The finite element and spectral methods are applied to two-dimensional bound state problems. A comparison of the spectral method, which requires a global basis set expansion of the wave functions, and the finite eleme...
It has been observed by Miura that the solutions of the modified Korteweg-deVries equation can be mapped into those of the Korteweg-deVries equation. In this note we show that all of the solutions of the former, decay...
A matrix of zeroes and ones is said to have the consecutive ones property if there is a permutation of its rows such that the ones in each column appear consecutively. This paper develops a data structure which may be...
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Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different acc...
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ISBN:
(数字)9783319564364
ISBN:
(纸本)9783319564357;9783030132590
Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resol...
Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.
The Athens Conference on applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes.;includes papers on applied probability in Honor of J...
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ISBN:
(数字)9781461207498
ISBN:
(纸本)9780387947884
The Athens Conference on applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes.;includes papers on applied probability in Honor of J.M. Gani. The topics include probability and probabilistic methods in recursive algorithms and stochastic models, Markov and other stochastic models such as Markov chains, branching processes and semi-Markov systems, biomathematical and genetic models, epidemilogical models including S-I-R (Susceptible-Infective-Removal), household and AIDS epidemics, financial models for option pricing and optimization problems, random walks, queues and their waiting times, and spatial models for earthquakes and inference on spatial models.
Targeted therapies, immunotherapies, and improved chemotherapies are being developed to reduce the suffering and mortality that come from human cancer. Although these approaches, and in particular combinations of them...
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Targeted therapies, immunotherapies, and improved chemotherapies are being developed to reduce the suffering and mortality that come from human cancer. Although these approaches, and in particular combinations of them, are expected to succeed eventually to a large degree, they all suffer one obstacle: Populations of replicating cells move away—typically in a high-dimensional space—from any opposing selection pressure they encounter. They evolve resistance. It is possible, however, to develop a precise mathematical understanding of the problem and to design treatment strategies that prevent resistance if possible or manage resistance otherwise. In this article, we present the fundamental equations that characterize the evolution of resistance. We provide formulas for the probability that resistant cells exist at the start of therapy, for the average number and sizes of resistant clones, and for the probability of successful combination treatment. We also demonstrate that developing new therapies that only maximize the killing rate of cancer cells may not be optimal, and that instead the parameters determining the fraction of resistant cells and their growth rate have a larger effect on the long-term control of cancer. These mathematical tools inform the search process for optimal therapies that aim to cure cancer.
Mathematical models of the human left ventricle are presented to determine the physiological response-oriented mechanical parameters of the LV, which have diagnostic significance. These parameters are (i) the rheologi...
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Mathematical models of the human left ventricle are presented to determine the physiological response-oriented mechanical parameters of the LV, which have diagnostic significance. These parameters are (i) the rheological parameters of the left ventricular muscle, namely the instantaneous values of stiffness of series elasticity, parallel elasticity, and the stress-strain rate relationship for the contractile unit that characterizes the deviatric stress-strain response of a left ventricular muscle element, (ii) the effective modulus of the LV, and (iii) the state of stress in the LV. The rheological parameters are obtained from a continuum model of the LV whose stress state equilibrates the chamber pressure and whose strain state equals the instantaneous strains in the actual LV, obtained from instantaneous changes in the geometry of the LV (as noted from cineangiocardiography); the constitutive equations for the model incorporate the known existing rheological models for the isolated cardiac muscle. The effective moduli of the LV are obtained by correlating the fundamental frequency of vibration of a spherical model of the LV with the corresponding frequencies of the second component of the first heart sound and the third heart sound; thus the values of representative moduli (and hence indices of the left ventricular stiffnesses) at systole and diastole are obtained. The stress state in the LV is obtained by utilizing single plane cineangiocardiographic information of the irregular geometry of the LV in anteroposterior projection. Plane stress finite element analysis of this planor irregular geometry of the LV is done and the resulting stresses are reduced by a factor, heuristically determined to make allowance for the actual 3-dimensional geometry of the LV; the stresses obtained thus bring out effects of irregular boundary of varying (and at times high) curvature.
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