700 research outputs found
A Variational Approach to the Structure and Thermodynamics of Linear Polyelectrolytes with Coulomb and Screened Coulomb Interactions
A variational approach, based on a discrete representation of the chain, is
used to calculate free energy and conformational properties in
polyelectrolytes. The true bond and Coulomb potentials are approximated by a
trial isotropic harmonic energy containing force constants between {\em
all}monomer-pairs as variational parameters. By a judicious choice of
representation and the use of incremental matrix inversion, an efficient and
fast-convergent iterative algorithm is constructed, that optimizes the free
energy. The computational demand scales as rather than as expected
in a more naive approach. The method has the additional advantage that in
contrast to Monte Carlo calculations the entropy is easily computed. An
analysis of the high and low temperature limits is given. Also, the variational
formulation is shown to respect the appropriate virial identities.The accuracy
of the approximations introduced are tested against Monte Carlo simulations for
problem sizes ranging from to 1024. Very good accuracy is obtained for
chains with unscreened Coulomb interactions. The addition of salt is described
through a screened Coulomb interaction, for which the accuracy in a certain
parameter range turns out to be inferior to the unscreened case. The reason is
that the harmonic variational Ansatz becomes less efficient with shorter range
interactions.
As a by-product a very efficient Monte Carlo algorithm was developed for
comparisons, providing high statistics data for very large sizes -- 2048
monomers. The Monte Carlo results are also used to examine scaling properties,
based on low- approximations to end-end and monomer-monomer separations. It
is argued that the former increases faster than linearly with the number of
bonds.Comment: 40 pages LaTeX, 13 postscript figure
Perturbing General Uncorrelated Networks
This paper is a direct continuation of an earlier work, where we studied
Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring
the formation of short cycles. Here, we generalize these results. We keep the
same interaction Hamiltonian but let it act on general graphs with uncorrelated
nodes and an arbitrary given degree distribution. It is shown that the results
obtained for Erd\"os-R\'enyi graphs are generic, at the qualitative level.
However, scale-free graphs are an exception to this general rule and exhibit a
singular behaviour, studied thoroughly in this paper, both analytically and
numerically.Comment: 7 pages, 7 eps figures, 2-column revtex format, references adde
A Potts Neuron Approach to Communication Routing
A feedback neural network approach to communication routing problems is
developed with emphasis on Multiple Shortest Path problems, with several
requests for transmissions between distinct start- and endnodes. The basic
ingredients are a set of Potts neurons for each request, with interactions
designed to minimize path lengths and to prevent overloading of network arcs.
The topological nature of the problem is conveniently handled using a
propagator matrix approach. Although the constraints are global, the
algorithmic steps are based entirely on local information, facilitating
distributed implementations. In the polynomially solvable single-request case
the approach reduces to a fuzzy version of the Bellman-Ford algorithm. The
approach is evaluated for synthetic problems of varying sizes and load levels,
by comparing with exact solutions from a branch-and-bound method. With very few
exceptions, the Potts approach gives legal solutions of very high quality. The
computational demand scales merely as the product of the numbers of requests,
nodes, and arcs.Comment: 10 pages LaTe
The Electrostatic Persistence Length Calculated from Monte Carlo, Variational and Perturbation Methods
Monte Carlo simulations and variational calculations using a Gaussian ansatz
are applied to a model consisting of a flexible linear polyelectrolyte chain as
well as to an intrinsically stiff chain with up to 1000 charged monomers.
Addition of salt is treated implicitly through a screened Coulomb potential for
the electrostatic interactions.
For the flexible model the electrostatic persistence length shows roughly
three regimes in its dependence on the Debye-H\"{u}ckel screening length,
.As long as the salt content is low and is longer
than the end-to-end distance, the electrostatic persistence length varies only
slowly with . Decreasing the screening length, a controversial
region is entered. We find that the electrostatic persistence length scales as
, in agreement with experiment on flexible
polyelectrolytes, where is a strength parameter measuring the
electrostatic interactions within the polyelectrolyte. For screening lengths
much shorter than the bond length, the dependence becomes
quadratic in the variational calculation. The simulations suffer from numerical
problems in this regime, but seem to give a relationship half-way between
linear and quadratic.
A low temperature expansion only reproduces the first regime and a high
temperature expansion, which treats the electrostatic interactions as a
perturbation to a Gaussian chain, gives a quadratic dependence on the Debye
length.
For a sufficiently stiff chain, the persistence length varies quadratically
with in agreement with earlier theories.Comment: 20 pages LaTeX, 9 postscript figure
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
Analysis of complex contagions in random multiplex networks
We study the diffusion of influence in random multiplex networks where links
can be of different types, and for a given content (e.g., rumor, product,
political view), each link type is associated with a content dependent
parameter in that measures the relative bias type- links
have in spreading this content. In this setting, we propose a linear threshold
model of contagion where nodes switch state if their "perceived" proportion of
active neighbors exceeds a threshold \tau. Namely, a node connected to
active neighbors and inactive neighbors via type- links will turn
active if exceeds its threshold \tau. Under this
model, we obtain the condition, probability and expected size of global
spreading events. Our results extend the existing work on complex contagions in
several directions by i) providing solutions for coupled random networks whose
vertices are neither identical nor disjoint, (ii) highlighting the effect of
content on the dynamics of complex contagions, and (iii) showing that
content-dependent propagation over a multiplex network leads to a subtle
relation between the giant vulnerable component of the graph and the global
cascade condition that is not seen in the existing models in the literature.Comment: Revised 06/08/12. 11 Pages, 3 figure
Relationships between two dimensions of employee perfectionism, postwork cognitive processing, and work day functioning
This daily diary study examined relations between two distinct perfectionism dimensions and work-related cognitions experienced by employees during evening leisure time. Drawing from perseverative cognitive processing theory, we hypothesized that perfectionistic concerns would be related to work-related worry and rumination during postwork evenings. In contrast, we hypothesized that a theoretically more adaptive perfectionist dimension (perfectionistic strivings) would be associated with positively valenced self-reflections about work across consecutive evenings. A sample of 148 full-time workers completed an initial survey, which included a trait perfectionism measure, reported their work-related cognitions across four consecutive evenings of a working week, rated their sleep quality immediately upon awakening on each subsequent morning, and their daily levels of emotional exhaustion and work engagement at the end of each work day. Results showed that perfectionistic concerns were indirectly negatively associated with sleep quality and work day functioning via the tendency to worry and ruminate about work. In contrast, perfectionistic strivings were indirectly positively associated with work day engagement via the propensity to experience positive thoughts about work during evening leisure time. The theoretical and practical implications of these findings are discussed
Graph Annotations in Modeling Complex Network Topologies
The coarsest approximation of the structure of a complex network, such as the
Internet, is a simple undirected unweighted graph. This approximation, however,
loses too much detail. In reality, objects represented by vertices and edges in
such a graph possess some non-trivial internal structure that varies across and
differentiates among distinct types of links or nodes. In this work, we
abstract such additional information as network annotations. We introduce a
network topology modeling framework that treats annotations as an extended
correlation profile of a network. Assuming we have this profile measured for a
given network, we present an algorithm to rescale it in order to construct
networks of varying size that still reproduce the original measured annotation
profile.
Using this methodology, we accurately capture the network properties
essential for realistic simulations of network applications and protocols, or
any other simulations involving complex network topologies, including modeling
and simulation of network evolution. We apply our approach to the Autonomous
System (AS) topology of the Internet annotated with business relationships
between ASs. This topology captures the large-scale structure of the Internet.
In depth understanding of this structure and tools to model it are cornerstones
of research on future Internet architectures and designs. We find that our
techniques are able to accurately capture the structure of annotation
correlations within this topology, thus reproducing a number of its important
properties in synthetically-generated random graphs
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