223,405 research outputs found
Noise bridges dynamical correlation and topology in coupled oscillator networks
We study the relationship between dynamical properties and interaction
patterns in complex oscillator networks in the presence of noise. A striking
finding is that noise leads to a general, one-to-one correspondence between the
dynamical correlation and the connections among oscillators for a variety of
node dynamics and network structures. The universal finding enables an accurate
prediction of the full network topology based solely on measuring the dynamical
correlation. The power of the method for network inference is demonstrated by
the high success rate in identifying links for distinct dynamics on both model
and real-life networks. The method can have potential applications in various
fields due to its generality, high accuracy and efficiency.Comment: 2 figures, 2 tables. Accepted by Physical Review Letter
Elastic heterogeneity of soft random solids
Spatial heterogeneity in the elastic properties of soft random solids is
investigated via a two-pronged approach. First, a nonlocal phenomenological
model for the elastic free energy is examined. This features a quenched random
kernel, which induces randomness in the residual stress and Lame coefficients.
Second, a semi-microscopic model network is explored using replica statistical
mechanics. The Goldstone fluctuations of the semi-microscopic model are shown
to reproduce the phenomenological model, and via this correspondence the
statistical properties of the residual stress and Lame coefficients are
inferred. Correlations involving the residual stress are found to be
long-ranged and governed by a universal parameter that also gives the mean
shear modulus.Comment: 5 page
Scaling laws and universality in the choice of election candidates
Nowadays there is an increasing interest of physicists in finding
regularities related to social phenomena. This interest is clearly motivated by
applications that a statistical mechanical description of the human behavior
may have in our society. By using this framework, we address this work to cover
an open question related to elections: the choice of elections candidates
(candidature process). Our analysis reveals that, apart from the social
motivations, this system displays features of traditional out-of-equilibrium
physical phenomena such as scale-free statistics and universality. Basically,
we found a non-linear (power law) mean correspondence between the number of
candidates and the size of the electorate (number of voters), and also that
this choice has a multiplicative underlying process (lognormal behavior). The
universality of our findings is supported by data from 16 elections from 5
countries. In addition, we show that aspects of network scale-free can be
connected to this universal behavior.Comment: Accepted for publication in EP
Universal Cyclic Topology in Polymer Networks
Polymer networks invariably possess topological defects: loops of different orders which have profound effects on network properties. Here, we demonstrate that all cyclic topologies are a universal function of a single dimensionless parameter characterizing the conditions for network formation. The theory is in excellent agreement with both experimental measurements of hydrogel loop fractions and Monte Carlo simulations without any fitting parameters. We demonstrate the superposition of the dilution effect and chain-length effect on loop formation. The one-to-one correspondence between the network topology and primary loop fraction demonstrates that the entire network topology is characterized by measurement of just primary loops, a single chain topological feature. Different cyclic defects cannot vary independently, in contrast to the intuition that the densities of all topological species are freely adjustable. Quantifying these defects facilitates studying the correlations between the topology and properties of polymer networks, providing a key step in overcoming an outstanding challenge in polymer physics.National Science Foundation (U.S.) (Award DMR-1253306
Neural Network Field Theories: Non-Gaussianity, Actions, and Locality
Both the path integral measure in field theory and ensembles of neural
networks describe distributions over functions. When the central limit theorem
can be applied in the infinite-width (infinite-) limit, the ensemble of
networks corresponds to a free field theory. Although an expansion in
corresponds to interactions in the field theory, others, such as in a small
breaking of the statistical independence of network parameters, can also lead
to interacting theories. These other expansions can be advantageous over the
-expansion, for example by improved behavior with respect to the universal
approximation theorem. Given the connected correlators of a field theory, one
can systematically reconstruct the action order-by-order in the expansion
parameter, using a new Feynman diagram prescription whose vertices are the
connected correlators. This method is motivated by the Edgeworth expansion and
allows one to derive actions for neural network field theories. Conversely, the
correspondence allows one to engineer architectures realizing a given field
theory by representing action deformations as deformations of neural network
parameter densities. As an example, theory is realized as an
infinite- neural network field theory.Comment: 49 pages, plus references and appendice
p-Adic Statistical Field Theory and Deep Belief Networks
In this work we initiate the study of the correspondence between p-adic statistical field theories (SFTs) and neural networks (NNs). In general quantum field theories over a p-adic spacetime can be formulated in a rigorous way. Nowadays these theories are considered just mathematical toy models for understanding the problems of the true theories. In this work we show these theories are deeply connected with the deep belief networks (DBNs). Hinton et al. constructed DBNs by stacking several restricted Boltzmann machines (RBMs). The purpose of this construction is to obtain a network with a hierarchical structure (a deep learning architecture). An RBM corresponds a certain spin glass, thus a DBN should correspond to an ultrametric (hierarchical) spin glass. A model of such system can be easily constructed by using p-adic numbers. In our approach, a p-adic SFT corresponds to a p-adic continuous DBN, and a discretization of this theory corresponds to a p-adic discrete DBN. We show that these last machines are universal approximators. In the p-adic framework, the correspondence between SFTs and NNs is not fully developed. We point out several open problems
New activity pattern in human interactive dynamics
We investigate the response function of human agents as demonstrated by
written correspondence, uncovering a new universal pattern for how the reactive
dynamics of individuals is distributed across the set of each agent's contacts.
In long-term empirical data on email, we find that the set of response times
considered separately for the messages to each different correspondent of a
given writer, generate a family of heavy-tailed distributions, which have
largely the same features for all agents, and whose characteristic times grow
exponentially with the rank of each correspondent. We furthermore show that
this universal behavioral pattern emerges robustly by considering weighted
moving averages of the priority-conditioned response-time probabilities
generated by a basic prioritization model. Our findings clarify how the range
of priorities in the inputs from one's environment underpin and shape the
dynamics of agents embedded in a net of reactive relations. These newly
revealed activity patterns might be present in other general interactive
environments, and constrain future models of communication and interaction
networks, affecting their architecture and evolution.Comment: 15 pages, 7 figure
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