487 research outputs found
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
Switching Control for Parameter Identifiability of Uncertain Systems
This paper considers the problem of identifying the parameters of an
uncertain linear system by means of feedback control. The problem is approached
by considering time-varying controllers. It is shown that even when the
uncertainty set is not finite, parameter identifiability can be generically
ensured by switching among a finite number of linear time-invariant
controllers. The results are shown to have several implications, ranging from
fault detection and isolation to adaptive and supervisory control. Practical
aspects of the problem are also discussed in details
Glassy phases in Random Heteropolymers with correlated sequences
We develop a new analytic approach for the study of lattice heteropolymers,
and apply it to copolymers with correlated Markovian sequences. According to
our analysis, heteropolymers present three different dense phases depending
upon the temperature, the nature of the monomer interactions, and the sequence
correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a
``frozen glass'' phase. The presence of the new intermediate ``soft glass''
phase is predicted for instance in the case of polyampholytes with sequences
that favor the alternation of monomers.
Our approach is based on the cavity method, a refined Bethe Peierls
approximation adapted to frustrated systems. It amounts to a mean field
treatment in which the nearest neighbor correlations, which are crucial in the
dense phases of heteropolymers, are handled exactly. This approach is powerful
and versatile, it can be improved systematically and generalized to other
polymeric systems
Identifiability of undirected dynamical networks:A graph-theoretic approach
This paper deals with identifiability of undirected dynamical networks with
single-integrator node dynamics. We assume that the graph structure of such
networks is known, and aim to find graph-theoretic conditions under which the
state matrix of the network can be uniquely identified. As our main
contribution, we present a graph coloring condition that ensures
identifiability of the network's state matrix. Additionally, we show how the
framework can be used to assess identifiability of dynamical networks with
general, higher-order node dynamics. As an interesting corollary of our
results, we find that excitation and measurement of all network nodes is not
required. In fact, for many network structures, identification is possible with
only small fractions of measured and excited nodes.Comment: 6 page
Reconstructing the Density of States by History-Dependent Metadynamics
We present a novel method for the calculation of the energy density of states
D(E) for systems described by classical statistical mechanics. The method
builds on an extension of a recently proposed strategy that allows the free
energy profile of a canonical system to be recovered within a pre-assigned
accuracy,[A. Laio and M. Parrinello, PNAS 2002]. The method allows a good
control over the error on the recovered system entropy. This fact is exploited
to obtain D(E) more efficiently by combining measurements at different
temperatures. The accuracy and efficiency of the method are tested for the
two-dimensional Ising model (up to size 50x50) by comparison with both exact
results and previous studies. This method is a general one and should be
applicable to more realistic model systems
Corner transfer matrix renormalization group method for two-dimensional self-avoiding walks and other O(n) models
We present an extension of the corner transfer matrix renormalisation group
(CTMRG) method to O(n) invariant models, with particular interest in the
self-avoiding walk class of models (O(n=0)). The method is illustrated using an
interacting self-avoiding walk model. Based on the efficiency and versatility
when compared to other available numerical methods, we present CTMRG as the
method of choice for two-dimensional self-avoiding walk problems.Comment: 4 pages 7 figures Substantial rewrite of previous version to include
calculations of critical points and exponents. Final version accepted for
publication in PRE (Rapid Communications
RNA denaturation: excluded volume, pseudoknots and transition scenarios
A lattice model of RNA denaturation which fully accounts for the excluded
volume effects among nucleotides is proposed. A numerical study shows that
interactions forming pseudoknots must be included in order to get a sharp
continuous transition. Otherwise a smooth crossover occurs from the swollen
linear polymer behavior to highly ramified, almost compact conformations with
secondary structures. In the latter scenario, which is appropriate when these
structures are much more stable than pseudoknot links, probability
distributions for the lengths of both loops and main branches obey scaling with
nonclassical exponents.Comment: 4 pages 3 figure
On the size of knots in ring polymers
We give two different, statistically consistent definitions of the length l
of a prime knot tied into a polymer ring. In the good solvent regime the
polymer is modelled by a self avoiding polygon of N steps on cubic lattice and
l is the number of steps over which the knot ``spreads'' in a given
configuration. An analysis of extensive Monte Carlo data in equilibrium shows
that the probability distribution of l as a function of N obeys a scaling of
the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could
be independent of knot type. As a consequence, the knot is weakly localized,
i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak
localization implies the existence of a peculiar characteristic length l^(nu) ~
N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the
whole ring, this length determines a leading power law correction which is much
stronger than that found in the case of unrestricted topology. The existence of
such correction is confirmed by an analysis of extensive Monte Carlo data for
the radius of gyration. The collapsed regime is studied by introducing in the
model sufficiently strong attractive interactions for nearest neighbor sites
visited by the self-avoiding polygon. In this regime knot length determinations
can be based on the entropic competition between two knotted loops separated by
a slip link. These measurements enable us to conclude that each knot is
delocalized (t ~ 1).Comment: 29 pages, 14 figure
Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to
the study of the three-dimensional antiferromagnetic q-state Potts models on a
simple cubic lattice. We systematically study the phase transition of the
models with q=3, 4, 5 and 6. We obtain the finite-temperature phase transition
for q= 3 and 4, whereas the transition temperature is down to zero for q=5. For
q=6 there exists no order for all the temperatures. We also study the
ground-state properties. The size-dependence of the ground-state entropy is
investigated. We find that the ground-state entropy is larger than the
contribution from the typical configurations of the broken-sublattice-symmetry
state for q=3. The same situations are found for q = 4, 5 and 6.Comment: 9 pages including 9 eps figures, RevTeX, to appear in J. Phys.
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