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A learning algorithm for Boltzmann machines
 Cognitive Science
, 1985
"... The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a probl ..."
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Cited by 586 (13 self)
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The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in o very short time. One kind of computation for which massively porollel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a generol parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge obout o task domain in on efficient way. We describe some simple examples in which the learning algorithm creates internal representations thot ore demonstrobly the most efficient way of using the preexisting connectivity structure. 1.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Mutualinformationbased registration of medical images: a survey
 IEEE Transcations on Medical Imaging
, 2003
"... Abstract—An overview is presented of the medical image processing literature on mutualinformationbased registration. The aim of the survey is threefold: an introduction for those new to the field, an overview for those working in the field, and a reference for those searching for literature on a s ..."
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Cited by 297 (3 self)
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Abstract—An overview is presented of the medical image processing literature on mutualinformationbased registration. The aim of the survey is threefold: an introduction for those new to the field, an overview for those working in the field, and a reference for those searching for literature on a specific application. Methods are classified according to the different aspects of mutualinformationbased registration. The main division is in aspects of the methodology and of the application. The part on methodology describes choices made on facets such as preprocessing of images, gray value interpolation, optimization, adaptations to the mutual information measure, and different types of geometrical transformations. The part on applications is a reference of the literature available on different modalities, on interpatient registration and on different anatomical objects. Comparison studies including mutual information are also considered. The paper starts with a description of entropy and mutual information and it closes with a discussion on past achievements and some future challenges. Index Terms—Image registration, literature survey, matching, mutual information. I.
Stochastic Geometry and Wireless Networks, Volume
 II — Applications. Foundations and Trends in Networking. NoW Publishers
"... i Preface A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a giv ..."
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Cited by 257 (37 self)
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i Preface A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a given time, several nodes transmit simultaneously, each toward its own receiver. Each transmitter–receiver pair requires its own wireless link. The signal received from the link transmitter may be jammed by the signals received from the other transmitters. Even in the simplest model where the signal power radiated from a point decays in an isotropic way with Euclidean distance, the geometry of the locations of the nodes plays a key role since it determines the signal to interference and noise ratio (SINR) at each receiver and hence the possibility of establishing simultaneously this collection of links at a given bit rate. The interference seen by a receiver is the sum of the signal powers received from all transmitters, except its own transmitter. Stochastic geometry provides a natural way of defining and computing macroscopic properties of such networks, by averaging over all potential geometrical patterns for the nodes, in the same way as queuing theory provides response times or congestion, averaged over all potential arrival patterns within a given parametric class.
ON RÉNYI DIVERGENCE MEASURES FOR CONTINUOUS ALPHABET SOURCES
, 2011
"... The idea of ‘probabilistic distances ’ (also called divergences), which in some sense assess how ‘close ’ two probability distributions are from one another, has been widely employed in probability, statistics, information theory, and related fields. Of particular importance due to their generality ..."
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Cited by 1 (0 self)
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and applicability are the Rényi divergence measures. While the closely related concept of Rényi entropy of a probability distribution has been studied extensively, and closedform expressions for the most common univariate and multivariate continuous distributions have been obtained and compiled [57, 45, 62
Graph Classification and Differential Privacy
, 2014
"... the nonexclusive right to publish the Work electronically and in a noncommercial purpose make it accessible on the Internet. The Authors warrants that they are the authors to the Work, and warrants that the Work does not contain text, pictures or other material that violates copyright law. The Aut ..."
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the nonexclusive right to publish the Work electronically and in a noncommercial purpose make it accessible on the Internet. The Authors warrants that they are the authors to the Work, and warrants that the Work does not contain text, pictures or other material that violates copyright law. The Authors shall, when transferring the rights of the Work to a third party (for example a publisher or a company), acknowledge the third party about this agreement. If the Authors has signed a copyright agreement with a third party regarding the Work, the Authors warrants hereby that they have obtained any necessary permission from this third party to
The BrunnMinkowski inequality
 Bull. Amer. Math. Soc. (N.S
, 2002
"... Abstract. In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The BrunnMinkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of R n, and deserves to be better known. This guide explains ..."
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Cited by 184 (9 self)
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Abstract. In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The BrunnMinkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of R n, and deserves to be better known. This guide explains the relationship between the BrunnMinkowski inequality and other inequalities in geometry and analysis, and some applications. 1.
The phase transition in inhomogeneous random graphs
, 2005
"... The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, powerlaw degree distributions. Thus there ..."
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Cited by 181 (31 self)
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The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, powerlaw degree distributions. Thus there has been a lot of recent interest in defining and studying ‘inhomogeneous ’ random graph models. One of the most studied properties of these new models is their ‘robustness’, or, equivalently, the ‘phase transition ’ as an edge density parameter is varied. For G(n, p), p = c/n, the phase transition at c = 1 has been a central topic in the study of random graphs for well over 40 years. Many of the new inhomogenous models are rather complicated; although there are exceptions, in most cases precise questions such as determining exactly the critical point of the phase transition are approachable only when there is independence between the edges. Fortunately, some models studied have this already, and others can be approximated by models with
Results 1  10
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