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  Outline of automation

  The following outline is provided as an overview of and topical guide to automation: Automation – use of control systems and information technologies to reduce the need for human work in the production of goods and services. In the scope of industrialization, automation is a step beyond mechanization. == Essence of automation == Control system – a device, or set of devices to manage, command, direct or regulate the behavior of other devices or systems. Industrial control system (ICS) – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed control systems (DCS), and other smaller control system configurations such as skid-mounted programmable logic controllers (PLC) often found in industrial sectors and critical infrastructures. Industrialization – period of social and economic change that transforms a human group from an agrarian society into an industrial one. Numerical control (NC) – refers to the automation of machine tools that are operated by abstractly programmed commands encoded on a storage medium, as opposed to controlled manually via handwheels or levers, or mechanically automated via cams alone. Robotics – the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots and computer systems for their control, sensory feedback, and information processing. == Branches of automation == === General purpose === Autonomous automation – autonomous software agents to adapt the controllers of computer controlled industrial machinery and processes Banking automation Broadcast automation Building automation – advanced functionality provided by the control system of a building. A building automation system (BAS) is an example of a distributed control system. Home automation – control system of a home. Office automation – the varied computer machinery and software used to digitally create, collect, store, manipulate, and relay office information needed for accomplishing basic tasks such as business process automation and robotic process automation. Console automation Database automation Integrated library system Laboratory automation === Specific purpose === Automated attendant Automated guided vehicle Autonomous mobile robot Automated highway system Automated pool cleaner Automated teller machine Automatic painting (robotic) Pop music automation Remotely operated vehicle Robotic lawn mower Telephone switchboard Vending machine == Fields contributing to automation == Cybernetics – the interdisciplinary study of the structure of regulatory systems. Cognitive science – interdisciplinary scientific study of the mind and its processes. It examines what cognition is, what it does and how it works. Robotics – the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots and computer systems for their control, sensory feedback, and information processing. == History of automation == History of mass production – Prerequisites of mass production were interchangeable parts, machine tools and power, especially in the form of electricity. Mass production was popularized in the 1910s and 1920s by Henry Ford's Ford Motor Company, which introduced electric motors to the then-well-known technique of chain or sequential production. History of home automation == Automated machines == Machine to Machine OLE for process control (OPC) Process control – a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range. Run Book Automation (RBA) Robot – a mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control. == Automated machine components == Artificial intelligence – the intelligence of machines and the branch of computer science that aims to create it. Friendly artificial intelligence – an artificial intelligence that has a positive rather than negative effect on humanity, and the field of knowledge required to build such an artificial intelligence. === Automation tools === Artificial neural network (ANN) – mathematical model or computational model that is inspired by the structure or functional aspects of biological neural networks. Human machine interface (HMI) – operator level local control panel that monitors field devices Laboratory information management system (LIMS) – software package that offers a set of key features that support a modern laboratory's operations. Industrial control system – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed control systems (DCS), and other smaller control system configurations such as skid-mounted programmable logic controllers (PLC) often found in the industrial sectors and critical infrastructures. Distributed control system (DCS) – control system usually of a manufacturing system, process or any kind of dynamic system, in which the controller elements are not central in location (like the brain) but are distributed throughout the system with each component sub-system controlled by one or more controllers. Manufacturing execution system (MES) – system that manages manufacturing operations in a factory, including management of resources, scheduling production processes, dispatching production orders, execution of production orders, etc. Programmable automation controller (PAC) – digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. Programmable logic controller (PLC)A Programmable Logic Controller, PLC or Programmable Controller is a digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. The abbreviation "PLC" and the term "Programmable Logic Controller" are registered trademarks of the Allen-Bradley Company (Rockwell Automation). PLCs are used in many industries and machines. Unlike general-purpose computers, the PLC is designed for multiple inputs and output arrangements, extended temperature ranges, immunity to electrical noise, and resistance to vibration and impact. Programs to control machine operation are typically stored in battery-backed-up or non-volatile memory. A PLC is an example of a hard real time system since output results must be produced in response to input conditions within a limited time, otherwise unintended operation will result. Supervisory control and data acquisition (SCADA) – generally refers to industrial control systems (ICS): computer systems that monitor and control industrial, infrastructure, or facility-based processes, as described below: Industrial processes include those of manufacturing, production, power generation, fabrication, and refining, and may run in continuous, batch, repetitive, or discrete modes. Simulation § Engineering Technology simulation or Process simulation == Social movements == Automation-related social movement – a movement that advocates semi- or fully automatic systems to provide for human needs globally. For example, automation of farming and food distribution throughout the world so that no one will go hungry. One goal is to automate all mundane labor, to free humans to engage in more creative activities (or less work). The Technocracy movement – social movement active from the Great Depression (1930s) to date that proposes replacing politicians and business people with scientists and engineers who have the technical expertise to manage the economy. The Zeitgeist Movement – movement advocating the replacement of the market economy with an economy in which all resources are equitably, commonly and sustainably shared. == Automation in the future == Android – a robot or synthetic organism designed to look and act like a human, and with a body having a flesh-like resemblance Technological singularity – the hypothetical future emergence of greater-than-human intelligence through technological means Semi-automation – using a centralized computer controller to orchestrate the activities of man and machine. == Automation-related publications == IEEE Spectrum – the flagship publication of the Institute of Electrical and Electronics Engineers (IEEE), explores the development, applications and implications of new technologies, and provides a forum for understanding, discussion and leadership in these areas. IEEE Transactions on Information Theory – peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE), focused on the study of information theory, the mathematics of communications, including computer communications, robotics communications, etc. IEEE Transactions on Control S

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  Modes of variation

  In statistics, modes of variation are a continuously indexed set of vectors or functions that are centered at a mean and are used to depict the variation in a population or sample. Typically, variation patterns in the data can be decomposed in descending order of eigenvalues with the directions represented by the corresponding eigenvectors or eigenfunctions. Modes of variation provide a visualization of this decomposition and an efficient description of variation around the mean. Both in principal component analysis (PCA) and in functional principal component analysis (FPCA), modes of variation play an important role in visualizing and describing the variation in the data contributed by each eigencomponent. In real-world applications, the eigencomponents and associated modes of variation aid to interpret complex data, especially in exploratory data analysis (EDA). == Formulation == Modes of variation are a natural extension of PCA and FPCA. === Modes of variation in PCA === If a random vector X = ( X 1 , X 2 , ⋯ , X p ) T {\displaystyle \mathbf {X} =(X_{1},X_{2},\cdots ,X_{p})^{T}} has the mean vector μ p {\displaystyle {\boldsymbol {\mu }}_{p}} , and the covariance matrix Σ p × p {\displaystyle \mathbf {\Sigma } _{p\times p}} with eigenvalues λ 1 ≥ λ 2 ≥ ⋯ ≥ λ p ≥ 0 {\displaystyle \lambda _{1}\geq \lambda _{2}\geq \cdots \geq \lambda _{p}\geq 0} and corresponding orthonormal eigenvectors e 1 , e 2 , ⋯ , e p {\displaystyle \mathbf {e} _{1},\mathbf {e} _{2},\cdots ,\mathbf {e} _{p}} , by eigendecomposition of a real symmetric matrix, the covariance matrix Σ {\displaystyle \mathbf {\Sigma } } can be decomposed as Σ = Q Λ Q T , {\displaystyle \mathbf {\Sigma } =\mathbf {Q} \mathbf {\Lambda } \mathbf {Q} ^{T},} where Q {\displaystyle \mathbf {Q} } is an orthogonal matrix whose columns are the eigenvectors of Σ {\displaystyle \mathbf {\Sigma } } , and Λ {\displaystyle \mathbf {\Lambda } } is a diagonal matrix whose entries are the eigenvalues of Σ {\displaystyle \mathbf {\Sigma } } . By the Karhunen–Loève expansion for random vectors, one can express the centered random vector in the eigenbasis X − μ = ∑ k = 1 p ξ k e k , {\displaystyle \mathbf {X} -{\boldsymbol {\mu }}=\sum _{k=1}^{p}\xi _{k}\mathbf {e} _{k},} where ξ k = e k T ( X − μ ) {\displaystyle \xi _{k}=\mathbf {e} _{k}^{T}(\mathbf {X} -{\boldsymbol {\mu }})} is the principal component associated with the k {\displaystyle k} -th eigenvector e k {\displaystyle \mathbf {e} _{k}} , with the properties E ⁡ ( ξ k ) = 0 , Var ⁡ ( ξ k ) = λ k , {\displaystyle \operatorname {E} (\xi _{k})=0,\operatorname {Var} (\xi _{k})=\lambda _{k},} and E ⁡ ( ξ k ξ l ) = 0 for l ≠ k . {\displaystyle \operatorname {E} (\xi _{k}\xi _{l})=0\ {\text{for}}\ l\neq k.} Then the k {\displaystyle k} -th mode of variation of X {\displaystyle \mathbf {X} } is the set of vectors, indexed by α {\displaystyle \alpha } , m k , α = μ ± α λ k e k , α ∈ [ − A , A ] , {\displaystyle \mathbf {m} _{k,\alpha }={\boldsymbol {\mu }}\pm \alpha {\sqrt {\lambda _{k}}}\mathbf {e} _{k},\alpha \in [-A,A],} where A {\displaystyle A} is typically selected as 2 or 3 {\displaystyle 2\ {\text{or}}\ 3} . === Modes of variation in FPCA === For a square-integrable random function X ( t ) , t ∈ T ⊂ R p {\displaystyle X(t),t\in {\mathcal {T}}\subset R^{p}} , where typically p = 1 {\displaystyle p=1} and T {\displaystyle {\mathcal {T}}} is an interval, denote the mean function by μ ( t ) = E ⁡ ( X ( t ) ) {\displaystyle \mu (t)=\operatorname {E} (X(t))} , and the covariance function by G ( s , t ) = Cov ⁡ ( X ( s ) , X ( t ) ) = ∑ k = 1 ∞ λ k φ k ( s ) φ k ( t ) , {\displaystyle G(s,t)=\operatorname {Cov} (X(s),X(t))=\sum _{k=1}^{\infty }\lambda _{k}\varphi _{k}(s)\varphi _{k}(t),} where λ 1 ≥ λ 2 ≥ ⋯ ≥ 0 {\displaystyle \lambda _{1}\geq \lambda _{2}\geq \cdots \geq 0} are the eigenvalues and { φ 1 , φ 2 , ⋯ } {\displaystyle \{\varphi _{1},\varphi _{2},\cdots \}} are the orthonormal eigenfunctions of the linear Hilbert–Schmidt operator G : L 2 ( T ) → L 2 ( T ) , G ( f ) = ∫ T G ( s , t ) f ( s ) d s . {\displaystyle G:L^{2}({\mathcal {T}})\rightarrow L^{2}({\mathcal {T}}),\,G(f)=\int _{\mathcal {T}}G(s,t)f(s)ds.} By the Karhunen–Loève theorem, one can express the centered function in the eigenbasis, X ( t ) − μ ( t ) = ∑ k = 1 ∞ ξ k φ k ( t ) , {\displaystyle X(t)-\mu (t)=\sum _{k=1}^{\infty }\xi _{k}\varphi _{k}(t),} where ξ k = ∫ T ( X ( t ) − μ ( t ) ) φ k ( t ) d t {\displaystyle \xi _{k}=\int _{\mathcal {T}}(X(t)-\mu (t))\varphi _{k}(t)dt} is the k {\displaystyle k} -th principal component with the properties E ⁡ ( ξ k ) = 0 , Var ⁡ ( ξ k ) = λ k , {\displaystyle \operatorname {E} (\xi _{k})=0,\operatorname {Var} (\xi _{k})=\lambda _{k},} and E ⁡ ( ξ k ξ l ) = 0 for l ≠ k . {\displaystyle \operatorname {E} (\xi _{k}\xi _{l})=0{\text{ for }}l\neq k.} Then the k {\displaystyle k} -th mode of variation of X ( t ) {\displaystyle X(t)} is the set of functions, indexed by α {\displaystyle \alpha } , m k , α ( t ) = μ ( t ) ± α λ k φ k ( t ) , t ∈ T , α ∈ [ − A , A ] {\displaystyle m_{k,\alpha }(t)=\mu (t)\pm \alpha {\sqrt {\lambda _{k}}}\varphi _{k}(t),\ t\in {\mathcal {T}},\ \alpha \in [-A,A]} that are viewed simultaneously over the range of α {\displaystyle \alpha } , usually for A = 2 or 3 {\displaystyle A=2\ {\text{or}}\ 3} . == Estimation == The formulation above is derived from properties of the population. Estimation is needed in real-world applications. The key idea is to estimate mean and covariance. === Modes of variation in PCA === Suppose the data x 1 , x 2 , ⋯ , x n {\displaystyle \mathbf {x} _{1},\mathbf {x} _{2},\cdots ,\mathbf {x} _{n}} represent n {\displaystyle n} independent drawings from some p {\displaystyle p} -dimensional population X {\displaystyle \mathbf {X} } with mean vector μ {\displaystyle {\boldsymbol {\mu }}} and covariance matrix Σ {\displaystyle \mathbf {\Sigma } } . These data yield the sample mean vector x ¯ {\displaystyle {\overline {\mathbf {x} }}} , and the sample covariance matrix S {\displaystyle \mathbf {S} } with eigenvalue-eigenvector pairs ( λ ^ 1 , e ^ 1 ) , ( λ ^ 2 , e ^ 2 ) , ⋯ , ( λ ^ p , e ^ p ) {\displaystyle ({\hat {\lambda }}_{1},{\hat {\mathbf {e} }}_{1}),({\hat {\lambda }}_{2},{\hat {\mathbf {e} }}_{2}),\cdots ,({\hat {\lambda }}_{p},{\hat {\mathbf {e} }}_{p})} . Then the k {\displaystyle k} -th mode of variation of X {\displaystyle \mathbf {X} } can be estimated by m ^ k , α = x ¯ ± α λ ^ k e ^ k , α ∈ [ − A , A ] . {\displaystyle {\hat {\mathbf {m} }}_{k,\alpha }={\overline {\mathbf {x} }}\pm \alpha {\sqrt {{\hat {\lambda }}_{k}}}{\hat {\mathbf {e} }}_{k},\alpha \in [-A,A].} === Modes of variation in FPCA === Consider n {\displaystyle n} realizations X 1 ( t ) , X 2 ( t ) , ⋯ , X n ( t ) {\displaystyle X_{1}(t),X_{2}(t),\cdots ,X_{n}(t)} of a square-integrable random function X ( t ) , t ∈ T {\displaystyle X(t),t\in {\mathcal {T}}} with the mean function μ ( t ) = E ⁡ ( X ( t ) ) {\displaystyle \mu (t)=\operatorname {E} (X(t))} and the covariance function G ( s , t ) = Cov ⁡ ( X ( s ) , X ( t ) ) {\displaystyle G(s,t)=\operatorname {Cov} (X(s),X(t))} . Functional principal component analysis provides methods for the estimation of μ ( t ) {\displaystyle \mu (t)} and G ( s , t ) {\displaystyle G(s,t)} in detail, often involving point wise estimate and interpolation. Substituting estimates for the unknown quantities, the k {\displaystyle k} -th mode of variation of X ( t ) {\displaystyle X(t)} can be estimated by m ^ k , α ( t ) = μ ^ ( t ) ± α λ ^ k φ ^ k ( t ) , t ∈ T , α ∈ [ − A , A ] . {\displaystyle {\hat {m}}_{k,\alpha }(t)={\hat {\mu }}(t)\pm \alpha {\sqrt {{\hat {\lambda }}_{k}}}{\hat {\varphi }}_{k}(t),t\in {\mathcal {T}},\alpha \in [-A,A].} == Applications == Modes of variation are useful to visualize and describe the variation patterns in the data sorted by the eigenvalues. In real-world applications, modes of variation associated with eigencomponents allow to interpret complex data, such as the evolution of function traits and other infinite-dimensional data. To illustrate how modes of variation work in practice, two examples are shown in the graphs to the right, which display the first two modes of variation. The solid curve represents the sample mean function. The dashed, dot-dashed, and dotted curves correspond to modes of variation with α = ± 1 , ± 2 , {\displaystyle \alpha =\pm 1,\pm 2,} and ± 3 {\displaystyle \pm 3} , respectively. The first graph displays the first two modes of variation of female mortality data from 41 countries in 2003. The object of interest is log hazard function between ages 0 and 100 years. The first mode of variation suggests that the variation of female mortality is smaller for ages around 0 or 100, and larger for ages around 25. An appropriate and intuitive interpretation is that mortality around 25 is driven by accidental death, while around 0 or 100, mortality is related to congenital disease or natural death. Compared to female mortality

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  Wolfram Mathematica

  Wolfram Mathematica (also known as Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. == Notebook interface == Mathematica is split into two parts: the kernel and the front end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by the front end. The original front end, designed by Theodore Gray in 1988, consists of a notebook interface and allows the creation and editing of notebook documents that can contain code, plaintext, images, and graphics. Code development is also supported through support in a range of standard integrated development environment (IDE) including Eclipse, IntelliJ IDEA, Atom, Vim, Visual Studio Code and Git. The Mathematica Kernel also includes a command line front end. Other interfaces include JMath, based on GNU Readline and WolframScript which runs self-contained Mathematica programs (with arguments) from the UNIX command line. == High-performance computing == Capabilities for high-performance computing were extended with the introduction of packed arrays in version 4 (1999) and sparse matrices (version 5, 2003), and by adopting the GNU Multiple Precision Arithmetic Library to evaluate high-precision arithmetic. Version 5.2 (2005) added automatic multi-threading when computations are performed on multi-core computers. This release included CPU-specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed. In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as Windows HPC Server 2008, Microsoft Compute Cluster Server and Sun Grid. Support for CUDA and OpenCL GPU hardware was added in 2010. == Extensions == As of Version 14, there are 6,602 built-in functions and symbols in the Wolfram Language. Stephen Wolfram announced the launch of the Wolfram Function Repository in June 2019 as a way for the public Wolfram community to contribute functionality to the Wolfram Language. There are currently more than 3000 functions contributed as Resource Functions. In addition to the Wolfram Function Repository, there is a Wolfram Data Repository with computable data and the Wolfram Neural Net Repository for machine learning. Wolfram Mathematica is the basis of the Combinatorica package, which adds discrete mathematics functionality in combinatorics and graph theory to the program. == Connections to other applications, programming languages, and services == Communication with other applications can be done using a protocol called Wolfram Symbolic Transfer Protocol (WSTP). It allows communication between the Wolfram Mathematica kernel and the front end and provides a general interface between the kernel and other applications. Wolfram Research freely distributes a developer kit for linking applications written in the programming language C to the Mathematica kernel through WSTP using J/Link., a Java program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link, but with .NET programs instead of Java programs. Other languages that connect to Mathematica include Haskell, AppleScript, Racket, Visual Basic, Python, and Clojure. Mathematica supports the generation and execution of Modelica models for systems modeling and connects with Wolfram System Modeler. Links are also available to many third-party software packages and APIs. Mathematica can also capture real-time data from a variety of sources and can read and write to public blockchains (Bitcoin, Ethereum, and ARK). It supports import and export of over 220 data, image, video, sound, computer-aided design (CAD), geographic information systems (GIS), document, and biomedical formats. In 2019, support was added for compiling Wolfram Language code to LLVM. Version 12.3 of the Wolfram Language added support for Arduino. == Computable data == Mathematica is also integrated with Wolfram Alpha, an online answer engine that provides additional data, some of which is kept updated in real time, for users who use Mathematica with an internet connection. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical, airplane, and weather data, in addition to mathematical data (such as knots and polyhedra). == Reception == BYTE in 1989 listed Mathematica as among the "Distinction" winners of the BYTE Awards, stating that it "is another breakthrough Macintosh application ... it could enable you to absorb the algebra and calculus that seemed impossible to comprehend from a textbook". Mathematica has been criticized for being closed source. Wolfram Research claims keeping Mathematica closed source is central to its business model and the continuity of the software.

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  Tensor sketch

  In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms. == Mathematical definition == Mathematically, a dimensionality reduction or sketching matrix is a matrix M ∈ R k × d {\displaystyle M\in \mathbb {R} ^{k\times d}} , where k < d {\displaystyle k Read more →

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  Screen space directional occlusion

  Screen space directional occlusion (SSDO) is a computer graphics technique enhancing screen space ambient occlusion (SSAO) by taking direction into account to sample the ambient light (both the light coming directly at an object, as well as the light reflected off of the object directly behind it), to better approximate global illumination. SSDO was introduced by Tobias Ritschel, Thorsten Grosch, and Hans-Peter Seidel in their 2009 ACM Symposium on Interactive 3D Graphics and Games paper Approximating dynamic global illumination in image space, which describes it as extending SSAO to directional occlusion with one diffuse indirect bounce of light; later literature notes that SSDO still suffers from common screen-space artifacts such as noise and banding. == Method == The original SSDO paper describes a two-pass screen-space approach, with one pass for direct lighting and a second pass for indirect bounces. Later literature describes SSDO as assuming a general shadowing direction that allows color bleeding and a single light bounce.

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  World Programming System

  The World Programming System, also known as WPS Analytics or WPS, is a software product developed by a company called World Programming (acquired by Altair Engineering). WPS Analytics supports users of mixed ability to access and process data and to perform data science tasks. It has interactive visual programming tools using data workflows, and it has coding tools supporting the use of the SAS language mixed with Python, R and SQL. == About == WPS can use programs written in the language of SAS without the need for translating them into any other language. In this regard WPS is compatible with the SAS system. WPS has a built-in language interpreter able to process the language of SAS and produce similar results. WPS is available to run on z/OS, Windows, macOS, Linux (x86, Armv8 64-bit, IBM Power LE, IBM Z), and AIX. On all supported platforms, programs written in the language of SAS can be executed from a WPS command line interface, often referred to as running in batch mode. WPS can also be used from a graphical user interface known as the WPS Workbench for managing, editing and running programs written in the language of SAS. The WPS Workbench user interface is based on Eclipse. WPS version 4 (released in March 2018) introduced a drag-and-drop workflow canvas providing interactive blocks for data retrieval, blending and preparation, data discovery and profiling, predictive modelling powered by machine learning algorithms, model performance validation and scorecards. WPS version 3 (released in February 2012) provided a new client/server architecture that allows the WPS Workbench GUI to execute SAS programs on remote server installations of WPS in a network or cloud. The resulting output, data sets, logs, etc., can then all be viewed and manipulated from inside the Workbench as if the workloads had been executed locally. SAS programs do not require any special language statements to use this feature. == Summary of main features == Runs on Windows, macOS, z/OS, Linux (x86, Armv8 64-bit, IBM Power LE, IBM Z), and AIX An integrated development environment based on Eclipse for Linux, macOS and Windows. Support for language of SAS elements. Support for the language of SAS Macros. Matrix Programming support using PROC IML. Support for generating band plots, bar charts, box plots, bubble plots, contour plots, dendrogram plots, ellipse plots, fringe plots, heat maps, high-low plots, histograms, loess plots, needle plots, pie charts, penalised b-spline, radar charts, reference lines, scatter plots, series plots, step plots, regression plots and vector plots. Support for statistical procedures ACECLUS, ASSOCRULES, ANOVA, BIN, BOXPLOT, CANCORR, CANDISC, CLUSTER, CORRESP, DISCRIM, DISTANCE, FACTOR, FASTCLUS, FREQ, GAM, GANNO, GENMOD, GLIMMIX, GLM, GLMMOD, GLMSELECT, ICLIFETEST, KDE, LIFEREG, LIFETEST, LOESS, LOGISTIC, MDS, MEANS, MI, MIANALYSE, MIXED, MODECLUS, NESTED, NLIN, NPAR1WAY, PHREG, PLAN, PLS, POWER, PRINCOMP, PROBIT, QUANTREG, RBF, REG, ROBUSTREG, RSREG, SCORE, SEGMENT, SIMNORMAL, STANDARD, STDSIZE, STDRATE, STEPDISC, SUMMARY, SURVEYMEANS, SURVEYSELECT, TPSPLINE, TRANSREG, TREE, TTEST, UNIVARIATE, VARCLUS, VARCOMP Support for time series procedures ARIMA, AUTOREG, ESM, EXPAND, FORECAST, LOAN, SEVERITY, SPECTRA, TIMESERIES, X12 Support for machine learning procedures DECISIONFOREST, DECISIONTREE, GMM, MLP, OPTIMALBIN, SEGMENT, SVM Support for ODS. Reads and writes SAS datasets (compressed or uncompressed). Access: Actian Matrix (previously known as ParAccel), DASD, DB2, Excel, Greenplum, Hadoop, Informix, Kognitio Archived 2012-08-24 at the Wayback Machine, MariaDB, MySQL, Netezza, ODBC, OLEDB, Oracle, PostgreSQL, SAND, Snowflake, SPSS/PSPP, SQL Server, Sybase, Sybase IQ, Teradata, VSAM, Vertica and XML. Support for SAS Tape Format. Direct output of reports to CSV, PDF and HTML. Support to connect WPS systems programmatically, remote submit parts of a program to execute on connected remote servers, upload and download data between the connected systems. Support for Hadoop Support for R Support for Python == Industry recognition == Gartner recognized World Programming in their Cool Vendors in Data Science, 2014 Report. == Lawsuit == In 2010 World Programming defended its use of the language of SAS in the High Court of England and Wales in SAS Institute Inc. v World Programming Ltd. The software was the subject of a lawsuit by SAS Institute. The EU Court of Justice ruled in favor of World Programming, stating that the copyright protection does not extend to the software functionality, the programming language used and the format of the data files used by the program. It stated that there is no copyright infringement when a company which does not have access to the source code of a program studies, observes and tests that program to create another program with the same functionality.

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  Constrained clustering

  In computer science, constrained clustering is a class of semi-supervised learning algorithms. Typically, constrained clustering incorporates either a set of must-link constraints, cannot-link constraints, or both, with a data clustering algorithm. A cluster in which the members conform to all must-link and cannot-link constraints is called a chunklet. == Types of constraints == Both a must-link and a cannot-link constraint define a relationship between two data instances. Together, the sets of these constraints act as a guide for which a constrained clustering algorithm will attempt to find chunklets (clusters in the dataset which satisfy the specified constraints). A must-link constraint is used to specify that the two instances in the must-link relation should be associated with the same cluster. A cannot-link constraint is used to specify that the two instances in the cannot-link relation should not be associated with the same cluster. Some constrained clustering algorithms will abort if no such clustering exists which satisfies the specified constraints. Others will try to minimize the amount of constraint violation should it be impossible to find a clustering which satisfies the constraints. Constraints could also be used to guide the selection of a clustering model among several possible solutions. == Examples == Examples of constrained clustering algorithms include: COP K-means PCKmeans (Pairwise Constrained K-means) CMWK-Means (Constrained Minkowski Weighted K-Means)

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  AdaBoost

  AdaBoost (short for Adaptive Boosting) is a statistical classification meta-algorithm formulated by Yoav Freund and Robert Schapire in 1995, who won the 2003 Gödel Prize for their work. It can be used in conjunction with many types of learning algorithm to improve performance. The output of multiple weak learners is combined into a weighted sum that represents the final output of the boosted classifier. Usually, AdaBoost is presented for binary classification, although it can be generalized to multiple classes or bounded intervals of real values. AdaBoost is adaptive in the sense that subsequent weak learners (models) are adjusted in favor of instances misclassified by previous models. In some problems, it can be less susceptible to overfitting than other learning algorithms. The individual learners can be weak, but as long as the performance of each one is slightly better than random guessing, the final model can be proven to converge to a strong learner. Although AdaBoost is typically used to combine weak base learners (such as decision stumps), it has been shown to also effectively combine strong base learners (such as deeper decision trees), producing an even more accurate model. Every learning algorithm tends to suit some problem types better than others, and typically has many different parameters and configurations to adjust before it achieves optimal performance on a dataset. AdaBoost (with decision trees as the weak learners) is often referred to as the best out-of-the-box classifier. When used with decision tree learning, information gathered at each stage of the AdaBoost algorithm about the relative 'hardness' of each training sample is fed into the tree-growing algorithm such that later trees tend to focus on harder-to-classify examples. == Training == AdaBoost refers to a particular method of training a boosted classifier. A boosted classifier is a classifier of the form F T ( x ) = ∑ t = 1 T f t ( x ) {\displaystyle F_{T}(x)=\sum _{t=1}^{T}f_{t}(x)} where each f t {\displaystyle f_{t}} is a weak learner that takes an object x {\displaystyle x} as input and returns a value indicating the class of the object. For example, in the two-class problem, the sign of the weak learner's output identifies the predicted object class and the absolute value gives the confidence in that classification. Each weak learner produces an output hypothesis h {\displaystyle h} which fixes a prediction h ( x i ) {\displaystyle h(x_{i})} for each sample in the training set. At each iteration t {\displaystyle t} , a weak learner is selected and assigned a coefficient α t {\displaystyle \alpha _{t}} such that the total training error E t {\displaystyle E_{t}} of the resulting t {\displaystyle t} -stage boosted classifier is minimized. E t = ∑ i E [ F t − 1 ( x i ) + α t h ( x i ) ] {\displaystyle E_{t}=\sum _{i}E[F_{t-1}(x_{i})+\alpha _{t}h(x_{i})]} Here F t − 1 ( x ) {\displaystyle F_{t-1}(x)} is the boosted classifier that has been built up to the previous stage of training and f t ( x ) = α t h ( x ) {\displaystyle f_{t}(x)=\alpha _{t}h(x)} is the weak learner that is being considered for addition to the final classifier. === Weighting === At each iteration of the training process, a weight w i , t {\displaystyle w_{i,t}} is assigned to each sample in the training set equal to the current error E ( F t − 1 ( x i ) ) {\displaystyle E(F_{t-1}(x_{i}))} on that sample. These weights can be used in the training of the weak learner. For instance, decision trees can be grown which favor the splitting of sets of samples with large weights. == Derivation == This derivation follows Rojas (2009): Suppose we have a data set { ( x 1 , y 1 ) , … , ( x N , y N ) } {\displaystyle \{(x_{1},y_{1}),\ldots ,(x_{N},y_{N})\}} where each item x i {\displaystyle x_{i}} has an associated class y i ∈ { − 1 , 1 } {\displaystyle y_{i}\in \{-1,1\}} , and a set of weak classifiers { k 1 , … , k L } {\displaystyle \{k_{1},\ldots ,k_{L}\}} each of which outputs a classification k j ( x i ) ∈ { − 1 , 1 } {\displaystyle k_{j}(x_{i})\in \{-1,1\}} for each item. After the ( m − 1 ) {\displaystyle (m-1)} -th iteration our boosted classifier is a linear combination of the weak classifiers of the form: C ( m − 1 ) ( x i ) = α 1 k 1 ( x i ) + ⋯ + α m − 1 k m − 1 ( x i ) , {\displaystyle C_{(m-1)}(x_{i})=\alpha _{1}k_{1}(x_{i})+\cdots +\alpha _{m-1}k_{m-1}(x_{i}),} where the class will be the sign of C ( m − 1 ) ( x i ) {\displaystyle C_{(m-1)}(x_{i})} . At the m {\displaystyle m} -th iteration we want to extend this to a better boosted classifier by adding another weak classifier k m {\displaystyle k_{m}} , with another weight α m {\displaystyle \alpha _{m}} : C m ( x i ) = C ( m − 1 ) ( x i ) + α m k m ( x i ) {\displaystyle C_{m}(x_{i})=C_{(m-1)}(x_{i})+\alpha _{m}k_{m}(x_{i})} So it remains to determine which weak classifier is the best choice for k m {\displaystyle k_{m}} , and what its weight α m {\displaystyle \alpha _{m}} should be. We define the total error E {\displaystyle E} of C m {\displaystyle C_{m}} as the sum of its exponential loss on each data point, given as follows: E = ∑ i = 1 N e − y i C m ( x i ) = ∑ i = 1 N e − y i C ( m − 1 ) ( x i ) e − y i α m k m ( x i ) {\displaystyle E=\sum _{i=1}^{N}e^{-y_{i}C_{m}(x_{i})}=\sum _{i=1}^{N}e^{-y_{i}C_{(m-1)}(x_{i})}e^{-y_{i}\alpha _{m}k_{m}(x_{i})}} Letting w i ( 1 ) = 1 {\displaystyle w_{i}^{(1)}=1} and w i ( m ) = e − y i C m − 1 ( x i ) {\displaystyle w_{i}^{(m)}=e^{-y_{i}C_{m-1}(x_{i})}} for m > 1 {\displaystyle m>1} , we have: E = ∑ i = 1 N w i ( m ) e − y i α m k m ( x i ) {\displaystyle E=\sum _{i=1}^{N}w_{i}^{(m)}e^{-y_{i}\alpha _{m}k_{m}(x_{i})}} We can split this summation between those data points that are correctly classified by k m {\displaystyle k_{m}} (so y i k m ( x i ) = 1 {\displaystyle y_{i}k_{m}(x_{i})=1} ) and those that are misclassified (so y i k m ( x i ) = − 1 {\displaystyle y_{i}k_{m}(x_{i})=-1} ): E = ∑ y i = k m ( x i ) w i ( m ) e − α m + ∑ y i ≠ k m ( x i ) w i ( m ) e α m = ∑ i = 1 N w i ( m ) e − α m + ∑ y i ≠ k m ( x i ) w i ( m ) ( e α m − e − α m ) {\displaystyle {\begin{aligned}E&=\sum _{y_{i}=k_{m}(x_{i})}w_{i}^{(m)}e^{-\alpha _{m}}+\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}e^{\alpha _{m}}\\&=\sum _{i=1}^{N}w_{i}^{(m)}e^{-\alpha _{m}}+\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}\left(e^{\alpha _{m}}-e^{-\alpha _{m}}\right)\end{aligned}}} Since the only part of the right-hand side of this equation that depends on k m {\displaystyle k_{m}} is ∑ y i ≠ k m ( x i ) w i ( m ) {\textstyle \sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}} , we see that the k m {\displaystyle k_{m}} that minimizes E {\displaystyle E} is the one in the set { k 1 , … , k L } {\displaystyle \{k_{1},\ldots ,k_{L}\}} that minimizes ∑ y i ≠ k m ( x i ) w i ( m ) {\textstyle \sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}} [assuming that α m > 0 {\displaystyle \alpha _{m}>0} ], i.e. the weak classifier with the lowest weighted error (with weights w i ( m ) = e − y i C m − 1 ( x i ) {\displaystyle w_{i}^{(m)}=e^{-y_{i}C_{m-1}(x_{i})}} ). To determine the desired weight α m {\displaystyle \alpha _{m}} that minimizes E {\displaystyle E} with the k m {\displaystyle k_{m}} that we just determined, we differentiate: d E d α m = d ( ∑ y i = k m ( x i ) w i ( m ) e − α m + ∑ y i ≠ k m ( x i ) w i ( m ) e α m ) d α m {\displaystyle {\frac {dE}{d\alpha _{m}}}={\frac {d(\sum _{y_{i}=k_{m}(x_{i})}w_{i}^{(m)}e^{-\alpha _{m}}+\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}e^{\alpha _{m}})}{d\alpha _{m}}}} The value of α m {\displaystyle \alpha _{m}} that minimizes the above expression is: α m = 1 2 ln ⁡ ( ∑ y i = k m ( x i ) w i ( m ) ∑ y i ≠ k m ( x i ) w i ( m ) ) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {\sum _{y_{i}=k_{m}(x_{i})}w_{i}^{(m)}}{\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}}\right)} We calculate the weighted error rate of the weak classifier to be ϵ m = ∑ y i ≠ k m ( x i ) w i ( m ) ∑ i = 1 N w i ( m ) {\displaystyle \epsilon _{m}={\frac {\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}{\sum _{i=1}^{N}w_{i}^{(m)}}}} , so it follows that: α m = 1 2 ln ⁡ ( 1 − ϵ m ϵ m ) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {1-\epsilon _{m}}{\epsilon _{m}}}\right)} which is the negative logit function multiplied by 0.5. Due to the convexity of E {\displaystyle E} as a function of α m {\displaystyle \alpha _{m}} , this new expression for α m {\displaystyle \alpha _{m}} gives the global minimum of the loss function. Note: This derivation only applies when k m ( x i ) ∈ { − 1 , 1 } {\displaystyle k_{m}(x_{i})\in \{-1,1\}} , though it can be a good starting guess in other cases, such as when the weak learner is biased ( k m ( x ) ∈ { a , b } , a ≠ − b {\displaystyle k_{m}(x)\in \{a,b\},a\neq -b} ), has multiple leaves ( k m ( x ) ∈ { a , b , … , n } {\displaystyle k_{m}(x)\in \{a,b,\dots ,n\}} ) or is some other function k m ( x ) ∈ R {\displaystyle k_{m}(x)\in \mathbb {R} } . Thus we have derived the AdaBoost algorithm: At each

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  Zolostays

  Zolostays is a real-tech co-living focused startup that provides ready-to-move rooms/beds. It was founded in 2015 by Nikhil Sikri, Akhil Sikri and Sneha Choudhry. == Overview == During the pandemic, Zolo provided 75 of rent-free accommodation to those who lost their jobs. Zolo uses bulk inventory in usually residential township and ties up with real estate companies to make the rooms/beds available. Zolostays has both revenue sharing and leased model. == History == Zolostays was founded in 2015 to solve the problem of students and young professionals who would move to temporarily go to other cities to study and work and look for affordable housing. In 2020, it was operating in 10 Indian cities. It has four round of funding, with total $98 million.

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  Witness set

  In combinatorics and computational learning theory, a witness set is a set of elements that distinguishes a given Boolean function from a given class of other Boolean functions. Let C {\displaystyle C} be a concept class over a domain X {\displaystyle X} (that is, a family of Boolean functions over X {\displaystyle X} ) and c {\displaystyle c} be a concept in X {\displaystyle X} (a single Boolean function). A subset S {\displaystyle S} of X {\displaystyle X} is a witness set for c {\displaystyle c} in X {\displaystyle X} if S {\displaystyle S} distinguishes c {\displaystyle c} from all the other functions in C {\displaystyle C} , in the sense that no other function in C {\displaystyle C} has the same values on S {\displaystyle S} . For a concept class with | C | {\displaystyle |C|} concepts, there exists a concept that has a witness of size at most log 2 ⁡ | C | {\displaystyle \log _{2}|C|} ; this bound is tight when C {\displaystyle C} consists of all Boolean functions over X {\displaystyle X} . By a result of Bondy (1972) there exists a single witness set of size at most | C | − 1 {\displaystyle |C|-1} that is valid for all concepts in C {\displaystyle C} ; this bound is tight when C {\displaystyle C} consists of the indicator functions of the empty set and some singleton sets. One way to construct this set is to interpret the concepts as bitstrings, and the domain elements as positions in these bitstrings. Then the set of positions at which a trie of the bitstrings branches forms the desired witness set. This construction is central to the operation of the fusion tree data structure. The minimum size of a witness set for c {\displaystyle c} is called the witness size or specification number and is denoted by w C ( c ) {\displaystyle w_{C}(c)} . The value max { w C ( c ) : c ∈ C } {\displaystyle \max\{w_{C}(c):c\in C\}} is called the teaching dimension of C {\displaystyle C} . It represents the number of examples of a concept that need to be presented by a teacher to a learner, in the worst case, to enable the learner to determine which concept is being presented. Witness sets have also been called teaching sets, keys, specifying sets, or discriminants. The "witness set" terminology is from Kushilevitz et al. (1996), who trace the concept of witness sets to work by Cover (1965).

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  Probit model

  In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such an estimation being called a probit regression. == Conceptual framework == Suppose a response variable Y is binary, that is it can have only two possible outcomes which we will denote as 1 and 0. For example, Y may represent presence/absence of a certain condition, success/failure of some device, answer yes/no on a survey, etc. We also have a vector of regressors X, which are assumed to influence the outcome Y. Specifically, we assume that the model takes the form P ( Y = 1 ∣ X ) = Φ ( X T β ) , {\displaystyle P(Y=1\mid X)=\Phi (X^{\operatorname {T} }\beta ),} where P is the probability and Φ {\displaystyle \Phi } is the cumulative distribution function (CDF) of the standard normal distribution. The parameters β are typically estimated by maximum likelihood. It is possible to motivate the probit model as a latent variable model. Suppose there exists an auxiliary random variable Y ∗ = X T β + ε , {\displaystyle Y^{\ast }=X^{T}\beta +\varepsilon ,} where ε ~ N(0, 1). Then Y can be viewed as an indicator for whether this latent variable is positive: Y = { 1 Y ∗ > 0 0 otherwise } = { 1 X T β + ε > 0 0 otherwise } {\displaystyle Y=\left.{\begin{cases}1&Y^{}>0\\0&{\text{otherwise}}\end{cases}}\right\}=\left.{\begin{cases}1&X^{\operatorname {T} }\beta +\varepsilon >0\\0&{\text{otherwise}}\end{cases}}\right\}} The use of the standard normal distribution causes no loss of generality compared with the use of a normal distribution with an arbitrary mean and standard deviation, because adding a fixed amount to the mean can be compensated by subtracting the same amount from the intercept, and multiplying the standard deviation by a fixed amount can be compensated by multiplying the weights by the same amount. To see that the two models are equivalent, note that P ( Y = 1 ∣ X ) = P ( Y ∗ > 0 ) = P ( X T β + ε > 0 ) = P ( ε > − X T β ) = P ( ε < X T β ) by symmetry of the normal distribution = Φ ( X T β ) {\displaystyle {\begin{aligned}P(Y=1\mid X)&=P(Y^{\ast }>0)\\&=P(X^{\operatorname {T} }\beta +\varepsilon >0)\\&=P(\varepsilon >-X^{\operatorname {T} }\beta )\\&=P(\varepsilon 0 {\displaystyle t,\lim _{n\rightarrow \infty }n_{t}/n=c_{t}>0} . Denote p ^ t = r t / n t {\displaystyle {\hat {p}}_{t}=r_{t}/n_{t}} σ ^ t 2 = 1 n t p ^ t ( 1 − p ^ t ) φ 2 ( Φ − 1 ( p ^ t ) ) {\displaystyle {\hat {\sigma }}_{t}^{2}={\frac {1}{n_{t}}}{\frac {{\hat {p}}_{t}(1-{\hat {p}}_{t})}{\varphi ^{2}{\big (}\Phi ^{-1}({\hat {p}}_{t}){\big )}}}} Then Berkson's minimum chi-square estimator is a generalized least squares estimator in a regression of Φ − 1 ( p ^ t ) {\displaystyle \Phi ^{-1}({\hat {p}}_{t})} on x ( t ) {\displaystyle x_{(t)}} with weights σ ^ t − 2 {\displaystyle {\hat {\sigma }}_{t}^{-2}} : β ^ = ( ∑ t = 1 T σ ^ t − 2 x ( t ) x ( t ) T ) − 1 ∑ t = 1 T σ ^ t − 2 x ( t ) Φ − 1 ( p ^ t ) {\displaystyle {\hat {\beta }}={\Bigg (}\sum _{t=1}^{T}{\hat {\sigma }}_{t}^{-2}x_{(t)}x_{(t)}^{\operatorname {T} }{\Bigg )}^{-1}\sum _{t=1}^{T}{\hat {\sigma }}_{t}^{-2}x_{(t)}\Phi ^{-1}({\hat {p}}_{t})} It can be shown that this estimator is consistent (as n→∞ and T fixed), asymptotically normal and efficient. Its advantage is the presence of a closed-form formula for the estimator. However, it is only meaningful to carry out this analysis when individual observations are not available, only their aggregated counts r t {\displaystyle r_{t}} , n t {\disp

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  Prefrontal cortex basal ganglia working memory

  Prefrontal cortex basal ganglia working memory (PBWM) is an algorithm that models working memory in the prefrontal cortex and the basal ganglia. It can be compared to long short-term memory (LSTM) in functionality, but is more biologically explainable. It uses the primary value learned value model to train prefrontal cortex working-memory updating system, based on the biology of the prefrontal cortex and basal ganglia. It is used as part of the Leabra framework and was implemented in Emergent in 2019. == Abstract == The prefrontal cortex has long been thought to subserve both working memory (the holding of information online for processing) and "executive" functions (deciding how to manipulate working memory and perform processing). Although many computational models of working memory have been developed, the mechanistic basis of executive function remains elusive. PBWM is a computational model of the prefrontal cortex to control both itself and other brain areas in a strategic, task-appropriate manner. These learning mechanisms are based on subcortical structures in the midbrain, basal ganglia and amygdala, which together form an actor/critic architecture. The critic system learns which prefrontal representations are task-relevant and trains the actor, which in turn provides a dynamic gating mechanism for controlling working memory updating. Computationally, the learning mechanism is designed to simultaneously solve the temporal and structural credit assignment problems. The model's performance compares favorably with standard backpropagation-based temporal learning mechanisms on the challenging 1-2-AX working memory task, and other benchmark working memory tasks. == Model == First, there are multiple separate stripes (groups of units) in the prefrontal cortex and striatum layers. Each stripe can be independently updated, such that this system can remember several different things at the same time, each with a different "updating policy" of when memories are updated and maintained. The active maintenance of the memory is in prefrontal cortex (PFC), and the updating signals (and updating policy more generally) come from the striatum units (a subset of basal ganglia units). PVLV provides reinforcement learning signals to train up the dynamic gating system in the basal ganglia. === Sensory input and motor output === The sensory input is connected to the posterior cortex which is connected to the motor output. The sensory input is also linked to the PVLV system. === Posterior cortex === The posterior cortex form the hidden layers of the input/output mapping. The PFC is connected with the posterior cortex to contextualize this input/output mapping. === PFC === The PFC (for output gating) has a localist one-to-one representation of the input units for every stripe. Thus, you can look at these PFC representations and see directly what the network is maintaining. The PFC maintains the working memory needed to perform the task. === Striatum === This is the dynamic gating system representing the striatum units of the basal ganglia. Every even-index unit within a stripe represents "Go", while the odd-index units represent "NoGo." The Go units cause updating of the PFC, while the NoGo units cause the PFC to maintain its existing memory representation. There are groups of units for every stripe. In the PBWM model in Emergent, the matrices represent the striatum. === PVLV === All of these layers are part of PVLV system. The PVLV system controls the dopaminergic modulation of the basal ganglia (BG). Thus, BG/PVLV form an actor-critic architecture where the PVLV system learns when to update. ==== SNrThal ==== SNrThal represents the substantia nigra pars reticulata (SNr) and the associated area of the thalamus, which produce a competition among the Go/NoGo units within a given stripe and mediates competition using k-winners-take-all dynamics. If there is more overall Go activity in a given stripe, then the associated SNrThal unit gets activated, and it drives updating in PFC. For every stripe, there is one unit in SNrThal. ==== VTA and SNc ==== Ventral tegmental area (VTA) and substantia nigra pars compacta (SNc) are part of the dopamine layer. This layer models midbrain dopamine neurons. They control the dopaminergic modulation of the basal ganglia.

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  Software requirements

  Software requirements for a system are the description of what the system should do, the service or services that it provides and the constraints on its operation. The IEEE Standard Glossary of Software Engineering Terminology defines a requirement as: A condition or capability needed by a user to solve a problem or achieve an objective A condition or capability that must be met or possessed by a system or system component to satisfy a contract, standard, specification, or other formally imposed document A documented representation of a condition or capability as in 1 or 2 The activities related to working with software requirements can broadly be broken down into elicitation, analysis, specification, and management. Note that the wording Software requirements is additionally used in software release notes to explain, which depending on software packages are required for a certain software to be built/installed/used. == Elicitation == Elicitation is the gathering and discovery of requirements from stakeholders and other sources. A variety of techniques can be used such as joint application design (JAD) sessions, interviews, document analysis, focus groups, etc. Elicitation is the first step of requirements development. == Analysis == Analysis is the logical breakdown that proceeds from elicitation. Analysis involves reaching a richer and more precise understanding of each requirement and representing sets of requirements in multiple, complementary ways. Requirements Triage or prioritization of requirements is another activity which often follows analysis. This relates to Agile software development in the planning phase, e.g. by Planning poker, however it might not be the same depending on the context and nature of the project and requirements or product/service that is being built. == Specification == Specification involves representing and storing the collected requirements knowledge in a persistent and well-organized fashion that facilitates effective communication and change management. Use cases, user stories, functional requirements, and visual analysis models are popular choices for requirements specification. == Validation == Validation involves techniques to confirm that the correct set of requirements has been specified to build a solution that satisfies the project's business objectives, and to detect and correct errors in the requirements before implementation. == Management == Requirements change during projects and there are often many of them. Management of this change becomes paramount to ensuring that the correct software is built for the stakeholders. == Tool support for Requirements Engineering == === Tools for Requirements Elicitation, Analysis and Validation === Taking into account that these activities may involve some artifacts such as observation reports (user observation), questionnaires (interviews, surveys and polls), use cases, user stories; activities such as requirement workshops (charrettes), brainstorming, mind mapping, role-playing; and even, prototyping; software products providing some or all of these capabilities can be used to help achieve these tasks. There is at least one author who advocates, explicitly, for mind mapping tools such as FreeMind; and, alternatively, for the use of specification by example tools such as Concordion. Additionally, the ideas and statements resulting from these activities may be gathered and organized with wikis and other collaboration tools such as Trello. The features actually implemented and standards compliance vary from product to product. === Tools for Requirements Specification === A Software requirements specification (SRS) document might be created using general-purpose software like a word processor or one of several specialized tools. Some of these tools can import, edit, export and publish SRS documents. It may help to make SRS documents while following a standardised structure and methodology, such as ISO/IEC/IEEE 29148:2018. Likewise, software may or not use some standard to import or export requirements (such as ReqIF) or not allow these exchanges at all. === Tools for Requirements Document Verification === Tools of this kind verify if there are any errors in a requirements document according to some expected structure or standard. === Tools for Requirements Comparison === Tools of this kind compare two requirement sets according to some expected document structure and standard. === Tools for Requirements Merge and Update === Tools of this kind allow the merging and update of requirement documents. === Tools for Requirements Traceability === Tools of this kind allow tracing requirements to other artifacts such as models and source code (forward traceability) or, to previous ones such as business rules and constraints (backwards traceability). === Tools for Model-Based Software or Systems Requirement Engineering === Model-based systems engineering (MBSE) is the formalised application of modelling to support system requirements, design, analysis, verification and validation activities beginning in the conceptual design phase and continuing throughout development and later lifecycle phases. It is also possible to take a model-based approach for some stages of the requirements engineering and, a more traditional one, for others. Very many combinations might be possible. The level of formality and complexity depends on the underlying methodology involved (for instance, i is much more formal than SysML and, even more formal than UML) === Tools for general Requirements Engineering === Tools in this category may provide some mix of the capabilities mentioned previously and others such as requirement configuration management and collaboration. The features actually implemented and standards compliance vary from product to product. There are even more capable or general tools that support other stages and activities. They are classified as ALM tools.

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  List of text mining software

  Text mining computer programs are available from many commercial and open source companies and sources. == Commercial == Angoss – Angoss Text Analytics provides entity and theme extraction, topic categorization, sentiment analysis and document summarization capabilities via the embedded AUTINDEX – is a commercial text mining software package based on sophisticated linguistics by IAI (Institute for Applied Information Sciences), Saarbrücken. DigitalMR – social media listening & text+image analytics tool for market research. FICO Score – leading provider of analytics. General Sentiment – Social Intelligence platform that uses natural language processing to discover affinities between the fans of brands with the fans of traditional television shows in social media. Stand alone text analytics to capture social knowledge base on billions of topics stored to 2004. IBM LanguageWare – the IBM suite for text analytics (tools and Runtime). IBM SPSS – provider of Modeler Premium (previously called IBM SPSS Modeler and IBM SPSS Text Analytics), which contains advanced NLP-based text analysis capabilities (multi-lingual sentiment, event and fact extraction), that can be used in conjunction with Predictive Modeling. Text Analytics for Surveys provides the ability to categorize survey responses using NLP-based capabilities for further analysis or reporting. Inxight – provider of text analytics, search, and unstructured visualization technologies. (Inxight was bought by Business Objects that was bought by SAP AG in 2008). Language Computer Corporation – text extraction and analysis tools, available in multiple languages. Lexalytics – provider of a text analytics engine used in Social Media Monitoring, Voice of Customer, Survey Analysis, and other applications. Salience Engine. The software provides the unique capability of merging the output of unstructured, text-based analysis with structured data to provide additional predictive variables for improved predictive models and association analysis. Linguamatics – provider of natural language processing (NLP) based enterprise text mining and text analytics software, I2E, for high-value knowledge discovery and decision support. Mathematica – provides built in tools for text alignment, pattern matching, clustering and semantic analysis. See Wolfram Language, the programming language of Mathematica. MATLAB offers Text Analytics Toolbox for importing text data, converting it to numeric form for use in machine and deep learning, sentiment analysis and classification tasks. Medallia – offers one system of record for survey, social, text, written and online feedback. NetMiner – software for network analysis and text mining. Supports social media and bibliographic data collection, NLP for english and chinese, sentiment analysis, work co-occurrence network(text network analysis) and visualization. NetOwl – suite of multilingual text and entity analytics products, including entity extraction, link and event extraction, sentiment analysis, geotagging, name translation, name matching, and identity resolution, among others. PolyAnalyst - text analytics environment. PoolParty Semantic Suite - graph-based text mining platform. RapidMiner with its Text Processing Extension – data and text mining software. SAS – SAS Text Miner and Teragram; commercial text analytics, natural language processing, and taxonomy software used for Information Management. Sketch Engine – a corpus manager and analysis software which providing creating text corpora from uploaded texts or the Web including part-of-speech tagging and lemmatization or detecting a particular website. Sysomos – provider social media analytics software platform, including text analytics and sentiment analysis on online consumer conversations. WordStat – Content analysis and text mining add-on module of QDA Miner for analyzing large amounts of text data. == Open source == Carrot2 – text and search results clustering framework. GATE – general Architecture for Text Engineering, an open-source toolbox for natural language processing and language engineering. Gensim – large-scale topic modelling and extraction of semantic information from unstructured text (Python). KH Coder – for Quantitative Content Analysis or Text Mining The KNIME Text Processing extension. Natural Language Toolkit (NLTK) – a suite of libraries and programs for symbolic and statistical natural language processing (NLP) for the Python programming language. OpenNLP – natural language processing. Orange with its text mining add-on. The PLOS Text Mining Collection. The programming language R provides a framework for text mining applications in the package tm. The Natural Language Processing task view contains tm and other text mining library packages. spaCy – open-source Natural Language Processing library for Python Stanbol – an open source text mining engine targeted at semantic content management. Voyant Tools – a web-based text analysis environment, created as a scholarly project.

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  Swish function

  The swish function is a family of mathematical function defined as follows: swish β ⁡ ( x ) = x sigmoid ⁡ ( β x ) = x 1 + e − β x . {\displaystyle \operatorname {swish} _{\beta }(x)=x\operatorname {sigmoid} (\beta x)={\frac {x}{1+e^{-\beta x}}}.} where β {\displaystyle \beta } can be constant (usually set to 1) or trainable and "sigmoid" refers to the logistic function. The swish family was designed to smoothly interpolate between a linear function and the Rectified linear unit (ReLU) function. When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in . Variants of the swish function include Mish. == Special values == For β = 0, the function is linear: f(x) = x/2. For β = 1, the function is the Sigmoid Linear Unit (SiLU). For β = 1.702, the function approximates GeLU. With β → ∞, the function converges to ReLU. Thus, the swish family smoothly interpolates between a linear function and the ReLU function. Since swish β ⁡ ( x ) = swish 1 ⁡ ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , all instances of swish have the same shape as the default swish 1 {\displaystyle \operatorname {swish} _{1}} , zoomed by β {\displaystyle \beta } . One usually sets β > 0 {\displaystyle \beta >0} . When β {\displaystyle \beta } is trainable, this constraint can be enforced by β = e b {\displaystyle \beta =e^{b}} , where b {\displaystyle b} is trainable. swish 1 ⁡ ( x ) = x 2 + x 2 4 − x 4 48 + x 6 480 + O ( x 8 ) {\displaystyle \operatorname {swish} _{1}(x)={\frac {x}{2}}+{\frac {x^{2}}{4}}-{\frac {x^{4}}{48}}+{\frac {x^{6}}{480}}+O\left(x^{8}\right)} swish 1 ⁡ ( x ) = x 2 tanh ⁡ ( x 2 ) + x 2 swish 1 ⁡ ( x ) + swish − 1 ⁡ ( x ) = x tanh ⁡ ( x 2 ) swish 1 ⁡ ( x ) − swish − 1 ⁡ ( x ) = x {\displaystyle {\begin{aligned}\operatorname {swish} _{1}(x)&={\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)+{\frac {x}{2}}\\\operatorname {swish} _{1}(x)+\operatorname {swish} _{-1}(x)&=x\tanh \left({\frac {x}{2}}\right)\\\operatorname {swish} _{1}(x)-\operatorname {swish} _{-1}(x)&=x\end{aligned}}} == Derivatives == Because swish β ⁡ ( x ) = swish 1 ⁡ ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , it suffices to calculate its derivatives for the default case. swish 1 ′ ⁡ ( x ) = x + sinh ⁡ ( x ) 4 cosh 2 ⁡ ( x 2 ) + 1 2 {\displaystyle \operatorname {swish} _{1}'(x)={\frac {x+\sinh(x)}{4\cosh ^{2}\left({\frac {x}{2}}\right)}}+{\frac {1}{2}}} so swish 1 ′ ⁡ ( x ) − 1 2 {\displaystyle \operatorname {swish} _{1}'(x)-{\frac {1}{2}}} is odd. swish 1 ″ ⁡ ( x ) = 1 − x 2 tanh ⁡ ( x 2 ) 2 cosh 2 ⁡ ( x 2 ) {\displaystyle \operatorname {swish} _{1}''(x)={\frac {1-{\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)}{2\cosh ^{2}\left({\frac {x}{2}}\right)}}} so swish 1 ″ ⁡ ( x ) {\displaystyle \operatorname {swish} _{1}''(x)} is even. == History == SiLU was first proposed alongside the GELU in 2016, then again proposed in 2017 as the Sigmoid-weighted Linear Unit (SiL) in reinforcement learning. The SiLU/SiL was then again proposed as the SWISH over a year after its initial discovery, originally proposed without the learnable parameter β, so that β implicitly equaled 1. The swish paper was then updated to propose the activation with the learnable parameter β. In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. It is believed that one reason for the improvement is that the swish function helps alleviate the vanishing gradient problem during backpropagation.

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