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

Balancing Rations for Milk Components

ABSTRACT: Yields of protein and fat are positively correlated with yield of milk but increased milk yield can dilute the percentages of protein and fat in milk. Milk components can be altered through ration formulation. Fat is easier to change than protein which is easier to change than lactose. Substrates for mammary synthesis of milk components are provided by fermentation in the rumen and by digestion in the small intestine. Substrates like trans octadecenoic acids can inhibit mammary synthesis of fat. Imbalances of amino acids can lower mammary synthesis of protein. Carbohydrates affect milk yield through the supply of glucose to the mammary gland and milk protein through growth of ruminal bacteria. Fibre is needed to maintain normal rumen function. Through altered carbohydrate fermentation and decreased bacterial growth, subclinical rumen acidosis can decrease yields of milk, protein and fat. Buffers affect milk fat by increasing acetate:propionate and by decreasing ruminal synthesis and mammary uptake of trans octadecenoic acids. Rumen bacteria need degradable protein. Escape protein should contain amino acids that promote synthesis of milk protein. Balancing rations for amino acids increases mammary synthesis of protein and milk yield is increased in early lactation cows. Rations with added fat need to contain more rumen escape protein. Ionophores provide a means of increasing the ratio of protein:fat in milk

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

On the study of jamming percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property

Rigidity percolation in a field

Rigidity Percolation with g degrees of freedom per site is analyzed on randomly diluted Erdos-Renyi graphs with average connectivity gamma, in the presence of a field h. In the (gamma,h) plane, the rigid and flexible phases are separated by a line of first-order transitions whose location is determined exactly. This line ends at a critical point with classical critical exponents. Analytic expressions are given for the densities n_f of uncanceled degrees of freedom and gamma_r of redundant bonds. Upon crossing the coexistence line, n_f and gamma_r are continuous, although their first derivatives are discontinuous. We extend, for the case of nonzero field, a recently proposed hypothesis, namely that the density of uncanceled degrees of freedom is a ``free energy'' for Rigidity Percolation. Analytic expressions are obtained for the energy, entropy, and specific heat. Some analogies with a liquid-vapor transition are discussed. Particularizing to zero field, we find that the existence of a (g+1)-core is a necessary condition for rigidity percolation with g degrees of freedom. At the transition point gamma_c, Maxwell counting of degrees of freedom is exact on the rigid cluster and on the (g+1)-rigid-core, i.e. the average coordination of these subgraphs is exactly 2g, although gamma_r, the average coordination of the whole system, is smaller than 2g. gamma_c is found to converge to 2g for large g, i.e. in this limit Maxwell counting is exact globally as well. This paper is dedicated to Dietrich Stauffer, on the occasion of his 60th birthday.Comment: RevTeX4, psfig, 16 pages. Equation numbering corrected. Minor typos correcte

Inhalation of Ultrafine Particles Alters Blood Leukocyte Expression of Adhesion Molecules in Humans

Ultrafine particles (UFPs; aerodynamic diameter < 100 nm) may contribute to the respiratory and cardiovascular morbidity and mortality associated with particulate air pollution. We tested the hypothesis that inhalation of carbon UFPs has vascular effects in healthy and asthmatic subjects, detectable as alterations in blood leukocyte expression of adhesion molecules. Healthy subjects inhaled filtered air and freshly generated elemental carbon particles (count median diameter ~ 25 nm, geometric standard deviation ~ 1.6), for 2 hr, in three separate protocols: 10 μg/m(3) at rest, 10 and 25 μg/m(3) with exercise, and 50 μg/m(3) with exercise. In a fourth protocol, subjects with asthma inhaled air and 10 μg/m(3) UFPs with exercise. Peripheral venous blood was obtained before and at intervals after exposure, and leukocyte expression of surface markers was quantitated using multiparameter flow cytometry. In healthy subjects, particle exposure with exercise reduced expression of adhesion molecules CD54 and CD18 on monocytes and CD18 and CD49d on granulocytes. There were also concentration-related reductions in blood monocytes, basophils, and eosinophils and increased lymphocyte expression of the activation marker CD25. In subjects with asthma, exposure with exercise to 10 μg/m(3) UFPs reduced expression of CD11b on monocytes and eosinophils and CD54 on granulocytes. Particle exposure also reduced the percentage of CD4(+) T cells, basophils, and eosinophils. Inhalation of elemental carbon UFPs alters peripheral blood leukocyte distribution and expression of adhesion molecules, in a pattern consistent with increased retention of leukocytes in the pulmonary vascular bed

Jamming percolation and glassy dynamics

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we review some of our previous works on Kinetically Constrained Models. The Knights models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when $\rho\nearrow\rho_c$. These properties give rise for Knight models to an ergodicity breaking transition at $\rho_c$: at and above $\rho_{c}$ a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.Comment: Submitted to the special issue of Journal of Statistical Physics on Spin glasses and related topic

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson-Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.Comment: 59 page