Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl

Standard decomposition of expansive ergodically supported dynamics

In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically supported dynamical system $(X,T)$ with the shadowing property establishes a sufficient criterion for the existence of quasigroup operations defined almost everywhere outside of universally null sets and for which $T$ is an automorphism. Furthermore, we find a decomposition of the dynamics of $T$ in terms of $T$-invariant weak topological subquasigroups.Comment: 18 pages, the conditions on the entropy in Theorem 3.5 was improved. Some small changes in the text, by adding more explanation

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

A discrete time neural network model with spiking neurons II. Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.Comment: 43 pages - revised version - to appear il Journal of Mathematical Biolog

A pharmacogenetics study to predict outcome in patients receiving anti-VEGF therapy in age related macular degeneration

John W Kitchens,1,* Nawal Kassem,2,* William Wood,1 Thomas W Stone,1 Rick Isernhagen,1 Edward Wood,1 Brad A Hancock,2 Milan Radovich,2,4 Josh Waymire,4 Lang Li,3,4 Bryan P Schneider2,41Ophthalmology, Retina Associates of Kentucky, Lexington, KY; 2Department of Medicine, Divisions of Hematology/Oncology, 3Biostatistics, 4Department of Medical and Molecular Genetics, Indiana University School of Medicine, Indianapolis, IN, USA *These authors contributed equallyPurpose: To ascertain whether single nucleotide polymorphisms (SNPs) in the Vascular Endothelial Growth factor (VEGFA), Complement Factor H (CFH), and LOC387715 genes could predict outcome to anti-VEGF therapy for patients with age related macular degeneration (AMD).Methods: Patients with “wet” AMD were identified by chart review. Baseline optical coherence tomography (OCT) and visual acuity (VA) data, and at least 6 months of clinical follow up after 3 initial monthly injections of bevacizumab or ranibizumab were required for inclusion. Based on OCT and VA, patients were categorized into two possible clinical outcomes: (a) responders and (b) non-responders. DNA was extracted from saliva and genotyped for candidate SNPs in the VEGFA, LOC387715, and CFH genes. Clinical outcomes were statistically compared to patient genotypes.Results: 101 patients were recruited, and one eye from each patient was included in the analysis. 97% of samples were successfully genotyped for all SNPs. We found a statistically significant association between the LOC387715 A69S TT genotype and outcome based on OCT.Conclusion: Genetic variation may be associated with outcome in patients receiving anti-VEGF therapy.Keywords: age related macular degeneration, ARMS2, bevacizumab, complement factor H (CFH), LOC387715, ranibizumab, single nucleotide polymorphisms, vascular endothelial growth facto