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NETWORK complexity AND SYNCHRONOUS BEHAVIOR - AN EXPERIMENTAL APPROACH

international JOURNAL OF NEURAL SYSTEMS 2010年第3期20卷 233-247页

作者： Neefs, P. J. Steur, E. Nijmeijer, H. Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands ASML DE IVS Immers NL-5504 DR Veldhoven Netherlands EUV Overlay NL-5504 DR Veldhoven Netherlands

We discuss synchronization in networks of Hindmarsh-Rose neurons that are interconnected via gap junctions, also known as electrical synapses. We present theoretical results for interactions without time-delay. These results are supported by experiments with a setup consisting of sixteen electronic equivalents of the Hindmarsh-Rose neuron. We show experimental results of networks where time-delay on the interaction is taken into account. We discuss in particular the influence of the network topology on the synchronization.

关键词： Network synchronization neuronal cell time-delay electronic brain

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INTRODUCTION

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international JOURNAL OF NEURAL SYSTEMS 2010年第1期20卷 V-V页

作者： Yu, Wen Sanchez, E. N. CINVESTAV IPN Mexico City DF Mexico CINVESTAV Unidad Guadalajara Mexico City 14000 DF Mexico

An introduction to the journal "international Journal of Neural Systems," is presented in which the editor discusses articles on the workshops coping with complexity: model reduction and data analysis, and T... 详细信息

关键词： workshopS (Adult education) MATHEMATICS

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PRINCIPAL MANIFOLDS AND GRAPHS IN PRACTICE: FROM MOLECULAR BIOLOGY TO DYNAMICAL SYSTEMS

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international JOURNAL OF NEURAL SYSTEMS 2010年第3期20卷 219-232页

作者： Gorban, Alexander N. Zinovyev, Andrei Curie Mines Paritech INSERM U900 Inst Curie F-75005 Paris France Univ Leicester Dept Math Leicester LE1 7RH Leics England

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.

关键词： Kohonen neural networks self-organizing maps principal manifolds principal graphs data visualization

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data COMPRESSION AND REGRESSION THROUGH LOCAL PRINCIPAL CURVES AND SURFACES

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international JOURNAL OF NEURAL SYSTEMS 2010年第3期20卷 177-192页

作者： Einbeck, Jochen Evers, Ludger Powell, Benedict Univ Durham Dept Math Sci Durham DH1 3LE England Univ Glasgow Dept Stat Glasgow G12 8QQ Lanark Scotland

We consider principal curves and surfaces in the context of multivariate regression modelling. For predictor spaces featuring complex dependency patterns between the involved variables, the intrinsic dimensionality of the data tends to be very small due to the high redundancy induced by the dependencies. In situations of this type, it is useful to approximate the high-dimensional predictor space through a low-dimensional manifold (i.e., a curve or a surface), and use the projections onto the manifold as compressed predictors in the regression problem. In the case that the intrinsic dimensionality of the predictor space equals one, we use the local principal curve algorithm for the the compression step. We provide a novel algorithm which extends this idea to local principal surfaces, thus covering cases of an intrinsic dimensionality equal to two, which is in principle extendible to manifolds of arbitrary dimension. We motivate and apply the novel techniques using astrophysical and oceanographic data examples.

关键词： Dimension reduction smoothing Iocalized PCA mean shift

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coping with complexity: model reduction and data analysis

Coping with Complexity: Model Reduction and Data Analysis

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international research workshop: coping with complexity: model reduction and data analysis

ISBN: (纸本)9783642149405

The proceedings contain 17 papers. The topics discussed include: the use of global sensitivity methods for the analysis, evaluation and improvement of complex modeling systems;optimization and linear control of large scale nonlinear systems: a review and a suite of model reduction-based techniques;universal algorithms, mathematics of semirings and parallel computations;scaling invariant interpolation for singularly perturbed vector fields (SPVF);think globally, move locally: coarse graining of effective free energy surfaces;extracting functional dependence from sparse data using dimensionality reduction: application to potential energy surface construction;a multilevel algorithm to compute steady states of lattice Boltzmann models;time step expansions and the invariant manifold approach to lattice Boltzmann models;and adaptive simplification of complex systems: a review of the relaxation- redistribution approach.

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Extracting functional dependence from sparse data using dimensionality reduction: Application to potential energy surface construction

Extracting functional dependence from sparse data using dime...

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international research workshop: coping with complexity: model reduction and data analysis

作者： Manzhos, Sergei Yamashita, Koichi Carrington, Tucker Department of Chemical System Engineering School of Engineering University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan Department of Chemistry Queens University Kingston ON K7L 3N6 Canada

To construct a continuous D-dimensional function that representssparse data, we use either a single function depending on dmax can reliably be recovered (or only coupling up to a certain order can be recovered if orig... 详细信息

ISBN: (纸本)9783642149405

关键词： Potential energy surfaces

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CLUSTER-BASED REGULARIZED SLICED INVERSE REGRESSION FOR FORECASTING MACROECONOMIC VARIABLES

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Journal of Systems Science & complexity 2014年第1期27卷 75-91页

作者： YU Yue CHEN Zhihong YANG Jie TradeLink L.L.CS. Wacker Drive Suite 1900 Chicago Illinois USA. School of International Trade and: Economics University of International Business and Economics BeijingChina. Department of Mathematics Statistics and Computer Science University of Illinois at Chicago Chicago Illinois USA.

This paper concerns the dimension reduction in regression for large data set. The authors introduce a new method based on the sliced inverse regression approach, cMled cluster-based regularized sliced inverse regression. The proposed method not only keeps the merit of considering both response and predictors＇ information, but also enhances the capability of handling highly correlated variables. It is justified under certain linearity conditions. An empirical application on a macroeconomic data set shows that the proposed method has outperformed the dynamic factor model and other shrinkage methods.

关键词： Cluster-based forecast macroeconomics sliced inverse regression.

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The use of global sensitivity methods for the analysis, evaluation and improvement of complex modelling systems

The use of global sensitivity methods for the analysis, eval...

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international research workshop: coping with complexity: model reduction and data analysis

作者： Tomlin, Alison S. Ziehn, Tilo Energy and Resources Research Institute School of Process Environmental and Materials Engineering University of Leeds Leeds LS2 9JT United Kingdom Department of Earth Sciences University of Bristol Bristol BS8 1RJ United Kingdom

ISBN: (纸本)9783642149405

models which involve the coupling of complex chemical and physical processes are being increasingly used within engineering design and decision making. Improvements in available compute power have allowed us to represent such processes with increasing levels of model detail. However, our ability to accurately specify the required high dimensional input data often does not keep pace with the development of model structure. The analysis ofmodel uncertainty must therefore form a key part of the evaluation of such models. Furthermore, sensitivity analysis methods, which determine the parameters contributing most to output uncertainty, can inform the process of model improvement. In this paper we show by example that global sensitivity methods, and in particular methods based onquasi-random sampling high dimensional model representation (QRS-HDMR), are capable of contributing to the model evaluation and improvement process by highlighting key parameters and model subcomponents which drive the output uncertainty of complex models. The method of QRS-HDMR will be described and its application within the fields of combustion and reactive pollution dispersion will be demonstrated. The key points addressed in the work are (1) the potential for complexity reduction using QRS-HDMR methods, (2) global vs. local sensitivity indices for exploring the response to parameters in complex non-linear models, (3) the possibilities for parameter tuning or feasible set reduction via comparison of models with experiment whilst incorporating uncertainty/sensitivity analysis, (4) model improvement through parameter importance ranking coupled with further ab initio modelling studies, (5) robustness to model structure. The generation of a meta-model via QRS-HDMR is shown to be a reasonably efficient global sensitivity method for systems where effects are limited to second-order. Where higher order effects exist, simple transformations of model outputs are shown to improve the accuracy of the met

关键词： Sensitivity analysis

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Geometric criteria for model reduction in chemical kinetics via optimization of trajectories

Geometric criteria for model reduction in chemical kinetics ...

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international research workshop: coping with complexity: model reduction and data analysis

作者： Lebiedz, Dirk Reinhardt, Volkmar Siehr, Jochen Unger, Jonas University of Heidelberg Im Neuenheimer Feld 368 Heidelberg 69120 Germany University of Freiburg Habsburgerstraße 49 79104 Freiburg Germany

ISBN: (纸本)9783642149405

The need for reduced models of chemical kinetics is motivated by the fact that the simulation of reactive flows with detailed chemistry is generally computationally expensive. In dissipative dynamical systems different time scales cause an anisotropically contracting phase flow. Most kinetic model reduction approaches explicitly exploit this and separate the dynamics into fast and slow modes. We propose an implicit approach for the approximation of slow attracting manifolds by computing trajectories as solutions of an optimization problem suggesting a variational principle characterizing trajectories near slow attracting manifolds. The objective functional for the identification of suitable trajectories is supposed to represent the extent of relaxation of chemical forces along the trajectories which is proposed to be minimal on the slow manifold. Corresponding geometric criteria are motivated via fundamental concepts from differential geometry and physics. They are compared to each other through three kinetic reaction mechanisms.

关键词： Trajectories

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Computing realizations of reaction kinetic networks with given properties

Computing realizations of reaction kinetic networks with giv...

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international research workshop: coping with complexity: model reduction and data analysis

作者： Szederkényi, Gábor Hangos, Katalin M. Csercsik, Dávid Process Control Research Group Computer and Automation Research Institute Hungarian Academy of Sciences Budapest 1518 Hungary Department of Electrical Engineering and Information Systems University of Pannonia Egyetem u. 10 Veszprém 8200 Hungary

ISBN: (纸本)9783642149405

The solution to the problem of finding the reaction kinetic realization of a given system obeying the mass action law containing the minimal/maximal number of reactions and complexes is shown in this paper. The proposed methods are based on Mixed Integer Linear Programming where the mass action kinetics is encoded into the linear constraints. Although the problems are NP-hard in the current setting, the developed algorithms give a usable answer to some of the questions first raised in [1].

关键词： Reaction kinetics

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