TY - JOUR AB - 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]. AU - László Erdös AU - Yau, Horng-Tzer ID - 2773 JF - Electronic Journal of Probability TI - A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices VL - 17 ER - TY - JOUR AB - We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis. AU - László Erdös AU - Hasler, David G ID - 2771 IS - 5 JF - Journal of Statistical Physics TI - Anderson localization at band edges for random magnetic fields VL - 146 ER - TY - JOUR AB - 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. AU - Bourgade, Paul AU - László Erdös AU - Yau, Horng-Tzer ID - 2778 IS - 9 JF - Journal of Mathematical Physics TI - Bulk universality of general β-ensembles with non-convex potential VL - 53 ER - TY - JOUR AB - 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. AU - László Erdös AU - Hasler, David G ID - 2779 IS - 8 JF - Annales Henri Poincare TI - Wegner estimate for random magnetic Laplacian on ℤ 2 VL - 13 ER - TY - JOUR AB - 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. AU - Lapp, Tobias AU - Rohloff, Martin AU - Vollmer, Jürgen T AU - Björn Hof ID - 2802 IS - 5 JF - Experiments in Fluids TI - Particle tracking for polydisperse sedimenting droplets in phase separation VL - 52 ER - TY - JOUR AB - 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. AU - de Lózar, Alberto AU - Mellibovsky, Fernando AU - Avila, Marc AU - Björn Hof ID - 2803 IS - 21 JF - Physical Review Letters TI - Edge state in pipe flow experiments VL - 108 ER - TY - JOUR AB - 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 AU - Blaschke, Johannes AU - Lapp, Tobias AU - Björn Hof AU - Vollmer, Jürgen T ID - 2804 IS - 6 JF - Physical Review Letters TI - Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets VL - 109 ER - TY - CONF AB - 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. AU - Lampert, Christoph ID - 2825 TI - Dynamic pruning of factor graphs for maximum marginal prediction VL - 1 ER - TY - JOUR AB - 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. AU - Chatterjee, Krishnendu AU - Zufferey, Damien AU - Nowak, Martin ID - 2848 JF - Journal of Theoretical Biology TI - Evolutionary game dynamics in populations with different learners VL - 301 ER - TY - JOUR AU - Edelsbrunner, Herbert AU - Strelkova, Nataliya ID - 2849 IS - 6 JF - Russian Mathematical Surveys TI - On the configuration space of Steiner minimal trees VL - 67 ER - TY - JOUR AB - 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. AU - Kiran, Nagavalli S AU - Eva Benková AU - Reková, Alena AU - Dubová, Jaroslava AU - Malbeck, Jiří AU - Palme, Klaus AU - Brzobohatý, Břetislav ID - 2876 JF - Phytochemistry TI - Retargeting a maize β-glucosidase to the vacuole - Evidence from intact plants that zeatin-O-glucoside is stored in the vacuole VL - 79 ER - TY - JOUR AB - 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. AU - Bielach, Agnieszka AU - Duclercq, Jérôme AU - Peter Marhavy AU - Eva Benková ID - 2875 IS - 1595 JF - Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences TI - Genetic approach towards the identification of auxin - cytokinin crosstalk components involved in root development VL - 367 ER - TY - JOUR AB - 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. AU - Guenot, Bernadette AU - Bayer, Emmanuelle AU - Kierzkowski, Daniel AU - Smith, Richard S AU - Mandel, Therese AU - Žádníková, Petra AU - Eva Benková AU - Kuhlemeier, Cris ID - 2878 IS - 4 JF - Plant Physiology TI - Pin1 independent leaf initiation in Arabidopsis VL - 159 ER - TY - JOUR AB - 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. AU - Bencivenga, Stefano AU - Simonini, Sara AU - Eva Benková AU - Colombo, Lucia ID - 2879 IS - 7 JF - Plant Cell TI - The transcription factors BEL1 and SPL are required for cytokinin and auxin signaling during ovule development in Arabidopsis VL - 24 ER - TY - CONF AB - 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. AU - Boker, Udi AU - Henzinger, Thomas A ID - 2891 T2 - Leibniz International Proceedings in Informatics TI - Approximate determinization of quantitative automata VL - 18 ER - TY - CONF AB - 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. AU - Cerny, Pavol AU - Gopi, Sivakanth AU - Henzinger, Thomas A AU - Radhakrishna, Arjun AU - Totla, Nishant ID - 2890 T2 - Proceedings of the tenth ACM international conference on Embedded software TI - Synthesis from incompatible specifications ER - TY - CONF AB - 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. AU - Henzinger, Thomas A ID - 2888 T2 - Conference proceedings MODELS 2012 TI - Quantitative reactive models VL - 7590 ER - TY - CONF AB - In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images. AU - Edelsbrunner, Herbert AU - Symonova, Olga ID - 2903 TI - The adaptive topology of a digital image ER - TY - CONF AB - The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a quantitative measure for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intu- itively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, and that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies. AU - Cerny, Pavol AU - Chmelik, Martin AU - Henzinger, Thomas A AU - Radhakrishna, Arjun ID - 2916 T2 - Electronic Proceedings in Theoretical Computer Science TI - Interface Simulation Distances VL - 96 ER - TY - JOUR AB - The search for extra-terrestrial intelligence (SETI) has been performed principally as a one-way survey, listening of radio frequencies across the Milky Way and other galaxies. However, scientists have engaged in an active messaging only rarely. This suggests the simple rationale that if other civilizations exist and take a similar approach to ours, namely listening but not broadcasting, the result is a silent universe. A simple game theoretical model, the prisoner's dilemma, explains this situation: each player (civilization) can passively search (defect), or actively search and broadcast (cooperate). In order to maximize the payoff (or, equivalently, minimize the risks) the best strategy is not to broadcast. In fact, the active search has been opposed on the basis that it might be dangerous to expose ourselves. However, most of these ideas have not been based on objective arguments, and ignore accounting of the possible gains and losses. Thus, the question stands: should we perform an active search? I develop a game-theoretical framework where civilizations can be of different types, and explicitly apply it to a situation where societies are either interested in establishing a two-way communication or belligerent and in urge to exploit ours. The framework gives a quantitative solution (a mixed-strategy), which is how frequent we should perform the active SETI. This frequency is roughly proportional to the inverse of the risk, and can be extremely small. However, given the immense amount of stars being scanned, it supports active SETI. The model is compared with simulations, and the possible actions are evaluated through the San Marino scale, measuring the risks of messaging. AU - Vladar, Harold ID - 2917 IS - 1 JF - International Journal of Astrobiology TI - The game of active search for extra terrestrial intelligence Breaking the Great Silence VL - 12 ER -