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

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

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

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

Infinite-cluster geometry in central-force networks

We show that the infinite percolating cluster (with density P_inf) of central-force networks is composed of: a fractal stress-bearing backbone (Pb) and; rigid but unstressed ``dangling ends'' which occupy a finite volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is then a first-order transition in P_inf = Pd + Pb, while Pb is second-order with exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations of triangular lattices give Beta'_tr = 0.255 +/- 0.03.Comment: 6 pages, 4 figures, uses epsfig. Accepted for publication in Physical Review Letter

Residential Indoor and Outdoor PM Measured Using Low-cost Monitors during the Heating Season in Monroe County, NY

Continuous 1-minute indoor and outdoor PM concentrations (~PM2.5) were measured from November through April of 2015/16 and 2016/17 at 50 single family residences in Monroe County, NY (25 per season) using Speck (Airviz Inc., Pittsburgh, PA) low-cost monitors (LCMs). While the accuracy of LCMs is inconsistent and source dependent, the LCMs provided reasonable precision for estimating indoor/outdoor (I/O) ratios based on laboratory and field testing, understanding the relationship between indoor sources and concentration, and comparing PM concentrations across residences for the detected size range (0.5-3 mm). The indoor PM2.5 concentration pattern showed clear morning and evening peaks as well as higher indoor concentrations during the weekends when people are typically at home. The mean I/O PM2.5 ratio was 1.1 for all homes and increased to 1.7 when a combustion source was in use as indicated by an elevated CO concentration whereas most prior studies have found this ratio to be < 1. Increases in wood-burning appliance temperature and indoor CO concentrations were found to be associated with an overall moderate (mean value of 2.1 µg/m3) increase in indoor PM concentration averaged over the heating season. Short-term PM increases greater than 100 µg/m3 were periodically observed in homes with and without wood-burning appliances operating. This study provides an approach for exposure assessment in homes that can be utilized by employing appropriate calibration and quality assurance procedures for the LCMs

Magnetic order in the Ising model with parallel dynamics

It is discussed how the equilibrium properties of the Ising model are described by an Hamiltonian with an antiferromagnetic low temperature behavior if only an heat bath dynamics, with the characteristics of a Probabilistic Cellular Automaton, is assumed to determine the temporal evolution of the system.Comment: 9 pages, 3 figure