A Markov partition in mathematics is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic dynamics. By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical characteristics of the system represented as a Markov shift. The appellation 'Markov' is appropriate because the resulting dynamics of the system obeys the Markov property. The Markov partition thus allows standard techniques from symbolic dynamics to be applied, including the computation of expectation values, correlations, topological entropy, topological zeta functions, Fredholm determinants and the like. == Motivation == Let ( M , φ ) {\displaystyle (M,\varphi )} be a discrete dynamical system. A basic method of studying its dynamics is to find a symbolic representation: a faithful encoding of the points of M {\displaystyle M} by sequences of symbols such that the map φ {\displaystyle \varphi } becomes the shift map. Suppose that M {\displaystyle M} has been divided into a number of pieces E 1 , E 2 , … , E r {\displaystyle E_{1},E_{2},\ldots ,E_{r}} which are thought to be as small and localized, with virtually no overlaps. The behavior of a point x {\displaystyle x} under the iterates of φ {\displaystyle \varphi } can be tracked by recording, for each n {\displaystyle n} , the part E i {\displaystyle E_{i}} which contains φ n ( x ) {\displaystyle \varphi ^{n}(x)} . This results in an infinite sequence on the alphabet { 1 , 2 , … , r } {\displaystyle \{1,2,\ldots ,r\}} which encodes the point. In general, this encoding may be imprecise (the same sequence may represent many different points) and the set of sequences which arise in this way may be difficult to describe. Under certain conditions, which are made explicit in the rigorous definition of a Markov partition, the assignment of the sequence to a point of M {\displaystyle M} becomes an almost one-to-one map whose image is a symbolic dynamical system of a special kind called a shift of finite type. In this case, the symbolic representation is a powerful tool for investigating the properties of the dynamical system ( M , φ ) {\displaystyle (M,\varphi )} . == Formal definition == A Markov partition is a finite cover of the invariant set of the manifold by a set of curvilinear rectangles { E 1 , E 2 , … , E r } {\displaystyle \{E_{1},E_{2},\ldots ,E_{r}\}} such that For any pair of points x , y ∈ E i {\displaystyle x,y\in E_{i}} , that W s ( x ) ∩ W u ( y ) ∈ E i {\displaystyle W_{s}(x)\cap W_{u}(y)\in E_{i}} Int E i ∩ Int E j = ∅ {\displaystyle \operatorname {Int} E_{i}\cap \operatorname {Int} E_{j}=\emptyset } for i ≠ j {\displaystyle i\neq j} If x ∈ Int E i {\displaystyle x\in \operatorname {Int} E_{i}} and φ ( x ) ∈ Int E j {\displaystyle \varphi (x)\in \operatorname {Int} E_{j}} , then φ [ W u ( x ) ∩ E i ] ⊃ W u ( φ x ) ∩ E j {\displaystyle \varphi \left[W_{u}(x)\cap E_{i}\right]\supset W_{u}(\varphi x)\cap E_{j}} φ [ W s ( x ) ∩ E i ] ⊂ W s ( φ x ) ∩ E j {\displaystyle \varphi \left[W_{s}(x)\cap E_{i}\right]\subset W_{s}(\varphi x)\cap E_{j}} Here, W u ( x ) {\displaystyle W_{u}(x)} and W s ( x ) {\displaystyle W_{s}(x)} are the unstable and stable manifolds of x, respectively, and Int E i {\displaystyle \operatorname {Int} E_{i}} simply denotes the interior of E i {\displaystyle E_{i}} . These last two conditions can be understood as a statement of the Markov property for the symbolic dynamics; that is, the movement of a trajectory from one open cover to the next is determined only by the most recent cover, and not the history of the system. It is this property of the covering that merits the 'Markov' appellation. The resulting dynamics is that of a Markov shift; that this is indeed the case is due to theorems by Yakov Sinai (1968) and Rufus Bowen (1975), thus putting symbolic dynamics on a firm footing. Variants of the definition are found, corresponding to conditions on the geometry of the pieces E i {\displaystyle E_{i}} . == Examples == Markov partitions have been constructed in several situations. Anosov diffeomorphisms of the torus. Dynamical billiards, in which case the covering is countable. Markov partitions make homoclinic and heteroclinic orbits particularly easy to describe. The system ( [ 0 , 1 ) , x ↦ 2 x m o d 1 ) {\displaystyle ([0,1),x\mapsto 2x\ mod\ 1)} has the Markov partition E 0 = ( 0 , 1 / 2 ) , E 1 = ( 1 / 2 , 1 ) {\displaystyle E_{0}=(0,1/2),E_{1}=(1/2,1)} , and in this case the symbolic representation of a real number in [ 0 , 1 ) {\displaystyle [0,1)} is its binary expansion. For example: x ∈ E 0 , T x ∈ E 1 , T 2 x ∈ E 1 , T 3 x ∈ E 1 , T 4 x ∈ E 0 ⇒ x = ( 0.01110... ) 2 {\displaystyle x\in E_{0},Tx\in E_{1},T^{2}x\in E_{1},T^{3}x\in E_{1},T^{4}x\in E_{0}\Rightarrow x=(0.01110...)_{2}} . The assignment of points of [ 0 , 1 ) {\displaystyle [0,1)} to their sequences in the Markov partition is well defined except on the dyadic rationals - morally speaking, this is because ( 0.01111 … ) 2 = ( 0.10000 … ) 2 {\displaystyle (0.01111\dots )_{2}=(0.10000\dots )_{2}} , in the same way as 1 = 0.999 … {\displaystyle 1=0.999\dots } in decimal expansions.
Collateral freedom
Collateral freedom is an anti-censorship strategy that attempts to make it economically prohibitive for censors to block content on the Internet. This is achieved by hosting content on cloud services that are considered by censors to be "too important to block", and then using encryption to prevent censors from identifying requests for censored information that is hosted among other content, forcing censors to either allow access to the censored information or take down entire services.
SQLf
SQLf is a SQL extended with fuzzy set theory application for expressing flexible (fuzzy) queries to traditional (or ″Regular″) Relational Databases. Among the known extensions proposed to SQL, at the present time, this is the most complete, because it allows the use of diverse fuzzy elements in all the constructions of the language SQL. SQLf is the only known proposal of flexible query system allowing linguistic quantification over set of rows in queries, achieved through the extension of SQL nesting and partitioning structures with fuzzy quantifiers. It also allows the use of quantifiers to qualify the quantity of search criteria satisfied by single rows. Several mechanisms are proposed for query evaluation, the most important being the one based on the derivation principle. This consists in deriving classic queries that produce, given a threshold t, a t-cut of the result of the fuzzy query, so that the additional processing cost of using a fuzzy language is diminished. == Basic block == The fundamental querying structure of SQLf is the multi-relational block. The conception of this structure is based on the three basic operations of the relational algebra: projection, cartesian product and selection, and the application of fuzzy sets’ concepts. The result of a SQLf query is a fuzzy set of rows that is a fuzzy relation instead of a regular relation. A basic block in SQLf consists of a SELECT clause, a FROM clause and an optional WHERE clause. The semantic of this query structure is: The SELECT clause corresponds to the projection. It specifies the relations’ attributes (or attribute expressions) that will be selected. The resulting table is a fuzzy set and it is given in decreasing ordered of satisfaction degree. The SELECT clause specifies also a calibration that is intended to restrict the set of rows retrieved. There are two kinds of calibrations: quantitative and qualitative. In quantitative calibration the user specifies the number of results to be retrieved, so that the query will retrieve the rows with highest membership degrees up to the number of required answers. In qualitative calibration the user specifies a minim level of satisfaction that must have any retrieved row. The FROM clause corresponds to the Cartesian Product. The consult is made on the Cartesian Product of the relations that are specified in this clause. The WHERE clause corresponds to the selection. It specifies the condition for which the satisfaction degree will be calculated. Rows that do not satisfy at all the condition are rejected. This condition is a fuzzy predicate that may involve any attribute of the relations. The following is an example of a SELECT query that returns a list of hotels that are cheap. The query retrieves all rows from the Hotels table that satisfice the fuzzy predicate cheap defined by the fuzzy set μ=(∞, ∞, 25, 30). The result is sorted in descending order by the membership degree of the query.
ECML PKDD
ECML PKDD, the European Conference on Machine Learning Principles and Practice of Knowledge Discovery in Databases, is one of the leading academic conferences on machine learning and knowledge discovery, held in Europe every year. == History == ECML PKDD is a merger of two European conferences, European Conference on Machine Learning (ECML) and European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD). ECML and PKDD have been co-located since 2001; however, both ECML and PKDD retained their own identity until 2007. For example, the 2007 conference was known as "the 18th European Conference on Machine Learning (ECML) and the 11th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD)", or in brief, "ECML/PKDD 2007", and both ECML and PKDD had their own conference proceedings. In 2008 the conferences were merged into one conference, and the division into traditional ECML topics and traditional PKDD topics was removed. The history of ECML dates back to 1986, when the European Working Session on Learning was first held. In 1993 the name of the conference was changed to European Conference on Machine Learning. PKDD was first organised in 1997. Originally PKDD stood for the European Symposium on Principles of Data Mining and Knowledge Discovery from Databases. The name European Conference on Principles and Practice of Knowledge Discovery in Databases was used since 1999. The conference remains highly competitive, consistently maintaining an average acceptance rate of around 25% for the main research track. == Upcoming conferences == == List of past conferences ==
IJCAI Computers and Thought Award
The IJCAI Computers and Thought Award is presented every two years by the International Joint Conference on Artificial Intelligence (IJCAI), recognizing outstanding young scientists in artificial intelligence. It was originally funded with royalties received from the book Computers and Thought (edited by Edward Feigenbaum and Julian Feldman), and is currently funded by IJCAI. It is considered to be "the premier award for artificial intelligence researchers under the age of 35". == Laureates == Terry Winograd (1971) Patrick Winston (1973) Chuck Rieger (1975) Douglas Lenat (1977) David Marr (1979) Gerald Sussman (1981) Tom Mitchell (1983) Hector Levesque (1985) Johan de Kleer (1987) Henry Kautz (1989) Rodney Brooks (1991) Martha E. Pollack (1991) Hiroaki Kitano (1993) Sarit Kraus (1995) Stuart Russell (1995) Leslie Kaelbling (1997) Nicholas Jennings (1999) Daphne Koller (2001) Tuomas Sandholm (2003) Peter Stone (2007) Carlos Guestrin (2009) Andrew Ng (2009) Vincent Conitzer (2011) Malte Helmert (2011) Kristen Grauman (2013) Ariel D. Procaccia (2015) Percy Liang (2016) for his contributions to both the approach of semantic parsing for natural language understanding and better methods for learning latent-variable models, sometimes with weak supervision, in machine learning. Devi Parikh (2017) Stefano Ermon (2018) Guy Van den Broeck (2019) for his contributions to statistical and relational artificial intelligence, and the study of tractability in learning and reasoning. Piotr Skowron (2020) for his contributions to computational social choice, and to the theory of committee elections. Fei Fang (2021) for her contributions to integrating machine learning with game theory and the use of these novel techniques to tackle societal challenges such as more effective deployment of security resources, enhancing environmental sustainability, and reducing food insecurity. Bo Li (2022) for her contributions to uncovering the underlying connections among robustness, privacy, and generalization in AI, showing how different models are vulnerable to malicious attacks, and how to eliminate these vulnerabilities using mathematical tools that provide robustness guarantees for learning models and privacy protection. Pin-Yu Chen (2023) for his contributions to consolidating properties of trust, robustness and safety into rigorous algorithmic procedures and computable metrics for improving AI systems. Nisarg Shah (2024) for his contributions to AI and society, in particular foundational work on the theory of algorithmic fairness using principles from social choice theory. Aditya Grover (2025) for his foundational contributions uniting deep generative models, representation learning, and reinforcement learning, and for their applications in advancing scientific reasoning.
MyChild App
MyChild App is an Android app that helps parents screen developmental disorders in their children between the age of 1 and 24 months. The app contains information for parents about the different stages of a child's development. == Background == Launched in 2015 on Google PlayStore, the app is a consumer product of the parent company, Time Ahead, Inc. Its office is based in Bhopal, Madhya Pradesh, India. As of August 2016, the app had been downloaded by 11,000+ users in 140+ countries and is a part of fbstart case study. == Funding == In 2015, MyChild App raised a seed round of $100k led by 500 Startups, followed by angel investors Samir Bangara, Anisha Mittal, Pallav Nadhani, Deobrat Singh, Lalit Mangal, Arihant Patni, Amit Gupta, Dr. Ritesh Malik, Saurab Paruthi, and Singapore Angel Network.
Galatea (video game)
Galatea is an interactive fiction video game by Emily Short featuring a modern rendition of the Greek myth of Galatea, the sculpture of a woman that gained life. It took "Best of Show" in the 2000 IF Art Show and won a XYZZY Award for Best non-player character. The game displays an unusually rich approach to non-player character dialogue and diverts from the typical puzzle-solving in interactive fiction: gameplay consists entirely of interacting with a single character in a single room. Galatea is licensed under the Creative Commons BY-NC-ND 3.0 US license. == Gameplay == Galatea alters the typical interactive fiction game mechanics by concentrating instead on the player's interactions with a single non-player character (NPC), the eponymous Galatea. Much of the interest of the piece derives from the ambiguous nature of the player–NPC dialogue: the form of the conversation and, indeed, the nature of Galatea herself shift depending on the focus the player places on certain aspects of the character's personality. Numerous endings are possible. Gameplay centers around the developing dialogue between Galatea and the player when asking about topics in the previous conversation. Two commands, "think about" and "recap", are provided to keep track of what has already been said; the former is also used to advance the storyline, as the player character draws conclusions about the story as it has unfolded to that point. The game also encourages using sensory commands ("touch", "listen to", "look at"), adding immersion to the experience. == Plot == Galatea is loosely based on the myth of Pygmalion, who carved the sculpture of a woman. In the myth, he falls in love with the statue, named Galatea or Elise in different versions, and the goddess Venus brings her to life. The story begins at the opening of an exhibition of artificial intelligences. The player, alone, discovers Galatea displayed on a pedestal with a small information placard. She is illuminated by a spotlight and wears an emerald dress. Seeing the player about to turn away, Galatea says, "They told me you were coming." From this point, the story may proceed in a number of ways depending on the player's words and actions. === Multilinear interactive fiction === Short describes this as "multilinear interactive fiction": while interactive fiction in general allows the player to find their own way through the story, this leads in most cases to a single ending (or at least a single desired 'correct' ending). With Galatea, Short presents a story with around 70 different endings and hundreds of possible ways of reaching them. The plot is thus designed to appear open-ended with the development of the story entirely dependent on what the player decides to talk or ask about or what actions they choose to perform. Thus the original author and the player share in the creation of a work of fiction. == Development == In interviews, Emily Short has explained that Galatea arose out of her efforts to develop advanced dialog coding for interactive fiction engines. Although code for simple conversational programs like ELIZA have existed since the 1960s, and limited dialog options have existed in interactive fiction since the 1970s, Short's efforts to develop chatterbot-like dialog required her to produce a simple test case scenario to test NPC interaction. Thus the single-room, single-occupant Galatea was a natural result. Development of the game progressed organically with Short engaging in test runs and drafting new dialog options for every conversational dead-end that arose. The game's multiple endings also arose in a similar fashion although Short had intended that there be multiple endings from the start. Although the nature of the game's development as well as its minimalist final form has led to questions regarding whether it is really a game and not just an experimental conversational program, Short has suggested that to her the definition of interactive fiction requires nothing more than a world model and a parser, and "anything you can cook up with those features counts as IF." Short has acknowledged the helpful influence of the close-knit IF community and the "atmosphere in which experimentation is valued" as leading to the success of her works like Galatea. == Reception == Galatea was well received, achieving critical acclaim from interactive fiction reviewers and literary scholars. The game is considered to aspire to a new level of art in interactive fiction, and thereby to have revolutionized the genre, establishing its author, Emily Short, as one of the key figures in the modern interactive fiction scene. Fellow award-winning IF author, Adam Cadre has called Galatea "the best NPC ever"—a view that was echoed by Joystiq's John Bardinelli. Cadre also describes the game as an example of an alternative kind of puzzle where "interactivity comes in deciding where to go, what to see, what to say. Rather than having to open gates along a path, you discover that they're all open at first, but stepping through one causes others to close." Galatea was described in 2007 by Indiegames.com as a "fascinating journey." In a 2009 article, Rock, Paper, Shotgun praised the depth and detail of the game, the complexities of the character design and its "masterful balance between intricacy and simplicity", and "Galatea's emotional turmoil" that is "encoded sweetly into the subtext of what's going on. By simply interacting in a logical manner, you learn more about this character than any cut-scene or info-dump could ever hope to convey." This was reiterated in a 2010 1UP.com article that listed Galatea as #2 in its "Top 5 Introductory Interactive Fiction Games" feature, describing it as intriguingly replayable, and as a "surprisingly rich game for its apparent minimalism". In 2011, PC Gamer highlighted Galatea as an example of the artistic and literary aspects of the interactive fiction genre. The titular character, Galatea, has been compared to the 2007 Portal character GLaDOS due to similarities in the personalities of the characters.