Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

The nonlinear lattice---a new and nonlinear class of periodic potentials---was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting---the cubic and quintic model---by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully `nonlinear quasi-crystal'. A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted \textit{Vakhitov-Kolokolov} stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode---the fundamental and vortex solitons---are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation (GPE) or nonlinear Schr\"{o}dinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.Comment: 8 pages,7 figures, Frontiers of Physics (In Press

Clausal Presentation of Theories in Deduction Modulo

International audienceResolution modulo is an extension of first-order resolution where axioms are replaced by rewrite rules, used to rewrite, or more generally narrow, clauses during the search. In the first version of this method, clauses were rewritten to arbitrary propositions, that needed to be dynamically transformed into clauses. This unpleasant feature can be eliminated when the rewrite system is clausal, i.e. when it transforms clauses to clauses. We show in this paper that how to transform any rewrite system into a clausal one, preserving the existence of cut free proof of any sequent

Assessing Protein Conformational Sampling Methods Based on Bivariate Lag-Distributions of Backbone Angles

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model that should be considered to accurately parameterize the joint distribution of the angles? and What is the order of the local sequence–structure dependency that should be considered by a prediction method? We assess the model fits for different methods using bivariate lag-distributions of the dihedral/planar angles. Moreover, the main information across the lags can be extracted using a technique called Lag singular value decomposition (LagSVD), which considers the joint distribution of the dihedral/planar angles over different lags using a nonparametric approach and monitors the behavior of the lag-distribution of the angles using singular value decomposition. As a result, we developed graphical tools and numerical measurements to compare and evaluate the performance of different model fits. Furthermore, we developed a web-tool (http://www.stat.tamu.edu/∼madoliat/LagSVD) that can be used to produce informative animations

Collective estimation of multiple bivariate density functions with application to angular-sampling-based protein loop modeling

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed method was used to estimate neighbor-dependent distributions of protein backbone dihedral angles (i.e., Ramachandran distributions). The estimated distributions were applied to protein loop modeling, one of the most challenging open problems in protein structure prediction, by feeding them into an angular-sampling-based loop structure prediction framework. Our estimated distributions compared favorably to the Ramachandran distributions estimated by fitting a hierarchical Dirichlet process model; and in particular, our distributions showed significant improvements on the hard cases where existing methods do not work well

A Novel Multiple Classifier Generation and Combination Framework Based on Fuzzy Clustering and Individualized Ensemble Construction

Multiple classifier system (MCS) has become a successful alternative for improving classification performance. However, studies have shown inconsistent results for different MCSs, and it is often difficult to predict which MCS algorithm works the best on a particular problem. We believe that the two crucial steps of MCS - base classifier generation and multiple classifier combination, need to be designed coordinately to produce robust results. In this work, we show that for different testing instances, better classifiers may be trained from different subdomains of training instances including, for example, neighboring instances of the testing instance, or even instances far away from the testing instance. To utilize this intuition, we propose Individualized Classifier Ensemble (ICE). ICE groups training data into overlapping clusters, builds a classifier for each cluster, and then associates each training instance to the top-performing models while taking into account model types and frequency. In testing, ICE finds the k most similar training instances for a testing instance, then predicts class label of the testing instance by averaging the prediction from models associated with these training instances. Evaluation results on 49 benchmarks show that ICE has a stable improvement on a significant proportion of datasets over existing MCS methods. ICE provides a novel choice of utilizing internal patterns among instances to improve classification, and can be easily combined with various classification models and applied to many application domains

Data-Gathering and Aggregation Protocol for Networked Carrier Ad Hoc Networks: The Optimal and Heuristic Approach

In this chapter, we address the problem of data-gathering and aggregation (DGA) in navigation carrier ad hoc networks (NC-NET), in order to reduce energy consumption and enhance network scalability and lifetime. Several clustering algorithms have been presented for vehicle ad hoc network (VANET) and other mobile ad hoc network (MANET). However, DGA approach in harsh environments, in terms of long-range transmission, high dynamic topology and three-dimensional monitor region, is still an open issue. In this chapter, we propose a novel clustering-based DGA approach, namely, distributed multiple-weight data-gathering and aggregation (DMDG) protocol, to guarantee quality of service (QoS)-aware DGA for heterogeneous services in above harsh environments. Our approach is explored by the synthesis of three kernel features. First, the network model is addressed according to specific conditions of networked carrier ad hoc networks (NC-NET), and several performance indicators are selected. Second, a distributed multiple-weight data-gathering and aggregation protocol (DMDG) is proposed, which contains all-sided active clustering scheme and realizes long-range real-time communication by tactical data link under a time-division multiple access/carrier sense multiple access (TDMA/CSMA) channel sharing mechanism. Third, an analytical paradigm facilitating the most appropriate choice of the next relay is proposed. Experimental results have shown that DMDG scheme can balance the energy consumption and extend the network lifetime notably and outperform LEACH, PEACH and DEEC in terms of network lifetime and coverage rate, especially in sparse node density or anisotropic topologies

Expression analysis of vasa in Asian paddle crab (Charybdis japonica) exposed to Bisphenol A

AbstractBackgroundBisphenol A (BPA) is an endocrine-disrupting chemical (EDC) with a weak estrogen-like activity in fish that is found ubiquitously in aquatic environments. However, there has been little study about BPA on the endocrine disrupting effects of crab. In the present study, cDNA of vasa was cloned and characterized in the Charybdis japonica. Histological structures of testis and expression patterns of vasa gene in the testis of C. japonica after treatment with BPA were investigated.ResultsThe cDNA of vasa is composed of 3051bp with a 2166bp open reading frame encoding 721 AA. The deduced amino acid sequence contained eight conserved domains of the DEAD-box protein family. The tissue distribution showed that vasa mRNA was specifically expressed in ovary and testis. Histologically, the sperm cells were decreased in number and an acellular zone was seen in the testis. The transcript level of vasa gradually increased with a significant difference between the experimental and control groups. After BPA exposure with 0.50 and 1.00mg/L for 1, 3, 6 and 9 d, the expression levels of vasa increased.ConclusionThese findings suggest that BPA can increase the expression level of vasa mRNA and influence the development of the testis in C. japonica