610 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
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
Long-term treatment of the developing retina with the metabotropic glutamate agonist APB induces long-term changes in the stratification of retinal ganglion cell dendrites
The gradual restriction of initially multistratified retinal ganglion cell (RGC) dendrites into ON and OFF sublaminae of the inner plexiform layer (IPL) can be effectively blocked by treating the developing retina with 2-amino-4-phosphonobutyrate (APB), the metabotropic glutamate agonist, or by light deprivation. Previous studies have focused on the short-term consequences of such manipulations, so the long-term effects of arresting dendritic stratification on the structural development of RGCs are as yet unknown. In the present study, we have addressed this issue by performing a morphological analysis of alpha RGCs labeled by retrograde transport of horseradish peroxidase injected into the dorsal lateral geniculate nucleus of adult cats that received monocular injections of APB from postnatal (P) day 2 until P30. A large proportion of the alpha cells in the APB-treated eye (44%) were found to have multistratified dendrites that terminated in both the ON and OFF sublaminae of the IPL. The dendritic arborization pattern in the sublaminae of the IPL of these cells was asymmetric, showing a variety of forms. Immunolabeling of retinal cross-sections showed that mGLUR6 receptors appeared normal in density and location, while qualitative observation suggested an increase in the axonal arborization of rod bipolar cells. These findings indicate that long-term treatment of the neonatal retina with APB induces a long- lasting structural reorganization in retinal circuitry that most likely accounts for some of the previously described changes in the functional properties of RGCs
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
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
Evaluation and Field Calibration of a Low-cost Ozone Monitor at a Regulatory Urban Monitoring Station
The performance of a low cost ozone monitor (Aeroqual Series 500 portable gas monitors coupled with a metal oxide sensor for ozone; model OZL) was assessed under field conditions. Ten ozone monitors were initially calibrated in clean-air laboratory conditions and tested at controlled ozone concentrations of 5 to 100 ppb. Results showed good linearity and fast response with respect to a conventional research-grade ozone monitor. One monitor was then co-located at a regulatory air quality monitoring station that uses a U.S. federal equivalent method (FEM) ozone analyzer. Raw data from the Aeroqual monitor collected over 4 months (JuneâOctober) at a 10-minute time-resolution, showed good agreement (r2 = 0.83) with the FEM values but with an overestimation of ~12%. Data were averaged to different time resolutions; 1 h time averaged concentrations showed the best fit with the FEM results (r2 = 0.87). An analysis of the ratio of FEM/monitor concentrations against chemical and meteorological variables suggested the potential of interferences due to temperature, relative humidity, nitrogen oxides, and volatile organic compounds. Three correction models using temperature, humidity, and nitrogen dioxide (NO2) were then tested to better relate the monitor concentrations to the FEM values. Temperature and humidity are two variables commonly available (or easily measurable) at sampling sites. The model (#3) that added NO2 did not provide a substantial improvement in the fit. Thus, the proposed models with only temperature and humidity can be easily adopted and adapted by any user. The corrected data explained up to 91% of the variance and showed statistically significant improvement of the goodness of fits as well as decreased influence of the interfering variables on the diurnal and weekly patterns. The correction models were also able to lower the effect of seasonal temperature changes, allowing the use of the monitors over long-term sampling campaigns. This study demonstrated that the Aeroqual ozone monitors can return âFEM-likeâ concentrations after appropriate corrections. Therefore, data provided by a network of monitors could determine the intra-urban spatial variations in ozone concentrations. These results suggest that these monitors could provide more accurate human exposure assessments and thereby reduce exposure misclassification and its resulting bias in epidemiological studies
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
Hourly land-use regression models based on low-cost PM monitor data
Land-use regression (LUR) models provide location and time specific estimates of exposure to air pollution and thereby improve the sensitivity of health effects models. However, they require pollutant concentrations at multiple locations along with land-use variables. Often, monitoring is performed over short durations using mobile monitoring with research-grade instruments. Low-cost PM monitors provide an alternative approach that increases the spatial and temporal resolution of the air quality data. LUR models were developed to predict hourly PM concentrations across a metropolitan area using PM concentrations measured simultaneously at multiple locations with low-cost monitors. Monitors were placed at 23 sites during the 2015/16 heating season. Monitors were externally calibrated using co-located measurements including a reference instrument (GRIMM particle spectrometer). LUR models for each hour of the day and weekdays/weekend days were developed using the deletion/substitution/addition algorithm. Coefficients of determination for hourly PM predictions ranged from 0.66 and 0.76 (average 0.7). The hourly-resolved LUR model results will be used in epidemiological studies to examine if and how quickly, increases in ambient PM concentrations trigger adverse health events by reducing the exposure misclassification that arises from using less time resolved exposure estimates
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
Boson-exchange parquet solver for dual fermions
We present and implement a parquet approximation within the dual-fermion formalism based on a partial bosonization of the dual vertex function which substantially reduces the computational cost of the calculation. The method relies on splitting the vertex exactly into single-boson exchange contributions and a residual four-fermion vertex, which physically embody, respectively, long- and short-range spatial correlations. After recasting the parquet equations in terms of the residual vertex, these are solved using the truncated-unity method of Eckhardt et al. [Phys. Rev. B 101, 155104 (2020)2469-995010.1103/PhysRevB.101.155104], which allows for a rapid convergence with the number of form factors in different regimes. While our numerical treatment of the parquet equations can be restricted to only a few Matsubara frequencies, reminiscent of Astretsov et al. [Phys. Rev. B 101, 075109 (2020)2469-995010.1103/PhysRevB.101.075109], the one- and two-particle spectral information is fully retained. In applications to the two-dimensional Hubbard model the method agrees quantitatively with a stochastic summation of diagrams over a wide range of parameters
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