A hybrid constraint programming and semidefinite programming approach for the stable set problem

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.Comment: 14 page

Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Asynchronous division by non-ring FtsZ in the gammaproteobacterial symbiont of <em>Robbea hypermnestra</em>

The reproduction mode of uncultivable microorganisms deserves investigation as it can largely diverge from conventional transverse binary fission. Here, we show that the rod-shaped gammaproteobacterium thriving on the surface of the Robbea hypermnestra nematode divides by FtsZ-based, non-synchronous invagination of its poles-that is, the host-attached and fimbriae-rich pole invaginates earlier than the distal one. We conclude that, in a naturally occurring animal symbiont, binary fission is host-oriented and does not require native FtsZ to polymerize into a ring at any septation stage

Distributions of flux vacua

We give results for the distribution and number of flux vacua of various types, supersymmetric and nonsupersymmetric, in IIb string theory compactified on Calabi-Yau manifolds. We compare this with related problems such as counting attractor points.Comment: 43 pages, 7 figures. v2: improved discussion of finding vacua with discrete flux, references adde

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

The influence of magnetic fields on the Sunyaev Zel'dovich effect in clusters of galaxies

We study the influence of intracluster large scale magnetic fields on the thermal Sunyaev-Zel'dovich (SZ) effect. In a macroscopic approach we complete the hydrostatic equilibrium equation with the magnetic field pressure component. Comparing the resulting mass distribution with a standard one, we derive a new electron density profile. For a spherically symmetric cluster model, this new profile can be written as the product of a standard ($\beta$-) profile and a radius dependent function, close to unity, which takes into account the magnetic field strength. For non-cooling flow clusters we find that the observed magnetic field values can reduce the SZ signal by $\sim 10$ with respect to the value estimated from X-ray observations and the $\beta$-model. If a cluster harbours a cooling flow, magnetic fields tend to weaken the cooling flow influence on the SZ-effect.Comment: Accepted for publication in New Astronom

Valuations on lattice polytopes

This survey is on classification results for valuations defined on lattice polytopes that intertwine the special linear group over the integers. The basic real valued valuations, the coefficients of the Ehrhart polynomial, are introduced and their characterization by Betke and Kneser is discussed. More recent results include classification theorems for vector and convex body valued valuations. © Springer International Publishing AG 2017

Brain structural correlates of insomnia severity in 1053 individuals with major depressive disorder : results from the ENIGMA MDD Working Group

It has been difficult to find robust brain structural correlates of the overall severity of major depressive disorder (MDD). We hypothesized that specific symptoms may better reveal correlates and investigated this for the severity of insomnia, both a key symptom and a modifiable major risk factor of MDD. Cortical thickness, surface area and subcortical volumes were assessed from T1-weighted brain magnetic resonance imaging (MRI) scans of 1053 MDD patients (age range 13-79 years) from 15 cohorts within the ENIGMA MDD Working Group. Insomnia severity was measured by summing the insomnia items of the Hamilton Depression Rating Scale (HDRS). Symptom specificity was evaluated with correlates of overall depression severity. Disease specificity was evaluated in two independent samples comprising 2108 healthy controls, and in 260 clinical controls with bipolar disorder. Results showed that MDD patients with more severe insomnia had a smaller cortical surface area, mostly driven by the right insula, left inferior frontal gyrus pars triangularis, left frontal pole, right superior parietal cortex, right medial orbitofrontal cortex, and right supramarginal gyrus. Associations were specific for insomnia severity, and were not found for overall depression severity. Associations were also specific to MDD; healthy controls and clinical controls showed differential insomnia severity association profiles. The findings indicate that MDD patients with more severe insomnia show smaller surfaces in several frontoparietal cortical areas. While explained variance remains small, symptom-specific associations could bring us closer to clues on underlying biological phenomena of MDD