Reducing the size and number of linear programs in a dynamic Gr\"obner basis algorithm

The dynamic algorithm to compute a Gr\"obner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no published followups. One reason for this may be that, at first glance, the added overhead seems to outweigh the benefit; the algorithm must solve many linear programs with many linear constraints. This paper describes two methods of reducing the cost substantially, answering the problem effectively.Comment: 11 figures, of which half are algorithms; submitted to journal for refereeing, December 201

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Effect of a multi-citrus extract-based feed additive on the survival of rainbow trout (Oncorhynchus mykiss) following challenge with Lactococcus garvieae

Growing global concerns about antibiotic resistance have generated a considerable interest in the search for alternative environmental-friendly approaches. This study was aimed to assess the antimicrobial activity of a multi-citrus extract-based feed additive (Biocitro®) against some fish pathogens, as well as evaluate its capacity to protect rainbow trout (Oncorhynchus mykiss) to lactococcosis. A broth dilution method was used to determine the minimum inhibitory concentration (MIC) of Biocitro®, and the results showed a strong antibacterial activity against Aeromonas salmonicida, Lactococcus garvieae and Yersinia ruckeri with MIC values of 2.0 µg/mL. Afterwards, rainbow trout juveniles were fed a Biocitro®-enriched diet (750 mg/kg feed) at a daily rate of 1.5% body weight for 4 weeks, then they were challenged with L. garvieae by the cohabitation method. At the end of the experimental period, fish treated with Biocitro® showed significantly (P¿<¿0.001) improved protection against L. garvieae compared to control fish. Although further studies are needed to understand how Biocitro® increases rainbow trout resistance to L. garvieae, this feed additive could be considered as a useful alternative to chemotherapeutic treatment in aquaculture

Geometrical organization of solutions to random linear Boolean equations

The random XORSAT problem deals with large random linear systems of Boolean variables. The difficulty of such problems is controlled by the ratio of number of equations to number of variables. It is known that in some range of values of this parameter, the space of solutions breaks into many disconnected clusters. Here we study precisely the corresponding geometrical organization. In particular, the distribution of distances between these clusters is computed by the cavity method. This allows to study the `x-satisfiability' threshold, the critical density of equations where there exist two solutions at a given distance.Comment: 20 page

Statistical mechanics of error exponents for error-correcting codes

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.Comment: 32 pages, 13 figure

High-Density Lipoprotein Cholesterol and Particle Concentrations, Carotid Atherosclerosis, and Coronary Events MESA (Multi-Ethnic Study of Atherosclerosis)

ObjectivesThe purpose of this study was to evaluate independent associations of high-density lipoprotein cholesterol (HDL-C) and particle (HDL-P) concentrations with carotid intima-media thickness (cIMT) and incident coronary heart disease (CHD).BackgroundHDL-C is inversely related to CHD, and also to triglycerides, low-density lipoprotein particles (LDL-P), and related metabolic risk. HDL-P associations with CHD may be partially independent of these factors.MethodsIn a multiethnic study of 5,598 men and women ages 45 to 84 years old, without baseline CHD, excluding subjects on lipid-lowering medications, triglycerides >400 mg/dl, or missing values, we evaluated associations of HDL-C and nuclear magnetic resonance spectroscopy-measured HDL-P with cIMT and incident CHD (myocardial infarction, CHD death, and angina, n = 227 events; mean 6.0 years follow-up). All models were adjusted for age, sex, ethnicity, hypertension, and smoking.ResultsHDL-C and HDL-P correlated with each other (ρ = 0.69) and LDL-P (ρ = −0.38, −0.25, respectively, p < 0.05 for all). For (1 SD) higher HDL-C (15 mg/dl) or HDL-P (6.64 μmol/l), cIMT differences were − 26.1 (95% confidence interval [CI]: −34.7 to −17.4) μm and −30.1 (95% CI: −38.8 to − 21.4) μm, and CHD hazard ratios were 0.74 (95% CI: 0.63 to 0.88) and 0.70 (95% CI: 0.59 to 0.82), respectively. Adjusted for each other and LDL-P, HDL-C was no longer associated with cIMT (2.3; 95% CI: − 9.5 to 14.2 μm) or CHD (0.97; 95% CI: 0.77 to 1.22), but HDL-P remained independently associated with cIMT (−22.2; 95% CI: − 33.8 to −10.6 μm) and CHD (0.75; 95% CI: 0.61 to 0.93). Interactions by sex, ethnicity, diabetes, and high-sensitivity C-reactive protein were not significant.ConclusionsAdjusting for each other and LDL-P substantially attenuated associations of HDL-C, but not HDL-P, with cIMT and CHD. Potential confounding by related lipids or lipoproteins should be carefully considered when evaluating HDL-related risk

New stable phase of non uniform black strings in AdSd{AdS}_d

We consider the non uniform $AdS$ black string equations in arbitrary number of dimension in a perturbative approach up to order 2 and in a non perturbative. We restrict the study in the perturbative approach to the backreacting modes, since they provide the first relevant corrections on the thermodynamical quantities of the solutions. We also present some preliminary results in the construction of non-perturbative solutions, in particular, we present a first part of the non uniform - uniform black string phase diagram. Our results suggests the existence of a new stable phase for $AdS$ non uniform black strings, namely long non uniform black string, with the extra direction length of the order of the $AdS$ curvature.Comment: Results extended. 14 pages, 5 figure

Molecular gas at supernova local environments unveiled by EDGE

CO observations allow estimations of the gas content of molecular clouds, which trace the reservoir of cold gas fuelling star formation, as well as to determine extinction via H$_2$ column density, N(H$_2$). Here, we studied millimetric and optical properties at 26 supernovae (SNe) locations of different types in a sample of 23 nearby galaxies by combining molecular $^{12}$C$^{16}$O (J = 1 $\rightarrow$ 0) resolved maps from the EDGE survey and optical Integral Field Spectroscopy from the CALIFA survey. We found an even clearer separation between type II and type Ibc SNe in terms of molecular gas than what we found in the optical using H$\alpha$ emission as a proxy for current SF rate, which reinforces the fact that SNe Ibc are more associated with SF-environments. While A$_V$ at SN locations is similar for SNe II and SNe Ibc, and higher compared to SNe Ia, N(H$_2$) is significantly higher for SNe Ibc than for SNe II and SNe Ia. When compared to alternative extinction estimations directly from SN photometry and spectroscopy, we find that our SNe Ibc have also redder color excess but showed standard Na I D absorption pseudo-equivalent widths ($\sim$1 \AA). In some cases we find no extinction when estimated from the environment, but high amounts of extinction when measured from SN observations, which suggests that circumstellar material or dust sublimation may be playing a role. This work serves as a benchmark for future studies combining last generation millimeter and optical IFS instruments to reveal the local environmental properties of extragalactic SNe.Comment: MNRAS accepted, 17 pages, 8 Figures, 4 Table

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. We then use techniques from statistical mechanics to derive a scaling principle relating the specificity (binding energy) of a TF to the minimum amount of training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references adde