7318403
Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives
In this paper, by introducing the fractional derivative in the sense of Caputo, the Adomian decomposition method is directly extended to study the coupled Burgers equations with time- and space-fractional derivatives. As a result, the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components. The figures show the effectiveness and good accuracy of the proposed method.
205398011
Weierstrass semi-rational expansion method and new doubly periodic solutions of the generalized Hirota-Satsuma coupled KdV system
In the paper, with the aid of symbolic computation, we investigate the generalized Hirota-Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of new Weierstrass elliptic function solutions via Weierstrass elliptic function P(Ξ;g2,g3) and its first-order derivative P'(Ξ;g2, g3). Moreover, the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented, and when Ξ; → ∞, these solitary wave solutions approach to some constants.
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.
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.
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.
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.
35232477
On Robust Stability of BAM Neural Networks with Constant Delays
The problems of determining the robust stability of bidirectional associative memory neural networks with delays are investigated in this paper. An approach combining the Lyapunov-Krasovskii stability theorem with the linear matrix inequality (LMI) technique is taken to study the problems, which provide bounds on the interconnection matrix and the activation functions. Some criteria for the robust stability, which give information on the delay-independence property, are derived. The results obtained in this paper provide one more set of easily verified guidelines for determining the robust stability of delayed BAM (DBAM) neural networks, which are less conservative and less restrictive than the ones reported recently in the literature. Some typical examples are presented to show the effectiveness of results.
56968749
Hiding I/O latency with pre-execution prefetching for parallel applications
Parallel applications are usually able to achieve high computational performance but suffer from large latency in I/O accesses. I/O prefetching is an effective solution for masking the latency. Most of existing I/O prefetching techniques, however, are conservative and their effectiveness is limited by low accuracy and coverage. As the processor-I/O performance gap has been increasing rapidly, data-access delay has become a dominant performance bottleneck. We argue that it is time to revisit the ldquoI/O wallrdquo problem and trade the excessive computing power with data-access speed. We propose a novel pre-execution approach for masking I/O latency. We describe the pre-execution I/O prefetching framework, the pre-execution thread construction methodology, the underlying library support, and the prototype implementation in the ROMIO MPI-IO implementation in MPICH2. Preliminary experiments show that the pre-execution approach is promising in reducing I/O access latency and has real potential.
40372820
Mining circumstance-oriented association rules using singular value decomposition technique
Association rule has evolved from the primitive form of single dimension intratransaction to the form of multi-dimension intertransaction. The challenge for mining multi-dimension intertransaction rules is the formidable search space. Researchers have proposed various methods to handle this problem, such as restricting the number of dimensions, confining search space in a small window, etc. These methods unavoidably have negative impact on mining result and they are less effective when the number of dimensions and the length of rule are really large. Moreover, all these methods are derived from the a priori algorithm and have common weaknesses: time consuming and redundancy caused by the iterative nature of the a priori algorithm. To approach this problem from a different angle, we propose to use the singular value decomposition technique (SVD). With SVD, the multi-dimension intertransaction rules can be easily identified.
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.
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.