Flows on Graphs with Random Capacities

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold that depends on the distribution of capacities. We then examine the maximal total flux from the root to the leaves. Our methods generalize to simple graphs with loops, e.g., to hierarchical lattices and to complete graphs.Comment: 8 pages, 6 figure

Genetic parameters of ovarian cyst incidence in Swedish dairy cattle

International audienc

Monotone graph limits and quasimonotone graphs

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasi-monotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1-W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.Comment: 38 page

Quicksort with unreliable comparisons: a probabilistic analysis

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.Comment: 29 pages, 3 figure

A network-based threshold model for the spreading of fads in society and markets

We investigate the behavior of a threshold model for the spreading of fads and similar phenomena in society. The model is giving the fad dynamics and is intended to be confined to an underlying network structure. We investigate the whole parameter space of the fad dynamics on three types of network models. The dynamics we discover is rich and highly dependent on the underlying network structure. For some range of the parameter space, for all types of substrate networks, there are a great variety of sizes and life-lengths of the fads -- what one see in real-world social and economical systems

Drinking related internal-external locus of control scale. Outcomes measurement tool: attitudes & feelings - attitudes (towards drug and alcohol use).

The DRIE was developed to define an individual’s beliefs about the extent to which life events are under personal control (internal locus of control) or under the influence of chance, fate, or powerful others (external locus of control). The DRIE assesses these beliefs specifically with respect to the individual’s perceptions of control around alcohol, drinking behaviour, and recovery

Crystal water induced switching of magnetically active orbitals in CuCl2

The dehydration of CuCl2*2(H2O) to CuCl2 leads to a dramatic change in magnetic behavior and ground state. Combining density functional electronic structure and model calculations with thermodynamical measurements we reveal the microscopic origin of this unexpected incident -- a crystal water driven switching of the magnetically active orbitals. This switching results in a fundamental change of the coupling regime from a three-dimensional antiferromagnet to a quasi one-dimensional behavior. CuCl2 can be well described as a frustrated J1-J2 Heisenberg chain with ferromagnetic exchange J1 and J2/J1 ~ -1.5 for which a helical ground state is predicted.Comment: 6 pages, 5 figures, 1 table (PRB, accepted

AKLT Models with Quantum Spin Glass Ground States

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered N\'eel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.Comment: 10 pages, 1 figur

Moderate deviations via cumulants

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis and Statulevicius. The examples of random objects we treat include dependency graphs, subgraph-counting statistics in Erd\H{o}s-R\'enyi random graphs and $U$-statistics. Moreover, we prove moderate deviation principles for certain statistics appearing in random matrix theory, namely characteristic polynomials of random unitary matrices as well as the number of particles in a growing box of random determinantal point processes like the number of eigenvalues in the GUE or the number of points in Airy, Bessel, and $\sin$ random point fields.Comment: 24 page

A novel bacterial l-arginine sensor controlling c-di-GMP levels in Pseudomonas aeruginosa

Nutrients such as amino acids play key roles in shaping the metabolism of microorganisms in natural environments and in host–pathogen interactions. Beyond taking part to cellular metabolism and to protein synthesis, amino acids are also signaling molecules able to influence group behavior in microorganisms, such as biofilm formation. This lifestyle switch involves complex metabolic reprogramming controlled by local variation of the second messenger 3′, 5′-cyclic diguanylic acid (c-di-GMP). The intracellular levels of this dinucleotide are finely tuned by the opposite activity of dedicated diguanylate cyclases (GGDEF signature) and phosphodiesterases (EAL and HD-GYP signatures), which are usually allosterically controlled by a plethora of environmental and metabolic clues. Among the genes putatively involved in controlling c-di-GMP levels in P. aeruginosa, we found that the multidomain transmembrane protein PA0575, bearing the tandem signature GGDEF-EAL, is an l-arginine sensor able to hydrolyse c-di-GMP. Here, we investigate the basis of arginine recognition by integrating bioinformatics, molecular biophysics and microbiology. Although the role of nutrients such as l-arginine in controlling the cellular fate in P. aeruginosa (including biofilm, pathogenicity and virulence) is already well established, we identified the first l-arginine sensor able to link environment sensing, c-di-GMP signaling and biofilm formation in this bacterium