Data quality refers to the state of qualitative or quantitative pieces of information. There are many definitions of data quality, but data is generally considered high quality if it is "fit for [its] intended uses in operations, decision making and planning". Data is deemed of high quality if it correctly represents the real-world construct to which it refers. Apart from these definitions, as the number of data sources increases, the question of internal data consistency becomes significant, regardless of fitness for use for any particular external purpose. People's views on data quality can often be in disagreement, even when discussing the same set of data used for the same purpose. When this is the case, businesses may adopt recognised international standards for data quality (See #International Standards for Data Quality below). Data governance can also be used to form agreed upon definitions and standards, including international standards, for data quality. In such cases, data cleansing, including standardization, may be required in order to ensure data quality. == Definitions == Defining data quality is difficult due to the many contexts data are used in, as well as the varying perspectives among end users, producers, and custodians of data. From a consumer perspective, data quality is: "data that are fit for use by data consumers" data "meeting or exceeding consumer expectations" data that "satisfies the requirements of its intended use" From a business perspective, data quality is: data that are "'fit for use' in their intended operational, decision-making and other roles" or that exhibits "'conformance to standards' that have been set, so that fitness for use is achieved" data that "are fit for their intended uses in operations, decision making and planning" "the capability of data to satisfy the stated business, system, and technical requirements of an enterprise" From a standards-based perspective, data quality is: the "degree to which a set of inherent characteristics (quality dimensions) of an object (data) fulfills requirements" "the usefulness, accuracy, and correctness of data for its application" Arguably, in all these cases, "data quality" is a comparison of the actual state of a particular set of data to a desired state, with the desired state being typically referred to as "fit for use," "to specification," "meeting consumer expectations," "free of defect," or "meeting requirements." These expectations, specifications, and requirements are usually defined by one or more individuals or groups, standards organizations, laws and regulations, business policies, or software development policies. == Dimensions of data quality == Drilling down further, those expectations, specifications, and requirements are stated in terms of characteristics or dimensions of the data, such as: accessibility or availability accuracy or correctness comparability completeness or comprehensiveness consistency, coherence, or clarity credibility, reliability, or reputation flexibility plausibility relevance, pertinence, or usefulness timeliness or latency uniqueness validity or reasonableness A systematic scoping review of the literature suggests that data quality dimensions and methods with real world data are not consistent in the literature, and as a result quality assessments are challenging due to the complex and heterogeneous nature of these data. == International standards for data quality == ISO 8000 is an international standard for data quality. Managed by the International Organization for Standardization, the ISO 8000 standards address and describe general aspects of data quality including principles, vocabulary and measurement data governance data quality management data quality assessment quality of master data, including exchange of characteristic data and identifiers quality of industrial data == History == Before the rise of the inexpensive computer data storage, massive mainframe computers were used to maintain name and address data for delivery services. This was so that mail could be properly routed to its destination. The mainframes used business rules to correct common misspellings and typographical errors in name and address data, as well as to track customers who had moved, died, gone to prison, married, divorced, or experienced other life-changing events. Government agencies began to make postal data available to a few service companies to cross-reference customer data with the National Change of Address registry (NCOA). This technology saved large companies millions of dollars in comparison to manual correction of customer data. Large companies saved on postage, as bills and direct marketing materials made their way to the intended customer more accurately. Initially sold as a service, data quality moved inside the walls of corporations, as low-cost and powerful server technology became available. Companies with an emphasis on marketing often focused their quality efforts on name and address information, but data quality is recognized as an important property of all types of data. Principles of data quality can be applied to supply chain data, transactional data, and nearly every other category of data found. For example, making supply chain data conform to a certain standard has value to an organization by: 1) avoiding overstocking of similar but slightly different stock; 2) avoiding false stock-out; 3) improving the understanding of vendor purchases to negotiate volume discounts; and 4) avoiding logistics costs in stocking and shipping parts across a large organization. For companies with significant research efforts, data quality can include developing protocols for research methods, reducing measurement error, bounds checking of data, cross tabulation, modeling and outlier detection, verifying data integrity, etc. == Overview == There are a number of theoretical frameworks for understanding data quality. A systems-theoretical approach influenced by American pragmatism expands the definition of data quality to include information quality, and emphasizes the inclusiveness of the fundamental dimensions of accuracy and precision on the basis of the theory of science (Ivanov, 1972). One framework, dubbed "Zero Defect Data" (Hansen, 1991) adapts the principles of statistical process control to data quality. Another framework seeks to integrate the product perspective (conformance to specifications) and the service perspective (meeting consumers' expectations) (Kahn et al. 2002). Another framework is based in semiotics to evaluate the quality of the form, meaning and use of the data (Price and Shanks, 2004). One highly theoretical approach analyzes the ontological nature of information systems to define data quality rigorously (Wand and Wang, 1996). A considerable amount of data quality research involves investigating and describing various categories of desirable attributes (or dimensions) of data. Nearly 200 such terms have been identified and there is little agreement in their nature (are these concepts, goals or criteria?), their definitions or measures (Wang et al., 1993). Software engineers may recognize this as a similar problem to "ilities". MIT has an Information Quality (MITIQ) Program, led by Professor Richard Wang, which produces a large number of publications and hosts a significant international conference in this field (International Conference on Information Quality, ICIQ). This program grew out of the work done by Hansen on the "Zero Defect Data" framework (Hansen, 1991). In practice, data quality is a concern for professionals involved with a wide range of information systems, ranging from data warehousing and business intelligence to customer relationship management and supply chain management. One industry study estimated the total cost to the U.S. economy of data quality problems at over U.S. $600 billion per annum (Eckerson, 2002). Incorrect data – which includes invalid and outdated information – can originate from different data sources – through data entry, or data migration and conversion projects. In 2002, the USPS and PricewaterhouseCoopers released a report stating that 23.6 percent of all U.S. mail sent is incorrectly addressed. One reason contact data becomes stale very quickly in the average database – more than 45 million Americans change their address every year. In fact, the problem is such a concern that companies are beginning to set up a data governance team whose sole role in the corporation is to be responsible for data quality. In some organizations, this data governance function has been established as part of a larger Regulatory Compliance function - a recognition of the importance of Data/Information Quality to organizations. Problems with data quality don't only arise from incorrect data; inconsistent data is a problem as well. Eliminating data shadow systems and centralizing data in a warehouse is one of the initiatives a company can take to ensure data consistency. En
Multi-agent reinforcement learning
Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment. Each agent is motivated by its own rewards, and does actions to advance its own interests; in some environments these interests are opposed to the interests of other agents, resulting in complex group dynamics. Multi-agent reinforcement learning is closely related to game theory and especially repeated games, as well as multi-agent systems. Its study combines the pursuit of finding ideal algorithms that maximize rewards with a more sociological set of concepts. While research in single-agent reinforcement learning is concerned with finding the algorithm that gets the biggest number of points for one agent, research in multi-agent reinforcement learning evaluates and quantifies social metrics, such as cooperation, reciprocity, equity, social influence, language and discrimination. == Definition == Similarly to single-agent reinforcement learning, multi-agent reinforcement learning is modeled as some form of a Markov decision process (MDP). Fix a set of agents I = { 1 , . . . , N } {\displaystyle I=\{1,...,N\}} . We then define: A set S {\displaystyle S} of environment states. One set A i {\displaystyle {\mathcal {A}}_{i}} of actions for each of the agents i ∈ I = { 1 , … , N } {\displaystyle i\in I=\{1,\dots ,N\}} . P a → ( s , s ′ ) = Pr ( s t + 1 = s ′ ∣ s t = s , a → t = a → ) {\displaystyle P_{\vec {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\vec {a}}_{t}={\vec {a}})} is the probability of transition (at time t {\displaystyle t} ) from state s {\displaystyle s} to state s ′ {\displaystyle s'} under joint action a → {\displaystyle {\vec {a}}} . R → a → ( s , s ′ ) {\displaystyle {\vec {R}}_{\vec {a}}(s,s')} is the immediate joint reward after the transition from s {\displaystyle s} to s ′ {\displaystyle s'} with joint action a → {\displaystyle {\vec {a}}} . In settings with perfect information, such as the games of chess and Go, the MDP would be fully observable. In settings with imperfect information, especially in real-world applications like self-driving cars, each agent would access an observation that only has part of the information about the current state. In the partially observable setting, the core model is the partially observable stochastic game in the general case, and the decentralized POMDP in the cooperative case. == Cooperation vs. competition == When multiple agents are acting in a shared environment their interests might be aligned or misaligned. MARL allows exploring all the different alignments and how they affect the agents' behavior: In pure competition settings, the agents' rewards are exactly opposite to each other, and therefore they are playing against each other. Pure cooperation settings are the other extreme, in which agents get the exact same rewards, and therefore they are playing with each other. Mixed-sum settings cover all the games that combine elements of both cooperation and competition. === Pure competition settings === When two agents are playing a zero-sum game, they are in pure competition with each other. Many traditional games such as chess and Go fall under this category, as do two-player variants of video games like StarCraft. Because each agent can only win at the expense of the other agent, many complexities are stripped away. There is no prospect of communication or social dilemmas, as neither agent is incentivized to take actions that benefit its opponent. The Deep Blue and AlphaGo projects demonstrate how to optimize the performance of agents in pure competition settings. One complexity that is not stripped away in pure competition settings is autocurricula. As the agents' policy is improved using self-play, multiple layers of learning may occur. === Pure cooperation settings === MARL is used to explore how separate agents with identical interests can communicate and work together. Pure cooperation settings are explored in recreational cooperative games such as Overcooked, as well as real-world scenarios in robotics. In pure cooperation settings all the agents get identical rewards, which means that social dilemmas do not occur. In pure cooperation settings, oftentimes there are an arbitrary number of coordination strategies, and agents converge to specific "conventions" when coordinating with each other. The notion of conventions has been studied in language and also alluded to in more general multi-agent collaborative tasks. === Mixed-sum settings === Most real-world scenarios involving multiple agents have elements of both cooperation and competition. For example, when multiple self-driving cars are planning their respective paths, each of them has interests that are diverging but not exclusive: Each car is minimizing the amount of time it's taking to reach its destination, but all cars have the shared interest of avoiding a traffic collision. Zero-sum settings with three or more agents often exhibit similar properties to mixed-sum settings, since each pair of agents might have a non-zero utility sum between them. Mixed-sum settings can be explored using classic matrix games such as prisoner's dilemma, more complex sequential social dilemmas, and recreational games such as Among Us, Diplomacy and StarCraft II. Mixed-sum settings can give rise to communication and social dilemmas. == Social dilemmas == As in game theory, much of the research in MARL revolves around social dilemmas, such as prisoner's dilemma, chicken and stag hunt. While game theory research might focus on Nash equilibria and what an ideal policy for an agent would be, MARL research focuses on how the agents would learn these ideal policies using a trial-and-error process. The reinforcement learning algorithms that are used to train the agents are maximizing the agent's own reward; the conflict between the needs of the agents and the needs of the group is a subject of active research. Various techniques have been explored in order to induce cooperation in agents: Modifying the environment rules, adding intrinsic rewards, and more. === Sequential social dilemmas === Social dilemmas like prisoner's dilemma, chicken and stag hunt are "matrix games". Each agent takes only one action from a choice of two possible actions, and a simple 2x2 matrix is used to describe the reward that each agent will get, given the actions that each agent took. In humans and other living creatures, social dilemmas tend to be more complex. Agents take multiple actions over time, and the distinction between cooperating and defecting is not as clear cut as in matrix games. The concept of a sequential social dilemma (SSD) was introduced in 2017 as an attempt to model that complexity. There is ongoing research into defining different kinds of SSDs and showing cooperative behavior in the agents that act in them. == Autocurricula == An autocurriculum (plural: autocurricula) is a reinforcement learning concept that's salient in multi-agent experiments. As agents improve their performance, they change their environment; this change in the environment affects themselves and the other agents. The feedback loop results in several distinct phases of learning, each depending on the previous one. The stacked layers of learning are called an autocurriculum. Autocurricula are especially apparent in adversarial settings, where each group of agents is racing to counter the current strategy of the opposing group. The Hide and Seek game is an accessible example of an autocurriculum occurring in an adversarial setting. In this experiment, a team of seekers is competing against a team of hiders. Whenever one of the teams learns a new strategy, the opposing team adapts its strategy to give the best possible counter. When the hiders learn to use boxes to build a shelter, the seekers respond by learning to use a ramp to break into that shelter. The hiders respond by locking the ramps, making them unavailable for the seekers to use. The seekers then respond by "box surfing", exploiting a glitch in the game to penetrate the shelter. Each "level" of learning is an emergent phenomenon, with the previous level as its premise. This results in a stack of behaviors, each dependent on its predecessor. Autocurricula in reinforcement learning experiments are compared to the stages of the evolution of life on Earth and the development of human culture. A major stage in evolution happened 2-3 billion years ago, when photosynthesizing life forms started to produce massive amounts of oxygen, changing the balance of gases in the atmosphere. In the next stages of evolution, oxygen-breathing life forms evolved, eventually leading up to land mammals and human beings. These later stages could only happen after the photosynthesis stage made oxygen widely available. Similarly, human culture could not have gone through the Industrial Revolution in the 18th century without the resources and insights gaine
Webometrics
The science of webometrics (also referred to as cybermetrics) aims to quantify the World Wide Web to get knowledge about the number and types of hyperlinks, the structure of the World Wide Web, and using patterns. According to Björneborn and Ingwersen, the definition of webometrics is "the study of the quantitative aspects of the construction and use of information resources, structures and technologies on the Web drawing on bibliometric and informetric approaches." The term webometrics was coined by Almind and Ingwersen (1997). A second definition of webometrics has also been introduced, "the study of web-based content with primarily quantitative methods for social science research goals using techniques that are not specific to one field of study", which emphasizes the development of applied methods for use in the wider social sciences. The purpose of this alternative definition was to help publicize appropriate methods outside the information-science discipline rather than to replace the original definition within information science. Similar scientific fields are: bibliometrics, informetrics, scientometrics, virtual ethnography, and web mining. One relatively straightforward measure is the "web impact factor" (WIF) introduced by Ingwersen (1998). The WIF measure may be defined as the number of web pages in a web site receiving links from other web sites, divided by the number of web pages published in the site that are accessible to the crawler. However, the use of WIF has been disregarded due to the mathematical artifacts derived from power law distributions of these variables. Other similar indicators using size of the institution instead of number of webpages have been proved more useful.
Whitehead's algorithm
Whitehead's algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is based on a classic 1936 paper of J. H. C. Whitehead. It is still unknown (except for the case n = 2) if Whitehead's algorithm has polynomial time complexity. == Statement of the problem == Let F n = F ( x 1 , … , x n ) {\displaystyle F_{n}=F(x_{1},\dots ,x_{n})} be a free group of rank n ≥ 2 {\displaystyle n\geq 2} with a free basis X = { x 1 , … , x n } {\displaystyle X=\{x_{1},\dots ,x_{n}\}} . The automorphism problem, or the automorphic equivalence problem for F n {\displaystyle F_{n}} asks, given two freely reduced words w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether there exists an automorphism φ ∈ Aut ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Thus the automorphism problem asks, for w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether Aut ( F n ) w = Aut ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} . For w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} one has Aut ( F n ) w = Aut ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} if and only if Out ( F n ) [ w ] = Out ( F n ) [ w ′ ] {\displaystyle \operatorname {Out} (F_{n})[w]=\operatorname {Out} (F_{n})[w']} , where [ w ] , [ w ′ ] {\displaystyle [w],[w']} are conjugacy classes in F n {\displaystyle F_{n}} of w , w ′ {\displaystyle w,w'} accordingly. Therefore, the automorphism problem for F n {\displaystyle F_{n}} is often formulated in terms of Out ( F n ) {\displaystyle \operatorname {Out} (F_{n})} -equivalence of conjugacy classes of elements of F n {\displaystyle F_{n}} . For an element w ∈ F n {\displaystyle w\in F_{n}} , | w | X {\displaystyle |w|_{X}} denotes the freely reduced length of w {\displaystyle w} with respect to X {\displaystyle X} , and ‖ w ‖ X {\displaystyle \|w\|_{X}} denotes the cyclically reduced length of w {\displaystyle w} with respect to X {\displaystyle X} . For the automorphism problem, the length of an input w {\displaystyle w} is measured as | w | X {\displaystyle |w|_{X}} or as ‖ w ‖ X {\displaystyle \|w\|_{X}} , depending on whether one views w {\displaystyle w} as an element of F n {\displaystyle F_{n}} or as defining the corresponding conjugacy class [ w ] {\displaystyle [w]} in F n {\displaystyle F_{n}} . == History == The automorphism problem for F n {\displaystyle F_{n}} was algorithmically solved by J. H. C. Whitehead in a classic 1936 paper, and his solution came to be known as Whitehead's algorithm. Whitehead used a topological approach in his paper. Namely, consider the 3-manifold M n = # i = 1 n S 2 × S 1 {\displaystyle M_{n}=\#_{i=1}^{n}\mathbb {S} ^{2}\times \mathbb {S} ^{1}} , the connected sum of n {\displaystyle n} copies of S 2 × S 1 {\displaystyle \mathbb {S} ^{2}\times \mathbb {S} ^{1}} . Then π 1 ( M n ) ≅ F n {\displaystyle \pi _{1}(M_{n})\cong F_{n}} , and, moreover, up to a quotient by a finite normal subgroup isomorphic to Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} , the mapping class group of M n {\displaystyle M_{n}} is equal to Out ( F n ) {\displaystyle \operatorname {Out} (F_{n})} ; see. Different free bases of F n {\displaystyle F_{n}} can be represented by isotopy classes of "sphere systems" in M n {\displaystyle M_{n}} , and the cyclically reduced form of an element w ∈ F n {\displaystyle w\in F_{n}} , as well as the Whitehead graph of [ w ] {\displaystyle [w]} , can be "read-off" from how a loop in general position representing [ w ] {\displaystyle [w]} intersects the spheres in the system. Whitehead moves can be represented by certain kinds of topological "swapping" moves modifying the sphere system. Subsequently, Rapaport, and later, based on her work, Higgins and Lyndon, gave a purely combinatorial and algebraic re-interpretation of Whitehead's work and of Whitehead's algorithm. The exposition of Whitehead's algorithm in the book of Lyndon and Schupp is based on this combinatorial approach. Culler and Vogtmann, in their 1986 paper that introduced the Outer space, gave a hybrid approach to Whitehead's algorithm, presented in combinatorial terms but closely following Whitehead's original ideas. == Whitehead's algorithm == Our exposition regarding Whitehead's algorithm mostly follows Ch.I.4 in the book of Lyndon and Schupp, as well as. === Overview === The automorphism group Aut ( F n ) {\displaystyle \operatorname {Aut} (F_{n})} has a particularly useful finite generating set W {\displaystyle {\mathcal {W}}} of Whitehead automorphisms or Whitehead moves. Given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} the first part of Whitehead's algorithm consists of iteratively applying Whitehead moves to w , w ′ {\displaystyle w,w'} to take each of them to an "automorphically minimal" form, where the cyclically reduced length strictly decreases at each step. Once we find automorphically these minimal forms u , u ′ {\displaystyle u,u'} of w , w ′ {\displaystyle w,w'} , we check if ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} . If ‖ u ‖ X ≠ ‖ u ′ ‖ X {\displaystyle \|u\|_{X}\neq \|u'\|_{X}} then w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} . If ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} , we check if there exists a finite chain of Whitehead moves taking u {\displaystyle u} to u ′ {\displaystyle u'} so that the cyclically reduced length remains constant throughout this chain. The elements w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} if and only if such a chain exists. Whitehead's algorithm also solves the search automorphism problem for F n {\displaystyle F_{n}} . Namely, given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} , if Whitehead's algorithm concludes that Aut ( F n ) w = Aut ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} , the algorithm also outputs an automorphism φ ∈ Aut ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Such an element φ ∈ Aut ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} is produced as the composition of a chain of Whitehead moves arising from the above procedure and taking w {\displaystyle w} to w ′ {\displaystyle w'} . === Whitehead automorphisms === A Whitehead automorphism, or Whitehead move, of F n {\displaystyle F_{n}} is an automorphism τ ∈ Aut ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} of F n {\displaystyle F_{n}} of one of the following two types: There is a permutation σ ∈ S n {\displaystyle \sigma \in S_{n}} of { 1 , 2 , … , n } {\displaystyle \{1,2,\dots ,n\}} such that for i = 1 , … , n {\displaystyle i=1,\dots ,n} τ ( x i ) = x σ ( i ) ± 1 {\displaystyle \tau (x_{i})=x_{\sigma (i)}^{\pm 1}} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the first kind. There is an element a ∈ X ± 1 {\displaystyle a\in X^{\pm 1}} , called the multiplier, such that for every x ∈ X ± 1 {\displaystyle x\in X^{\pm 1}} τ ( x ) ∈ { x , x a , a − 1 x , a − 1 x a } . {\displaystyle \tau (x)\in \{x,xa,a^{-1}x,a^{-1}xa\}.} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the second kind. Since τ {\displaystyle \tau } is an automorphism of F n {\displaystyle F_{n}} , it follows that τ ( a ) = a {\displaystyle \tau (a)=a} in this case. Often, for a Whitehead automorphism τ ∈ Aut ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} , the corresponding outer automorphism in Out ( F n ) {\displaystyle \operatorname {Out} (F_{n})} is also called a Whitehead automorphism or a Whitehead move. ==== Examples ==== Let F 4 = F ( x 1 , x 2 , x 3 , x 4 ) {\displaystyle F_{4}=F(x_{1},x_{2},x_{3},x_{4})} . Let τ : F 4 → F 4 {\displaystyle \tau :F_{4}\to F_{4}} be a homomorphism such that τ ( x 1 ) = x 2 x 1 , τ ( x 2 ) = x 2 , τ ( x 3 ) = x 2 x 3 x 2 − 1 , τ ( x 4 ) = x 4 {\displaystyle \tau (x_{1})=x_{2}x_{1},\quad \tau (x_{2})=x_{2},\quad \tau (x_{3})=x_{2}x_{3}x_{2}^{-1},\quad \tau (x_{4})=x_{4}} Then τ {\displaystyle \tau } is actually an automorphism of F 4 {\displaystyle F_{4}} , and, moreover, τ {\displaystyle \tau } is a Whitehead automorphism of the second kind, with the multiplier a = x 2 − 1 {\displaystyle a=x_{2}^{-1}} . Let τ ′ : F 4 → F 4 {\displaystyle \tau ':F_{4}\to F_{4}} be a homomorphism such that τ ′ ( x 1 ) = x 1 , τ ′ ( x 2 ) = x 1 − 1 x 2 x 1 , τ ′ ( x 3 ) = x 1 − 1 x 3 x 1 , τ ′ ( x 4 ) = x 1 − 1 x 4 x 1 {\displaystyle \tau '(x_{1})=x_{1},\quad \tau '(x_{2})=x_{1}^{-1}x_{2}x_{1},\quad \tau '(x_{3})=x_{1}^{-1}x_{3}x_{1},\quad \tau '(x_{4})=x_{1}^{-1}x_{4}x_{1}} Then τ ′ {\displaystyle \tau '} is actually an inner automorphism of F 4 {\displaystyle F_{4}} given by conjugation by x 1 {\displaystyle x_{1}} , and, moreover, τ ′ {\displaystyle \
Anyword
Anyword is a technology company that offers an artificial intelligence platform, using natural language processing to generate and optimize marketing text for websites, social media, email, and ads. The company also offers a complete managed service to publishers and brands to help them increase their revenue through social ads. It is used by National Geographic, Red Bull, The New York Times, BBC, Ted Baker, etc. The company has an office in New York, and Tel Aviv. == History == It was founded in 2013 — its original name was Keywee Inc. In March 2015, Anyword received $9.1 million in the Series A funding round led by a notable group of investors. In July 2016, the company was selected as an official Facebook Marketing Partner. In August 2019, Anyword was named Best Content Marketing Platform in the Digiday Technology Award winners. In November 2021, it raised $21 million in its Series B funding round.
Flo (app)
Flo is a period-tracking app that provides menstrual cycle, ovulation and pregnancy tracking as well as perimenopause symptom tracking that was developed by Flo Health, Inc. It has over 380 million downloads worldwide and over 70 million monthly active users as of November 2024. In mid-2024, it reached unicorn status, and became Europe’s first femtech unicorn. The company has been accused of sharing users' sensitive health data with third parties without consent and misleading its users about data practices. == History == Flo Health, Inc. was co-founded in 2015 by Dmitry and Yuri Gurski, in Belarus. Their backgrounds helped build the first version of the software having experience in other fitness and health apps. Dmitry serves as the company's CEO. The company's development hubs are in London, Amsterdam and Vilnius. In 2016, the company raised $1 million in seed round funding from Flint Capital and Haxus Venture Fund. In 2017, Flo received an investment of $5 million from Flint Capital and model Natalia Vodianova with Vodianova helping develop an awareness campaign for the company. In 2018, Flo received an investment of $6 million from Mangrove Capital Partners, with participation from Flint Capital and Haxus, giving the company a valuation of $200 million. In mid-2019, Flo received an additional investment of $7.5 million led by Founders Fund. In 2020, the Federal Trade Commission alleged that Flo had misled users about its handling of health information to third parties including Google, Facebook, AppsFlyer, and Flurry since 2016. These allegations followed a 2019 report by The Wall Street Journal in reference to Facebook. The company reached a settlement in 2021 and was required to notify users of how their personal information was shared and obtain permission before any further information was shared. The agreement also required that Flo to undertake an independent privacy audit which it completed in March 2022. In early September 2021, Flo announced it closed $50M in a Series B financing, bringing the total capital raised to $65 million and company valuation to $800M led by VNV Global and Target Global. In March 2024, the Supreme Court of British Columbia certified a class action suit against Flo for sharing intimate data with Facebook and other third parties without user knowledge. In July 2024, Flo announced it raised more than $200M in Series C financing from General Atlantic bringing its valuation beyond $1 billion. As of November 2024, the app had over 380 million downloads world wide, and over 70 million monthly active users. In 2025, Flo adopted a data intelligence platform from Databricks to power its analytics and AI features, allowing users personalized cycle predictions. In 2025, a class action lawsuit in California was settled for $56 million with Flo paying $8 million and Google paying $48 million. == Features and privacy == Flo was initially created as a period and ovulation tracking application. It now provides reminders of upcoming menstrual cycles and a place to record various other health symptoms such as contraceptive methods, vaginal discharge (leukorrhea), water intake, pains, mood swings, and sexual activity. The application is available on iOS and Android. Flo is free to download and the free basic version gives you access to period and ovulation tracking and predictions, symptom tracking, cycle history, and anonymous mode. In Pregnancy mode, the app provides tracking features and educational material for pregnancy. In October 2023, Flo launched Flo for Partners, a feature that allows users to share their Flo data with their partner. In September 2022, as a response to Roe v. Wade being overturned, Flo sped up the release of a feature called "Anonymous Mode". Flo said this mode allows users to access the app without any personal identifiers such as name, email address, or technical identifiers being associated with their health data. Flo said it uses a technology called Oblivious HTTP to help protect user privacy in Anonymous Mode. == Recognition == Flo was named to Bloomberg’s Top 25 UK Startups to Watch for 2024. Flo's Anonymous Mode feature was recognized on both Fast Company's World Changing Ideas 2023 and TIME's Best Inventions List 2023. Flo is a CES 2019 Innovation Awards Honoree in the Software and Mobile Applications category.
Artificial intelligence in Indonesia
Artificial intelligence in Indonesia refers to development, use and governance of artificial intelligence in Indonesia. Indonesia has treated AI as a national policy area through the Strategi Nasional Kecerdasan Artifisial or National Artificial Intelligence Strategy for 2020–2045. Public discussion has focused on the role of AI in sectors such as health, agriculture, education, mobile technology and e-commerce. Recent developments include AI ethics guidance issued by the communications ministry. Proposals for a national AI roadmap and sovereign AI fund, investment in cloud and AI infrastructure, and local-language AI initiatives for Bahasa Indonesia and regional Indonesian languages. == National strategy == Indonesia's National Artificial Intelligence Strategy is known in Indonesian as Strategi Nasional Kecerdasan Artifisial or Stranas KA. The strategy was published as a long-term framework for the development and use of AI between 2020 and 2045. It is intended to guide ministries, government agencies, regional governments and other stakeholders. The strategy identifies five priority sectors: health services, bureaucratic reform, education and research, food security, and mobility and smart cities. OECD lists the Ministry of Research and Technology and the National Research and Innovation Agency as organisations associated with the strategy. The strategy was developed through consultation with public and private stakeholders. == Institutions == The Indonesian Artificial Intelligence Industry Research and Innovation Collaboration, known as KORIKA is the nodal agency for the national AI strategy. KORIKA describes its vision as creating a collaborative ecosystem to accelerate implementation of the national AI strategy towards Vision Indonesia 2045. The Ministry of Communication and Digital Affairs has also been involved in AI governance, digital policy and public communication. In 2025, Reuters reported that the ministry was preparing a national AI roadmap to give investors and developers a clearer view of Indonesia's market, infrastructure and computing capacity. == AI Governance == Indonesia has introduced policy guidance on the ethical use of artificial intelligence. The policy sets out ethical values for the development and use of AI. These include humanity, security, transparency, credibility and accountability, personal data protection, sustainable development and intellectual property protection. A UNESCO country profile on Indonesia noted that Indonesia had adopted a national AI strategy and had policy frameworks. It also identified gaps in internet access, gender inclusion, language datasets, digital talent and cybersecurity. UNESCO recommended that Indonesia update its AI standards, invest in ethical AI, strengthen research coordination and consider establishing a national agency for artificial intelligence. In May 2026, Antara News reported comments by Deputy Minister of Communication and Digital Affairs Nezar Patria. Who said that AI safety requires partnerships, shared standards and continuing dialogue. == Sectors == AI policy discussions in Indonesia have identified health, agriculture, education, government services, mobility and smart cities as areas where AI could be applied. Mobile technology and e-commerce have been discussed as important areas of AI adoption in Indonesia. Research on AI adoption in Indonesia by Siddhartha Paul Tiwari and Adi Fahrudin has also examined mobile and e-commerce sectors. UNESCO has also noted that Indonesia's large digital economy and startup ecosystem have supported AI adoption, while also pointing to challenges in talent, research capacity and cybersecurity. Indonesia is one of the developing-country markets attracting AI infrastructure investment, including data centres. == Challenges == Indonesia faces several challenges in developing and governing AI. These include gaps in computing infrastructure, uneven connectivity outside major cities, shortages of skilled workers, limited research funding, cybersecurity risks, misinformation, data leaks and the underrepresentation of Indonesian and indigenous languages in AI datasets. UNESCO noted that Bahasa is spoken by around 200 million people but remains underrepresented in AI. It also noted that Indonesia has more than 700 indigenous languages, many of which face the risk of extinction. UNESCO recommended stronger coordination in AI research and a more unified strategy for using AI in language preservation.