Random sampling scattered data with multivariate Bernstein polynomials

Among the applications of the Bernstein polynomials in one variable is their use in solving problems associated with stochastic computing. Taking as a starting point the notion of stochastic logic in the sense of Qian-Riedel-Rosenberg, the aim of this paper is to investigate some necessary and sufficient conditions for guaranteeing whether polynomial operations can be implemented with stochastic logic based on multivariate Bernstein polynomials with coefficients in the unit interval.

Analysis of occupants' behavior related to the use of windows in German households

A certain time may elapse for the occurrence of a first nucleation after a solution is made supersaturated. Thus, the supersaturated solution looks as if it could be in a metastable state though in a limited time. Such metastability of a supersaturated solution has been evaluated (rather technically) by the magnitude of the metastable zone width (MSZW), i.e., the supercooling at which a first nucleation event is detected when supersaturation is increased by cooling, or the induction time, i.e., the time elapsed until a first nucleation event is detected at a constant temperature. The larger these values are, the higher the metastability is. Surprisingly, however, these two nucleation-related quantities are not clearly understood. There is still much confusion. This chapter provides an overview of recent understandings of the MSZW and induction time with focus on the problems of (1) stochastic and deterministic aspects, (2) time-dependent change of solution structure, (3) role of nucleation, and (4) relevance to the operation of an industrial batch crystallizer.

Simulation and generation of spectrum-compatible ground motions based on wavelet packet method

We answer and generalize an open problem on the two-dimensional Bernstein polynomials on the unit triangle.

Regions of nonmodal phonation, which exhibit deviations from uniform glottal-pulse periods and amplitudes, occur often in speech and convey information about linguistic content, speaker identity, and vocal health. Some aspects of these deviations are random, including small perturbations, known as jitter and shimmer, as well as more significant aperiodicities. Other aspects are deterministic, including repeating patterns of fluctuations such as diplophonia and triplophonia. These deviations are often the source of misinterpretation of the spectrum. In this paper, we introduce a general signal-processing framework for interpreting the effects of both stochastic and deterministic aspects of nonmodality on the short-time spectrum. As an example, we show that the spectrum is sensitive to even small perturbations in the timing and amplitudes of glottal pulses. In addition, we illustrate important characteristics that can arise in the spectrum, including apparent shifting of the harmonics and the appearance of multiple pitches. For stochastic perturbations, we arrive at a formulation of the power-spectral density as the sum of a low-pass line spectrum and a high-pass noise floor. Our findings are relevant to a number of speech-processing areas including linear-prediction analysis, sinusoidal analysis-synthesis, spectrally derived features, and the analysis of disordered voices.

: Synthesis procedures for nonlinear stochastic feedback control of gas turbine engines were developed and evaluated. Modern estimation and control procedures based upon separating the stochastic and deterministic aspects of the control problem were employed. The resulting closed-loop control consists of nonlinear deterministic feedback control logic designed using piecewise-linear/piecewise-optimal techniques, and an estimator designed using nonlinear filtering logic. Engine variables estimated from noise-corrupted measurements are fed back through the deterministic control logic to generate commanded inputs to the engine. Mode-switching logic was developed to provide smooth transition between small-signal regulation and large-signal transient modes of estimator/controller operation.

This paper explores the nature of the Go game. Go has been played on different size of the board in its long history where it was born in 2356 BC and played on 9×9 board, and later played on 13×13, 15×15, 17×17, 19×19, and 21×21 board. Self-play experiments using an open-source implementation of AlphaZero, namely LeelaZero, as the artificial intelligence (AI) player, are conducted for data collection, whereas game refinement (GR) measures had been employed for the assessment. An informational analysis indicates that Go game have been searching not only for a harmonic balance between deterministic and stochastic aspects found in the similar board games (Chess and Mahjong) but also the expected fairness when playing Go. Three aspects of the game have been analyzed: the perspective of game designer (using the GR measure), the perspective of Go evolution relative to Chess and Mahjong evolutionary histories, and other perspectives that closely related to the cultural and strategic development of Go game. Based on such aspects, the impact of komi values and the reasons for 19×19 board size to the contemporary Go popularity had been identified.

Deterministic and stochastic aspects of constructed wetland performance and design

This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of their offspring during sexual reproduction. The corresponding models are large, nonlinear dynamical systems (for the deterministic treatment that applies in the infinite-population limit), or interacting particle systems (for the stochastic treatment required for finite populations). We review recent progress on these difficult problems. In particular, we present a closed solution of the deterministic continuous-time system, for the important special case of single crossovers; we extract an underlying linearity; we analyse how this carries over to the corresponding stochastic setting; and we provide a solution of the analogous deterministic discrete-time dynamics, in terms of its generalised eigenvalues and a simple recursion for the corresponding coefficients.

A mathematical model of survivorship kinetics is presented. It takes into account both deterministic and stochastic aspects of survival curves. Earlier reports [Piantanelli: Arch Gerontol Geriatr 1986;5:107-118; Piantanelli: Ann NY Acad Sci 1988; 521:99-109] described a model capable of making distinct predictions on the mean and standard deviation of an index of physiological function, fitting data even in the tail of survivorship curves, and accounting for the selection of the cohort at advanced ages. However, it contains four parameters whose biological interpretation is unclear. In the present paper we propose a modification of the model which maintains the main characteristics of the previous one and, in addition, results in two significant improvements. First, the number of free parameters is reduced to only two, making much easier both their estimation and interpretation, particularly when the model is applied to data from various animal groups manipulated in different ways. Second, it is possible to relate the parameters to well-defined deterministic and stochastic factors: specifically, a deterministic component describing the environmental and genetic influence on physiological functions, and a stochastic component representing the fluctuating interactions of the living organism and its environment.

A stochastic model for highway traffic

Lévy flights and superdiffusion in the context of biological encounters and random searches

Transient pulse formation in jasmonate signaling pathway

Decision-Making in Bacteriophage Lambda: A View From the Single Phage