Abstract:
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system. The numerical method presented here involves using an iterative scheme for solving a two-point boundary value problem for the Hamiltonian system. We validate our method by applying it to both continuous stochastic systems, such as nonlinear oscillators governed by the Duffing equation, and finite discrete systems, such as epidemic problems, which are governed by a set of master equations. Furthermore, we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations.

Abstract:
We propose iterative methods for obtaining solvation structures on a solid plate which use force distributions measured by surface force apparatus (SFA) and atomic force microscopy (AFM) as input data. Two model systems are considered here. In the model system for SFA, the same two solid plates are immersed in a solvent, and a probe tip and a solid plate are immersed in a solvent in the model system for AFM. Advantages of the iterative methods are as follows: The iterative method for SFA can obtain the solvation structure, for example, in a Lennard-Jones liquid; The iterative method for AFM can obtain the solvation structure without an input datum of solvation structure around the probe tip.

Abstract:
A classical result about minimal geodesics on R^2 with Z^2 periodic metric that goes back to H.M. Morse asserts that a minimal geodesic that is asymptotic to a periodic minimal geodesic cannot intersect any periodic minimal geodesic of the same period. This paper treats a similar theorem for nonparametric minimizing hypersurfaces without selfintersections -- as were studied by J. Moser, V. Bangert, P.H. Rabinowitz, E. Stredulinsky and others.

Abstract:
The parametric iterative methods of quadratic convergence without the derivative for solving nonlinear equations are discussed in this paper. We deduce the iterative formulas by the theory of the dynamic system, prove the quadratic convergence under weak conditions, and do the numerical experiments.

Abstract:
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless case our algorithm is exact. For rank-one matrices, the new algorithm is fast, admits a highly-parallel implementation, and produces an error minimizing estimate that is qualitatively close to our theoretical and the state-of-the-are Nuclear Norm and OptSpace methods.

Abstract:
This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

Abstract:
This article concerns the existence, multiplicity of positive solutions for the integral boundary-value problem with $phi$-Laplacian, $$displaylines{ ig(phi(u'(t))ig)'+f(t,u(t),u'(t))=0,quad tin[0,1],cr u(0)=int_0^1 u(r)g(r),dr,quad u(1)=int_0^1u(r)h(r),dr, }$$ where phi is an odd, increasing homeomorphism from R to R. Using a monotone iterative technique, we obtain the existence of positive solutions for this problem, and present iterative schemes for approximating the solutions.

Abstract:
This paper addresses the problem of unsupervised soft bit error rate (BER) estimation for any communications system, where no prior knowledge either about transmitted information bits, or the transceiver scheme is available. We show that the problem of BER estimation is equivalent to estimating the conditional probability density functions (pdf)s of soft channel/receiver outputs. Assuming that the receiver has no analytical model of soft observations, we propose a non parametric Kernel-based pdf estimation technique, and show that the resulting BER estimator is asymptotically unbiased and point-wise consistent. We then introduce an iterative Stochastic Expectation Maximization (EM) algorithm for the estimation of both a priori and a posteriori probabilities of transmitted information bits, and the classification of soft observations according to transmitted bit values. These inputs serve in the iterative Kernel-based estimation procedure of conditional pdfs. We analyze the performance of the proposed unsupervised and non parametric BER estimator in the framework of a multiuser code division multiple access (CDMA) system with single user detection, and show that attractive performance are achieved compared with conventional Monte Carlo (MC)-aided techniques.

Abstract:
this paper describes an inexpensive and secure cage system for housing venomous snakes. the cages are easily constructed from commercially available plastic containers and are lightweight and can be stacked, minimizing the area needed to house numerous animals. they allow easy access to the animal and can be adequately disinfected. these cages can be individually locked and also allow for full viewing of the animal.

Abstract:
A parametric learning based robust iterative learning control (ILC) scheme is applied to the time varying delay multiple-input and multiple-output (MIMO) linear systems. The convergence conditions are derived by using the and linear matrix inequality (LMI) approaches, and the convergence speed is analyzed as well. A practical identification strategy is applied to optimize the learning laws and to improve the robustness and performance of the control system. Numerical simulations are illustrated to validate the above concepts. 1. Introduction Learning mechanism enables the human beings to master skills, while the experiences gained from practices play important roles in this procedure. It is expected that the learning mechanism can also be introduced to machines, which enables them to achieve satisfactory performance from previous acquired input-output information. The method of ILC was firstly applied to control manipulators at high speed which is proposed by Uchiyama [1]. In 1984, Arimoto [2] published the first English paper of ILC for accurate tracking of robot trajectories. The basic idea of ILC is utilizing the information of the previous iteration to realize perfect tracking without exact knowledge of the system parameters, and a typical ILC scheme is shown as in Figure 1. In the recent three decades, many kinds of learning laws are utilized which can be mainly divided by two categories: the linear learning laws and the nonlinear learning laws. For example, the linear learning laws include but are not limited to the parametric learning law [3, 4], the robust learning law [5], the high-order learning law [6, 7], the PD type learning law [8, 9], and so on [10]. On the other hand, the Newton learning law and the Secant learning law belong to the nonlinear ones [11, 12] which have faster convergence speed comparing to some linear cases. Moreover, the control objectives are mainly focused on the linear continuous and discrete forms [13, 14] and the nonlinear systems with relative degree one [15] or the quasilinear forms [16] and so forth [17–27]. Figure 1: The basic idea of ILC. The time delay systems are ubiquitous in real world control problems [28] such as networked control systems, chemical processes, hydraulic, and rolling mill systems. The time delay affects the system performance in a large scale. Serious performance degradation and even instability can be led by time delay [29]. For decades, considerable efforts have been paid to assure the robust performance of time delay systems in both theories and applications [30]. The research of time