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  List of data science software

  This is a list of data science software and platforms used in data science, which includes programming languages, programming environments, machine learning frameworks, data engineering tools, statistical software, data analysis, plotting, MLOps systems, and more. == Programming languages == == Development environments == These interactive notebooks, IDEs, and platforms provide specialised development environments. Apache Zeppelin Architect — Eclipse (software) CoCalc Dataiku Data Science Studio FreeMat GNU Octave Google Colab DataSpell Jupyter Notebook / JupyterLab Kaggle Notebooks MATLAB O-Matrix PyCharm RStudio SAS (software) and SAS Studio Spyder Visual Studio Code == Machine and deep learning software == The Machine learning / deep learning tools support development in those fields. == Data engineering == Examples of Data engineering tools. Apache Airflow Apache Flink Apache Hadoop Apache Kafka Apache NiFi Apache Spark Dask Data build tool (dbt) == Data mining == Examples of Data mining tools. === Free and open-source === === Proprietary === == Database management == === List of RDBMS === ==== Proprietary ==== == Data warehouses == Data warehouse environments include: Amazon Redshift Snowflake Google BigQuery Microsoft Azure Synapse Teradata Vertica == Data lakes == Data lake environments include: Apache Hadoop Cloudera Databricks Delta Lake Amazon S3 Google Cloud Storage Azure Data Lake == Algorithms == Apriori algorithm – frequent itemset mining and association rule learning in market basket analysis Backpropagation – algorithm for training artificial neural networks using gradient descent Decision Trees – tree-based algorithm for classification and regression Expectation–maximization algorithm – iterative procedure for maximum likelihood estimation with latent variables Gradient descent – iterative optimization algorithm for minimizing a loss function ID3 algorithm – used to generate a decision tree from a dataset K-Means – clustering algorithm based on minimizing within-cluster distances K-Nearest Neighbors (KNN) – instance-based learning and classification method Linear regression – estimation method for predicting a dependent variable based on independent variables Logistic regression – classification algorithm for predicting a binary outcome Naive Bayes – probabilistic classifier based on Bayes' theorem Ordinary least squares – estimation method for parameters in linear regression PageRank – graph-based algorithm for link analysis and search ranking Principal component analysis – technique to reduce high-dimensional data while preserving variance Q-learning – reinforcement learning algorithm for learning optimal actions Random forest – ensemble of decision trees for improved classification or regression Sequential minimal optimization – solver for training support vector machines Stochastic gradient descent – randomized variant of gradient descent for large-scale machine learning Support Vector Machines (SVM) – algorithm for finding a hyperplane to separate classes == Statistical software == === Open-source === === Public domain === CSPro Dataplot Epi Map X-13ARIMA-SEATS === Freeware === BV4.1 MINUIT WinBUGS Winpepi === Proprietary === == Data processing == Tools for Data processing and analysis: == Data and information visualization == Software for Data visualization: == Plotting software == Software for plotting data to support processing and visualise results. == Maps and geospatial visualization == ArcGIS Carto Epi Map GeoDA Google Earth Engine Leaflet Mapbox MountainsMap QGIS == Machine learning == MLOps and model deployment: BentoML Data Version Control (DVC) Kubeflow MLflow Seldon Core Streamlit TensorFlow Serving Weights & Biases == Data repositories == Kaggle – platform for data science competitions, datasets, and notebooks. OpenML – collaborative platform for sharing datasets, algorithms, and experiments. University of California, Irvine Machine Learning Repository Zenodo – open-access repository supported by CERN and the EU. == Educational data science software == Kaggle – online platform for data science education, competitions, datasets, and collaborative learning. KNIME – open-source data analytics platform used for teaching data science, machine learning, and workflow-based analysis. RapidMiner – used in academic research and education for data mining and machine learning. Statistics Online Computational Resource (SOCR) – online tools and instructional resources for statistics education. Tanagra (machine learning) – data mining software developed for research and teaching purposes. TinkerPlots – explore and analyze data through visual modeling.

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  Information professional

  The term information professional or information specialist refers to professionals responsible for the collection, documentation, organization, storage, preservation, retrieval, and dissemination of printed and digital information. The service delivered to the client is known as an information service. The term "information professional" is a versatile one, used to describe similar and sometimes overlapping professions, such as librarians, archivists, information managers, information systems specialists, information scientists, records managers, and information consultants. However, terminology differs among sources and organisations. Information professionals are employed in a variety of private, public, and academic institutions, as well as independently. == Skills == Since the term information professional is broad, the skills required for this profession are also varied. A Gartner report in 2011 pointed out that "Professional roles focused on information management will be different to that of established IT roles. An 'information professional' will not be one type of role or skill set, but will in fact have a number of specializations". Thus, an information professional can possess a variety of different skills, depending on the sector in which the person is employed. Some essential cross-sector skills are: IT skills, such as word-processing and spreadsheets, digitisation skills, and conducting Internet searches, together with skills loan systems, databases, content management systems, and specially designed programmes and packages. Customer service. An information professional should have the ability to address the information needs of customers. Language proficiency. This is essential in order to manage the information at hand and deal with customer needs. Soft skills. These include skills such as negotiating, conflict resolution, and time management. Management training. An information professional should be familiar with notions such as strategic planning and project management. Moreover, an information professional should be skilled in planning and using relevant systems, in capturing and securing information, and in accessing it to deliver service whenever the information is required. == Associations == Most countries have a professional association who oversee the professional and academic standards of librarians and other information professionals. There are also international associations related to LIS (library and information science), the most prominent of which is the International Federation of Library Associations and Institutions (IFLA). In many countries, LIS courses are accredited by the relevant professional association, as the American Library Association (ALA) in the USA, the Chartered Institute of Library and Information Professionals (CILIP) in the UK, and the Australian Library and Information Association (ALIA) in Australia. == Qualifications == Educational institutions around the world offer academic degrees, or degrees on related subjects such as Archival Studies, Information Systems, Information Management, and Records Management. Some of the institutions offering information science education refer to themselves as an iSchool, such as the CiSAP (Consortium of iSchools Asia Pacific, founded 2006) in Asia and the iSchool Caucus in the USA. There are also online e-learning resources, some of which offer certification for information professionals. === Africa === Information development in Africa started later than in other continents, mainly due to a lack of internet access, expertise and resources to manage digital infrastructure, and "opportunities for capacity development and knowledge-sharing". Nowadays, academic degrees in information studies are available at many universities of African countries, such as the University of Pretoria (South Africa), University of Nairobi (Kenya), Makerere University (Uganda), University of Botswana (Botswana), and University of Nigeria (Nigeria). === Asia === LIS-related studies are available in more than 30 Asian countries. Some examples listed by iSchools Inc. are the University of Hong Kong, University of Tsukuba, Japan, Yonsei University, South Korea, National Taiwan University and Wuhan University, China. Centre of Library and Information Management Science (CLIMS) at Tata Institute of Social Science in Mumbai, India. In Southeast Asia, the Congress of Southeast Asian Librarians (CONSAL) connects librarians and libraries in more than 10 countries with resources, networking opportunities, and support for growing library systems. === Australasia === The Australian Library and Information Association (ALIA) as of 2021 lists six schools offering undergraduate and postgraduate accredited university courses for "Librarian and Information Specialists" on their website. In New Zealand, the Open Polytechnic of New Zealand and the Victoria University of Wellington offer undergraduate and postgraduate degree courses for information professionals. === Europe === The majority of European countries have universities, colleges, or schools which offer bachelor's degrees in LIS studies. Over 40 universities offer master's degrees in LIS-related fields, and many institutions, such as the Swedish School of Library and Information Science at the University of Borås (Sweden), the University of Barcelona (Spain), Loughborough University (UK), and Aberystwyth University (Wales, UK) also offer PhD degrees. === North America === Information studies and degrees are available at numerous academic institutions throughout the U.S. and Canada. U.S. professional associations, together with their European counterparts, have undertaken many educational initiatives and pioneered many advances in the field of Information studies, such as increased interdisciplinarity and more effective delivery of distance learning. The Association for Intelligent Information Management, based in Silver Spring, Maryland, offers a qualification called Certified Information Professional (CIP), earned upon passing an examination, with certification remaining valid for three years. === South America === There are many schools and colleges in Latin America, which offer courses in Library Science, Archival Studies, and Information Studies, however these subjects are taught completely separately.

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  Informedia Digital Library

  The Informedia Digital Library is an ongoing research program at Carnegie Mellon University to build search engines and information visualization technology for many types of media. The program has carried out research on spoken document retrieval, video information retrieval, video segmentation, face recognition, and cross-language information retrieval. The Lycos search engine was an early product of the Informedia Digital Library Project. The project is led by Howard Wactlar. Researchers on the project have included: Michael Mauldin, Alex Hauptmann, Michael Christel, Michael Witbrock, Raj Reddy, Takeo Kanade and Scott Stevens.

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  Computer and information science

  Computer and information science (CIS; also known as information and computer science) is a field that emphasizes both computing and informatics, upholding the strong association between the fields of information sciences and computer sciences and treating computers as a tool rather than a field. Information science is one with a long history, unlike the relatively very young field of computer science, and is primarily concerned with gathering, storing, disseminating, sharing and protecting any and all forms of information. It is a broad field, covering a myriad of different areas but is often referenced alongside computer science because of the incredibly useful nature of computers and computer programs in helping those studying and doing research in the field – particularly in helping to analyse data and in spotting patterns too broad for a human to intuitively perceive. While information science is sometimes confused with information theory, the two have vastly different subject matter. Information theory focuses on one particular mathematical concept of information while information science is focused on all aspects of the processes and techniques of information. Computer science, in contrast, is less focused on information and its different states, but more, in a very broad sense, on the use of computers – both in theory and practice – to design and implement algorithms in order to aid the processing of information during the different states described above. It has strong foundations in the field of mathematics, as the very first recognised practitioners of the field were renowned mathematicians such as Alan Turing. Information science and computing began to converge in the 1950s and 1960s, as information scientists started to realize the many ways computers would improve information storage and retrieval. == Terminology == Due to the distinction between computers and computing, some of the research groups refer to computing or datalogy. The French refer to computer science as the term informatique. The term information and communications technology (ICT), refers to how humans communicate with using machines and computers, making a distinction from information and computer science, which is how computers use and gain information. Informatics is also distinct from computer science, which encompasses the study of logic and low-level computing issues. == Education == Universities may confer degrees with a major in computer and information science, not to be confused with a more specific Bachelor of Computer Science or respective graduate computer science degrees. The QS World University Rankings is one of the most widely recognised and distinguished university comparisons. They ranked the top 10 universities for computer science and information systems in 2015. They are: Massachusetts Institute of Technology (MIT) Stanford University University of Oxford Carnegie Mellon University Harvard University University of California, Berkeley (UCB) University of Cambridge The Hong Kong University of Science and Technology Swiss Federal Institute of Technology (ETH Zurich) Princeton University A Computer Information Science degree gives students both network and computing knowledge which is needed to design, develop, and assist information systems which helps to solve business problems and to support business problems and to support business operations and decision making at a managerial level also. == Areas of information and computer science == Due to the nature of this field, many topics are also shared with computer science and information systems. The discipline of Information and Computer Science spans a vast range of areas from basic computer science theory (algorithms and computational logic) to in depth analysis of data manipulation and use within technology. === Programming theory === The process of taking a given algorithm and encoding it into a language that can be understood and executed by a computer. There are many different types of programming languages and various different types of computers, however, they all have the same goal: to turn algorithms into machine code. Popular programming languages used within the academic study of CIS include, but are not limited to: Java, Python, C#, C++, Perl, Ruby, Pascal, Swift, Visual Basic. === Information and information systems === The academic study of software and hardware systems that process large quantities and data, support large scale data management and how data can be used. This is where the field is unique from the standard study of computer science. The area of information systems focuses on the networks of hardware and software that are required to process, manipulate and distribute such data. === Computer systems and organisations === The process of analysing computer architecture and various logic circuits. This involves looking at low level computer processes at bit level computation. This is an in-depth look into the hardware processing of a computational system, involving looking at the basic structure of a computer and designing such systems. This can also involve evaluating complex circuit diagrams, and being able to construct these to solve a main problem. The main purpose behind this area of study is to achieve an understanding of how computers function on a basic level, often through tracing machine operations. === Machines, languages, and computation === This is the study into fundamental computer algorithms, which are the basis to computer programs. Without algorithms, no computer programs would exist. This also involves the process of looking into various mathematical functions behind computational algorithms, basic theory and functional (low level) programming. In an academic setting, this area would introduce the fundamental mathematical theorems and functions behind theoretical computer science which are the building blocks for other areas in the field. Complex topics such as; proofs, algebraic functions and sets will be introduced during studies of CIS. == Developments == Information and computer science is a field that is rapidly developing with job prospects for students being extremely promising with 75.7% of graduates gaining employment. Also the IT industry employs one in twenty of the workforce with it predicted to increase nearly five times faster than the average of the UK and between 2012 and 2017 more than half a million people will be needed within the industry and the fact that nine out of ten tech firms are suffering from candidate shortages which is having a negative impact on their business as it delays the creation and development of new products, and it's predicted in the US that in the next decade there will be more than one million jobs in the technology sector than computer science graduates to fill them. Because of this programming is now being taught at an earlier age with an aim to interest students from a young age into computer and information science hopefully leading more children to study this at a higher level. For example, children in England will now be exposed to computer programming at the age of 5 due to an updated national curriculum. == Employment == Due to the wide variety of jobs that now involve computer and information science related tasks, it is difficult to provide a comprehensive list of possible jobs in this area, but some of the key areas are artificial intelligence, software engineering and computer networking and communication. Work in this area also tends to require sufficient understanding of mathematics and science. Moreover, jobs that having a CIS degree can lead to, include: systems analyst, network administrator, system architect, information systems developer, web programmer, or software developer. The earning potential for CIS graduates is quite promising. A 2013 survey from the National Association of Colleges and Employers (NACE) found that the average starting salary for graduates who earned a degree in a computer related field was $59,977, up 4.3% from the prior year. This is higher than other popular degrees such as business ($54,234), education ($40,480) and math and sciences ($42,724). Furthermore, Payscale ranked 129 college degrees based on their graduates earning potential with engineering, math, science, and technology fields dominating the ranking. With eight computer related degrees appearing among the top 30. With the lowest starting salary for these jobs being $49,900. A Rasmussen College article describes various jobs CIS graduates may obtain with software applications developers at the top making a median income of $98,260. According to the National Careers Service an Information Scientist can expect to earn £24,000+ per year as a starting salary.

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  Structural risk minimization

  Structural risk minimization (SRM) is an inductive principle of use in machine learning. Commonly in machine learning, a generalized model must be selected from a finite data set, with the consequent problem of overfitting – the model becoming too strongly tailored to the particularities of the training set and generalizing poorly to new data. The SRM principle addresses this problem by balancing the model's complexity against its success at fitting the training data. This principle was first set out in a 1974 book by Vladimir Vapnik and Alexey Chervonenkis and uses the VC dimension. In practical terms, Structural Risk Minimization is implemented by minimizing E t r a i n + β H ( W ) {\displaystyle E_{train}+\beta H(W)} , where E t r a i n {\displaystyle E_{train}} is the train error, the function H ( W ) {\displaystyle H(W)} is called a regularization function, and β {\displaystyle \beta } is a constant. H ( W ) {\displaystyle H(W)} is chosen such that it takes large values on parameters W {\displaystyle W} that belong to high-capacity subsets of the parameter space. Minimizing H ( W ) {\displaystyle H(W)} in effect limits the capacity of the accessible subsets of the parameter space, thereby controlling the trade-off between minimizing the training error and minimizing the expected gap between the training error and test error. The SRM problem can be formulated in terms of data. Given n data points consisting of data x and labels y, the objective J ( θ ) {\displaystyle J(\theta )} is often expressed in the following manner: J ( θ ) = 1 2 n ∑ i = 1 n ( h θ ( x i ) − y i ) 2 + λ 2 ∑ j = 1 d θ j 2 {\displaystyle J(\theta )={\frac {1}{2n}}\sum _{i=1}^{n}(h_{\theta }(x^{i})-y^{i})^{2}+{\frac {\lambda }{2}}\sum _{j=1}^{d}\theta _{j}^{2}} The first term is the mean squared error (MSE) term between the value of the learned model, h θ {\displaystyle h_{\theta }} , and the given labels y {\displaystyle y} . This term is the training error, E t r a i n {\displaystyle E_{train}} , that was discussed earlier. The second term, places a prior over the weights, to favor sparsity and penalize larger weights. The trade-off coefficient, λ {\displaystyle \lambda } , is a hyperparameter that places more or less importance on the regularization term. Larger λ {\displaystyle \lambda } encourages sparser weights at the expense of a more optimal MSE, and smaller λ {\displaystyle \lambda } relaxes regularization allowing the model to fit to data. Note that as λ → ∞ {\displaystyle \lambda \to \infty } the weights become zero, and as λ → 0 {\displaystyle \lambda \to 0} , the model typically suffers from overfitting.

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  Media aggregation platform

  A Media Aggregation Platform or Media Aggregation Portal (MAP) is an over the top service for distributing web-based streaming media content from multiple sources to a large audience. MAPs consist of networks of sources who host their own content which viewers can choose and access directly from a larger variety of content to choose from than a single source can offer. The service is used by content providers, looking to extend the reach of their content. Unlike multichannel video programming distributor (MVPD) or multiple-system operators (MSO), MAPs rely on the Internet rather than cables or satellite. As more network television channels have moved online in the early 21st century, joining web-native channels like Netflix, MAPs aggregate content the way that MSOs and MVPDs have used cable, and to a lesser extent satellite and IPTV infrastructure. There are companies that offer a similar service for free, including Yidio and StreamingMoviesRight, while others charge a subscription fee like as FreeCast Inc's Rabbit TV Plus. When compared with MSOs and MVPDs, MAP networks have much lower costs due to lack of physical infrastructure. The majority of revenue from MAP services are retained by the content creators, and revenue is instead collected from advertisements, pay-per-view, and subscription-based content offerings instead of licensing and reselling content. MAP service consumers interact and purchase content directly from its source, without the markup added by a middleman.

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  Virtual facility

  A Virtual Facility (VF) is a highly realistic digital representation of a data center, used to model all relevant aspects of a physical data center with a high degree of precision. The term "virtual" in Virtual Facility refers to its use of virtual reality, rather than the abstraction of computer resources as seen in platform virtualization. The VF mirrors the characteristics of a physical facility over time and allows for detailed analysis and modeling. == VF Model features == A standard VF model includes: Three-dimensional physical facility layout Network connectivity of facility equipment Full inventory of facility equipment, including electronics and electrical systems such as power distribution units (PDUs) and uninterruptible power supplies (UPSs) Full air conditioning system (ACUs) and controls within the room The term Virtual Facility was introduced to address the emerging environmental problems facing modern Mission Critical Facilities (MCFs). This concept combines virtual reality (VR), computer simulation, and expert systems applied to the domain of facilities. The VF type of computer simulation allows for detailed analysis and prototyping of airflow in the data center using computational fluid dynamics (CFD) techniques. This enables the visualization and numerical analysis of airflow and temperatures within the facility, helping to predict real-world outcomes. == VF applications == The VF model can be used to assist with the following: Greenfield design Asset management Troubleshooting existing data centers Making existing data centers more resilient Making existing data centers more energy efficient Cost prediction Staff training Capacity planning Load growth management Many organizations use VF models to virtually assess scenarios before committing resources to physical changes. This allows for better decision-making regarding the addition or modification of equipment, helping to avoid logistical or thermal problems.

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  Universal Data Element Framework

  The Universal Data Element Framework (UDEF) was a controlled vocabulary developed by The Open Group. It provided a framework for categorizing, naming, and indexing data. It assigned to every item of data a structured alphanumeric tag plus a controlled vocabulary name that describes the meaning of the data. This allowed relating data elements to similar elements defined by other organizations. UDEF defined a Dewey-decimal like code for each concept. For example, an "employee number" is often used in human resource management. It has a UDEF tag a.5_12.35.8 and a controlled vocabulary description "Employee.PERSON_Employer.Assigned.IDENTIFIER". UDEF has been superseded by the Open Data Element Framework (ODEF). == Examples == In an application used by a hospital, the last name and first name of several people could include the following example concepts: Patient Person Family Name – find the word “Patient” under the UDEF object “Person” and find the word “Family” under the UDEF property “Name” Patient Person Given Name – find the word “Patient” under the UDEF object “Person” and find the word “Given” under the UDEF property “Name” Doctor Person Family Name – find the word “Doctor” under the UDEF object “Person” and find the word “Family” under the UDEF property “Name” Doctor Person Given Name – find the word “Doctor” under the UDEF object “Person” and find the word “Given” under the UDEF property “Name” For the examples above, the following UDEF IDs are available: “Patient Person Family Name” the UDEF ID is “au.5_11.10” “Patient Person Given Name” the UDEF ID is “au.5_12.10” “Doctor Person Family Name” the UDEF ID is “aq.5_11.10” “Doctor Person Given Name” the UDEF ID is “aq.5_12.10”

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  List of COBOL software and tools

  This is a list of software and programming tools for the COBOL programming language, which includes compilers, IDEs, build tools, testing, frameworks, and related projects. == Compilers and runtimes == Fujitsu NetCOBOL — COBOL compiler for Windows, Linux, and mainframes GnuCOBOL — open-source COBOL compiler translating COBOL to C and then compiling with GCC IBM COBOL — mainframe COBOL compiler for IBM z/OS and IBM i platforms Micro Focus COBOL — commercial COBOL compiler and runtime for enterprise systems FairCom RTG – A commercial real-time database and runtime solution developed by FairCom Corporation. It provides integration with COBOL applications for transaction processing and modernization projects, and is used in enterprise environments requiring high-performance data management. == Integrated development environments == Eclipse IDE — with COBOL plugin support, Micro Focus or Bitlang extensions. IBM Developer for z/OS — IDE for COBOL and PL/I mainframe development Micro Focus Visual COBOL — IDE integration for Visual Studio, Visual Studio Code, and Eclipse OpenCOBOLIDE — open-source lightweight IDE for GnuCOBOL Visual Studio Code — with COBOL extensions via Bitlang COBOL and GnuCOBOL Language Server == Frameworks, libraries, and APIs == ACUCOBOL-GT — runtime and API library suite from Micro Focus CICS — IBM middleware for transaction processing in COBOL applications DB2 and IMS APIs — database access libraries commonly used with COBOL applications == Build tools and package managers == Apache Ant — scripting and build automation for COBOL/Java hybrid systems GNU Make — common build tool for compiling COBOL via GnuCOBOL Jenkins — used for CI/CD automation with COBOL builds == Testing and quality assurance == COBOL Check — open-source unit testing framework for COBOL IBM Rational Performance Tester — automated performance testing of web and server-based applications from the Rational Software division of IBM Micro Focus Unit Testing Framework — integrated COBOL unit testing tool == Debugging and profiling tools == GnuCOBOL debug mode — command-line debugging integrated in GnuCOBOL compiler IBM Debug Tool for z/OS — mainframe debugging for COBOL and PL/I Micro Focus Animator — step-through debugger for COBOL code

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  Generalized distributive law

  The generalized distributive law (GDL) is a generalization of the distributive property which gives rise to a general message passing algorithm. It is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. The law and algorithm were introduced in a semi-tutorial by Srinivas M. Aji and Robert J. McEliece with the same title. == Introduction == "The distributive law in mathematics is the law relating the operations of multiplication and addition, stated symbolically, a ∗ ( b + c ) = a ∗ b + a ∗ c {\displaystyle a(b+c)=ab+ac} ; that is, the monomial factor a {\displaystyle a} is distributed, or separately applied, to each term of the binomial factor b + c {\displaystyle b+c} , resulting in the product a ∗ b + a ∗ c {\displaystyle ab+ac} " – Britannica. As it can be observed from the definition, application of distributive law to an arithmetic expression reduces the number of operations in it. In the previous example the total number of operations reduced from three (two multiplications and an addition in a ∗ b + a ∗ c {\displaystyle ab+ac} ) to two (one multiplication and one addition in a ∗ ( b + c ) {\displaystyle a(b+c)} ). Generalization of distributive law leads to a large family of fast algorithms. This includes the FFT and Viterbi algorithm. This is explained in a more formal way in the example below: α ( a , b ) = d e f ∑ c , d , e ∈ A f ( a , c , b ) g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c,d,e\in A}f(a,\,c,\,b)\,g(a,\,d,\,e)} where f ( ⋅ ) {\displaystyle f(\cdot )} and g ( ⋅ ) {\displaystyle g(\cdot )} are real-valued functions, a , b , c , d , e ∈ A {\displaystyle a,b,c,d,e\in A} and | A | = q {\displaystyle |A|=q} (say) Here we are "marginalizing out" the independent variables ( c {\displaystyle c} , d {\displaystyle d} , and e {\displaystyle e} ) to obtain the result. When we are calculating the computational complexity, we can see that for each q 2 {\displaystyle q^{2}} pairs of ( a , b ) {\displaystyle (a,b)} , there are q 3 {\displaystyle q^{3}} terms due to the triplet ( c , d , e ) {\displaystyle (c,d,e)} which needs to take part in the evaluation of α ( a , b ) {\displaystyle \alpha (a,\,b)} with each step having one addition and one multiplication. Therefore, the total number of computations needed is 2 ⋅ q 2 ⋅ q 3 = 2 q 5 {\displaystyle 2\cdot q^{2}\cdot q^{3}=2q^{5}} . Hence the asymptotic complexity of the above function is O ( n 5 ) {\displaystyle O(n^{5})} . If we apply the distributive law to the RHS of the equation, we get the following: α ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) ⋅ ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)\cdot \sum _{d,\,e\in A}g(a,\,d,\,e)} This implies that α ( a , b ) {\displaystyle \alpha (a,\,b)} can be described as a product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} where α 1 ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) {\displaystyle \alpha _{1}(a,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)} and α 2 ( a ) = d e f ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha _{2}(a){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{d,\,e\in A}g(a,\,d,\,e)} Now, when we are calculating the computational complexity, we can see that there are q 3 {\displaystyle q^{3}} additions in α 1 ( a , b ) {\displaystyle \alpha _{1}(a,\,b)} and α 2 ( a ) {\displaystyle \alpha _{2}(a)} each and there are q 2 {\displaystyle q^{2}} multiplications when we are using the product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} to evaluate α ( a , b ) {\displaystyle \alpha (a,\,b)} . Therefore, the total number of computations needed is q 3 + q 3 + q 2 = 2 q 3 + q 2 {\displaystyle q^{3}+q^{3}+q^{2}=2q^{3}+q^{2}} . Hence the asymptotic complexity of calculating α ( a , b ) {\displaystyle \alpha (a,b)} reduces to O ( n 3 ) {\displaystyle O(n^{3})} from O ( n 5 ) {\displaystyle O(n^{5})} . This shows by an example that applying distributive law reduces the computational complexity which is one of the good features of a "fast algorithm". == History == Some of the problems that used distributive law to solve can be grouped as follows: Decoding algorithms: A GDL like algorithm was used by Gallager's for decoding low density parity-check codes. Based on Gallager's work Tanner introduced the Tanner graph and expressed Gallagers work in message passing form. The tanners graph also helped explain the Viterbi algorithm. It is observed by Forney that Viterbi's maximum likelihood decoding of convolutional codes also used algorithms of GDL-like generality. Forward–backward algorithm: The forward backward algorithm helped as an algorithm for tracking the states in the Markov chain. And this also was used the algorithm of GDL like generality Artificial intelligence: The notion of junction trees has been used to solve many problems in AI. Also the concept of bucket elimination used many of the concepts. == The MPF problem == MPF or marginalize a product function is a general computational problem which as special case includes many classical problems such as computation of discrete Hadamard transform, maximum likelihood decoding of a linear code over a memory-less channel, and matrix chain multiplication. The power of the GDL lies in the fact that it applies to situations in which additions and multiplications are generalized. A commutative semiring is a good framework for explaining this behavior. It is defined over a set K {\displaystyle K} with operators " + {\displaystyle +} " and " . {\displaystyle .} " where ( K , + ) {\displaystyle (K,\,+)} and ( K , . ) {\displaystyle (K,\,.)} are a commutative monoids and the distributive law holds. Let p 1 , … , p n {\displaystyle p_{1},\ldots ,p_{n}} be variables such that p 1 ∈ A 1 , … , p n ∈ A n {\displaystyle p_{1}\in A_{1},\ldots ,p_{n}\in A_{n}} where A {\displaystyle A} is a finite set and | A i | = q i {\displaystyle |A_{i}|=q_{i}} . Here i = 1 , … , n {\displaystyle i=1,\ldots ,n} . If S = { i 1 , … , i r } {\displaystyle S=\{i_{1},\ldots ,i_{r}\}} and S ⊂ { 1 , … , n } {\displaystyle S\,\subset \{1,\ldots ,n\}} , let A S = A i 1 × ⋯ × A i r {\displaystyle A_{S}=A_{i_{1}}\times \cdots \times A_{i_{r}}} , p S = ( p i 1 , … , p i r ) {\displaystyle p_{S}=(p_{i_{1}},\ldots ,p_{i_{r}})} , q S = | A S | {\displaystyle q_{S}=|A_{S}|} , A = A 1 × ⋯ × A n {\displaystyle \mathbf {A} =A_{1}\times \cdots \times A_{n}} , and p = { p 1 , … , p n } {\displaystyle \mathbf {p} =\{p_{1},\ldots ,p_{n}\}} Let S = { S j } j = 1 M {\displaystyle S=\{S_{j}\}_{j=1}^{M}} where S j ⊂ { 1 , . . . , n } {\displaystyle S_{j}\subset \{1,...\,,n\}} . Suppose a function is defined as α i : A S i → R {\displaystyle \alpha _{i}:A_{S_{i}}\rightarrow R} , where R {\displaystyle R} is a commutative semiring. Also, p S i {\displaystyle p_{S_{i}}} are named the local domains and α i {\displaystyle \alpha _{i}} as the local kernels. Now the global kernel β : A → R {\displaystyle \beta :\mathbf {A} \rightarrow R} is defined as: β ( p 1 , . . . , p n ) = ∏ i = 1 M α ( p S i ) {\displaystyle \beta (p_{1},...\,,p_{n})=\prod _{i=1}^{M}\alpha (p_{S_{i}})} Definition of MPF problem: For one or more indices i = 1 , . . . , M {\displaystyle i=1,...\,,M} , compute a table of the values of S i {\displaystyle S_{i}} -marginalization of the global kernel β {\displaystyle \beta } , which is the function β i : A S i → R {\displaystyle \beta _{i}:A_{S_{i}}\rightarrow R} defined as β i ( p S i ) = ∑ p S i c ∈ A S i c β ( p ) {\displaystyle \beta _{i}(p_{S_{i}})\,=\displaystyle \sum \limits _{p_{S_{i}^{c}}\in A_{S_{i}^{c}}}\beta (p)} Here S i c {\displaystyle S_{i}^{c}} is the complement of S i {\displaystyle S_{i}} with respect to { 1 , . . . , n } {\displaystyle \mathbf {\{} 1,...\,,n\}} and the β i ( p S i ) {\displaystyle \beta _{i}(p_{S_{i}})} is called the i t h {\displaystyle i^{th}} objective function, or the objective function at S i {\displaystyle S_{i}} . It can observed that the computation of the i t h {\displaystyle i^{th}} objective function in the obvious way needs M q 1 q 2 q 3 ⋯ q n {\displaystyle Mq_{1}q_{2}q_{3}\cdots q_{n}} operations. This is because there are q 1 q 2 ⋯ q n {\displaystyle q_{1}q_{2}\cdots q_{n}} additions and ( M − 1 ) q 1 q 2 . . . q n {\displaystyle (M-1)q_{1}q_{2}...q_{n}} multiplications needed in the computation of the i th {\displaystyle i^{\text{th}}} objective function. The GDL algorithm which is explained in the next section can reduce this computational complexity. The following is an example of the MPF problem. Let p 1 , p 2 , p 3 , p 4 , {\displaystyle p_{1},\,p_{2},\,p_{3},\,p_{4},} and p 5 {\displaystyle p_{5}} be variables such that p 1 ∈ A 1 , p 2 ∈ A 2 , p 3 ∈ A 3 , p 4 ∈ A 4 , {\displaystyle p_{1}\in

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  Virtual data room

  A virtual data room (sometimes called a VDR or Deal Room) is an online repository of information that is used for the storing and distribution of documents. In many cases, a virtual data room is used to facilitate the due diligence process during an M&A transaction, loan syndication, or private equity and venture capital transactions. This due diligence process has traditionally used a physical data room to accomplish the disclosure of documents. For reasons of cost, efficiency and security, virtual data rooms have widely replaced the more traditional physical data room. A virtual data room is an extranet to which the bidders and their advisers are given access via the internet. An extranet is essentially a website with limited controlled access, using a secure log-on supplied by the vendor, which can be disabled at any time, by the vendor, if a bidder withdraws. Much of the information released is confidential and restrictions are applied to the viewer's ability to release this to third parties (by means of forwarding, copying or printing). This can be effectively applied to protect the data using digital rights management. The virtual data room provides access to secure documents for authorized users through a dedicated web site, or through secure agent applications. In the process of mergers and acquisitions the data room is set up as part of the central repository of data relating to companies or divisions being acquired or sold. The data room enables the interested parties to view information relating to the business in a controlled environment where confidentiality can be preserved. Conventionally this was achieved by establishing a supervised, physical data room in secure premises with controlled access. In most cases, with a physical data room, only one bidder team can access the room at a time. A virtual data room is designed to have the same advantages as a conventional data room (controlling access, viewing, copying and printing, etc.) with fewer disadvantages. Due to their increased efficiency, many businesses and industries have moved to using virtual data rooms instead of physical data rooms. In 2006, a spokesperson for a company which sets up virtual deal rooms was reported claiming that the process reduced the bidding process by about thirty days compared to physical data rooms. In the process of startup fundraising, a virtual data room is set up to be a central location for key data, documents, and financials. These are shared with venture capital and angel investors and allows them to streamline due diligence. == Application == Any business dealing with private data can apply VDRs when secure transaction processing is required. This includes financial institutions that need to negotiate confidential customer information without involving third parties. VDRs have traditionally been used for IPOs and real estate asset management. Technology companies may use them to exchange and review code or confidential data needed for operations. The same is true for clients, who entrust their valuable code only to the most qualified people in the organisation. The code is not something that can be printed out and brought in a folder. It resides on a computer and must be used together. VDR can find application in any business that manages data in the form of documents, especially law firms, financial advisers or the B2B sector. The latter work with documents that must always be handled and controlled confidentially, and it is difficult to store them securely when they are on a server that other people can access. In addition, in B2B, it is important to close the deal as quickly as possible: the average sales cycle is one to three months. VDR can be compared to a locked filing cabinet where all those folders and documents are kept. It automates the mathematics of pricing to prevent revenue leakage, and initially integrates CRM to ensure accurate synchronisation of all account data, which is important for B2B in particular and sales in general. While virtual data rooms offer many advantages, they are not suitable for every industry. For example, some governments may decide to continue using physical data rooms for highly confidential information sharing. The damage from potential cyberattacks and data breaches exceeds the benefits offered by virtual data rooms. In such cases, the use of VDRs is not considered. Data breaches have particularly affected the US healthcare system from March 2021 to March 2022 - according to IBM Security the cost of the breach was a record high of $10.1 million.

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  Algorithmic paradigm

  An algorithmic paradigm or algorithm design paradigm is a generic model or framework which underlies the design of a class of algorithms. An algorithmic paradigm is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program. == List of well-known paradigms == === General === Backtracking Branch and bound Brute-force search Divide and conquer Dynamic programming Greedy algorithm Recursion Prune and search === Parameterized complexity === Kernelization Iterative compression === Computational geometry === Sweep line algorithms Rotating calipers Randomized incremental construction

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  Scale-space axioms

  In image processing and computer vision, a scale space framework can be used to represent an image as a family of gradually smoothed images. This framework is very general and a variety of scale space representations exist. A typical approach for choosing a particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the representation useful in practical applications. Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters. A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision. == Scale space axioms for the linear scale-space representation == The linear scale space representation L ( x , y , t ) = ( T t f ) ( x , y ) = g ( x , y , t ) ∗ f ( x , y ) {\displaystyle L(x,y,t)=(T_{t}f)(x,y)=g(x,y,t)f(x,y)} of signal f ( x , y ) {\displaystyle f(x,y)} obtained by smoothing with the Gaussian kernel g ( x , y , t ) {\displaystyle g(x,y,t)} satisfies a number of properties 'scale-space axioms' that make it a special form of multi-scale representation: linearity T t ( a f + b h ) = a T t f + b T t h {\displaystyle T_{t}(af+bh)=aT_{t}f+bT_{t}h} where f {\displaystyle f} and h {\displaystyle h} are signals while a {\displaystyle a} and b {\displaystyle b} are constants, shift invariance T t S ( Δ x , Δ y ) f = S ( Δ x , Δ y ) T t f {\displaystyle T_{t}S_{(\Delta x,\Delta _{y})}f=S_{(\Delta x,\Delta _{y})}T_{t}f} where S ( Δ x , Δ y ) {\displaystyle S_{(\Delta x,\Delta _{y})}} denotes the shift (translation) operator ( S ( Δ x , Δ y ) f ) ( x , y ) = f ( x − Δ x , y − Δ y ) {\displaystyle (S_{(\Delta x,\Delta _{y})}f)(x,y)=f(x-\Delta x,y-\Delta y)} semi-group structure g ( x , y , t 1 ) ∗ g ( x , y , t 2 ) = g ( x , y , t 1 + t 2 ) {\displaystyle g(x,y,t_{1})g(x,y,t_{2})=g(x,y,t_{1}+t_{2})} with the associated cascade smoothing property L ( x , y , t 2 ) = g ( x , y , t 2 − t 1 ) ∗ L ( x , y , t 1 ) {\displaystyle L(x,y,t_{2})=g(x,y,t_{2}-t_{1})L(x,y,t_{1})} existence of an infinitesimal generator A {\displaystyle A} ∂ t L ( x , y , t ) = ( A L ) ( x , y , t ) {\displaystyle \partial _{t}L(x,y,t)=(AL)(x,y,t)} non-creation of local extrema (zero-crossings) in one dimension, non-enhancement of local extrema in any number of dimensions ∂ t L ( x , y , t ) ≤ 0 {\displaystyle \partial _{t}L(x,y,t)\leq 0} at spatial maxima and ∂ t L ( x , y , t ) ≥ 0 {\displaystyle \partial _{t}L(x,y,t)\geq 0} at spatial minima, rotational symmetry g ( x , y , t ) = h ( x 2 + y 2 , t ) {\displaystyle g(x,y,t)=h(x^{2}+y^{2},t)} for some function h {\displaystyle h} , scale invariance g ^ ( ω x , ω y , t ) = h ^ ( ω x φ ( t ) , ω x φ ( t ) ) {\displaystyle {\hat {g}}(\omega _{x},\omega _{y},t)={\hat {h}}({\frac {\omega _{x}}{\varphi (t)}},{\frac {\omega _{x}}{\varphi (t)}})} for some functions φ {\displaystyle \varphi } and h ^ {\displaystyle {\hat {h}}} where g ^ {\displaystyle {\hat {g}}} denotes the Fourier transform of g {\displaystyle g} , positivity g ( x , y , t ) ≥ 0 {\displaystyle g(x,y,t)\geq 0} , normalization ∫ x = − ∞ ∞ ∫ y = − ∞ ∞ g ( x , y , t ) d x d y = 1 {\displaystyle \int _{x=-\infty }^{\infty }\int _{y=-\infty }^{\infty }g(x,y,t)\,dx\,dy=1} . In fact, it can be shown that the Gaussian kernel is a unique choice given several different combinations of subsets of these scale-space axioms: most of the axioms (linearity, shift-invariance, semigroup) correspond to scaling being a semigroup of shift-invariant linear operator, which is satisfied by a number of families integral transforms, while "non-creation of local extrema" for one-dimensional signals or "non-enhancement of local extrema" for higher-dimensional signals are the crucial axioms which relate scale-spaces to smoothing (formally, parabolic partial differential equations), and hence select for the Gaussian. The Gaussian kernel is also separable in Cartesian coordinates, i.e. g ( x , y , t ) = g ( x , t ) g ( y , t ) {\displaystyle g(x,y,t)=g(x,t)\,g(y,t)} . Separability is, however, not counted as a scale-space axiom, since it is a coordinate dependent property related to issues of implementation. In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian. There exists a generalization of the Gaussian scale-space theory to more general affine and spatio-temporal scale-spaces. In addition to variabilities over scale, which original scale-space theory was designed to handle, this generalized scale-space theory also comprises other types of variabilities, including image deformations caused by viewing variations, approximated by local affine transformations, and relative motions between objects in the world and the observer, approximated by local Galilean transformations. In this theory, rotational symmetry is not imposed as a necessary scale-space axiom and is instead replaced by requirements of affine and/or Galilean covariance. The generalized scale-space theory leads to predictions about receptive field profiles in good qualitative agreement with receptive field profiles measured by cell recordings in biological vision. In the computer vision, image processing and signal processing literature there are many other multi-scale approaches, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; please see the article on related multi-scale approaches. There has also been work on discrete scale-space concepts that carry the scale-space properties over to the discrete domain; see the article on scale space implementation for examples and references.

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  Document

  A document is a written, drawn, presented, or memorialized representation of thought, often the manifestation of non-fictional, as well as fictional, content. The etymology of the word "document" derives from the Latin documentum, which denotes a "teaching" or "lesson": the verb doceō denotes "to teach". Historically, the term "document" was usually used to indicate written proof useful as evidence of a truth or fact. In the Computer Age, the term "document" typically refers to a primarily textual computer file, encompassing its structural and format elements, such as fonts, colors, and images. In the contemporary era, the definition of "document" has expanded beyond its traditional medium, such as paper, to encompass electronic documents as well. History, events, examples, opinions, stories, and creativity can all be expressed in documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize or represent thought. Documents are usually considered to be two-dimensional representations. == Abstract definitions == The concept of "document" has been defined by Suzanne Briet as "any concrete or symbolic indication, preserved or recorded, for reconstructing or for proving a phenomenon, whether physical or mental." An often-cited article concludes that "the evolving notion of document" among Jonathan Priest, Paul Otlet, Briet, Walter Schürmeyer, and the other documentalists increasingly emphasized whatever functioned as a document rather than traditional physical forms of documents. The shift to digital technology would seem to make this distinction even more important. David M. Levy has said that an emphasis on the technology of digital documents has impeded our understanding of digital documents as documents. A conventional document, such as a mail message or a technical report, exists physically in digital technology as a string of bits, as does everything else in a digital environment. As an object of study, it has been made into a document. It has become physical evidence by those who study it. "Document" is defined in library and information science and documentation science as a fundamental, abstract idea: the word denotes everything that may be represented or memorialized to serve as evidence. The classic example provided by Briet is an antelope: "An antelope running wild on the plains of Africa should not be considered a document[;] she rules. But if it were to be captured, taken to a zoo and made an object of study, it has been made into a document. It has become physical evidence being used by those who study it. Indeed, scholarly articles written about the antelope are secondary documents, since the antelope itself is the primary document." This opinion has been interpreted as an early expression of actor–network theory. == Kinds == A document can be structured, like tabular documents, lists, forms, or scientific charts, semi-structured like a book or a newspaper article, or unstructured like a handwritten note. Documents are sometimes classified as secret, private, or public. They may also be described as drafts or proofs. When a document is copied, the source is denominated the "original". Documents are used in numerous fields, e.g.: Academia: manuscript, thesis, paper, journal, chart, and technical drawing Media: mock-up, script, image, photography, and newspaper article Administration, law, and politics: application, brief, certificate, commission, constitutional document, form, gazette, identity document, license, manifesto, summons, census, and white paper Business: invoice, request for proposal, proposal, contract, packing slip, manifest, report (detailed and summary), spreadsheet, material safety data sheet, waybill, bill of lading, financial statement, nondisclosure agreement (NDA), mutual nondisclosure agreement, and user guide Geography and planning: topographic map, cadastre, legend, and architectural plan Such standard documents can be drafted based on a template. == Drafting == The page layout of a document is how information is graphically arranged in the space of the document, e.g., on a page. If the appearance of the document is of concern, the page layout is generally the responsibility of a graphic designer. Typography concerns the design of letter and symbol forms and their physical arrangement in the document (see typesetting). Information design concerns the effective communication of information, especially in industrial documents and public signs. Simple textual documents may not require visual design and may be drafted only by an author, clerk, or transcriber. Forms may require a visual design for their initial fields, but not to complete the forms. == Media == Traditionally, the medium of a document was paper and the information was applied to it in ink, either by handwriting (to make a manuscript) or by a mechanical process (e.g., a printing press or laser printer). Today, some short documents also may consist of sheets of paper stapled together. Historically, documents were inscribed with ink on papyrus (starting in ancient Egypt) or parchment; scratched as runes or carved on stone using a sharp tool, e.g., the Tablets of Stone described in the Bible; stamped or incised in clay and then baked to make clay tablets, e.g., in the Sumerian and other Mesopotamian civilizations. The papyrus or parchment was often rolled into a scroll or cut into sheets and bound into a codex (book). Contemporary electronic means of memorializing and displaying documents include: Monitor of a desktop computer, laptop, tablet; optionally with a printer to produce a hard copy; Personal digital assistant; Dedicated e-book device; Electronic paper, typically, using the Portable Document Format (PDF); Information appliance; Digital audio player; and Radio and television service provider. Digital documents usually require a specific file format to be presentable in a specific medium. == In law == Documents in all forms frequently serve as material evidence in criminal and civil proceedings. The forensic analysis of such a document is within the scope of questioned document examination. To catalog and manage the large number of documents that may be produced during litigation, Bates numbering is often applied to all documents in the lawsuit so that each document has a unique, arbitrary, identification number.

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  Wearable technology

  Wearable technology is a category of small electronic and mobile devices with wireless communications capability designed to be worn on the human body and are incorporated into gadgets, accessories, or clothes. Common types of wearable technology include smartwatches, fitness trackers, and smartglasses. Wearable electronic devices are often close to or on the surface of the skin, where they detect, analyze, and transmit information such as vital signs, and/or ambient data and which allow in some cases immediate biofeedback to the wearer. Wearable devices collect vast amounts of data from users making use of different behavioral and physiological sensors, which monitor their health status and activity levels. Wrist-worn devices include smartwatches with a touchscreen display, while wristbands are mainly used for fitness tracking but do not contain a touchscreen display. Wearable devices such as activity trackers are an example of the Internet of things, since "things" such as electronics, software, sensors, and connectivity are effectors that enable objects to exchange data (including data quality) through the internet with a manufacturer, operator, and/or other connected devices, without requiring human intervention. Wearable technology offers a wide range of possible uses, from communication and entertainment to improving health and fitness, however, there are worries about privacy and security because wearable devices have the ability to collect personal data. Wearable technology has a variety of use cases which is growing as the technology is developed and the market expands. It can be used to encourage individuals to be more active and improve their lifestyle choices. Healthy behavior is encouraged by tracking activity levels and providing useful feedback to enable goal setting. This can be shared with interested stakeholders such as healthcare providers. Wearables are popular in consumer electronics, most commonly in the form factors of smartwatches, smart rings, and implants. Apart from commercial uses, wearable technology is being incorporated into navigation systems, advanced textiles (e-textiles), and healthcare. As wearable technology is being proposed for use in critical applications, like other technology, it is vetted for its reliability and security properties. == History == In the 1500s, German inventor Peter Henlein (1485–1542) created small watches that were worn as necklaces. A century later, pocket watches grew in popularity as waistcoats became fashionable for men. Wristwatches were created in the late 1600s but were worn mostly by women as bracelets. Pedometers were developed around the same time as pocket watches. The concept of a pedometer was described by Leonardo da Vinci around 1500, and the Germanic National Museum in Nuremberg has a pedometer in its collection from 1590. In the late 1800s, the first wearable hearing aids were introduced. In 1904, aviator Alberto Santos-Dumont pioneered the modern use of the wristwatch. In 1949, American biophysicist Norman Holter invented the very first health monitoring device. His invention, the Holter monitor, was groundbreaking as one of the first wearable devices capable of tracking vital health data outside of a clinical setting. In the 1970s, calculator watches became available, reaching the peak of their popularity in the 1980s. From the early 2000s, wearable cameras were being used as part of a growing sousveillance movement. Expectations, operations, usage and concerns about wearable technology was floated on the first International Conference on Wearable Computing. In 2008, Ilya Fridman incorporated a hidden Bluetooth microphone into a pair of earrings. Big tech companies such as Apple, Samsung, and Fitbit have expanded on this idea by interfacing with smartphones and personal computer software to collect a wide variety of data. Wearable devices include dedicated health monitors, fitness bands, and smartwatches. In 2010, Fitbit released its first step counter. Wearable technology which tracks information such as walking and heart rate is part of the quantified self movement. In 2013, McLear, also known as NFC Ring, released a "smart ring". The smart ring could make bitcoin payments, unlock other devices, and transfer personally identifying information, and also had other features. In 2013, one of the first widely available smartwatches was the Samsung Galaxy Gear. Apple followed in 2015 with the Apple Watch. === Prototypes === From 1991 to 1997, Rosalind Picard and her students, Steve Mann and Jennifer Healey, at the MIT Media Lab designed, built, and demonstrated data collection and decision making from "Smart Clothes" that monitored continuous physiological data from the wearer. These "smart clothes", "smart underwear", "smart shoes", and smart jewellery collected data that related to affective state and contained or controlled physiological sensors and environmental sensors like cameras and other devices. At the same time, also at the MIT Media Lab, Thad Starner and Alex "Sandy" Pentland develop augmented reality. In 1997, their smartglass prototype is featured on 60 Minutes and enables rapid web search and instant messaging. Though the prototype's glasses are nearly as streamlined as modern smartglasses, the processor was a computer worn in a backpack – the most lightweight solution available at the time. In 2009, Sony Ericsson teamed up with the London College of Fashion for a contest to design digital clothing. The winner was a cocktail dress with Bluetooth technology making it light up when a call is received. Zach "Hoeken" Smith of MakerBot fame made keyboard pants during a "Fashion Hacking" workshop at a New York City creative collective. The Tyndall National Institute in Ireland developed a "remote non-intrusive patient monitoring" platform which was used to evaluate the quality of the data generated by the patient sensors and how the end users may adopt to the technology. More recently, London-based fashion company CuteCircuit created costumes for singer Katy Perry featuring LED lighting so that the outfits would change color both during stage shows and appearances on the red carpet such as the dress Katy Perry wore in 2010 at the MET Gala in NYC. In 2012, CuteCircuit created the world's first dress to feature Tweets, as worn by singer Nicole Scherzinger. In 2010, McLear, also known as NFC Ring, developed prototypes of its "smart ring" devices, before a Kickstarter fundraising in 2013. In 2014, graduate students from the Tisch School of Arts in New York designed a hoodie that sent pre-programmed text messages triggered by gesture movements. Around the same time, prototypes for digital eyewear with heads up display (HUD) began to appear. The US military employs headgear with displays for soldiers using a technology called holographic optics. In 2010, Google started developing prototypes of its optical head-mounted display Google Glass, which went into customer beta in March 2013. == Usage == In the consumer space, sales of smart wristbands (aka activity trackers such as the Jawbone UP and Fitbit Flex) started accelerating in 2013. One in five American adults have a wearable device, according to the 2014 PriceWaterhouseCoopers Wearable Future Report. As of 2009, decreasing cost of processing power and other components was facilitating widespread adoption and availability. In professional sports, wearable technology has applications in monitoring and real-time feedback for athletes. Examples of wearable technology in sport include accelerometers, pedometers, and GPS's which can be used to measure an athlete's energy expenditure and movement pattern. In cybersecurity and financial technology, secure wearable devices have captured part of the physical security key market. McLear, also known as NFC Ring, and VivoKey developed products with one-time pass secure access control. In health informatics, wearable devices have enabled better capturing of human health statistics for data driven analysis. This has facilitated data-driven machine learning algorithms to analyse the health condition of users. In business, wearable technology helps managers easily supervise employees by knowing their locations and what they are currently doing. Employees working in a warehouse also have increased safety when working around chemicals or lifting something. Smart helmets are employee safety wearables that have vibration sensors that can alert employees of possible danger in their environment. == Wearable technology and health == Wearable technology is often used to monitor a user's health. Given that such a device is in close contact with the user, it can easily collect data. It started as soon as 1980 where first wireless ECG was invented. In the last decades, there has been substantial growth in research of e.g. textile-based, tattoo, patch, and contact lenses as well as circulation of a notion of "quantified self", transhumanism-related ideas, and growth of life ex

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