Evolving Stochastic Learning Algorithm based on Tsallis entropic index

In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight, and applies a form of noise that is characterized by the nonextensive entropic index q, regulated by a weight decay term. The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values. This is achieved by introducing a formula that defines a time-dependent relationship between these two important learning parameters. Our experimental study verifies that there are indeed improvements in the convergence speed of this new evolving stochastic learning algorithm, which makes learning faster than using the original Hybrid Learning Scheme (HLS). In addition, experiments are conducted to explore the influence of the entropic index q and temperature T on the convergence speed and stability of the proposed method.     

A hybrid genetic algorithm–neural network strategy for simulation optimization

Simulation optimization aims at determining the best values of input parameters, while the analytical objective function and constraints are not explicitly known in terms of design variables and their values only can be estimated by complicated analysis or time-consuming simulation. In this paper, a hybrid genetic algorithm–neural network strategy (GA–NN) is proposed for such kind of optimization problems. The good approximation performance of neural network (NN) and the effective and robust evolutionary searching ability of genetic algorithm (GA) are applied in hybrid sense, where NNs are employed in predicting the objective value, and GA is adopted in searching optimal designs based on the predicted fitness values. Numerical simulation results and comparisons based on a well-known pressure vessel design problem demonstrate the feasibility and effectiveness of the framework, and much better results are achieved than some existed literature results.     

双阈值二元神经网络极限环的存在惟一性

研究具负反馈的双阈值二元神经网络模型的动力学性质。在一定的初始函数空间内，对设定的阈值范围证明了模型存在惟一稳定极限环。     

网络流在清理三角债问题中的应用

本文把清理三角债中两种优化数学模型问题，化成求解相应网络上最小费用流的问题，从而得到（强）多项式算法，并把另外的一种优化数学模型问题。化成线性规划问题.于是解答了文[3]中提出的清理三角债的三个基本问题．     

Spin-orbit scattering in the quantum Hall effect

We study dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing, while the intrachannel potential is periodic (non-random); the channels represent two spin states. We consider channel mixing as function of the energy separation of the two extended states, and show that the phase diagram is different from the standard quantum Hall diagram for random intrachannel potential.     

Inverse estimation of temperature dependent emissivity of solid metals

An algorithm in the form of inverse problem to estimate the surface emissivity versus temperature of solids of variable thermal properties separated by a non-participating medium is proposed. The estimations are reproduced by the connection of variable slope stretches (piece-wise function) with no information of the temperature dependence of the emissivity. The input data (measurements) come from the solution of the direct problem by adding a random error to the temperature field. Both the direct and inverse problem are numerically solved by means of the network simulation method. The influence of different parameters in the estimation is studied and the resulting estimations are compared with exact solutions in order to verify the effectiveness of the proposed method.     

Definitions of equilibrium in network formation games

We examine a variety of stability and equilibrium definitions that have been used to study the formation of social networks among a group of players. In particular we compare variations on three types of definitions: those based on a pairwise stability notion, those based on the Nash equilibria of a link formation game, and those based on equilibria of a link formation game where transfers are possible.Bloch is also affiliated with the University of Warwick.     

A framework and algorithms for circular drawings of graphs

In this paper, we present a framework and two linear time algorithms for obtaining circular drawings of graphs. The first technique produces circular drawings of biconnected graphs and finds a zero crossing circular drawing if one exists. The second technique finds multiple embedding circle drawings. Techniques for the reduction of edge crossings are also discussed. Results of experimental studies are included.     

Bifurcation and stability analysis of a neural network model with distributed delays

In this paper, the dynamics of a generalized two-neuron model with self-connections and distributed delays are investigated, together with the stability of the equilibrium. In particular, the conditions under which the Hopf bifurcation occurs at the equilibrium are obtained for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. Explicit algorithms for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [20]. Some numerical simulations are given to illustrate the effectiveness of the results found. The obtained results are new and they complement previously known results.This work was supported by the National Natural Science Foundation of China under Grants 60574043 and 60373067, the Natural Science Foundation of Jiangsu Province, China under Grants BK2003053.     

Extending the stochastic programming framework for the modeling of several decision makers: pricing and competition in the telecommunication sector

In a previous paper, Gouveia and Magnanti (2003) found diameter-constrained minimal spanning and Steiner tree problems to be more difficult to solve when the tree diameter D is odd. In this paper, we provide an alternate modeling approach that views problems with odd diameters as the superposition of two problems with even diameters. We show how to tighten the resulting formulation to develop a model with a stronger linear programming relaxation. The linear programming gaps for the tightened model are very small, typically less than 0.5–, and are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti (2003). Moreover, the new model permits us to solve large Euclidean problem instances that are not solvable by prior approaches. Research funded in part by the Research Projects POCTI-ISFL-1-152,POSI/CPS/41459/2001 and POCTI/MAT/139/94 Research funded in part by the Singapore-MITAlliance(SMA)