@article{1704,
abstract = {Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.},
author = {Deuchert, Andreas and Hainzl, Christian and Seiringer, Robert},
journal = {Letters in Mathematical Physics},
number = {10},
pages = {1449 -- 1466},
publisher = {Springer},
title = {{Note on a family of monotone quantum relative entropies}},
doi = {10.1007/s11005-015-0787-5},
volume = {105},
year = {2015},
}
@article{1730,
abstract = {How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given combinatorial map in triangulated combinatorial surfaces (or their dual cross-metric counterpart). Our work builds upon Riemannian systolic inequalities, which bound the minimum length of non-trivial closed curves in terms of the genus and the area of the surface. We first describe a systematic way to translate Riemannian systolic inequalities to a discrete setting, and vice-versa. This implies a conjecture by Przytycka and Przytycki (Graph structure theory. Contemporary Mathematics, vol. 147, 1993), a number of new systolic inequalities in the discrete setting, and the fact that a theorem of Hutchinson on the edge-width of triangulated surfaces and Gromov’s systolic inequality for surfaces are essentially equivalent. We also discuss how these proofs generalize to higher dimensions. Then we focus on topological decompositions of surfaces. Relying on ideas of Buser, we prove the existence of pants decompositions of length O(g^(3/2)n^(1/2)) for any triangulated combinatorial surface of genus g with n triangles, and describe an O(gn)-time algorithm to compute such a decomposition. Finally, we consider the problem of embedding a cut graph (or more generally a cellular graph) with a given combinatorial map on a given surface. Using random triangulations, we prove (essentially) that, for any choice of a combinatorial map, there are some surfaces on which any cellular embedding with that combinatorial map has length superlinear in the number of triangles of the triangulated combinatorial surface. There is also a similar result for graphs embedded on polyhedral triangulations.},
author = {Colin De Verdière, Éric and Hubard, Alfredo and De Mesmay, Arnaud N},
journal = {Discrete & Computational Geometry},
number = {3},
pages = {587 -- 620},
publisher = {Springer},
title = {{Discrete systolic inequalities and decompositions of triangulated surfaces}},
doi = {10.1007/s00454-015-9679-9},
volume = {53},
year = {2015},
}
@article{1728,
abstract = {In the vertebrate neural tube, the morphogen Sonic Hedgehog (Shh) establishes a characteristic pattern of gene expression. Here we quantify the Shh gradient in the developing mouse neural tube and show that while the amplitude of the gradient increases over time, the activity of the pathway transcriptional effectors, Gli proteins, initially increases but later decreases. Computational analysis of the pathway suggests three mechanisms that could contribute to this adaptation: transcriptional upregulation of the inhibitory receptor Ptch1, transcriptional downregulation of Gli and the differential stability of active and inactive Gli isoforms. Consistent with this, Gli2 protein expression is downregulated during neural tube patterning and adaptation continues when the pathway is stimulated downstream of Ptch1. Moreover, the Shh-induced upregulation of Gli2 transcription prevents Gli activity levels from adapting in a different cell type, NIH3T3 fibroblasts, despite the upregulation of Ptch1. Multiple mechanisms therefore contribute to the intracellular dynamics of Shh signalling, resulting in different signalling dynamics in different cell types.},
author = {Cohen, Michael H and Anna Kicheva and Ribeiro, Ana C and Blassberg, Robert A and Page, Karen M and Barnes, Chris P and Briscoe, James},
journal = {Nature Communications},
publisher = {Nature Publishing Group},
title = {{Ptch1 and Gli regulate Shh signalling dynamics via multiple mechanisms}},
doi = {10.1038/ncomms7709},
volume = {6},
year = {2015},
}
@article{1684,
abstract = {Many species groups, including mammals and many insects, determine sex using heteromorphic sex chromosomes. Diptera flies, which include the model Drosophila melanogaster, generally have XY sex chromosomes and a conserved karyotype consisting of six chromosomal arms (five large rods and a small dot), but superficially similar karyotypes may conceal the true extent of sex chromosome variation. Here, we use whole-genome analysis in 37 fly species belonging to 22 different families of Diptera and uncover tremendous hidden diversity in sex chromosome karyotypes among flies. We identify over a dozen different sex chromosome configurations, and the small dot chromosome is repeatedly used as the sex chromosome, which presumably reflects the ancestral karyotype of higher Diptera. However, we identify species with undifferentiated sex chromosomes, others in which a different chromosome replaced the dot as a sex chromosome or in which up to three chromosomal elements became incorporated into the sex chromosomes, and others yet with female heterogamety (ZW sex chromosomes). Transcriptome analysis shows that dosage compensation has evolved multiple times in flies, consistently through up-regulation of the single X in males. However, X chromosomes generally show a deficiency of genes with male-biased expression, possibly reflecting sex-specific selective pressures. These species thus provide a rich resource to study sex chromosome biology in a comparative manner and show that similar selective forces have shaped the unique evolution of sex chromosomes in diverse fly taxa.},
author = {Vicoso, Beatriz and Bachtrog, Doris},
journal = {PLoS Biology},
number = {4},
publisher = {Public Library of Science},
title = {{Numerous transitions of sex chromosomes in Diptera}},
doi = {10.1371/journal.pbio.1002078},
volume = {13},
year = {2015},
}
@article{1677,
abstract = {We consider real symmetric and complex Hermitian random matrices with the additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale.},
author = {Alt, Johannes},
journal = {Journal of Mathematical Physics},
number = {10},
publisher = {American Institute of Physics},
title = {{The local semicircle law for random matrices with a fourfold symmetry}},
doi = {10.1063/1.4932606},
volume = {56},
year = {2015},
}