Dynamics of Triangulations

We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the expected distribution of the degrees of the nodes seems to follow the power law $d^{-4}$

The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur

Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations

A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the attractors. A mutation introduces some new aspects: the emergence of structurally stable attractors, and chaotic itinerant behavior. In addition, it is reported that a neutral attractor can exist in the mutataion rate -> +0 region.Comment: 4 pages, 9 figure

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

ELMO1 has an essential role in the internalization of Salmonella Typhimurium into enteric macrophages that impacts disease outcome.

Backgrounds and aims4-6 million people die of enteric infections each year. After invading intestinal epithelial cells, enteric bacteria encounter phagocytes. However, little is known about how phagocytes internalize the bacteria to generate host responses. Previously, we have shown that BAI1 (Brain Angiogenesis Inhibitor 1) binds and internalizes Gram-negative bacteria through an ELMO1 (Engulfment and cell Motility protein 1)/Rac1-dependent mechanism. Here we delineate the role of ELMO1 in host inflammatory responses following enteric infection.MethodsELMO1-depleted murine macrophage cell lines, intestinal macrophages and ELMO1 deficient mice (total or myeloid-cell specific) was infected with Salmonella enterica serovar Typhimurium. The bacterial load, inflammatory cytokines and histopathology was evaluated in the ileum, cecum and spleen. The ELMO1 dependent host cytokines were detected by a cytokine array. ELMO1 mediated Rac1 activity was measured by pulldown assay.ResultsThe cytokine array showed reduced release of pro-inflammatory cytokines, including TNF-α and MCP-1, by ELMO1-depleted macrophages. Inhibition of ELMO1 expression in macrophages decreased Rac1 activation (~6 fold) and reduced internalization of Salmonella. ELMO1-dependent internalization was indispensable for TNF-α and MCP-1. Simultaneous inhibition of ELMO1 and Rac function virtually abrogated TNF-α responses to infection. Further, activation of NF-κB, ERK1/2 and p38 MAP kinases were impaired in ELMO1-depleted cells. Strikingly, bacterial internalization by intestinal macrophages was completely dependent on ELMO1. Salmonella infection of ELMO1-deficient mice resulted in a 90% reduction in bacterial burden and attenuated inflammatory responses in the ileum, spleen and cecum.ConclusionThese findings suggest a novel role for ELMO1 in facilitating intracellular bacterial sensing and the induction of inflammatory responses following infection with Salmonella

Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary state as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.Comment: Revised version, published in Journal of Statistical Physic

Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force

We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted $L^{\infty}$ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force

Macroscopic fluctuations theory of aerogel dynamics

We consider the thermodynamic potential describing the macroscopic fluctuation of the current and local energy of a general class of Hamiltonian models including aerogels. We argue that this potential is neither analytic nor strictly convex, a property that should be expected in general but missing from models studied in the literature. This opens the possibility of describing in terms of a thermodynamic potential non-equilibrium phase transitions in a concrete physical context. This special behaviour of the thermodynamic potential is caused by the fact that the energy current is carried by particles which may have arbitrary low speed with sufficiently large probability.Comment: final versio

tuppence-based SERS for the detection of illicit materials

Deposition of silver onto British 2p coins has been demonstrated as an efficient and cost effective approach to producing substrates capable of promoting surface enhanced Raman scattering (SERS). Silver application to the copper coins is undemanding taking just 20 s, and results in the formation of multiple hierarchial dendritic structures. To demonstrate that the silver deposition sites were capable of SERS the highly fluorescent Rhodamine 6G (R6G) probe was used. Analyses indicated that Raman enhancement only occurs at the silver deposition sites and not from the roughened copper surface. The robustness of the substrate in the identification and discrimination of illegal and legal drugs of abuse was then explored. Application of the drugs to the substrates was carried out using spotting and soaking methodologies. Whilst little or no SERS spectra of the drugs were generated upon spotting, soaking of the substrate in a methanolic solution of the drugs yielded a vast amount of spectral information. Excellent reproducibility of the SERS method and classification of three of the drugs, 4-methylmethcathinone (mephedrone), 5,6-methylenedioxy-2-aminoindane (MDAI) and 3,4-methylenedioxy-N-methylamphetamine (MDMA) were demonstrated using principal components analysis and partial least squares

Summability of the perturbative expansion for a zero-dimensional disordered spin model

We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.Comment: LaTeX, 12 pages and 4 figure