15,779 research outputs found
Understanding Complex Systems: From Networks to Optimal Higher-Order Models
To better understand the structure and function of complex systems,
researchers often represent direct interactions between components in complex
systems with networks, assuming that indirect influence between distant
components can be modelled by paths. Such network models assume that actual
paths are memoryless. That is, the way a path continues as it passes through a
node does not depend on where it came from. Recent studies of data on actual
paths in complex systems question this assumption and instead indicate that
memory in paths does have considerable impact on central methods in network
science. A growing research community working with so-called higher-order
network models addresses this issue, seeking to take advantage of information
that conventional network representations disregard. Here we summarise the
progress in this area and outline remaining challenges calling for more
research.Comment: 8 pages, 4 figure
Space-time random walk loop measures
In this work, we investigate a novel setting of Markovian loop measures and
introduce a new class of loop measures called Bosonic loop measures. Namely, we
consider loop soups with varying intensity (chemical potential in
physics terms), and secondly, we study Markovian loop measures on graphs with
an additional "time" dimension leading to so-called space-time random walks and
their loop measures and Poisson point loop processes. Interesting phenomena
appear when the additional coordinate of the space-time process is on a
discrete torus with non-symmetric jump rates. The projection of these
space-time random walk loop measures onto the space dimensions is loop measures
on the spatial graph, and in the scaling limit of the discrete torus, these
loop measures converge to the so-called [Bosonic loop measures]. This provides
a natural probabilistic definition of [Bosonic loop measures]. These novel loop
measures have similarities with the standard Markovian loop measures only that
they give weights to loops of certain lengths, namely any length which is
multiple of a given length which serves as an additional
parameter. We complement our study with generalised versions of Dynkin's
isomorphism theorem (including a version for the whole complex field) as well
as Symanzik's moment formulae for complex Gaussian measures. Due to the lacking
symmetry of our space-time random walks, the distributions of the occupation
time fields are given in terms of complex Gaussian measures over complex-valued
random fields ([B92,BIS09]. Our space-time setting allows obtaining quantum
correlation functions as torus limits of space-time correlation functions.Comment: 3 figure
Perspectives on Multi-Level Dynamics
As Physics did in previous centuries, there is currently a common dream of
extracting generic laws of nature in economics, sociology, neuroscience, by
focalising the description of phenomena to a minimal set of variables and
parameters, linked together by causal equations of evolution whose structure
may reveal hidden principles. This requires a huge reduction of dimensionality
(number of degrees of freedom) and a change in the level of description. Beyond
the mere necessity of developing accurate techniques affording this reduction,
there is the question of the correspondence between the initial system and the
reduced one. In this paper, we offer a perspective towards a common framework
for discussing and understanding multi-level systems exhibiting structures at
various spatial and temporal levels. We propose a common foundation and
illustrate it with examples from different fields. We also point out the
difficulties in constructing such a general setting and its limitations
Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
We compute exactly the distribution of the occupation time in a discrete {\em
non-Markovian} toy sequence which appears in various physical contexts such as
the diffusion processes and Ising spin glass chains. The non-Markovian property
makes the results nontrivial even for this toy sequence. The distribution is
shown to have non-Gaussian tails characterized by a nontrivial large deviation
function which is computed explicitly. An exact mapping of this sequence to an
Ising spin glass chain via a gauge transformation raises an interesting new
question for a generic finite sized spin glass model: at a given temperature,
what is the distribution (over disorder) of the thermally averaged number of
spins that are aligned to their local fields? We show that this distribution
remains nontrivial even at infinite temperature and can be computed explicitly
in few cases such as in the Sherrington-Kirkpatrick model with Gaussian
disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included
The Markovian metamorphosis of a simple turbulent cascade model
Markovian properties of a discrete random multiplicative cascade model of
log-normal type are discussed. After taking small-scale resummation and
breaking of the ultrametric hierarchy into account, qualitative agreement with
Kramers-Moyal coefficients, recently deduced from a fully developed turbulent
flow, is achieved.Comment: 6 pages, 2 figure
A survey on gain-scheduled control and filtering for parameter-varying systems
Copyright © 2014 Guoliang Wei 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 paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany
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