Normal edge-colorings of cubic graphs

A normal $k$-edge-coloring of a cubic graph is an edge-coloring with $k$ colors having the additional property that when looking at the set of colors assigned to any edge $e$ and the four edges adjacent it, we have either exactly five distinct colors or exactly three distinct colors. We denote by $\chi'_{N}(G)$ the smallest $k$, for which $G$ admits a normal $k$-edge-coloring. Normal $k$-edge-colorings were introduced by Jaeger in order to study his well-known Petersen Coloring Conjecture. More precisely, it is known that proving $\chi'_{N}(G)\leq 5$ for every bridgeless cubic graph is equivalent to proving Petersen Coloring Conjecture and then, among others, Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture. Considering the larger class of all simple cubic graphs (not necessarily bridgeless), some interesting questions naturally arise. For instance, there exist simple cubic graphs, not bridgeless, with $\chi'_{N}(G)=7$. On the other hand, the known best general upper bound for $\chi'_{N}(G)$ was $9$. Here, we improve it by proving that $\chi'_{N}(G)\leq7$ for any simple cubic graph $G$, which is best possible. We obtain this result by proving the existence of specific no-where zero $\mathbb{Z}_2^2$-flows in $4$-edge-connected graphs.Comment: 17 pages, 6 figure

What do you expect from an unfamiliar talker?

Speech perception is made much harder by variability betweentalkers. As a result, listeners need to adapt to each differenttalker’s particular acoustic cue distributions. Thinking of thisadaptation as a form of statistical inference, we explore the rolethat listeners’ prior expectations play in adapting to an unfa-miliar talker. Specifically, we test the hypothesis that listenerswill have a harder time adapting to talkers whose cue distribu-tions fall outside the range of normal variation across talkers.We also show that it is possible to infer listeners’ shared priorexpectations based on patterns of adaptation to different cuedistributions. This provides a potentially powerful tool for di-rectly probing listeners’ prior expectations about talkers thatdoes not rely on speech produced by many different talkers,which is costly to collect and annotate, and only indirectly re-lated to listeners’ subjective expectations

Optoelectronic Reservoir Computing

Reservoir computing is a recently introduced, highly efficient bio-inspired approach for processing time dependent data. The basic scheme of reservoir computing consists of a non linear recurrent dynamical system coupled to a single input layer and a single output layer. Within these constraints many implementations are possible. Here we report an opto-electronic implementation of reservoir computing based on a recently proposed architecture consisting of a single non linear node and a delay line. Our implementation is sufficiently fast for real time information processing. We illustrate its performance on tasks of practical importance such as nonlinear channel equalization and speech recognition, and obtain results comparable to state of the art digital implementations.Comment: Contains main paper and two Supplementary Material

A model for the onset of transport in systems with distributed thresholds for conduction

We present a model supported by simulation to explain the effect of temperature on the conduction threshold in disordered systems. Arrays with randomly distributed local thresholds for conduction occur in systems ranging from superconductors to metal nanocrystal arrays. Thermal fluctuations provide the energy to overcome some of the local thresholds, effectively erasing them as far as the global conduction threshold for the array is concerned. We augment this thermal energy reasoning with percolation theory to predict the temperature at which the global threshold reaches zero. We also study the effect of capacitive nearest-neighbor interactions on the effective charging energy. Finally, we present results from Monte Carlo simulations that find the lowest-cost path across an array as a function of temperature. The main result of the paper is the linear decrease of conduction threshold with increasing temperature: $V_t(T) = V_t(0) (1 - 4.8 k_BT P(0)/ p_c)$, where $1/P(0)$ is an effective charging energy that depends on the particle radius and interparticle distance, and $p_c$ is the percolation threshold of the underlying lattice. The predictions of this theory compare well to experiments in one- and two-dimensional systems.Comment: 14 pages, 10 figures, submitted to PR

Metastability of a granular surface in a spinning bucket

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.

Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model

We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to \emph{stable patterns} and \emph{signed-patterns}, we give general results which allow us to find \emph{all} chiral $q$-state spin-edge Potts models when the number of states $q$ is a prime or the square of a prime, as well as several $q$-dependent family of models. We also prove the absence of monocolor stable signed-pattern with more than four states. This demonstrates a conjecture about cyclic Hadamard matrices in a particular case. The birational transformations associated to these lattice spin-edge models show complexity reduction. In particular we recover a one-parameter family of integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the results into two sections : results pertaining to Physics and results pertaining to Mathematic

Percolating through networks of random thresholds: Finite temperature electron tunneling in metal nanocrystal arrays

We investigate how temperature affects transport through large networks of nonlinear conductances with distributed thresholds. In monolayers of weakly-coupled gold nanocrystals, quenched charge disorder produces a range of local thresholds for the onset of electron tunneling. Our measurements delineate two regimes separated by a cross-over temperature $T^*$. Up to $T^*$ the nonlinear zero-temperature shape of the current-voltage curves survives, but with a threshold voltage for conduction that decreases linearly with temperature. Above $T^*$ the threshold vanishes and the low-bias conductance increases rapidly with temperature. We develop a model that accounts for these findings and predicts $T^*$.Comment: 5 pages including 3 figures; replaced 3/30/04: minor changes; final versio

Statistical Mechanics of Vibration-Induced Compaction of Powders

We propose a theory which describes the density relaxation of loosely packed, cohesionless granular material under mechanical tapping. Using the compactivity concept we develope a formalism of statistical mechanics which allows us to calculate the density of a powder as a function of time and compactivity. A simple fluctuation-dissipation relation which relates compactivity to the amplitude and frequency of a tapping is proposed. Experimental data of E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of initially deposited in a fluffy state powder evolves under carefully controlled tapping towards a random close packing (RCP) density. Ramping the vibration amplitude repeatedly up and back down again reveals the existence of reversible and irreversible branches in the response. In the framework of our approach the reversible branch (along which the RCP density is obtained) corresponds to the steady state solution of the Fokker-Planck equation whereas the irreversible one is represented by a superposition of "excited states" eigenfunctions. These two regimes of response are analyzed theoretically and a qualitative explanation of the hysteresis curve is offered.Comment: 11 pages, 2 figures, Latex. Revised tex

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

Carbon dioxide adsorption and interaction with formation fluids of Jordanian unconventional reservoirs

Shales are mostly unexploited energy resources. However, the extraction and production of their hydrocarbons require innovative methods. Applications involving carbon dioxide in shales could combine its potential use in oil recovery with its storage in view of its impact on global climate. The success of these approaches highly depends on various mechanisms taking place in the rock pores simultaneously. In this work, properties governing these mechanisms are presented at technically relevant conditions. The pendant and sessile drop methods are utilized to measure interfacial tension and wettability, respectively. The gravimetric method is used to quantify CO2 adsorption capacity of shale and gas adsorption kinetics is evaluated to determine diffusion coefficients. It is found that interfacial properties are strongly affected by the operating pressure. The oil-CO2 interfacial tension shows a decrease from approx. 21 mN/m at 0.1 MPa to around 3 mN/m at 20 MPa. A similar trend is observed in brine-CO2 systems. The diffusion coefficient is observed to slightly increase with pressure at supercritical conditions. Finally, the contact angle is found to be directly related to the gas adsorption at the rock surface: Up to 3.8 wt% of CO2 is adsorbed on the shale surface at 20 MPa and 60 °C where a maximum in contact angle is also found. To the best of the author’s knowledge, the affinity of calcite-rich surfaces toward CO2 adsorption is linked experimentally to the wetting behavior for the first time. The results are discussed in terms of CO2 storage scenarios occurring optimally at 20 MPa