Randomized k-server algorithms for growth-rate bounded graphs

The k-server problem is a fundamental online problem where k mobile servers should be scheduled to answer a sequence of requests for points in a metric space as to minimize the total movement cost. While the deterministic competitive ratio is at least k, randomized k-server algorithms have the potential of reaching o(k)-competitive ratios. Prior to this work only few specific cases of this problem were solved. For arbitrary metric spaces, this goal may be approached by using probabilistic metric approximation techniques. This paper gives the first results in this direction, obtaining o(k)-competitive ratio for a natural class of metric spaces, including d-dimensional grids, and wide range of k.     

A law of large numbers for finite‐range dependent random matrices

We consider random Hermitian matrices in which distant above‐diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has an algebraic Stieltjes transform by an argument based on dimension theory of Noetherian local rings. © 2008 Wiley Periodicals, Inc.     

Binomial moment equations for stochastic reaction systems

A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be easily truncated to include moments up to any desired order. The number of equations is dramatically reduced compared to the master equation. This formulation enables the simulation of complex reaction networks, involving a large number of reactive species much beyond the feasibility limit of any existing method. It provides an equation-based paradigm to the analysis of stochastic networks, complementing the commonly used Monte Carlo simulations.     

Asymptotic formulae for likelihood-based tests of new physics

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the “Asimov data set”, which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.     

A Quenched CLT for Super-Brownian Motion with Random Immigration

A quenched central limit theorem is derived for the super-Brownian motion with super-Brownian immigration, in dimension d≥4. At the critical dimension d=4, the quenched and annealed fluctuations are of the same order but are not equal. W. Hong was supported by the Program for New Century Excellent Talents in University (NCET) and NSFC (Grant No. 10121101). O. Zeitouni was partially supported by NSF grant DMS-0503775.     

Evaluating the Influence of Warmup on Singing Voice Quality Using Acoustic Measures

Vocal warmup is generally accepted as vital for singing performance. However, only a limited number of studies have evaluated this effect quantitatively. In this study, we evaluated the effect of vocal warmup on voice production, among young female singers, using a set of acoustic parameters. Warmup reduced frequency-perturbation (p < 0.001) and amplitude-perturbation values (p < 0.05). In addition, warmup increased singer's formant amplitude (p < 0.05) and improved noise-to-harmonic ratio (p < 0.05). Tone-matching accuracy, however, was not affected by warmup. The effect of vocal warmup on frequency-perturbation parameters was more evident among mezzo-soprano singers than it was among soprano singers. It was also more evident in the low pitch-range than in the higher pitch-ranges (p < 0.05). The results of this study provide valid support for the advantageous effect of vocal warmup on voice quality and present acoustic analysis as a valuable and sensitive tool for quantifying this effect.     

Boundary force effects exerted on solitons in highly nonlinear media

We study the effects caused by remote boundaries on soliton dynamics in nonlinear media with a large range of nonlocality, and demonstrate theoretically and experimentally how asymmetric boundary forces can lead to soliton steering and oscillation in predetermined trajectories.     

L''exactitude du rendement des machines agricoles

Precision of the working height, or depth, of earth-moving equipment and other farm machinery can have a marked effect on the quality of the operation. The main factors affecting a machine's performance in maintaining the correct working height are its geometric parameters and the soil surface upon which it operates. The soil surface profile is defined by the “mean slope”, by the “root-mean-square” (RMS) of the deviations from the mean slope, and by the wavelengths calculated by Fourier analysis. The shortest wavelength with an amplitude above 1 cm was used in this study to find the effect of the soil surface waves on the accuracy of farm machinery operations. The machine's geometric parameters affecting its accuracy are its wheelbase and the lengthwise location of the working point (above or under ground) in relation to the wheels. A computer simulation analysis showed that the minimum deviations from the required height are found at the wheels of the machine. The deviations increased at the middle of the machine's span and rose steeply outside the span. The shorter the wheel-span of the machine relative to the wavelengths, the smaller the deviations will be. Smoothed surfaces have longer wavelengths and smaller deviations and as a result, higher accuracy of the working height, or depth, of the machines working on them.