools of the Aalto University, The School of Art, Design and Architecture and the School of Science. He has presented his thoughts on his studies and work in the joint blog 375 Humanists. Timo Honkela conducted research on several areas related to knowledge engineering, cognitive modeling and natural language processing. Honkela was born in Kalajoki. From 1998 to 2000 he worked as a professor in the Aalto Media Lab. To the media Lab Honkela brought his expertise in Kohonen self-organising map (SOM) and worked closely with artist and designers around the topic. In 2001 Honkela collaborated with George Legrady to produce an interactive museum installation, Pockets Full of Memories to the Centre Georges Pompidou, National Museum of Modern Art in Paris. The concept, created by Legrady, provided for visitors a possibility to scan their own objects to a database and then organise them by Kohonen Self-Organizing Map algorithm. In 2017 Honkela published a book in Finnish. The book Rauhankone (English: Peace Machine) presents his idea of designing artificial intelligence and machine learning to serve humanity, in practice to help people to live in peace with each other. He died in Helsinki. == Publications == Timo Honkela, Wlodzislaw Duch, Mark Girolami and Samuel Kaski (editors): Artificial Neural Networks and Machine Learning, Springer, 2011. Jorma Laaksonen and Timo Honkela (editors): Advances in Self-Organizing Maps, Springer, 2011. Timo Honkela: Rauhankone. Gaudeamus, 2017.
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Mark Keane (cognitive scientist)

Mark Thomas Gerard Keane (Irish: Marcus Ó Cathain, born 3 July 1961, Dublin, Ireland) is a cognitive scientist and author of several books on human cognition and artificial intelligence, including Cognitive Psychology: A Student's Handbook (8 editions, with Michael Eysenck), Advances in the Psychology of Thinking (1992, with Ken Gilhooly), Novice Programming Environments (1992/2018, with Marc Eisenstadt and Tim Rajan), Advances in Case-Based Reasoning (1995, with J-P Haton and Michel Manago)., Case-Based Reasoning: Research & Development (2022, with N Wiratunga). == Education == Keane received a B.A. in Psychology from University College Dublin in 1982. He then received a Ph.D. from Trinity College Dublin in 1987. He then moved to postdoctoral positions in Queen Mary University of London and the Open University. == Academic career == He was a Lecturer in Psychology at Cardiff University. He became a lecturer in Computer Science at Trinity College Dublin in 1990, and became a fellow in 1994. Keane moved to become Chair of Computer Science at University College Dublin in 1998. In 2006, he was seconded to Science Foundation Ireland as Director of ICT, overseeing on a $700m research investment. He advised the Irish Government on its 3.7B euro Strategy for Science, Technology & Innovation (SSTI). From 2006 to 2007, he was Director General of Science Foundation Ireland before returning to University College Dublin where he was appointed VP of Innovation & Partnerships (2007-2009). Keane's research has been split between cognitive science and computer science. His cognitive science research has been in analogy, metaphor, conceptual combination and similarity. His computer science research has been in natural language processing, machine learning, case-based reasoning, text analytics and explainable artificial intelligence. He has been a PI in the Science Foundation Ireland funded Insight Centre for Data Analytics working on digital journalism and digital humanities. More recently, he was deputy director of the VistaMilk SFI Research Centre that is exploring precision agriculture in the dairy sector.
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ELMo

ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirectional LSTM which takes character-level as inputs and produces word-level embeddings, trained on a corpus of about 30 million sentences and 1 billion words. The architecture of ELMo accomplishes a contextual understanding of tokens. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. ELMo was historically important as a pioneer of self-supervised generative pretraining followed by fine-tuning, where a large model is trained to reproduce a large corpus, then the large model is augmented with additional task-specific weights and fine-tuned on supervised task data. It was an instrumental step in the evolution towards transformer-based language modelling. == Architecture == ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The forward part is a 2-layered LSTM with 4096 units and 512 dimension projections, and a residual connection from the first to second layer. The backward part has the same architecture, but processes the sequence back-to-front. The outputs from all 5 components (embedding layer, two forward LSTM layers, and two backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token. ELMo was pretrained on a text corpus of 1 billion words. The forward part is trained by repeatedly predicting the next token, and the backward part is trained by repeatedly predicting the previous token. After the ELMo model is pretrained, its parameters are frozen, except for the projection matrix, which can be fine-tuned to minimize loss on specific language tasks. This is an early example of the pretraining-fine-tune paradigm. The original paper demonstrated this by improving state of the art on six benchmark NLP tasks. === Contextual word representation === The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all subsequent tokens. The second forward LSTM would then incorporate those to further contextualize each token. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. For example, consider the sentenceShe went to the bank to withdraw money.In order to represent the token "bank", the model must resolve its polysemy in context. The first forward LSTM would process "bank" in the context of "She went to the", which would allow it to represent the word to be a location that the subject is going towards. The first backward LSTM would process "bank" in the context of "to withdraw money", which would allow it to disambiguate the word as referring to a financial institution. The second forward LSTM can then process "bank" using the representation vector provided by the first backward LSTM, thus allowing it to represent it to be a financial institution that the subject is going towards. == Historical context == ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each word in the document is treated independently, and its frequency is used as a feature for classification. This was computationally cheap but ignored the order of words and their context within the sentence. GloVe and Word2Vec built upon this by learning fixed vector representations (embeddings) for words based on their co-occurrence patterns in large text corpora. Like BERT (but unlike "bag of words" such as Word2Vec and GloVe), ELMo word embeddings are context-sensitive, producing different representations for words that share the same spelling. It was trained on a corpus of about 30 million sentences and 1 billion words. Previously, bidirectional LSTM was used for contextualized word representation. ELMo applied the idea to a large scale, achieving state of the art performance. After the 2017 publication of Transformer architecture, the architecture of ELMo was changed from a multilayered bidirectional LSTM to a Transformer encoder, giving rise to BERT. BERT has a similar pretrain-fine-tune workflow, but uses a Transformer with implications for more parallelizable training.
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Best AI Website Builders in 2026

Comparing the best AI website builder? An AI website builder 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 website builder 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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How to Choose an AI Photo Editor

In search of the best AI photo editor? An AI photo editor 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 photo editor 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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