In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W. Stewart in 1971, it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\displaystyle A} and B {\displaystyle B} to transform A X − X B = C {\displaystyle AX-XB=C} into a triangular system that can then be solved using forward or backward substitution. In 1979, G. Golub, C. Van Loan and S. Nash introduced an improved version of the algorithm, known as the Hessenberg–Schur algorithm. It remains a standard approach for solving Sylvester equations when X {\displaystyle X} is of small to moderate size. == The algorithm == Let X , C ∈ R m × n {\displaystyle X,C\in \mathbb {R} ^{m\times n}} , and assume that the eigenvalues of A {\displaystyle A} are distinct from the eigenvalues of B {\displaystyle B} . Then, the matrix equation A X − X B = C {\displaystyle AX-XB=C} has a unique solution. The Bartels–Stewart algorithm computes X {\displaystyle X} by applying the following steps: 1.Compute the real Schur decompositions R = U T A U , {\displaystyle R=U^{T}AU,} S = V T B T V . {\displaystyle S=V^{T}B^{T}V.} The matrices R {\displaystyle R} and S {\displaystyle S} are block-upper triangular matrices, with diagonal blocks of size 1 × 1 {\displaystyle 1\times 1} or 2 × 2 {\displaystyle 2\times 2} . 2. Set F = U T C V . {\displaystyle F=U^{T}CV.} 3. Solve the simplified system R Y − Y S T = F {\displaystyle RY-YS^{T}=F} , where Y = U T X V {\displaystyle Y=U^{T}XV} . This can be done using forward substitution on the blocks. Specifically, if s k − 1 , k = 0 {\displaystyle s_{k-1,k}=0} , then ( R − s k k I ) y k = f k + ∑ j = k + 1 n s k j y j , {\displaystyle (R-s_{kk}I)y_{k}=f_{k}+\sum _{j=k+1}^{n}s_{kj}y_{j},} where y k {\displaystyle y_{k}} is the k {\displaystyle k} th column of Y {\displaystyle Y} . When s k − 1 , k ≠ 0 {\displaystyle s_{k-1,k}\neq 0} , columns [ y k − 1 ∣ y k ] {\displaystyle [y_{k-1}\mid y_{k}]} should be concatenated and solved for simultaneously. 4. Set X = U Y V T . {\displaystyle X=UYV^{T}.} === Computational cost === Using the QR algorithm, the real Schur decompositions in step 1 require approximately 10 ( m 3 + n 3 ) {\displaystyle 10(m^{3}+n^{3})} flops, so that the overall computational cost is 10 ( m 3 + n 3 ) + 2.5 ( m n 2 + n m 2 ) {\displaystyle 10(m^{3}+n^{3})+2.5(mn^{2}+nm^{2})} . === Simplifications and special cases === In the special case where B = − A T {\displaystyle B=-A^{T}} and C {\displaystyle C} is symmetric, the solution X {\displaystyle X} will also be symmetric. This symmetry can be exploited so that Y {\displaystyle Y} is found more efficiently in step 3 of the algorithm. == The Hessenberg–Schur algorithm == The Hessenberg–Schur algorithm replaces the decomposition R = U T A U {\displaystyle R=U^{T}AU} in step 1 with the decomposition H = Q T A Q {\displaystyle H=Q^{T}AQ} , where H {\displaystyle H} is an upper-Hessenberg matrix. This leads to a system of the form H Y − Y S T = F {\displaystyle HY-YS^{T}=F} that can be solved using forward substitution. The advantage of this approach is that H = Q T A Q {\displaystyle H=Q^{T}AQ} can be found using Householder reflections at a cost of ( 5 / 3 ) m 3 {\displaystyle (5/3)m^{3}} flops, compared to the 10 m 3 {\displaystyle 10m^{3}} flops required to compute the real Schur decomposition of A {\displaystyle A} . == Software and implementation == The subroutines required for the Hessenberg-Schur variant of the Bartels–Stewart algorithm are implemented in the SLICOT library. These are used in the MATLAB control system toolbox. == Alternative approaches == For large systems, the O ( m 3 + n 3 ) {\displaystyle {\mathcal {O}}(m^{3}+n^{3})} cost of the Bartels–Stewart algorithm can be prohibitive. When A {\displaystyle A} and B {\displaystyle B} are sparse or structured, so that linear solves and matrix vector multiplies involving them are efficient, iterative algorithms can potentially perform better. These include projection-based methods, which use Krylov subspace iterations, methods based on the alternating direction implicit (ADI) iteration, and hybridizations that involve both projection and ADI. Iterative methods can also be used to directly construct low rank approximations to X {\displaystyle X} when solving A X − X B = C {\displaystyle AX-XB=C} .
Flask (web framework)
Flask is a micro web framework written in Python. It is classified as a microframework because it does not require particular tools or libraries. It has no database abstraction layer, form validation, or any other components where pre-existing third-party libraries provide common functions. However, Flask supports extensions that can add application features as if they were implemented in Flask itself. Extensions exist for object-relational mappers, form validation, upload handling, various open authentication technologies and several common framework related tools. Applications that use the Flask framework include Pinterest and LinkedIn. == History == Flask was created by Armin Ronacher of Pocoo, an international group of Python enthusiasts formed in 2004. According to Ronacher, the idea was originally an April Fool's joke that was popular enough to make into a serious application. The name is a play on the earlier Bottle framework. When Ronacher and Georg Brandl created a bulletin board system written in Python in 2004, the Pocoo projects Werkzeug and Jinja were developed. In April 2016, the Pocoo team was disbanded and development of Flask and related libraries passed to the newly formed Pallets project. Flask has become popular among Python enthusiasts. As of October 2020, it has the second-most number of stars on GitHub among Python web-development frameworks, only slightly behind Django, and was voted the most popular web framework in the Python Developers Survey for years between and including 2018 and 2022. == Components == The microframework Flask is part of the Pallets Projects (formerly Pocoo), and based on several others of them, all under a BSD license. === Werkzeug === Werkzeug (German for "tool") is a utility library for the Python programming language for Web Server Gateway Interface (WSGI) applications. Werkzeug can instantiate objects for request, response, and utility functions. It can be used as the basis for a custom software framework and supports Python 2.7 and 3.5 and later. === Jinja === Jinja, also by Ronacher, is a template engine for the Python programming language. Similar to the Django web framework, it handles templates in a sandbox. === MarkupSafe === MarkupSafe is a string handling library for the Python programming language. The eponymous MarkupSafe type extends the Python string type and marks its contents as "safe"; combining MarkupSafe with regular strings automatically escapes the unmarked strings, while avoiding double escaping of already marked strings. === ItsDangerous === ItsDangerous is a safe data serialization library for the Python programming language. It is used to store the session of a Flask application in a cookie without allowing users to tamper with the session contents. === Click === Click is a Python package used by Flask to create command-line interfaces (CLI) by providing a simple and composable way to define commands, arguments, and options. == Features == Development server and debugger Integrated support for unit testing RESTful request dispatching Uses Jinja templating Support for secure cookies (client side sessions) 100% WSGI 1.0 compliant Unicode-based Complete documentation Google App Engine compatibility Extensions available to extend functionality == Example == The following code shows a simple web application that displays "Hello World!" when visited: === Render Template with Flask === ==== Jinja in HTML for the Render Template ====
CodeCheck
CodeCheck is a mobile app that provides consumers with information about the ingredients in cosmetic products, as well as the ingredients and nutritional values of food. Users can access this information by scanning the product’s barcode with a smartphone or by using a text-based search. The app is available for iOS and Android devices in Germany, Austria, Switzerland, the United Kingdom, the United States, and the Netherlands. == History == CodeCheck was founded in 2010 as an association, online database, and app by Roman Bleichenbacher, who was then a student in Zurich. A website of the same name had already been launched in 2002, where users could enter information about ingredients, nutritional values, and manufacturers of products. The first round of financing took place in July 2014 and raised over 1.1 million Swiss francs, which coincided with the founding of CodeCheck AG. Investors included Doodle founders Myke Näf and Paul E. Sevinç. The company subsequently expanded to Austria and Germany. In the same year, Boris Manhart became CEO. CodeCheck GmbH was established in Berlin in 2016. The app became available in the United States in 2017 and in the United Kingdom in November 2019. In 2020, it was also launched in the Netherlands. Following insolvency proceedings, the app has been owned by Producto Check GmbH since 2022. == Functions == The app can be used to scan the barcode of food and cosmetic products. It then displays information about ingredients, nutritional values, manufacturers and certification labels. For many years, users were able to enter and edit product information themselves and indicate advantages and disadvantages of individual products. Since 2020, the app has placed greater emphasis on machine text recognition. The collected data is combined with substance ratings using an algorithm. These ratings are based on scientific studies and expert assessments, including those from the Consumer Advice Centre in Hamburg, Greenpeace, the WWF and the German Association for the Environment and Nature Conservation (BUND e. V.), and cannot be modified by users or manufacturers. The app also provides information on the sugar and fat content of food products. In addition, it indicates whether a product contains hormone-active substances, microplastics, palm oil, animal-derived ingredients, lactose or gluten. Since 2020, the app has displayed a climate score for food products in cooperation with the Eaternity Institute. == Financing == CodeCheck is primarily financed through native advertising and banner ads. Since 2018, the company has also offered analysis services and survey tools directly to fast-moving consumer goods (FMCG) manufacturers. In addition, access to the API is available, enabling other companies to use the product database. With the introduction of a subscription model in 2019, the CodeCheck app can be used ad-free and in offline mode. Since 2021, CodeCheck has also offered its own “Green Label” certification for manufacturers. Products are certified if at least 90 percent of their ingredients are classified as harmless. == Awards == In May 2015, the app topped the download charts for the first time, reaching 2.3 million installations. By September 2019, the app had once again reached the top of the German app charts, surpassing five million downloads.
Optical granulometry
Optical granulometry is the process of measuring the different grain sizes in a granular material, based on a photograph. Technology has been created to analyze a photograph and create statistics based on what the picture portrays. This information is vital in maintaining machinery in various trades worldwide. Mining companies can use optical granulometry to analyze inactive or moving rock to quantify the size of these fragments. Forestry companies can zero in on wood chip sizes without stopping the production process, and minimize sizing errors. With more photoanalysis technologies being produced, mining companies have shown an increased interest in these types of systems because of their ability to maintain efficiency throughout the mining process. Companies are saving millions of dollars annually because of this new technology, and are cutting back on maintenance costs on equipment. In order for optical granulometry to be completely successful, an accurate photo must be taken – under sufficient lighting, and using proper technology – to obtain quantified results. If these requirements are met, an image analysis system can be implemented. == The process == Software uses four basic steps in determining the average size of material: See the Wikipedia article on Photoanalysis to see how mining, forestry and agricultural companies are using this technology to improve quality control techniques. == Smartphone-based, segmentation-free estimation of grain size distribution == Recently, a methodology has emerged by which soil grain size distribution can be inferred from optical images acquired with commodity smartphones by training convolutional neural networks to predict parameters of the distribution curve directly from the image, without explicit image segmentation . In this approach, a standardized image of a soil surface is captured under controlled conditions, preprocessed to reduce device-specific variability, and passed to a regression model that outputs the parameters of a cumulative distribution function e.g., a two-parameter Weibull curve. The resulting distribution can be used to derive geotechnical descriptors and class boundaries.
Moving object detection
Moving object detection is a technique used in computer vision and image processing. Multiple consecutive frames from a video are compared by various methods to determine if any moving object is detected. Moving objects detection has been used for wide range of applications like video surveillance, activity recognition, road condition monitoring, airport safety, monitoring of protection along marine border, etc. == Definition == Moving object detection is to recognize the physical movement of an object in a given place or region. By acting segmentation among moving objects and stationary area or region, the moving objects' motion can be tracked and thus analyzed later. To achieve this, consider a video is a structure built upon single frames, moving object detection is to find the foreground moving target(s), either in each video frame or only when the moving target shows the first appearance in the video. == Traditional methods == Among all the traditional moving object detection methods, we could categorize them into four major approaches: Background subtraction, Frame differencing, Temporal Differencing, and Optical Flow. === Frame differencing === Instead of using traditional approach, to use image subtraction operator by subtracting second and images afterwards, the frame differencing method makes comparisons between two successive frames to detect moving targets. === Temporal differencing === The temporal differencing method identifies the moving object by applying pixel-wise difference method with two or three consecutive frames.
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.
Flo (app)
Flo is a period-tracking app that provides menstrual cycle, ovulation and pregnancy tracking as well as perimenopause symptom tracking that was developed by Flo Health, Inc. It has over 380 million downloads worldwide and over 70 million monthly active users as of November 2024. In mid-2024, it reached unicorn status, and became Europe’s first femtech unicorn. The company has been accused of sharing users' sensitive health data with third parties without consent and misleading its users about data practices. == History == Flo Health, Inc. was co-founded in 2015 by Dmitry and Yuri Gurski, in Belarus. Their backgrounds helped build the first version of the software having experience in other fitness and health apps. Dmitry serves as the company's CEO. The company's development hubs are in London, Amsterdam and Vilnius. In 2016, the company raised $1 million in seed round funding from Flint Capital and Haxus Venture Fund. In 2017, Flo received an investment of $5 million from Flint Capital and model Natalia Vodianova with Vodianova helping develop an awareness campaign for the company. In 2018, Flo received an investment of $6 million from Mangrove Capital Partners, with participation from Flint Capital and Haxus, giving the company a valuation of $200 million. In mid-2019, Flo received an additional investment of $7.5 million led by Founders Fund. In 2020, the Federal Trade Commission alleged that Flo had misled users about its handling of health information to third parties including Google, Facebook, AppsFlyer, and Flurry since 2016. These allegations followed a 2019 report by The Wall Street Journal in reference to Facebook. The company reached a settlement in 2021 and was required to notify users of how their personal information was shared and obtain permission before any further information was shared. The agreement also required that Flo to undertake an independent privacy audit which it completed in March 2022. In early September 2021, Flo announced it closed $50M in a Series B financing, bringing the total capital raised to $65 million and company valuation to $800M led by VNV Global and Target Global. In March 2024, the Supreme Court of British Columbia certified a class action suit against Flo for sharing intimate data with Facebook and other third parties without user knowledge. In July 2024, Flo announced it raised more than $200M in Series C financing from General Atlantic bringing its valuation beyond $1 billion. As of November 2024, the app had over 380 million downloads world wide, and over 70 million monthly active users. In 2025, Flo adopted a data intelligence platform from Databricks to power its analytics and AI features, allowing users personalized cycle predictions. In 2025, a class action lawsuit in California was settled for $56 million with Flo paying $8 million and Google paying $48 million. == Features and privacy == Flo was initially created as a period and ovulation tracking application. It now provides reminders of upcoming menstrual cycles and a place to record various other health symptoms such as contraceptive methods, vaginal discharge (leukorrhea), water intake, pains, mood swings, and sexual activity. The application is available on iOS and Android. Flo is free to download and the free basic version gives you access to period and ovulation tracking and predictions, symptom tracking, cycle history, and anonymous mode. In Pregnancy mode, the app provides tracking features and educational material for pregnancy. In October 2023, Flo launched Flo for Partners, a feature that allows users to share their Flo data with their partner. In September 2022, as a response to Roe v. Wade being overturned, Flo sped up the release of a feature called "Anonymous Mode". Flo said this mode allows users to access the app without any personal identifiers such as name, email address, or technical identifiers being associated with their health data. Flo said it uses a technology called Oblivious HTTP to help protect user privacy in Anonymous Mode. == Recognition == Flo was named to Bloomberg’s Top 25 UK Startups to Watch for 2024. Flo's Anonymous Mode feature was recognized on both Fast Company's World Changing Ideas 2023 and TIME's Best Inventions List 2023. Flo is a CES 2019 Innovation Awards Honoree in the Software and Mobile Applications category.