AI Detector Spanish

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Display list

A display list, also called a command list in Direct3D 12 and a command buffer in Vulkan, is a series of graphics commands or instructions that are run when the list is executed. Systems that make use of display list functionality are called retained mode systems, while systems that do not are as opposed to immediate mode systems. In OpenGL, display lists are useful to redraw the same geometry or apply a set of state changes multiple times. This benefit is also used with Direct3D 12's bundle command lists. In Direct3D 12 and Vulkan, display lists are regularly used for per-frame recording and execution. == Origins in vector displays == The vector monitors or calligraphic displays of the 1960s and 1970s used electron beam deflection to draw line segments, points, and sometimes curves directly on a CRT screen. Because the image would immediately fade, it needed to be redrawn many times a second (storage tube CRTs retained the image until blanked, but they were unsuitable for interactive graphics). To refresh the display, a dedicated CPU called a Display Processor or Display Processing Unit (DPU) was used, which had a memory buffer for a "display list", "display file", or "display program" containing line segment coordinates and other information. Advanced Display Processors also supported control flow instructions, which were useful for drawing repetitive graphics such as text, and some could perform coordinate transformations such as 3D projection. == Home computer display list functionality == One of the earliest systems with a true display list was the Atari 8-bit computers. The display list (actually called so in Atari terminology) is a series of instructions for ANTIC, the video co-processor used in these machines. This program, stored in the computer's memory and executed by ANTIC in real-time, can specify blank lines, any of six text modes and eight graphics modes, which sections of the screen can be horizontally or vertically fine-scrolled, and trigger Display List Interrupts (called raster interrupts or HBI on other systems). The Amstrad PCW family contains a Display List function called the 'Roller RAM'. This is a 512-byte RAM area consisting of 256 16-bit pointers in RAM, one for each line of the 720 × 256 pixel display. Each pointer identifies the location of 90 bytes of monochrome pixels that hold the line's 720 pixel states. The 90 bytes of 8 pixel states are spaced at 8-byte intervals, so there are 7 unused bytes between each byte of pixel data. This suits how the text-orientated PCW constructs a typical screen buffer in RAM, where the first character's 8 rows are stored in the first 8 bytes, the second character's rows in the next 8 bytes, and so on. The Roller RAM was implemented to speed up display scrolling as it would have been unacceptably slow for its 3.4 MHz Z80 to move up the 23 KB display buffer 'by hand' i.e. in software. The Roller RAM starting entry used at the beginning of a screen refresh is controlled by a Z80-writable I/O register. Therefore, the screen can be scrolled simply by changing this I/O register. Another system using a Display List-like feature in hardware is the Amiga, which, not coincidentally, was also designed by some of the same people who developed the custom hardware for the Atari 8-bit computers. Once directed to produce a display mode, it would continue to do so automatically for every following scan line. The computer also included a dedicated co-processor, called "Copper", which ran a simple program or 'Copper List' intended for modifying hardware registers in sync with the display. The Copper List instructions could direct the Copper to wait for the display to reach a specific position on the screen, and then change the contents of hardware registers. In effect, it was a processor dedicated to servicing raster interrupts. The Copper was used by Workbench to mix multiple display modes (multiple resolutions and color palettes on the monitor at the same time), and by numerous programs to create rainbow and gradient effects on the screen. The Amiga Copper was also capable of reconfiguring the sprite engine mid-frame, with only one scanline of delay. This allowed the Amiga to draw more than its 8 hardware sprites, so long as the additional sprites did not share scanlines (or the one scanline gap) with more than 7 other sprites. i.e., so long as at least one sprite had finished drawing, another sprite could be added below it on the screen. Additionally, the later 32-bit AGA chipset allowed the drawing of bigger sprites (more pixels per row) while retaining the same multiplexing. The Amiga also had dedicated block-shifter ("blitter") hardware, which could draw larger objects into a framebuffer. This was often used in place of, or in addition to, sprites. In more primitive systems, the results of a display list can be simulated, though at the cost of CPU-intensive writes to certain display modes, color control, or other visual effect registers in the video device, rather than a series of rendering commands executed by the device. Thus, one must create the displayed image using some other rendering process, either before or while the CPU-driven display generation executes. In many cases, the image is also modified or re-rendered between frames. The image is then displayed in various ways, depending on the exact way in which the CPU-driven display code is implemented. Examples of the results possible on these older machines requiring CPU-driven video include effects such as Commodore 64/128's FLI mode, or Rainbow Processing on the ZX Spectrum. == Usage in OpenGL == To delimit a display list, the glNewList and glEndList functions are used, and to execute the list, the glCallList function is used. Almost all rendering commands that occur between the function calls are stored in the display list. Commands that affect the client state are not stored in display lists. Display lists are named with an integer value, and creating a display list with the same name as one already created overrides the first. The glNewList function expects two arguments: an integer representing the name of the list, and an enumeration for the compilation mode. The two modes include GL_COMPILE_AND_EXECUTE, which compiles and immediately executes, and GL_COMPILE, which only compiles the list. Display lists enable the use of the retained mode rendering pattern, which is a system in which graphics commands are recorded (retained) to execute in succession at a later time. This is contrary to immediate mode, where graphics commands are immediately executed on client calls. == Usage in Direct3D 12 == Command lists are created using the ID3D12Device::CreateCommandList function. Command lists may be created in several types: direct, bundle, compute, copy, video decode, video process, and video encoding. Direct command lists specify that a command list the GPU can execute, and doesn't inherit any GPU state. Bundles, are best used for storing and executing small sets of commands any number of times. This is used differently than regular command lists, where commands stored in a command list are typically executed only once. Compute command lists are used for general computations, with a common use being calculating mipmaps. A copy command list is strictly for copying and the video decode and video process command lists are for video decoding and processing respectively. Upon creation, command lists are in the recording state. Command lists may be re-used by calling the ID3D12GraphicsCommandList::Reset function. After recording commands, the command list must be transitioned out of the recording state by calling ID3D12GraphicsCommandList::Close. The command list is then executed by calling ID3D12CommandQueue::ExecuteCommandLists.
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International Computer Archive of Modern and Medieval English

The International Computer Archive of Modern and Medieval English (ICAME) is an international group of linguists and data scientists working in corpus linguistics to digitise English texts. The organisation was founded in Oslo, Norway in 1977 as the International Computer Archive of Modern English, before being renamed to its current title. Its primary objectives were: collecting and distributing information on English language material available for computer processing; and linguistic research completed or in progress on this material; compiling an archive of corpora to be located at the University of Bergen, from where copies of the material can be obtained at cost. The portal to their materials is hosted at the University of Bergen, where they have set out the aim of the organization to "collect and distribute information on English language material available for computer processing and on linguistic research to compile an archive of English text corpora in machine-readable form, and to make material available to research institutions." Creating computer corpora, i.e. collections of texts in machine-readable form, is the most accessible way to study both transcribed spoken language and various genres of written texts for modern scholars, including both "descriptive and more theoretically-minded linguists". The ICAME group hosts academic conferences that focus on corpus linguistic studies of historical changes and contemporary grammatical descriptions of English, and makes corpora of different varieties of English available to scholars, starting with editions of the 1960s Brown Corpus. Their first academic conference was held in Bergen, Norway in 1979, and scholars who were interested in corpus linguistics continued to meet each spring in different European and English-speaking countries. At these meetings, the compilation and distribution of corpora they enabled played a key role in the creation of the field of corpus linguistics in the 20th century, a precursor to current big data analytics. In summarizing the field, Kennedy's Introduction to Corpus Linguistics notes that "for corpus linguists with an interest in the description of English, the International Computer Archive of Modern and Medieval English has been the major resource". The influence of ICAME on the field has also be laid out in Facchinetti's history, Corpus Linguistics Twenty-five Years On. One influential resource that ICAME made available was a CD of 20 different corpora, including those covering different regional Englishes (such as the Australian Corpus of English, the Wellington Corpus of Spoken New Zealand English, the Kolhapur Corpus of Indian English, the Bergen Corpus of London Teenage Language (COLT), the Helsinki Corpus of Older Scots, and the International Corpus of English—East-African component), as well as versions of the Brown Corpus and the Lancaster-Bergen-Oslo (LOB) corpus tagged for part of speech. ICAME also published an annual journal, the ICAME Journal, formerly ICAME News, that contains articles, conference reports, reviews and notices related to corpus linguistics. The current editors of the ICAME Journal are Merja Kytö and Anna-Brita Stenström.I am wearing a tie clip in the shape of a monkey wrench... The story behind this peculiar piece of jewelry goes back to the early 60s when I was assembling the notorious Brown Corpus and others were using computers to make concordances of William Butler Yeats and other poets. One of my colleagues, a specialist in modem Irish literature, was heard to remark that anyone who would use a computer on good literature was nothing but a plumber. Some of my students responded by forming a linguistic plumber's union, the symbol of which was, of course, a monkey wrench.
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Jerome H. Friedman

Jerome Harold Friedman (born December 29, 1939) is an American statistician, consultant and Professor of Statistics at Stanford University, known for his contributions in the field of statistics and data mining. == Biography == Friedman studied at Chico State College for two years before transferring to the University of California, Berkeley in 1959, where he received his AB in Physics in 1962, and his PhD in High Energy Particle Physics in 1967. In 1968 he started his academic career as research physicist at the Lawrence Berkeley National Laboratory. In 1972 he started at Stanford University as leader of the Computation Research Group at the Stanford Linear Accelerator Center, where he would participate until 2003. In the year 1976–77 he was a visiting scientist at CERN in Geneva. From 1981 to 1984 he was visiting professor at the University of California, Berkeley. In 1982 he was appointed Professor of Statistics at Stanford University. In 1984 he was elected as a Fellow of the American Statistical Association. In 2002 he was awarded the SIGKDD Innovation Award by the Association for Computing Machinery (ACM). In 2010 he was elected as a member of the National Academy of Sciences (Applied mathematical sciences). == Publications == Friedman has authored and co-authored many publications in the field of data-mining including "nearest neighbor classification, logistical regressions, and high dimensional data analysis. His primary research interest is in the area of machine learning." A selection: Friedman, Jerome H. & Tukey, John W. (1974). "A projection pursuit algorithm for exploratory data analysis". IEEE Transactions on Computers. 23 (9): 881–890. doi:10.1109/T-C.1974.224051. OSTI 1442925. S2CID 7997450. Friedman, Jerome H. & Stuetzle, Werner (1981). "Projection pursuit regression". Journal of the American Statistical Association. 76 (376): 817–823. doi:10.1080/01621459.1981.10477729. OSTI 1445517. Friedman, Jerome H. (1991). "Multivariate adaptive regression splines". Annals of Statistics. 19 (1): 1–67. CiteSeerX 10.1.1.382.970. doi:10.1214/aos/1176347963. JSTOR 2241837. Friedman, Jerome H. (2001). "Greedy function approximation: a gradient boosting machine". Annals of Statistics. 29 (5): 1189–1232. doi:10.1214/aos/1013203451. JSTOR 2699986.
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Language and Computers

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

The Graphical Kernel System (GKS) is a 2D computer graphics system using vector graphics, introduced in 1977. It was suitable for making line and bar charts and similar tasks. A key concept was cross-system portability, based on an underlying coordinate system that could be represented on almost any hardware. GKS is best known as the basis for the graphics in the GEM GUI system used on the Atari ST and as part of Ventura Publisher. A draft international standard was circulated for review in September 1983. Final ratification of the standard was achieved in 1985, making it the first ISO graphics standard. A 3D system modelled on GKS was introduced as PHIGS, which saw some use in the 1980s and early 1990s. == Overview == GKS provides a set of drawing features for two-dimensional vector graphics suitable for charting and similar duties. The calls are designed to be portable across different programming languages, graphics devices and hardware, so that applications written to use GKS will be readily portable to many platforms and devices. GKS was fairly common on computer workstations in the 1980s and early 1990s. GKS formed the basis of Digital Research's GSX which evolved into VDI, one of the core components of GEM. GEM was the native GUI on the Atari ST and was occasionally seen on PCs, particularly in conjunction with Ventura Publisher. GKS was little used commercially outside these markets, but remains in use in some scientific visualization packages. It is also the underlying API defining the Computer Graphics Metafile. One popular application based on an implementation of GKS is the GR Framework, a C library for high-performance scientific visualization that has become a common plotting backend among Julia users. A main developer and promoter of the GKS was José Luis Encarnação, formerly director of the Fraunhofer Institute for Computer Graphics (IGD) in Darmstadt, Germany. GKS has been standardized in the following documents: ANSI standard ANSI X3.124 of 1985. ISO 7942:1985 standard, revised as ISO 7942:1985/Amd 1:1991 and ISO/IEC 7942-1:1994, as well as ISO/IEC 7942-2:1997, ISO/IEC 7942-3:1999 and ISO/IEC 7942-4:1998 The language bindings are ISO standard ISO 8651. GKS-3D (Graphical Kernel System for Three Dimensions) functional definition is ISO standard ISO 8805, and the corresponding C bindings are ISO/IEC 8806. The functionality of GKS is wrapped up as a data model standard in the STEP standard, section ISO 10303-46.
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RAMnets

RAMnets is one of the oldest practical neurally inspired classification algorithms. The RAMnets is also known as a type of "n-tuple recognition method" or "weightless neural network". == Algorithm == Consider (let us say N) sets of n distinct bit locations are selected randomly. These are the n-tuples. The restriction of a pattern to an n-tuple can be regarded as an n-bit number which, together with the identity of the n-tuple, constitutes a `feature' of the pattern. The standard n-tuple recognizer operates simply as follows: A pattern is classified as belonging to the class for which it has the most features in common with at least one training pattern of that class. This is the Θ {\displaystyle \Theta } = 0 case of a more general rule whereby the class assigned to unclassified pattern u is a c r g m a x ( ∑ i = 1 N Θ ( ∑ v ∈ D c δ ( α i ( u ) , α i ( v ) ) ) ) {\displaystyle {\begin{aligned}{\underset {c}{a}}rgmax(\sum _{i=1}^{N}\Theta (\sum _{v\in D_{c}}\delta (\alpha _{i}(u),\alpha _{i}(v))))\end{aligned}}} where Dc is the set of training patterns in class c, Θ ( x ) {\displaystyle \Theta (x)} = x for 0 ≤ x ≤ θ {\displaystyle 0\leq x\leq \theta } , Θ ( x ) = θ {\displaystyle \Theta (x)=\theta } for x ≥ θ {\displaystyle x\geq \theta } , δ i , j {\displaystyle \delta _{i,j}} is the Kronecker delta( δ i , j {\displaystyle \delta _{i,j}} =1 if i=j and 0 otherwise.)and ( α i ( u ) ) {\displaystyle (\alpha _{i}(u))} is the ith feature of the pattern u: ∑ j = 0 n − 1 u η i ( j ) 2 j {\displaystyle \sum _{j=0}^{n-1}u_{\eta }i(j)2^{j}} Here uk is the kth bit of u and u η i ( j ) {\displaystyle u_{\eta }i(j)} is the jth bit location of the ith n-tuple. With C classes to distinguish, the system can be implemented as a network of NC nodes, each of which is a random access memory (RAM); hence the term RAMnet. The memory content m c i α {\displaystyle m_{ci\alpha }} at address α {\displaystyle \alpha } of the ith node allocated to class c is set to m c i α {\displaystyle m_{ci\alpha }} = Θ ( ∑ v ∈ D c δ ( α , α i ( v ) ) ) {\displaystyle \Theta (\sum _{v\in D_{c}}\delta (\alpha ,\alpha _{i}(v)))} In the usual θ {\displaystyle \theta } = 1 case, the 1-bit content of m c i α {\displaystyle m_{ci\alpha }} is set if any pattern of Dc has feature α {\displaystyle \alpha } and unset otherwise. Recognition is accomplished by summing the contents of the nodes of each class at the addresses given by the features of the unclassified pattern. That is, pattern u is assigned to class a c r g m a x ( ∑ i = 1 N m c i α ( u ) ) {\displaystyle {\begin{aligned}{\underset {c}{a}}rgmax(\sum _{i=1}^{N}m_{ci\alpha }(u))\end{aligned}}} == RAM-discriminators and WiSARD == The RAMnets formed the basis of a commercial product known as WiSARD (Wilkie, Stonham and Aleksander Recognition Device) was the first artificial neural network machine to be patented. A RAM-discriminator consists of a set of X one-bit word RAMs with n inputs and a summing device (Σ). Any such RAM-discriminator can receive a binary pattern of X⋅n bits as input. The RAM input lines are connected to the input pattern by means of a biunivocal pseudo-random mapping. The summing device enables this network of RAMs to exhibit – just like other ANN models based on synaptic weights – generalization and noise tolerance. In order to train the discriminator one has to set all RAM memory locations to 0 and choose a training set formed by binary patterns of X⋅n bits. For each training pattern, a 1 is stored in the memory location of each RAM addressed by this input pattern. Once the training of patterns is completed, RAM memory contents will be set to a certain number of 0's and 1's. The information stored by the RAM during the training phase is used to deal with previous unseen patterns. When one of these is given as input, the RAM memory contents addressed by the input pattern are read and summed by Σ. The number r thus obtained, which is called the discriminator response, is equal to the number of RAMs that output 1. r reaches the maximum X if the input belongs to the training set. r is equal to 0 if no n-bit component of the input pattern appears in the training set (not a single RAM outputs 1). Intermediate values of r express a kind of “similarity measure” of the input pattern with respect to the patterns in the training set. A system formed by various RAM-discriminators is called WiSARD. Each RAM-discriminator is trained on a particular class of patterns, and classification by the multi-discriminator system is performed in the following way. When a pattern is given as input, each RAM-discriminator gives a response to that input. The various responses are evaluated by an algorithm which compares them and computes the relative confidence c of the highest response (e.g., the difference d between the highest response and the second highest response, divided by the highest response). A schematic representation of a RAM-discriminator and a 10 RAM-discriminator WiSARD is shown in Figure 1.
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Paola Velardi

Paola Velardi (born in Rome, April 26, 1955) is a full professor of computer science at Sapienza University in Rome, Italy. Her research encompasses Artificial Intelligence and specifically, natural language processing, machine learning business intelligence and semantic web. Velardi is one of the hundred female scientists included in the database "100esperte.it" (translated from Italian with "100 female experts"). This online, open database champions the recognition of top-rated female scientists in Science, Technology, Engineering and Mathematics (STEM) areas. Among her prestigious appointments and honors, her inclusion stands out —alongside 45 other international female scientists from the past, present, and future— in the Women in Science pavilion of UNESCO’s Virtual Science Museum. == Research == Paola Velardi's research activity has focused, since the early 1980s, on Artificial Intelligence, with a particular emphasis on natural language processing (NLP), Machine learning, and data mining. Her scientific contributions have evolved over time, following the sector's primary paradigms: Semantic Web and Ontologies: She is known for her pioneering work on semantic disambiguation and automated ontology learning, collaborating on the development of systems such as OntoLearn. Social Computing and Predictive Analysis: She has conducted research on extracting information from social media for epidemiological monitoring (syndromic surveillance) and for the identification of opinion leaders. In the educational field, she has developed machine learning models to predict the risk of student dropout. AI for Health and Elder Monitoring: She has coordinated projects to support frailty in the elderly, developing systems based on ambient intelligence and wearables to detect clinical and behavioral anomalies. She has also contributed to models for analyzing behavioral changes through dynamic clustering. Generative AI and Finance: More recently, her research has expanded into the use of generative AI and deep learning for finance, including benchmark studies on price trend prediction based on Limit Order Books (LOB) and the development of diffusion models for realistic market simulation (the TRADES project). According to Google Scholar bibliometrics updated until December 2025, Velardi's scientific publications have been cited more than 8100 times. Her h-index was 42. She has published more than 200 papers in international journals and conference proceedings. Some of her publications have been published in top rated journals such as Artificial Intelligence, Computational Linguistics, Knowledge-Based Systems, IEEE Transactions on Data and Knowledge Engineering , IEEE Transactions on Pattern Analysis and Machine Intelligence, IEEE Transactions on Computers, IEEE Transactions on Software Engineering , Data Mining and Knowledge Discovery, and Journal of Web Semantics. == Education and previous employments == Velardi graduated in electronic engineering from Sapienza University in 1978. From 1978 to 1983, she worked for the Ugo Bordoni Foundation, a research institution focusing on ICT and working under the supervision of the Italian Ministry of Economic Development. In 1983, she was a visiting scholar at Stanford University. During this period she became passionate about Artificial Intelligence, which will remain her area of research throughout her career. From 1984 to 1986, she came back to her natal city and worked as a researcher for IBM. From 1986 to 1996 she was an associate professor in the engineering faculty of Polytechnic University of the Marches (Ancona, Italy). Starting in November 1996, she taught in and did research for the Department of Computer Science at the Sapienza University. Velardi was the head of Bachelor and Master Programs in Computer Science at Sapienza University from 2010 to 2013 and from 2015 to 2016. == Current employment == Since November 2001, Velardi has been a full professor in the department of computer science ("Dipartimento di Informatica" in Italian) at Sapienza University in Rome, Italy. Since 2013, she has been the coordinator of the Distance Learning Degree in Computer Science at Sapienza University. As of today, Velardi is a Senior Associate at the Institute of Cognitive Sciences and Technologies (ISTC) of the CNR. == Recognition == Velardi is one of the hundred female scientists included in the database "100esperte.it" (translated from Italian with "100 female experts"). This database lists top Italian female STEM scientists. Six out of one hundred scientists in the 100esperte's database are computer scientists like Velardi. Velardi is in the list of the top Italian scientists. A top scientist appearing in the Top-Italian-Scientists database is a scientist whose h-index is greater than 30. In March 2017, she was given an IBM Faculty Award for her research on social recommender systems. In December 2018, Velardi was included in the list of the 50 most influential Italian women in science and technology by Inspiring Fifty, a non-profit that aims to increase diversity in STEM by making female role models in tech more visible. In September 2019 she was the local co-organizer and Program Chair of the 6th ACM Celebration of Women in Computing. In November 2019 Velardi received the Standout Woman Award International at the seat of the Italian Parliament in Montecitorio. == Causes == Velardi aims at debunking the myth of computer science as a man-oriented and "inflexible" discipline. She is the founder of the project "NERD? Non e' roba per donne?" (translated from Italian: "NERD? Is it not stuff for women?"). This project was launched by Velardi in 2012 in the Department of Computer Science at Sapienza University. Since 2013 the project has been carried out in partnership with IBM Italy, which later created a spin-off of the project. The goal of the project is two-fold: (1) conveying computer science as creative, interdisciplinary and problem-solving-oriented science, and (2) encouraging young female students in studying computer science by, for instance, developing apps for smartphones. She has been the program chair of the 19th ACM celebration of Women in Computing. She is the creator and coordinator of the G4GRETA, an educational project that involves students of the third and fourth grades of Rome and Lazio. The project combines the development of IT skills with the themes of environmental sustainability and soft skills (teambuilding, pitching, social networking, etc.) Velardi is also involved in scientific dissemination. In 2020 and 2021 she cooperated with RaiCultura, the cultural division of RAI, the national broadcasting company.
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Markov chain geostatistics

Markov chain geostatistics uses Markov chain spatial models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical modeling. A Markov chain random field is still a single spatial Markov chain. The spatial Markov chain moves or jumps in a space and decides its state at any unobserved location through interactions with its nearest known neighbors in different directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition probability matrices are difficult to estimate from sparse sample data and are impractical in representing the complex spatial heterogeneity of states, the transiogram, which is defined as a transition probability function over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.
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Control engineering

Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering, chemical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance. Systems designed to perform without requiring human input are called automatic control systems (such as cruise control for regulating the speed of a car). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of a diverse range of systems. == Overview == Modern day control engineering is a relatively new field of study that gained significant attention during the 20th century with the advancement of technology. It can be broadly defined or classified as practical application of control theory. Control engineering plays an essential role in a wide range of control systems, from simple household washing machines to high-performance fighter aircraft. It seeks to understand physical systems, using mathematical modelling, in terms of inputs, outputs and various components with different behaviors; to use control system design tools to develop controllers for those systems; and to implement controllers in physical systems employing available technology. A system can be mechanical, electrical, fluid, chemical, financial or biological, and its mathematical modelling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem. Control engineering is the engineering discipline that focuses on the modeling of a diverse range of dynamic systems (e.g. mechanical systems) and the design of controllers that will cause these systems to behave in the desired manner. Although such controllers need not be electrical, many are and hence control engineering is often viewed as a subfield of electrical engineering. Electrical circuits, digital signal processors and microcontrollers can all be used to implement control systems. Control engineering has a wide range of applications from the flight and propulsion systems of commercial airliners to the cruise control present in many modern automobiles. In most cases, control engineers utilize feedback when designing control systems. This is often accomplished using a proportional–integral–derivative controller (PID controller) system. For example, in an automobile with cruise control the vehicle's speed is continuously monitored and fed back to the system, which adjusts the motor's torque accordingly. Where there is regular feedback, control theory can be used to determine how the system responds to such feedback. In practically all such systems stability is important and control theory can help ensure stability is achieved. Although feedback is an important aspect of control engineering, control engineers may also work on the control of systems without feedback. This is known as open loop control. A classic example of open loop control is a washing machine that runs through a pre-determined cycle without the use of sensors. == History == Automatic control systems were first developed over two thousand years ago. The first feedback control device on record is thought to be the ancient Ktesibios's water clock in Alexandria, Egypt, around the third century BCE. It kept time by regulating the water level in a vessel and, therefore, the water flow from that vessel. This certainly was a successful device as water clocks of similar design were still being made in Baghdad when the Mongols captured the city in 1258 CE. A variety of automatic devices have been used over the centuries to accomplish useful tasks or simply just to entertain. The latter includes the automata, popular in Europe in the 17th and 18th centuries, featuring dancing figures that would repeat the same task over and over again; these automata are examples of open-loop control. Milestones among feedback, or "closed-loop" automatic control devices, include the temperature regulator of a furnace attributed to Drebbel, circa 1620, and the centrifugal flyball governor used for regulating the speed of steam engines by James Watt in 1788. In his 1868 paper "On Governors", James Clerk Maxwell was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system. This demonstrated the importance and usefulness of mathematical models and methods in understanding complex phenomena, and it signaled the beginning of mathematical control and systems theory. Elements of control theory had appeared earlier but not as dramatically and convincingly as in Maxwell's analysis. Control theory made significant strides over the next century. New mathematical techniques, as well as advances in electronic and computer technologies, made it possible to control significantly more complex dynamical systems than the original flyball governor could stabilize. New mathematical techniques included developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s and 1980s. Applications of control methodology have helped to make possible space travel and communication satellites, safer and more efficient aircraft, cleaner automobile engines, and cleaner and more efficient chemical processes. Before it emerged as a unique discipline, control engineering was practiced as a part of mechanical engineering and control theory was studied as a part of electrical engineering since electrical circuits can often be easily described using control theory techniques. In the first control relationships, a current output was represented by a voltage control input. However, not having adequate technology to implement electrical control systems, designers were left with the option of less efficient and slow responding mechanical systems. A very effective mechanical controller that is still widely used in some hydro plants is the governor. Later on, previous to modern power electronics, process control systems for industrial applications were devised by mechanical engineers using pneumatic and hydraulic control devices, many of which are still in use today. === Mathematical modelling === David Quinn Mayne, (1930–2024) was among the early developers of a rigorous mathematical method for analysing Model predictive control algorithms (MPC). It is currently used in tens of thousands of applications and is a core part of the advanced control technology by hundreds of process control producers. MPC's major strength is its capacity to deal with nonlinearities and hard constraints in a simple and intuitive fashion. His work underpins a class of algorithms that are probably correct, heuristically explainable, and yield control system designs which meet practically important objectives. == Control systems == == Control theory == == Education == At many universities around the world, control engineering courses are taught primarily in electrical engineering and mechanical engineering, but some courses can be instructed in mechatronics engineering, and aerospace engineering. In others, control engineering is connected to computer science, as most control techniques today are implemented through computers, often as embedded systems (as in the automotive field). The field of control within chemical engineering is often known as process control. It deals primarily with the control of variables in a chemical process in a plant. It is taught as part of the undergraduate curriculum of any chemical engineering program and employs many of the same principles in control engineering. Other engineering disciplines also overlap with control engineering as it can be applied to any system for which a suitable model can be derived. However, specialised control engineering departments do exist, for example, in Italy there are several master in Automation & Robotics that are fully specialised in Control engineering or the Department of Automatic Control and Systems Engineering at the University of Sheffield or the Department of Robotics and Control Engineering at the United States Naval Academy and the Department of Control and Automation Engineering at the Istanbul Technical University. Control engineering has diversified applications that include science, finance management, and even human behavior. Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which req
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Chelsea Finn

Chelsea Finn (born October 8, 1992) is an American computer scientist and assistant professor at Stanford University. Her research investigates intelligence through the interactions of robots, with the hope to create robotic systems that can learn how to learn. She previously worked for Google and currently is a co-founder of the startup Physical Intelligence. == Early life and education == Finn was an undergraduate student in electrical engineering and computer science at Massachusetts Institute of Technology. She then moved to the University of California, Berkeley, where she earned her Ph.D. in 2018 under Pieter Abbeel and Sergey Levine. Her work in the Berkeley Artificial Intelligence Lab (BAIR) focused on gradient based algorithms . Such algorithms allow machines to 'learn to learn', more akin to human learning than traditional machine learning systems. These “meta-learning” techniques train machines to quickly adapt, such that when they encounter new scenarios they can learn quickly. As a doctoral student she worked as an intern at Google Brain, where she worked on robot learning algorithms from deep predictive models. She delivered a massive open online course on deep reinforcement learning. She was the first woman to win the C.V. & Daulat Ramamoorthy Distinguished Research Award. == Research and career == Finn investigates the capabilities of robots to develop intelligence through learning and interaction. She has made use of deep learning algorithms to simultaneously learn visual perception and control robotic skills. She developed meta-learning approaches to train neural networks to take in student code and output useful feedback. She showed that the system could quickly adapt without too much input from the instructor. She trialled the programme on Code in Place, a 12,000 student course delivered by Stanford University every year. She found that 97.9% of the time the students agreed with the feedback being given. == Awards and honors == 2016 C.V. & Daulat Ramamoorthy Distinguished Research Award 2017 Electrical engineering and computer science rising star 2018 MIT Technology Review 35 Under 35 2018 ACM Doctoral Dissertation Award 2020 Samsung Advanced Institute of Technology AI Researcher of the Year 2020 Intel Rising Star Faculty Award 2021 Office of Naval Research Young Investigator Award 2022 IEEE Robotics and Automation Society Early Academic Career Award == Select publications == Finn, Chelsea; Abbeel, Pieter; Levine, Sergey (2017-07-17). "Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks". International Conference on Machine Learning. PMLR: 1126–1135. arXiv:1703.03400. Sergey Levine; Chelsea Finn; Trevor Darrell; Pieter Abbeel (2016). "End-to-End Training of Deep Visuomotor Policies". Journal of Machine Learning Research. 17 (39): 1–40. arXiv:1504.00702. ISSN 1533-7928. Wikidata Q90313375. Chelsea Finn; Ian Goodfellow; Sergey Levine (2016). "Unsupervised Learning for Physical Interaction through Video Prediction" (PDF). Advances in Neural Information Processing Systems 29. Advances in Neural Information Processing Systems. Wikidata Q46993574.
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Nicholas Carlini

Nicholas Carlini is an American researcher affiliated with Anthropic and previously with Google DeepMind who has published research in the fields of computer security and machine learning. He is known for his work on adversarial machine learning, particularly his work on the Carlini & Wagner attack in 2016. This attack was particularly useful in defeating defensive distillation, a method used to increase model robustness, and has since been effective against other defenses against adversarial input. In 2018, Carlini demonstrated an attack on Mozilla's DeepSpeech model, showing that hidden commands could be embedded in speech inputs, which the model would execute even if they were inaudible to humans. He also led a team at UC Berkeley that successfully broke seven out of nine defenses against adversarial attacks presented at the 2018 International Conference on Learning Representations. In addition to his work on adversarial attacks, Carlini has made significant contributions to understanding the privacy risks of machine learning models. In 2020, he revealed that large language models, like GPT-2, could memorize and output personally identifiable information. His research demonstrated that this issue worsened with larger models, and he later showed similar vulnerabilities in generative image models, such as Stable Diffusion. == Life and career == Nicholas Carlini obtained his Bachelor of Arts in Computer Science and Mathematics from the University of California, Berkeley, in 2013. He then continued his studies at the same university, where he pursued a PhD under the supervision of David Wagner, completing it in 2018. Carlini became known for his work on adversarial machine learning. In 2016, he worked alongside Wagner to develop the Carlini & Wagner attack, a method of generating adversarial examples against machine learning models. The attack was proved to be useful against defensive distillation, a popular mechanism where a student model is trained based on the features of a parent model to increase the robustness and generalizability of student models. The attack gained popularity when it was shown that the methodology was also effective against most other defenses, rendering them ineffective. In 2018, Carlini demonstrated an attack against Mozilla Foundation's DeepSpeech model where he showed that by hiding malicious commands inside normal speech input the speech model would respond to the hidden commands even when the commands were not discernible by humans. In the same year, Carlini and his team at UC Berkeley showed that out of the 11 papers presenting defenses to adversarial attacks accepted in that year's ICLR conference, seven of the defenses could be broken. Since 2021, he and his team have been working on large language models, creating a questionnaire where humans typically scored 35% whereas AI models scored in the 40%, with GPT-3 getting 38% which could be improved to 40% through few shot prompting. The best performer in the test was UnifiedQA, a model developed by Google specifically for answer questions and answer sets. Carlini has also developed methods to cause large language models like ChatGPT to answer harmful questions like how to construct bombs. He is also known for his work studying the privacy of machine learning models. In 2020, he showed for the first time that large language models would memorize some of the text data that they were trained on. For example, he found that GPT-2 could output personally identifiable information. He then led an analysis of larger models and studied how memorization increased with model size. Then, in 2022 he showed the same vulnerability in generative image models, and specifically diffusion models, by showing that Stable Diffusion could output images of people's faces that it was trained on. Following on this, Carlini then showed that ChatGPT would also sometimes output exact copies of webpages it was trained on, including personally identifiable information. Some of these studies have since been referenced by the courts in debating the copyright status of AI models. == Other work == Carlini received the Best of Show award at the 2020 IOCCC for implementing a tic-tac-toe game entirely with calls to printf, expanding on work from a research paper of his from 2015. The judges commented on his submission "This year's Best of Show (carlini) is such a novel way of obfuscation that it would be worth of a special mention in the (future) Best of IOCCC list!". [sic] == Awards == Best Student Paper Award, IEEE S&P 2017 ("Towards Evaluating the Robustness of Neural Networks") Best Paper Award, ICML 2018 ("Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples") Distinguished Paper Award, USENIX 2021 ("Poisoning the Unlabeled Dataset of Semi-Supervised Learning") Distinguished Paper Award, USENIX 2023 ("Tight Auditing of Differentially Private Machine Learning") Best Paper Award, ICML 2024 ("Stealing Part of a Production Language Model") Best Paper Award, ICML 2024 ("Considerations for Differentially Private Learning with Large-Scale Public Pretraining")
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David Blei

David Meir Blei is a professor in the Statistics and Computer Science departments at Columbia University. Prior to fall 2014 he was an associate professor in the Department of Computer Science at Princeton University. His work is primarily in machine learning. == Research == His research interests include topic models and he was one of the original developers of latent Dirichlet allocation, along with Andrew Ng and Michael I. Jordan. As of June 18, 2020, his publications have been cited 109,821 times, giving him an h-index of 116. == Honors and awards == Blei received the ACM Infosys Foundation Award in 2013. (This award is given to a computer scientist under the age of 45. It has since been renamed the ACM Prize in Computing.) He was named Fellow of ACM "For contributions to the theory and practice of probabilistic topic modeling and Bayesian machine learning" in 2015.
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List of large language models

A large language model (LLM) is a type of machine learning model designed for natural language processing tasks such as language generation. LLMs are language models with many parameters, and are trained with self-supervised learning on a vast amount of text. == List == For the training cost column, 1 petaFLOP-day equals 1 petaFLOP/sec × 1 day, or 8.64×1019 FLOP (floating point operations). Only the cost of the largest model is shown. The number of parameters is measured in billions, and the training cost is measured in petaFLOP-days. === 2018 === === 2019 === === 2020 === === 2021 === === 2022 === === 2023 === === 2024 === === 2025 === === 2026 ===
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Pumping lemma for regular languages

In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long strings in a regular language may be pumped—that is, have a middle section of the string repeated an arbitrary number of times—to produce a new string that is also part of the language. The pumping lemma is useful for proving that a specific language is not a regular language, by showing that the language does not have the property. Specifically, the pumping lemma says that for any regular language L {\displaystyle L} , there exists a constant p {\displaystyle p} such that any string w {\displaystyle w} in L {\displaystyle L} with length at least p {\displaystyle p} can be split into three substrings x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} ( w = x y z {\displaystyle w=xyz} , with y {\displaystyle y} being non-empty), such that the strings x z , x y z , x y y z , x y y y z , . . . {\displaystyle xz,xyz,xyyz,xyyyz,...} are also in L {\displaystyle L} . The process of repeating y {\displaystyle y} zero or more times is known as "pumping". Moreover, the pumping lemma guarantees that the length of x y {\displaystyle xy} will be at most p {\displaystyle p} , thus giving a "small" substring x y {\displaystyle xy} that has the desired property. Languages with a finite number of strings vacuously satisfy the pumping lemma by having p {\displaystyle p} equal to the maximum string length in L {\displaystyle L} plus one. By doing so, no strings at all in L {\displaystyle L} have length at least p {\displaystyle p} . The pumping lemma was first proven by Michael Rabin and Dana Scott in 1959, and rediscovered shortly after by Yehoshua Bar-Hillel, Micha A. Perles, and Eli Shamir in 1961, as a simplification of their pumping lemma for context-free languages. == Formal statement == Let L {\displaystyle L} be a regular language. Then there exists an integer p ≥ 1 {\displaystyle p\geq 1} depending only on L {\displaystyle L} such that every string w {\displaystyle w} in L {\displaystyle L} of length at least p {\displaystyle p} ( p {\displaystyle p} is called the "pumping length") can be written as w = x y z {\displaystyle w=xyz} (i.e., w {\displaystyle w} can be divided into three substrings), satisfying the following conditions: | y | ≥ 1 {\displaystyle |y|\geq 1} | x y | ≤ p {\displaystyle |xy|\leq p} ( ∀ n ≥ 0 ) ( x y n z ∈ L ) {\displaystyle (\forall n\geq 0)(xy^{n}z\in L)} y {\displaystyle y} is the substring that can be pumped (removed or repeated any number of times, and the resulting string is always in L {\displaystyle L} ). (1) means the loop y {\displaystyle y} to be pumped must be of length at least one, that is, not an empty string; (2) means the loop must occur within the first p {\displaystyle p} characters. | x | {\displaystyle |x|} must be smaller than p {\displaystyle p} (conclusion of (1) and (2)), but apart from that, there is no restriction on x {\displaystyle x} and z {\displaystyle z} . In simple words, for any regular language L {\displaystyle L} , any sufficiently long string w {\displaystyle w} (in L {\displaystyle L} ) can be split into 3 parts, i.e. w = x y z {\displaystyle w=xyz} , such that all the strings x y n z {\displaystyle xy^{n}z} for n ≥ 0 {\displaystyle n\geq 0} are also in L {\displaystyle L} . Below is a formal expression of the pumping lemma. ∀ L ⊆ Σ ∗ , regular ( L ) ⟹ ∃ p ≥ 1 , ∀ w ∈ L , | w | ≥ p ⟹ ∃ x , y , z ∈ Σ ∗ , ( w = x y z ) ∧ ( | y | ≥ 1 ) ∧ ( | x y | ≤ p ) ∧ ( ∀ n ≥ 0 , x y n z ∈ L ) {\displaystyle {\begin{array}{l}\forall L\subseteq \Sigma ^{},{\mbox{regular}}(L)\implies \\\quad \exists p\geq 1,\forall w\in L,|w|\geq p\implies \\\qquad \exists x,y,z\in \Sigma ^{},(w=xyz)\land (|y|\geq 1)\land (|xy|\leq p)\land (\forall n\geq 0,xy^{n}z\in L)\end{array}}} == Use of the lemma to prove non-regularity == The pumping lemma is often used to prove that a particular language is non-regular: a proof by contradiction may consist of exhibiting a string (of the required length) in the language that lacks the property outlined in the pumping lemma. Example: The language L = { a n b n : n ≥ 0 } {\displaystyle L=\{a^{n}b^{n}:n\geq 0\}} over the alphabet Σ = { a , b } {\displaystyle \Sigma =\{a,b\}} can be shown to be non-regular as follows: Assume that some constant p ≥ 1 {\displaystyle p\geq 1} exists as required by the lemma. Let w {\displaystyle w} in L {\displaystyle L} be given by w = a p b p {\displaystyle w=a^{p}b^{p}} , which is a string longer than p {\displaystyle p} . By the pumping lemma, there must exist a decomposition w = x y z {\displaystyle w=xyz} with | x y | ≤ p {\displaystyle |xy|\leq p} and | y | ≥ 1 {\displaystyle |y|\geq 1} such that x y i z {\displaystyle xy^{i}z} in L {\displaystyle L} for every i ≥ 0 {\displaystyle i\geq 0} . Since | x y | ≤ p {\displaystyle |xy|\leq p} , the string y {\displaystyle y} only consists of instances of a {\displaystyle a} . Because | y | ≥ 1 {\displaystyle |y|\geq 1} , it contains at least one instance of the letter a {\displaystyle a} . Pumping y {\displaystyle y} to give x y 2 z {\displaystyle xy^{2}z} gives a word with more instances of the letter a {\displaystyle a} than the letter b {\displaystyle b} , since some instances of a {\displaystyle a} but none of b {\displaystyle b} were added. Therefore, x y 2 z {\displaystyle xy^{2}z} is not in L {\displaystyle L} which contradicts the pumping lemma. Therefore, L {\displaystyle L} cannot be regular. The proof that the language of balanced (i.e., properly nested) parentheses is not regular follows the same idea. Given p {\displaystyle p} , there is a string of balanced parentheses that begins with more than p {\displaystyle p} left parentheses, so that y {\displaystyle y} will consist entirely of left parentheses. By repeating y {\displaystyle y} , a string can be produced that does not contain the same number of left and right parentheses, and so they cannot be balanced. == Proof of the pumping lemma == For every regular language there is a finite-state automaton (FSA) that accepts the language. The number of states in such an FSA are counted and that count is used as the pumping length p {\displaystyle p} . For a string of length at least p {\displaystyle p} , let q 0 {\displaystyle q_{0}} be the start state and let q 1 , . . . , q p {\displaystyle q_{1},...,q_{p}} be the sequence of the next p {\displaystyle p} states visited as the string is emitted. Because the FSA has only p {\displaystyle p} states, within this sequence of p + 1 {\displaystyle p+1} visited states there must be at least one state that is repeated. Write q s {\displaystyle q_{s}} for such a state. The transitions that take the machine from the first encounter of state q s {\displaystyle q_{s}} to the second encounter of state q s {\displaystyle q_{s}} match some string. This string is called y {\displaystyle y} in the lemma, and since the machine will match a string without the y {\displaystyle y} portion, or with the string y {\displaystyle y} repeated any number of times, the conditions of the lemma are satisfied. For example, the following image shows an FSA. The FSA accepts the string: abcd. Since this string has a length at least as large as the number of states, which is four (so the total number of states that the machine passes through to scan abcd would be 5), the pigeonhole principle indicates that there must be at least one repeated state among the start state and the next four visited states. In this example, only q 1 {\displaystyle q_{1}} is a repeated state. Since the substring bc takes the machine through transitions that start at state q 1 {\displaystyle q_{1}} and end at state q 1 {\displaystyle q_{1}} , that portion could be repeated and the FSA would still accept, giving the string abcbcd. Alternatively, the bc portion could be removed and the FSA would still accept giving the string ad. In terms of the pumping lemma, the string abcd is broken into an x {\displaystyle x} portion a, a y {\displaystyle y} portion bc and a z {\displaystyle z} portion d. As a side remark, the problem of checking whether a given string can be accepted by a given nondeterministic finite automaton without visiting any state repeatedly, is NP hard. == General version of pumping lemma for regular languages == If a language L {\displaystyle L} is regular, then there exists a number p ≥ 1 {\displaystyle p\geq 1} (the pumping length) such that every string u w v {\displaystyle uwv} in L {\displaystyle L} with | w | ≥ p {\displaystyle |w|\geq p} can be written in the form u w v = u x y z v {\displaystyle uwv=uxyzv} with strings x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} such that | x y | ≤ p {\displaystyle |xy|\leq p} , | y | ≥ 1 {\displaystyle |y|\geq 1} and u x y i z v {\displaystyle uxy^{i}zv} is in L {\displaystyle L} for every integer i ≥ 0 {\displaystyle i\geq 0} . From this, the above standard v
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Additive smoothing

In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts x = ⟨ x 1 , x 2 , … , x d ⟩ {\displaystyle \mathbf {x} =\langle x_{1},x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts gives the estimator θ ^ i = x i + α N + α d ( i = 1 , … , d ) , {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\alpha }{N+\alpha d}}\qquad (i=1,\ldots ,d),} where the smoothed count x ^ i = N θ ^ i {\displaystyle {\hat {x}}_{i}=N{\hat {\theta }}_{i}} , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) x i / N {\displaystyle x_{i}/N} and the uniform probability 1 / d . {\displaystyle 1/d.} Common choices for α are 0 (no smoothing), +1⁄2 (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empirically based on the observed data. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution. == History == Laplace came up with this smoothing technique when he tried to estimate the chance that the sun will rise tomorrow. His rationale was that even given a large sample of days with the rising sun, we still can not be completely sure that the sun will still rise tomorrow (known as the sunrise problem). == Pseudocount == A pseudocount is an amount (not generally an integer, despite its name) added to the number of observed cases in order to change the expected probability in a model of those data, when not known to be zero. It is so named because, roughly speaking, a pseudo-count of value α {\displaystyle \alpha } weighs into the posterior distribution similarly to each category having an additional count of α {\displaystyle \alpha } . If the number of occurrences of each item i {\displaystyle i} is x i {\displaystyle x_{i}} out of N {\displaystyle N} samples, the empirical probability of event i {\displaystyle i} is p i , empirical = x i N , {\displaystyle p_{i,{\text{empirical}}}={\frac {x_{i}}{N}},} but the posterior probability when additively smoothed is p i , α -smoothed = x i + α N + α d , {\displaystyle p_{i,\alpha {\text{-smoothed}}}={\frac {x_{i}+\alpha }{N+\alpha d}},} as if to increase each count x i {\displaystyle x_{i}} by α {\displaystyle \alpha } a priori. Depending on the prior knowledge, which is sometimes a subjective value, a pseudocount may have any non-negative finite value. It may only be zero (or the possibility ignored) if impossible by definition, such as the possibility of a decimal digit of π being a letter, or a physical possibility that would be rejected and so not counted, such as a computer printing a letter when a valid program for π is run, or excluded and not counted because of no interest, such as if only interested in the zeros and ones. Generally, there is also a possibility that no value may be computable or observable in a finite time (see the halting problem). But at least one possibility must have a non-zero pseudocount, otherwise no prediction could be computed before the first observation. The relative values of pseudocounts represent the relative prior expected probabilities of their possibilities. The sum of the pseudocounts, which may be very large, represents the estimated weight of the prior knowledge compared with all the actual observations (one for each) when determining the expected probability. In any observed data set or sample there is the possibility, especially with low-probability events and with small data sets, of a possible event not occurring. Its observed frequency is therefore zero, apparently implying a probability of zero. This oversimplification is inaccurate and often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. By artificially adjusting the probability of rare (but not impossible) events so those probabilities are not exactly zero, zero-frequency problems are avoided. Also see Cromwell's rule. === Choice of pseudocount === ==== Weakly informative prior ==== One common approach is to add 1 to each observed number of events, including the zero-count possibilities. This is sometimes called Laplace's rule of succession. This approach is equivalent to assuming a uniform prior distribution over the probabilities for each possible event (spanning the simplex where each probability is between 0 and 1, and they all sum to 1). Using the Jeffreys prior approach, a pseudocount of one half should be added to each possible outcome. Pseudocounts should be set to one or one-half only when there is no prior knowledge at all – see the principle of indifference. However, given appropriate prior knowledge, the sum should be adjusted in proportion to the expectation that the prior probabilities should be considered correct, despite evidence to the contrary – see further analysis. Higher values are appropriate inasmuch as there is prior knowledge of the true values (for a mint-condition coin, say); lower values inasmuch as there is prior knowledge that there is probable bias, but of unknown degree (for a bent coin, say). ==== Frequentist interval ==== One way to motivate pseudocounts, particularly for binomial data, is via a formula for the midpoint of an interval estimate, particularly a binomial proportion confidence interval. The best-known is due to Edwin Bidwell Wilson, in Wilson (1927): the midpoint of the Wilson score interval corresponding to ⁠ z {\displaystyle z} ⁠ standard deviations on either side is n S + z n + 2 z {\displaystyle {\frac {n_{S}+z}{n+2z}}} Taking z = 2 {\displaystyle z=2} standard deviations to approximate a 95% confidence interval (⁠ z ≈ 1.96 {\displaystyle z\approx 1.96} ⁠) yields pseudocount of 2 for each outcome, so 4 in total, colloquially known as the "plus four rule": n S + 2 n + 4 {\displaystyle {\frac {n_{S}+2}{n+4}}} This is also the midpoint of the Agresti–Coull interval (Agresti & Coull 1998). ==== Known incidence rates ==== Often the bias of an unknown trial population is tested against a control population with known parameters (incidence rates) μ = ⟨ μ 1 , μ 2 , … , μ d ⟩ . {\displaystyle {\boldsymbol {\mu }}=\langle \mu _{1},\mu _{2},\ldots ,\mu _{d}\rangle .} In this case the uniform probability 1 / d {\displaystyle 1/d} should be replaced by the known incidence rate of the control population μ i {\displaystyle \mu _{i}} to calculate the smoothed estimator: θ ^ i = x i + μ i α d N + α d ( i = 1 , … , d ) . {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\mu _{i}\alpha d}{N+\alpha d}}\qquad (i=1,\ldots ,d).} As a consistency check, if the empirical estimator happens to equal the incidence rate, i.e. μ i = x i / N , {\displaystyle \mu _{i}=x_{i}/N,} the smoothed estimator is independent of α {\displaystyle \alpha } and also equals the incidence rate. == Applications == === Classification === Additive smoothing is commonly a component of naive Bayes classifiers. === Statistical language modelling === In a bag of words model of natural language processing and information retrieval, the data consists of the number of occurrences of each word in a document. Additive smoothing allows the assignment of non-zero probabilities to words which do not occur in the sample. Studies have shown that additive smoothing is more effective than other probability smoothing methods in several retrieval tasks such as language-model-based pseudo-relevance feedback and recommender systems.
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