Critical branching processes in digital memcomputing machines

Memcomputing is a novel computing paradigm that employs time non-locality (memory) to solve combinatorial optimization problems. It can be realized in practice by means of non-linear dynamical systems whose point attractors represent the solutions of the original problem. It has been previously shown that during the solution search digital memcomputing machines go through a transient phase of avalanches (instantons) that promote dynamical long-range order. By employing mean-field arguments we predict that the distribution of the avalanche sizes follows a Borel distribution typical of critical branching processes with exponent $\tau= 3/2$. We corroborate this analysis by solving various random 3-SAT instances of the Boolean satisfiability problem. The numerical results indicate a power-law distribution with exponent $\tau = 1.51 \pm 0.02$, in very good agreement with the mean-field analysis. This indicates that memcomputing machines self-tune to a critical state in which avalanches are characterized by a branching process, and that this state persists across the majority of their evolution.Comment: 5 pages, 3 figure

The effect of phenytoin, phenobarbitone, dexamethasone and flurbiprofen on misonidazole neurotoxicity in mice.

Using a quantitative cytochemical technique for measuring beta-glucuronidase activity in the peripheral nerves of mice, we have investigated the effectiveness of four potential adjuncts for reducing the dose limiting neurotoxicity of misonidazole (MISO) in the clinic. Under the conditions used, the most effective adjunct was the steroid anti-inflammatory agent dexamethasone. When given over the week previous to MISO treatment, this agent almost completely eliminated the MISO neurotoxicity as determined at week 4 after commencement of MISO dosing. The second most effective adjunct was phenytoin, the third flurbiprofen and the last adjunct, phenobarbitone, was ineffective. Dexamethasone, phenytoin and phenobarbitone all reduced the clearance half-life of MISO and hence the drug exposure dose calculated as the area under the curve of MISO tissue concentration against time. However, no correlation was evident with these parameters and MISO neurotoxicity in the mouse. Dexamethasone, whilst affording protection against MISO toxicity, did not alter the radiosensitivity of the anaplastic MT tumour

Conformal symmetry and light flavor baryon spectra

The degeneracy among parity pairs systematically observed in the N and Delta spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS_5/CFT_4. The case is made by showing that all the observed N and Delta resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on the AdS_5 cone, conformally compactified to R^1*S^3. The free geodesic motion on the S^3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon type. The equation is then gauged by the "curved" Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11-S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11-S11 pairs through the nucleon spectrum as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean-square charge radii and electric charge form-factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.Comment: Latex, 5 figures, 2 tables; Paper upgraded in accord with the published version. Discussion on the meson sector include

Mathematical Analysis and Optimization of Infiltration Processes

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants

The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for maxBCG Galaxy Clusters

The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202+/-10 km/s for small groups to more than 854+/-102 km/s for large clusters. We show the scatter to be at most 40.5+/-3.5%, declining to 14.9+/-9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.Comment: 25 pages, 15 figures, 2 tables, published in Ap

The influence of nonrandom extra-pair paternity on heritability estimates derived from wild pedigrees

Quantitative genetic analysis is often fundamental for understanding evolutionary processes in wild populations. Avian populations provide a model system due to the relative ease of inferring relatedness among individuals through observation. However, extra-pair paternity (EPP) creates erroneous links within the social pedigree. Previous work has suggested this causes minor underestimation of heritability if paternal misassignment is random and hence not influenced by the trait being studied. Nevertheless, much literature suggests numerous traits are associated with EPP and the accuracy of heritability estimates for such traits remains unexplored. We show analytically how nonrandom pedigree errors can influence heritability estimates. Then, combining empirical data from a large great tit (Parus major) pedigree with simulations, we assess how heritability estimates derived from social pedigrees change depending on the mode of the relationship between EPP and the focal trait. We show that the magnitude of the underestimation is typically small (<15%). Hence, our analyses suggest that quantitative genetic inference from pedigrees derived from observations of social relationships is relatively robust; our approach also provides a widely applicable method for assessing the consequences of nonrandom EPP

Antibody responses to avian influenza viruses in wild birds broaden with age

For viruses such as avian influenza, immunity within a host population can drive the emergence of new strains by selecting for viruses with novel antigens that avoid immune recognition. The accumulation of acquired immunity with age is hypothesized to affect how influenza viruses emerge and spread in species of different lifespans. Despite its importance for understanding the behaviour of avian influenza viruses, little is known about age-related accumulation of immunity in the virus's primary reservoir, wild birds. To address this, we studied the age structure of immune responses to avian influenza virus in a wild swan population (Cygnus olor), before and after the population experienced an outbreak of highly pathogenic H5N1 avian influenza in 2008. We performed haemagglutination inhibition assays on sampled sera for five avian influenza strains and show that breadth of response accumulates with age. The observed age-related distribution of antibody responses to avian influenza strains may explain the age-dependent mortality observed during the highly pathogenic H5N1 outbreak. Age structures and species lifespan are probably important determinants of viral epidemiology and virulence in birds

Impact of Systematics on SZ-Optical Scaling Relations

One of the central goals of multi-wavelength galaxy cluster cosmology is to unite all cluster observables to form a consistent understanding of cluster mass. Here, we study the impact of systematic effects from optical cluster catalogs on stacked SZ signals. We show that the optically predicted Y-decrement can vary by as much as 50% based on the current 2 sigma systematic uncertainties in the observed mass-richness relationship. Mis-centering and impurities will suppress the SZ signal compared to expectations for a clean and perfectly centered optical sample, but to a lesser degree. We show that the level of these variations and suppression is dependent on the amount of systematics in the optical cluster catalogs. We also study X-ray luminosity-dependent sub-sampling of the optical catalog and find that it creates Malmquist bias increasing the observed Y-decrement of the stacked signal. We show that the current Planck measurements of the Y-decrement around SDSS optical clusters and their X-ray counterparts are consistent with expectations after accounting for the 1 sigma optical systematic uncertainties using the Johnston mass richness relation.Comment: 6 pages, 4 figures. Revised to match version accepted in the Astrophysical Journa