Entropy gain and the Choi-Jamiolkowski correspondence for infinite-dimensional quantum evolutions

We consider the entropy gain for infinite-dimensional evolutions and show that unlike in the finitedimensional case, there are many channels with positive minimal entropy gain. We obtain a new lower bound and compute the minimal entropy gain for a broad class of bosonic Gaussian channels. We mathematically formulate the Choi-Jamiolkowski (CJ) correspondence between channels and states in the infinite-dimensional case in a form close to the form used in quantum information theory. In particular, we obtain an explicit expression for the CJ operator defining a general nondegenerate bosonic Gaussian channel and compute its norm.     

Measurement of time-varying multiple-input multiple-output channels

We derive a criterion on the measurability/identifiability of multiple-input multiple-output (MIMO) channels based on the size of the so-called spreading support of its subchannels. Novel MIMO transmission techniques provide high-capacity communication channels in time-varying environments and exact knowledge of the transmission channel operator is of key importance when trying to transmit information at a rate close to channel capacity.     

汇率的就业传导渠道及其效应测算——基于中国制造业面板数据的实证研究

文章研究了汇率的就业传导渠道,及其行业异质性。本文基于传统的生产函数理论,通过建模和理论分析得出:汇率影响就业的传导渠道主要有出口需求、资源配置和效率的三渠道。并基于中国制造业30个行业的2003年至2009年的面板数据,运用残差替代法和面板平滑机制转换回归,测算出各传导渠道在汇率影响就业过程中所起到的作用,结果表明:在整个传导机制中,出口需求对就业的作用较强,效率渠道和资源配置作用相对较弱;人民币升值对就业的总体效应为负效应,且传导机制中各渠道均具不同程度不同特征的行业异质性。     

p-Adic model of quantum mechanics and quantum channels

A p-adic realization of the standard statistical model of quantum mechanics is constructed. Within this realization, a p-adic linear bosonic channel is defined, and its properties are analyzed. In particular, a criterion for the existence of a linear Gaussian bosonic channel is obtained, and its explicit construction is described. It is shown that the p-adic Gaussian bosonic channels possess an additivity property.     

Extreme bosonic linear channels

The set of all channels with a fixed input and output is convex. We first give a convenient formulation of the necessary and sufficient condition for a channel to be an extreme point of this set in terms of the complementary channel, a notion of great importance in quantum information theory. This formulation is based on the general approach to extremality of completely positive maps in an operator algebra in the spirit of Arveson. We then use this formulation to prove our main result: under certain nondegeneracy conditions, environmental purity is necessary and sufficient for the extremality of a bosonic linear (quasifree) channel. It hence follows that a Gaussian channel between finite-mode bosonic systems is extreme if and only if it has minimum noise.     

Optimal transmission of Gaussian signals through a feedback channel

Using the methodology and results of the theory of filtering of conditionally Gaussian processes, the optimal schemes of transmission of Gaussian signals through the noisy feedback channel are constructed under the new power conditions.     

On the capacity of the continuous time Gaussian channel with feedback

We discuss the capacity of the Gaussian channel with feedback. In general it is not easy to give an explicit formula for the capacity of a Gaussian channel, unless the channel is without feedback or a white Gaussian channel. We consider the case where a constraint, given in terms of the covariance functions of the input processes, is imposed on the input processes. It is shown that the capacity of the Gaussian channel can be achieved by transmitting a Gaussian message and using additive linear feedback.     

Capacity of mismatched Gaussian channels with and without feedback

Summary Continuous time communication channels with additive noise are considered under an average power constraint. The noises are assumed to be Gaussian processes equivalent (or mutually absolutely continuous) to a Brownian motion. We study the problem whether the capacity of the channel is increased by feedback or not. It is given a sufficient condition under which the capacity is not increased by feedback. It is also given an example of a channel whose capacity is doubled by feedback.Research partially supported by ONR contract N00014-84-0212     

ILUCP: a Crout ILU preconditioner with pivoting

We introduce a new preconditioner, ILUCP, to be used with an iterative method for solving sparse linear systems. It is based on an incomplete LU factorization combining Crout's formulation of Gaussian elimination with pivoting by columns. It is usually faster than ILUTP, which is based on a delayed update version of Gaussian elimination with pivoting, but requires more memory. For applications where memory is not a primary concern, ILUCP can be an attractive alternative to ILUTP. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal transmission of “television type” gaussian signals through a noiseless feedback channel

Using the methods and results of the theory of conditionally Gaussian filtering of stochastic processes and fields, an optimal scheme of “television type” signal transmission through a noiseless feedback channel is constructed under the usual power conditions, the signals being evolutionary Gaussian fields θ={θ_t(x)),tε[0,T),xεDεRⁿ . Explicit representations for optimal coding and decoding functionals, which are optimal in the sense of a special square criterion, and the expression for the error of signal reproduction are given.     

Inducing normality from non‐Gaussian long memory time series and its application to stock return data

Motivated by Lee and Ko (Appl. Stochastic Models. Bus. Ind. 2007; 23 :493–502) but not limited to the study, this paper proposes a wavelet‐based Bayesian power transformation procedure through the well‐known Box–Cox transformation to induce normality from non‐Gaussian long memory processes. We consider power transformations of non‐Gaussian long memory time series under the assumption of an unknown transformation parameter, a situation that arises commonly in practice, while most research has been devoted to non‐linear transformations of Gaussian long memory time series with known transformation parameter. Specially, this study is mainly focused on the simultaneous estimation of the transformation parameter and long memory parameter. To this end, posterior estimations via Markov chain Monte Carlo methods are performed in the wavelet domain. Performances are assessed on a simulation study and a German stock return data set. Copyright © 2009 John Wiley & Sons, Ltd.     

Communication games with partially soft power constraints

We consider a class of communication games which involves the transmission of a Gaussian random variable through a conditionally Gaussian memoryless channel in the presence of an intelligent jammer. The jammer is allowed to tap the channel and feed a correlated signal back into it. The transmitter-receiver pair is assumed to cooperate in minimizing some quadratic fidelity criterion while the jammer maximizes this same criterion. Security strategies which protect against irrational jammer behavior and which yield an upper bound on the cost are shown to exist for the transmitter-receiver pair over a class of fidelity criteria. Closed-form expressions for these strategies are provided in the paper, which are, in all cases but one, linear in the available information.This work was supported in part by the US Air Force under Grant No. AFOSR-84-0056 and in part by the Joint Services Electronics Program under Contract No. N00014-84-C-0149. An earlier version of this paper was presented at the 1986 IEEE Symposium on Information Theory, Ann Arbor, Michigan, 1986.     

Image reconstruction in multi-channel model under Gaussian noise

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in a growing number, N, of independent channels in the Gaussian white noise. In each channel, the image and the background intensities are unknown. They define a set of unidentifiable nuisance parameters that slow down the typical minimax rate of convergence. The asymptotically minimax rate is found as N → ∞, and an asymptotically optimal estimator of the boundary function is suggested.      

Markovian receiver collision analysis of high‐speed multi‐channel networks

Two synchronous transmission multi‐channel multi‐access protocols for high‐speed network architecture are studied in this paper. Analytic discrete time Markovian models are developed for finite number of stations and finite number of channels for the symmetric and asymmetric access rights proposed protocols. The effect of receiver collision phenomenon is examined and analysed on the performance measures evaluation and estimated by the probability of packet rejection at destination. Also, numerical results are presented for comparison for various numbers of data channels and stations. Copyright © 2005 John Wiley & Sons, Ltd.     

Rotated Dn-lattices

Based on algebraic number theory we construct some families of rotated $D_n$-lattices with full diversity which can be good for signal transmission over both Gaussian and Rayleigh fading channels. Closed-form expressions for the minimum product distance of those lattices are obtained through algebraic properties.     

A supply chain model with direct and retail channels

We study a dual channel supply chain in which a manufacturer sells to a retailer as well as to consumers directly. Consumers choose the purchase channel based on price and service qualities. The manufacturer decides the price of the direct channel and the retailer decides both price and order quantity. We develop conditions under which the manufacturer and the retailer share the market in equilibrium. We show that the difference in marginal costs of the two channels plays an important role in determining the existence of dual channels in equilibrium. We also show that demand variability has a major influence on the equilibrium prices and on the manufacturer’s motivation for opening a direct channel. In the case that the manufacturer and the retailer coordinate and follow a centralized decision maker, we show that adding a direct channel will increase the overall profit. Our numerical results show that an increase in retailer’s service quality may increase the manufacturer’s profit in dual channel and a larger range of consumer service sensitivity may benefit both parties in the dual channel. Our results suggest that the manufacturer is likely to be better off in the dual channel than in the single channel when the retailer’s marginal cost is high and the wholesale price, consumer valuation and the demand variability are low.     

Dynamic channel control and pricing of a single perishable product on multiple distribution channels

This paper studies dynamic channel control and pricing of a single perishable product distributed through multiple channels with the objective of maximizing the total expected profit over a finite horizon. We consider two types of commissions, namely proportional and fixed commissions, on the third-party channels and utilize stylized linear functions to characterize dependent demand flows from different channels. We show that, the magnitude of the opportunity cost of capacity uniquely determines the optimal channel control, at any given inventory level and periods to go. Consequently, we are able to derive the optimal price offered on each channel as a function of the opportunity cost of capacity in closed form. This significantly reduces the computational complexity of the stochastic dynamic program when parameters are constant with time. When channels are independent, we provide a necessary and sufficient condition for the optimality of a nested channel control policy by commission rates. The same condition is also sufficient for the optimality of the nested channel control policy in a distribution system with two dependent channels. We then characterize the structural properties of the optimal pricing and channel control policies. Finally, we explore the impact of the substitution effect on the channel control through numerical studies and gain managerial insights.     

The FEXP estimator for potentially non-stationary linear time series

We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential non-invertibility of the differenced series. We propose a method of pooling the tapered periodogram which leads to more efficient estimators of d than existing pooled, tapered estimators. We establish asymptotic normality of the tapered FEXP estimator in the Gaussian case with or without pooling. We establish asymptotic normality of the estimator in the linear case if pooling is used. Finally, we consider minimax rate-optimality and feasible nearly rate-optimal estimators in the Gaussian case.     

Some convergence results on quadratic forms for random fields and application to empirical covariances

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (J. Contemp. Math. Anal. 34(2):1?C15) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example of quadratic forms. We show that it is possible to obtain a Gaussian limit when the spectral density is not in L ². Therefore the dichotomy observed in dimension d?=?1 between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in d?>?1.