Ground state of the Bethe-lattice spin glass and running time of an exact optimization algorithm

We study the Ising spin glass on random graphs with fixed connectivity z and with a Gaussian distribution of the couplings, with mean \mu and unit variance. We compute exact ground states by using a sophisticated branch-and-cut method for z=4,6 and system sizes up to N=1280 for different values of \mu. We locate the spin-glass/ferromagnet phase transition at \mu = 0.77 +/- 0.02 (z=4) and \mu = 0.56 +/- 0.02 (z=6). We also compute the energy and magnetization in the Bethe-Peierls approximation with a stochastic method, and estimate the magnitude of replica symmetry breaking corrections. Near the phase transition, we observe a sharp change of the median running time of our implementation of the algorithm, consistent with a change from a polynomial dependence on the system size, deep in the ferromagnetic phase, to slower than polynomial in the spin-glass phase.Comment: 10 pages, RevTex, 10 eps figures. Some changes in the tex

QTL and Drought Effects on Leaf Physiology in Lowland Panicum virgatum

Switchgrass is a key component of plans to develop sustainable cellulosic ethanol production for bioenergy in the USA. We sought quantitative trait loci (QTL) for leaf structure and function, using the Albany full-sib mapping population, an F1 derived from lowland tetraploid parents. We also assessed both genotype × environment interactions (G×E) in response to drought and spatial trends within experimental plots, using the mapping population and check clones drawn from the parent cultivars. Phenotypes for leaf structure and physiological performance were determined under well-watered conditions in two consecutive years, and we applied drought to one of two replicates to test for G×E. Phenotypes for check clones varied with location in our plot and were impacted by drought, but there was limited evidence of G×E except in quantum yield (ΦPSII). Phenotypes of Albany were also influenced by plant location within our plot, and after correcting for experimental design factors and spatial effects, we detected QTL for leaf size, tissue density (LMA), and stomatal conductance (gs). Clear evidence of G×E was detected at a QTL for intrinsic water use efficiency (iWUE) that was expressed only under drought. Loci influencing physiological traits had small additive effects, showed complex patterns of heritability, and did not co-localize with QTL for morphological traits. These insights into the genetic architecture of leaf structure and function set the stage for consideration of leaf physiological phenotypes as a component of switchgrass improvement for bioenergy purposes

Low Energy Excitations in Spin Glasses from Exact Ground States

We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ``TNT'' picture, with only minimal corrections to scaling. When allowing for very large corrections to scaling, the data are also consistent with a picture with space-filling surfaces, such as replica symmetry breaking. The energy of the excitations scales with their size with a small exponent \theta', which is compatible with zero if we allow moderate corrections to scaling. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on corrections to scaling. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with more discussion of the numerical data. Fig.11 adde

Optic chiasm measurements may be useful markers of anterior optic pathway degeneration in neuromyelitis optica spectrum disorders

Objectives: We aimed to evaluate optic chiasm (OC) measures as potential imaging marker for anterior optic pathway damage assessment in the context of neuromyelitis optica spectrum disorders (NMOSD). Materials and method: This cross-sectional study included 39 patients exclusively with aquaporin 4-IgG seropositive NMOSD of which 25 patients had a history of optic neuritis (NMOSD-ON) and 37 age- and sex-matched healthy controls (HC). OC heights, width, and area were measured using standard 3D T1-weighted MRI. Sensitivity of these measures to detect neurodegeneration in the anterior optic pathway was assessed in receiver operating characteristics analyses. Correlation coefficients were used to assess associations with structural measures of the anterior optic pathway (optic nerve dimensions, retinal ganglion cell loss) and clinical measures (visual function and disease duration). Results: OC heights and area were significantly smaller in NMOSD-ON compared to HC (NMOSD-ON vs. HC p < 0.0001). An OC area smaller than 22.5 mm2 yielded a sensitivity of 0.92 and a specificity of 0.92 in separating chiasms of NMOSD-ON from HC. OC area correlated well with structural and clinical measures in NMOSD-ON: optic nerve diameter (r = 0.4, p = 0.047), peripapillary retinal nerve fiber layer thickness (r = 0.59, p = 0.003), global visual acuity (r = - 0.57, p = 0.013), and diseases duration (r = - 0.5, p = 0.012). Conclusion: Our results suggest that OC measures are promising and easily accessible imaging markers for the assessment of anterior optic pathway damage

Exact Facetial Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization

The exact solution of the NP-hard (nondeterministic polynomial-time hard) maximum cut problem is important in many applications across, for example, physics, chemistry, neuroscience, and circuit layout-which is also due to its equivalence to the unconstrained binary quadratic optimization problem. Leading solution methods are based on linear or semidefinite programming and require the separation of the so-called odd-cycle inequalities. In their groundbreaking research, F. Barahona and A. R. Mahjoub have given an informal description of a polynomial-time algorithm for this problem. As pointed out recently, however, additional effort is necessary to guarantee that the inequalities obtained correspond to facets of the cut polytope. In this paper, we shed more light on a so enhanced separation procedure and investigate experimentally how it performs in comparison with an ideal setting where one could even employ the sparsest, most violated, or geometrically most promising facet-defining odd-cycle inequalities. Summary of Contribution: This paper aims at a better capability to solve binary quadratic optimization or maximum cut problems and their various applications using integer programming techniques. To this end, the paper describes enhancements to a well-known algorithm for the central separation problem arising in this context; it is demonstrated experimentally that these enhancements are worthwhile from a computational point of view. The linear relaxations of the aforementioned problems are typically solved using fewer iterations and cutting planes than with a nonenhanced approach. It is also shown that the enhanced procedure is only slightly inferior to an ideal, enumerative, and, in practice, intractable global cutting-plane selection

An integer programming approach to optimal basic block instruction scheduling for single-issue processors

We present a novel integer programming formulation for basic block instruction scheduling on single-issue processors. The problem can be considered as a very general sequential task scheduling problem with delayed precedence constraints. Our model is based on the linear ordering problem and has, in contrast to the last IP model proposed, numbers of variables and constraints that are strongly polynomial in the instance size. Combined with improved preprocessing techniques and given a time limit of ten minutes of CPU and system time, our branch-and-cut implementation is capable to solve all but eleven of the 369,861 basic blocks of the SPEC 2000 integer and floating point benchmarks to proven optimality. This is competitive to the current state-of-the art constraint programming approach that has also been evaluated on this test suite. (C) 2015 Elsevier B.V. All rights reserved

More Compact Orthogonal Drawings by Allowing Additional Bends

Compacting orthogonal drawings is a challenging task. Usually, algorithms try to compute drawings with small area or total edge length while preserving the underlying orthogonal shape. We suggest a moderate relaxation of the orthogonal compaction problem, namely the one-dimensional monotone flexible edge compaction problem with fixed vertex star geometry. We further show that this problem can be solved in polynomial time using a network flow model. An experimental evaluation shows that by allowing additional bends could reduce the total edge length and the drawing area

Lifting and separation procedures for the cut polytope

The max-cut problem and the associated cut polytope on complete graphs have been extensively studied over the last 25 years. However, in comparison, only little research has been conducted for the cut polytope on arbitrary graphs, in particular separation algorithms have received only little attention. In this study we describe new separation and lifting procedures for the cut polytope on general graphs. These procedures exploit algorithmic and structural results known for the cut polytope on complete graphs to generate valid, and sometimes facet defining, inequalities for the cut polytope on arbitrary graphs in a cutting plane framework. We report computational results on a set of well-established benchmark problems