35905099
Travelling wave solutions for a class of the generalized Benjamin-Bona-Mahoney equations
Abstract In this paper, a class of the generalized Benjamin–Bona–Mahony (GBBM) equations with negative exponents are investigated by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, perodic, kink and anti-kink wave solutions are obtained. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given and some exact solutions are shown.
11714898
On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation
Abstract This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C 9 1 ⊃ [ C 1 1 + 2 ( C 3 2 ⊃ 2 C 1 2 ) ] . These results in the paper are useful for the study of the weakened Hilbert’s 16th problem.
29892228
Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation
Abstract By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin–Bona–Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
45935923
Responses of strongly non-linear oscillator parametrically excited by random narrow-band noise
The principal response of a strongly Van der Pol-Duffing oscillator subjected to parametric random narrow-band excitation is investigated. The technique of modified Lindstedt Poincare (MLP) method is used to transform the strongly non-linear system to a weak one by introducing a new expansion parameter, and then the multiple scales method is applied to determine the modulation equations for amplitude and phase of the response of the system. The effect of damping, detuning, and bandwidth on the dynamic behaviors such as stability, bifurcation are examined by computing the maximum Lyapunov exponent analytically. Also the numerical simulation is carried out to verify the analytical results, and random jump phenomenon may be observed in the region of the parameters of the system. The excellent agreement between theoretical results and numerical ones can be found immediately, and so the present method in this paper is applicable to solve strongly non-linear problems.
5556814
Travelling wave solutions in the generalized Hirota-Satsuma coupled KdV system
By using the bifurcation theory of dynamical systems to the generalized Hirota-Satsuma coupled KdV system, bifurcation parameter sets are shown. Numbers of solitary waves, kink waves and periodic waves are given. Under various parameter conditions, all explicit formulas of solitary wave solutions and kink wave solutions and periodic wave solutions are listed.
644571
Parametric inference for progressive Type-I hybrid censored data on a simple step-stress accelerated life test model
This paper considers a simple step-stress accelerated life test model under progressive Type-I hybrid censoring scheme. The progressive Type-I hybrid censoring scheme and statistical method in synthetic accelerated stresses are provided so as to decrease the lifetime and reduce the test cost. An exponentially distributed life of test units and a cumulative exposure model are assumed. The maximum likelihood estimates of the model parameters are obtained using a pivotal quantity. Two useful lemmas and a theorem are given to construct the approximate confidence intervals for the model parameters. Finally, simulation results are provided to assess the method of inference developed in this article. The simulation results show that the method does improve for large sample size.
16323266
EzArray: A web-based highly automated Affymetrix expression array data management and analysis system
BackgroundThough microarray experiments are very popular in life science research, managing and analyzing microarray data are still challenging tasks for many biologists. Most microarray programs require users to have sophisticated knowledge of mathematics, statistics and computer skills for usage. With accumulating microarray data deposited in public databases, easy-to-use programs to re-analyze previously published microarray data are in high demand.ResultsEzArray is a web-based Affymetrix expression array data management and analysis system for researchers who need to organize microarray data efficiently and get data analyzed instantly. EzArray organizes microarray data into projects that can be analyzed online with predefined or custom procedures. EzArray performs data preprocessing and detection of differentially expressed genes with statistical methods. All analysis procedures are optimized and highly automated so that even novice users with limited pre-knowledge of microarray data analysis can complete initial analysis quickly. Since all input files, analysis parameters, and executed scripts can be downloaded, EzArray provides maximum reproducibility for each analysis. In addition, EzArray integrates with Gene Expression Omnibus (GEO) and allows instantaneous re-analysis of published array data.ConclusionEzArray is a novel Affymetrix expression array data analysis and sharing system. EzArray provides easy-to-use tools for re-analyzing published microarray data and will help both novice and experienced users perform initial analysis of their microarray data from the location of data storage. We believe EzArray will be a useful system for facilities with microarray services and laboratories with multiple members involved in microarray data analysis. EzArray is freely available from http://www.ezarray.com/.
20174343
An operator splitting method for variational inequalities with partially unknown mappings
In this paper, we propose a new operator splitting method for solving a class of variational inequality problems in which part of the underlying mappings are unknown. This class of problems arises frequently from engineering, economics and transportation equilibrium problems. At each iteration, by using the information observed from the system, the method solves a system of nonlinear equations, which is well-defined. Under mild assumptions, the global convergence of the method is proved, and its efficiency is demonstrated with numerical examples.
850350
Online System Problem Detection by Mining Patterns of Console Logs
We describe a novel application of using data mining and statistical learning methods to automatically monitor and detect abnormal execution traces from console logs in an online setting. Different from existing solutions, we use a two stage detection system. The first stage uses frequent pattern mining and distribution estimation techniques to capture the dominant patterns (both frequent sequences and time duration). The second stage use principal component analysis based anomaly detection technique to identify actual problems. Using real system data from a 203-node Hadoop [1] cluster, we show that we can not only achieve highly accurate and fast problem detection, but also help operators better understand execution patterns in their system.
115232895
Elastostatic inverse formulation
Abstract. In this paper an inverse method for solving elastostatic problems with incomplete boundary conditions is presented. In general, inverse problems are ill-posed boundary value problems whose stability and uniqueness of solution and sensitivity-based formulations require additional constraints. In the development we use the Betti-reciprocal theorem to represent the boundary traction field in terms of the boundary and field displacements in an integral form. Initially, we assume the unknown boundary conditions and deformations required to solve the problem. In this way we equate the work done by the exact solution (unknown) to the work done by an assumed solution. Discretizing the resulting equations and using an iterative procedure each step in the solution process becomes the solution to a well-posed problem. Thus, with sufficient perturbations the correct boundary conditions are reconstructed.

18672998
Latent Pose Estimator for Continuous Action Recognition
Recently, models based on conditional random fields (CRF) have produced promising results on labeling sequential data in several scientific fields. However, in the vision task of continuous action recognition, the observations of visual features have dimensions as high as hundreds or even thousands. This might pose severe difficulties on parameter estimation and even degrade the performance. To bridge the gap between the high dimensional observations and the random fields, we propose a novel model that replace the observation layer of a traditional random fields model with a latent pose estimator. In training stage, the human pose is not observed in the action data, and the latent pose estimator is learned under the supervision of the labeled action data, instead of image-to-pose data. The advantage of this model is twofold. First, it learns to convert the high dimensional observations into more compact and informative representations. Second, it enables transfer learning to fully utilize the existing knowledge and data on image-to-pose relationship. The parameters of the latent pose estimator and the random fields are jointly optimized through a gradient ascent algorithm. Our approach is tested on HumanEva [1] --- a publicly available dataset. The experiments show that our approach can improve recognition accuracy over standard CRF model and its variations. The performance can be further significantly improved by using additional image-to-pose data for training. Our experiments also show that the model trained on HumanEva can generalize to different environment and human subjects.