On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem

We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were known to coincide for continuous piecewise linear functions with rational breakpoints. We show that two of the notions, extreme functions and facets, coincide for the case of continuous piecewise linear functions, removing the hypothesis regarding rational breakpoints. We then separate the three notions using discontinuous examples.Comment: 18 pages, 2 figure

Software for cut-generating functions in the Gomory--Johnson model and beyond

We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on Mathematical Software 201

Scaling and universality in coupled driven diffusive models

Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-like model in one dimension (1d), a generalization of the Burgers model to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to MHD, this model serves as a 1d reduced model for driven binary fluid mixtures. Here we have performed a comprehensive study of the universal properties of the generalized d-dimensional version of the reduced model. We employ both analytical and numerical approaches. In particular, we determine the scaling exponents and the amplitude-ratios of the relevant two-point time-dependent correlation functions in the model. We demonstrate that these quantities vary continuously with the amplitude of the noise cross-correlation. Further our numerical studies corroborate the continuous dependence of long wavelength and long time-scale physics of the model on the amplitude of the noise cross-correlations, as found in our analytical studies. We construct and simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to the universality class of our coupled Burgers-like model, which display similar behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral methods) and analytical (Dynamic Renormalization Group, Self-Consistent Mode-Coupling Theory and Functional Renormalization Group) approaches for our work. The results from our different approaches complement one another. Possible realizations of our results in various nonequilibrium models are discussed.Comment: To appear in JSTAT (2009); 52 pages in JSTAT format. Some figure files have been replace

Exercise and hypertrophic cardiomyopathy: Two incompatible entities?

A greater understanding of the pathogenic mechanisms underpinning hypertrophic cardiomyopathy (HCM) has translated to improved medical care and better survival of affected individuals. Historically these patients were considered to be at high risk of sudden cardiac death (SCD) during exercise; therefore, exercise recommendations were highly conservative and promoted a sedentary life style. There is emerging evidence that suggests that exercise in HCM has a favorable effect on cardiovascular remodeling and moderate exercise programs have not raised any safety concerns. Furthermore, individuals with HCM have a similar burden of atherosclerotic risk factors as the general population in whom exercise has been associated with a reduction in myocardial infarction, stroke, and heart failure, especially among those with a high-risk burden. Small studies revealed that athletes who choose to continue with regular competition do not demonstrate adverse outcomes when compared to those who discontinue sport, and active individuals implanted with an implantable cardioverter defibrillator do not have an increased risk of appropriate shocks or other adverse events. The recently published exercise recommendations from the European Association for Preventative Cardiology account for more contemporary evidence and adopt a more liberal stance regarding competitive and high intensity sport in individuals with low-risk HCM. This review addresses the issue of exercise in individuals with HCM, and explores current evidence supporting safety of exercise in HCM, potential caveats, and areas of further research

The structure of the infinite models in integer programming

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data)

Helioseismic analysis of the hydrogen partition function in the solar interior

The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Dappen 1998). The effect stems from internal partition function of hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium-abundance of the solar convection zone.Comment: 30 pages, 4 figures, 1 table. Revised version submitted to Ap

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.Comment: article (4 pages, 9 eps figures) + Supplement (8 pages, 9 eps figures); Phys. Rev. Lett. 201

Solar models and electron screening

We investigate the sensitivity of the solar model to changes in the nuclear reaction screening factors. We show that the sound speed profile as determined by helioseismology certainly rules out changes in the screening factors exceeding more than 10%. A slightly improved solar model could be obtained by enhancing screening by about 5% over the Salpeter value. We also discuss how envelope properties of the Sun depend on screening, too. We conclude that the solar model can be used to help settling the on-going dispute about the ``correct'' screening factors.Comment: accepted for publication by Astron. Astrophy

Evolution of Topological Defects During Inflation

Topological defects can be formed during inflation by phase transitions as well as by quantum nucleation. We study the effect of the expansion of the Universe on the internal structure of the defects. We look for stationary solutions to the field equations, i.e. solutions that depend only on the proper distance from the defect core. In the case of very thin defects, whose core dimensions are much smaller than the de Sitter horizon, we find that the solutions are well approximated by the flat space solutions. However, as the flat space thickness parameter $\delta_0$ increases we notice a deviation from this, an effect that becomes dramatic as $\delta_0$ approaches $(H)^{-1}/{\sqrt 2}$. Beyond this critical value we find no stationary solutions to the field equations. We conclude that only defects that have flat space thicknesses less than the critical value survive, while thicker defects are smeared out by the expansion.Comment: 14 page

How much do helioseismological inferences depend upon the assumed reference model?

We investigate systematic uncertainties in determining the profiles of the solar sound speed, density, and adiabatic index by helioseismological techniques. We find that rms uncertainties-averaged over the sun of ~ 0.2%-0.4% are contributed to the sound speed profile by each of three sources: 1)the choice of assumed reference model, 2) the width of the inversion kernel, and 3) the measurements errors. The density profile is about an order of magnitude less well determined by the helioseismological measurements. The profile of the adiabatic index is determined to an accuracy of about 0.2% . We find that even relatively crude reference models yield reasonably accurate solar parameters.Comment: Accepted for publication in ApJ . Related material at http://www.sns.ias.edu/~jn