32,125 research outputs found
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
Finite-time Lagrangian transport analysis: Stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents
We consider issues associated with the Lagrangian characterisation of flow
structures arising in aperiodically time-dependent vector fields that are only
known on a finite time interval. A major motivation for the consideration of
this problem arises from the desire to study transport and mixing problems in
geophysical flows where the flow is obtained from a numerical solution, on a
finite space-time grid, of an appropriate partial differential equation model
for the velocity field. Of particular interest is the characterisation,
location, and evolution of "transport barriers" in the flow, i.e. material
curves and surfaces. We argue that a general theory of Lagrangian transport has
to account for the effects of transient flow phenomena which are not captured
by the infinite-time notions of hyperbolicity even for flows defined for all
time. Notions of finite-time hyperbolic trajectories, their finite time stable
and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE) fields
and associated Lagrangian coherent structures have been the main tools for
characterizing transport barriers in the time-aperiodic situation. In this
paper we consider a variety of examples, some with explicit solutions, that
illustrate, in a concrete manner, the issues and phenomena that arise in the
setting of finite-time dynamical systems. Of particular significance for
geophysical applications is the notion of "flow transition" which occurs when
finite-time hyperbolicity is lost, or gained. The phenomena discovered and
analysed in our examples point the way to a variety of directions for rigorous
mathematical research in this rapidly developing, and important, new area of
dynamical systems theory
Noise-enhanced computation in a model of a cortical column
Varied sensory systems use noise in order to enhance detection of weak
signals. It has been conjectured in the literature that this effect, known as
stochastic resonance, may take place in central cognitive processes such as the
memory retrieval of arithmetical multiplication. We show in a simplified model
of cortical tissue, that complex arithmetical calculations can be carried out
and are enhanced in the presence of a stochastic background. The performance is
shown to be positively correlated to the susceptibility of the network, defined
as its sensitivity to a variation of the mean of its inputs. For nontrivial
arithmetic tasks such as multiplication, stochastic resonance is an emergent
property of the microcircuitry of the model network
Detecting Topology Variations in Dynamical Networks
This paper considers the problem of detecting topology variations in
dynamical networks. We consider a network whose behavior can be represented via
a linear dynamical system. The problem of interest is then that of finding
conditions under which it is possible to detect node or link disconnections
from prior knowledge of the nominal network behavior and on-line measurements.
The considered approach makes use of analysis tools from switching systems
theory. A number of results are presented along with examples
Numerical detection of the Gardner transition in a mean-field glass former
Recent theoretical advances predict the existence, deep into the glass phase,
of a novel phase transition, the so-called Gardner transition. This transition
is associated with the emergence of a complex free energy landscape composed of
many marginally stable sub-basins within a glass metabasin. In this study, we
explore several methods to detect numerically the Gardner transition in a
simple structural glass former, the infinite-range Mari-Kurchan model. The
transition point is robustly located from three independent approaches: (i) the
divergence of the characteristic relaxation time, (ii) the divergence of the
caging susceptibility, and (iii) the abnormal tail in the probability
distribution function of cage order parameters. We show that the numerical
results are fully consistent with the theoretical expectation. The methods we
propose may also be generalized to more realistic numerical models as well as
to experimental systems.Comment: 17 pages, 16 figure
Critical Transitions In a Model of a Genetic Regulatory System
We consider a model for substrate-depletion oscillations in genetic systems,
based on a stochastic differential equation with a slowly evolving external
signal. We show the existence of critical transitions in the system. We apply
two methods to numerically test the synthetic time series generated by the
system for early indicators of critical transitions: a detrended fluctuation
analysis method, and a novel method based on topological data analysis
(persistence diagrams).Comment: 19 pages, 8 figure
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