A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning dynamics. Previous numerical works have reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on the neural network evolution. Furthermore, we show that the sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest

A practical regularization technique for modified nodal analysis in large-scale time-domain circuit simulation

Fast full-chip time-domain simulation calls for advanced numerical integration techniques with capability to handle the systems with (tens of) millions of variables resulting from the modified nodal analysis (MNA). General MNA formulation, however, leads to a differential algebraic equation (DAE) system with singular coefficient matrix, for which most of explicit methods, which usually offer better scalability than implicit methods, are not readily available. In this paper, we develop a practical two-stage strategy to remove the singularity in MNA equations of large-scale circuit networks. A topological index reduction is first applied to reduce the DAE index of the MNA equation to one. The index-1 system is then fed into a systematic process to eliminate excess variables in one run, which leads to a nonsingular system. The whole regularization process is devised with emphasis on exact equivalence, low complexity, and sparsity preservation, and is thus well suited to handle extremely large circuits. © 2012 IEEE.published_or_final_versio

Recent Developments of World-Line Monte Carlo Methods

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.Comment: To appear in Journal of Physical Society of Japa

Estimating causal networks in biosphere–atmosphere interaction with the PCMCI approach

Local meteorological conditions and biospheric activity are tightly coupled. Understanding these links is an essential prerequisite for predicting the Earth system under climate change conditions. However, many empirical studies on the interaction between the biosphere and the atmosphere are based on correlative approaches that are not able to deduce causal paths, and only very few studies apply causal discovery methods. Here, we use a recently proposed causal graph discovery algorithm, which aims to reconstruct the causal dependency structure underlying a set of time series. We explore the potential of this method to infer temporal dependencies in biosphere-atmosphere interactions. Specifically we address the following questions: How do periodicity and heteroscedasticity influence causal detection rates, i.e. the detection of existing and non-existing links? How consistent are results for noise-contaminated data? Do results exhibit an increased information content that justifies the use of this causal-inference method? We explore the first question using artificial time series with well known dependencies that mimic real-world biosphere-atmosphere interactions. The two remaining questions are addressed jointly in two case studies utilizing observational data. Firstly, we analyse three replicated eddy covariance datasets from a Mediterranean ecosystem at half hourly time resolution allowing us to understand the impact of measurement uncertainties. Secondly, we analyse global NDVI time series (GIMMS 3g) along with gridded climate data to study large-scale climatic drivers of vegetation greenness. Overall, the results confirm the capacity of the causal discovery method to extract time-lagged linear dependencies under realistic settings. The violation of the method's assumptions increases the likelihood to detect false links. Nevertheless, we consistently identify interaction patterns in observational data. Our findings suggest that estimating a directed biosphere-atmosphere network at the ecosystem level can offer novel possibilities to unravel complex multi-directional interactions. Other than classical correlative approaches, our findings are constrained to a few meaningful set of relations which can be powerful insights for the evaluation of terrestrial ecosystem models

Direct and indirect measurements on electrocaloric effect : recent developments and perspectives

Y.L. and B.D. acknowledge the China Scholarship Council (CSC) for funding Y.L.'s stay in France and a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d'Avenir” program (Reference: ANR-10-LABX-0035, Labex NanoSaclay).It has been ten years since the discovery of the giant electrocaloric effect in ferroelectric materials showed that it is possible to employ this effect for substantial cooling applications. This last decade has been marked by increasing research interest, especially in characterizing and measuring the electrocaloric effect using both the so-called indirect and direct approaches. In this context, a comprehensive summary and careful reexamination of these approaches are very timely and of great importance to justify the assumptions used in different measurement techniques. This review is therefore dedicated to cover recent important and rapid advances from both the indirect and direct measurements and provides critical insights relevant for quantifying the electrocaloric effect. It involves electrocaloric materials from normal ferroelectrics, antiferroelectrics, and relaxors, and it fundamentally focuses on how the electrocaloric entropy changes in response to electric field in these typical electrocalorics. The article addresses recent developments, especially during the past three years, such as technical selection of proper polarization-electric field loops, negative electrocaloric effect in antiferroelectrics and relaxors, the controversial debate on the indirect method in relaxors, the important role of field dependence of specific heat, kinetic factors, and so on. Moreover, this review also is concerned with extracting reliable data by direct measurements. Four typical techniques and devices used recently, such as thermocouples, differential scanning calorimeters, specifically designed calorimeters, and scanning thermal microscopy, are briefly reviewed, while infrared cameras are emphasized. We hope that our review will not only provide a useful background to understand fundamentally the electrocaloric effect and what one really measures but also may act as a practical guide to exploit and develop electrocalorics towards the design of suitable devices.Publisher PDFPeer reviewe

Constitutive modeling for isotropic materials (HOST)

The results of the first year of work on a program to validate unified constitutive models for isotropic materials utilized in high temperature regions of gas turbine engines and to demonstrate their usefulness in computing stress-strain-time-temperature histories in complex three-dimensional structural components. The unified theories combine all inelastic strain-rate components in a single term avoiding, for example, treating plasticity and creep as separate response phenomena. An extensive review of existing unified theories is given and numerical methods for integrating these stiff time-temperature-dependent constitutive equations are discussed. Two particular models, those developed by Bodner and Partom and by Walker, were selected for more detailed development and evaluation against experimental tensile, creep and cyclic strain tests on specimens of a cast nickel base alloy, B19000+Hf. Initial results comparing computed and test results for tensile and cyclic straining for temperature from ambient to 982 C and strain rates from 10(exp-7) 10(exp-3) s(exp-1) are given. Some preliminary date correlations are presented also for highly non-proportional biaxial loading which demonstrate an increase in biaxial cyclic hardening rate over uniaxial or proportional loading conditions. Initial work has begun on the implementation of both constitutive models in the MARC finite element computer code

Freshwater ecosystem services in mining regions : modelling options for policy development support

The ecosystem services (ES) approach offers an integrated perspective of social-ecological systems, suitable for holistic assessments of mining impacts. Yet for ES models to be policy-relevant, methodological consensus in mining contexts is needed. We review articles assessing ES in mining areas focusing on freshwater components and policy support potential. Twenty-six articles were analysed concerning (i) methodological complexity (data types, number of parameters, processes and ecosystem-human integration level) and (ii) potential applicability for policy development (communication of uncertainties, scenario simulation, stakeholder participation and management recommendations). Articles illustrate mining impacts on ES through valuation exercises mostly. However, the lack of ground-and surface-water measurements, as well as insufficient representation of the connectivity among soil, water and humans, leave room for improvements. Inclusion of mining-specific environmental stressors models, increasing resolution of topographies, determination of baseline ES patterns and inclusion of multi-stakeholder perspectives are advantageous for policy support. We argue that achieving more holistic assessments exhorts practitioners to aim for high social-ecological connectivity using mechanistic models where possible and using inductive methods only where necessary. Due to data constraints, cause-effect networks might be the most feasible and best solution. Thus, a policy-oriented framework is proposed, in which data science is directed to environmental modelling for analysis of mining impacts on water ES