AI Analytics Healthcare

AI Analytics Healthcare — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Intelligent database

  Until the 1980s, databases were viewed as computer systems that stored record-oriented and business data such as manufacturing inventories, bank records, and sales transactions. A database system was not expected to merge numeric data with text, images, or multimedia information, nor was it expected to automatically notice patterns in the data it stored. In the late 1980s the concept of an intelligent database was put forward as a system that manages information (rather than data) in a way that appears natural to users and which goes beyond simple record keeping. The term was introduced in 1989 by the book Intelligent Databases by Kamran Parsaye, Mark Chignell, Setrag Khoshafian and Harry Wong. The concept postulated three levels of intelligence for such systems: high level tools, the user interface and the database engine. The high level tools manage data quality and automatically discover relevant patterns in the data with a process called data mining. This layer often relies on the use of artificial intelligence techniques. The user interface uses hypermedia in a form that uniformly manages text, images and numeric data. The intelligent database engine supports the other two layers, often merging relational database techniques with object orientation. In the twenty-first century, intelligent databases have now become widespread, e.g. hospital databases can now call up patient histories consisting of charts, text and x-ray images just with a few mouse clicks, and many corporate databases include decision support tools based on sales pattern analysis.

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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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  Gcore

  Gcore is an edge AI, cloud, network, and security company headquartered in Luxembourg. Founded in 2014, the company provides low-latency services to industries including finance, healthcare, manufacturing, gaming, media and telecommunications internationally. As of March 2024, its global network includes over 180 Points of Presence (PoPs) across six continents. == History == Gcore was founded in 2014 in Luxembourg. The company built its own content delivery network, originally designed for the needs of the gaming industry. In 2016, Gcore's infrastructure expanded to multiple regions that were underserved by hyperscale cloud providers. In 2020, the company formed partnerships with Intel and Equinix. In 2022, Gcore launched the European AI Cloud, providing access to infrastructure for machine learning tasks. In March 2024, Gcore announced the acquisition of a web application and API protection (WAAP) solution from StackPath. In April 2024, Gcore received a commendation in the Industry Innovation category at the NVIDIA Partner Network Awards EMEA for developing the first speech-to-text technology for Luxembourgish, using the LuxemBERT AI model. In May 2024, Philipp Rösler, former vice-chancellor of Germany and federal minister of health joined the Gcore board. In July 2024, Gcore raised $60 million in a Series A funding round, marking the company's first external investment since its founding. In August 2024, Gcore was recognized as a Major Player in the IDC MarketScape report for European public cloud Infrastructure (IaaS) 2024 by IDC, the global market intelligence firm. In May 2025, Feiyu Xu became a member of the Gcore advisory board. == Network infrastructure == According to the company's website, Gcore has network locations in six continents: Europe, North America, Asia, South America, Africa, and Australia with over 14,000 peering partners and a network capacity exceeding 200 Tbps. According to a 2025 review by Geekflare, Gcore's CDN achieved an average global response time of around 30 milliseconds. Gcore offers AI cloud clusters, including a generative AI cluster with Nvidia GPUs in Luxembourg and additional sites in the Netherlands and Wales, as part of its European AI infrastructure. == Products and services == Gcore offers a range of services, including content delivery network (CDN), cloud computing,virtual machines, bare-metal servers, object storage AI infrastructure and inference, Kubernetes, video streaming, DDoS mitigation, web application and API protection (WAAP), Domain Name System (DNS). Gcore provides AI services and GPU cloud infrastructure to support model development, training, fine-tuning, and inference. In January 2025, the company introduced Everywhere Inference, a serverless inference solution that enables AI model deployment. == Controversies == Correctiv and Tageszeitung reported that Gcore supported the distribution of the TV network RT until April 2023, which has been under sanctions by the EU since March 2022. However, Gcore denies these allegations. == Collaborations == In 2024, Gcore and Qareeb Data Centres, a data center provider in the Middle East, launched a collaboration to integrate Gcore's AI, cloud and edge services across data centers in multiple Middle Eastern countries. In June 2025, Gcore joined the SmartSpires initiative, a €3.1 million smart city project co-funded by the Connecting Europe Facility. The three-year programme is coordinated by a public–private consortium including 5SKYE, the Luxembourg Institute of Science and Technology (LIST), Orange Luxembourg, and Gcore. The project aims to transform the Belval campus into a smart city by deploying 5G-enabled smart towers that integrate edge computing, artificial intelligence and IoT services. Within the consortium, Gcore acts as project coordinator and is responsible for the deployment of the edge infrastructure.

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  Web Dynpro

  Web Dynpro (WD) is a web application technology developed by SAP SE that focuses on the development of server-side business applications. For modern releases (for instance as of NetWeaver 750, software layer SAP_UI) the user interface is rendered according to the HTML5 web standard. Since Netweaver 754 (software layer SAP_UI, ABAP Platform 1909) a touch enabled user interface is available. The newly released versions usually follow the SAP Fiori design principles. One of its main design features is that the user interface is defined in an entirely declarative manner. Web Dynpro applications can be developed using either the Java (Web Dynpro for Java, WDJ or WD4J) or ABAP (Web Dynpro ABAP, WDA or WD4A) development infrastructure. == Overview == The earliest version of Web Dynpro appeared in 2003 and was based on Java. This variant was released approximately 18 months before the ABAP variant. As of 2010, the Java variant of Web Dynpro was put into maintenance mode. WD follows a design architecture based on an interpretation of the MVC design pattern and uses a model driven development approach ("minimize coding, maximize design"). The Web Dynpro Framework is a server-side runtime environment into which many dedicated "hook methods" are available. The developer then places their own custom coding within these hook methods in order to implement the desired business functionality. These hook methods belong to one of the broad categories of either "life-cycle" and "round-trip"; that is, those methods that are concerned with the life-cycle of a software component (i.e. processing that takes place at start up and shut down etc.), and those methods that are concerned with processing the fixed sequence of events that take place during a client-initiated round trip to the server. Web Dynpro is aimed at the development of business applications that follow standardized UI principles, applications that connect to backend systems and which are scalable. Key Capabilities Declarative way of development: Web Dynpro offers a graphical and declarative means of UI development. UI controls, building blocks, views and windows are modeled, and the business logic can be coded separately. Separation of user interface and business logic: One advantage of Web Dynpro over SAP GUI is the separation between business logic and user interface, and the structured development process with less implementation effort. Support of stateful application: The state of the application is kept in the back-end. This leads to a reduced data transfer from ABAP server to browser and vice versa. Regarding Web Dynpro ABAP there is only one programming language (ABAP) and only one system necessary. Therefore, development can be easier and cost efficient.

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  DoorDash

  DoorDash, Inc. is an American company operating online food ordering and food delivery. It trades under the symbol DASH. With a 56% market share, DoorDash is the largest food delivery platform in the United States. It also has a 60% market share in the convenience delivery category. As of December 31, 2020, the platform was used by 450,000 merchants, 20 million consumers, and had over one million delivery couriers. Founded by Tony Xu, Andy Fang, Stanley Tang and Evan Moore, DoorDash made its debut on the Fortune 500 list in 2024, ranking No. 443. DoorDash has been sued for or held legally liable for withholding tips, reducing tip transparency, antitrust price manipulation, listing restaurants without permission, misclassifying workers, withholding sick time, and illegally selling personal data. As of April 2026, DoorDash operates in the United States (including Puerto Rico), Canada, Australia, and New Zealand. Through its subsidiaries Deliveroo and Wolt, the company also operates across Europe, as well as in Azerbaijan, Georgia, Israel, Kazakhstan, Kuwait, and the United Arab Emirates. == History == In January 2013, Stanford University students Tony Xu, Stanley Tang, Andy Fang and Evan Moore launched PaloAltoDelivery.com in Palo Alto, California. In the summer of 2013, it received US$120,000 in seed money from Y Combinator in exchange for a 7% stake. It incorporated as DoorDash in June 2013. DoorDash's first partnership with a fast food burger restaurant chain was in April 2016, when it partnered with CKE Restaurants, parent company of Carl's Jr. and Hardee's, for food delivery. In December 2017, DoorDash announced its partnership with Wendy's for delivery from its restaurants. In December 2018, DoorDash overtook Uber Eats to hold the second position in total US food delivery sales, behind GrubHub. By March 2019, it had exceeded GrubHub in total sales, at 27.6% of the on-demand delivery market. By early 2019, DoorDash was the largest food delivery provider in the U.S., as measured by consumer spending. In October 2019, DoorDash opened its first ghost kitchen, DoorDash Kitchen, in Redwood City, California, with four restaurants operating at the location. By June 2020, DoorDash had raised more than $2.5 billion over several financing rounds from investors including Y Combinator, Charles River Ventures, SV Angel, Khosla Ventures, Sequoia Capital, SoftBank Group, GIC, and Kleiner Perkins. DoorDash announced a partnership with KFC in September 2020, followed by Taco Bell in October 2020. In November 2020, DoorDash announced the opening of its first physical restaurant location, partnering up with Bay Area restaurant Burma Bites to offer delivery and pick-up orders. In December 2020, it became a public company via an initial public offering, raising $3.37 billion. In November 2021, DoorDash acquired Finland's Wolt for €7bn. In August 2022, DoorDash announced it would end its partnership with Walmart in September, ending the companies' cooperation agreement from 2018. In November 2022, DoorDash announced plans to lay off 1,250 corporate employees, or about six percent of its workforce, to rein in expenses. In June 2023, DoorDash announced it would give its drivers the option of earning an hourly minimum wage instead of being paid per delivery. However, drivers are only paid hourly when on an active delivery. In September 2023, the company transferred its stock listing from the New York Stock Exchange to the Nasdaq. On December 18, 2023, DoorDash was added to the Nasdaq-100 index. In March 2025, DoorDash announced a partnership with Klarna, a Buy Now, Pay Later (BNPL) service, letting customers schedule small payments over a set period of time. DoorDash received widespread criticism from this decision, including internet mockery, given concerns about the increase of household debt in America. In 2025, DoorDash acquired the UK-based delivery service Deliveroo for $3.88 billion. The combined company operates in 40 countries and serves 50 million users monthly. In September 2025, DoorDash and Ace Hardware (the largest hardware cooperative) announced their partnership to offer delivery for home use products from over 4,000 Ace locations. == Lawsuits against DoorDash == === 2017 class-action lawsuit for misclassifying workers === In 2017, a class-action lawsuit was filed against DoorDash for allegedly misclassifying delivery drivers in California and Massachusetts as independent contractors. In 2022, a tentative settlement was reached in which DoorDash would pay $100 million total, with $61 million going to over 900,000 drivers, paying out just over $130 per driver, and $28 million for the lawyers. Gizmodo criticized the settlement, noting that the $413 million that DoorDash CEO Tony Xu received the previous year was one of the largest CEO compensation packages of all time. === 2019 data breach lawsuit === On May 4, 2019, DoorDash confirmed 4.9 million customers, delivery workers and merchants had sensitive information stolen via a data breach. Those who joined the platform after April 5, 2018, were unaffected by the breach. A class-action lawsuit for the breach was filed against DoorDash in October 2019. === Withholding of tips and subsequent class-action lawsuits === In July 2019, the company's tipping policy was criticized by The New York Times, and later The Verge and Vox and Gothamist. Drivers receive a guaranteed minimum per order that is paid by DoorDash by default. When a customer added a tip, instead of going directly to the driver, it first went to the company to cover the guaranteed minimum. Drivers then only directly received the part of the tip that exceeded the guaranteed minimum per order. In January 2020, it was reported that DoorDash had lied about skimming tips from its drivers, causing them to earn an average of $1.45 an hour after expenses, and that after the company had allegedly overhauled its tipping system, DoorDash was still manipulating per-delivery payouts at the expense of drivers. A DoorDash customer filed a class action lawsuit against the company for its "materially false and misleading" tipping policy. The case was referred to arbitration in August 2020. Under pressure, the company revised its policy. The company settled a lawsuit with District of Columbia Attorney General Karl Racine for $2.5 million, with funds going to deliverers, the government, and to charity. ==== 2021 driver strike for tip transparency ==== In July 2021, DoorDash drivers went on strike to protest lack of tip transparency and to ask for higher pay. At the time of the strike, and, as of June 2022, DoorDash did not allow drivers to see the full tip amounts prior to accepting a delivery in the app. If customers tip over a set amount for the order total, Doordash hides a portion of the tip until the delivery is complete. The strike occurred after DoorDash rewrote its code to cut off access to Para, a third-party app that drivers had been using to see the full tip amounts. ==== 2025 class-action lawsuit settlement ==== In 2025, DoorDash agreed to pay around $17 million for "misleading both consumers and delivery workers" with tips being docked from drivers' pay instead of directly going to drivers. === 2020 antitrust litigation === In April 2020, in the case of Davitashvili v. GrubHub Inc. DoorDash, Grubhub, Postmates, and Uber Eats were accused of monopolistic power by only listing restaurants on its apps if the restaurant owners signed contracts which include clauses that require prices be the same for dine-in customers as for customers receiving delivery. The plaintiffs stated that this arrangement increases the cost for dine-in customers, as they are required to subsidize the cost of delivery; and that the apps charge "exorbitant" fees, which range from 13% to 40% of revenue, while the average restaurant's profit ranges from 3% to 9% of revenue. The lawsuit seeks treble damages, including for overcharges, since April 14, 2016, for dine-in and delivery customers in the United States at restaurants using the defendants’ delivery apps. Although several preliminary documents in the case have now been filed, a trial date has not yet been set. === Litigation for illegal unauthorized restaurant listing === In May 2021, DoorDash was criticized for unauthorized listings of restaurants who had not given permission to appear on the app. The company was sued by Lona's Lil Eats in St. Louis, with the lawsuit claiming that DoorDash had listed them without permission, then prevented any orders to the restaurant from going through and redirecting customers to other restaurants instead, because Lona's was "too far away," when in reality it had not paid DoorDash a fee for listing. This aspect of DoorDash's business practice is illegal in California. === 2021 lawsuit by the city of Chicago === In August 2021, the city of Chicago sued DoorDash and GrubHub. According to Chicago mayor Lori Lightfoot, the companies broke the law by using "unfair and deceptive t

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  FarPoint Spread

  FarPoint Spread is a suite of Microsoft Excel-compatible spreadsheet components available for .NET, COM, and Microsoft BizTalk Server. Software developers use the components to embed Microsoft Excel-compatible spreadsheet features into their applications, such as importing and exporting Microsoft Excel files, displaying, modifying, analyzing, and visualizing data. Spread components handle spreadsheet data at the cell, row, column, or worksheet level. This article is about the last FarPoint edition of the Spread product line. Spread is now developed by GrapeCity, Inc. Since the acquisition, Spread for Biztalk Server has been removed from the product line and SpreadJS, a JavaScript version, has been added. == History == 1991 Spread released as a DLL control as the initial product offering from FarPoint Technologies, Inc. 1990s Spread VBX released. Spread ActiveX released. These components are now known as Spread COM. 2003 Spread for Windows Forms released as a completely new managed C# version prompted by the launch of Visual Studio .NET. 2003 Spread for Web Forms (now Spread for ASP.NET) released. 2006 Spread for BizTalk released. 2009 FarPoint Technologies acquired by GrapeCity. == Versions == Spread for Windows Forms: 5.0 Spread for Web Forms: 5.0 Spread COM: 8.0 Spread for BizTalk: 3.0 === Spread for Windows Forms === FarPoint Spread for Windows Forms is a Microsoft Excel-compatible spreadsheet component for Windows Forms applications developed using Microsoft Visual Studio and the .NET Framework. Developers use it to add grids and spreadsheets to their applications, and to bind them to data sources. In version 4.0, new cell types were added to display barcodes and fractions, and exports for XML and PDF were added. === Spread for ASP.NET === FarPoint Spread for ASP.NET is a Microsoft Excel-compatible spreadsheet component for ASP.NET applications. Developers use it to add grids and spreadsheets to their applications, === Spread for COM === FarPoint Spread 8 COM allows COM and ActiveX applications to incorporate spreadsheet features. In the 1997 book Visual Basic 5 for Windows for Dummies, Wally Wang lists an early version of Spread COM in Chapter 35: The Ten Most Useful Visual Basic Add-On Programs. === Spread for BizTalk === FarPoint Spread for BizTalk Server allows developers to integrate Microsoft Excel documents into Microsoft BizTalk applications. Spread for BizTalk Server includes two components: Spreadsheet Pipeline Disassembler - Parses data from Microsoft Excel (XLS and Excel 2007 XML, CSV, TXT) documents into XML data for processing through Microsoft BizTalk Server receive pipelines. Spreadsheet Pipeline Assembler - Assembles data from Microsoft BizTalk applications into Microsoft Excel (XLS or Excel 2007 XML) or PDF documents for transport through Microsoft BizTalk Server send pipelines. Developers find it a useful tool for organizations with Microsoft BizTalk Server Enterprise Application Integration. Prior to this release, BizTalk users wanting to use Excel data had to manually open the files and copy and paste data between the two applications. == Features == These features are common to all versions. Predefined cell types, including: currency date time number percent regular expression button check box combo box hyperlink image Formula support, including: cross-sheet referencing over 300 built-in functions Import and export: import to Microsoft Excel-compatible files export to Microsoft Excel-compatible files export to HTML files export to XML files Design-time spreadsheet designer Data-binding with customizable options Hierarchical data views, with parent rows and child views Grouping of rows or columns Sorting by row or column on multiple keys Cell spanning Multiple row and column headers Bound and unbound modes == Version-Specific Features == === Spread for Windows Forms === Support for Microsoft Visual Studio 2010 Support for Windows Azure AppFabric Integrated chart control Custom cell types Cell notes Child controls Splitter bars Built-in and custom skins and styles PDF export Microsoft Excel 2007 XML Support (Office Open XML, XLSX) Floating Formula Bar Range Selection for Formula Automatic Completion (type ahead) === Spread for ASP.NET === Support for Microsoft Visual Studio 2010 Support for Windows Azure AppFabric Integrated chart control AJAX-enabled Support for Open Document Format (ODF) files Multiple edits on multiple rows without server round trips Client-side column and row resizing Load on demand, which loads data from the server as needed for viewing Native Microsoft Excel import and export In-cell editing Multiple edits on multiple rows without server round trips Client-side column and row resizing Multiple sheets Searching Filtering Validations Cell spans PDF export === Spread COM === Custom cell types Cell notes Virtual mode for data loading Unicode support Customizable printing Text tips Import and export: Microsoft Excel 97 Excel 2000 Excel 2007 (requires the .NET Framework) Enhanced printing 64 bit DLL === Spread for BizTalk === Integration of Microsoft Excel data into Microsoft BizTalk applications Design-time spreadsheet schema wizard and spreadsheet format designer == Supported document formats == Adobe Portable Document Format PDF (.pdf) HTML Web Page (.html) Microsoft Excel Workbook (.xls) Plain Text (.txt) Comma-Separated Values (.csv) Open Document Format (Spread for ASP.NET)

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  Application Lifecycle Framework

  The Application Lifecycle Framework (ALF) was a project by the Eclipse Foundation that aimed to create a standardized, open-source system to allow different application lifecycle management (ALM) tools to work together more easily. The goal was to provide common protocols and integration services that would let software development tools from different vendors communicate and share data. However, the project failed to gain sufficient support from major industry players and was terminated in 2008.

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  24SevenOffice

  24SevenOffice is a Norwegian software company headquartered in Oslo, Norway, with offices in Stockholm, Sweden and London, United Kingdom. Founded in 1997, the company specializes in web-based (SaaS) ERP and CRM systems. == Company history == 24SevenOffice was founded in 1997 in Porsgrunn, Norway, as IKT Interactive AS and marketed as kontorplassen.no. The name "24SevenOffice" was introduced for the company's London branch when the company entered the British market in 2003. The company changed its name to 24SevenOffice in February 2005. Originally based in Skien, the company later moved to Oslo Innovation Center, then to Tjuvholmen in the waterfront Fjord City of Oslo, and now the headquarters are located in Inkognitogaten 33, Solli plass, Oslo. The idea for the company's product was developed in 1996, and 24SevenOffice was an early innovator in the Scandinavian market in web-based enterprise resource planning solutions (ERP). A British office was established at Surrey Business Park in May 2003, with the company launching its web-based (SaaS) utility computing system to the UK SME market in 2004. An office in Chennai, India, was established in 2005, and 24SevenOffice entered the Swedish market when they acquired the leading competitor and ERP-provider Start & Run in a cash deal. In August 2005, the company had an initial public offering that raised NOK 15 million, and the company entered The Norwegian Over the Counter Market list as of 5 October 2005 (the ticker was 24SO), reaching a market value of NOK 175 million, with 5000 customers in Norway. In 2006, the company signed a deal to sponsor rally driver Petter Solberg, at the time the largest private sponsorship in Norwegian sport. Instead of receiving NOK 5 million in cash, Solberg received a 2.9 per cent ownership in the company. The company entered the German-speaking market in April 2006 when an office in Frankfurt am Main was opened. In late August/early September, they established an office with ten sales agents plus a general manager in Stockholm for the Swedish market. 24SevenOffice initiated strategic cooperation with Active 24 in early 2006 to develop a common platform. During the summer, Active 24 was bought by 24SevenOffice's ERP/CRM competitor Mamut (company), and 24SevenOffice terminated the contract with Active 24 in October demanding NOK 200 million in compensation for lost revenue. After a breakdown of settlement negotiations in the Forliksråd in January 2007, 24SevenOffice filed a case against Active 24 for breach of agreement in the Oslo District Court in March. 24SevenOffice lost on all counts in the District Court in December 2007. In January 2008, 24SevenOffice appealed the case to the Borgarting Court of Appeal, reducing the cause of action from NOK 250 to 30 million. 24SevenOffice lost on all counts in the Court of Appeal in December 2008, and was ordered to cover the costs incurred by Active 24 in connection with the dispute totaling NOK 6.91 million. 24SevenOffice appealed the case to the Supreme Court of Norway, but the Supreme Court Appeals Committee in March 2008 unanimously rejected the appeal from 24SevenOffice over the Borgarting Appeal Court's unanimous judgment of December 2008. On a counterclaim from Active 24 and Mamut against 24SevenOffice, the Oslo District Court in May 2010 found, that 24SevenOffice should pay Active 24 NOK 12 million in compensation for wrongfully having terminated the agreement, and a further NOK 360.000 of the opponent's legal costs. 24SevenOffice disagreed with the court ruling, and appealed once again. The Borgarting Court of Appeal in November 2011, ruled to reduce the amount of damages to NOK 4.4 million plus NOK 900.000 in penal interest. With several scrip issues, 24SevenOffice raised 25 million NOK (about $4 million at the time) between October 2005 and July 2006. They entered into a strategic partnership with Bluegarden, who for 30 years had delivered digital services for payroll, human resource planning, recruitment and training, in March 2006, and they made a large-scale agreement in April 2006, with US telecommunications software company Webex, a competitor to Norwegian Tandberg videoconferencing equipment manufacturer. In September 2006, 24SevenOffice signed an agreement with Fokus Bank to provide their customers with extended functionality in Internet banking. 24SevenOffice had by 2007 reportedly 9000 customers, joined the OpenAjax Alliance, and entered into a strategic partnership with Dun & Bradstreet in May 2007, but despite getting listed on Oslo Axess on 22 June (ticker: TFSO), reaching a market capitalization of NOK 120 million, the company was still losing money. The company ended 2007 with a revenue of NOK 21.7 million. In 2008, 24SevenOffice bought 50% of the stocks in telecommunication company Oyatel, partnered with Nets Group to facilitate invoicing for businesses, and telecommunications company Telipol chose 24SevenOffice's second-generation Internet platform for its 8,000 users. They announced an increase in revenues in Q2 to 11.1 million, up from 4.7 million in the same period the year before. 24SevenOffice had a turnover of NOK 37 million in the first half of 2009, a doubling compared to the same period the previous year, and presented its first positive EBITDA in Q2. The Norwegian Association of Auditors signed an agreement with 24SevenOffice in 2011, whereby they only recommend 24SevenOffice as a system for their members to use. On 27 June 2013, the shareholders of 24SevenOffice took off from the stock exchange and privatized the company. In recent years, the company has invested heavily in finance and accounting – and got leading auditing companies such as PwC and KPMG on the customer list. == Products == 24SevenOffice is a web-based (SaaS) ERP system. It includes modules for CRM, accounting, invoicing, e-mail, file/document management and project management. == Awards == 24SevenOffice won the Seal of Excellence in Multimedia Award at the 2004 CeBIT, became Norwegian Gazelle Company of the year 2004, chosen by Dagens Næringsliv and Dun & Bradstreet, won Product of the Year in the Norwegian finance magazine Kapital, and the IKT Grenland Innovation Award in 2008.

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  Attempto Controlled English

  Attempto Controlled English (ACE) is a controlled natural language, i.e. a subset of standard English with a restricted syntax and restricted semantics described by a small set of construction and interpretation rules. It has been under development at the University of Zurich since 1995. In 2013, ACE version 6.7 was announced. ACE can serve as knowledge representation, specification, and query language, and is intended for professionals who want to use formal notations and formal methods, but may not be familiar with them. Though ACE appears perfectly natural—it can be read and understood by any speaker of English—it is in fact a formal language. ACE and its related tools have been used in the fields of software specifications, theorem proving, proof assistants, text summaries, ontologies, rules, querying, medical documentation and planning. Here are some simple examples: Every woman is a human. A woman is a human. A man tries-on a new tie. If the tie pleases his wife then the man buys it. ACE construction rules require that each noun be introduced by a determiner (a, every, no, some, at least 5, ...). Regarding the list of examples above, ACE interpretation rules decide that (1) is interpreted as universally quantified, while (2) is interpreted as existentially quantified. Sentences like "Women are human" do not follow ACE syntax and are consequently not valid. Interpretation rules resolve the anaphoric references in (3): the tie and it of the second sentence refer to a new tie of the first sentence, while his and the man of the second sentence refer to a man of the first sentence. Thus an ACE text is a coherent entity of anaphorically linked sentences. The Attempto Parsing Engine (APE) translates ACE texts unambiguously into discourse representation structures (DRS) that use a variant of the language of first-order logic. A DRS can be further translated into other formal languages, for instance AceRules with various semantics, OWL, and SWRL. Translating an ACE text into (a fragment of) first-order logic allows users to reason about the text, for instance to verify, to validate, and to query it. == Overview == As an overview of the current version 6.6 of ACE this section: Briefly describes the vocabulary Gives an account of the syntax Summarises the handling of ambiguity Explains the processing of anaphoric references. === Vocabulary === The vocabulary of ACE comprises: Predefined function words (e.g. determiners, conjunctions) Predefined phrases (e.g. "it is false that ...", "it is possible that ...") Content words (e.g. nouns, verbs, adjectives, adverbs). === Grammar === The grammar of ACE defines and constrains the form and the meaning of ACE sentences and texts. ACE's grammar is expressed as a set of construction rules. The meaning of sentences is described as a small set of interpretation rules. A Troubleshooting Guide describes how to use ACE and how to avoid pitfalls. ==== ACE texts ==== An ACE text is a sequence of declarative sentences that can be anaphorically interrelated. Furthermore, ACE supports questions and commands. ==== Simple sentences ==== A simple sentence asserts that something is the case—a fact, an event, a state. The temperature is −2 °C. A customer inserts 2 cards. A card and a code are valid. Simple ACE sentences have the following general structure: subject + verb + complements + adjuncts Every sentence has a subject and a verb. Complements (direct and indirect objects) are necessary for transitive verbs (insert something) and ditransitive verbs (give something to somebody), whereas adjuncts (adverbs, prepositional phrases) are optional. All elements of a simple sentence can be elaborated upon to describe the situation in more detail. To further specify the nouns customer and card, we could add adjectives: A trusted customer inserts two valid cards. possessive nouns and of-prepositional phrases: John's customer inserts a card of Mary. or variables as appositions: John inserts a card A. Other modifications of nouns are possible through relative sentences: A customer who is trusted inserts a card that he owns. which are described below since they make a sentence composite. We can also detail the insertion event, e.g. by adding an adverb: A customer inserts some cards manually. or, equivalently: A customer manually inserts some cards. or, by adding prepositional phrases: A customer inserts some cards into a slot. We can combine all of these elaborations to arrive at: John's customer who is trusted inserts a valid card of Mary manually into a slot A. ==== Composite sentences ==== Composite sentences are recursively built from simpler sentences through coordination, subordination, quantification, and negation. Note that ACE composite sentences overlap with what linguists call compound sentences and complex sentences. ===== Coordination ===== Coordination by and is possible between sentences and between phrases of the same syntactic type. A customer inserts a card and the machine checks the code. There is a customer who inserts a card and who enters a code. A customer inserts a card and enters a code. An old and trusted customer enters a card and a code. Note that the coordination of the noun phrases a card and a code represents a plural object. Coordination by or is possible between sentences, verb phrases, and relative clauses. A customer inserts a card or the machine checks the code. A customer inserts a card or enters a code. A customer owns a card that is invalid or that is damaged. Coordination by and and or is governed by the standard binding order of logic, i.e. and binds stronger than or. Commas can be used to override the standard binding order. Thus the sentence: A customer inserts a VisaCard or inserts a MasterCard, and inserts a code. means that the customer inserts a VisaCard and a code, or alternatively a MasterCard and a code. ===== Subordination ===== There are four constructs of subordination: relative sentences, if-then sentences, modality, and sentence subordination. Relative sentences starting with who, which, and that allow to add detail to nouns: A customer who is trusted inserts a card that he owns. With the help of if-then sentences we can specify conditional or hypothetical situations: If a card is valid then a customer inserts it. Note the anaphoric reference via the pronoun it in the then-part to the noun phrase a card in the if-part. Modality allows us to express possibility and necessity: A trusted customer can/must insert a card. It is possible/necessary that a trusted customer inserts a card. Sentence subordination comes in various forms: It is true/false that a customer inserts a card. It is not provable that a customer inserts a card. A clerk believes that a customer inserts a card. ===== Quantification ===== Quantification allows us to speak about all objects of a certain class (universal quantification), or to denote explicitly the existence of at least one object of this class (existential quantification). The textual occurrence of a universal or existential quantifier opens its scope that extends to the end of the sentence, or in coordinations to the end of the respective coordinated sentence. To express that all involved customers insert cards we can write Every customer inserts a card. This sentence means that each customer inserts a card that may, or may not, be the same as the one inserted by another customer. To specify that all customers insert the same card—however unrealistic that situation seems—we can write: A card is inserted by every customer. or, equivalently: There is a card that every customer inserts. To state that every card is inserted by a customer we write: Every card is inserted by a customer. or, somewhat indirectly: For every card there is a customer who inserts it. ===== Negation ===== Negation allows us to express that something is not the case: A customer does not insert a card. A card is not valid. To negate something for all objects of a certain class one uses no: No customer inserts more than 2 cards. or, there is no: There is no customer who inserts a card. To negate a complete statement one uses sentence negation: It is false that a customer inserts a card. These forms of negation are logical negations, i.e. they state that something is provably not the case. Negation as failure states that a state of affairs cannot be proved, i.e. there is no information whether the state of affairs is the case or not. It is not provable that a customer inserts a card. ==== Queries ==== ACE supports two forms of queries: yes/no-queries and wh-queries. Yes/no-queries ask for the existence or non-existence of a specified situation. If we specified: A customer inserts a card. then we can ask: Does a customer insert a card? to get a positive answer. Note that interrogative sentences always end with a question mark. With the help of wh-queries, i.e. queries with query words, we can interrogate a text for details of the specified situation. If we specified: A

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  Orleans (software framework)

  Orleans is a cross-platform software framework for building scalable and robust distributed interactive applications based on the .NET Framework or on the more recent .NET. == Overview == Orleans was originally created by the eXtreme Computing Group at Microsoft Research and introduced the virtual actor model as a new approach to building distributed systems for the cloud. Orleans scales from a single on-premises server to highly-available and globally distributed applications in the cloud. The virtual actor model is based on the actor model but has several differences: A virtual actor always exists, it cannot be explicitly created or destroyed. Virtual actors are automatically instantiated. If a server hosting an actor crashes, the next message sent to the actor causes it to be reinstantiated automatically. The server that an actor is on is transparent to the application code. Orleans can automatically create multiple instances of the same stateless actor. Starting with cloud services for the Halo franchise, the framework has been used by a number of cloud services at Microsoft and other companies since 2011. The core Orleans technology was transferred to 343 Industries and is available as open source since January 2015. The source code is licensed under MIT License and hosted on GitHub. Orleans runs on Microsoft Windows, Linux, and macOS and is compatible with .NET Standard 2.0 and above. == Features == Some Orleans features include: Persistence Distributed ACID transactions Streams Timers & Reminders Fault tolerance == Related implementations == The Electronic Arts BioWare division created Project Orbit. It is a Java implementation of virtual actors that was heavily inspired by the Orleans project.

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  Color vision

  Color vision (CV), a feature of visual perception, is an ability to perceive differences between light composed of different frequencies independently of light intensity. Color perception is a part of the larger visual system and is mediated by a complex process between neurons that begins with differential stimulation of different types of photoreceptors by light entering the eye. Those photoreceptors then emit outputs that are propagated through many layers of neurons ultimately leading to higher cognitive functions in the brain. Color vision is found in many animals and is mediated by similar underlying mechanisms with common types of biological molecules and a complex history of the evolution of color vision within different animal taxa. In primates, color vision may have evolved under selective pressure for a variety of visual tasks including the foraging for nutritious young leaves, ripe fruit, and flowers, as well as detecting predator camouflage and emotional states in other primates. == Wavelength == Isaac Newton discovered that white light after being split into its component colors when passed through a dispersive prism could be recombined to make white light by passing them through a different prism. The visible light spectrum ranges from about 380 to 740 nanometers. Spectral colors (colors that are produced by a narrow band of wavelengths) such as red, orange, yellow, green, cyan, blue, and violet can be found in this range. These spectral colors do not refer to a single wavelength, but rather to a set of wavelengths: red, 625–740 nm; orange, 590–625 nm; yellow, 565–590 nm; green, 500–565 nm; cyan, 485–500 nm; blue, 450–485 nm; violet, 380–450 nm. Wavelengths longer or shorter than this range are called infrared or ultraviolet, respectively. Humans cannot generally see these wavelengths, but other animals may. === Hue detection === Sufficient differences in wavelength cause a difference in the perceived hue; the just-noticeable difference in wavelength varies from about 1 nm in the blue-green and yellow wavelengths to 10 nm and more in the longer red and shorter blue wavelengths. Although the human eye can distinguish up to a few hundred hues, when those pure spectral colors are mixed together or diluted with white light, the number of distinguishable chromaticities can be much higher. In very low light levels, vision is scotopic: light is detected by rod cells of the retina. Rods are maximally sensitive to wavelengths near 500 nm and play little, if any, role in color vision. In brighter light, such as daylight, vision is photopic: light is detected by cone cells which are responsible for color vision. Cones are sensitive to a range of wavelengths, but are most sensitive to wavelengths near 555 nm. Between these regions, mesopic vision comes into play and both rods and cones provide signals to the retinal ganglion cells. The shift in color perception from dim light to daylight gives rise to differences known as the Purkinje effect. The perception of "white" is formed by the entire spectrum of visible light, or by mixing colors of just a few wavelengths in animals with few types of color receptors. In humans, white light can be perceived by combining wavelengths such as red, green, and blue, or just a pair of complementary colors such as blue and yellow. === Non-spectral colors === There are a variety of colors in addition to spectral colors and their hues. These include grayscale colors, shades of colors obtained by mixing grayscale colors with spectral colors, violet-red colors, impossible colors, and metallic colors. Grayscale colors include white, gray, and black. Rods contain rhodopsin, which reacts to light intensity, providing grayscale coloring. Shades include colors such as pink or brown. Pink is obtained from mixing red and white. Brown may be obtained from mixing orange with gray or black. Navy is obtained from mixing blue and black. Violet-red colors include hues and shades of magenta. The light spectrum is a line on which violet is one end and the other is red, and yet we see hues of purple that connect those two colors. Impossible colors are a combination of cone responses that cannot be naturally produced. For example, medium cones cannot be activated completely on their own; if they were, we would see a 'hyper-green' color. == Dimensionality == Color vision is categorized foremost according to the dimensionality of the color gamut, which is defined by the number of primaries required to represent the color vision. This is generally equal to the number of photopsins expressed: a correlation that holds for vertebrates but not invertebrates. The common vertebrate ancestor possessed four photopsins (expressed in cones) plus rhodopsin (expressed in rods), so was tetrachromatic. However, many vertebrate lineages have lost one or many photopsin genes, leading to lower-dimension color vision. The dimensions of color vision range from 1-dimensional and up: == Physiology of color perception == Perception of color begins with specialized retinal cells known as cone cells. Cone cells contain different forms of opsin – a pigment protein – that have different spectral sensitivities. Humans contain three types, resulting in trichromatic color vision. Each individual cone contains pigments composed of opsin apoprotein covalently linked to a light-absorbing prosthetic group: either 11-cis-hydroretinal or, more rarely, 11-cis-dehydroretinal. The cones are conventionally labeled according to the ordering of the wavelengths of the peaks of their spectral sensitivities: short (S), medium (M), and long (L) cone types. These three types do not correspond well to particular colors as we know them. Rather, the perception of color is achieved by a complex process that starts with the differential output of these cells in the retina and which is finalized in the visual cortex and associative areas of the brain. For example, while the L cones have been referred to simply as red receptors, microspectrophotometry has shown that their peak sensitivity is in the greenish-yellow region of the spectrum. Similarly, the S cones and M cones do not directly correspond to blue and green, although they are often described as such. The RGB color model, therefore, is a convenient means for representing color but is not directly based on the types of cones in the human eye. The peak response of human cone cells varies, even among individuals with typical color vision; in some non-human species this polymorphic variation is even greater, and it may well be adaptive. === Theories === Two complementary theories of color vision are the trichromatic theory and the opponent process theory. The trichromatic theory, or Young–Helmholtz theory, proposed in the 19th century by Thomas Young and Hermann von Helmholtz, posits three types of cones preferentially sensitive to blue, green, and red, respectively. Others have suggested that the trichromatic theory is not specifically a theory of color vision but a theory of receptors for all vision, including color but not specific or limited to it. Equally, it has been suggested that the relationship between the phenomenal opponency described by Ewald Hering and the physiological opponent processes are not straightforward (see below), making of physiological opponency a mechanism that is relevant to the whole of vision, and not just to color vision alone. Hering proposed the opponent process theory in 1872. It states that the visual system interprets color in an antagonistic way: red vs. green, blue vs. yellow, black vs. white. Both theories are generally accepted as valid, describing different stages in visual physiology, visualized in the adjacent diagram. Green–magenta and blue–yellow are scales with mutually exclusive boundaries. In the same way that there cannot exist a "slightly negative" positive number, a single eye cannot perceive a bluish-yellow or a reddish-green. Although these two theories are both currently widely accepted theories, past and more recent work has led to criticism of the opponent process theory, stemming from a number of what are presented as discrepancies in the standard opponent process theory. For example, the phenomenon of an after-image of complementary color can be induced by fatiguing the cells responsible for color perception, by staring at a vibrant color for a length of time, and then looking at a white surface. This phenomenon of complementary colors shows that cyan, rather than green, is the complement of red, and that magenta, rather than red, is the complement of green. It therefore also shows that the reddish-green color supposed to be impossible by opponent process theory is actually the color yellow. Although this phenomenon is more readily explained by the trichromatic theory, explanations for the discrepancy may include alterations to the opponent process theory, such as redefining the opponent colors as red vs. cyan, to reflect this effect. Despite such criticis

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  Crucible (software)

  Crucible is a collaborative code review application by Australian software company Atlassian. Like other Atlassian products, Crucible is a Web-based application primarily aimed at enterprise, and certain features that enable peer review of a codebase may be considered enterprise social software. Crucible is particularly tailored to remote workers, and facilitates asynchronous review and commenting on code. Crucible also integrates with popular source control tools, such as Git and Subversion. Crucible is not open source, but customers are allowed to view and modify the code for their own use.

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  InstallCore

  InstallCore (stylized as installCore) was an installation and content distribution platform created by ironSource, considered potentially unwanted programs (PUP) by a number of anti-malware vendors. It included a software development kit (SDK) for Windows and Mac OS X. The program allowed those using it for distribution to include monetization by advertisements or charging for installation, and made its installations invisible to the user and its anti-virus software. The platform and its programs have been rated potentially unwanted programs (PUP) or potentially unwanted applications (PUA) by anti-malware product vendors since 2014, and by Windows Defender Antivirus since 2015. The platform was primarily designed for efficient web-based deployment of various types of application software. As of August 2012, InstallCore was managing 100 million installations every month, offering services for paid, unpaid, and free software by using the SDK version. == History == The InstallCore team introduced the first version of the SDK at the beginning of 2011. The SDK was a fork of the FoxTab installer and had only basic Installation features. InstallCore was discontinued as part of a company flotation in late 2020. == Criticism and malware classification == InstallCore and its software packages have been classified as potentially unwanted programs (PUP) or potentially unwanted applications (PUA), by anti-malware product vendors and Windows Defender Antivirus from 2014–2015 onwards, with many stating that it installs adware and other additional PUPs. Malwarebytes identified the program as "a family of bundlers that installs more than one application on the user's computer". It has been described as "crossing the line into full-blown malware" and a "nasty Trojan".

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  GNU toolchain

  The GNU toolchain is a broad collection of programming tools produced by the GNU Project. These tools form a toolchain (a suite of tools used in a serial manner) used for developing software applications and operating systems. The GNU toolchain plays a vital role in development of Linux, some BSD systems, and software for embedded systems. Parts of the GNU toolchain are also directly used with or ported to other platforms such as Solaris, macOS, Microsoft Windows (via Cygwin and MinGW/MSYS/WSL2), Sony PlayStation Portable (used by PSP modding scene) and Sony PlayStation 3. == Components == Projects in the GNU toolchain are: GNU Autotools (build system) – Software build toolset from GNU GNU Binutils – GNU software development tools for executable code GNU Bison – Yacc-compatible parser generator program GNU C Library – GNU implementation of the standard C libraryPages displaying short descriptions of redirect targets GNU Compiler Collection – Free and open-source compiler for various programming languages GNU Debugger – Source-level debugger GNU m4 – General-purpose macro processor GNU make – Software build automation tool

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  Deconvolution

  In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of weather forecasting and economics. == Description == In general, the objective of deconvolution is to find the solution f of a convolution equation of the form: f ∗ g = h {\displaystyle fg=h\,} Usually, h is some recorded signal, and f is some signal that we wish to recover, but has been convolved with a filter or distortion function g, before we recorded it. Usually, h is a distorted version of f and the shape of f can't be easily recognized by the eye or simpler time-domain operations. The function g represents the impulse response of an instrument or a driving force that was applied to a physical system. If we know g, or at least know the form of g, then we can perform deterministic deconvolution. However, if we do not know g in advance, then we need to estimate it. This can be done using methods of statistical estimation or building the physical principles of the underlying system, such as the electrical circuit equations or diffusion equations. There are several deconvolution techniques, depending on the choice of the measurement error and deconvolution parameters: === Raw deconvolution === When the measurement error is very low (ideal case), deconvolution collapses into a filter reversing. This kind of deconvolution can be performed in the Laplace domain. By computing the Fourier transform of the recorded signal h and the system response function g, you get H and G, with G as the transfer function. Using the convolution theorem, F = H / G {\displaystyle F=H/G\,} where F is the estimated Fourier transform of f. Finally, the inverse Fourier transform of the function F is taken to find the estimated deconvolved signal f. Note that G is at the denominator and could amplify elements of the error model if present. === Deconvolution with noise === In physical measurements, the situation is usually closer to ( f ∗ g ) + ε = h {\displaystyle (fg)+\varepsilon =h\,} In this case ε is noise that has entered our recorded signal. If a noisy signal or image is assumed to be noiseless, the statistical estimate of g will be incorrect. In turn, the estimate of ƒ will also be incorrect. The lower the signal-to-noise ratio, the worse the estimate of the deconvolved signal will be. That is the reason why inverse filtering the signal (as in the "raw deconvolution" above) is usually not a good solution. However, if at least some knowledge exists of the type of noise in the data (for example, white noise), the estimate of ƒ can be improved through techniques such as Wiener deconvolution. == Applications == === Seismology === The concept of deconvolution had an early application in reflection seismology. In 1950, Enders Robinson was a graduate student at MIT. He worked with others at MIT, such as Norbert Wiener, Norman Levinson, and economist Paul Samuelson, to develop the "convolutional model" of a reflection seismogram. This model assumes that the recorded seismogram s(t) is the convolution of an Earth-reflectivity function e(t) and a seismic wavelet w(t) from a point source, where t represents recording time. Thus, our convolution equation is s ( t ) = ( e ∗ w ) ( t ) . {\displaystyle s(t)=(ew)(t).\,} The seismologist is interested in e, which contains information about the Earth's structure. By the convolution theorem, this equation may be Fourier transformed to S ( ω ) = E ( ω ) W ( ω ) {\displaystyle S(\omega )=E(\omega )W(\omega )\,} in the frequency domain, where ω {\displaystyle \omega } is the frequency variable. By assuming that the reflectivity is white, we can assume that the power spectrum of the reflectivity is constant, and that the power spectrum of the seismogram is the spectrum of the wavelet multiplied by that constant. Thus, | S ( ω ) | ≈ k | W ( ω ) | . {\displaystyle |S(\omega )|\approx k|W(\omega )|.\,} If we assume that the wavelet is minimum phase, we can recover it by calculating the minimum phase equivalent of the power spectrum we just found. The reflectivity may be recovered by designing and applying a Wiener filter that shapes the estimated wavelet to a Dirac delta function (i.e., a spike). The result may be seen as a series of scaled, shifted delta functions (although this is not mathematically rigorous): e ( t ) = ∑ i = 1 N r i δ ( t − τ i ) , {\displaystyle e(t)=\sum _{i=1}^{N}r_{i}\delta (t-\tau _{i}),} where N is the number of reflection events, r i {\displaystyle r_{i}} are the reflection coefficients, t − τ i {\displaystyle t-\tau _{i}} are the reflection times of each event, and δ {\displaystyle \delta } is the Dirac delta function. In practice, since we are dealing with noisy, finite bandwidth, finite length, discretely sampled datasets, the above procedure only yields an approximation of the filter required to deconvolve the data. However, by formulating the problem as the solution of a Toeplitz matrix and using Levinson recursion, we can relatively quickly estimate a filter with the smallest mean squared error possible. We can also do deconvolution directly in the frequency domain and get similar results. The technique is closely related to linear prediction. === Optics and other imaging === In optics and imaging, the term "deconvolution" is specifically used to refer to the process of reversing the optical distortion that takes place in an optical microscope, electron microscope, telescope, or other imaging instrument, thus creating clearer images. It is usually done in the digital domain by a software algorithm, as part of a suite of microscope image processing techniques. Deconvolution is also practical to sharpen images that suffer from fast motion or jiggles during capturing. Early Hubble Space Telescope images were distorted by a flawed mirror and were sharpened by deconvolution. The usual method is to assume that the optical path through the instrument is optically perfect, convolved with a point spread function (PSF), that is, a mathematical function that describes the distortion in terms of the pathway a theoretical point source of light (or other waves) takes through the instrument. Usually, such a point source contributes a small area of fuzziness to the final image. If this function can be determined, it is then a matter of computing its inverse or complementary function, and convolving the acquired image with that. The result is the original, undistorted image. In practice, finding the true PSF is impossible, and usually an approximation of it is used, theoretically calculated or based on some experimental estimation by using known probes. Real optics may also have different PSFs at different focal and spatial locations, and the PSF may be non-linear. The accuracy of the approximation of the PSF will dictate the final result. Different algorithms can be employed to give better results, at the price of being more computationally intensive. Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information. Regularization in iterative algorithms (as in expectation-maximization algorithms) can be applied to avoid unrealistic solutions. When the PSF is unknown, it may be possible to deduce it by systematically trying different possible PSFs and assessing whether the image has improved. This procedure is called blind deconvolution. Blind deconvolution is a well-established image restoration technique in astronomy, where the point nature of the objects photographed exposes the PSF thus making it more feasible. It is also used in fluorescence microscopy for image restoration, and in fluorescence spectral imaging for spectral separation of multiple unknown fluorophores. The most common iterative algorithm for the purpose is the Richardson–Lucy deconvolution algorithm; the Wiener deconvolution (and approximations) are the most common non-iterative algorithms. For some specific imaging systems such as laser pulsed terahertz systems, PSF can be modeled mathematically. As a result, as shown in the figure, deconvolution of the modeled PS

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