3,268 research outputs found
A network-based threshold model for the spreading of fads in society and markets
We investigate the behavior of a threshold model for the spreading of fads
and similar phenomena in society. The model is giving the fad dynamics and is
intended to be confined to an underlying network structure. We investigate the
whole parameter space of the fad dynamics on three types of network models. The
dynamics we discover is rich and highly dependent on the underlying network
structure. For some range of the parameter space, for all types of substrate
networks, there are a great variety of sizes and life-lengths of the fads --
what one see in real-world social and economical systems
beta-Cu2V2O7: a spin-1/2 honeycomb lattice system
We report on band structure calculations and a microscopic model of the
low-dimensional magnet beta-Cu2V2O7. Magnetic properties of this compound can
be described by a spin-1/2 anisotropic honeycomb lattice model with the
averaged coupling \bar J1=60-66 K. The low symmetry of the crystal structure
leads to two inequivalent couplings J1 and J1', but this weak spatial
anisotropy does not affect the essential physics of the honeycomb spin lattice.
The structural realization of the honeycomb lattice is highly non-trivial: the
leading interactions J1 and J1' run via double bridges of VO4 tetrahedra
between spatially separated Cu atoms, while the interactions between structural
nearest neighbors are negligible. The non-negligible inter-plane coupling
Jperp~15 K gives rise to the long-range magnetic ordering at TN~26 K. Our model
simulations improve the fit of the magnetic susceptibility data, compared to
the previously assumed spin-chain models. Additionally, the simulated ordering
temperature of 27 K is in remarkable agreement with the experiment. Our study
evaluates beta-Cu2V2O7 as the best available experimental realization of the
spin-1/2 Heisenberg model on the honeycomb lattice. We also provide an
instructive comparison of different band structure codes and computational
approaches to the evaluation of exchange couplings in magnetic insulators.Comment: 11 pages, 10 figures, 2 tables: revised version, extended description
of simulation result
Training product unit neural networks with genetic algorithms
The training of product neural networks using genetic algorithms is discussed. Two unusual neural network techniques are combined; product units are employed instead of the traditional summing units and genetic algorithms train the network rather than backpropagation. As an example, a neural netork is trained to calculate the optimum width of transistors in a CMOS switch. It is shown how local minima affect the performance of a genetic algorithm, and one method of overcoming this is presented
Distance distribution in random graphs and application to networks exploration
We consider the problem of determining the proportion of edges that are
discovered in an Erdos-Renyi graph when one constructs all shortest paths from
a given source node to all other nodes. This problem is equivalent to the one
of determining the proportion of edges connecting nodes that are at identical
distance from the source node. The evolution of this quantity with the
probability of existence of the edges exhibits intriguing oscillatory behavior.
In order to perform our analysis, we introduce a new way of computing the
distribution of distances between nodes. Our method outperforms previous
similar analyses and leads to estimates that coincide remarkably well with
numerical simulations. It allows us to characterize the phase transitions
appearing when the connectivity probability varies.Comment: 12 pages, 8 figures (18 .eps files
Cluster approximations for infection dynamics on random networks
In this paper, we consider a simple stochastic epidemic model on large
regular random graphs and the stochastic process that corresponds to this
dynamics in the standard pair approximation. Using the fact that the nodes of a
pair are unlikely to share neighbors, we derive the master equation for this
process and obtain from the system size expansion the power spectrum of the
fluctuations in the quasi-stationary state. We show that whenever the pair
approximation deterministic equations give an accurate description of the
behavior of the system in the thermodynamic limit, the power spectrum of the
fluctuations measured in long simulations is well approximated by the
analytical power spectrum. If this assumption breaks down, then the cluster
approximation must be carried out beyond the level of pairs. We construct an
uncorrelated triplet approximation that captures the behavior of the system in
a region of parameter space where the pair approximation fails to give a good
quantitative or even qualitative agreement. For these parameter values, the
power spectrum of the fluctuations in finite systems can be computed
analytically from the master equation of the corresponding stochastic process.Comment: the notation has been changed; Ref. [26] and a new paragraph in
Section IV have been adde
Thermodynamic versus Topological Phase Transitions: Cusp in the Kert\'esz Line
We present a study of phase transitions of the Curie--Weiss Potts model at
(inverse) temperature , in presence of an external field . Both
thermodynamic and topological aspects of these transitions are considered. For
the first aspect we complement previous results and give an explicit equation
of the thermodynamic transition line in the -- plane as well as the
magnitude of the jump of the magnetization (for . The signature
of the latter aspect is characterized here by the presence or not of a giant
component in the clusters of a Fortuin--Kasteleyn type representation of the
model. We give the equation of the Kert\'esz line separating (in the
-- plane) the two behaviours. As a result, we get that this line
exhibits, as soon as , a very interesting cusp where it
separates from the thermodynamic transition line
Cutting edges at random in large recursive trees
We comment on old and new results related to the destruction of a random
recursive tree (RRT), in which its edges are cut one after the other in a
uniform random order. In particular, we study the number of steps needed to
isolate or disconnect certain distinguished vertices when the size of the tree
tends to infinity. New probabilistic explanations are given in terms of the
so-called cut-tree and the tree of component sizes, which both encode different
aspects of the destruction process. Finally, we establish the connection to
Bernoulli bond percolation on large RRT's and present recent results on the
cluster sizes in the supercritical regime.Comment: 29 pages, 3 figure
Electronic structure and magnetic properties of the spin-1/2 Heisenberg system CuSe2O5
A microscopic magnetic model for the spin-1/2 Heisenberg chain compound
CuSe2O5 is developed based on the results of a joint experimental and
theoretical study. Magnetic susceptibility and specific heat data give evidence
for quasi-1D magnetism with leading antiferromagnetic (AFM) couplings and an
AFM ordering temperature of 17 K. For microscopic insight, full-potential DFT
calculations within the local density approximation (LDA) were performed. Using
the resulting band structure, a consistent set of transfer integrals for an
effective one-band tight-binding model was obtained. Electronic correlations
were treated on a mean-field level starting from LDA (LSDA+U method) and on a
model level (Hubbard model). In excellent agreement of experiment and theory,
we find that only two couplings in CuSe2O5 are relevant: the nearest-neighbour
intra-chain interaction of 165 K and a non-frustrated inter-chain coupling of
20 K. From a comparison with structurally related systems (Sr2Cu(PO4)2,
Bi2CuO4), general implications for a magnetic ordering in presence of
inter-chain frustration are made.Comment: 20 pages, 8 figures, 3 table
Rainbow matchings in Dirac bipartite graphs
This is the peer reviewed version of the following article: Coulson, M, Perarnau, G. Rainbow matchings in Dirac bipartite graphs. Random Struct Alg. 2019; 55: 271– 289., which has been published in final form at https://doi.org/10.1002/rsa.20835. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsWe show the existence of rainbow perfect matchings in µn-bounded edge colorings of Dirac bipartite graphs, for a sufficiently small µ¿>¿0. As an application of our results, we obtain several results on the existence of rainbow k-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree
Unicyclic Components in Random Graphs
The distribution of unicyclic components in a random graph is obtained
analytically. The number of unicyclic components of a given size approaches a
self-similar form in the vicinity of the gelation transition. At the gelation
point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a
result, the total number of unicyclic components grows logarithmically with the
system size.Comment: 4 pages, 2 figure
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