Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices

In this paper, we extend our analysis of lattice systems using the wavelet transform to systems for which exact enumeration is impractical. For such systems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm, which hierarchically coarse-grains a lattice model by computing the probability distribution for successively larger block spins. We demonstrate that although the method perturbs the system by changing its Hamiltonian and by allowing block spins to take on values not permitted for individual spins, the results obtained agree with the analytical results in the preceding paper, and ``converge'' to exact results obtained in the absence of coarse-graining. Additionally, we show that the decorrelation time for the WAMC is no worse than that of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed from data performed in several short simulations to estimate the results that would be obtained from the original simulation. Although the algorithm is not asymptotically faster than traditional MMC, because of its hierarchical design, the new algorithm executes several orders of magnitude faster than a full simulation of the original problem. Consequently, the new method allows for rapid analysis of a phase diagram, allowing computational time to be focused on regions near phase transitions.Comment: 11 pages plus 7 figures in PNG format (downloadable separately

Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties

The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets representing local averages and local differences. Although one-to-one transformations of data sets are possible, the advantage of the wavelet transform is as an approximation scheme for the efficient calculation of thermodynamic and ensemble properties. Even under the most drastic of approximations, the resulting errors in the values obtained for average absolute magnetization, free energy, and heat capacity are on the order of 10%, with a corresponding computational efficiency gain of two orders of magnitude for a system such as a $4\times 4$ Ising lattice. In addition, the errors in the results tend toward zero in the neighborhood of fixed points, as determined by renormalization group theory.Comment: 13 pages plus 7 figures (PNG

Quantitative linkage of physiology and gene expression through empirical model construction: an investigation of diabetes

A methodology for the construction of predictive empirical models of physiological characteristics from microarray data is presented. The method, applied here to the study of the development of diabetes and insulin resistance, can be further expanded to other cases and to also include a variety of other data, such as protein expression, or metabolic flux data. The importance of several of the genes identified by the modeling methodology can be verified by comparison with results from prior literature. This implies potentially significant roles in diabetes for several of the uncharacterized genes discovered during the modeling procedure.Singapore-MIT Alliance (SMA

Технологические решения для строительства эксплуатационной наклонно-направленной скважины на Торгинскую свиту нефтегазоконденсатного месторождения

Цель работы – проектирование технологического решения на строительство нефтяной эксплуатационной наклонно – направленной скважины на Торгинскую свиту нефтегазоконденсатного месторождения (Якутия). В процессе работы проводилось проектирование технологических решений по строительству эксплуатационной наклонно-направленной скважины на нефтегазоконденсатном месторождении республики Саха (Якутия), построение геолого-технического наряда и компоновки низа бурильной колонны, рассмотрены химические реагенты и добавки в буровой раствор для борьбы с: асфальтосмолопарафиновыми отложениями, солеотложениями, коррозией оборудования.The purpose of the work is to design a technological solution for the construction of an oil production directional well at the Torginskaya suite of an oil and gas condensate field (Yakutia). In the course of the work, the design of technological solutions for the construction of a production directional well at the oil and gas condensate field of the Republic of Sakha (Yakutia), construction of a geological and technical order and the layout of the bottom of the drill string, considered chemical reagents and additives in the drilling fluid to combat: asphalt-resin-paraffin deposits, scale deposits , equipment corrosion

Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B.C. Goodwin, Temporal Oscillations in Cells, (Academic Press, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comp. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein, and metabolite concentrations. Further, we present results for a three gene case in co-regulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological systemComment: 21 pages, 7 figures; also selected in vjbio of August 2005; this version corrects a misorder in the last three references of the published versio

Исследование процесса совместной переработки прямогонных дизельных фракций и растительных масел на цеолитном катализаторе

В работе определены состав и свойства образца прямогонного дизельного топлива, подсолнечного масла и их смеси; осуществлена переработка на цеолитном катализаторе прямогонного и смесевого дизельного топлива в условиях варьирования температуры процесса; определены состав и свойства полученных продуктов; выявлены закономерности влияния температуры процесса на состав и свойства полученных продуктов; оценена целесообразность совместной переработки прямогонного дизельного топлива и растительного масла на цеолитном катализаторе.The work defines the composition and properties of a sample of straight-run diesel fuel, sunflower oil and their mixture; processing on a zeolite catalyst of straight-run and mixed diesel fuel under conditions of varying process temperature; the composition and properties of the products obtained have been determined; the regularities of the influence of the process temperature on the composition and properties of the obtained products were revealed; the feasibility of joint processing of straight-run diesel fuel and vegetable oil on a zeolite catalyst has been evaluated