@inproceedings{2268, abstract = {This paper presents an analytic formulation for anti-aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell-Netravali filter family. This enables high-quality rasterization of triangles and tetrahedra with linearly interpolated vertex values to regular and non-regular grids. A closed form solution of the convolution is presented and an efficient implementation on the GPU using DirectX and CUDA C is described. }, author = {Thomas Auzinger and Guthe, Michael and Stefan Jeschke}, number = {121}, pages = {335 -- 344}, publisher = {Wiley-Blackwell}, title = {{Analytic anti-aliasing of linear functions on polytopes}}, doi = {http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x}, volume = {31}, year = {2012}, } @inproceedings{2316, abstract = {We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion and the corresponding binding-unbinding transition. We also consider the Pekar-Tomasevich approximation to the ground state energy and we study radial symmetry of the ground state density. }, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer and Thomas, Lawrence E}, pages = {477 -- 485}, publisher = {World Scientific Publishing}, title = {{Ground state properties of multi-polaron systems}}, doi = {10.1142/9789814449243_0045}, year = {2012}, } @inproceedings{2317, abstract = {We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. }, author = {Frank, Rupert L and Hainzl, Christian and Robert Seiringer and Solovej, Jan P}, pages = {575 -- 583}, publisher = {World Scientific Publishing}, title = {{Microscopic derivation of the Ginzburg-Landau model}}, doi = {10.1142/9789814449243_0060}, year = {2012}, } @article{2318, abstract = {We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential. }, author = {Seiringer, Robert}, journal = {Journal of Spectral Theory}, number = {3}, pages = {321--328}, publisher = {European Mathematical Society}, title = {{Absence of bound states implies non-negativity of the scattering length}}, doi = {10.4171/JST/31}, volume = {2}, year = {2012}, } @article{2395, abstract = {We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. }, author = {Frank, Rupert L and Hainzl, Christian and Robert Seiringer and Solovej, Jan P}, journal = {Journal of the American Mathematical Society}, number = {3}, pages = {667 -- 713}, publisher = {American Mathematical Society}, title = {{Microscopic derivation of Ginzburg-Landau theory}}, doi = {10.1090/S0894-0347-2012-00735-8}, volume = {25}, year = {2012}, } @article{2396, abstract = {A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range.}, author = {Landon, Benjamin and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {3}, pages = {237 -- 243}, publisher = {Springer}, title = {{The scattering length at positive temperature}}, doi = {10.1007/s11005-012-0566-5}, volume = {100}, year = {2012}, } @article{2397, abstract = {We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {2}, pages = {119 -- 138}, publisher = {Springer}, title = {{Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs}}, doi = {10.1007/s11005-011-0535-4}, volume = {100}, year = {2012}, } @misc{2398, abstract = {We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.}, author = {Jakšić, Vojkan and Ogata, Yoshiko and Pillet, Claude A and Robert Seiringer}, booktitle = {Reviews in Mathematical Physics}, number = {6}, publisher = {World Scientific Publishing}, title = {{Quantum hypothesis testing and non-equilibrium statistical mechanics}}, doi = {10.1142/S0129055X12300026}, volume = {24}, year = {2012}, } @article{2400, abstract = {If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {405 -- 424}, publisher = {Springer}, title = {{Binding of polarons and atoms at threshold}}, doi = {10.1007/s00220-012-1436-9}, volume = {313}, year = {2012}, } @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{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{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}, } @article{2459, abstract = {Coordinated, subcellular trafficking of proteins is one of the fundamental properties of the multicellular eukaryotic organisms. Trafficking involves a large diversity of compartments, pathways, cargo molecules, and vesicle-sorting events. It is also crucial in regulating the localization and, thus, the activity of various proteins, but the process is still poorly genetically defined in plants. In the past, forward genetics screens had been used to determine the function of genes by searching for a specific morphological phenotype in the organism population in which mutations had been induced chemically or by irradiation. Unfortunately, these straightforward genetic screens turned out to be limited in identifying new regulators of intracellular protein transport, because mutations affecting essential trafficking pathways often lead to lethality. In addition, the use of these approaches has been restricted by functional redundancy among trafficking regulators. Screens for mutants that rely on the observation of changes in the cellular localization or dynamics of fluorescent subcellular markers enable, at least partially, to circumvent these issues. Hence, such image-based screens provide the possibility to identify either alleles with weak effects or components of the subcellular trafficking machinery that have no strong impact on the plant growth.}, author = {Zwiewka, Marta and Friml, Jirí}, journal = {Frontiers in Plant Science}, number = {May}, publisher = {Frontiers Research Foundation}, title = {{Fluorescence imaging-based forward genetic screens to identify trafficking regulators in plants}}, doi = {10.3389/fpls.2012.00097}, volume = {3}, year = {2012}, } @unpublished{2696, author = {László Erdös}, booktitle = {ArXiv}, publisher = {ArXiv}, title = {{Universality for random matrices and log-gases}}, year = {2012}, } @inproceedings{2700, author = {László Erdös}, pages = {3 -- 98}, publisher = {Oxford University Press}, title = {{Lecture notes on quantum Brownian motion}}, volume = {95}, year = {2012}, } @inproceedings{2715, abstract = {We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning vertices from where the objective can be ensured with probability 1. We study for the first time the average case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average case running time is linear (as compared to the worst case linear number of iterations and quadratic time complexity). Second, for the average case analysis over all MDPs we show that the expected number of iterations is constant and the average case running time is linear (again as compared to the worst case linear number of iterations and quadratic time complexity). Finally we also show that given that all MDPs are equally likely, the probability that the classical algorithm requires more than constant number of iterations is exponentially small.}, author = {Chatterjee, Krishnendu and Joglekar, Manas and Shah, Nisarg}, location = {Hyderabad, India}, pages = {461 -- 473}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives}}, doi = {10.4230/LIPIcs.FSTTCS.2012.461}, volume = {18}, year = {2012}, } @article{2848, abstract = {We study evolutionary game theory in a setting where individuals learn from each other. We extend the traditional approach by assuming that a population contains individuals with different learning abilities. In particular, we explore the situation where individuals have different search spaces, when attempting to learn the strategies of others. The search space of an individual specifies the set of strategies learnable by that individual. The search space is genetically given and does not change under social evolutionary dynamics. We introduce a general framework and study a specific example in the context of direct reciprocity. For this example, we obtain the counter intuitive result that cooperation can only evolve for intermediate benefit-to-cost ratios, while small and large benefit-to-cost ratios favor defection. Our paper is a step toward making a connection between computational learning theory and evolutionary game dynamics.}, author = {Chatterjee, Krishnendu and Zufferey, Damien and Nowak, Martin}, journal = {Journal of Theoretical Biology}, pages = {161 -- 173}, publisher = {Elsevier}, title = {{Evolutionary game dynamics in populations with different learners}}, doi = {10.1016/j.jtbi.2012.02.021}, volume = {301}, year = {2012}, }