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In network on chips (NoCs) design, reconfiguration of NoC is a very effective option for minimizing power consumption, and Gaussian networks can provide significant advantage over the mesh networks in terms of network diameter, av...
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In network on chips (NoCs) design, reconfiguration of NoC is a very effective option for minimizing power consumption, and Gaussian networks can provide significant advantage over the mesh networks in terms of network diameter, average hop distance and so on. In this paper, based on the special topology structure and the static connection rules within Gaussian networks, we present the reconfiguration representation for Gaussian networks and the nature of reconfigurable Gaussian networks. Furthermore, reconfigurable rules of Gaussian networks are proposed to design the constraints for automatic reconfiguration of NoC.
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Network embedding aims to encode nodes into a low-dimensional space with the structure and inherent properties of the networks preserved. It is an upstream technique for network analyses such as link prediction and node clustering...
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Network embedding aims to encode nodes into a low-dimensional space with the structure and inherent properties of the networks preserved. It is an upstream technique for network analyses such as link prediction and node clustering. Most existing efforts are devoted to homogeneous or heterogeneous plain networks. However, networks in real-world scenarios are usually heterogeneous and not plain, i.e., they contain multi-type nodes/links and diverse node attributes. We refer such kind of networks with both heterogeneities and attributes as attributed heterogeneous networks (AHNs). Embedding AHNs faces two challenges: (1) how to fuse heterogeneous information sources including network structures, semantic information and node attributes; (2) how to capture uncertainty of node embeddings caused by diverse attributes. To tackle these challenges, we propose a unified embedding model which represents each node in an AHN with a Gaussian distribution (AHNG). AHNG fuses multi-type nodes/links and diverse attributes through a two-layer neural network and captures the uncertainty by embedding nodes as Gaussian distributions. Furthermore, the incorporation of node attributes makes AHNG inductive, embedding previously unseen nodes or isolated nodes without additional training. Extensive experiments on a large real-world dataset validate the effectiveness and efficiency of the proposed model.
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Network coding is a method for information transmission in a network, based on the idea of enabling internal nodes to forward a function of the incoming messages, typically a linear combination. In this paper we discuss generaliza...
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Network coding is a method for information transmission in a network, based on the idea of enabling internal nodes to forward a function of the incoming messages, typically a linear combination. In this paper we discuss generalizations of the network coding problem with additional constraints on the coding functions called network code completion problem, NCCP. We give both randomized and deterministic algorithms for maximum throughput-achieving network code construction for the NCCP in the multicast case. We also introduce the related problem of fixable pairs, investigating when a certain subset of coding coefficients in the linear combination functions can be fixed to arbitrary nonzero values such that the network code can always be completed to achieve maximum throughput. We give a sufficient condition for a set of coding coefficients to be fixable. For both problems we present applications in different wireless and heterogeneous network models.
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The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only mod...
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The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model Gaussian marginal distributions. To model non-Gaussian data, a GP can be warped by a nonlinear transformation (or warping) as performed by warped GPs (WGPs) and more computationally-demanding alternatives such as Bayesian WGPs and deep GPs. However, the WGP requires a numerical approximation of the inverse warping for prediction, which increases the computational complexity in practice. To sidestep this issue, we construct a novel class of warpings consisting of compositions of multiple elementary functions, for which the inverse is known explicitly. We then propose the compositionally-warped GP (CWGP), a non-Gaussian generative model whose expressiveness follows from its deep compositional architecture, and its computational efficiency is guaranteed by the analytical inverse warping. Experimental validation using synthetic and real-world datasets confirms that the proposed CWGP is robust to the choice of warpings and provides more accurate point predictions, better trained models and shorter computation times than WGP. (C) 2019 Elsevier Ltd. All rights reserved.
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We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been ad...
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We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to perform community detection, exploration tasks and to study temporal networks. Moreover, they have been used also to generate networks with different topologies (e.g., scale-free). In this work, we define a random walker that plays the role of "edges-generator". In particular, the random walker generates new connections and uses these ones to visit each node of a network. As result, the proposed model allows to achieve networks provided with a Gaussian degree distribution; moreover we found that some properties of achieved Gaussian networks, as the clustering coefficient and the assortativity, show a critical behavior. Finally, we performed numerical simulations to study the behavior and the properties of the cited model.
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Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined ...
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Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
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We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi to linear determi...
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We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial-time versions of our algorithm and show that for a network with $g$ destinations, our deterministic algorithm can achieve the capacity in $left lceil log (g+1)right rceil $ uses of the network and has the fastest construction time among algorithms for this problem.
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The study of feedback has been mostly limited to single-hop communication settings. In this paper, we consider Gaussian networks where sources and destinations can communicate with the help of intermediate relays over multiple hop...
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The study of feedback has been mostly limited to single-hop communication settings. In this paper, we consider Gaussian networks where sources and destinations can communicate with the help of intermediate relays over multiple hops. We assume that links in the network can be bidirected providing opportunities for feedback. We ask the following question: can the information transfer in both directions of a link be critical to maximizing the end-to-end communication rates in the network? Equivalently, could one of the directions in each bidirected link (and more generally at least one of the links forming a cycle) be shut down and the capacity of the network still be approximately maintained? We show that in any arbitrary Gaussian network with bidirected edges and cycles and unicast traffic, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. For Gaussian networks with multiple-access and broadcast traffic, an acyclic subnetwork is sufficient to achieve every rate point in the capacity region of the original network, however, there may not be a single acyclic subnetwork that maintains the whole capacity region. For networks with multicast and multiple unicast traffic, on the other hand, bidirected information flow across certain links can be critically needed to maximize the end-to-end capacity region. These results can be regarded as generalizations of the conclusions regarding the usefulness of feedback in various single-hop Gaussian settings and can provide opportunities for simplifying operation in Gaussian multihop networks.
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A new method for model selection for Gaussian Bayesian networks and Markov networks, with extensions towards ancestral graphs, is constructed to have good mean squared error properties. The method is based on the focused informati...
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A new method for model selection for Gaussian Bayesian networks and Markov networks, with extensions towards ancestral graphs, is constructed to have good mean squared error properties. The method is based on the focused information criterion, and offers the possibility of fitting individual-tailored models. The focus of the research, that is, the purpose of the model, directs the selection. It is shown that using the focused information criterion leads to a graph with small mean squared error. The low mean squared error ensures accurate estimation using a graphical model; here estimation rather than explanation is the main objective. Two situations that commonly occur in practice are treated: a data-driven estimation of a graphical model and the improvement of an already pre-specified feasible model. The search algorithms are illustrated by means of data examples and are compared with existing methods in a simulation study.
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We present a theory for connecting quantum Markov components into a network with quantum input processes in a Gaussian state (including thermal and squeezed). One would expect on physical grounds that the connection rules should b...
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We present a theory for connecting quantum Markov components into a network with quantum input processes in a Gaussian state (including thermal and squeezed). One would expect on physical grounds that the connection rules should be independent of the state of the input to the network. To compute statistical properties, we use a version of Wicks' theorem involving fictitious vacuum fields (Fock space based representation of the fields) and while this aids computation, and gives a rigorous formulation, the various representations need not be unitarily equivalent. In particular, a naive application of the connection rules would lead to the wrong answer. We establish the correct interconnection rules, and show that while the quantum stochastic differential equations of motion display explicitly the covariances (thermal and squeezing parameters) of the Gaussian input fields we introduce the Wick-Stratonovich form which leads to a way of writing these equations that does not depend on these covariances and so corresponds to the universal equations written in terms of formal quantum input processes. We show that a wholly consistent theory of quantum open systems in series can be developed in this way, and as required physically, is universal and in particular representation-free.
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