The Experts below are selected from a list of 117 Experts worldwide ranked by ideXlab platform
Radu Precup - One of the best experts on this subject based on the ideXlab platform.
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a Vector Version of the fixed point theorem of cone compression and expansion for a sum of two operators
Nonlinear Studies, 2020Co-Authors: Lyna Benzenati, Karima Mebarki, Radu PrecupAbstract:In this work, we establish a Vector Version of fixed point theorem of cone compression and expansion for an expansive operator with constant h>1 perturbed by a k-set contraction when 0\leq k
nonlinear term of a system to have different behaviors both in components and in variables. An example is given to illustrate our theoretical result. -
positive solutions for discontinuous systems via a multivalued Vector Version of krasnosel skiĭ s fixed point theorem in cones
Mathematics, 2019Co-Authors: Rodrigo Lopez Pouso, Radu Precup, Jorge RodriguezlopezAbstract:We establish the existence of positive solutions for systems of second–order differential equations with discontinuous nonlinear terms. To this aim, we give a multivalued Vector Version of Krasnosel’skiĭ’s fixed point theorem in cones which we apply to a regularization of the discontinuous integral operator associated to the differential system. We include several examples to illustrate our theory.
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fourth order p laplacian nonlinear systems via the Vector Version of krasnosel skiĭ s fixed point theorem
Mediterranean Journal of Mathematics, 2009Co-Authors: Smail Djebali, Toufik Moussaoui, Radu PrecupAbstract:In this paper, existence results for a fourth-order nonlinear system are obtained. Both classical and Vector Versions of the Krasnosel’skiĭ’s fixed point theorem are used and a comparison of the obtained results to those from the literature is provided.
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the role of matrices that are convergent to zero in the study of semilinear operator systems
Mathematical and Computer Modelling, 2009Co-Authors: Radu PrecupAbstract:In this paper we explain the advantage of Vector-valued norms and the role of matrices that are convergent to zero in the study of semilinear operator systems by means of some basic methods of nonlinear analysis: the contraction principle, Schauder's fixed point theorem, the Leray-Schauder continuation principle and Krasnoselskii's cone fixed point theorem. A Vector Version of Krasnoselskii's theorem is also established.
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a Vector Version of krasnosel skiĭ s fixed point theorem in cones and positive periodic solutions of nonlinear systems
Journal of Fixed Point Theory and Applications, 2007Co-Authors: Radu PrecupAbstract:A new Version of Krasnosel’skiĭ’s fixed point theorem in cones is established for systems of operator equations, where the compression-expansion conditions are expressed on components. In applications, this allows the nonlinear term of a system to have different behaviors both in components and in variables.
Bhaskar D Rao - One of the best experts on this subject based on the ideXlab platform.
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analysis of multiple antenna systems with finite rate feedback using high resolution quantization theory
IEEE Transactions on Signal Processing, 2007Co-Authors: Jun Zheng, Ethan Robert Duni, Bhaskar D RaoAbstract:This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple-antenna systems with finite-rate feedback. Inspired by the results of classical high-resolution quantization theory, the problem of finite-rate quantized communication system is formulated as a general fixed-rate Vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean-squared distortion functions and constrained source Vectors. Asymptotic distortion analysis of the proposed general quantization problem is provided by extending the Vector Version of the Bennett's integral. Specifically, tight lower and upper bounds of the average asymptotic distortion are proposed. Sufficient conditions for the achievability of the distortion bounds are also provided and related to corresponding classical fixed-rate quantization problems. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, we consider the analysis of a finite-rate feedback multiple-input single-output (MISO) beamforming system over independent and identically distributed (i.i.d.) Rayleigh flat-fading channels. Numerical and simulation results are presented that further confirm the accuracy of the analytical results
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analysis of multiple antenna systems with finite rate feedback using high resolution quantization theory
Data Compression Conference, 2006Co-Authors: Jun Zheng, Ethan Robert Duni, Bhaskar D RaoAbstract:This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple antenna systems with finite-rate feedback. Inspired by the results of classical high resolution quantization theory, the problem of a finite-rate quantized communication system is formulated as a general fixed-rate Vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean square distortion functions, and constrained source Vectors. The result of the asymptotic distortion analysis of the proposed general quantization problem is presented, which extends the Vector Version of Bennett's integral. Specifically, tight lower and upper bounds on the average asymptotic distortion are proposed. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, the analysis of a finite-rate feedback MISO beamforming system over i.i.d. Rayleigh flat fading channels is derived. Numerical and simulation results are presented to further confirm the accuracy of the analytical results.
Gomes, Jeremias Moreira - One of the best experts on this subject based on the ideXlab platform.
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Execução eficiente do padrão de propagação de ondas irregulares na arquitetura Many Integrated Core
'Biblioteca Central da UNB', 2016Co-Authors: Gomes, Jeremias MoreiraAbstract:Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, Programa de Pós-Graducação em Informática, 2016.A execução eficiente de algoritmos de processamento de imagens é uma área ativa da Bioinformática. Uma das classes de algoritmos em processamento de imagens ou de padrão de computação comum nessa área é a Irregular Wavefront Propagation Pattern (IWPP). Nessa classe, elementos propagam informações para seus vizinhos em forma de ondas de propagação. Esse padrão de propagação resulta em acessos a dados e expansões irregulares. Por essa característica irregular, implementações paralelas atuais dessa classe de algoritmos necessitam de operações atômicas, o que acaba sendo muito custoso e também inviabiliza a implementação por meio de instruções Single Instruction, Multiple Data (SIMD) na arquitetura Many Integrated Core (MIC), que são fundamentais para atingir alto desempenho nessa arquitetura. O objetivo deste trabalho é reprojetar o algoritmo Irregular Wavefront Propagation Pattern, de forma a possibilitar sua eficiente execução em processadores com arquitetura Many Integrated Core que utilizem instruções SIMD. Neste trabalho, utilizando o Intel® Xeon Phi™, foram implementadas uma versão vetorizada, apresentando ganhos de até 5:63 em relação à versão não-vetorizada; uma versão paralela utilizando fila First In, First Out (FIFO) cuja escalabilidade demonstrou-se boa com speedups em torno de 55 em relação à um núcleo do coprocessador; uma versão utilizando fila de prioridades cuja velocidade foi de 1:62 mais veloz que a versão mais rápida em GPU conhecida na literatura, e uma versão cooperativa entre processadores heterogêneos que permitem processar imagens que ultrapassem a capacidade de memória do Intel® Xeon Phi™, e também possibilita a utilização de múltiplos dispositivos na execução do algoritmo.The efficient execution of image processing algorithms is an active area of Bioinformatics. In image processing, one of the classes of algorithms or computing pattern that works with irregular data structures is the Irregular Wavefront Propagation Pattern (IWPP). In this class, elements propagate information to neighbors in the form of wave propagation. This propagation results in irregular access to data and expansions. Due to this irregularity, current implementations of this class of algorithms requires atomic operations, which is very costly and also restrains implementations with Single Instruction, Multiple Data (SIMD) instructions in Many Integrated Core (MIC) architectures, which are critical to attain high performance on this processor. The objective of this study is to redesign the Irregular Wavefront Propagation Pattern algorithm in order to enable the efficient execution on processors with Many Integrated Core architecture using SIMD instructions. In this work, using the Intel® Xeon Phi™ coprocessor, we have implemented a Vector Version of IWPP with up to 5:63 gains on non-Vectored Version, a parallel Version using First In, First Out (FIFO) queue that attained speedup up to 55 as compared to the single core Version on the coprocessor, a Version using priority queue whose performance was 1:62 better than the fastest Version of GPU based implementation available in the literature, and a cooperative Version between heterogeneous processors that allow to process images bigger than the Intel® Xeon Phi™ memory and also provides a way to utilize all the available devices in the computation
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Execução eficiente do padrão de propagação de ondas irregulares na arquitetura Many Integrated Core
2016Co-Authors: Gomes, Jeremias MoreiraAbstract:A execução eficiente de algoritmos de processamento de imagens é uma área ativa da Bioinformática. Uma das classes de algoritmos em processamento de imagens ou de padrão de computação comum nessa área é a Irregular Wavefront Propagation Pattern (IWPP). Nessa classe, elementos propagam informações para seus vizinhos em forma de ondas de propagação. Esse padrão de propagação resulta em acessos a dados e expansões irregulares. Por essa característica irregular, implementações paralelas atuais dessa classe de algoritmos necessitam de operações atômicas, o que acaba sendo muito custoso e também inviabiliza a implementação por meio de instruções Single Instruction, Multiple Data (SIMD) na arquitetura Many Integrated Core (MIC), que são fundamentais para atingir alto desempenho nessa arquitetura. O objetivo deste trabalho é reprojetar o algoritmo Irregular Wavefront Propagation Pattern, de forma a possibilitar sua eficiente execução em processadores com arquitetura Many Integrated Core que utilizem instruções SIMD. Neste trabalho, utilizando o Intel® Xeon Phi™, foram implementadas uma versão vetorizada, apresentando ganhos de até 5:63 em relação à versão não-vetorizada; uma versão paralela utilizando fila First In, First Out (FIFO) cuja escalabilidade demonstrou-se boa com speedups em torno de 55 em relação à um núcleo do coprocessador; uma versão utilizando fila de prioridades cuja velocidade foi de 1:62 mais veloz que a versão mais rápida em GPU conhecida na literatura, e uma versão cooperativa entre processadores heterogêneos que permitem processar imagens que ultrapassem a capacidade de memória do Intel® Xeon Phi™, e também possibilita a utilização de múltiplos dispositivos na execução do algoritmo. ________________________________________________________________________________________________ ABSTRACTThe efficient execution of image processing algorithms is an active area of Bioinformatics. In image processing, one of the classes of algorithms or computing pattern that works with irregular data structures is the Irregular Wavefront Propagation Pattern (IWPP). In this class, elements propagate information to neighbors in the form of wave propagation. This propagation results in irregular access to data and expansions. Due to this irregularity, current implementations of this class of algorithms requires atomic operations, which is very costly and also restrains implementations with Single Instruction, Multiple Data (SIMD) instructions in Many Integrated Core (MIC) architectures, which are critical to attain high performance on this processor. The objective of this study is to redesign the Irregular Wavefront Propagation Pattern algorithm in order to enable the efficient execution on processors with Many Integrated Core architecture using SIMD instructions. In this work, using the Intel® Xeon Phi™ coprocessor, we have implemented a Vector Version of IWPP with up to 5:63 gains on non-Vectored Version, a parallel Version using First In, First Out (FIFO) queue that attained speedup up to 55 as compared to the single core Version on the coprocessor, a Version using priority queue whose performance was 1:62 better than the fastest Version of GPU based implementation available in the literature, and a cooperative Version between heterogeneous processors that allow to process images bigger than the Intel® Xeon Phi™ memory and also provides a way to utilize all the available devices in the computation
Anant Sahai - One of the best experts on this subject based on the ideXlab platform.
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1Information Embedding meets Distributed Control
2016Co-Authors: Pulkit Grover, Aaron B. Wagner, Anant SahaiAbstract:We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode the message, and the decoder recovers both the embedded message and the modified host signal. This extends the recent work of Sumszyk and Steinberg to the continuous-alphabet Gaussian setting. We show that a dirty-paper-coding based strategy achieves the optimal rate for perfect recovery of the modified host and the message. We also provide bounds for the extension wherein the modified host signal is recovered only to within a specified distortion. When specialized to the zero-rate case, our results provide the tightest known lower bounds on the asymptotic costs for the Vector Version of a famous open problem in distributed control — the Witsenhausen counterexample. Using this bound, we characterize the asymptotically optimal costs for the Vector Witsenhausen problem numerically to within a factor of 1.3 for all problem parameters, improving on the earlier best known bound of 2. I
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approximately optimal solutions to the finite dimensional witsenhausen counterexample
IEEE Transactions on Automatic Control, 2013Co-Authors: Pulkit Grover, Seyong Park, Anant SahaiAbstract:Recently, a Vector Version of Witsenhausen's counterexample was considered and it was shown that in the asymptotic limit of infinite Vector length, certain Vector-quantization-based control strategies are provably within a constant factor of the asymptotically optimal cost for all possible problem parameters. While suggestive, a constant factor result for the finite-dimensional problem has remained elusive. In this paper, we provide a resolution to this issue. By applying a large-deviation “sphere-packing” philosophy, we derive a lower bound to the optimal cost for the finite dimensional case that uses appropriate shadows of an existing Vector lower bound that is the same for all dimensions. Using this new lower bound, we show that good lattice-quantization-based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the Vector length. For Witsenhausen's original problem-which is the scalar case-the gap between regular lattice-quantization-based strategies and the lower bound is provably never more than a factor of 100, and computer calculations strongly suggest that the factor in fact may be no larger than 8. Finally, to obtain a numerical understanding of the possible room for improvement in costs using alternative strategies, we also include numerical comparison with strategies that are conjectured to be optimal. Using this comparison, we posit that there is more room for improvement in our lower bounds than in our upper bounds.
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the finite dimensional witsenhausen counterexample
arXiv: Information Theory, 2010Co-Authors: Pulkit Grover, Seyong Park, Anant SahaiAbstract:Recently, a Vector Version of Witsenhausen's counterexample was considered and it was shown that in that limit of infinite Vector length, certain quantization-based control strategies are provably within a constant factor of the optimal cost for all possible problem parameters. In this paper, finite Vector lengths are considered with the dimension being viewed as an additional problem parameter. By applying a large-deviation "sphere-packing" philosophy, a lower bound to the optimal cost for the finite dimensional case is derived that uses appropriate shadows of the infinite-length bound. Using the new lower bound, we show that good lattice-based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the Vector length. For Witsenhausen's original problem -- the scalar case -- the gap between regular lattice-based strategies and the lower bound is numerically never more than a factor of 8.
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a Vector Version of witsenhausen s counterexample a convergence of control communication and computation
Conference on Decision and Control, 2008Co-Authors: Pulkit Grover, Anant SahaiAbstract:We argue that Witsenhausen's counterexample provides a useful conceptual bridge between distributed control, communication and computation. Inspired by the utility of studying long block-lengths in information theory, we formulate a Vector Version of the counterexample. Information-theoretic arguments are then used to derive bounds on the minimum cost for the Vector problem. Restricted to the scalar case, the lower bounds are a strict improvement over Witsenhausen's lower bound for some parameter values. The upper bounds are based on two strategies that can asymptotically outperform optimal linear and nonlinear scalar strategies. To investigate the computational aspects of such problems, we then consider a simpler problem of lossless source coding. From a distributed control perspective, the computations required for encoding and decoding can be viewed as internal communication between virtually distributed agents. We derive new lower bounds that establish a tradeoff between the computation, communication and distortion costs for lossless source coding.
Jun Zheng - One of the best experts on this subject based on the ideXlab platform.
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analysis of multiple antenna systems with finite rate feedback using high resolution quantization theory
IEEE Transactions on Signal Processing, 2007Co-Authors: Jun Zheng, Ethan Robert Duni, Bhaskar D RaoAbstract:This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple-antenna systems with finite-rate feedback. Inspired by the results of classical high-resolution quantization theory, the problem of finite-rate quantized communication system is formulated as a general fixed-rate Vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean-squared distortion functions and constrained source Vectors. Asymptotic distortion analysis of the proposed general quantization problem is provided by extending the Vector Version of the Bennett's integral. Specifically, tight lower and upper bounds of the average asymptotic distortion are proposed. Sufficient conditions for the achievability of the distortion bounds are also provided and related to corresponding classical fixed-rate quantization problems. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, we consider the analysis of a finite-rate feedback multiple-input single-output (MISO) beamforming system over independent and identically distributed (i.i.d.) Rayleigh flat-fading channels. Numerical and simulation results are presented that further confirm the accuracy of the analytical results
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analysis of multiple antenna systems with finite rate feedback using high resolution quantization theory
Data Compression Conference, 2006Co-Authors: Jun Zheng, Ethan Robert Duni, Bhaskar D RaoAbstract:This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple antenna systems with finite-rate feedback. Inspired by the results of classical high resolution quantization theory, the problem of a finite-rate quantized communication system is formulated as a general fixed-rate Vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean square distortion functions, and constrained source Vectors. The result of the asymptotic distortion analysis of the proposed general quantization problem is presented, which extends the Vector Version of Bennett's integral. Specifically, tight lower and upper bounds on the average asymptotic distortion are proposed. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, the analysis of a finite-rate feedback MISO beamforming system over i.i.d. Rayleigh flat fading channels is derived. Numerical and simulation results are presented to further confirm the accuracy of the analytical results.
