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Limiting spectral distribution of a symmetrized auto-cross covariance matrix

Annals of applied Probability 2014年第3期24卷 1199-1225页

作者： Jin, Baisuo Wang, Chen Bai, Z.D. Nair, Krishnan Harding, Matthew University of Science and Technology of China National University of Singapore Northeast Normal University and National University of Singapore China Department of Statistics and Finance University of Science and Technology of China Hefei 96 Jinzhai Road China Department of Statistics and Applied Probability National University of Singapore Singapore Klasmoe and School of Math. and Stat Northeast Normal University Changchun 5268 Renmin Street China Department of Civil and Environmental Engineering Stanford University Stanford CA94305 439 Panama Mall United States Department of Economics Stanford University StanfordCA94305 579 Serra Mall United States

This paper studies the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix. The auto-cross covariance matrix is defined as Mτ= 1/2T ∑Tj =1(eje*j+τ +ej+τe*j), where ej is an N dimensi...

This paper studies the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix. The auto-cross covariance matrix is defined as M_τ= 1/2T ∑^T_j ₌₁(e_je^*_j+τ ⁺e_j+τe^*_j), where ej is an N dimensional vectors of independent standard complex components with properties stated in Theorem 1.1, and τ is the lag. M0 is well studied in the literature whose LSD is theMarčenko-Pastur (MP) Law. The contribution of this paper is in determining the LSD of M_τ where τ ≥ 1. It should be noted that the LSD of the M_τ does not depend on τ . This study arose from the investigation of and plays an key role in the model selection of any large dimensional model with a lagged time series structure, which is central to large dimensional factor models and singular spectrum analysis. ©Institute of math.matical Statistics, 2014.

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Calculation of ℌ∞-optimal actuator location for distributed parameter systems

Calculation of ℌ∞-optimal actuator location for distribute...

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American Control Conference (ACC)

作者： Dhanaraja Kasinathan Kirsten Morris Steven Yang Department of Mechl & Mechatronics Engineering (DK) Department of Applied Math. (KM) Department of Elecectrical& Computer Engineering (SY) University of Waterloo Waterloo ONT Canada

In control of distributed parameter systems, there is usually freedom on where to place the actuators. The actuator location should be chosen to optimize the performance objectives and regarded as part of the controller design. In this paper, H ∞ -performance with full information is considered. An algorithm to solve the problem is described and the optimal actuator locations are calculated for several examples.

关键词： Actuators Attenuation Approximation methods Riccati equations math.matical model Distributed parameter systems Cost function

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The δ- sensitivity and its application to stochastic optimal control of nonlinear diffusions.

The δ- sensitivity and its application to stochastic optima...

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American Control Conference

作者： Evangelos A. Theodorou Emo Todorov the Department of Computer Science and Engineering University of Washington Seattle. Departments of Computer Science and Engineering and Applied Math University of Washington

ISBN: (纸本)9781479901777

We provide optimal control laws by using tools from stochastic calculus of variations and the math.matical concept of δ-sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ-sensitivity of the logarithmic transformation of the value function for the case of nonlinear diffusion processes affine in control and noise.

关键词： nonlinear diffusions PDEs value functions

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PCPs via Low-Degree Long Code and Hardness for Constrained Hypergraph Coloring

PCPs via Low-Degree Long Code and Hardness for Constrained H...

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Annual IEEE Symposium on Foundations of computer science

作者： Irit Dinur Venkatesan Guruswami Dept. of Applied Math and Computer Science The Weizmann Institute of Science Rehovot Israel Computer Science Department Carnegie Mellon University Pittsburgh USA

We develop new techniques to incorporate the recently proposed “short code” (a low-degree version of the long code) into the construction and analysis of PCPs in the classical “Label Cover + Fourier Analysis” framework. As a result, we obtain more size-efficient PCPs that yield improved hardness results for approximating CSPs and certain coloringtype problems. In particular, we show a hardness for a variant of hypergraph coloring (with hyperedges of size 6), with a gap between 2 and exp(2 Ω (√log log N)) number of colors where N is the number of vertices. This is the first hardness result to go beyond the O(log N) barrier for a coloring-type problem. Our hardness bound is a doubly exponential improvement over the previously known O(log log N)-coloring hardness for 2-colorable hypergraphs, and an exponential improvement over the (logN) Ω(1) -coloring hardness for O(1)-colorable hypergraphs. Stated in terms of “covering complexity,” we show that for 6-ary Boolean CSPs, it is hard to decide if a given instance is perfectly satisfiable or if it requires more than 2Ω(√log log N) assignments for covering all of the constraints. While our methods do not yield a result for conventional hypergraph coloring due to some technical reasons, we also prove hardness of (log N) Ω(1) -coloring 2-colorable 6-uniform hypergraphs (this result relies just on the long code). A key algebraic result driving our analysis concerns a very low-soundness error testing method for Reed-Muller codes. We prove that if a function β : F 2 m → F 2 is 2 Ω(d) far in absolute distance from polynomials of degree m-d, then the probability that deg(βg) ≤ m-3d/4 for a random degree d/4 polynomial g is doubly exponentially small in d.

关键词： Frequency modulation Polynomials Color Testing Approximation methods Noise computer science

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Multi-Robot Active SLAM with Relative Entropy Optimization

Multi-Robot Active SLAM with Relative Entropy Optimization

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American Control Conference

作者： Michail Kontitsis Evangelos A. Theodorou Emanuel Todorov Department of Electrical Engineering University of Denver Colorado Department of Computer Science and Engineering University of Washington Seattle Department of Computer Science and Engineering and the Applied Math Department University of Washington Seattle

ISBN: (纸本)9781479901777

This paper presents a new approach for Active Simultaneous Localization and Mapping that uses the Relative Entropy (RE) optimization method to select trajectories which minimize both the localization error and the corresponding uncertainty bounds. To that end we construct a planning cost function which includes, besides the state and control cost, a term that encapsulates the uncertainty of the state. This term is the trace of the state covariance matrix produced by the estimator, in this case an Extended Kalman Filter. The role of the RE method is to iteratively guide the selection of the trajectories towards the ones minimizing the aforementioned cost. Once the method has converged, the result is a near-optimal path in terms of achieving the pre-defined goal in the state space while also improving the localization error and the total uncertainty. In essence the method integrates motion planning with robot localization. To evaluate the approach we consider scenarios with single and multiple robots navigating in presence of obstacles and various conditions of landmark densities. The results show a behavior consistent with our expectations.

关键词： Relative Entropy Optimization SLAM RE

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Free energy based policy gradients

Free energy based policy gradients

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IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning, (ADPRL)

作者： Evangelos A. Theodorou Jiri Najemnik Emo Todorov Department of Computer Science and Engineering University of Washington Seattle University of Washington Seattle Departments of Computer Science and Engineering and Applied Math University of Washington Seattle

Despite the plethora of reinforcement learning algorithms in machine learning and control, the majority of the work in this area relies on discrete time formulations of stochastic dynamics. In this work we present a new policy gradient algorithm for reinforcement learning in continuous state action spaces and continuous time for free energy-like cost functions. The derivation is based on successive application of Girsanov's theorem and the use of the Radon Nikodým derivative as formulated for Markov diffusion processes. The resulting policy gradient is reward weighted. The use of Radon Nikodým extends analysis and results to more general models of stochasticity in which jump diffusions processes are considered. We apply the resulting algorithm in two simple examples for learning attractor landscapes in rhythmic and discrete movements.

关键词： Learning (artificial intelligence) Diffusion processes Markov processes Cost function Equations Heuristic algorithms

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Time Varying Nonlinear Policy Gradients

Time Varying Nonlinear Policy Gradients

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IEEE Annual Conference on Decision and Control

作者： Evangelos A. Theodorou Krishnamurthy Dvijotham Emo Todorov School of Aerospace Engineering Georgia Institute of Technology Atlanta Department of Computer Science and Engineering University of Washington Seattle Departments of Computer Science and Engineering and Applied Math University of Washington Seattle

ISBN: (纸本)9781467357159

We derive Policy Gradients(PGs) with time varying parameterizations for nonlinear diffusion processes affine in noise. The resulting policies have the form of reward weighted gradient. The analysis is in continuous time and includes the case of linear and nonlinear parameterizations. Examples on stochastic control problems for diffusions processes are provided.

关键词： Trajectory Linear programming Noise Diffusion processes Aerodynamics Educational institutions Equations

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On the Sum of Squared η-μ Random Variates With Application to the Performance of Wireless Communication Systems

On the Sum of Squared η-μ Random Variates With Application...

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IEEE Vehicular Technology Conference

作者： Imran Shafique Ansari Ferkan Yilmaz Mohamed-Slim Alouini Computer Electrical and Mathematical Sciences and Engineering (CEMSE) Division at King Abdullah University of Science and Technology (KAUST) Al-Khawarizmi Applied Math. Building (Bldg. #1) Thuwal 23955-6900 Makkah Province Kingdom of Saudi Arabia

ISBN: (纸本)9781467363365

The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed squared η-μ variates, applicable to the output statistics of maximal ratio combining (MRC) receiver operating over η-μ fading channels that includes the Hoyt and the Nakagami-m models as special cases, is presented in closed-form in terms of the Fox's H function. Further analysis, particularly on the bit error rate via PDF-based approach, is also represented in closed form in terms of the extended Fox's H function (H). The proposed new analytical results complement previous results and are illustrated by extensive numerical and Monte Carlo simulation results.

关键词： η-μ variates cellular mobile radio systems non-integer parameters diversity maximal ratio combining binary modulation schemes bit error rate Fox's H function Meijer's G function and extended Fox's H function Bit error rate diversity reception Wireless communication systems Mobile radio systems closed forms sums Cumulative distribution function Hydrogen

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pVOCL: Power-Aware Dynamic Placement and Migration in Virtualized GPU Environments

pVOCL: Power-Aware Dynamic Placement and Migration in Virtua...

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International Conference on Distributed Computing Systems

作者： Palden Lama Yan Li Ashwin M. Aji Pavan Balaji James Dinan Shucai Xiao Yunquan Zhang Wu-chun Feng Rajeev Thakur Xiaobo Zhou Department of Computer Science University of Colorado Colorado Springs USA Math. and Comp. Sci. Div. Argonne National Laboratory USA Institute of Software Chinese Academy of Sciences China Department of Computer Science Virginia Tech USA Advanced Micro Devices USA

Power-hungry Graphics processing unit (GPU) accelerators are ubiquitous in high performance computing data centers today. GPU virtualization frameworks introduce new opportunities for effective management of GPU resources by decoupling them from application execution. However, power management of GPU-enabled server clusters faces significant challenges. The underlying system infrastructure shows complex power consumption characteristics depending on the placement of GPU workloads across various compute nodes, power-phases and cabinets in a datacenter. GPU resources need to be scheduled dynamically in the face of time-varying resource demand and peak power constraints. We propose and develop a power-aware virtual OpenCL (pVOCL) framework that controls the peak power consumption and improves the energy efficiency of the underlying server system through dynamic consolidation and power-phase topology aware placement of GPU workloads. Experimental results show that pVOCL achieves significant energy savings compared to existing power management techniques for GPU-enabled server clusters, while incurring negligible impact on performance. It drives the system towards energy-efficient configurations by taking an optimal sequence of adaptation actions in a virtualized GPU environment and meanwhile keeps the power consumption below the peak power budget.

关键词： Graphics processing units Power demand Topology Kernel Servers Monitoring Power measurement

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Using Ontology Patterns for Building a Reference Software Testing Ontology

Using Ontology Patterns for Building a Reference Software Te...

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International Workshop on Enterprise Distributed Object Computing, EDOCW

作者： E.F. Souza R.A. Falbo N.L. Vijaykumar Applied Computing National Institute for Space Research INPE São José dos Campos SP Brazil Department of Computer Science Federal University of Espírito Santo UFES Vitória ES Brazil Lab. of Comp. and Applied Math. National Institute for Space Research INPE São José dos Campos SP Brazil

Software testing is a critical process for achieving product quality. Its importance is more and more recognized, and there is a growing concern in improving the accomplishment of this process. In this context, Knowledge Management emerges as an important supporting tool. However, managing relevant knowledge to reuse is difficult and it requires some means to represent and to associate semantics to a large volume of test information. In order to address this problem, we have developed a Reference Ontology on Software Testing (ROost). ROost is built reusing ontology patterns from the Software Process Ontology Pattern Language (SP-OPL). In this paper, we discuss how ROost was developed, and present a fragment of Roost that concerns with software testing process, its activities, artifacts, and procedures.

关键词： Ontologies Software testing Unified modeling language Software Standards Context

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