5576433
New exact solutions for modified nonlinear dispersive equations mK(m, n) in higher dimensions spaces
With the use of some proper transformations and symbolic computation, we present a general and unified method for investigating the general modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces. The work formally shows how to construct the general solutions and some special exact-solutions for mK(m,n) equations in higher dimensional spatial domains. The general solutions not only contain the solutions by Wazwaz [Math. Comput. Simulation 59 (2002) 519] but also contain many new compact and noncompact solutions.
41322043
New exact travelling wave solutions for the shallow long wave approximate equations
Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the shallow long wave approximate equations. New and more general form solutions are obtained, including kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions. The properties of the new formal solitary wave solutions are shown by some figures.
12162530
A new general algebraic method with symbolic computation to construct new doubly-periodic solutions of the (2 + 1)-dimensional dispersive long wave equation
For constructing more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations, a new direct and unified algebraic method, named Jacobi elliptic function rational expansion method, is presented and implemented in a computer algebraic system. Compared with most of the existing Jacobi elliptic function expansion methods, the proposed method can be expected to obtain new and more general formal solutions. We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method.
27234161
Two-dimensional symmetry reduction of (2 + 1)-dimensional nonlinear Klein-Gordon equation
In this paper, one-dimensional optimal system of group invariant solutions of (2+1)-dimensional Klein-Gordon system is constructed. Then the classification of group invariant solutions is given out and the corresponding two-dimensional symmetry reduced equations are obtained. At last some symmetry transformations are gained in detail. Especially, we obtain the most general solution from a given solution by use of six variable one-parameter subgroups transformations.
18967560
Generalized Cascade Synchronization of Discrete-time Henon-like Map
This Letter addresses the generalized cascade synchronization problem of discrete-time hyperchaotic systems. By choosing a general kind of proportional scaling error functions and based on rigorous control theory, we take the discrete-time Henon-like map as a example to achieve the generalized cascade synchronization. Numerical simulations are used to show the effectiveness of the proposed technique.
20461063
The function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems
The function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized. Based on Lyapunov stability theory and the proposed scheme, the Lu system and Chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously. Numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme.
8082956
Statistical Neurodynamics for Sequence Processing Neural Networks with Finite Dilution
We extend the statistical neurodynamics to study transient dynamics of sequence processing neural networks with finite dilution, and the theoretical results are supported by extensive numerical simulations. It is found that the order parameter equations are completely equivalent to those of the Generating Functional Method, which means that crosstalk noise follows normal distribution even in the case of failure in retrieval process. In order to verify the gaussian assumption of crosstalk noise, we numerically obtain the cumulants of crosstalk noise, and third- and fourth-order cumulants are found to be indeed zero even in non-retrieval case.
20203347
RBF Kernel Based Support Vector Machine with Universal Approximation and Its Application
The SVM has been used to the nonlinear function mapping successfully, but the universal approximation property of the SVM has never been proved in theory. This paper proves the universal approximation of the SVM with RBF kernel to arbitrary functions on a compact set and deduces it to the approximation of discrete function. From simulation we can see that the RBF kernel based LS-SVM is more effective in nonlinear function estimation and can prevent the system from noise pollution, so it has high generalization ability.
20327796
An effective algorithm of motif finding problem
Identification of the short DNA sequence motif, which serves as binding targets for transcription factors, is a fundamental problem in both computer science and molecular biology. Especially, finding the subtle motifs with variable gaps is more challenging. In this paper, a new algorithm is presented, which explores some new strategies. Based on a neighbourhood set concept, a new probability matrix is defined, which can capture the target motifs effectively. An iterative restart strategy is used, by which we can use several similar motifs' information to detect the real motif to demonstrate the effectiveness of our algorithm. We test it on several kinds of data and compare it with some other current representation algorithms. Simulation shows that the algorithm can effectively detect the subtle motifs.
41811097
A Neural Network Architecture for Perceptual Grouping, Attention Modulation and Boundary-Surface Interaction
A neural network architecture is introduced for context-sensitive binding processing in visual cortex areas such as perceptual grouping, attention and boundary-surface interaction. The present architecture, based on LAMINART and FACADE theory, shows how layered circuits in cortex areas enable feedforward, horizontal, and feedback interactions and intractions, together with balanced connections, to complete perceptual groupings with attention modulation. Thus, a pre-attentive/attentive interface for cortex has been established within the same circuits. Moreover, this architecture exhibits the invisible perceptual grouping and visible surface filling-in interaction with complementary computing property, introduced in FACADE theory. By implementing SOC filtering, preattentive perception can response well to contrast-sensitive stimuli. Also the simulations illustrates selective propagation of the attention along an object grouping as well as surface filling and the protection of them from competitive masking. At the same time it demonstrates the generation of attention modulation by boundary-surface interactions as well as translation of the attention across complementary visual processing streams.
16254824
Trust Propagation in Small Worlds
The possibility of a massive, networked infrastructure of diverse entities partaking in collaborative applications with each other increases more and more with the proliferation of mobile devices and the development of ad hoc networking technologies. In this context, traditional security measures do not scale well. We aim to develop trust-based security mechanisms using small world concepts to optimise formation and propagation of trust amongst entities in these vast networks. In this regard, we surmise that in a very large mobile ad hoc network, trust, risk, and recommendations can be propagated through relatively short paths connecting entities. Our work describes the design of trust-formation and risk-assessment systems, as well as that of an entity recognition scheme, within the context of the small world network topology.