@article{2401,
abstract = {We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞].},
author = {Lieb, Élliott H and Robert Seiringer},
journal = {Journal of Statistical Physics},
number = {1},
pages = {86 -- 91},
publisher = {Springer},
title = {{Further implications of the Bessis-Moussa-Villani conjecture}},
doi = {10.1007/s10955-012-0585-8},
volume = {149},
year = {2012},
}
@article{2402,
abstract = {We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power.},
author = {Frank, Rupert L and Robert Seiringer},
journal = {Journal of Mathematical Physics},
number = {9},
publisher = {American Institute of Physics},
title = {{Lieb-Thirring inequality for a model of particles with point interactions}},
doi = {10.1063/1.3697416},
volume = {53},
year = {2012},
}
@article{2403,
abstract = {We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.},
author = {Robert Seiringer and Yngvason, Jakob and Zagrebnov, Valentin A},
journal = {Journal of Statistical Mechanics Theory and Experiment},
number = {11},
publisher = {IOP Publishing Ltd.},
title = {{Disordered Bose-Einstein condensates with interaction in one dimension}},
doi = {10.1088/1742-5468/2012/11/P11007},
volume = {2012},
year = {2012},
}
@article{241,
abstract = {The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ.},
author = {de la Bretèche, Régis and Timothy Browning},
journal = {Israel Journal of Mathematics},
number = {2},
pages = {973 -- 1012},
publisher = {Springer},
title = {{Binary forms as sums of two squares and Châtelet surfaces}},
doi = {10.1007/s11856-012-0019-y},
volume = {191},
year = {2012},
}
@article{2411,
abstract = {The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses.},
author = {Ebersberger, Ingo and De Matos Simoes, Ricardo and Kupczok, Anne and Gube, Matthias and Kothe, Erika and Voigt, Kerstin and Von Haeseler, Arndt},
journal = {Molecular Biology and Evolution},
number = {5},
pages = {1319 -- 1334},
publisher = {Oxford University Press},
title = {{A consistent phylogenetic backbone for the fungi}},
doi = {10.1093/molbev/msr285},
volume = {29},
year = {2012},
}
@article{242,
abstract = {We investigate the first and second moments of shifted convolutions of the generalized divisor function d 3(n).},
author = {Baier, Stephan and Timothy Browning and Marasingha, Gihan and Zhao, Liangyi},
journal = {Proceedings of the Edinburgh Mathematical Society},
number = {3},
pages = {551 -- 576},
publisher = {Cambridge University Press},
title = {{Averages of shifted convolutions of d3 (n)}},
doi = {10.1017/S001309151100037X},
volume = {55},
year = {2012},
}
@article{243,
abstract = {Let P(t) ∈ ℚ[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of ℚ containing the roots of P(t). Let N K/ℚ(X) be a full norm form for the extension K/ℚ. We show that the variety P(t) =N K/ℚ(X)≠ 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.},
author = {Timothy Browning and Heath-Brown, Roger},
journal = {Geometric and Functional Analysis},
number = {5},
pages = {1124 -- 1190},
publisher = {Springer Basel},
title = {{Quadratic polynomials represented by norm forms}},
doi = {10.1007/s00039-012-0168-5},
volume = {22},
year = {2012},
}
@article{2438,
abstract = {The colored Tverberg theorem asserts that for eve;ry d and r there exists t=t(d,r) such that for every set C ⊂ ℝ d of cardinality (d + 1)t, partitioned into t-point subsets C 1, C 2,...,C d+1 (which we think of as color classes; e. g., the points of C 1 are red, the points of C 2 blue, etc.), there exist r disjoint sets R 1, R 2,...,R r⊆C that are rainbow, meaning that {pipe}R i∩C j{pipe}≤1 for every i,j, and whose convex hulls all have a common point. All known proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojević, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof more concrete and intuitive, and accessible to a wider audience.},
author = {Matoušek, Jiří and Martin Tancer and Uli Wagner},
journal = {Discrete & Computational Geometry},
number = {2},
pages = {245 -- 265},
publisher = {Springer},
title = {{A geometric proof of the colored Tverberg theorem}},
doi = {10.1007/s00454-011-9368-2},
volume = {47},
year = {2012},
}
@article{2439,
abstract = {A Monte Carlo approximation algorithm for the Tukey depth problem in high dimensions is introduced. The algorithm is a generalization of an algorithm presented by Rousseeuw and Struyf (1998) . The performance of this algorithm is studied both analytically and experimentally.},
author = {Chen, Dan and Morin, Pat and Uli Wagner},
journal = {Computational Geometry: Theory and Applications},
number = {5},
pages = {566 -- 573},
publisher = {Elsevier},
title = {{Absolute approximation of Tukey depth: Theory and experiments}},
doi = {10.1016/j.comgeo.2012.03.001},
volume = {46},
year = {2012},
}
@article{244,
abstract = {We investigate the solubility of the congruence xy ≡ 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.},
author = {Timothy Browning and Haynes, Alan K},
journal = {International Journal of Number Theory},
number = {2},
pages = {481 -- 486},
publisher = {World Scientific Publishing},
title = {{Incomplete kloosterman sums and multiplicative inverses in short intervals}},
doi = { https://doi.org/10.1142/S1793042112501448},
volume = {9},
year = {2012},
}