Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects

Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies are significantly improved not only for nuclear masses but also for single-nucleon separation energies. Due to the inclusion of the shell effect, in the unknown region, the BNN approach predicts a similar shell-correction structure to that in the known region, e.g., the predictions of underestimation of nuclear mass around the magic numbers in the relativistic mean-field model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach.Comment: 15 pages, 4 figures, and 3 table

The Tate-Shafarevich group for elliptic curves with complex multiplication II

Let E be an elliptic curve over Q with complex multiplication. The aim of the present paper is to strengthen the theoretical and numerical results of \cite{CZS}. For each prime p, let t_{E/Q, p} denote the Z_p-corank of the p-primary subgroup of the Tate-Shafarevich group of E/Q. For each \epsilon 0, we prove that t_{E/Q, p} is bounded above by (1/2+\epsilon)p for all sufficiently large good ordinary primes p. We also do numerical calculations on one such E of rank 3, and 5 such E of rank 2, showing in all cases that t_{E/Q, p} = 0 for all good ordinary primes p < 30,000. In fact, we show that, with the possible exception of one good ordinary prime in this range for just one of the curves of rank 2, the p-primary subgroup of the Tate-Shafarevich group of the curve is zero (always supposing p is a good ordinary prime).Comment: 24 page

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures

On passivity and passification of stochastic fuzzy systems with delays: The discrete-time case

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Takagi–Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.This work was supported in part by the Royal Society Sino–British Fellowship Trust Award of the U.K., by the National Natural Science Foundation of China under Grant 60804028, by the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers in China under Grant 200802861044, and by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ‘delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page