Clustering is the problem of partitioning data points into groups based on similarity or dissimilarity. Correlation clustering is a clustering framework in which a set of objects is partitioned into clusters based on pairwise similarity and dissimilarity information, without requiring the number of clusters to be specified in advance. == Description of the problem == In machine learning, correlation clustering (also known as cluster editing) considers settings in which pairwise similarity or dissimilarity relationships between objects are known. A standard formulation models the input as an unweighted complete graph G = ( V , E ) {\displaystyle G=(V,E)} , where each edge is labeled either + {\displaystyle +} or − {\displaystyle -} (that is, the graph is a signed graph), indicating whether the corresponding endpoints are similar or dissimilar. The goal is to find a clustering (that is, a partition of V {\displaystyle V} ) that either maximizes the number of agreements—the sum of positive edges whose endpoints lie in the same cluster and negative edges whose endpoints lie in different clusters—or minimizes the number of disagreements—the sum of positive edges whose endpoints are separated and negative edges whose endpoints lie in the same cluster. Unlike other clustering methods such as k-means, correlation clustering does not require choosing the number of clusters k {\displaystyle k} in advance. It is not always possible to find a clustering with zero disagreements. For example, consider a triangle graph containing two positive edges and one negative edge. In this case, every clustering incurs at least one disagreement. Such configurations are referred to in the literature as bad triangles. From a computational perspective, optimizing the correlation clustering objective is challenging. The (decision version of the) problem is NP-complete. A large body of subsequent work has developed approximation algorithms for correlation clustering under various assumptions, including complete or general graphs and unweighted or weighted graphs, for both minimization and maximization objectives. This problem is considered one of the fundamental combinatorial optimization problems, and many algorithmic techniques have been developed to address it. The problem has also been studied extensively across multiple disciplines. A comprehensive literature review of early correlation clustering research is provided by Wahid and Hassini. == Formal Definitions == Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph with nodes V {\displaystyle V} and edges E {\displaystyle E} . A clustering of G {\displaystyle G} is a partition of its node set Π = { π 1 , … , π k } {\displaystyle \Pi =\{\pi _{1},\dots ,\pi _{k}\}} with V = π 1 ∪ ⋯ ∪ π k {\displaystyle V=\pi _{1}\cup \dots \cup \pi _{k}} and π i ∩ π j = ∅ {\displaystyle \pi _{i}\cap \pi _{j}=\emptyset } for i ≠ j {\displaystyle i\neq j} . For a given clustering Π {\displaystyle \Pi } , let δ ( Π ) = { { u , v } ∈ E ∣ { u , v } ⊈ π ∀ π ∈ Π } {\displaystyle \delta (\Pi )=\{\{u,v\}\in E\mid \{u,v\}\not \subseteq \pi \;\forall \pi \in \Pi \}} denote the subset of edges of G {\displaystyle G} whose endpoints are in different subsets of the clustering Π {\displaystyle \Pi } . Now, let w : E → R ≥ 0 {\displaystyle w\colon E\to \mathbb {R} _{\geq 0}} be a function that assigns a non-negative weight to each edge of the graph and let E = E + ∪ E − {\displaystyle E=E^{+}\cup E^{-}} be a partition of the edges into attractive ( E + {\displaystyle E^{+}} ) and repulsive ( E − {\displaystyle E^{-}} ) edges; that is, the edges are signed. The minimum disagreement correlation clustering problem is the following optimization problem: minimize Π ∑ e ∈ E + ∩ δ ( Π ) w e + ∑ e ∈ E − ∖ δ ( Π ) w e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {minimize} }}&&\sum _{e\in E^{+}\cap \delta (\Pi )}w_{e}+\sum _{e\in E^{-}\setminus \delta (\Pi )}w_{e}\;.\end{aligned}}} Here, the set E + ∩ δ ( Π ) {\displaystyle E^{+}\cap \delta (\Pi )} contains the attractive edges whose endpoints are in different components with respect to the clustering Π {\displaystyle \Pi } and the set E − ∖ δ ( Π ) {\displaystyle E^{-}\setminus \delta (\Pi )} contains the repulsive edges whose endpoints are in the same component with respect to the clustering Π {\displaystyle \Pi } . Together these two sets contain all edges that disagree with the clustering Π {\displaystyle \Pi } . Similarly to the minimum disagreement correlation clustering problem, the maximum agreement correlation clustering problem is defined as maximize Π ∑ e ∈ E + ∖ δ ( Π ) w e + ∑ e ∈ E − ∩ δ ( Π ) w e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {maximize} }}&&\sum _{e\in E^{+}\setminus \delta (\Pi )}w_{e}+\sum _{e\in E^{-}\cap \delta (\Pi )}w_{e}\;.\end{aligned}}} Here, the set E + ∖ δ ( Π ) {\displaystyle E^{+}\setminus \delta (\Pi )} contains the attractive edges whose endpoints are in the same component with respect to the clustering Π {\displaystyle \Pi } and the set E − ∩ δ ( Π ) {\displaystyle E^{-}\cap \delta (\Pi )} contains the repulsive edges whose endpoints are in different components with respect to the clustering Π {\displaystyle \Pi } . Together these two sets contain all edges that agree with the clustering Π {\displaystyle \Pi } . Instead of formulating the correlation clustering problem in terms of non-negative edge weights and a partition of the edges into attractive and repulsive edges the problem is also formulated in terms of positive and negative edge costs without partitioning the set of edges explicitly. For given weights w : E → R ≥ 0 {\displaystyle w\colon E\to \mathbb {R} _{\geq 0}} and a given partition E = E + ∪ E − {\displaystyle E=E^{+}\cup E^{-}} of the edges into attractive and repulsive edges, the edge costs can be defined by c e = { w e if e ∈ E + − w e if e ∈ E − {\displaystyle {\begin{aligned}c_{e}={\begin{cases}\;\;w_{e}&{\text{if }}e\in E^{+}\\-w_{e}&{\text{if }}e\in E^{-}\end{cases}}\end{aligned}}} for all e ∈ E {\displaystyle e\in E} . An edge whose endpoints are in different clusters is said to be cut. The set δ ( Π ) {\displaystyle \delta (\Pi )} of all edges that are cut is often called a multicut of G {\displaystyle G} . The minimum cost multicut problem is the problem of finding a clustering Π {\displaystyle \Pi } of G {\displaystyle G} such that the sum of the costs of the edges whose endpoints are in different clusters is minimal: minimize Π ∑ e ∈ δ ( Π ) c e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {minimize} }}&&\sum _{e\in \delta (\Pi )}c_{e}\;.\end{aligned}}} Similar to the minimum cost multicut problem, coalition structure generation in weighted graph games is the problem of finding a clustering such that the sum of the costs of the edges that are not cut is maximal: maximize Π ∑ e ∈ E ∖ δ ( Π ) c e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {maximize} }}&&\sum _{e\in E\setminus \delta (\Pi )}c_{e}\;.\end{aligned}}} This formulation is also known as the clique partitioning problem. It can be shown that all four problems that are formulated above are equivalent. This means that a clustering that is optimal with respect to any of the four objectives is optimal for all of the four objectives. == Algorithms == If the graph admits a clustering with zero disagreements, then deleting all negative edges and computing the connected components of the remaining graph yields an optimal clustering. A necessary and sufficient condition for the existence of such a clustering was given by Davis: no cycle in the graph may contain exactly one negative edge. Bansal et al. discuss the NP-completeness proof and also present both a constant factor approximation algorithm and polynomial-time approximation scheme to find the clusters in this setting. Ailon et al. propose a randomized 3-approximation algorithm for the same problem. CC-Pivot(G=(V,E+,E−)) Pick random pivot i ∈ V Set C = { i } {\displaystyle C=\{i\}} , V'=Ø For all j ∈ V, j ≠ i; If (i,j) ∈ E+ then Add j to C Else (If (i,j) ∈ E−) Add j to V' Let G' be the subgraph induced by V' Return clustering C,CC-Pivot(G') The authors show that the above algorithm is a 3-approximation algorithm for correlation clustering. The best polynomial-time approximation algorithm known at the moment for this problem achieves a ~2.06 approximation by rounding a linear program, as shown by Chawla, Makarychev, Schramm, and Yaroslavtsev. Karpinski and Schudy proved existence of a polynomial time approximation scheme (PTAS) for that problem on complete graphs and fixed number of clusters. == Optimal number of clusters == In 2011, it was shown by Bagon and Galun that the optimization of the correlation clustering functional is closely related to well known discrete optimization methods. In their work they proposed a probabilistic analysis of the underlying implicit model that allows the correlation clustering functional to estimate the
Psychology of reasoning
The psychology of reasoning (also known as the cognitive science of reasoning) is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps with psychology, philosophy, linguistics, cognitive science, artificial intelligence, logic, and probability theory. Psychological experiments on how humans and other animals reason have been carried out for over 100 years. An enduring question is whether or not people have the capacity to be rational. Current research in this area addresses various questions about reasoning, rationality, judgments, intelligence, relationships between emotion and reasoning, and development. == Everyday reasoning == One of the most obvious areas in which people employ reasoning is with sentences in everyday language. Most experimentation on deduction has been carried out on hypothetical thought, in particular, examining how people reason about conditionals, e.g., If A then B. Participants in experiments make the modus ponens inference, given the indicative conditional If A then B, and given the premise A, they conclude B. However, given the indicative conditional and the minor premise for the modus tollens inference, not-B, about half of the participants in experiments conclude not-A and the remainder concludes that nothing follows. The ease with which people make conditional inferences is affected by context, as demonstrated in the well-known selection task developed by Peter Wason. Participants are better able to test a conditional in an ecologically relevant context, e.g., if the envelope is sealed then it must have a 50 cent stamp on it compared to one that contains symbolic content, e.g., if the letter is a vowel then the number is even. Background knowledge can also lead to the suppression of even the simple modus ponens inference Participants given the conditional if Lisa has an essay to write then she studies late in the library and the premise Lisa has an essay to write make the modus ponens inference 'she studies late in the library', but the inference is suppressed when they are also given a second conditional if the library stays open then she studies late in the library. Interpretations of the suppression effect are controversial Other investigations of propositional inference examine how people think about disjunctive alternatives, e.g., A or else B, and how they reason about negation, e.g., It is not the case that A and B. Many experiments have been carried out to examine how people make relational inferences, including comparisons, e.g., A is better than B. Such investigations also concern spatial inferences, e.g. A is in front of B and temporal inferences, e.g. A occurs before B. Other common tasks include categorical syllogisms, used to examine how people reason about quantifiers such as All or Some, e.g., Some of the A are not B. For example if all A are B and some B are C, what (if anything) follows? == Theories of reasoning == There are several alternative theories of the cognitive processes that human reasoning is based on. One view is that people rely on a mental logic consisting of formal (abstract or syntactic) inference rules similar to those developed by logicians in the propositional calculus. Another view is that people rely on domain-specific or content-sensitive rules of inference. A third view is that people rely on mental models, that is, mental representations that correspond to imagined possibilities. A fourth view is that people compute probabilities. One controversial theoretical issue is the identification of an appropriate competence model, or a standard against which to compare human reasoning. Initially classical logic was chosen as a competence model. Subsequently, some researchers opted for non-monotonic logic and Bayesian probability. Research on mental models and reasoning has led to the suggestion that people are rational in principle but err in practice. Connectionist approaches towards reasoning have also been proposed. Despite the ongoing debate about the cognitive processes involved in human reasoning, recent research has shown that multiple approaches can be useful in modeling human thinking. For instance, studies have found that people's reasoning is often influenced by their prior beliefs, which can be modeled using Bayesian probability theory. Additionally, research on mental models has shown that people tend to reason about problems by constructing multiple mental representations of the situation, which can help them to identify relevant features and make inferences based on their understanding of the problem. Moreover, connectionist approaches to reasoning have also gained attention, which focus on the neural network models that can learn from data and generalize to new situations. == Development of reasoning == It is an active question in psychology how, why, and when the ability to reason develops from infancy to adulthood. Jean Piaget's theory of cognitive development posited general mechanisms and stages in the development of reasoning from infancy to adulthood. According to the neo-Piagetian theories of cognitive development, changes in reasoning with development come from increasing working memory capacity, increasing speed of processing, and enhanced executive functions and control. Increasing self-awareness is also an important factor. In their book The Enigma of Reason, the cognitive scientists Hugo Mercier and Dan Sperber put forward an "argumentative" theory of reasoning, claiming that humans evolved to reason primarily to justify our beliefs and actions and to convince others in a social environment. Key evidence for their theory includes the errors in reasoning that solitary individuals are prone to when their arguments are not criticized, such as logical fallacies, and how groups become much better at performing cognitive reasoning tasks when they communicate with one another and can evaluate each other's arguments. Sperber and Mercier offer one attempt to resolve the apparent paradox that the confirmation bias is so strong despite the function of reasoning naively appearing to be to come to veridical conclusions about the world. The study of the development of reasoning abilities is an ongoing area of research in psychology, and multiple factors have been proposed to explain how, why, and when reasoning develops from infancy to adulthood. Recent research has suggested that early experiences and social interactions play a critical role in the development of reasoning abilities. For example, studies have shown that infants as young as six months old can engage in basic logical reasoning, such as reasoning about the relationship between objects and their properties. Furthermore, research has highlighted the importance of parental interaction and cognitive stimulation in the development of children's reasoning abilities. Additionally, studies have suggested that cultural factors, such as educational practices and the emphasis on critical thinking, can also influence the development of reasoning skills across different populations. == Different sorts of reasoning == Philip Johnson-Laird trying to taxonomize thought, distinguished between goal-directed thinking and thinking without goal, noting that association was involved in unrelated reading. He argues that goal directed reasoning can be classified based on the problem space involved in a solution, citing Allen Newell and Herbert A. Simon. Inductive reasoning makes broad generalizations from specific cases or observations. In this process of reasoning, general assertions are made based on past specific pieces of evidence. This kind of reasoning allows the conclusion to be false even if the original statement is true. For example, if one observes a college athlete, one makes predictions and assumptions about other college athletes based on that one observation. Scientists use inductive reasoning to create theories and hypotheses. Philip Johnson-Laird distinguished inductive from deductive reasoning, in that the former creates semantic information while the later does not . In opposition, deductive reasoning is a basic form of valid reasoning. In this reasoning process a person starts with a known claim or a general belief and from there asks what follows from these foundations or how will these premises influence other beliefs. In other words, deduction starts with a hypothesis and examines the possibilities to reach a conclusion. Deduction helps people understand why their predictions are wrong and indicates that their prior knowledge or beliefs are off track. An example of deduction can be seen in the scientific method when testing hypotheses and theories. Although the conclusion usually corresponds and therefore proves the hypothesis, there are some cases where the conclusion is logical, but the generalization is not. For example, the argument, "All young girls wear skirts; Julie is a young
Protecting Our Kids from Social Media Addiction Act
Protecting Our Kids from Social Media Addiction Act also known as California SB 976 is a law that was enacted in September 2024 that is meant to address problematic social media usage among minors. The law prohibitions minors to have "addictive feeds" unless they have verifiable parental consent, minor's notifications are also restricted between 12 am to 6 am and during school hours between 8 am and 3 pm it also well requires minors to have default privacies settings and have social media companies to publicly disclose certain metrics about their users. The law was set to take effect in two steps the first being the restrictions on social media feeds, notifications, disclosures from social media companies and default settings which would have taken effect on January 1, 2025, and the age verification provision which would have taken effect on January 1, 2027. However, has faced legal challenges since its enactment delaying its enactment. == Legal Challenges == In November 2024 NetChoice a trade association representing many of the biggest social media companies such as YouTube, Facebook and Instagram sued the attorney general of California Rob Bonta hoping to get an injunction before the first set of the law's provisions would take effect in January of the next year. However, judge Edward Davila would only grant Netchoice's request as to the restrictions on notifications and public disclosures and would deny their request as to the rest of the law. The law was later fully enjoined temporarily by the District Court and Appellant Court pending appeal, and the case is now in the Ninth Circuit Court of Appeals and is pending a decision. === Social media platforms challenges to law === In November 2025 Meta, Google and TikTok filed lawsuits against the law arguing it violates the first amendment.
Social media coverage of the Olympics
Over the years, television broadcast rights have distinguished what Olympic-related content can be accessed by fans online. By doing so, mobile-friendly social platforms began to integrate into the Olympics. Athletes and fans use these platforms to share live updates, special moments, and behind-the-scenes specials. Various social media platforms have been used for Olympic content, including Twitter and Facebook. Some marketers credit social media for prompting the official U.S. broadcasters, NBC, to live stream events, including early rounds. == Background == The Olympics is able to advertise to its viewers and its host country with the use of data it collects through Social media marketing. Prominent social media platforms include: Twitter, Facebook, Instagram, Tumblr, YouTube, Google, MSN, Yahoo and many more. Campaign Initiatives and Artificial Intelligence technologies have been used to analyze the social media content of users. Information from consumers such as their preferences, demographics, age and locality are all analyzed to gain consumer insight. Campaign initiatives and AI technologies were used for such purposes in the 2010 Vancouver Winter Olympics and are in use currently. Social media marketing of the Olympics is a new phenomena, beginning prior to the 2008 Beijing Olympics == Variations == There are two classifications of social media marketing recognized by the IOC: Officially sanctioned content from rights holders and sponsors that maximizes the use of Olympic content (imagery, hashtag) Unofficial content that is generated by brands that leverage the excitement of the Olympics == 2008 Beijing Summer Olympics == Social media marketing emerged as a phenomenon during the 2008 Beijing Olympics, which progressed as a marketing and an advertising tactic ever since. The Beijing Olympics became the test subject for social media marketing initiatives started by advertising agencies. In 2008, social media marketing began the transition from one-sided communication to mass communication of the Olympic Games. Although social media marketing of the Olympic Games began in 2008, the audience to the Olympics was still primarily reached through television–reaching an audience of 4.3 billion viewers. At the time, the viewers of the Olympic Games through Internet website platforms made up an audience of approximately 390 million individuals. What was the beginning of Olympic social media marketing, was also the beginning of a more globalized experience of the Olympic Games via social media. Twitter, now a prominent social media platform, began in 2006 and grew to three million active users by the beginning of the 2008 Beijing Olympics. Members of Facebook, another prominent social media platform, tracking the Olympic Games grew from approximately one million during the Olympic Games of Athens 2004 to 90 million during the 2008 Beijing Olympics. Social media use, in general, increased by 24 percent between 2007 and 2008–from 63 percent of U.S. adults to 87 percent of U.S. adults. == 2010 Vancouver Winter Olympics == The International Olympic Committee (IOC) deemed The Vancouver Winter Olympics as "the first social media games” based on its fan base through social media platforms. The IOC launched their Facebook page a month before the games began, attracting 1.5 million fans. Shifting to online viewing attracted a younger audience than past Olympic games with over 60 percent of Facebook fans being under 24 years of age. Athletes like Lindsey Vonn and Shaun White reached fans on social media as the platform posted behind-the-scenes coverage on their experiences. The IOC used social media to create competitions between athletes and fans streamed online. Its YouTube channel hosted a “Best of Us” challenge in which the public could compete in games with their favorite athletes, acquiring three million viewers. Photos spread across social media platforms, such as Flickr, which had 11,000 photos posted by 600 photographers, bringing a new perspective to the games. Twitter contributed constant live updates of the competitions. The IOC's Twitter following doubled to 12,000 followers during the Vancouver Olympics, creating a larger viewer population for the games. The IOC created social media guidelines as more athletes and fans got online to interact with the Olympics. Social media was still relatively new as a marketing platform, so these guidelines confused many individuals. == 2012 London Summer Olympics == The London 2012 Olympic Games succeeded in broadcasting, participation and marketing. For the first time, the IOC broadcast the Olympic Games live and on-demand through YouTube, allowing fans to access the Games anytime, anywhere through live streaming. The combination of conventional broadcasting and mobile platforms reached a global audience of 4.8 billion people. Social media soared with Facebook, Twitter and Google+, attracting 4.7 million followers. Athletes shared photographs, interacted online with fans and updated daily, either in person or via an agent. Instagram was established by 2012, making itself a premier photo-sharing platform perfect for athletes to capture their emotions. Lewis Wiltshire, head of sport for Twitter UK said, "Never before have fans had such direct access to their sporting heroes." Social media created conversation on fan opinions regarding athletes, including 962,756 total mentions of Usain Bolt, “Fastest Man in History,” who defended the 100 meter and 200 meter gold medals. Michael Phelps followed with 828,081 total mentions. Olympic sponsors were active on social media; created several campaigns to promote their brands; and inspired viewers with mass participation and personalized events. The Adidas “Take the Stage” Campaign recognized talent around the world, installing a photo booth and inviting the 550 Olympics athletes to take the stage. (IOC Marketing Report 2012). David Beckham surprised fans at the photo booth in Westfield shopping centre, gaining popularity in UK media. Coca-Cola, Acer Inc., McDonald's, Visa Inc. and several others used similar tactics of participation to attract viewers. == 2014 Sochi Winter Olympics == === Channels === The 2014 Winter Olympic Games were held in Sochi, a city in Krasnodar Krai, Russia, establishing the first “social media Olympics” for Russia. The most popular Russian social media and networking service, VK, created an Olympic page, similar to Facebook's. The Olympic VK page has 2.8 million fans and—the most popular official community on the platform. Throughout the games, VK had 54 million Olympic mentions, an average of 1.5 million per day. Numbers grew on other social media pages: more than 2 million fans joined the Olympic Facebook page, 168,101 followed the Olympic Twitter, 150,000 followed the Olympic Instagram and three million visited the Olympic website in February 2014. There were 90,000 total updates on social media by Sochi 2014 Olympians and teams. The United States was the most active country during the games logging 22,598 posts across Facebook, Twitter, and Instagram. === Engagement === With social media there is also hashtags. The most popular hashtag was #sochi2014 with almost 11,000 uses. The next top five hashtags were #wearewinter, #teamusa, #olympics, #goaus and #wirfuerD. Another popular hashtag was #Sochiproblems, depicting local struggles. Photos of the poor state of Sochi on all platforms made the games the number one trending topic one week before the opening ceremony. #SochiFail and #SochiProblems gave multiple reports of the poor living arrangements, incomplete construction, broken elevators, and polluted waters. This was one way that social media provided awareness to its users. === Media Perceptions === Media perceptions varied during the games; the Olympics was viewed as a confrontation between Eastern and Western Civilizations. The LGBT community took a stand against the games. Sponsors for the games including Coca-Cola, Mcdonald's, and P&G protested against Russian authorities and Russian anti-LGBT laws. Many protests took a stand against Russian laws, which created a discussion between human rights advocates. Advocates believed organizations should not promote certain values in western markets while supporting an anti-human rights government in another market. == 2016 Rio Summer Olympics == Social media marketing was an influential tool in the promotion and analysis of the 2016 Rio Olympics. Thomas Bach, President of the International Olympic Committee said that the power of sport demonstrates that diversity and interconnectedness can enlighten us all. With over 25,000+ sources of accredited media covering the games, the 2016 games were the most consumed Olympic games to date. Marketing for the Rio Olympics began in 2013 and ultimately lasted 3 years. There were 26 million visits to Olympic.org, the official website of the Olympic games, and over 7 billion views of official Olympic content on social media. There were o
Frame (networking)
A frame is a digital data transmission unit in computer networking and telecommunications. In packet switched systems, a frame is a simple container for a single network packet. In other telecommunications systems, a frame is a repeating structure supporting time-division multiplexing. A frame typically includes frame synchronization features consisting of a sequence of bits or symbols that indicate to the receiver the beginning and end of the payload data within the stream of symbols or bits it receives. If a receiver is connected to the system during frame transmission, it ignores the data until it detects a new frame synchronization sequence. == Packet switching == In the OSI model of computer networking, a frame is the protocol data unit at the data link layer. Frames are the result of the final layer of encapsulation before the data is transmitted over the physical layer. A frame is "the unit of transmission in a link layer protocol, and consists of a link layer header followed by a packet." Each frame is separated from the next by an interframe gap. A frame is a series of bits generally composed of frame synchronization bits, the packet payload, and a frame check sequence. Examples are Ethernet frames, Wi-Fi frames, 4G frames, Point-to-Point Protocol (PPP) frames, Fibre Channel frames, and V.42 modem frames. Often, frames of several different sizes are nested inside each other. For example, when using Point-to-Point Protocol (PPP) over asynchronous serial communication, the eight bits of each individual byte are framed by start and stop bits, the payload data bytes in a network packet are framed by the header and footer, and several packets can be framed with frame boundary octets. == Time-division multiplex == In telecommunications, specifically in time-division multiplex (TDM) and time-division multiple access (TDMA) variants, a frame is a cyclically repeated data block that consists of a fixed number of time slots, one for each logical TDM channel or TDMA transmitter. In this context, a frame is typically an entity at the physical layer. TDM application examples are SONET/SDH and the ISDN circuit-switched B-channel, while TDMA examples are Circuit Switched Data used in early cellular voice services. The frame is also an entity for time-division duplex, where the mobile terminal may transmit during some time slots and receive during others.
Moj
Moj is an Indian short-form video-sharing social networking service owned by Mohalla Tech Pvt Ltd, the parent company of ShareChat. Launched on 29 June 2020, shortly after the Government of India banned TikTok and several other Chinese apps, Moj quickly gained popularity as one of the leading domestic alternatives for short-form video content in India. == History == Moj was introduced by Mohalla Tech, the Bengaluru-based parent company of ShareChat, within days of the TikTok ban in India in June 2020. The app targeted the growing demand for short-form video platforms in the country. By early 2021, Moj had amassed over 100 million downloads on the Google Play Store. In February 2021, Mohalla Tech raised significant funding from investors like Tiger Global, Snapchat, and others, which supported both Moj and ShareChat’s growth. In 2022, Moj partnered with several music labels to expand its licensed music library, competing directly with global platforms such as Instagram Reels and YouTube Shorts. == Features == Short Videos: Users can create and watch videos up to 15–60 seconds. Filters & Effects: The platform provides AR filters, editing tools, stickers, and music integration. Regional Language Support: Moj supports more than 15 Indian languages including Hindi, Bengali, Tamil, Telugu, Kannada, and Marathi. Music Integration: Users can add music tracks to their videos from licensed Indian and international music libraries. Creator Program: Moj launched initiatives to support influencers and creators, offering training, monetization, and promotional opportunities. == Popularity == By mid-2021, Moj reported over 160 million monthly active users. According to reports, Moj consistently ranked among the top social media apps in India in terms of downloads. The app gained traction in Tier-2 and Tier-3 cities due to its multilingual support and focus on local content. == Competitors == Moj competes with several other short video platforms in India, including: Instagram Reels (Meta) YouTube Shorts (Google) Josh (Dailyhunt/VerSe Innovation) Roposo (InMobi) MX TakaTak (later merged with Moj in 2022) RedPost (an emerging Indian social networking platform) == Merger with MX TakaTak == In February 2022, Mohalla Tech announced that Moj would merge with MX TakaTak, another leading short video app owned by Times Internet. The merger created one of the largest short-video ecosystems in India, with a combined user base of over 300 million monthly active users.
Dynamic knowledge repository
The dynamic knowledge repository (DKR) is a concept developed by Douglas C. Engelbart as a primary strategic focus for allowing humans to address complex problems. He has proposed that a DKR will enable us to develop a collective IQ greater than any individual's IQ. References and discussion of Engelbart's DKR concept are available at the Doug Engelbart Institute. == Definition == A knowledge repository is a computerized system that systematically captures, organizes and categorizes an organization's knowledge. The repository can be searched and data can be quickly retrieved. The effective knowledge repositories include factual, conceptual, procedural and meta-cognitive techniques. The key features of knowledge repositories include communication forums. A knowledge repository can take many forms to "contain" the knowledge it holds. A customer database is a knowledge repository of customer information and insights – or electronic explicit knowledge. A Library is a knowledge repository of books – physical explicit knowledge. A community of experts is a knowledge repository of tacit knowledge or experience. The nature of the repository only changes to contain/manage the type of knowledge it holds. A repository (as opposed to an archive) is designed to get knowledge out. It should therefore have some rules of structure, classification, taxonomy, record management, etc., to facilitate user engagement.