2,506 research outputs found
Multiscale Granger causality
In the study of complex physical and biological systems represented by
multivariate stochastic processes, an issue of great relevance is the
description of the system dynamics spanning multiple temporal scales. While
methods to assess the dynamic complexity of individual processes at different
time scales are well-established, multiscale analysis of directed interactions
has never been formalized theoretically, and empirical evaluations are
complicated by practical issues such as filtering and downsampling. Here we
extend the very popular measure of Granger causality (GC), a prominent tool for
assessing directed lagged interactions between joint processes, to quantify
information transfer across multiple time scales. We show that the multiscale
processing of a vector autoregressive (AR) process introduces a moving average
(MA) component, and describe how to represent the resulting ARMA process using
state space (SS) models and to combine the SS model parameters for computing
exact GC values at arbitrarily large time scales. We exploit the theoretical
formulation to identify peculiar features of multiscale GC in basic AR
processes, and demonstrate with numerical simulations the much larger
estimation accuracy of the SS approach compared with pure AR modeling of
filtered and downsampled data. The improved computational reliability is
exploited to disclose meaningful multiscale patterns of information transfer
between global temperature and carbon dioxide concentration time series, both
in paleoclimate and in recent years
Multiscale Analysis of Information Dynamics for Linear Multivariate Processes
In the study of complex physical and physiological systems represented by
multivariate time series, an issue of great interest is the description of the
system dynamics over a range of different temporal scales. While
information-theoretic approaches to the multiscale analysis of complex dynamics
are being increasingly used, the theoretical properties of the applied measures
are poorly understood. This study introduces for the first time a framework for
the analytical computation of information dynamics for linear multivariate
stochastic processes explored at different time scales. After showing that the
multiscale processing of a vector autoregressive (VAR) process introduces a
moving average (MA) component, we describe how to represent the resulting VARMA
process using state-space (SS) models and how to exploit the SS model
parameters to compute analytical measures of information storage and
information transfer for the original and rescaled processes. The framework is
then used to quantify multiscale information dynamics for simulated
unidirectionally and bidirectionally coupled VAR processes, showing that
rescaling may lead to insightful patterns of information storage and transfer
but also to potentially misleading behaviors
Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
The surveillance, analysis and ultimately the efficient long-term prediction
and control of epidemic dynamics appear to be one of the major challenges
nowadays. Detailed atomistic mathematical models play an important role towards
this aim. In this work it is shown how one can exploit the Equation Free
approach and optimization methods such as Simulated Annealing to bridge
detailed individual-based epidemic simulation with coarse-grained,
systems-level, analysis. The methodology provides a systematic approach for
analyzing the parametric behavior of complex/ multi-scale epidemic simulators
much more efficiently than simply simulating forward in time. It is shown how
steady state and (if required) time-dependent computations, stability
computations, as well as continuation and numerical bifurcation analysis can be
performed in a straightforward manner. The approach is illustrated through a
simple individual-based epidemic model deploying on a random regular connected
graph. Using the individual-based microscopic simulator as a black box
coarse-grained timestepper and with the aid of Simulated Annealing I compute
the coarse-grained equilibrium bifurcation diagram and analyze the stability of
the stationary states sidestepping the necessity of obtaining explicit closures
at the macroscopic level under a pairwise representation perspective
Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations
For more than a century, cerebral cartography has been driven by
investigations of structural and morphological properties of the brain across
spatial scales and the temporal/functional phenomena that emerge from these
underlying features. The next era of brain mapping will be driven by studies
that consider both of these components of brain organization simultaneously --
elucidating their interactions and dependencies. Using this guiding principle,
we explored the origin of slowly fluctuating patterns of synchronization within
the topological core of brain regions known as the rich club, implicated in the
regulation of mood and introspection. We find that a constellation of densely
interconnected regions that constitute the rich club (including the anterior
insula, amygdala, and precuneus) play a central role in promoting a stable,
dynamical core of spontaneous activity in the primate cortex. The slow time
scales are well matched to the regulation of internal visceral states,
corresponding to the somatic correlates of mood and anxiety. In contrast, the
topology of the surrounding "feeder" cortical regions show unstable, rapidly
fluctuating dynamics likely crucial for fast perceptual processes. We discuss
these findings in relation to psychiatric disorders and the future of
connectomics.Comment: 35 pages, 6 figure
An isogeometric analysis for elliptic homogenization problems
A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method
Coupling different levels of resolution in molecular simulations
Simulation schemes that allow to change molecular representation in a
subvolume of the simulation box while preserving the equilibrium with the
surrounding introduce conceptual problems of thermodynamic consistency. In this
work we present a general scheme based on thermodynamic arguments which ensures
thermodynamic equilibrium among the molecules of different representation. The
robustness of the algorithm is tested for two examples, namely an adaptive
resolution simulation, atomistic/coarse-grained, for a liquid of tetrahedral
molecules and an adaptive resolution simulation of a binary mixture of
tetrahedral molecules and spherical solutes
Multi-level agent-based modeling - A literature survey
During last decade, multi-level agent-based modeling has received significant
and dramatically increasing interest. In this article we present a
comprehensive and structured review of literature on the subject. We present
the main theoretical contributions and application domains of this concept,
with an emphasis on social, flow, biological and biomedical models.Comment: v2. Ref 102 added. v3-4 Many refs and text added v5-6 bibliographic
statistics updated. v7 Change of the name of the paper to reflect what it
became, many refs and text added, bibliographic statistics update
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
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