481 research outputs found
On -Core Percolation in Four Dimensions
The -core percolation on the Bethe lattice has been proposed as a simple
model of the jamming transition because of its hybrid first-order/second-order
nature. We investigate numerically -core percolation on the four-dimensional
regular lattice. For the presence of a discontinuous transition is
clearly established but its nature is strictly first order. In particular, the
-core density displays no singular behavior before the jump and its
correlation length remains finite. For the transition is continuous
GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs
We present a prototype of a software tool for exploration of multiple
combinatorial optimisation problems in large real-world and synthetic complex
networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial
Explorer), provides a unified framework for scalable computation and
presentation of high-quality suboptimal solutions and bounds for a number of
widely studied combinatorial optimisation problems. Efficient representation
and applicability to large-scale graphs and complex networks are particularly
considered in its design. The problems currently supported include maximum
clique, graph colouring, maximum independent set, minimum vertex clique
covering, minimum dominating set, as well as the longest simple cycle problem.
Suboptimal solutions and intervals for optimal objective values are estimated
using scalable heuristics. The tool is designed with extensibility in mind,
with the view of further problems and both new fast and high-performance
heuristics to be added in the future. GraphCombEx has already been successfully
used as a support tool in a number of recent research studies using
combinatorial optimisation to analyse complex networks, indicating its promise
as a research software tool
Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics
We show that facilitated spin models of cooperative dynamics introduced by
Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar
to the one predicted by the mode-coupling theory of supercooled liquids and the
dynamical theory of mean-field disordered systems. At low temperature such
cooperative models show a two-step relaxation and their equilibration time
diverges at a finite temperature according to a power-law. The geometric nature
of the dynamical arrest corresponds to a bootstrap percolation process which
leads to a phase space organization similar to the one of mean-field disordered
systems. The relaxation dynamics after a subcritical quench exhibits aging and
converges asymptotically to the threshold states that appear at the bootstrap
percolation transition.Comment: 7 pages, 6 figures, minor changes, final version to appear in
Europhys. Let
Dynamics of bootstrap percolation
Bootstrap percolation transition may be first order or second order, or it
may have a mixed character where a first order drop in the order parameter is
preceded by critical fluctuations. Recent studies have indicated that the mixed
transition is characterized by power law avalanches, while the continuous
transition is characterized by truncated avalanches in a related sequential
bootstrap process. We explain this behavior on the basis of a through
analytical and numerical study of the avalanche distributions on a Bethe
lattice.Comment: Proceedings of the International Workshop and Conference on
Statistical Physics Approaches to Multidisciplinary Problems, IIT Guwahati,
India, 7-13 January 200
Remarks on Bootstrap Percolation in Metric Networks
We examine bootstrap percolation in d-dimensional, directed metric graphs in
the context of recent measurements of firing dynamics in 2D neuronal cultures.
There are two regimes, depending on the graph size N. Large metric graphs are
ignited by the occurrence of critical nuclei, which initially occupy an
infinitesimal fraction, f_* -> 0, of the graph and then explode throughout a
finite fraction. Smaller metric graphs are effectively random in the sense that
their ignition requires the initial ignition of a finite, unlocalized fraction
of the graph, f_* >0. The crossover between the two regimes is at a size N_*
which scales exponentially with the connectivity range \lambda like_* \sim
\exp\lambda^d. The neuronal cultures are finite metric graphs of size N \simeq
10^5-10^6, which, for the parameters of the experiment, is effectively random
since N<< N_*. This explains the seeming contradiction in the observed finite
f_* in these cultures. Finally, we discuss the dynamics of the firing front
The Routing of Complex Contagion in Kleinberg's Small-World Networks
In Kleinberg's small-world network model, strong ties are modeled as
deterministic edges in the underlying base grid and weak ties are modeled as
random edges connecting remote nodes. The probability of connecting a node
with node through a weak tie is proportional to , where
is the grid distance between and and is the
parameter of the model. Complex contagion refers to the propagation mechanism
in a network where each node is activated only after neighbors of the
node are activated.
In this paper, we propose the concept of routing of complex contagion (or
complex routing), where we can activate one node at one time step with the goal
of activating the targeted node in the end. We consider decentralized routing
scheme where only the weak ties from the activated nodes are revealed. We study
the routing time of complex contagion and compare the result with simple
routing and complex diffusion (the diffusion of complex contagion, where all
nodes that could be activated are activated immediately in the same step with
the goal of activating all nodes in the end).
We show that for decentralized complex routing, the routing time is lower
bounded by a polynomial in (the number of nodes in the network) for all
range of both in expectation and with high probability (in particular,
for and
for in expectation),
while the routing time of simple contagion has polylogarithmic upper bound when
. Our results indicate that complex routing is harder than complex
diffusion and the routing time of complex contagion differs exponentially
compared to simple contagion at sweetspot.Comment: Conference version will appear in COCOON 201
Optimizing spread dynamics on graphs by message passing
Cascade processes are responsible for many important phenomena in natural and
social sciences. Simple models of irreversible dynamics on graphs, in which
nodes activate depending on the state of their neighbors, have been
successfully applied to describe cascades in a large variety of contexts. Over
the last decades, many efforts have been devoted to understand the typical
behaviour of the cascades arising from initial conditions extracted at random
from some given ensemble. However, the problem of optimizing the trajectory of
the system, i.e. of identifying appropriate initial conditions to maximize (or
minimize) the final number of active nodes, is still considered to be
practically intractable, with the only exception of models that satisfy a sort
of diminishing returns property called submodularity. Submodular models can be
approximately solved by means of greedy strategies, but by definition they lack
cooperative characteristics which are fundamental in many real systems. Here we
introduce an efficient algorithm based on statistical physics for the
optimization of trajectories in cascade processes on graphs. We show that for a
wide class of irreversible dynamics, even in the absence of submodularity, the
spread optimization problem can be solved efficiently on large networks.
Analytic and algorithmic results on random graphs are complemented by the
solution of the spread maximization problem on a real-world network (the
Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem
Balancing Rations for Milk Components
ABSTRACT: Yields of protein and fat are positively correlated with yield of milk but increased milk yield can dilute the percentages of protein and fat in milk. Milk components can be altered through ration formulation. Fat is easier to change than protein which is easier to change than lactose. Substrates for mammary synthesis of milk components are provided by fermentation in the rumen and by digestion in the small intestine. Substrates like trans octadecenoic acids can inhibit mammary synthesis of fat. Imbalances of amino acids can lower mammary synthesis of protein. Carbohydrates affect milk yield through the supply of glucose to the mammary gland and milk protein through growth of ruminal bacteria. Fibre is needed to maintain normal rumen function. Through altered carbohydrate fermentation and decreased bacterial growth, subclinical rumen acidosis can decrease yields of milk, protein and fat. Buffers affect milk fat by increasing acetate:propionate and by decreasing ruminal synthesis and mammary uptake of trans octadecenoic acids. Rumen bacteria need degradable protein. Escape protein should contain amino acids that promote synthesis of milk protein. Balancing rations for amino acids increases mammary synthesis of protein and milk yield is increased in early lactation cows. Rations with added fat need to contain more rumen escape protein. Ionophores provide a means of increasing the ratio of protein:fat in milk
Laboratory and Field Testing of an Automated Atmospheric Particle-Bound Reactive Oxygen Species Sampling-Analysis System
In this study, various laboratory and field tests were performed to develop an effective automated particle-bound ROS sampling-analysis system. The system uses 2′ 7′-dichlorofluorescin (DCFH) fluorescence method as a nonspecific, general indicator of the particle-bound ROS. A sharp-cut cyclone and a particle-into-liquid sampler (PILS) were used to collect PM2.5 atmospheric particles into slurry produced by a DCFH-HRP solution. The laboratory results show that the DCFH and H2O2 standard solutions could be kept at room temperature for at least three and eight days, respectively. The field test in Rochester, NY, shows that the average ROS concentration was 8.3 ± 2.2 nmol of equivalent H2O2 m−3 of air. The ROS concentrations were observed to be greater after foggy conditions. This study demonstrates the first practical automated sampling-analysis system to measure this ambient particle component
Hysteresis in the Random Field Ising Model and Bootstrap Percolation
We study hysteresis in the random-field Ising model with an asymmetric
distribution of quenched fields, in the limit of low disorder in two and three
dimensions. We relate the spin flip process to bootstrap percolation, and show
that the characteristic length for self-averaging increases as in 2d, and as in 3d, for disorder
strength much less than the exchange coupling J. For system size , the coercive field varies as for
the square lattice, and as on the cubic lattice.
Its limiting value is 0 for L tending to infinity, both for square and cubic
lattices. For lattices with coordination number 3, the limiting magnetization
shows no jump, and tends to J.Comment: 4 pages, 4 figure
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