In this paper, an algorithm is presented for the transshipment problem that is an adaption of the method used by Jones, Saigal, and Schneider for solving singlecommodity, spatial-equilibrium problems. The approach use...
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Several problems that deal with smoothness of discrete functions and that are motivated by the task of deciding whether an N × N array of distances is a feasible laser radar (LADAR) image are investigated. The ma...
A theory of generalized gradients is presented for a class of Lipschitz vector-valued mappings from a Banach space to a locally convex order complete vector lattice. Necessary optimality conditions are obtained for no...
The complete genomes of living organisms have provided much information on their phylogenetic relationships. In the past few years, we proposed three alternative methods to model the noise background in the compositio...
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We study the almost-sure large time exponential growth of the solution to a linear stochastic parabolic equation with continuous space parameter, and a Gaussian-correlated potential that is white noise in time and hom...
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We study the almost-sure large time exponential growth of the solution to a linear stochastic parabolic equation with continuous space parameter, and a Gaussian-correlated potential that is white noise in time and homogeneous in space. We use the evolution form of that equation,for which existence and uniqueness are known. We establish a Feynman-Kac formula for the solution. By using a method of discretization of time and space, we prove that for small diffusion parameter κ, there is a deterministic constant c such that almost surely
As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the unce...
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We propose a Bayesian method to detect change points for functional data. We extract the features of a sequence of functional data by the discrete wavelet transform (DWT), and treat each sequence of feature independen...
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Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo variou...
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A measure representation of protein sequences similar to the measure representation of DNA sequences proposed in our previous paper [Yu et al., Phys. Rev. E 64, 031903 (2001)] and another induced measure are introduce...
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A measure representation of protein sequences similar to the measure representation of DNA sequences proposed in our previous paper [Yu et al., Phys. Rev. E 64, 031903 (2001)] and another induced measure are introduced. Multifractal analysis is then performed on these two kinds of measures of a large number of protein sequences derived from corresponding complete genomes. From the values of the Dq (generalized dimensions) spectra and related Cq (analogous specific heat) curves, it is concluded that these protein sequences are not completely random sequences. For substrings with length K=5, the Dq spectra of all organisms studied are multifractal-like and sufficiently smooth for the Cq curves to be meaningful. The Cq curves of all bacteria resemble a classical phase transition at a critical point. But the “analogous” phase transitions of higher organisms studied exhibit the shape of double-peaked specific heat function. But for the classification problem, the multifractal property is not sufficient. When the measure representations of protein sequences from complete genomes are considered as time series, a method based on correlation analysis after removing some memory from the time series is proposed to construct a phylogenetic tree. This construction is shown to be reasonably satisfactory.
We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random se...
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