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Piotr Indyk
Piotr Indyk is Thomas D. and Virginia W. Cabot Professor in the Theory of Computation Group at the Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology. Academic biography Indyk received the Magister (MA) degree from the University of Warsaw in 1995 and a PhD in computer science from Stanford University in 2000 under the supervision of Rajeev Motwani. In 2000, Indyk joined MIT where he currently holds the title of Thomas D. and Virginia W. Cabot Professor in the Department of Electrical Engineering and Computer Science. Research Indyk's research focuses primarily on computational geometry in high-dimensions, streaming algorithms, and computational learning theory. He has made a range of contributions to these fields, particularly in the study of low-distortion embeddings, algorithmic coding theory, and geometric and combinatorial pattern matching. He has also made contributions to the theory of compressed sensing. His work on algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poland
Poland, officially the Republic of Poland, , is a country in Central Europe. Poland is divided into Voivodeships of Poland, sixteen voivodeships and is the fifth most populous member state of the European Union (EU), with over 38 million people, and the List of European countries by area, seventh largest EU country, covering a combined area of . It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordering seven countries. The territory is characterised by a varied landscape, diverse ecosystems, and Temperate climate, temperate transitional climate. The capital and List of cities and towns in Poland, largest city is Warsaw; other major cities include Kraków, Wrocław, Łódź, Poznań, and Gdańsk. Prehistory and protohistory of Poland, Humans have been present on Polish soil since the Lower Paleolithic, with continuous settlement since the end of the Last Glacial Period over 12,000 years ago. Culturally diverse throughout ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David And Lucile Packard Foundation
The David and Lucile Packard Foundation is a private foundation that provides grants to not-for-profit organizations. It was created in 1964 by David Packard (co-founder of HP) and his wife Lucile Salter Packard. Following David Packard's death in 1996, the Foundation became the beneficiary of part of his estate. The foundation's goals, through the use of grants, are to "improve the lives of children, enable creative pursuit of science, advance reproductive health, and conserve and restore earth’s natural systems." As of 2016, The David and Lucile Packard Foundation was the 20th wealthiest foundation in the United States. Financials As of December 2015, the Foundation's investment portfolio totaled $6.7 billion. General program grant awards for 2015 totaled $307 million. According to the OECD, the David and Lucile Packard Foundation provided USD 122.9 million for development in 2018, all of which was related to its grant-making activities. Areas of funding The majority of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude ( absolute value) of the complex value represents the amplitude of a constituent complex sinusoid wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compressed Sensing
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible. The first one is sparsity, which requires the signal to be sparse in some domain. The second one is incoherence, which is applied through the isometric property, which is sufficient for sparse signals. Overview A common goal of the engineering field of signal processing is to reconstruct a signal from a series of sampling measurements. In general, this task is impossible because there is no way to reconstruct a signal during the times that the signal is not measured. Nevertheless, with prior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Matching
In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually has to be exact: "either it will or will not be a match." The patterns generally have the form of either sequences or tree structures. Uses of pattern matching include outputting the locations (if any) of a pattern within a token sequence, to output some component of the matched pattern, and to substitute the matching pattern with some other token sequence (i.e., search and replace). Sequence patterns (e.g., a text string) are often described using regular expressions and matched using techniques such as backtracking. Tree patterns are used in some programming languages as a general tool to process data based on its structure, e.g. C#, F#, Haskell, ML, Python, Ruby, Rust, Scala, Swift and the symbolic mathematics language Mathematica have special syntax for expressing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson–Lindenstrauss Lemma
In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. The map used for the embedding is at least Lipschitz, and can even be taken to be an orthogonal projection. The lemma has applications in compressed sensing, manifold learning, dimensionality reduction, and graph embedding. Much of the data stored and manipulated on computers, including text and images, can be represented as points in a high-dimensional space (see vector space model for the case of text). However, the essential algorithms for working with such data tend to become bogged down very quickly as dimension increases. It is therefore desirable to reduce the dimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Learning Theory
In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms. Overview Theoretical results in machine learning mainly deal with a type of inductive learning called supervised learning. In supervised learning, an algorithm is given samples that are labeled in some useful way. For example, the samples might be descriptions of mushrooms, and the labels could be whether or not the mushrooms are edible. The algorithm takes these previously labeled samples and uses them to induce a classifier. This classifier is a function that assigns labels to samples, including samples that have not been seen previously by the algorithm. The goal of the supervised learning algorithm is to optimize some measure of performance such as minimizing the number of mistakes made on new samples. In addition to performance bounds, computational learning theory studies the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Streaming Algorithm
In computer science, streaming algorithms are algorithms for processing data streams in which the input is presented as a sequence of items and can be examined in only a few passes (typically just one). In most models, these algorithms have access to limited memory (generally logarithmic in the size of and/or the maximum value in the stream). They may also have limited processing time per item. These constraints may mean that an algorithm produces an approximate answer based on a summary or "sketch" of the data stream. History Though streaming algorithms had already been studied by Munro and Paterson as early as 1978, as well as Philippe Flajolet and G. Nigel Martin in 1982/83, the field of streaming algorithms was first formalized and popularized in a 1996 paper by Noga Alon, Yossi Matias, and Mario Szegedy. For this paper, the authors later won the Gödel Prize in 2005 "for their foundational contribution to streaming algorithms." There has since been a large body of work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity. Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(''n''2) and O(''n'' log ''n'') may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Computer Science And Artificial Intelligence Laboratory
Computer Science and Artificial Intelligence Laboratory (CSAIL) is a research institute at the Massachusetts Institute of Technology (MIT) formed by the 2003 merger of the Laboratory for Computer Science (LCS) and the Artificial Intelligence Laboratory (AI Lab). Housed within the Ray and Maria Stata Center, CSAIL is the largest on-campus laboratory as measured by research scope and membership. It is part of the Schwarzman College of Computing but is also overseen by the MIT Vice President of Research. Research activities CSAIL's research activities are organized around a number of semi-autonomous research groups, each of which is headed by one or more professors or research scientists. These groups are divided up into seven general areas of research: * Artificial intelligence * Computational biology * Graphics and vision * Language and learning * Theory of computation * Robotics * Systems (includes computer architecture, databases, distributed systems, networks and network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
