The Experts below are selected from a list of 46959 Experts worldwide ranked by ideXlab platform
Behrouz Touri - One of the best experts on this subject based on the ideXlab platform.
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On the Convergence Properties of Social Hegselmann-Krause Dynamics
arXiv: Optimization and Control, 2019Co-Authors: Rohit Parasnis, Massimo Franceschetti, Behrouz TouriAbstract:We study the convergence properties of Social Hegselmann-Krause dynamics, a {variant} of the Hegselmann-Krause (HK) model of opinion dynamics where a physical Connectivity Graph that accounts for the extrinsic factors that could prevent interaction between certain pairs of agents is incorporated. As opposed to the original HK dynamics (which terminate in finite time), we show that for any underlying connected and incomplete Graph, under a certain mild assumption, the expected termination time of social HK dynamics is infinity. We then investigate the rate of convergence to the steady state, and provide bounds on the maximum $\epsilon$-convergence time in terms of the properties of the physical Connectivity Graph. We extend this discussion and observe that for almost all $n$, there exists an $n$-vertex physical Connectivity Graph on which social HK dynamics may not even $\epsilon$-converge to the steady state within a bounded time frame. We then provide nearly tight necessary and sufficient conditions for arbitrarily slow merging (a phenomenon that is essential for arbitrarily slow $\epsilon$-convergence to the steady state). Using the necessary conditions, we show that complete $r$-partite Graphs have bounded $\epsilon$-convergence times.
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CDC - On Graphs with Bounded and Unbounded Convergence Times in Social Hegselmann-Krause Dynamics
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Rohit Parasnis, Massimo Franceschetti, Behrouz TouriAbstract:We address the problem of identifying physical Connectivity Graphs that guarantee a finite upper bound on the time required for the associated social Hegselmann-Krause dynamics to ϵ-converge to the steady state. We handle the cases of consensus as well as non-consensus steady states, and for each case, we provide sufficient conditions for a physical Connectivity Graph to have unbounded ϵ-convergence time. We then show that every complete r-partite Graph on n vertices has a finite maximum ϵ-convergence time, regardless of the values of r and n. Finally, we show that enhancing the Connectivity of agents may not always speed up convergence to the steady state, even when the steady state is a consensus.
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CDC - Hegselmann-Krause Dynamics with Limited Connectivity
2018 IEEE Conference on Decision and Control (CDC), 2018Co-Authors: Rohit Parasnis, Massimo Franceschetti, Behrouz TouriAbstract:We investigate a variant of the Hegselmann-Krause model of opinion dynamics that relaxes the assumption that every agent has knowledge of every other agent's opinion at all points in time. This is done by incorporating a physical Connectivity Graph that accounts for the external factors that may prevent interaction between certain pairs of agents. As opposed to the original Hegselmann-Krause dynamics (which terminate in finite time), we show that for any underlying Graph that is connected but not complete, there exists an initial condition under which the dynamics never terminate. As a result, we show that for any continuous probability density function having the state space as its support, the expected termination time of the modified dynamics is infinity. We also study the rate of convergence to the steady state and derive bounds on the maximum convergence time in terms of the properties of the physical Connectivity Graph.
Laurent Vercueil - One of the best experts on this subject based on the ideXlab platform.
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Directed differential Connectivity Graph of interictal epileptiform discharges
IEEE Transactions on Biomedical Engineering, 2011Co-Authors: Ladan Amini, Sophie Achard, Christian Jutten, Hamid Soltanian-zadeh, Olivier David, Gh. Ali Hossein-zadeh, Philippe Kahane, Lorella Minotti, Laurent VercueilAbstract:In this paper, we study temporal couplings between interictal events of spatially remote regions in order to localize the leading epileptic regions from intracerebral EEG (iEEG). We aim to assess whether quantitative epileptic Graph analysis during interictal period may be helpful to predict the seizure onset zone of ictal iEEG. Using wavelet transform, cross-correlation coefficient, and multiple hypothesis test, we propose a differential Connectivity Graph (DCG) to represent the connections that change significantly between epileptic and nonepileptic states as defined by the interictal events. Postprocessings based on mutual information and multiobjective optimization are proposed to localize the leading epileptic regions through DCG. The suggested approach is applied on iEEG recordings of five patients suffering from focal epilepsy. Quantitative comparisons of the proposed epileptic regions within ictal onset zones detected by visual inspection and using electrically stimulated seizures, reveal good performance of the present method.
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Sparse Differential Connectivity Graph of Scalp EEG for Epileptic Patients
2009Co-Authors: Ladan Amini, Sophie Achard, Christian Jutten, Hamid Soltanian-zadeh, Gholam Ali Hossein-zadeh, Olivier David, Laurent VercueilAbstract:The aim of the work is to integrate the information modulation of the inter-relations between EEG scalp measurements of two brain states in a Connectivity Graph. We present a sparse differential Connectivity Graph (SDCG) to distinguish the effectively modulated connections between epileptiform and non-epileptiform states of the brain from all the common connections created by noise, artifact, unwanted background activities and their related volume conduction effect. The proposed method is applied on real epileptic EEG data. Clustering the extracted features from SDCG may present valuable information about the epileptiform focus and their relations.
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ESANN - Sparse differential Connectivity Graph of scalp EEG for epileptic patients
2009Co-Authors: Ladan Amini, Sophie Achard, Christian Jutten, Hamid Soltanian-zadeh, Gholam Ali Hossein-zadeh, Olivier David, Laurent VercueilAbstract:The aim of the work is to integrate the information modula- tion of the inter-relations between EEG scalp measurements of two brain states in a Connectivity Graph. We present a sparse differential connec- tivity Graph (SDCG) to distinguish the effectively modulated connections between epileptiform and non-epileptiform states of the brain from all the common connections created by noise, artifact, unwanted background ac- tivities and their related volume conduction effect. The proposed method is applied on real epileptic EEG data. Clustering the extracted features from SDCG may present valuable information about the epileptiform focus and their relations.
Jean-loup Guillaume - One of the best experts on this subject based on the ideXlab platform.
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Temporal Reachability Graphs
2012Co-Authors: John Whitbeck, Vania Conan, Marcelo Dias De Amorim, Jean-loup GuillaumeAbstract:While a natural fit for modeling and understanding mobile networks, time-varying Graphs remain poorly understood. Indeed, many of the usual concepts of static Graphs have no obvious counterpart in time-varying ones. In this paper, we introduce the notion of temporal reachability Graphs. A (τ, δ)-reachability Graph is a time-varying directed Graph derived from an existing Connectivity Graph. An edge exists from one node to another in the reachability Graph at time t if there exists a journey (i.e., a spatiotemporal path) in the Connectivity Graph from the first node to the second, leaving after t, with a positive edge traversal time τ , and arriving within a maximum delay δ. We make three contributions. First, we develop the theoretical framework around temporal reachability Graphs. Second, we harness our theoretical findings to propose an algorithm for their efficient computation. Finally, we demonstrate the analytic power of the temporal reachability Graph concept by applying it to synthetic and real-life datasets. On top of defining clear upper bounds on communication capabilities, reachability Graphs highlight asymmetric communication opportunities and offloading potential.
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Temporal Reachability Graphs
arXiv: Networking and Internet Architecture, 2012Co-Authors: John Whitbeck, Marcelo Dias De Amorim, Vania Conan, Jean-loup GuillaumeAbstract:While a natural fit for modeling and understanding mobile networks, time-varying Graphs remain poorly understood. Indeed, many of the usual concepts of static Graphs have no obvious counterpart in time-varying ones. In this paper, we introduce the notion of temporal reachability Graphs. A (tau,delta)-reachability Graph} is a time-varying directed Graph derived from an existing Connectivity Graph. An edge exists from one node to another in the reachability Graph at time t if there exists a journey (i.e., a spatiotemporal path) in the Connectivity Graph from the first node to the second, leaving after t, with a positive edge traversal time tau, and arriving within a maximum delay delta. We make three contributions. First, we develop the theoretical framework around temporal reachability Graphs. Second, we harness our theoretical findings to propose an algorithm for their efficient computation. Finally, we demonstrate the analytic power of the temporal reachability Graph concept by applying it to synthetic and real-life datasets. On top of defining clear upper bounds on communication capabilities, reachability Graphs highlight asymmetric communication opportunities and offloading potential.
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MobiCom - Temporal reachability Graphs
Proceedings of the 18th annual international conference on Mobile computing and networking - Mobicom '12, 2012Co-Authors: John Whitbeck, Marcelo Dias De Amorim, Vania Conan, Jean-loup GuillaumeAbstract:While a natural fit for modeling and understanding mobile networks, time-varying Graphs remain poorly understood. Indeed, many of the usual concepts of static Graphs have no obvious counterpart in time-varying ones. In this paper, we introduce the notion of temporal reachability Graphs. A (tau,delta)-reachability Graph is a time-varying directed Graph derived from an existing Connectivity Graph. An edge exists from one node to another in the reachability Graph at time t if there exists a journey (i.e., a spatiotemporal path) in the Connectivity Graph from the first node to the second, leaving after t, with a positive edge traversal time tau, and arriving within a maximum delay delta. We make three contributions. First, we develop the theoretical framework around temporal reachability Graphs. Second, we harness our theoretical findings to propose an algorithm for their efficient computation. Finally, we demonstrate the analytic power of the temporal reachability Graph concept by applying it to synthetic and real-life datasets. On top of defining clear upper bounds on communication capabilities, reachability Graphs highlight asymmetric communication opportunities and offloading potential.
Rohit Parasnis - One of the best experts on this subject based on the ideXlab platform.
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On the Convergence Properties of Social Hegselmann-Krause Dynamics
arXiv: Optimization and Control, 2019Co-Authors: Rohit Parasnis, Massimo Franceschetti, Behrouz TouriAbstract:We study the convergence properties of Social Hegselmann-Krause dynamics, a {variant} of the Hegselmann-Krause (HK) model of opinion dynamics where a physical Connectivity Graph that accounts for the extrinsic factors that could prevent interaction between certain pairs of agents is incorporated. As opposed to the original HK dynamics (which terminate in finite time), we show that for any underlying connected and incomplete Graph, under a certain mild assumption, the expected termination time of social HK dynamics is infinity. We then investigate the rate of convergence to the steady state, and provide bounds on the maximum $\epsilon$-convergence time in terms of the properties of the physical Connectivity Graph. We extend this discussion and observe that for almost all $n$, there exists an $n$-vertex physical Connectivity Graph on which social HK dynamics may not even $\epsilon$-converge to the steady state within a bounded time frame. We then provide nearly tight necessary and sufficient conditions for arbitrarily slow merging (a phenomenon that is essential for arbitrarily slow $\epsilon$-convergence to the steady state). Using the necessary conditions, we show that complete $r$-partite Graphs have bounded $\epsilon$-convergence times.
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CDC - On Graphs with Bounded and Unbounded Convergence Times in Social Hegselmann-Krause Dynamics
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Rohit Parasnis, Massimo Franceschetti, Behrouz TouriAbstract:We address the problem of identifying physical Connectivity Graphs that guarantee a finite upper bound on the time required for the associated social Hegselmann-Krause dynamics to ϵ-converge to the steady state. We handle the cases of consensus as well as non-consensus steady states, and for each case, we provide sufficient conditions for a physical Connectivity Graph to have unbounded ϵ-convergence time. We then show that every complete r-partite Graph on n vertices has a finite maximum ϵ-convergence time, regardless of the values of r and n. Finally, we show that enhancing the Connectivity of agents may not always speed up convergence to the steady state, even when the steady state is a consensus.
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CDC - Hegselmann-Krause Dynamics with Limited Connectivity
2018 IEEE Conference on Decision and Control (CDC), 2018Co-Authors: Rohit Parasnis, Massimo Franceschetti, Behrouz TouriAbstract:We investigate a variant of the Hegselmann-Krause model of opinion dynamics that relaxes the assumption that every agent has knowledge of every other agent's opinion at all points in time. This is done by incorporating a physical Connectivity Graph that accounts for the external factors that may prevent interaction between certain pairs of agents. As opposed to the original Hegselmann-Krause dynamics (which terminate in finite time), we show that for any underlying Graph that is connected but not complete, there exists an initial condition under which the dynamics never terminate. As a result, we show that for any continuous probability density function having the state space as its support, the expected termination time of the modified dynamics is infinity. We also study the rate of convergence to the steady state and derive bounds on the maximum convergence time in terms of the properties of the physical Connectivity Graph.
Eric L. Schwartz - One of the best experts on this subject based on the ideXlab platform.
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Space Variant Image Processing
International Journal of Computer Vision, 1994Co-Authors: Richard S. Wallace, Ping-wen Ong, Benjamin B. Bederson, Eric L. SchwartzAbstract:This paper describes a Graph-based approach to image processing, intended for use with images obtained from sensors having space variant sampling grids. The Connectivity Graph (CG) is presented as a fundamental framework for posing image operations in any kind of space variant sensor. Partially motivated by the observation that human vision is strongly space variant, a number of research groups have been experimenting with space variant sensors. Such systems cover wide solid angles yet maintain high acuity in their central regions. Implementation of space variant systems pose at least two outstanding problems. First, such a system must be active, in order to utilize its high acuity region; second, there are significant image processing problems introduced by the non-uniform pixel size, shape and Connectivity. Familiar image processing operations such as connected components, convolution, template matching, and even image translation, take on new and different forms when defined on space variant images. The present paper provides a general method for space variant image processing, based on a Connectivity Graph which represents the neighbor-relations in an arbitrarily structured sensor. We illustrate this approach with the following applications: (1) Connected components is reduced to its Graph theoretic counterpart. We illustrate this on a logmap sensor, which possesses a difficult topology due to the branch cut associated with the complex logarithm function. (2) We show how to write local image operators in the Connectivity Graph that are independent of the sensor geometry. (3) We relate the Connectivity Graph to pyramids over irregular tessalations, and implement a local binarization operator in a 2-level pyramid. (4) Finally, we expand the Connectivity Graph into a structure we call a transformation Graph, which represents the effects of geometric transformations in space variant image sensors. Using the transformation Graph, we define an efficient algorithm for matching in the logmap images and solve the template matching problem for space variant images. Because of the very small number of pixels typical of logarithmic structured space variant arrays, the Connectivity Graph approach to image processing is suitable for real-time implementation, and provides a generic solution to a wide range of image processing applications with space variant sensors.
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Connectivity Graphs for Space-variant Active Vision
Neural Networks in Robotics, 1993Co-Authors: Richard S. Wallace, Ping-wen Ong, Benjamin B. Bederson, Eric L. SchwartzAbstract:Space-variant sensors have nonuniform sampling across the image plane. Partially motivated by the observation that human vision is strongly space-variant, yielding an image compression for the human system that is estimated to be as much as four orders of magnitude, a number of research groups have been experimenting with space-variant sensors. Such systems cover wide solid angles yet maintain high acuity in their central regions. Implementation of space-variant systems pose at least two outstanding problems. First, such a system must be active, in order to utilize its high acuity region; second, there are fascinating image processing problems introduced by the non-uniform pixel size, shape and Connectivity. Familiar image processing operations such as connected components, convolution, template matching, and even image translation, take on new and different forms when defined on space-variant arrays. The present paper provides a general method for space-variant image processing, based on a Connectivity Graph which represents the neighbor-relations in an arbitrarily structured sensor. We illustrate this approach with the following applications: Connected components is reduced to ils Graph theoretic counterpart. We illustrate this on a logmap sensor, which possesses a difficult topology due to the branch cut associated with the complex logarithm function We show how to write local image operators in the connec-tivity Graph that are independent of the sensor geometry. We relate the Connectivity Graph to pyramids over irregular tessalations, and implement a local binarization operator in a 2-level pyramid Finally, we expand the Connectivity Graph into a structure we call a translation Graph, representing the effects of translation in space-variant image sensors. Using the translation Graph, we define an efficient algorithm for translation in the logmap image and solve the template matching problem for space-variant images