Computer-intensive methods in statistical analysis

As far back as the late 1970s, the impact of affordable, high-speed computers on the theory and practice of modern statistics was recognized by Efron (1979, 1982). As a result, the bootstrap and other computer-intensive statistical methods (such as subsampling and the jackknife) have been developed extensively since that time and now constitute very powerful (and intuitive) tools to do statistics with. This article provides a readable, self-contained introduction to the bootstrap and jackknife methodology for statistical inference; in particular, the focus is on the derivation of confidence intervals in general situations. A guide to the available bibliography on bootstrap methods is also offered     

On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem

We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1082–1088, August, 1998. The present work was partially supported by the International Soros Program of Educational Support in Exact Sciences (grant No. APU 061086).     

Second Quantization of the Stueckelberg Relativistic Quantum Theory and Associated Gauge Fields

The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrödinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed.     

Gordon-Haus timing jitter reduction in dispersion-managed solitoncommunications

An analytic theory is presented which demonstrates that the noise induced Gordon-Haus timing jitter in arbitrary dispersion-managed transmission systems is reduced by the power-enhancement factor required to support a dispersion-managed solitons provided the path-average soliton period is much greater than the dispersion-map period. The analysis further predicts the behaviour of the amplitude, width, and quadratic chirp fluctuations due to the amplified spontaneous emission (ASE) noise     

Symbol rate and modulation level-controlled adaptivemodulation/TDMA/TDD system for high-bit-rate wireless data transmission

This paper proposes a time-division multiple-access/time-division duplex (TDMA/TDD)-based symbol rate and modulation level-controlled adaptive modulation system for high-bit-rate data transmission. The proposed system controls both the symbol rate and modulation level for the next transmission time slot according to the estimated carrier power to noise spectral density ratio (C/N₀) and delay spread for the time slot to achieve higher bit rate and higher transmission quality as well as higher delay-spread immunity. It is demonstrated by computer simulation and laboratory experiments that the proposed system can achieve a higher average bit rate with higher transmission quality in comparison with the fixed-rate quaternary phase-shift keying (QPSK) system and modulation level-controlled adaptive modulation system in both flat Rayleigh and frequency-selective fading environments. The simulated and experimental results also show that the proposed adaptive modulation techniques can be applied to 1-2-Mb/s indoor and outdoor microcellular systems with its delay spread of up to 250 ns and its terminal mobility of up to pedestrian speed without employing any special antifrequency-selective fading techniques, such as the adaptive equalizer and space diversity     

Photoluminescence of cadmium telluride recrystallized by nanosecond pulsed laser irradiation

The influence of nanosecond pulsed laser irradiation on the morphology and low-temperature photoluminescence of n-type CdTe at energy densities sufficient to melt the material (0.2–0.5 J/cm²) is investigated. After recrystallization the material has an “orange-peel” appearance. The low-temperature photoluminescence spectrum corresponds to low-grade single-crystalline p-type CdTe containing a large number of dislocations and clusters of point defects. The laser treatment has a long-range effect, significantly altering the impurity-defect system in a way characteristic of n→p conductivity conversion at distances greater than 50 μm from the site where laser radiation is absorbed. Fiz. Tekh. Poluprovodn. 32, 32–35 (January 1998)     

On finite-dimensional approximation of solutions of ill-posed problems

We show that the modified method for finite-dimensional approximation of solutions of Fredholm integral equations of the first kind presented in this paper is more economical than traditional methods for finite-dimensional approximation. Institute of Mathematies, Ukrainian Academy of Science, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 289–295, February, 1997.     

Vector algorithm for Reed-Muller expansions

A novel vector algorithm for Reed-Muller (RM) expansions is proposed which can save as many as a factor of 2^n-1 memory elements compared with previous matrix algorithms     

The effect of multiple time scales and subexponentiality in MPEGvideo streams on queueing behavior

Guided by the empirical observation that real-time MPEG video streams exhibit both multiple time scale and subexponential characteristics, we construct a video model that captures both of these characteristics and is amenable to queueing analysis. We investigate two fundamental approaches for extracting the model parameters: using sample path and second-order statistics-based methods. The model exhibits the following two canonical queueing behaviors. When strict stability conditions are satisfied, i.e., the conditional mean of each scene is smaller than the capacity of the server, precise modeling of the interscene dynamics (long-term dependency) is not essential for the accurate prediction of small to moderately large queue sizes. In this case, the queue length distribution is determined using quasistationary (perturbation theory) analysis. When weak stability conditions are satisfied, i.e., the conditional mean of at least one scene type is greater than the capacity of the server, the dominant effect for building a large queue size is the subexponential (long-tailed) scene length distribution. In this case, precise modeling of intrascene statistics is of secondary importance for predicting the large queueing behavior. A fluid model, whose arrival process is obtained from the video data by replacing scene statistics with their means, is shown to asymptotically converge to the exact queue distribution. Using the transition scenario of moving from one stability region to the other by a change in the value of the server capacity, we synthesize recent queueing theoretic advances and ad hoc results in video modeling, and unify a broad range of seemingly contradictory experimental observations found in the literature. As a word of caution for the widespread usage of second-order statistics modeling methods, we construct two processes with the same second-order statistics that produce distinctly different queueing behaviors