Eigenvalue Distributions of Sums and Products of Large Random Matrices Via Incremental Matrix Expansions

This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using - and -transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser code-division multiple-access (CDMA) system with a minimum mean-square error linear receiver.     

On waiting for simultaneous access to two resources: Deterministic service distribution

Suppose that a test customer in anM/D/1queueing system can get service only if he has access to the server and a separate eventEhas occurred. All other customers only require access to the server. The time until the eventEoccurs is assumed to be an exponentially distributed random variable, if the test customer reaches the server beforeEoccurs, he must then return to the back of the queue. At any time, however, the test customer is allowed to give up his place in the queue and join the back of the queue. The test customer represents a computational task that depends upon the results of an associated task. The test customer's mean delay until service is derived assuming that he always maintains his position in the queue until he reaches the server. Conditions are given for which this "move-along" policy is optimal, i.e., minimizes the test customer's mean delay until service. A condition is also given for which the move-along policy is not optimal.     

What is the value of limited feedback for MIMO channels?

Feedback in a communications system can enable the transmitter to exploit channel conditions and avoid interference. In the case of a multiple-input multiple-output channel, feedback can be used to specify a precoding matrix at the transmitter, which activates the strongest channel modes. In situations where the feedback is severely limited, important issues are how to quantize the information needed at the transmitter and how much improvement in associated performance can be obtained as a function of the amount of feedback available. We give an overview of some recent work in this area. Methods are presented for constructing a set of possible precoding matrices, from which a particular choice can be relayed to the transmitter. Performance results show that even a few bits of feedback can provide performance close to that with full channel knowledge at the transmitter.     

A fluid analysis of a utility-based wireless scheduling policy

In this paper, we consider packet scheduling for the downlink in a wireless network, where each packet's service preferences are captured by a utility function that depends on the total delay incurred. The goal is to schedule packet transmissions to maximize the total utility. In this setting, we examine a simple gradient-based scheduling algorithm called the U/spl dot/R-rule, which is a type of generalized c/spl mu/-rule (Gc/spl mu/) that takes into account both a user's channel condition and derived utility when making scheduling decisions. We study the performance of this scheduling rule for a draining problem, where there is a given set of initial packets and no further arrivals. We formulate a "large system" fluid model for this draining problem where the number of packets becomes large while the packet-size decreases to zero, and give a complete characterization of the behavior of the U/spl dot/R scheduling rule in this limiting regime. Comparison with simulation results show that the fluid limit accurately predicts the corresponding behavior of finite systems of interest. We then give an optimal control formulation for finding the optimal scheduling policy for the fluid draining model. Using Pontryagin's minimum principle, we show that, when the user rates are chosen from a TDM-type of capacity region, the U/spl dot/R rule is in fact optimal in many cases. Sufficient conditions for optimality are also given. Finally, we consider a general capacity region and show that the U/spl dot/R rule is optimal only in special cases.     

Utility-based power control for a two-cell CDMA data network

Power allocation across users in two adjacent cells is studied for a code-division multiple access (CDMA) data service. The forward link is considered and cells are modeled as one-dimensional with uniformly distributed users and orthogonal signatures within each cell. Each user is assumed to have a utility function that describes the user's received utility, or willingness to pay, for a received signal-to-interference-plus-noise ratio (SINR). The objective is to allocate the transmitted power to maximize the total utility summed over all users subject to power constraints in each cell. It is first shown that this optimization can be achieved by a pricing scheme in which each base station announces a price per unit transmitted power to the users, and each user requests power to maximize individual surplus (utility minus cost). Setting prices to maximize total revenue over both cells is also considered, and it is shown that, in general, the solution is different from the one obtained by maximizing total utility. Conditions are given for which independent optimization in each cell, which leads to a Nash equilibrium (NE), is globally optimal. It is shown that, in general, coordination between the two cells is needed to achieve the maximum utility or revenue.     

Exploring the structure of a neuropsychological battery across healthy elders and those with questionable dementia and Alzheimer's disease.

An exploratory factor analysis (EFA) and a series of confirmatory factor analyses were conducted on 17 variables designed to assess different cognitive abilities in a sample of healthy older adults. In the EFA, 4 factors emerged corresponding to language, memory, processing speed, and fluid ability constructs. The results of the confirmatory factor analyses suggested that a 5-factor model with an additional Attention factor improved the fit. The invariance of the 5-factor model was examined across 3 groups: a group of cognitively healthy older adults, a group of patients diagnosed with questionable dementia (QD), and a group of patients diagnosed with probable Alzheimer's disease (AD). Results of the invariance analysis suggest that the model may have configural invariance across the 3 groups but not metric invariance. Specifically, preliminary analyses suggest that the memory construct may represent something different in the QD and AD groups as compared to the healthy older adult group, consistent with the underlying pathology in early AD. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Secondary ion quadrupole mass spectrometer for depth profiling--design and performance evaluation

A quadrupole-based secondary ion mass spectrometer designed for depth profiling is described which combines ultrahigh vacuum construction with high sputtering rate, detection sensitivity, depth resolution, mass spectral purity, and abundance sensitivity. Impurities such as B and Al implanted in Si can be profiled to levels below one part per million atomic (ppma), at a depth resolution equal to that obtained by commercial ion microprobes. The primary beam consists of 5-keV, mass-analyzed (40)Ar(+) ions, focused to about 70 microm in diameter. Its high current density (>25mA/cm(2)) permits adequate beam rastering and electronic signal-gating to optimize depth resolution. A secondary ion extraction lens and spherical energy filter are responsible for achieving abundance sensitivities of five to six orders of magnitude on the low mass side of a matrix peak. The ultrahigh vacuum environment of the sample dramatically reduces molecular peaks containing H, C, and O, allowing even hydrogen to be profiled to concentrations below 10 ppma. Because large amounts of data are generated by multi-element depth profiling, means for automated instrument control and data acquisition have been developed.     

Heat capacity of VO2 single crystals

The heat capacity of VO₂ was remeasured both above and below the transition temperature range of 330 – 345 K. For 150 < T < 320 K the results could be fit to the standard Debye theory with a Debye temperature θ_D = 750 K; for 360 < T < 720 K no Debye temperature could be assigned to the data, which exceeded the equipartition value for C_v above 580 K. The enthalpy of transition was found to be 1.12 k cal/mole VO₂.