Searcharxiv⌕ Search

arXiv subjects

Bin Liu

Publications and source records attributed to Bin Liu.

At least 505 records · Page 28Linked to original sources
arXiv2017

Almost periodic solutions for an asymmetric oscillation

In this paper we study the dynamical behaviour of the differential equation \begin{equation*} x''+ax^+ -bx^-=f(t), \end{equation*} where $x^+=\max\{x,0\}$,\ $x^-=\max\{-x,0\}$, $a$ and $b$ are two different positive constants, $f(t)$ is a real analytic almost periodic function. For this purpose, firstly, we have to establish some variants of the invariant curve theorem of planar almost periodic mappings, which was proved recently by the authors (see \cite{Huang}).\ Then we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the above asymmetric oscillation.

math.DS↗
arXiv2017

The large twist theorem and boundedness of solutions for polynomial potentials with $C^1$ time dependent coefficients

In this paper we first prove the so-called large twist theorem, then using it to prove the boundedness of all solutions and the existence of quasi-periodic solutions for Duffing's equation $$ \ddot{x}+x^{2n+1}+\dsum_{i=0}^{2n}p_i(t)x^i=0, $$ where $p_i(t)\in C^1(\mathbb{S}) (n+1\leq i\leq 2n)$ and $p_i(t)\in C^0(\mathbb{S}) (0\leq i\leq n)$ with $\mathbb{S}=\mathbb{R}/\mathbb{Z}$.

math.CA↗
arXiv2017

State Space Model based Trust Evaluation over Wireless Sensor Networks: An Iterative Particle Filter Approach

In this paper we propose a state space modeling approach for trust evaluation in wireless sensor networks. In our state space trust model (SSTM), each sensor node is associated with a trust metric, which measures to what extent the data transmitted from this node would better be trusted by the server node. Given the SSTM, we translate the trust evaluation problem to be a nonlinear state filtering problem. To estimate the state based on the SSTM, a component-wise iterative state inference procedure is proposed to work in tandem with the particle filter, and thus the resulting algorithm is termed as iterative particle filter (IPF). The computational complexity of the IPF algorithm is theoretically linearly related with the dimension of the state. This property is desirable especially for high dimensional trust evaluation and state filtering problems. The performance of the proposed algorithm is evaluated by both simulations and real data analysis.

cs.DC↗
arXiv2017

Effects of the third-order dispersion on continuous waves in complex potentials

A class of constant-amplitude (CA) solutions of the nonlinear Schrodinger equation with the third-order spatial dispersion (TOD) and complex potentials are considered. The system can be implemented in specially designed planar nonlinear optical waveguides carrying a distribution of local gain and loss elements, in a combination with a photonic-crystal structure. The complex potential is built as a solution of the inverse problem, which predicts the potential supporting a required phase-gradient structure of the CA state. It is shown that the diffraction of truncated CA states with a correct phase structure can be strongly suppressed. The main subject of the analysis is the modulational instability (MI) of the CA states. The results show that the TOD term tends to attenuate the MI. In particular, simulations demonstrate a phenomenon of weak stability, which occurs when the linear-stability analysis predicts small values of the MI growth rate. The stability of the zero state, which is a nontrivial issue in the framework of the present model, is studied too

physics.optics↗
arXiv2017

Modified evolution of stellar binaries from supermassive black hole binaries

The evolution of main sequence binaries resided in the galactic centre is influenced a lot by the central super massive black hole (SMBH). Due to this perturbation, the stars in a dense environment are likely to experience mergers or collisions through secular or non-secular interactions. In this work, we study the dynamics of the stellar binaries at galactic center, perturbed by another distant SMBH. Geometrically, such a four-body system is supposed to be decomposed into the inner triple (SMBH-star-star) and the outer triple (SMBH-stellar binary-SMBH). We survey the parameter space and determine the criteria analytically for the stellar mergers and the tidal disruption events (TDEs). For a relative distant and equal masses SMBH binary, the stars have more opportunities to merge as a result from the Lidov-Kozai(LK) oscillations in the inner triple. With a sample of tight stellar binaries, our numerical experiments reveal that a significant fraction of the binaries, ~70 per cent, experience merger eventually. Whereas the majority of the stellar TDEs are likely to occur at a close periapses to the SMBH, induced by the outer Kozai effect. The tidal disruptions are found numerically as many as ~10 per cent for a close SMBH binary that is enhanced significantly than the one without the external SMBH. These effects require the outer perturber to have an inclined orbit (>=40 degree) relatively to the inner orbital plane and may lead to a burst of the extremely astronomical events associated with the detection of the SMBH binary.

astro-ph.GA↗
arXiv2016

Online Fault-Tolerant Dynamic Event Region Detection in Sensor Networks via Trust Model

This paper proposes a Bayesian modeling approach to address the problem of online fault-tolerant dynamic event region detection in wireless sensor networks. In our model every network node is associated with a virtual community and a trust index, which quantitatively measures the trustworthiness of this node in its community. If a sensor node's trust value is smaller than a threshold, it suggests that this node encounters a fault and thus its sensor reading can not be trusted at this moment. This concept of sensor node trust discriminates our model with the other alternatives, e.g.,the Markov random fields. The practical issues, including spatiotemporal correlations of neighbor nodes' sensor readings, the presence of sensor faults and the requirement of online processing are linked together by the concept trust and are all taken into account in the modeling stage. Based on the proposed model, the trust value of each node is updated online by a particle filter algorithm upon the arrival of new observations. The decision on whether a node is located in the event region is made based upon the current estimate of this node's trust value. Experimental results demonstrate that the proposed solution can provide striking better performance than existent methods in terms of error rate in detecting the event region.

cs.DC↗
arXiv2016

Vision-based Traffic Flow Prediction using Dynamic Texture Model and Gaussian Process

In this paper, we describe work in progress towards a real-time vision-based traffic flow prediction (TFP) system. The proposed method consists of three elemental operators, that are dynamic texture model based motion segmentation, feature extraction and Gaussian process (GP) regression. The objective of motion segmentation is to recognize the target regions covering the moving vehicles in the sequence of visual processes. The feature extraction operator aims to extract useful features from the target regions. The extracted features are then mapped to the number of vehicles through the operator of GP regression. A training stage using historical visual data is required for determining the parameter values of the GP. Using a low-resolution visual data set, we performed preliminary evaluations on the performance of the proposed method. The results show that our method beats a benchmark solution based on Gaussian mixture model, and has the potential to be developed into qualified and practical solutions to real-time TFP.

cs.CV↗
arXiv2016

Robust Particle Filter by Dynamic Averaging of Multiple Noise Models

State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which may result in a major degradation in performance when the measurements are with the presence of outliers. A robust algorithm immune to the presence of outliers is desirable. To this end, a robust particle filter (PF) algorithm is proposed, in which the heavier tailed Student's t distributions are employed together with the Gaussian distribution to model the measurement noise. The effect of each model is automatically and dynamically adjusted via a Bayesian model averaging mechanism. The validity of the proposed algorithm is evaluated by illustrative simulations.

stat.ME↗
arXiv2016

Student's t Distribution based Estimation of Distribution Algorithms for Derivative-free Global Optimization

In this paper, we are concerned with a branch of evolutionary algorithms termed estimation of distribution (EDA), which has been successfully used to tackle derivative-free global optimization problems. For existent EDA algorithms, it is a common practice to use a Gaussian distribution or a mixture of Gaussian components to represent the statistical property of available promising solutions found so far. Observing that the Student's t distribution has heavier and longer tails than the Gaussian, which may be beneficial for exploring the solution space, we propose a novel EDA algorithm termed ESTDA, in which the Student's t distribution, rather than Gaussian, is employed. To address hard multimodal and deceptive problems, we extend ESTDA further by substituting a single Student's t distribution with a mixture of Student's t distributions. The resulting algorithm is named as estimation of mixture of Student's t distribution algorithm (EMSTDA). Both ESTDA and EMSTDA are evaluated through extensive and in-depth numerical experiments using over a dozen of benchmark objective functions. Empirical results demonstrate that the proposed algorithms provide remarkably better performance than their Gaussian counterparts.

cs.NE↗
arXiv2016

Uniqueness of stochastic entropy solutions for stochastic balance laws with Lipschitz fluxes

In this paper, we consider a stochastic balance law with a Lipschitz flux and gain the uniqueness for stochastic entropy solutions. The argument is supported by the stochastic kinetic formulation, the Itô formula and the regularization techniques. Furthermore, as an application, we derive the uniqueness of stochastic entropy solutions for stochastic porous media type equations.

math.AP↗
arXiv2016

Tensor Decomposition via Variational Auto-Encoder

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to represent nonlinear relationships in data. Another assumption of these methods is that a predefined rank should be known. However, the rank of tensors is hard to estimate, especially for cases with missing values. To address these issues, we design a Bayesian generative model for tensor decomposition. Different from the traditional Bayesian methods, the high-order interactions of tensor entries are modeled with variational auto-encoder. The proposed model takes advantages of Neural Networks and nonparametric Bayesian models, by replacing the multi-linear product in traditional Bayesian tensor decomposition with a complex nonlinear function (via Neural Networks) whose parameters can be learned from data. Experimental results on synthetic data and real-world chemometrics tensor data have demonstrated that our new model can achieve significantly higher prediction performance than the state-of-the-art tensor decomposition approaches.

stat.ML↗
arXiv2016

Robust video object tracking via Bayesian model averaging based feature fusion

In this article, we are concerned with tracking an object of interest in video stream. We propose an algorithm that is robust against occlusion, the presence of confusing colors, abrupt changes in the object feature space and changes in object size. We develop the algorithm within a Bayesian modeling framework. The state space model is used for capturing the temporal correlation in the sequence of frame images by modeling the underlying dynamics of the tracking system. The Bayesian model averaging (BMA) strategy is proposed for fusing multi-clue information in the observations. Any number of object features are allowed to be involved in the proposed framework. Every feature represents one source of information to be fused and is associated with an observation model. The state inference is performed by employing the particle filter methods. In comparison with related approaches, the BMA based tracker is shown to have robustness, expressivity, and comprehensibility.

cs.CV↗
arXiv2016

Two objective and independent fracture parameters for interface cracks and a paradox

Due to the oscillatory singular stress field around a crack tip, interface fracture has some peculiar features. This paper is focused on two of them. One can be reflected by a proposed paradox that geometrically similar structures with interface cracks under similar loadings may have different failure behaviors. The other one is that the existing fracture parameters of the oscillatory singular stress field, such as a complex stress intensity factor, exhibit some non-objectivity because their phase angle depend on an arbitrarily chosen length. Two objective and independent fracture parameters are proposed which can fully characterize the stress field near the crack tip. One parameter represents the stress intensity with classical unit of stress intensity factors. It is interesting to find that the loading mode can be characterized by a length as the other parameter, which can properly reflect the phase of the stress oscillation with respect to the distance to the crack tip. This is quite different from other crack tip fields in which the loading mode is usually expressed by a phase angle. The corresponding failure criterion for interface cracks does not include any arbitrarily chosen quantity, and therefore is convenient for comparing and accumulating experimental results, even existing ones.

cond-mat.other↗
arXiv2016

Volume conservation during finite plastic deformation

An elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. This paper discusses how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted or unique in the elastoplastic theories. An accurate condition of volume conservation is clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e. the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free state lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress, and interestingly find that the zero trace of the plastic stress rate is equivalent to the accurate condition of volume conservation. Two strategies are further proposed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples.

cond-mat.soft↗
arXiv2016

Posterior Exploration based Sequential Monte Carlo for Global Optimization

We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of annealed target pdfs is designed to asymptotically converge on the set of global optima. A sequential importance sampling (SIS) procedure is performed to simulate the resulting targets, and the maxima of the objective function is assessed from the yielded samples. The disturbing issue lies in the design of the importance sampling (IS) pdf, which crucially influences the IS efficiency. We propose an approach to design the IS pdf online by embedding a posterior exploration (PE) procedure into each iteration of the SMC framework. The PE procedure can also explore the important regions of the parameter space supported by the target pdf. A byproduct of the PE procedure is an adaptive mechanism to design the annealing temperature schedule online. We compare the performance of the proposed algorithm with those of several existing related alternatives by applying them to over a dozen standard benchmark functions. The result demonstrates the appealing properties of our algorithm.

stat.CO↗
arXiv2016

The surface-forming energy release rate versus the local energy release rate

This paper identifies two ways to extract the energy (or power) flowing into a crack tip during propagation based on the power balance of areas enclosed by a stationary contour and a comoving contour. It is very interesting to find a contradiction that two corresponding energy release rates (ERRs), a surface-forming ERR and a local ERR, are different when stress singularity exists at a crack tip. Besides a rigorous mathematical interpretation, we deduce that the stress singularity leads to an accompanying kinetic energy at the crack tip. The local ERR represents the driving force to overcome the surface energy and the accompanying kinetic energy, while the surface-forming ERR represents the driving force to overcome the surface energy only. Their advantages and disadvantages are discussed. We recommend using the surface-forming ERR based fracture criterion for a crack propagation in elastic-plastic materials, since it has a wide applicability and concise formulae which are easy to compute among all energy based criteria.

cond-mat.other↗
arXiv2016

Invariant curves of almost periodic twist mappings

In this paper we are concerned with the existence of invariant curves of planar twist mappings which are almost periodic in a spatial variable. As an application of this result to differential equations we will discuss the existence of almost periodic solutions and the boundedness of all solutions for superlinear Duffing's equation with an almost periodic external force.

math.DS↗