Shor's algorithmShor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
Regret (decision theory)In decision theory, on making decisions under uncertainty—should information about the best course of action arrive after taking a fixed decision—the human emotional response of regret is often experienced, and can be measured as the value of difference between a made decision and the optimal decision. The theory of regret aversion or anticipated regret proposes that when facing a decision, individuals might anticipate regret and thus incorporate in their choice their desire to eliminate or reduce this possibility.
Recursion (computer science)In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement.
Parameterized complexityIn computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input.
Sparse approximationSparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in , signal processing, machine learning, medical imaging, and more. Consider a linear system of equations , where is an underdetermined matrix and . The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest.
Hall-type theorems for hypergraphsIn the mathematical field of graph theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs. Such theorems were proved by Ofra Kessler, Ron Aharoni, Penny Haxell, Roy Meshulam, and others. Hall's marriage theorem provides a condition guaranteeing that a bipartite graph (X + Y, E) admits a perfect matching, or - more generally - a matching that saturates all vertices of Y. The condition involves the number of neighbors of subsets of Y.
Allocative efficiencyAllocative efficiency is a state of the economy in which production is aligned with consumer preferences; in particular, the set of outputs is chosen so as to maximize the wellbeing of society. This is achieved if every good or service is produced up until the last unit provides a marginal benefit to consumers equal to the marginal cost of production. In economics, allocative efficiency entails production at the point on the production possibilities frontier that is optimal for society.
Loss functionIn mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.
Multi-user dungeonA MUD (mʌd; originally multi-user dungeon, with later variants multi-user dimension and multi-user domain) is a multiplayer real-time virtual world, usually text-based or storyboarded. MUDs combine elements of role-playing games, hack and slash, player versus player, interactive fiction, and online chat. Players can read or view descriptions of rooms, objects, other players, and non-player characters, and perform actions in the virtual world that are typically also described.
Chernoff boundIn probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian). It is especially useful for sums of independent random variables, such as sums of Bernoulli random variables. The bound is commonly named after Herman Chernoff who described the method in a 1952 paper, though Chernoff himself attributed it to Herman Rubin.
Economic efficiencyIn microeconomics, economic efficiency, depending on the context, is usually one of the following two related concepts: Allocative or Pareto efficiency: any changes made to assist one person would harm another. Productive efficiency: no additional output of one good can be obtained without decreasing the output of another good, and production proceeds at the lowest possible average total cost. These definitions are not equivalent: a market or other economic system may be allocatively but not productively efficient, or productively but not allocatively efficient.
Internet privacyInternet privacy involves the right or mandate of personal privacy concerning the storage, re-purposing, provision to third parties, and display of information pertaining to oneself via the Internet. Internet privacy is a subset of data privacy. Privacy concerns have been articulated from the beginnings of large-scale computer sharing and especially relate to mass surveillance enabled by the emergence of computer technologies. Privacy can entail either personally identifiable information (PII) or non-PII information such as a site visitor's behaviour on a website.
