应用图论分析与最优化理论来数据挖掘大规模水牛普里昂蛋白结构数据

图论、最优化理论显然在蛋白质结构的研究中大有用场. 首先, 调查/回顾了研究蛋白质结构的所有图论模型. 其后, 建立了一个图论模型: 让蛋白质的侧链来作为图的顶点, 应用图论的诸如团、 $k$-团、 社群、 枢纽、聚类等概念来建立图的边. 然后, 应用数学最优化的现代摩登数据挖掘算法/方法来分析水牛普里昂蛋白结构的大数据. 成功与令人耳目一新的数值结果将展示给朋友们.     

Multisite interactions in the lattice gas model: shapes of binding isotherm of macromolecules

The effect of interactions between binding sites of a lattice that are not pairwise additive (multisite interactions) on the shape of the ligand binding isotherm is investigated theoretically. The mean-field approximation treats the multisite interaction as an effective two-site interaction, the coupling constant becoming a function of the fraction of occupied sites. In general, the binding curve will show multiple vertical jumps. The sufficient condition for the existence of a critical temperature below which a vertical jump occurs in the binding curve is the presence of a cooperative two-site interaction. The functional dependence of the effective J on the saturation, and the value of the temperature determines the number and location of the vertical jumps. The existence of more than one point of inflection is shown to be unambiguous proof of the existence of multisite coupling. The occurrence of a point of inflection is dependent on temperature and it disappears above a critical temperature. The relationship of these results with experimental results reported in the literature on the binding of alkyl sulphates and sulphonates to the protein bovine serum albumin and alkyl ammonium chlorides on biotite surface which show the phenomenon of temperature-dependent vertical jumps in the binding isotherm is pointed out.     

Shear-induced effects on miscibility in polymer solutions

Methods of macromolecular integral equation theory are employed to calcuate the correlation functions of flexible linear homopolymers deformed by shear flow. The extent of coil deformation is calculated from bead-spring models that include corrections for finite chain extensibility and pre-averaged hydrodynamic interactions. The spinodal boundaries for sheared polymer solutions are obtained from the compressibility route under conditions of constant strain rate. It is shown that accounting for changes in the cohesive energy arising from flow-induced coil deformation may lead to non-monotonic shifts in the cloud point as a function of applied shear, even in the absence of nonlinear viscoelastic response. These model calculations are compared with experimental measurements of the cloud point for sheared solutions of polystyrene in dioctyl phthalate.     

Ionization of Rydberg atoms by the kicks of half-cycle pulses

We present a quantum mechanical model to study the ionization of quasione-dimensional Rydberg atoms interacting with half-cycle pulses (HCPs) and use it to demonstrate the inadequacy of semiclassical approaches to calculate ionization probabilities of such atoms subject to the impact of more than one HCP. For a single-kicked atom both models correctly reproduce the experimentally observed ‘s-curve’ as can be seen by plotting the ionization probability P as a function of momentum transfer q₁. We demonstrate that for a twice-kicked atom, the semiclassical model yields numbers for P which are not physically realizable. For fixed values of momentum transfers q₁ and q₂, in a twice-kicked atom, the ionization probability as a function of time delay between the kicks exhibits periodic decay and revival. The results of the semiclassical approach appear to agree with the quantum mechanical values at the times of revival of P, else these show considerable deviation. We attempt to provide a physical explanation for the limitation of the semiclassical approach.     

Similarities between 2D and 3D convection for large Prandtl number

Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum E_u(k)～k^?13/3, and the entropy spectrum exhibits a dual branch with a dominant k^?2 spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers.     

Molecular and impedance spectroscopy of Na 2 Mo 2 O 7 ceramics

The fine (i.e. 38 nm) powder of polycrystalline Na₂Mo₂O₇ was prepared by the high-temperature solid-state reaction technique. The formation of the compound in orthorhombic system is confirmed by preliminary structural analysis using X-ray diffraction (XRD) data. Spectroscopic studies of the compound have been carried out by vibration spectroscopy (Raman/FTIR) to understand its molecular structure at microscopic level. The complex impedance spectroscopy (CIS) technique has been used to study the electrical properties of the material as a function of frequency (10²–10⁶ Hz) at different temperatures (23–450^°C), and also to investigate the fundamental mechanism involved in the material. Impedance analysis also indicates that below 300^°C, the electrical conduction in the material is due to grain interior only. At and above 325^°C, the contribution of grain boundary is clearly evident. The electrical processes in the material are found to be temperature-dependent and are due to the relaxation phenomena in it. A frequency-dependent maximum of the imaginary electrical impedance is found to obey the Vogel–Fulcher law.     

Measuring the ‘complexity’ of sound

Sounds in the natural environment form an important class of biologically relevant non-stationary signals. We propose a dynamic spectral measure to characterize the spectral dynamics of such non-stationary sound signals and classify them based on rate of change of spectral dynamics. We categorize sounds with slowly varying spectral dynamics as simple and those with rapidly changing spectral dynamics as complex. We propose rate of spectral dynamics as a possible scheme to categorize sounds in the environment.     

Effect of nonthermal distributed electrons and temperature on phase shifts during the collision of inward and outward ion-acoustic solitary waves in nonplanar geometry

Interaction of nonplanar ion-acoustic solitary waves is an important source of information for studying the nature and characteristics of ion-acoustic solitary waves (IASWs). The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising of nonthermal distributed electrons and warm ions is investigated using the extended version of Poincaré–Lighthill–Kuo (PLK) perturbation method. How the interactions are taking place in cylindrical and spherical geometries are shown numerically. Analytical phase shifts are derived for nonplanar geometry. The effects of the ion to electron temperature parameter and the nonthermal electrons parameter on the phase shift are studied. It is shown that the properties of the interaction of IASWs in different geometries are very different.     

Nonplanar ion-acoustic shocks in electron–positron–ion plasmas: Effect of superthermal electrons

Ion-acoustic shock waves (IASWs) in a homogeneous unmagnetized plasma, comprising superthermal electrons, positrons, and singly charged adiabatically hot positive ions are investigated via two-dimensional nonplanar Kadomstev–Petviashvili–Burgers (KPB) equation. It is found that the profiles of the nonlinear shock structures depend on the superthermality of electrons. The influence of other plasma parameters such as, ion kinematic viscosity and ion temperature, is discussed in the presence of superthermal electrons in nonplanar geometry. It is also seen that the IASWs propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on.     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.