Algorithms and Combinatorics

Algorithms and Combinatorics

Algorithms and Combinatorics (ISSN 0937-5511) is a book series in mathematics, and particularly in combinatorics and the design and analysis of algorithms. It is published by Springer Science+Business Media, and was founded in 1987. == Books == The books published in this series include: The Simplex Method: A Probabilistic Analysis (Karl Heinz Borgwardt, 1987, vol. 1) Geometric Algorithms and Combinatorial Optimization (Martin Grötschel, László Lovász, and Alexander Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász, and Rainer Schrader, 1991, vol. 4) Mathematics of Ramsey Theory (Jaroslav Nešetřil and Vojtěch Rödl, eds., 1990, vol. 5) Matroid Theory and its Applications in Electric Network Theory and in Statics (Andras Recszki, 1989, vol. 6) Irregularities of Partitions: Papers from the meeting held in Fertőd, July 7–11, 1986 (Gábor Halász and Vera T. Sós, eds., 1989, vol. 8) Paths, Flows, and VLSI-Layout: Papers from the meeting held at the University of Bonn, Bonn, June 20–July 1, 1988 (Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, eds., 1990, vol. 9) New Trends in Discrete and Computational Geometry (János Pach, ed., 1993, vol. 10) Discrete Images, Objects, and Functions in Z n {\displaystyle \mathbb {Z} ^{n}} (Klaus Voss, 1993, vol. 11) Linear Optimization and Extensions (Manfred Padberg, 1999, vol. 12) The Mathematics of Paul Erdős I (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 13) The Mathematics of Paul Erdős II (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 14) Geometry of Cuts and Metrics (Michel Deza and Monique Laurent, 1997, vol. 15) Probabilistic Methods for Algorithmic Discrete Mathematics (M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, 1998, vol. 16) Modern Cryptography, Probabilistic Proofs and Pseudorandomness (Oded Goldreich, 1999, vol. 17) Geometric Discrepancy: An Illustrated Guide (Jiří Matoušek, 1999, vol. 18) Applied Finite Group Actions (Adalbert Kerber, 1999, vol. 19) Matrices and Matroids for Systems Analysis (Kazuo Murota, 2000, vol. 20; corrected ed., 2010) Combinatorial Optimization (Bernhard Korte and Jens Vygen, 2000, vol. 21; 5th ed., 2012) The Strange Logic of Random Graphs (Joel Spencer, 2001, vol. 22) Graph Colouring and the Probabilistic Method (Michael Molloy and Bruce Reed, 2002, Vol. 23) Combinatorial Optimization: Polyhedra and Efficiency (Alexander Schrijver, 2003, vol. 24. In three volumes: A. Paths, flows, matchings; B. Matroids, trees, stable sets; C. Disjoint paths, hypergraphs) Discrete and Computational Geometry: The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, and M. Sharir, eds., 2003, vol. 25) Topics in Discrete Mathematics: Dedicated to Jarik Nešetril on the Occasion of his 60th birthday (M. Klazar, J. Kratochvíl, M. Loebl, J. Matoušek, R. Thomas, and P. Valtr, eds., 2006, vol. 26) Boolean Function Complexity: Advances and Frontiers (Stasys Jukna, 2012, Vol. 27) Sparsity: Graphs, Structures, and Algorithms (Jaroslav Nešetřil and Patrice Ossona de Mendez, 2012, vol. 28) Optimal Interconnection Trees in the Plane (Marcus Brazil and Martin Zachariasen, 2015, vol. 29) Combinatorics and Complexity of Partition Functions (Alexander Barvinok, 2016, vol. 30)

Windows Live OneCare Safety Scanner

Windows Live OneCare Safety Scanner (formerly Windows Live Safety Center and codenamed Vegas) was an online scanning, PC cleanup, and diagnosis service to help remove of viruses, spyware/adware, and other malware. It was a free web service that was part of Windows Live. On November 18, 2008, Microsoft announced the discontinuation of Windows Live OneCare, offering users a new free anti-malware suite Microsoft Security Essentials, which had been available since the second half of 2009. However, Windows Live OneCare Safety Scanner, under the same branding as Windows Live OneCare, was not discontinued during that time. The service was officially discontinued on April 15, 2011 and replaced with Microsoft Safety Scanner. == Overview == Windows Live OneCare Safety Scanner offered a free online scanning and protection from threats. The Windows Live OneCare Safety Scanner must be downloaded and installed to your computer to scan your computer. The "Full Service Scan" looks for common PC health issues such as viruses, temporary files, and open network ports. It searches and removes viruses, improves a computer's performance, and removes unnecessary clutter on the PC's hard disk. The user can choose between a "Full Scan" (which can be customized) or a "Quick Scan". The "Full Scan" scans for viruses (comprehensive scan or quick scan), hard disk performance (Disk fragmentation scan and/or Desk cleanup scan) and network safety (open port scan). The "Quick Scan" only scans for viruses, only on specific areas on the computer. The quick scan is faster than the full scan, hence that appellation. The service also provides a virus database, information about online threats, and general computer security documentation and tools. == Limits == The virus scanner on the Windows Live OneCare Safety Scanner site runs a scan of the user's computer only when the site is visited. It does not run periodic scans of the system, and does not provide features to prevent viruses from infecting the computer at the time, or thereafter. It simply resolves detected infections. Many users who have posted on the Product Feedback forum report script errors relating to Internet Explorer 7 (besides IE being the only browser supported by this service). The OneCare safety scanner team have been actively solving these problems, many of them registry-related.

Networked Help Desk

Networked Help Desk is an open standard initiative to provide a common API for sharing customer support tickets between separate instances of issue tracking, bug tracking, customer relationship management (CRM) and project management systems to improve customer service and reduce vendor lock-in. The initiative was created by Zendesk in June 2011 in collaboration with eight other founding member organizations including Atlassian, New Relic, OTRS, Pivotal Tracker, ServiceNow and SugarCRM. The first integration, between Zendesk and Atlassian's issue tracking product, Jira, was announced at the 2011 Atlassian Summit. By August 2011, 34 member companies had joined the initiative. A year after launching, over 50 organizations had joined. Within Zendesk instances this feature is branded as ticket sharing. == Basis == Support tools are generally built around a common paradigm that begins with a customer making a request or an incident report, these create a ticket. Each ticket has a progress status and is updated with annotations and attachments. These annotations and attachments may be visible to the customer (public), or only visible to analysts (private). Customers are notified of progress made on their ticket until it is complete. If the people necessary to complete a ticket are using separate support tools, additional overhead is introduced in maintaining the relevant information in the ticket in each tool while notifying the customer of progress made by each group in completing their ticket. For example, if a customer support issue is caused by a software bug and reported to a help desk using one system, and then the fix is documented by the developers in another, and analyzed in a customer relationship management tool, keeping the records in each system up-to-date and notifying the customer manually using a swivel chair approach is unnecessarily time-consuming and error-prone. If information is not transferred correctly, a customer may have to re-explain their problem each time their ticket is transferred. For systems with the Networked Help Desk API implemented, it is possible for several different applications related to a customer's support experience to synchronize data in one uniquely identified shared ticket. While many applications in these domains have implemented APIs that allow data to be imported, exported and modified, Network Help Desk provide a common standard for customer support information to automatically synchronize between several systems. Once implemented, two systems can quickly share tickets with just a configuration change as they both understand the same interface. Communication between two instances on a specific ticket occurs in three steps, an invitation agreement, sharing of ticket data and continued synchronization of tickets. The standard allows for "full delegation" (analysts in both systems each make public and private comments and synchronize status) as well as "partial delegation" where the instance receiving the ticket can only make private comments and status changes are not synchronized. Tickets may be shared with multiple instances. == Implementation list ==

Infogram

Infogram is a web-based data visualization and infographics platform, created in Riga, Latvia. It allows people to make and share digital charts, infographics and maps. Infogram offers an intuitive WYSIWYG editor that converts users’ data into infographics that can be published, embedded or shared. Users do not need coding skills to use this tool; users include newsrooms, marketing teams, governments, educators and students. The company that created Infogram, also called Infogram, was founded in 2012 in Riga, Latvia and has another office in San Francisco. As of October 2017, Infogram says it has 3 million users who have created charts and infographics that have been viewed more than 1.5 billion times. Infogram was bought by Prezi, a web-based presentation software company, in May 2017. == History == Infogram was founded in February 2012 in Riga, Latvia by Uldis Leiterts, Raimonds Kaže and Alise Dīrika. In January 2013, Infogram won the international Hy Berlin pitch contest. During his pitch, Infogram CEO Uldis Leiterts announced that the company had created more templates and was working with Microsoft to integrate its platform with the contemporaneous version of Microsoft Office. The company also won the 2013 Kantar Information Is Beautiful Award, which “celebrates excellence and beauty in data visualizations, infographics, interactives & information art.” In December 2014, Infogram acquired the Brazil-based data visualization blog, Visualoop. In an effort to expand sales and marketing in the U.S., Infogram secured $1.8 million in funding in February 2014. The announcement was made at TechChill, a startup conference for the Baltics in Riga, Latvia. At the time, the funding was believed to be the largest to date for the company. Infogram won the 2017 National Design Award of Latvia. == Acquisition by Prezi == Prezi, a web-based presentation software company, acquired Infogram in May 2017. Infogram is now a wholly owned subsidiary of Prezi. Infogram was rated #1 on Forbes’ list of “The Best Infographic Tools for 2017,” which was published in September 2017. In October 2017, Infogram announced a new version of its data visualization platform, including a drag-and-drop editor, over 40 new designer templates and social media support.

Process map

Process map is a global-system process model that is used to outline the processes that make up the business system and how they interact with each other. Process map shows the processes as objects, which means it is a static and non-algorithmic view of the processes. It should be differentiated from a detailed process model, which shows a dynamic and algorithmic view of the processes, usually known as a process flow diagram. There are different notation standards that can be used for modelling process maps, but the most notable ones are TOGAF Event Diagram, Eriksson-Penker notation, and ARIS Value Added Chain. == Global process models == Global characteristics of the business system are captured by global or system models. Global process models are presented using different methodologies and sometimes under different names. Most notably, they are named process map in Visual Paradigm and MMABP, value-added chain in ARIS, and process diagram in Eriksson-Penker notation – which can easily lead to the confusion with process flow (detailed process model). Global models are mainly object-oriented and present a static view of the business system; they do not describe dynamic aspects of processes. A process map shows the presence of processes and their mutual relationships. The requirement for the global perspective of the system as a supplementary to the internal process logic description results from the necessity of taking into consideration not only the internal process logic but also its significant surroundings. The algorithmic process model cannot take the place of this perspective since it represents the system model of the process. The detailed process model and the global process model represent different perspectives on the same business system, so these models must be mutually consistent. A macro process map represents the major processes required to deliver a product or service to the customer. These macro process maps can be further detailed in sub-diagrams. It is often the case that process maps cross different functional areas of the organization. Process maps are used by many companies to have a holistic view of all processes and the connections between them. Maps help in navigating the sub-processes and make understanding of the organization's operations easier. The process map shows relationships and dependencies between processes and its focus should be on core business processes of the organization. A process map can be seen as the most abstract level of the process architecture, and it acts as the introduction to the more detailed levels. A process map that is correctly designed is able to provide a general understanding of a company's operations. Designing the process map is an important and strategic step for the organization, and it is followed by further business process modelling implementation. == Context == Methodology for Modelling and Analysis of Business Process (MMABP) is a business process modelling methodology developed at the Department of Information Technology, Faculty of Informatics and Statistics of the Prague University of Economics and Business. The methodology is defined as a “general methodology for modelling business systems using informatics methods and approaches”. Methodology is used to analyse business processes and to develop a comprehensive model of the system. The goal of developing a model is to be used for process optimization. The model should be created following the characteristics and specifics of the organization in question and following external influences that can affect the organization. The model should be optimal from an economic perspective, but it should also be optimal from a factual perspective, meaning that it should be as simple as possible while maintaining complete functionality. Business system modelling is based on a two-dimensional approach: Real World structure (substance) – set of objects and their relationships Real World behaviour – set of mutually connected business processes Additionally, there are also two views of the systems: Global view of the system Detailed view of the system's parts This results in the need to model the system from four different perspectives in order to achieve the complete and comprehensive view of the business system. MMABP also proposes which notation languages can be used for modelling each perspective, and it also suggests some improvements to the notation languages in order to fit the purpose. Global view of the objects – Conceptual model (Class diagram) Detailed view of the objects – Object life cycle (State Chart) Global view of the processes – Process map (Eriksson-Penker Diagram/TOGAF Event Diagram/ARIS VAC) Detailed view of the processes – Model of the process flow (BPMN Diagram) Data Flow Diagram (DFD) is additional diagram used for describing the required functionalities of the information system. == Notation standards == === Eriksson-Penker Diagram === Eriksson-Penker diagram is a tool used in business model analysis and design. It is named after Hans-Erik Eriksson and Magnus Penker, who developed the concept in their book "Business modelling with UML: Business Patterns at Work”. Eriksson-Penker diagrams are used to map out the key components of a business model and how they interact with one another. The diagrams typically consist of a series of boxes and lines that represent the different elements of the business model, such as the value proposition, customer segments, channels, revenue streams, and key resources. The lines between the boxes represent the relationships and dependencies between the different elements of the business model. These diagrams are useful for visualizing and understanding the various components of a business model, and can help organizations identify potential areas for improvement or areas of risk. They can also be used as a communication tool to help stakeholders understand the business model and its underlying assumptions. These diagrams are useful for visualizing and understanding the various components of a business model, and can help organizations identify potential areas for improvement or areas of risk. They can also be used as a communication tool to help stakeholders understand the business model and its underlying assumptions. It is possible to use Eriksson-Penker diagrams to create a global process view of a business. In this case, a diagram would be used to map out the key processes and activities that are involved in the business, as well as the relationships and dependencies between these processes. For example, an Eriksson-Penker diagram could be used to depict the various steps involved in the product development process, from concept development to market launch. It could also be used to show how different functions within the organization, such as marketing, sales, and production, interact and depend on one another to support the overall business. Eriksson-Penker diagram is one of the most popular de facto standards that can be used for an object-oriented global view of business processes. It is developed as an extension of the UML, and it is often used together with the BPMN to compensate for the lack of possibility to model the global view with this widely accepted standard. === TOGAF Event Diagram === TOGAF (The Open Group Architecture Framework) is a framework for enterprise architecture that provides a common language and set of standards for designing, planning, implementing, and governing an enterprise's IT architecture. TOGAF event diagrams are diagrams used in the TOGAF framework to represent the flow of events within a system or process. The TOGAF Event Diagram is a visual representation of the events within an organization or system. It can be used to show the sequence of events that occur in a particular process, as well as the relationships between the events and the stakeholders involved. TOGAF Event Diagrams can be useful in creating a global process view because they provide a visual representation of the events, which can be helpful in understanding how the process fits into the larger context of the organization. TOGAF Event Diagram is the most perspective standard for the system view of processes today. It is used to represent the system of processes as well as their connections to the functional organizational structure. === ARIS Value Added Chain === ARIS (Architecture of Integrated Information Systems) is a methodology and a set of tools for designing and managing business processes. It is based on the idea that business processes are the core of an organization and that they can be modelled and optimized to improve efficiency and effectiveness. The ARIS methodology provides a framework for understanding and analysing business processes, as well as for designing and implementing improvements to those processes. It includes a set of graphical modelling languages and tools for creating process models, as well as a database for storing and managing pr

Landweber iteration

The Landweber iteration or Landweber algorithm is an algorithm to solve ill-posed linear inverse problems, and it has been extended to solve non-linear problems that involve constraints. The method was first proposed in the 1950s by Louis Landweber, and it can be now viewed as a special case of many other more general methods. == Basic algorithm == The original Landweber algorithm attempts to recover a signal x from (noisy) measurements y. The linear version assumes that y = A x {\displaystyle y=Ax} for a linear operator A. When the problem is in finite dimensions, A is just a matrix. When A is nonsingular, then an explicit solution is x = A − 1 y {\displaystyle x=A^{-1}y} . However, if A is ill-conditioned, the explicit solution is a poor choice since it is sensitive to any noise in the data y. If A is singular, this explicit solution doesn't even exist. The Landweber algorithm is an attempt to regularize the problem, and is one of the alternatives to Tikhonov regularization. We may view the Landweber algorithm as solving: min x ‖ A x − y ‖ 2 2 / 2 {\displaystyle \min _{x}\|Ax-y\|_{2}^{2}/2} using an iterative method. The algorithm is given by the update x k + 1 = x k − ω A ∗ ( A x k − y ) . {\displaystyle x_{k+1}=x_{k}-\omega A^{}(Ax_{k}-y).} where the relaxation factor ω {\displaystyle \omega } satisfies 0 < ω < 2 / σ 1 2 {\displaystyle 0<\omega <2/\sigma _{1}^{2}} . Here σ 1 {\displaystyle \sigma _{1}} is the largest singular value of A {\displaystyle A} . If we write f ( x ) = ‖ A x − y ‖ 2 2 / 2 {\displaystyle f(x)=\|Ax-y\|_{2}^{2}/2} , then the update can be written in terms of the gradient x k + 1 = x k − ω ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\omega \nabla f(x_{k})} and hence the algorithm is a special case of gradient descent. For ill-posed problems, the iterative method needs to be stopped at a suitable iteration index, because it semi-converges. This means that the iterates approach a regularized solution during the first iterations, but become unstable in further iterations. The reciprocal of the iteration index 1 / k {\displaystyle 1/k} acts as a regularization parameter. A suitable parameter is found, when the mismatch ‖ A x k − y ‖ 2 2 {\displaystyle \|Ax_{k}-y\|_{2}^{2}} approaches the noise level. Using the Landweber iteration as a regularization algorithm has been discussed in the literature. == Nonlinear extension == In general, the updates generated by x k + 1 = x k − τ ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\tau \nabla f(x_{k})} will generate a sequence f ( x k ) {\displaystyle f(x_{k})} that converges to a minimizer of f whenever f is convex and the stepsize τ {\displaystyle \tau } is chosen such that 0 < τ < 2 / ( ‖ ∇ f ‖ 2 ) {\displaystyle 0<\tau <2/(\|\nabla f\|^{2})} where ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is the spectral norm. Since this is special type of gradient descent, there currently is not much benefit to analyzing it on its own as the nonlinear Landweber, but such analysis was performed historically by many communities not aware of unifying frameworks. The nonlinear Landweber problem has been studied in many papers in many communities; see, for example. == Extension to constrained problems == If f is a convex function and C is a convex set, then the problem min x ∈ C f ( x ) {\displaystyle \min _{x\in C}f(x)} can be solved by the constrained, nonlinear Landweber iteration, given by: x k + 1 = P C ( x k − τ ∇ f ( x k ) ) {\displaystyle x_{k+1}={\mathcal {P}}_{C}(x_{k}-\tau \nabla f(x_{k}))} where P {\displaystyle {\mathcal {P}}} is the projection onto the set C. Convergence is guaranteed when 0 < τ < 2 / ( ‖ A ‖ 2 ) {\displaystyle 0<\tau <2/(\|A\|^{2})} . This is again a special case of projected gradient descent (which is a special case of the forward–backward algorithm) as discussed in. == Applications == Since the method has been around since the 1950s, it has been adopted and rediscovered by many scientific communities, especially those studying ill-posed problems. In X-ray computed tomography it is called simultaneous iterative reconstruction technique (SIRT). It has also been used in the computer vision community and the signal restoration community. It is also used in image processing, since many image problems, such as deconvolution, are ill-posed. Variants of this method have been used also in sparse approximation problems and compressed sensing settings.

ReactiveX

ReactiveX (Rx, also known as Reactive Extensions) is a software library originally created by Microsoft that allows imperative programming languages to operate on sequences of data regardless of whether the data is synchronous or asynchronous. It provides a set of sequence operators that operate on each item in the sequence. It is an implementation of reactive programming and provides a blueprint for the tools to be implemented in multiple programming languages. == Overview == ReactiveX is an API for asynchronous programming with observable streams. Asynchronous programming allows programmers to call functions and then have the functions "callback" when they are done, usually by giving the function the address of another function to execute when it is done. Programs designed in this way often avoid the overhead of having many threads constantly starting and stopping. Observable streams (i.e. streams that can be observed) in the context of Reactive Extensions are like event emitters that emit three events: next, error, and complete. An observable emits next events until it either emits an error event or a complete event. However, at that point it will not emit any more events, unless it is subscribed to again. The examples below use the RxJS implementation of Reactive Extensions for the JavaScript programming language. === Motivation === For sequences of data, it combines the advantages of iterators with the flexibility of event-based asynchronous programming. It also works as a simple promise, eliminating the pyramid of doom that results from multiple layers of callbacks. === Observables and observers === ReactiveX is a combination of ideas from the observer and the iterator patterns and from functional programming. An observer subscribes to an observable sequence. The sequence then sends the items to the observer one at a time, usually by calling the provided callback function. The observer handles each one before processing the next one. If many events come in asynchronously, they must be stored in a queue or dropped. In ReactiveX, an observer will never be called with an item out of order or (in a multi-threaded context) called before the callback has returned for the previous item. Asynchronous calls remain asynchronous and may be handled by returning an observable. It is similar to the iterators pattern in that if a fatal error occurs, it notifies the observer separately (by calling a second function). When all the items have been sent, it completes (and notifies the observer by calling a third function). The Reactive Extensions API also borrows many of its operators from iterator operators in other programming languages. Reactive Extensions is different from functional reactive programming as the Introduction to Reactive Extensions explains: It is sometimes called "functional reactive programming" but this is a misnomer. ReactiveX may be functional, and it may be reactive, but "functional reactive programming" is a different animal. One main point of difference is that functional reactive programming operates on values that change continuously over time, while ReactiveX operates on discrete values that are emitted over time. (See Conal Elliott's work for more-precise information on functional reactive programming.) === Reactive operators === An operator is a function that takes one observable (the source) as its first argument and returns another observable (the destination, or outer observable). Then for every item that the source observable emits, it will apply a function to that item, and then emit it on the destination Observable. It can even emit another Observable on the destination observable. This is called an inner observable. An operator that emits inner observables can be followed by another operator that in some way combines the items emitted by all the inner observables and emits the item on its outer observable. Examples include: switchAll – subscribes to each new inner observable as soon as it is emitted and unsubscribes from the previous one. mergeAll – subscribes to all inner observables as they are emitted and outputs their values in whatever order it receives them. concatAll – subscribes to each inner observable in order and waits for it to complete before subscribing to the next observable. Operators can be chained together to create complex data flows that filter events based on certain criteria. Multiple operators can be applied to the same observable. Some of the operators that can be used in Reactive Extensions may be familiar to programmers who use functional programming language, such as map, reduce, group, and zip. There are many other operators available in Reactive Extensions, though the operators available in a particular implementation for a programming language may vary. ==== Reactive operator examples ==== Here is an example of using the map and reduce operators. We create an observable from a list of numbers. The map operator will then multiply each number by two and return an observable. The reduce operator will then sum up all the numbers provided to it (the value of 0 is the starting point). Calling subscribe will register an observer that will observe the values from the observable produced by the chain of operators. With the subscribe method, we are able to pass in an error-handling function, called whenever an error is emitted in the observable, and a completion function when the observable has finished emitting items. ==== Usage in stream-oriented programming ==== Certain RxJS primitives such as BehaviorSubject make it possible to create pure stateful streams to track application state of arbitrary complexity in simple terms. The button below will feed an event to the stream, which in turn will re-emit the next natural number every time, back into the tag that follows and displays the count of clicks detected. Libraries such as Rimmel.js, designed around RxJS Observables, enable integration between reactive streams and the HTML DOM: == History == Reactive Extensions was created by the Cloud Programmability Team at Microsoft around 2011, as a byproduct of a larger effort called Volta. It was originally intended to provide an abstraction for events across different tiers in an application to support tier splitting in Volta. The project's logo represents an electric eel, which is a reference to Volta. The extensions suffix in the name is a reference to the Parallel Extensions technology which was invented around the same time; the two are considered complementary. The initial implementation of Rx was for .NET Framework and was released on June 21, 2011. Later, the team started the implementation of Rx for other platforms, including JavaScript and C++. The technology was released as open source in late 2012, initially on CodePlex. Later, the code moved to GitHub and has been ported to several other languages, including Go, Java, Kotlin, PHP and Rust.