Stochastic on-line knapsack problems

Different classes of on-line algorithms are developed and analyzed for the solution of {0, 1} and relaxed stochastic knapsack problems, in which both profit and size coefficients are random variables. In particular, a linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value isO(log^3/2 n). An(1) lower bound on the expected difference between the optimum and the solution found by any on-line algorithm is also shown to hold.Corresponding author.Partially supported by the Basic Research Action of the European Communities under Contract 3075 (Alcom).Partially supported by research project Models and Algorithms for Optimization of the Italian Ministry of University and Scientific and Technological Research (MURST 40%).     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

Droplet dynamics for asymmetric Ising model

Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

β微管蛋白中紫杉醇(Taxol)结合腔的性质分析

采用多拷贝同时搜寻法(MCSS), 并结合现有微管抑制剂的SAR及3D-QSAR对β微管蛋白中Taxol(紫杉醇)结合腔的性质进行了分析. 结构研究结果表明, Taxol结合腔以疏水性质为主, 并指出官能团分布的具体位置: 在Phe270上方(Leu361-Pro272-Leu273-Leu228之间)的弧形区域、Asp26羧基下方及其与Glu22羧基之间、M-loop的中部, 以及Asp224内侧且靠近Arg276的胍基的位置. 而Asp224的内侧又是新提出的结合位点. 研究结果符合现有微管抑制剂的SAR, 为现有抗肿瘤药物的结构改造以及小分子微管抑制剂设计提供了理论依据.     

Conformational analysis of [Met5]-enkephalin: Solvation and ionization considerations

[Met5]-Enkephalin has the sequence Tyr-Gly-Gly-Phe-Met. Only the extended conformation of the peptide has been observed by X-ray crystallography. Nuclear magnetic resonance spectroscopy supports the presence of a turn at Gly 3 and Phe 4 in dimethyl sulfoxide. In this study, the peptide conformational states and thermodynamic properties are understood in terms of ionization state and solvent environment. In the calculation, final conformations obtained from multiple independent Monte Carlo simulated annealing conformational searches are starting points for molecular dynamics simulations. In an aqueous environment given by the use of solvation free energy and the zwitterionic state, dominant structural motifs computed are G-P Type II bend, G-G Type II bend, and G-G Type I bend motifs, in order of increasing free energy. In the calculation of the peptide with neutral N- and C-termini and solvation free energy, the extended conformer dominates (by at least a factor of 2.5), and the conformation of another low free energy conformer superimposes well on the pharmacophoric groups of morphine. Neutralization of charge and solvation induce and stabilize the extended conformation, respectively. A mechanism of inter-conversion between the extended conformer and three bent conformers is supported by /-scatter plots, and by the conformer relative free energies. An estimate of the entropy change of receptor unbinding is 8.3 cal K-1 mol-1, which gives rise to a -2.5 kcal/mol entropy contribution to the free energy of unbinding at 25 °C. The conformational analysis methodology described here should be useful in studies on short peptides and flexible protein surface loops that have important biological implications.     

Stochastic resonance is applied to quantitative analysis for weak chromatographic signal of glyburide in plasma

Based on the theory of stochastic resonance, a new method carried on the quantitive analysis to weak chromatographic signal of glyburide in plasma, which was embedded in the noise background and the signal-to-noise ratio (SNR) of HPLC-UV is enhanced remarkably. This method enhances the quantification limit to 1 ng ml⁻¹, which is the same as HPLC-MS, and makes it possible to detect the weak signal accurately by HPLC-UV, which was not suitable before. The results showed good recovery and linear range from 1 to 50 ng ml⁻¹ of glyburide in plasma and the method can be used for quantitative analysis of glyburide.     

Observations of trends for singular values and eigenvectors from library searching ultraviolet-visible spectra with spectral subtraction

A promising procedure for computerized library searching and identification of ultraviolet-visible spectra for one- and two-component mixtures is evaluated. The procedure is based on singular value decomposition and utilizes band position and shape. Searching more than one library spectrum at a time is possible. Library spectra which have similar spectra (collinear) with the sample and each other are indicated by two measures. First, a large condition index must be obtained, and second, two or more large variance-decomposition proportions in the same row need to be associated with the large condition index. The searching procedure has a significant degree of differentiation between the actual sample and potential candidates and is compared with the dot product, Euclidean distance and the correlation coefficient.     

A proposal for the molecular basis of μ and δ opiate receptor differentiation based on modeling of two types of cyclic enkephalins and a narcotic alkaloid

Summary The molecular basis underlying the divergent receptor selectivity of two cyclic opioid peptides Tyr-c[N -d-Orn²-Gly-Phe-Leu-] (c-ORN) and [d-Pen², l-Cys⁵]-enkephalinamide (c-PEN) was investigated using a molecular modeling approach. Ring closure and conformational searching procedures were used to determine low-energy cyclic backbone conformers. Following reinsertion of amino acid side chains, the narcotic alkaloid 7-[(1R)-1-methyl-1-hydroxy-3-phenylpropyl]-6,14-endoethenotetrahydro oripavine (PEO) was used as a flexible template for bimolecular superpositions with each of the determined peptide ring conformers using the coplanarity and cocentricity of the phenolic rings as the minimum constraint. A vector space of PEO, accounting for all possible orientations for the C₂₁-aromatic ring of PEO served as a geometrical locus for the aromatic ring of the Phe⁴ residue in the opioid peptides. Although a vast number of polypeptide conformations satisfied the criteria of the opiate pharmacophore, they could be grouped into three classes differing in magnitude and sign of the torsional angle values of the tyrosyl side chain. Only class III conformers for both c-ORN and c-PEN, having tyramine dihedral angles ₁ =–150° ± 30° and ₂=–155° ± 20°, had significant structural and conformational properties that were mutually compatible while respecting the PEO vector space. Comparison of these properties in the context of the divergent receptor selectivity of the studied opioid peptides suggests that the increased distortion of the peptide backbone in the closure region of c-PEN together with the pendant ,-dimethyl group, combine to generate a steric volume which is absent in c-ORN and that may be incompatible with a restrictive topography of the receptor. The nature and stereo-chemistry of substituents adjacent to the closure region of the peptides could also modulate receptor selection by interacting with a charged () or neutral () subsite.