23,969 research outputs found
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
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)
Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal experiments under asymmetric loss
Local asymptotic minimax risk bounds in a locally asymptotically mixture of
normal family of distributions have been investigated under asymmetric loss
functions and the asymptotic distribution of the optimal estimator that attains
the bound has been obtained.Comment: Published at http://dx.doi.org/10.1214/074921706000000527 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Local-Global Principle for Transvection Groups
In this article we extend the validity Suslin's Local-Global Principle for
the elementary transvection subgroup of the general linear group, the
symplectic group, and the orthogonal group, where n > 2, to a Local-Global
Principle for the elementary transvection subgroup of the automorphism group
Aut(P) of either a projective module P of global rank > 0 and constant local
rank > 2, or of a nonsingular symplectic or orthogonal module P of global
hyperbolic rank > 0 and constant local hyperbolic rank > 2. In Suslin's
results, the local and global ranks are the same, because he is concerned only
with free modules. Our assumption that the global (hyperbolic) rank > 0 is used
to define the elementary transvection subgroups. We show further that the
elementary transvection subgroup ET(P) is normal in Aut(P), that ET(P) = T(P)
where the latter denotes the full transvection subgroup of Aut(P), and that the
unstable K_1-group K_1(Aut(P)) = Aut(P)/ET(P) = Aut(P)/T(P) is nilpotent by
abelian, provided R has finite stable dimension. The last result extends
previous ones of Bak and Hazrat for the above mentioned classical groups.
An important application to the results in the current paper can be found in
the work of last two named authors where they have studied the decrease in the
injective stabilization of classical modules over a non-singular affine algebra
over perfect C_1-fields. We refer the reader to that article for more details.Comment: 15 page
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
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