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Random Walk on an Arbitrary Set

by C. Harris, Robin Sibson, David Williams
"... Let I be a countably infinite set of points in R, and suppose that I has no points of accumulation and that its convex hull is the whole of R. It will be convenient to index I as {ui: i ∈ Z}, with ui < ui+1 for every i. Consider a continuous-time Markov chain Y = {Y (t) : t ≥ 0} on I, with the pr ..."
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Let I be a countably infinite set of points in R, and suppose that I has no points of accumulation and that its convex hull is the whole of R. It will be convenient to index I as {ui: i ∈ Z}, with ui < ui+1 for every i. Consider a continuous-time Markov chain Y = {Y (t) : t ≥ 0} on I

ABSTRACT FACTORIALS OF ARBITRARY SETS OF INTEGERS

by Angelo B. Mingarelli , 2007
"... Given any subset of Z we associate to it another set on which we can define one or more (generally independent) abstract factorial functions. These associated sets are studied and arithmetic relations are revealed. In addition, we show that for an abstract factorial function of an infinite subset ..."
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Given any subset of Z we associate to it another set on which we can define one or more (generally independent) abstract factorial functions. These associated sets are studied and arithmetic relations are revealed. In addition, we show that for an abstract factorial function of an infinite subset

The Characteristic Mapping Method for the Linear Advection of Arbitrary Sets

by Olivier Mercier, Jean-christophe Nave
"... In this paper, we present a new numerical method for advecting arbitrary sets in a vector field. The method computes a transformation of the domain instead of dealing with particular sets. We propose a way of decoupling the advection and representation steps of the computations, resulting in signifi ..."
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In this paper, we present a new numerical method for advecting arbitrary sets in a vector field. The method computes a transformation of the domain instead of dealing with particular sets. We propose a way of decoupling the advection and representation steps of the computations, resulting

Fast approximate energy minimization via graph cuts

by Yuri Boykov, Olga Veksler, Ramin Zabih - IEEE Transactions on Pattern Analysis and Machine Intelligence , 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
Abstract - Cited by 2120 (61 self) - Add to MetaCart
very large moves are allowed. The first move we consider is an α-βswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases

General Characterizations of inductive Inference over Arbitrary Sets of Data Presentations

by Kevin T. Kelly, Kevin T. Kelly
"... General characterizations of inductive inference over arbitrary sets of data presentations ..."
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General characterizations of inductive inference over arbitrary sets of data presentations

Boosting and differential privacy

by Cynthia Dwork, Guy N. Rothblum, Salil Vadhan , 2010
"... Boosting is a general method for improving the accuracy of learning algorithms. We use boosting to construct improved privacy-preserving synopses of an input database. These are data structures that yield, for a given set Q of queries over an input database, reasonably accurate estimates of the resp ..."
Abstract - Cited by 648 (14 self) - Add to MetaCart
algorithm obtains a synopsis that is good for all of Q. We ensure privacy for the rows of the database, but the boosting is performed on the queries. We also provide the first synopsis generators for arbitrary sets of arbitrary low sensitivity

Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors

by Moshe Mishali, Yonina C. Eldar , 2008
"... The rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of non-adaptive linear measurements, under appropriate conditions on the measurement matrix. The vector model has been ext ..."
Abstract - Cited by 100 (41 self) - Add to MetaCart
The rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of non-adaptive linear measurements, under appropriate conditions on the measurement matrix. The vector model has been

Approximation by Superpositions of a Sigmoidal Function

by G. Cybenko , 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
Abstract - Cited by 1248 (2 self) - Add to MetaCart
In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate

Some optimal inapproximability results

by Johan Håstad , 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for Max-Ek-Sat for k * 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
Abstract - Cited by 751 (11 self) - Add to MetaCart
We prove optimal, up to an arbitrary ffl? 0, inapproximability results for Max-Ek-Sat for k * 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds

Maximum entropy markov models for information extraction and segmentation

by Andrew McCallum, Dayne Freitag, Fernando Pereira , 2000
"... Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many text-related tasks, such as part-of-speech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial ..."
Abstract - Cited by 561 (18 self) - Add to MetaCart
as multinomial distributions over a discrete vocabulary, and the HMM parameters are set to maximize the likelihood of the observations. This paper presents a new Markovian sequence model, closely related to HMMs, that allows observations to be represented as arbitrary overlapping features (such as word
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