@article{2773, abstract = {Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2].}, author = {László Erdös and Yau, Horng-Tzer}, journal = {Electronic Journal of Probability}, publisher = {Institute of Mathematical Statistics}, title = {{A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices}}, doi = {10.1214/EJP.v17-1779}, volume = {17}, year = {2012}, } @article{2774, abstract = {We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given by a two term expansion c 1Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.}, author = {László Erdös and Fournais, Søren and Solovej, Jan P}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {847 -- 882}, publisher = {Springer}, title = {{Scott correction for large atoms and molecules in a self-generated magnetic field}}, doi = {10.1007/s00220-012-1468-1}, volume = {312}, year = {2012}, } @article{2775, abstract = {The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix ensemble. For invariant matrix models, the eigenvalue distributions are given by a log-gas with potential V and inverse temperature β = 1, 2, 4, corresponding to the orthogonal, unitary and symplectic ensembles. For β ∉ {1, 2, 4}, there is no natural random matrix ensemble behind this model, but the statistical physics interpretation of the log-gas is still valid for all β > 0. The universality conjecture for invariant ensembles asserts that the local eigenvalue statistics are independent of V. In this article, we review our recent solution to the universality conjecture for both invariant and non-invariant ensembles. We will also demonstrate that the local ergodicity of the Dyson Brownian motion is the intrinsic mechanism behind the universality. Furthermore, we review the solution of Dyson's conjecture on the local relaxation time of the Dyson Brownian motion. Related questions such as delocalization of eigenvectors and local version of Wigner's semicircle law will also be discussed.}, author = {László Erdös and Yau, Horng-Tzer}, journal = {Bulletin of the American Mathematical Society}, number = {3}, pages = {377 -- 414}, publisher = {American Mathematical Society}, title = {{Universality of local spectral statistics of random matrices}}, doi = {10.1090/S0273-0979-2012-01372-1}, volume = {49}, year = {2012}, } @article{2776, abstract = {We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least 4 + ε moments.}, author = {László Erdös and Knowles, Antti and Yau, Horng-Tzer and Yin, Jun}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {587 -- 640}, publisher = {Springer}, title = {{Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues}}, doi = {10.1007/s00220-012-1527-7}, volume = {314}, year = {2012}, } @article{2777, abstract = {We consider a large neutral molecule with total nuclear charge Z in a model with self-generated classical magnetic field and where the kinetic energy of the electrons is treated relativistically. To ensure stability, we assume that Zα < 2/π, where α denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is fixed. The leading term in the energy asymptotics is independent of κ, it is given by the Thomas-Fermi energy of order Z7/3 and it is unchanged by including the self-generated magnetic field. We prove the first correction term to this energy, the so-called Scott correction of the form S(αZ)Z2. The current paper extends the result of Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)] on the Scott correction for relativistic molecules to include a self-generated magnetic field. Furthermore, we show that the corresponding Scott correction function S, first identified by Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)], is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields.}, author = {László Erdös and Fournais, Søren and Solovej, Jan P}, journal = {Journal of Mathematical Physics}, number = {9}, publisher = {American Institute of Physics}, title = {{Relativistic Scott correction in self-generated magnetic fields}}, doi = {10.1063/1.3697417}, volume = {53}, year = {2012}, } @article{2778, abstract = {We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification.}, author = {Bourgade, Paul and László Erdös and Yau, Horng-Tzer}, journal = {Journal of Mathematical Physics}, number = {9}, publisher = {American Institute of Physics}, title = {{Bulk universality of general β-ensembles with non-convex potential}}, doi = {10.1063/1.4751478}, volume = {53}, year = {2012}, } @article{2779, abstract = {We consider a two-dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate that does not rely on the monotonicity of the energy on the random parameters.}, author = {László Erdös and Hasler, David G}, journal = {Annales Henri Poincare}, number = {8}, pages = {1719 -- 1731}, publisher = {Birkhäuser}, title = {{Wegner estimate for random magnetic Laplacian on ℤ 2}}, doi = {10.1007/s00023-012-0177-9}, volume = {13}, year = {2012}, } @article{2802, abstract = {When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase-separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4-40 μm are detected and tracked. Based on these data, we resolve the oscillations in the droplet size distribution that are coupled to the convective flow.}, author = {Lapp, Tobias and Rohloff, Martin and Vollmer, Jürgen T and Björn Hof}, journal = {Experiments in Fluids}, number = {5}, pages = {1187 -- 1200}, publisher = {Springer}, title = {{Particle tracking for polydisperse sedimenting droplets in phase separation}}, doi = {10.1007/s00348-011-1243-7}, volume = {52}, year = {2012}, } @article{2803, abstract = {Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border.}, author = {de Lózar, Alberto and Mellibovsky, Fernando and Avila, Marc and Björn Hof}, journal = {Physical Review Letters}, number = {21}, publisher = {American Physical Society}, title = {{Edge state in pipe flow experiments}}, doi = {10.1103/PhysRevLett.108.214502}, volume = {108}, year = {2012}, } @article{2804, abstract = {The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution}, author = {Blaschke, Johannes and Lapp, Tobias and Björn Hof and Vollmer, Jürgen T}, journal = {Physical Review Letters}, number = {6}, publisher = {American Physical Society}, title = {{Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets}}, doi = {10.1103/PhysRevLett.109.068701}, volume = {109}, year = {2012}, } @inproceedings{2825, abstract = {We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: one estimates each variable's marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy.}, author = {Lampert, Christoph}, location = {Lake Tahoe, NV, United States}, pages = {82 -- 90}, publisher = {Neural Information Processing Systems}, title = {{Dynamic pruning of factor graphs for maximum marginal prediction}}, volume = {1}, 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}, } @article{2849, author = {Edelsbrunner, Herbert and Strelkova, Nataliya}, journal = {Russian Mathematical Surveys}, number = {6}, pages = {1167 -- 1168}, publisher = {IOP Publishing Ltd.}, title = {{On the configuration space of Steiner minimal trees}}, doi = {10.1070/RM2012v067n06ABEH004820}, volume = {67}, year = {2012}, } @article{2875, abstract = {Phytohormones are important plant growth regulators that control many developmental processes, such as cell division, cell differentiation, organogenesis and morphogenesis. They regulate a multitude of apparently unrelated physiological processes, often with overlapping roles, and they mutually modulate their effects. These features imply important synergistic and antagonistic interactions between the various plant hormones. Auxin and cytokinin are central hormones involved in the regulation of plant growth and development, including processes determining root architecture, such as root pole establishment during early embryogenesis, root meristem maintenance and lateral root organogenesis. Thus, to control root development both pathways put special demands on the mechanisms that balance their activities and mediate their interactions. Here, we summarize recent knowledge on the role of auxin and cytokinin in the regulation of root architecture with special focus on lateral root organogenesis, discuss the latest findings on the molecular mechanisms of their interactions, and present forward genetic screen as a tool to identify novel molecular components of the auxin and cytokinin crosstalk.}, author = {Bielach, Agnieszka and Duclercq, Jérôme and Peter Marhavy and Eva Benková}, journal = {Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences}, number = {1595}, pages = {1469 -- 1478}, publisher = {Royal Society, The}, title = {{Genetic approach towards the identification of auxin - cytokinin crosstalk components involved in root development}}, doi = {10.1098/rstb.2011.0233}, volume = {367}, year = {2012}, } @article{2876, abstract = {Cytokinin (CK) activity is regulated by the complex interplay of their metabolism, transport, stability and cellular/tissue localization. O-glucosides of zeatin-type CKs are postulated to be storage and/or transport forms. Active CK levels are determined in part by their differential distribution of CK metabolites across different subcellular compartments. We have previously shown that overexpressing chloroplast-localized Zm-p60.1, a maize β-glucosidase capable of releasing active cytokinins from their O- and N3-glucosides, perturbs CK homeostasis in transgenic tobacco. We obtained tobacco (Nicotiana tabacum L., cv Petit Havana SR1) plants overexpressing a recombinant Zm-p60.1 that is targeted to the vacuole. The protein is correctly processed and localized to the vacuole. When grown on medium containing exogenous zeatin, transgenic seedlings rapidly accumulate fresh weight due to ectopic growths at the base of the hypocotyl. The presence of the enzyme in these ectopic structures is shown by histochemical staining. CK quantification reveals that these transgenic seedlings are unable to accumulate zeatin-O-glucoside to levels similar to those observed in the wild type. When crossed with tobacco overexpressing the zeatin-O-glucosyltransferase gene from Phaseolus, the vacuolar variant shows an almost complete reversion in the root elongation assay. This is the first evidence from intact plants that the vacuole is the storage organelle for CK O-glucosides and that they are available to attack by Zm-p60.1. We propose the use of Zm-p60.1 as a robust molecular tool that exploits the reversibility of O-glucosylation and enables delicate manipulations of active CK content at the cellular level.}, author = {Kiran, Nagavalli S and Eva Benková and Reková, Alena and Dubová, Jaroslava and Malbeck, Jiří and Palme, Klaus and Brzobohatý, Břetislav}, journal = {Phytochemistry}, pages = {67 -- 77}, publisher = {Elsevier}, title = {{Retargeting a maize β-glucosidase to the vacuole - Evidence from intact plants that zeatin-O-glucoside is stored in the vacuole}}, doi = {10.1016/j.phytochem.2012.03.012}, volume = {79}, year = {2012}, } @article{2878, abstract = {Phyllotaxis, the regular arrangement of leaves and flowers around the stem, is a key feature of plant architecture. Current models propose that the spatiotemporal regulation of organ initiation is controlled by a positive feedback loop between the plant hormone auxin and its efflux carrier PIN-FORMED1 (PIN1). Consequently, pin1 mutants give rise to naked inflorescence stalks with few or no flowers, indicating that PIN1 plays a crucial role in organ initiation. However, pin1 mutants do produce leaves. In order to understand the regulatory mechanisms controlling leaf initiation in Arabidopsis (Arabidopsis thaliana) rosettes, we have characterized the vegetative pin1 phenotype in detail. We show that although the timing of leaf initiation in vegetative pin1 mutants is variable and divergence angles clearly deviate from the canonical 137° value, leaves are not positioned at random during early developmental stages. Our data further indicate that other PIN proteins are unlikely to explain the persistence of leaf initiation and positioning during pin1 vegetative development. Thus, phyllotaxis appears to be more complex than suggested by current mechanistic models.}, author = {Guenot, Bernadette and Bayer, Emmanuelle and Kierzkowski, Daniel and Smith, Richard S and Mandel, Therese and Žádníková, Petra and Eva Benková and Kuhlemeier, Cris}, journal = {Plant Physiology}, number = {4}, pages = {1501 -- 1510}, publisher = {American Society of Plant Biologists}, title = {{Pin1 independent leaf initiation in Arabidopsis}}, doi = {10.1104/pp.112.200402}, volume = {159}, year = {2012}, } @article{2879, abstract = {Hormones, such as auxin and cytokinin, are involved in the complex molecular network that regulates the coordinated development of plant organs. Genes controlling ovule patterning have been identified and studied in detail; however, the roles of auxin and cytokinin in ovule development are largely unknown. Here we show that key cytokinin pathway genes, such as isopentenyltransferase and cytokinin receptors, are expressed during ovule development. Also, in a cre1-12 ahk2-2 ahk3-3 triple mutant with severely reduced cytokinin perception, expression of the auxin efflux facilitator PIN-FORMED 1 (PIN1) was severely reduced. In sporocyteless/nozzle (spl/nzz) mutants, which show a similar phenotype to the cre1-12 ahk2-2 ahk3-3 triple mutant, PIN1 expression is also reduced. Treatment with the exogenous cytokinin N6-benzylaminopurine also altered both auxin distribution and patterning of the ovule; this process required the homeodomain transcription factor BELL1 (BEL1). Thus, this article shows that cytokinin regulates ovule development through the regulation of PIN1. Furthermore, the transcription factors BEL1 and SPL/NZZ, previously described as key regulators of ovule development, are needed for the auxin and cytokinin signaling pathways for the correct patterning of the ovule.}, author = {Bencivenga, Stefano and Simonini, Sara and Eva Benková and Colombo, Lucia}, journal = {Plant Cell}, number = {7}, pages = {2886 -- 2897}, publisher = {American Society of Plant Biologists}, title = {{The transcription factors BEL1 and SPL are required for cytokinin and auxin signaling during ovule development in Arabidopsis}}, doi = {10.1105/tpc.112.100164}, volume = {24}, year = {2012}, } @inproceedings{2888, abstract = {Formal verification aims to improve the quality of hardware and software by detecting errors before they do harm. At the basis of formal verification lies the logical notion of correctness, which purports to capture whether or not a circuit or program behaves as desired. We suggest that the boolean partition into correct and incorrect systems falls short of the practical need to assess the behavior of hardware and software in a more nuanced fashion against multiple criteria.}, author = {Henzinger, Thomas A}, booktitle = {Conference proceedings MODELS 2012}, location = {Innsbruck, Austria}, pages = {1 -- 2}, publisher = {Springer}, title = {{Quantitative reactive models}}, doi = {10.1007/978-3-642-33666-9_1}, volume = {7590}, year = {2012}, } @inproceedings{2890, abstract = {Systems are often specified using multiple requirements on their behavior. In practice, these requirements can be contradictory. The classical approach to specification, verification, and synthesis demands more detailed specifications that resolve any contradictions in the requirements. These detailed specifications are usually large, cumbersome, and hard to maintain or modify. In contrast, quantitative frameworks allow the formalization of the intuitive idea that what is desired is an implementation that comes "closest" to satisfying the mutually incompatible requirements, according to a measure of fit that can be defined by the requirements engineer. One flexible framework for quantifying how "well" an implementation satisfies a specification is offered by simulation distances that are parameterized by an error model. We introduce this framework, study its properties, and provide an algorithmic solution for the following quantitative synthesis question: given two (or more) behavioral requirements specified by possibly incompatible finite-state machines, and an error model, find the finite-state implementation that minimizes the maximal simulation distance to the given requirements. Furthermore, we generalize the framework to handle infinite alphabets (for example, realvalued domains). We also demonstrate how quantitative specifications based on simulation distances might lead to smaller and easier to modify specifications. Finally, we illustrate our approach using case studies on error correcting codes and scheduler synthesis.}, author = {Cerny, Pavol and Gopi, Sivakanth and Henzinger, Thomas A and Radhakrishna, Arjun and Totla, Nishant}, booktitle = {Proceedings of the tenth ACM international conference on Embedded software}, location = {Tampere, Finland}, pages = {53 -- 62}, publisher = {ACM}, title = {{Synthesis from incompatible specifications}}, doi = {10.1145/2380356.2380371}, year = {2012}, } @inproceedings{2891, abstract = {Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential of approximate determinization. We define approximate determinization with respect to a distance function, and investigate this potential. We show that sum automata cannot be determinized approximately with respect to any distance function. However, restricting to nonnegative weights allows for approximate determinization with respect to some distance functions. Discounted-sum automata allow for approximate determinization, as the influence of a word’s suffix is decaying. However, the naive approach, of unfolding the automaton computations up to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states. We prove matching lower bounds, showing exponential dependency on each of these three parameters. Average and limit-average automata are shown to prohibit approximate determinization with respect to any distance function, and this is the case even for two weights, 0 and 1.}, author = {Boker, Udi and Henzinger, Thomas A}, booktitle = {Leibniz International Proceedings in Informatics}, location = {Hyderabad, India}, pages = {362 -- 373}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Approximate determinization of quantitative automata}}, doi = {10.4230/LIPIcs.FSTTCS.2012.362}, volume = {18}, year = {2012}, }