Alt TikTok (or 2020 Alt) was an online youth subculture and internet community that emerged on TikTok in 2020. Alt TikTok users (also known as alt girls, alt boys, or alt kids) emerged as primarily LGBTQ+ individuals who were in contrast to "Straight TikTok" which was seen as the mainstream and heteronormative side of the platform. The subculture became closely associated with music surrounding the hyperpop scene, particularly 100 gecs and also led to a short-lived fashion style and Internet aesthetic adopted by Generation Z during the COVID-19 lockdowns. Notable artists associated with the movement included Girl in Red, Freddie Dredd, David Shawty, WHOKILLEDXIX, and 645AR. While "alt kid" might imply a general association with traditional alternative fashion, the subculture was more an offshoot of e-girls and e-boys. In 2023, the hashtag #altfashion on TikTok amassed over 1.8 billion views. == History == Around mid-2020, users on TikTok began to group different content on the site into labels like "elite TikTok", "deep TikTok", and "floptok". These categories acted as different "sides of TikTok", deviating from mainstream lip syncing, online trends, and dance videos. Alt TikTok became one of the many subcultural communities to emerge during this period, initially referred to interchangeably with "elite TikTok". The movement quickly identified itself with alternative and queer users, in contrast to "Straight TikTok", also known as the "straight side of TikTok", which was seen as the mainstream and heteronormative side of the platform. Alt TikTok was accompanied by memes with surrealist or supernatural themes (sometimes being described as cursed), such as videos with heavy saturation and humanoid animals. One of the popular videos from Alt TikTok, gaining 18 million likes, shows a llama dancing to a cover of a song from a Russian commercial by the cereal brand Miel Pops, later becoming a viral audio. Some Alt TikTok users personified brands and products in what was referred to as Retail TikTok. In 2020, Rolling Stone described Alt TikTok as "one of the primary countercultures on the app." In 2020, American journalist Taylor Lorenz stated in an article of The New York Times, "Every pop sensation needs its ironic counterpoints. Alt Tiktok gets it done. [...] alt TikTok stars like Mooptopia are mainstays on the more indie side of the app. They aren't the popular crowd, but their cool, quirky content still attracts millions." === Trump rally trolling === In June 2020, alt TikTok and K-pop twitter users coordinated a strategy to ruin a Trump rally in Tulsa, Oklahoma. American politician and activist Alexandria Ocasio-Cortez later saluted the individuals for their "Trump troll". == Alt subculture == In 2020, Alt TikTok was one of many subcultural communities to emerge on TikTok, alongside Deep TikTok (aka DeepTok) and Flop TikTok (aka Floptok). The alt kid subculture emerged from Alt TikTok primarily among young Gen Z women, influenced by online fashion and aesthetics shaped by e-girls and e-boys. The movement was accelerated by the COVID-19 lockdowns, while the subculture itself stood in opposition to mainstream "Straight TikTok" and the VSCO girl movement, primarily adopting aspects of queer and alternative culture. While the phrase might imply a general association with alternative fashion or alternative culture, it is more accurately understood as a specific internet-driven outgrowth of online aesthetic youth subcultures like e-girls and e-boys. The alt subculture's visual style blended influences from goth, punk, emo, and grunge, often expressed through fashion, music taste, and online presence. === Style and music === The style of alt-girls is reminiscent of a myriad of previous alternative fashion trends, often blending these influences with online aesthetics. In 2020, TikTok alt-girls were teens ranging from ages 13 to 16, who tended to wear friendship bracelets, goth boots, Dr. Martens, bunny and frog hats, piercings, and split-dyed hair, as well as iconography lifted from Monster Energy and Hello Kitty. Some alt-girls displayed a love of cosplay, while drawing from Japanese anime and manga, particularly Danganronpa and Haikyu!!, which originally gained traction on the app through Anime TikTok (aka Anitok). Alt TikTok has been noted for being primarily influenced by queer and alternative culture, positioning itself in contrast to "Straight TikTok", which focused on mainstream dances and music. Alt kids frequently intersected with the e-girls and e-boys subculture, in terms of music, style, visual media, and aesthetics. Several musicians and artists were closely associated with the alt subculture, particularly those in the hyperpop scene, while alt tiktok users became important in the wider popularization of artists like 100 gecs. Notable prominent artists associated with Alt Tiktok included Girl in Red, Freddie Dredd, David Shawty, WHOKILLEDXIX, and 645AR, alongside music by YouTubers turned musicians such as Wilbur Soot's "I'm in Love With an E‐Girl" and Corpse Husband's "E-Girls Are Ruining My Life!". == Legacy == In 2020, Pitchfork claimed Alt TikTok as having an influence on wider music trends, stating: "Alt TikTok's music is now a hot zone for major record labels, pushing it even further into the mainstream". After the COVID-19 lockdowns, Alt TikTok, alongside its subculture, fell out of prominence and was taken over by other Gen Z-related internet aesthetics, developments, and online trends.
Sentence extraction
Sentence extraction is a technique used for automatic summarization of a text. In this shallow approach, statistical heuristics are used to identify the most salient sentences of a text. Sentence extraction is a low-cost approach compared to more knowledge-intensive deeper approaches which require additional knowledge bases such as ontologies or linguistic knowledge. In short, sentence extraction works as a filter that allows only meaningful sentences to pass. The major downside of applying sentence-extraction techniques to the task of summarization is the loss of coherence in the resulting summary. Nevertheless, sentence extraction summaries can give valuable clues to the main points of a document and are frequently sufficiently intelligible to human readers. == Procedure == Usually, a combination of heuristics is used to determine the most important sentences within the document. Each heuristic assigns a (positive or negative) score to the sentence. After all heuristics have been applied, the highest-scoring sentences are included in the summary. The individual heuristics are weighted according to their importance. === Early approaches and some sample heuristics === Seminal papers which laid the foundations for many techniques used today have been published by Hans Peter Luhn in 1958 and H. P Edmundson in 1969. Luhn proposed to assign more weight to sentences at the beginning of the document or a paragraph. Edmundson stressed the importance of title-words for summarization and was the first to employ stop-lists in order to filter uninformative words of low semantic content (e.g. most grammatical words such as of, the, a). He also distinguished between bonus words and stigma words, i.e. words that probably occur together with important (e.g. the word form significant) or unimportant information. His idea of using key-words, i.e. words which occur significantly frequently in the document, is still one of the core heuristics of today's summarizers. With large linguistic corpora available today, the tf–idf value which originated in information retrieval, can be successfully applied to identify the key words of a text: If for example the word cat occurs significantly more often in the text to be summarized (TF = "term frequency") than in the corpus (IDF means "inverse document frequency"; here the corpus is meant by document), then cat is likely to be an important word of the text; the text may in fact be a text about cats.
Business intelligence
Business intelligence (BI) consists of strategies, methodologies, and technologies used by enterprises for data analysis and management of business information to inform business strategies and business operations. Common functions of BI technologies include reporting, online analytical processing, analytics, dashboard development, data mining, process mining, complex event processing, business performance management, benchmarking, text mining, predictive analytics, and prescriptive analytics. BI tools can handle large amounts of structured and sometimes unstructured data to help organizations identify, develop, and otherwise create new strategic business opportunities. They aim to allow for the easy interpretation of these big data. Identifying new opportunities and implementing an effective strategy based on insights is assumed to potentially provide businesses with a competitive market advantage and long-term stability, and help them take strategic decisions. Business intelligence can be used by enterprises to support a wide range of business decisions ranging from operational to strategic. Basic operating decisions include product positioning or pricing. Strategic business decisions involve priorities, goals, and directions at the broadest level. In all cases, business intelligence is considered most effective when it combines data from the market in which a company operates (external data) with data from internal company sources, such as financial and operational information. When integrated, external and internal data provide a comprehensive view that creates ‘intelligence’ not possible from any single data source alone. Among their many uses, business intelligence tools empower organizations to gain insight into new markets, to assess demand and suitability of products and services for different market segments, and to gauge the impact of marketing efforts. BI applications use data gathered from a data warehouse (DW) or from a data mart, and the concepts of BI and DW combine as "BI/DW" or as "BIDW". A data warehouse contains a copy of analytical data that facilitates decision support. == History == The earliest known use of the term business intelligence is in Richard Millar Devens' Cyclopædia of Commercial and Business Anecdotes (1865). Devens used the term to describe how the banker Sir Henry Furnese gained profit by receiving and acting upon information about his environment, prior to his competitors: Throughout Holland, Flanders, France, and Germany, he maintained a complete and perfect train of business intelligence. The news of the many battles fought was thus received first by him, and the fall of Namur added to his profits, owing to his early receipt of the news. The ability to collect and react accordingly based on the information retrieved, Devens says, is central to business intelligence. When Hans Peter Luhn, a researcher at IBM, used the term business intelligence in an article published in 1958, he employed the Webster's Dictionary definition of intelligence: "the ability to apprehend the interrelationships of presented facts in such a way as to guide action towards a desired goal." In 1989, Howard Dresner (later a Gartner analyst) proposed business intelligence as an umbrella term to describe "concepts and methods to improve business decision making by using fact-based support systems." It was not until the late 1990s that this usage was widespread. == Definition == According to Solomon Negash and Paul Gray, business intelligence (BI) can be defined as systems that combine: Data gathering Data storage Knowledge management with analysis to evaluate complex corporate and competitive information for presentation to planners and decision makers, with the objective of improving the timeliness and the quality of the input to the decision process." According to Forrester Research, business intelligence is "a set of methodologies, processes, architectures, and technologies that transform raw data into meaningful and useful information used to enable more effective strategic, tactical, and operational insights and decision-making." Under this definition, business intelligence encompasses information management (data integration, data quality, data warehousing, master-data management, text- and content-analytics, et al.). Therefore, Forrester refers to data preparation and data usage as two separate but closely linked segments of the business-intelligence architectural stack. Some elements of business intelligence are: Multidimensional aggregation and allocation Denormalization, tagging, and standardization Realtime reporting with analytical alert A method of interfacing with unstructured data sources Group consolidation, budgeting, and rolling forecasts Statistical inference and probabilistic simulation Key performance indicators optimization Version control and process management Open item management Forrester distinguishes this from the business-intelligence market, which is "just the top layers of the BI architectural stack, such as reporting, analytics, and dashboards." === Compared with competitive intelligence === Though the term business intelligence is sometimes a synonym for competitive intelligence (because they both support decision making), BI uses technologies, processes, and applications to analyze mostly internal, structured data and business processes while competitive intelligence gathers, analyzes, and disseminates information with a topical focus on company competitors. If understood broadly, competitive intelligence can be considered as a subset of business intelligence. === Compared with business analytics === Business intelligence and business analytics are sometimes used interchangeably, but there are alternate definitions. Thomas Davenport, professor of information technology and management at Babson College argues that business intelligence should be divided into querying, reporting, Online analytical processing (OLAP), an "alerts" tool, and business analytics. In this definition, business analytics is the subset of BI focusing on statistics, prediction, and optimization, rather than the reporting functionality. == Unstructured data == Business operations can generate a very large amount of data in the form of emails, memos, notes from call centers, news, user groups, chats, reports, web pages, presentations, image files, video files, and marketing material. According to Merrill Lynch, more than 85% of all business information exists in these forms; a company might only use such a document a single time. Because of the way it is produced and stored, this information is either unstructured or semi-structured. The management of semi-structured data is an unsolved problem in the information technology industry. According to projections from Gartner (2003), white-collar workers spend 30–40% of their time searching, finding, and assessing unstructured data. BI uses both structured and unstructured data. The former is easy to search, and the latter contains a large quantity of the information needed for analysis and decision-making. Because of the difficulty of properly searching, finding, and assessing unstructured or semi-structured data, organizations may not draw upon these vast reservoirs of information, which could influence a particular decision, task, or project. This can ultimately lead to poorly informed decision-making. Therefore, when designing a business intelligence/DW solution, the specific problems associated with semi-structured and unstructured data must be accommodated, as well as those associated with structured data. === Limitations of semi-structured and unstructured data === There are several challenges to developing BI with semi-structured data. According to Inmon & Nesavich, some of those are: Physically accessing unstructured textual data – unstructured data is stored in a huge variety of formats. Terminology – Among researchers and analysts, there is a need to develop standardized terminology. Volume of data – As stated earlier, up to 85% of all data exists as semi-structured data. Couple that with the need for word-to-word and semantic analysis. Searchability of unstructured textual data – A simple search on some data, e.g. apple, results in links where there is a reference to that precise search term. (Inmon & Nesavich, 2008) gives an example: "a search is made on the term felony. In a simple search, the term felony is used, and everywhere there is a reference to felony, a hit to an unstructured document is made. But a simple search is crude. It does not find references to crime, arson, murder, embezzlement, vehicular homicide, and such, even though these crimes are types of felonies". === Metadata === To solve problems with searchability and assessment of data, it is necessary to know something about the content. This can be done by adding context through the use of metadata. Many systems already capture some metadata (e.g. filename, author, size, etc.), but more usef
Data transformation (computing)
In computing, data transformation is the process of converting data from one format or structure into another format or structure. It is a fundamental aspect of most data integration and data management tasks such as data wrangling, data warehousing, data integration and application integration. Data transformation can be simple or complex based on the required changes to the data between the source (initial) data and the target (final) data. Data transformation is typically performed via a mixture of manual and automated steps. Tools and technologies used for data transformation can vary widely based on the format, structure, complexity, and volume of the data being transformed. A master data recast is another form of data transformation where the entire database of data values is transformed or recast without extracting the data from the database. All data in a well-designed database is directly or indirectly related to a limited set of master database tables by a network of foreign key constraints. Each foreign key constraint is dependent upon a unique database index from the parent database table. Therefore, when the proper master database table is recast with a different unique index, the directly and indirectly related data are also recast or restated. The directly and indirectly related data may also still be viewed in the original form since the original unique index still exists with the master data. Also, the database recast must be done in such a way as to not impact the applications architecture software. When the data mapping is indirect via a mediating data model, the process is also called data mediation. == Data transformation process == Data transformation can be divided into the following steps, each applicable as needed based on the complexity of the transformation required. Data discovery Data mapping Code generation Code execution Data review These steps are often the focus of developers or technical data analysts who may use multiple specialized tools to perform their tasks. The steps can be described as follows: Data discovery is the first step in the data transformation process. Typically the data is profiled using profiling tools or sometimes using manually written profiling scripts to better understand the structure and characteristics of the data and decide how it needs to be transformed. Data mapping is the process of defining how individual fields are mapped, modified, joined, filtered, aggregated etc. to produce the final desired output. Developers or technical data analysts traditionally perform data mapping since they work in the specific technologies to define the transformation rules (e.g. visual ETL tools, transformation languages). Code generation is the process of generating executable code (e.g. SQL, Python, R, or other executable instructions) that will transform the data based on the desired and defined data mapping rules. Typically, the data transformation technologies generate this code based on the definitions or metadata defined by the developers. Code execution is the step whereby the generated code is executed against the data to create the desired output. The executed code may be tightly integrated into the transformation tool, or it may require separate steps by the developer to manually execute the generated code. Data review is the final step in the process, which focuses on ensuring the output data meets the transformation requirements. It is typically the business user or final end-user of the data that performs this step. Any anomalies or errors in the data that are found and communicated back to the developer or data analyst as new requirements to be implemented in the transformation process. == Types of data transformation == === Batch data transformation === Traditionally, data transformation has been a bulk or batch process, whereby developers write code or implement transformation rules in a data integration tool, and then execute that code or those rules on large volumes of data. This process can follow the linear set of steps as described in the data transformation process above. Batch data transformation is the cornerstone of virtually all data integration technologies such as data warehousing, data migration and application integration. When data must be transformed and delivered with low latency, the term "microbatch" is often used. This refers to small batches of data (e.g. a small number of rows or a small set of data objects) that can be processed very quickly and delivered to the target system when needed. === Benefits of batch data transformation === Traditional data transformation processes have served companies well for decades. The various tools and technologies (data profiling, data visualization, data cleansing, data integration etc.) have matured and most (if not all) enterprises transform enormous volumes of data that feed internal and external applications, data warehouses and other data stores. === Limitations of traditional data transformation === This traditional process also has limitations that hamper its overall efficiency and effectiveness. The people who need to use the data (e.g. business users) do not play a direct role in the data transformation process. Typically, users hand over the data transformation task to developers who have the necessary coding or technical skills to define the transformations and execute them on the data. This process leaves the bulk of the work of defining the required transformations to the developer, which often in turn do not have the same domain knowledge as the business user. The developer interprets the business user requirements and implements the related code/logic. This has the potential of introducing errors into the process (through misinterpreted requirements), and also increases the time to arrive at a solution. This problem has given rise to the need for agility and self-service in data integration (i.e. empowering the user of the data and enabling them to transform the data themselves interactively). There are companies that provide self-service data transformation tools. They are aiming to efficiently analyze, map and transform large volumes of data without the technical knowledge and process complexity that currently exists. While these companies use traditional batch transformation, their tools enable more interactivity for users through visual platforms and easily repeated scripts. Still, there might be some compatibility issues (e.g. new data sources like IoT may not work correctly with older tools) and compliance limitations due to the difference in data governance, preparation and audit practices. === Interactive data transformation === Interactive data transformation (IDT) is an emerging capability that allows business analysts and business users the ability to directly interact with large datasets through a visual interface, understand the characteristics of the data (via automated data profiling or visualization), and change or correct the data through simple interactions such as clicking or selecting certain elements of the data. Although interactive data transformation follows the same data integration process steps as batch data integration, the key difference is that the steps are not necessarily followed in a linear fashion and typically don't require significant technical skills for completion. There are a number of companies that provide interactive data transformation tools, including Trifacta, Alteryx and Paxata. They are aiming to efficiently analyze, map and transform large volumes of data while at the same time abstracting away some of the technical complexity and processes which take place under the hood. Interactive data transformation solutions provide an integrated visual interface that combines the previously disparate steps of data analysis, data mapping and code generation/execution and data inspection. That is, if changes are made at one step (like for example renaming), the software automatically updates the preceding or following steps accordingly. Interfaces for interactive data transformation incorporate visualizations to show the user patterns and anomalies in the data so they can identify erroneous or outlying values. Once they've finished transforming the data, the system can generate executable code/logic, which can be executed or applied to subsequent similar data sets. By removing the developer from the process, interactive data transformation systems shorten the time needed to prepare and transform the data, eliminate costly errors in the interpretation of user requirements and empower business users and analysts to control their data and interact with it as needed. == Transformational languages == There are numerous languages available for performing data transformation. Many transformation languages require a grammar to be provided. In many cases, the grammar is structured using something closely resembling Backus–Naur form (BNF). There are numerous languages
List of cryptography journals
List of cryptography journals includes notable peer-reviewed academic journals that focus on cryptography, cryptanalysis, information security, and related areas in computer science and mathematics. == Notable journals == Cryptologia Designs, Codes and Cryptography IEEE Transactions on Information Theory International Journal of Information Security Journal of Cryptology Journal of Computer Security ACM Transactions on Privacy and Security Information Processing Letters Information and Computation
Brain technology
Brain technology, or self-learning know-how systems, defines a technology that employs latest findings in neuroscience. [see also neuro implants] The term was first introduced by the Artificial Intelligence Laboratory in Zurich, Switzerland, in the context of the Roboy project. Brain Technology can be employed in robots, know-how management systems and any other application with self-learning capabilities. In particular, Brain Technology applications allow the visualization of the underlying learning architecture often coined as "know-how maps". == Research and applications == The first demonstrations of BC in humans and animals took place in the 1960s when Grey Walter demonstrated use of non-invasively recorded encephalogram (EEG) signals from a human subject to control a slide projector (Graimann et al., 2010). Soon after Jacques J. Vidal coined the term brain–computer interface (BCI) in 1971, the Defense Advanced Research Projects Agency (DARPA) first starting funding brain–computer interface research and has since funded several brain–computer interface projects. That market is expected to reach a value of $1.72 billion by 2022. Brain–computer interfaces record brain activity, transmit the information out of the body, signal-process the data via algorithms, and convert them into command control signals. In 2012, a landmark study in Nature, led by pioneer Leigh Hochberg, MD, PhD, demonstrated that two people with tetraplegia were able to control robotic arms through thought when connected to the BrainGate neural interface system. The two participants were able to reach for and grasp objects in three-dimensional space, and one participant used the system to serve herself coffee for the first time since becoming paralyzed nearly 15 years prior. And in October 2020, two patients were able to wirelessly control an operating system to text, email, shop and bank using direct thought through the Stentrode brain computer interface (Journal of NeuroInterventional Surgery) in a study led by Thomas Oxley. This was the first time a brain–computer interface was implanted via the patient's blood vessels, eliminating the need for open brain surgery. Currently a number of groups are exploring a range of experimental devices using brain–computer interfaces, which have the potential to fundamentally change the way of life for patients with paralysis and a wide range of neurological disorders. These include: as Elon Musk, Facebook, and the University of California in San Francisco. The systems. This technology is also being explored as a neuromodulation device and may ultimately help diagnose and treat a range of brain pathologies, such as epilepsy and Parkinson's disease.
Multistage interconnection networks
Multistage interconnection networks (MINs) are a class of high-speed computer networks usually composed of processing elements (PEs) on one end of the network and memory elements (MEs) on the other end, connected by switching elements (SEs). The switching elements themselves are usually connected to each other in stages, hence the name. MINs are typically used in high-performance or parallel computing as a low-latency interconnection (as opposed to traditional packet switching networks), though they could be implemented on top of a packet switching network. Though the network is typically used for routing purposes, it could also be used as a co-processor to the actual processors for such uses as sorting; cyclic shifting, as in a perfect shuffle network; and bitonic sorting. == Background == Interconnection network are used to connect nodes, where nodes can be a single processor or group of processors, to other nodes. Interconnection networks can be categorized on the basis of their topology. Topology is the pattern in which one node is connected to other nodes. There are two main types of topology: static and dynamic. Static interconnect networks are hard-wired and cannot change their configurations. A regular static interconnect is mainly used in small networks made up of loosely couple nodes. The regular structure signifies that the nodes are arranged in specific shape and the shape is maintained throughout the networks. Some examples of static regular interconnections are: Completely connected network In a mesh network, multiple nodes are connected with each other. Each node in the network is connected to every other node in the network. This arrangement allows proper communication of the data between the nodes. But, there are a lot of communication overheads due to the increased number of node connections. Shared busThis network topology involves connection of the nodes with each other over a bus. Every node communicates with every other node using the bus. The bus utility ensures that no data is sent to the wrong node. But, the bus traffic is an important parameter which can affect the system. RingThis is one of the simplest ways of connecting nodes with each other. The nodes are connected with each other to form a ring. For a node to communicate with some other node, it has to send the messages to its neighbor. Therefore, the data message passes through a series of other nodes before reaching the destination. This involves increased latency in the system. TreeThis topology involves connection of the nodes to form a tree. The nodes are connected to form clusters and the clusters are in-turn connected to form the tree. This methodology causes increased complexity in the network. Hypercube This topology consists of connections of the nodes to form cubes. The nodes are also connected to the nodes on the other cubes. ButterflyThis is one of the most complex connections of the nodes. As the figure suggests, there are nodes which are connected and arranged in terms of their ranks. They are arranged in the form of a matrix. In dynamic interconnect networks, the nodes are interconnected via an array of simple switching elements. This interconnection can then be changed by use of routing algorithms, such that the path from one node to other nodes can be varied. Dynamic interconnections can be classified as: Single stage Interconnect Network Multistage interconnect Network Crossbar switch connections == Crossbar Switch Connections == In crossbar switch, there is a dedicated path from one processor to other processors. Thus, if there are n inputs and m outputs, we will need nm switches to realize a crossbar. As the number of outputs increases, the number of switches increases by factor of n. For large network this will be a problem. An alternative to this scheme is staged switching. == Single Stage Interconnect Network == In a single stage interconnect network, the input nodes are connected to output via a single stage of switches. The figure shows 88 single stage switch using shuffle exchange. As one can see, from a single shuffle, not all input can reach all output. Multiple shuffles are required for all inputs to be connected to all the outputs. == Multistage Interconnect Network == A multistage interconnect network is formed by cascading multiple single stage switches. The switches can then use their own routing algorithm, or be controlled by a centralized router, to form a completely interconnected network. Multistage Interconnect Network can be classified into three types: Non-blocking: A non-blocking network can connect any idle input to any idle output, regardless of the connections already established across the network. Crossbar is an example of this type of network. Rearrangeable non-blocking: This type of network can establish all possible connections between inputs and outputs by rearranging its existing connections. Blocking: This type of network cannot realize all possible connections between inputs and outputs. This is because a connection between one free input to another free output is blocked by an existing connection in the network. The number of switching elements required to realize a non-blocking network in highest, followed by rearrangeable non-blocking. Blocking network uses least switching elements. == Examples == Multiple types of multistage interconnection networks exist. === Omega network === An Omega network consists of multiple stages of 22 switching elements. Each input has a dedicated connection to an output. An NN omega network has log2(N) stages and N/2 switching elements in each stage for a perfect shuffle between stages. Thus the network has complexity of 0(N log(N)). Each switching element can employ its own switching algorithm. Consider an 88 omega network. There are 8! = 40320 1-to-1 mappings from input to output. There are 12 switching element for a total permutation of 2^12 = 4096. Thus, it is a blocking network. === Clos network === A Clos network uses 3 stages to switch from N inputs to N outputs. In the first stage, there are r= N/n crossbar switches and each switch is of size nm. In the second stage there are m switches of size rr and finally the last stage is a mirror of the first stage with r switches of size mn. A clos network will be completely non-blocking if m >= 2n-1. The number of connections, though more than omega network is much less than that of a crossbar network. === Beneš network === A Beneš network is a rearrangeably non-blocking network derived from the clos network by initializing n = m = 2. There are (2log2(N) - 1) stages, with each stage containing N/2 22 crossbar switches. An 88 Beneš network has 5 stages of switching elements, and each stage has 4 switching elements. The center three stages has two 44 benes network. The 44 Beneš network, can connect any input to any output recursively.