On kk-Core Percolation in Four Dimensions

The $k$-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 $k$-core percolation on the four-dimensional regular lattice. For $k=4$ the presence of a discontinuous transition is clearly established but its nature is strictly first order. In particular, the $k$-core density displays no singular behavior before the jump and its correlation length remains finite. For $k=3$ 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

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

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

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 (June–October) 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 “FEM-like” 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 $u$ with node $v$ through a weak tie is proportional to $1/|uv|^\alpha$, where $|uv|$ is the grid distance between $u$ and $v$ and $\alpha\ge 0$ is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after $k \ge 2$ 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 $n$ (the number of nodes in the network) for all range of $\alpha$ both in expectation and with high probability (in particular, $\Omega(n^{\frac{1}{\alpha+2}})$ for $\alpha \le 2$ and $\Omega(n^{\frac{\alpha}{2(\alpha+2)}})$ for $\alpha > 2$ in expectation), while the routing time of simple contagion has polylogarithmic upper bound when $\alpha = 2$. 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

Protein Folding and Spin Glass

We explicitly show the connection between the protein folding problem and spin glass transition. This is then used to identify appropriate quantities that are required to describe the transition. A possible way of observing the spin glass transition is proposed.Comment: Revtex3+epsf, 8 pages and one postscript figure tarred, compressed and uuencoded--appended at the end of the file. Minor TeX change