Entropically Dominant State of Proteins

Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains to be a grand challenge in computational analysis of relevant processes. Here we propose and demonstrate an entropy estimation method that is based on physical partition of configurational space and can be readily combined with currently available methodologies. Tests with two globular proteins suggest that for flexible macromolecules with large and complex configurational space, accurate configurational entropy estimation may be achieved simply by considering the entropically most important subspace. This conclusion effectively converts an exhaustive sampling problem into a local sampling one, and defines entropically dominant state for proteins and other complex macromolecules. The conceptional breakthrough is likely to positively impact future theoretical analysis, computational algorithm development and experimental design of diverse chemical and biological molecular systems.Comment: 10 pages, 4 figure and 27 reference

On the structure of almost Einstein manifolds

In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense, Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a sequence of almost Einstein manifolds has most properties which is known for the limit space of Einstein manifolds. As applications, we can apply our structure results to study the properties of K\"ahler manifolds.Comment: 40 pages, 3 figure

Larger-Context Language Modelling

In this work, we propose a novel method to incorporate corpus-level discourse information into language modelling. We call this larger-context language model. We introduce a late fusion approach to a recurrent language model based on long short-term memory units (LSTM), which helps the LSTM unit keep intra-sentence dependencies and inter-sentence dependencies separate from each other. Through the evaluation on three corpora (IMDB, BBC, and PennTree Bank), we demon- strate that the proposed model improves perplexity significantly. In the experi- ments, we evaluate the proposed approach while varying the number of context sentences and observe that the proposed late fusion is superior to the usual way of incorporating additional inputs to the LSTM. By analyzing the trained larger- context language model, we discover that content words, including nouns, adjec- tives and verbs, benefit most from an increasing number of context sentences. This analysis suggests that larger-context language model improves the unconditional language model by capturing the theme of a document better and more easily

Dynamic Transition and Pattern Formation in Taylor Problem

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular we show that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter $R$. In addition, we show that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.Comment: To appear in Chinese Annuals of Mathematic

Is the Preferred Basis selected by the environment?

We show that in a quantum measurement, the preferred basis is determined by the interaction between the apparatus and the quantum system, instead of by the environment. This interaction entangles three degrees of freedom, one system degree of freedom we are interested in and preserved by the interaction, one system degree of freedom that carries the change due to the interaction, and the apparatus degree of freedom which is always ignored. Considering all three degrees of freedom the composite state only has one decomposition, and this guarantees that the apparatus would end up in the expected preferred basis of our daily experiences. We also point out some problems with the environment-induced super-selection (Einselection) solution to the preferred basis problem, and clarifies a common misunderstanding of environmental decoherence and the preferred basis problem.Comment: 5 pages, 1 figur

Metric Learning in Codebook Generation of Bag-of-Words for Person Re-identification

Person re-identification is generally divided into two part: first how to represent a pedestrian by discriminative visual descriptors and second how to compare them by suitable distance metrics. Conventional methods isolate these two parts, the first part usually unsupervised and the second part supervised. The Bag-of-Words (BoW) model is a widely used image representing descriptor in part one. Its codebook is simply generated by clustering visual features in Euclidian space. In this paper, we propose to use part two metric learning techniques in the codebook generation phase of BoW. In particular, the proposed codebook is clustered under Mahalanobis distance which is learned supervised. Extensive experiments prove that our proposed method is effective. With several low level features extracted on superpixel and fused together, our method outperforms state-of-the-art on person re-identification benchmarks including VIPeR, PRID450S, and Market1501

Unified Field Theory and Principle of Representation Invariance

This article consists of two parts. The main objectives of Part 1 are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction dynamics (PID). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, and PRI requires that physical laws be independent of representations of the gauge groups. One important outcome of this field model is a natural duality between the interacting fields and the adjoint bosonic fields. This duality predicts two Higgs particles of similar mass with one due to weak interaction and the other due to strong interaction. The field model can be naturally decoupled to study individual interactions, leading to 1) modified Einstein equations, giving rise to a unified theory for dark matter and dark energy, 2) three levels of strong interaction potentials for quark, nucleon/hadron, and atom respectively, and 3) two weak interaction potentials. These potential/force formulas offer a clear mechanism for both quark confinement and asymptotic freedom. The main objectives of Part 2 are 1) to propose a sub-leptons and sub-quark model, which we call weakton model, and 2) to derive a mechanism for all sub-atomic decays and bremsstrahlung. The weakton model postulates that all matter particles and mediators are made up of massless weaktons. The weakton model offers a perfect explanation for all sub-atomic decays and all generation/annihilation precesses of matter-antimatter. In particular, the precise constituents of particles involved in all decays both before and after the reaction can now be precisely derived. In addition, the bremsstrahlung phenomena can be understood using the weakton model. Also, the weakton model offers an explanation to the baryon asymmetry problem.Comment: expanded version with minor typos corrected as wel

Research on the recurrence relations for the spin-weighted spheroidal harmonics

In this paper we study the recurrence relations in the spin-weighted spheroidal harmonics (SWSHs) through super-symmetric quantum mechanics. We use the shape invariance property to solve the spin-weighted spheroidal wave equations. The result shows the relation among SWSHs with a special condition of the same parameter magnetic quantum number m but different spin-weight s. The conclusions can be reduced to the famous recurrence relations of spin-weighted spherical harmonics. These contents are the first investigation of this kind recurrence relation concerning SWSHs and make it possible to derive SWSHs from the spheroidal harmonics, so they are very important both in theoretical background and in the astrophysical applications. Keywords: spin-weighted spheroidal harmonics, recurrence relation, super-symmetric quantum mechanics, shape-invarianceComment: some modification, including some formula, error correcte

Existence of peakons for a cubic generalization of the Camassa-Holm equation

In this paper, we study the following generalized Camassa-Holm equation with both cubic and quadratic nonlinearities: $$m_{t}+k_{1}(3uu_{x}m+u^2m_{x})+k_{2}(2mu_{x}+m_{x}u)=0, \quad m=u-u_{xx},$$ which is presented as a linear combination of the Novikov equation and the Camassa-Holm equation with constants $k_{1}$ and $k_{2}$. The model is a cubic generalization of the Camassa-Holm equation. It is shown that the equation admits single-peaked soliton and periodic peakons

Dynamic Transition and Pattern Formation for Chemotactic Systems

The main objective of this article is to study the dynamic transition and pattern formation for chemotactic systems modeled by the Keller-Segel equations. We study chemotactic systems with either rich or moderated stimulant supplies. For the rich stimulant chemotactic system, we show that the chemotactic system always undergoes a Type-I or Type-II dynamic transition from the homogeneous state to steady state solutions. The type of transition is dictated by the sign of a non dimensional parameter $b$. For the general Keller-Segel model where the stimulant is moderately supplied, the system can undergo a dynamic transition to either steady state patterns or spatiotemporal oscillations. From the pattern formation point of view, the formation and the mechanism of both the lamella and rectangular patterns are derived