Capacity of the Class of MIMO Channels With Incomplete CDI—Properties of Mutual Information for a Class of Channels

This paper is concerned with multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix p(H) is modelled by a relative entropy D(middot||middot) such that D(p||p_nom) les d, d ges 0, where d is the distance from the so-called nominal channel matrix distribution p_nom(H). The capacity of this compound channel is equal to the maximin of the mutual information, where the minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. The existence of a minimizing probability distribution is proved, and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution p_nom(H) and parameter d. A number of properties of the mutual information, minimized over the set of channel distributions, are derived. Specifically, upper and lower bounds are derived for the minimized mutual information, while its convexity with respect to d is shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived.     

Rigid continua and transfinite inductive dimension

We introduce a general method of resolving first countable, compact spaces that allows accurate estimate of inductive dimensions. We apply this method to construct, inter alia, for each ordinal number α>1 of cardinality ?c, a rigid, first countable, non-metrizable continuum Sα with . Sα is the increment in some compactification of [0,1) and admits a fully closed, ring-like map onto a metric continuum. Moreover, every subcontinuum of Sα is separable. Additionally, Sα can be constructed so as to be: (1) a hereditarily indecomposable Anderson-Choquet continuum with covering dimension a given natural number n, provided α>n, (2) a hereditarily decomposable and chainable weak Cook continuum, (3) a hereditarily decomposable and chainable Cook continuum, provided α is countable, (4) a hereditarily indecomposable Cook continuum with covering dimension one, or (5) a Cook continuum with covering dimension two, provided α>2.We also produce a chainable and hereditarily decomposable space Sω(c⁺) with , , trind₀Sω(c⁺) and trInd₀Sω(c⁺) all equal to ω(c⁺), the first ordinal of cardinality c⁺.     

Flexible working arrangements in context: An empirical investigation through self-organizing maps

This is one of the first studies to utilize Kohonen’s self-organizing maps on flexible work arrangements (FWAs), employee turnover and absenteeism within different national contexts and an array of organizational factors. While the majority of FWAs did not reduce significantly employee turnover or absenteeism, country and industry were significant contextual variables in FWA use: we deciphered six main country regions, where service and manufacturing organizations were important to FWA preferences. We found a curvilinear relationship between turnover and shift-work among manufacturing firms regardless of country: turnover decreases at low levels and increases at high levels of shift-work. We also found strong positive relationships between weekend work and turnover among manufacturing firms regardless of country and firms in the region comprising of Germany, Austria, Sweden, Finland, Denmark, Czech Republic and Belgium. Finally, we found consistently high concentration of organizations with low absenteeism throughout certain industries and countries: noteworthy are service organizations in the Netherlands and manufacturing organizations in Australia. The results demonstrate the contextuality of FWA use across countries and industries, and the usefulness of SOMs for research within human resource management.     

Acceleration of the leastpth algorithm for minimax optimization with engineering applications

Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.This work was supported by the National Research Council of Canada under Grant A4414, and from the University of Waterloo.     

On conditions for optimality of the nonlinearl 1 problem

The purpose of this paper is to present necessary and sufficient conditions for optimality in the nonlinearl ₁ problem. Furthermore, the relationship of thel ₁ problem and the Pietrzykowski's approach to solve the nonlinear programming problem is discussed in detail.     

Nonlinear programming using minimax techniques

A minimax approach to nonlinear programming is presented. The original nonlinear programming problem is formulated as an unconstrained minimax problem. Under reasonable restrictions, it is shown that a point satisfying the necessary conditions for a minimax optimum also satisfies the Kuhn-Tucker necessary conditions for the original problem. A leastpth type of objective function for minimization with extremely large values ofp is proposed to solve the problem. Several numerical examples compare the present approach with the well-known SUMT method of Fiacco and McCormick. In both cases, a recent minimization algorithm by Fletcher is used.This paper is based on work presented at the 5th Hawaii International Conference on System Sciences, Honolulu, Hawaii, 1972. The authors are greatly indebted to V. K. Jha for his programming assistance and J. H. K. Chen who obtained some of the numerical results. This work was supported in part by the National Research Council of Canada under Grant No. A7239, by a Frederick Gardner Cottrell Grant from the Research Corporation, and through facilities and support from the Communications Research Laboratory of McMaster University.     

Minimal systems of binomial generators and the indispensable complex of a toric ideal

Let be a vector configuration and its corresponding toric ideal. The paper consists of two parts. In the first part we completely determine the number of different minimal systems of binomial generators of . In the second part we associate to a simplicial complex . We show that the vertices of correspond to the indispensable monomials of the toric ideal , while one dimensional facets of with minimal binomial -degree correspond to the indispensable binomials of .

     

Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films

In the modelling of the flow of thin films higher-order derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial variable from the viewpoint of Lie symmetry analysis. Values of the parameters which allow for a greater number of Lie point symmetries are identified. As the equations can be recast in potential form, we consider their potential symmetries. We also consider the singularity properties of the corresponding steady-state equations.     

Performance evaluation of TCP extensions on ATM over high bandwidthdelay product networks

Practical experiments in a satellite network environment assist in the design and understanding of future global networks. This article describes the practical experiences gained from TCP/IP on ATM networks over a high-speed satellite link and presents performance comparison studies of such networks with the same host/traffic configurations over local area and wide area networks. These comparison studies on the LAN, WAN, and satellite environments increase our understanding of the behavior of high-bandwidth networks. NASA's Advanced Communications Technology Satellite (ACTS), with its special characteristics and high data rate satellite channels, and the ACTS ATM Internetwork (AAI) were used in these experiments to deliver broadband traffic. Network performance tests were carried out using application-level software (Netspec) on SONET OC-3 (155.52 Mb/s) satellite links. Finally, we experimentally study the performance, efficiency, fairness, and aggressiveness of TCP Reno, TCP New Reno, and TCP SACK end hosts on ATM networks over high BDP networks