Improved error bound for multivariate Chebyshev polynomial interpolation

ABSTRACT

Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties which provides tremendous application potential in mathematical finance. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, a sharp error bound is essential, in particular for high-dimensional applications. For tensorized Chebyshev interpolation, we present an error bound that improves existing results significantly.     

On the coexistence of a primary user with an energy harvesting secondary user: a case of cognitive cooperation

In this paper, we consider a cognitive scenario where an energy harvesting secondary user shares the spectrum with a primary user. The secondary source helps the primary source in delivering its undelivered packets during periods of silence of the primary source. The primary source has a queue for storing its data packets, whereas the secondary source has two data queues: a queue for storing its own packets and the other for storing the fraction of the undelivered primary packets accepted for relaying. The secondary source is assumed to be a battery‐based node, which harvests energy packets from the environment. In addition to its data queues, the secondary user has an energy queue to store the harvested energy packets. The secondary energy packets are used for primary packets decoding and data packets transmission. More specifically, if the secondary energy queue is empty, the secondary source can neither help the primary source nor transmit a packet from the data queues. The energy queue is modeled as a discrete‐time queue with Markov arrival and service processes. Because of the interaction of the queues, we provide inner and outer bounds on the stability region of the proposed system. We investigate the impact of the energy arrival rate on the stability region. Numerical results show the significant gain of cooperation.Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of capacity and coverage region for Rayleigh fading MIMO relay channel

In this paper, we consider Rayleigh fading MIMO relay channel with channel state information at the receivers. First, we extend the previously obtained results for the ergodic capacity of uncorrelated and semi‐correlated MIMO channels and derive closed‐form expressions for the capacity bounds of MIMO relay channel. Next, we study this channel from a new point of view, maximizing coverage region for a desired transmission rate, and investigate the optimal relay location in the sense of maximizing coverage region. However, in order to overcome the mathematical complexity in desired transmission rate analysis, because of the randomness of the multiple antenna channel matrices, we evaluate this rate by using an existing exact formula and also by an approximation we find in the high signal‐to‐noise ratio regime. Numerical results show a perfect match between the Monte Carlo simulations and the obtained analytical closed‐form expressions and also confirm the effectiveness of our approach in cooperative vehicular communication for determining optimal relay location at which the coverage region is maximum. Copyright © 2013 John Wiley & Sons, Ltd.     

Recovery error bounds on compressed sensing of noisy signals

Compressed sensing is an emerging technique in the field of digital signal acquisition. It promises almost exact recovery of high‐dimensional signals from a very small set of measurements. However, this technique is challenged by the task of recovering signals immersed in noise. In this paper, we derive upper and lower bounds on mean squared recovery error of noisy signals. These bounds are valid for any number of acquired measurements and at any signal‐to‐noise ratio. This work is highly useful for the design of any compressed sensing‐based real world application by quantifying recovery error entailed with realistic digital signal acquisition scenarios. Copyright © 2013 John Wiley & Sons, Ltd.     

A comprehensive study on thermal conductivity of the lithium-ion battery

The reliable thermal conductivity of lithium-ion battery is significant for the accurate prediction of battery thermal characteristics during the charging/discharging process. Both isotropic and anisotropic thermal conductivities are commonly employed while exploring battery thermal characteristics. However, the study on the difference between the use of two thermal conductivities is relatively scarce. In this study, the isotropic and anisotropic thermal conductivities of the four commercially available lithium-ion batteries, ie, LiCoO₂, LiMn₂O₄, LiFePO₄, and Li (NiCoMn)O₂, were reviewed and evaluated numerically through the heat conduction characteristics inside the battery. The results showed that there are significant differences in the temperature distribution in the battery caused by the isotropic and anisotropic thermal conductivities, which could affect the layout and cooling effectiveness of battery thermal management system. Furthermore, the effective thermal conductivities of porous electrodes and separator were determined to establish thermal conductivity bounds of lithium-ion batteries combined with the thicknesses of battery components. The thermal conductivity bounds could be applied to evaluate the rationality of the thermal conductivity data used in battery thermal models.     

Complete convergence of stochastic approximation algorithm in ℝd under random noises

In this article, we study a stochastic approximation algorithm that approximates the exact root θ of a function M defined in ?^d into ?^d. The function M cannot be known exactly, but only noisy measurements are available at each point x_n with the error ξ_n. The sequence of noise (_ξn)n is random; we treat both cases where it is independent and dependent and we establish the complete convergence of the approximated sequence of θ.     

耦合非线性波动方程爆破时间的下确界

考虑带有阻尼和源项的非线性耦合波动方程,为了获得波动方程爆破时间的下确界,在有限时间爆破的结果下,选择适当辅助函数G(t),利用Cauchy不等式和能量初值E(0)的估计得到有关G(t)和G′(t)的微分不等式,并最终通过对时间积分进而得到非线性耦合波动方程爆破时间的下确界.     

Nonequidistant modified predictor-corrector methods for solving systems of differential equations

This paper shows that it is possible to develop nonequidistant predictor-corrector formulae with minimum error bounds for solving systems of differential equations such that the tedious difficulties which arise in practical applications can be overcome. General predictor-corrector formulae with variable steps are constructed. Explicit third order- and fourth order-two points formulae are derived. Also fourth order-three points formulae are represented. Two theorems are given. A flow chart for general nonequidistant predictor-corrector methods using automatic control for the step length is compactly represented for solving systems of differential equations. These methods are recommended to be used widely in practice because of many advantages.     

On problems without polynomial kernels

Kernelization is a strong and widely-applied technique in parameterized complexity. A kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any given parameterized instance to an equivalent instance of the same problem, with size and parameter bounded by a function of the parameter in the input. A kernel is polynomial if the size and parameter of the output are polynomially-bounded by the parameter of the input.In this paper we develop a framework which allows showing that a wide range of FPT problems do not have polynomial kernels. Our evidence relies on hypothesis made in the classical world (i.e. non-parametric complexity), and revolves around a new type of algorithm for classical decision problems, called a distillation algorithm, which is of independent interest. Using the notion of distillation algorithms, we develop a generic lower-bound engine that allows us to show that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomial hierarchy collapses. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth and other structural parameters.