TY - JOUR AB - 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. AU - Timothy Browning AU - Heath-Brown, Roger ID - 243 IS - 5 JF - Geometric and Functional Analysis TI - Quadratic polynomials represented by norm forms VL - 22 ER - TY - CONF AB - We present an algorithm for computing [X, Y], i.e., all homotopy classes of continuous maps X → Y, where X, Y are topological spaces given as finite simplicial complexes, Y is (d - 1)-connected for some d ≥ 2 (for example, Y can be the d-dimensional sphere S d), and dim X ≤ 2d - 2. These conditions on X, Y guarantee that [X, Y] has a natural structure of a finitely generated Abelian group, and the algorithm finds generators and relations for it. We combine several tools and ideas from homotopy theory (such as Postnikov systems, simplicial sets, and obstruction theory) with algorithmic tools from effective algebraic topology (objects with effective homology). We hope that a further extension of the methods developed here will yield an algorithm for computing, in some cases of interest, the ℤ 2-index, which is a quantity playing a prominent role in Borsuk-Ulam style applications of topology in combinatorics and geometry, e.g., in topological lower bounds for the chromatic number of a graph. In a certain range of dimensions, deciding the embeddability of a simplicial complex into ℝ d also amounts to a ℤ 2-index computation. This is the main motivation of our work. We believe that investigating the computational complexity of questions in homotopy theory and similar areas presents a fascinating research area, and we hope that our work may help bridge the cultural gap between algebraic topology and theoretical computer science. AU - Čadek, Martin AU - Marek Krcál AU - Matoušek, Jiří AU - Sergeraert, Francis AU - Vokřínek, Lukáš AU - Uli Wagner ID - 2440 TI - Computing all maps into a sphere ER - TY - JOUR AB - 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. AU - Matoušek, Jiří AU - Martin Tancer AU - Uli Wagner ID - 2438 IS - 2 JF - Discrete & Computational Geometry TI - A geometric proof of the colored Tverberg theorem VL - 47 ER - TY - JOUR AB - 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. AU - Timothy Browning AU - Haynes, Alan K ID - 244 IS - 2 JF - International Journal of Number Theory TI - Incomplete kloosterman sums and multiplicative inverses in short intervals VL - 9 ER - TY - JOUR AB - 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. AU - Chen, Dan AU - Morin, Pat AU - Uli Wagner ID - 2439 IS - 5 JF - Computational Geometry: Theory and Applications TI - Absolute approximation of Tukey depth: Theory and experiments VL - 46 ER - TY - CONF AB - Eigenvalues associated to graphs are a well-studied subject. In particular the spectra of the adjacency matrix and of the Laplacian of random graphs G(n, p) are known quite precisely. We consider generalizations of these matrices to simplicial complexes of higher dimensions and study their eigenvalues for the Linial-Meshulam model X k(n, p) of random k-dimensional simplicial complexes on n vertices. We show that for p = Ω(log n/n), the eigenvalues of both, the higher-dimensional adjacency matrix and the Laplacian, are a.a.s. sharply concentrated around two values. In a second part of the paper, we discuss a possible higherdimensional analogue of the Discrete Cheeger Inequality. This fundamental inequality expresses a close relationship between the eigenvalues of a graph and its combinatorial expansion properties; in particular, spectral expansion (a large eigenvalue gap) implies edge expansion. Recently, a higher-dimensional analogue of edge expansion for simplicial complexes was introduced by Gromov, and independently by Linial, Meshulam and Wallach and by Newman and Rabinovich. It is natural to ask whether there is a higher-dimensional version of Cheeger's inequality. We show that the most straightforward version of a higher-dimensional Cheeger inequality fails: for every k > 1, there is an infinite family of k-dimensional complexes that are spectrally expanding (there is a large eigenvalue gap for the Laplacian) but not combinatorially expanding. AU - Gundert, Anna AU - Uli Wagner ID - 2441 TI - On Laplacians of random complexes ER - TY - JOUR AB - Constitutive endocytic recycling is a crucial mechanism allowing regulation of the activity of proteins at the plasma membrane and for rapid changes in their localization, as demonstrated in plants for PIN-FORMED (PIN) proteins, the auxin transporters. To identify novel molecular components of endocytic recycling, mainly exocytosis, we designed a PIN1-green fluorescent protein fluorescence imaging-based forward genetic screen for Arabidopsis thaliana mutants that showed increased intracellular accumulation of cargos in response to the trafficking inhibitor brefeldin A (BFA). We identified bex5 (for BFA-visualized exocytic trafficking defective), a novel dominant mutant carrying a missense mutation that disrupts a conserved sequence motif of the small GTPase, RAS GENES FROM RAT BRAINA1b. bex5 displays defects such as enhanced protein accumulation in abnormal BFA compartments, aberrant endosomes, and defective exocytosis and transcytosis. BEX5/RabA1b localizes to trans-Golgi network/early endosomes (TGN/EE) and acts on distinct trafficking processes like those regulated by GTP exchange factors on ADP-ribosylation factors GNOM-LIKE1 and HOPM INTERACTOR7/BFA-VISUALIZED ENDOCYTIC TRAFFICKING DEFECTIVE1, which regulate trafficking at the Golgi apparatus and TGN/EE, respectively. All together, this study identifies Arabidopsis BEX5/RabA1b as a novel regulator of protein trafficking from a TGN/EE compartment to the plasma membrane. AU - Feraru, Elena AU - Feraru, Mugurel Ioan AU - Asaoka, Rin AU - Paciorek, Tomasz AU - De Rycke, Riet M AU - Tanaka, Hirokazu AU - Nakano, Akihiko AU - Jirí Friml ID - 2453 IS - 7 JF - Plant Cell TI - BEX5/RabA1b regulates trans-Golgi network-to-plasma membrane protein trafficking in Arabidopsis VL - 24 ER - TY - JOUR AB - The third EMBO Conference on Plant Molecular Biology, which focused on ‘Plant development and environmental interactions’,was held in May 2012 in Matera, Italy. Here, we review some of the topics and themes that emerged from the various contributions; namely, steering technologies, transcriptional networks and hormonal regulation, small RNAs, cell and tissue polarity, environmental control and natural variation. We intend to provide the reader who might have missed this remarkable event with a glimpse of the recent progress made in this blossoming research field. AU - Beeckman, Tom AU - Friml, Jirí ID - 2456 IS - 20 JF - Development TI - Plant developmental biologists meet on stairways in Matera VL - 139 ER - TY - JOUR AB - 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. AU - Zwiewka, Marta AU - Friml, Jirí ID - 2459 IS - May JF - Frontiers in Plant Science TI - Fluorescence imaging-based forward genetic screens to identify trafficking regulators in plants VL - 3 ER - TY - JOUR AB - Initiation and successive development of organs induce mechanical stresses at the cellular level. Using the tomato shoot apex, a new study now proposes that mechanical strain regulates the plasma membrane abundance of the PIN1 auxin transporter, thereby reinforcing a positive feed-back loop between growth and auxin accumulation. AU - Li, Hongjiang AU - Friml, Jirí AU - Grunewald, Wim ID - 2458 IS - 16 JF - Current Biology TI - Cell polarity: Stretching prevents developmental cramps VL - 22 ER - TY - JOUR AB - Recently developed pharmacogenetic and optogenetic approaches, with their own advantages and disadvantages, have become indispensable tools in modern neuroscience. Here, we employed a previously described knock-in mouse line (GABA ARγ2 77Ilox) in which the γ2 subunit of the GABA A receptor (GABA AR) was mutated to become zolpidem insensitive (γ2 77I) and used viral vectors to swap γ2 77I with wild-type, zolpidem-sensitive γ2 subunits (γ2 77F). The verification of unaltered density and subcellular distribution of the virally introduced γ2 subunits requires their selective labelling. For this we generated six N- and six C-terminal-tagged γ2 subunits, with which cortical cultures of GABA ARγ2 -/- mice were transduced using lentiviruses. We found that the N-terminal AU1 tag resulted in excellent immunodetection and unimpaired synaptic localization. Unaltered kinetic properties of the AU1-tagged γ2 ( AU1γ2 77F) channels were demonstrated with whole-cell patch-clamp recordings of spontaneous IPSCs from cultured cells. Next, we carried out stereotaxic injections of lenti- and adeno-associated viruses containing Cre-recombinase and the AU1γ2 77F subunit (Cre-2A- AU1γ2 77F) into the neocortex of GABA ARγ2 77Ilox mice. Light microscopic immunofluorescence and electron microscopic freeze-fracture replica immunogold labelling demonstrated the efficient immunodetection of the AU1 tag and the normal enrichment of the AU1γ2 77F subunits in perisomatic GABAergic synapses. In line with this, miniature and action potential-evoked IPSCs whole-cell recorded from transduced cells had unaltered amplitudes, kinetics and restored zolpidem sensitivity. Our results obtained with a wide range of structural and functional verification methods reveal unaltered subcellular distributions and functional properties of γ2 77I and AU1γ2 77F GABA ARs in cortical pyramidal cells. This transgenic-viral pharmacogenetic approach has the advantage that it does not require any extrinsic protein that might endow some unforeseen alterations of the genetically modified cells. In addition, this virus-based approach opens up the possibility of modifying multiple cell types in distinct brain regions and performing alternative recombination-based intersectional genetic manipulations. AU - Sümegi, Máté AU - Fukazawa, Yugo AU - Matsui, Ko AU - Lörincz, Andrea AU - Eyre, Mark D AU - Nusser, Zoltán AU - Ryuichi Shigemoto ID - 2476 IS - 7 JF - Journal of Physiology TI - Virus-mediated swapping of zolpidem-insensitive with zolpidem-sensitive GABA A receptors in cortical pyramidal cells VL - 590 ER - TY - JOUR AB - Background: One of the best-characterized causative factors of Alzheimer's disease (AD) is the generation of amyloid-β peptide (Aβ). AD subjects are at high risk of epileptic seizures accompanied by aberrant neuronal excitability, which in itself enhances Aβ generation. However, the molecular linkage between epileptic seizures and Aβ generation in AD remains unclear. Results: X11 and X11-like (X11L) gene knockout mice suffered from epileptic seizures, along with a malfunction of hyperpolarization-activated cyclic nucleotide gated (HCN) channels. Genetic ablation of HCN1 in mice and HCN1 channel blockage in cultured Neuro2a (N2a) cells enhanced Aβ generation. Interestingly, HCN1 levels dramatically decreased in the temporal lobe of cynomolgus monkeys (Macaca fascicularis) during aging and were significantly diminished in the temporal lobe of sporadic AD patients. Conclusion: Because HCN1 associates with amyloid-β precursor protein (APP) and X11/X11L in the brain, genetic deficiency of X11/X11L may induce aberrant HCN1 distribution along with epilepsy. Moreover, the reduction in HCN1 levels in aged primates may contribute to augmented Aβ generation. Taken together, HCN1 is proposed to play an important role in the molecular linkage between epileptic seizures and Aβ generation, and in the aggravation of sporadic AD. AU - Saito, Yuhki AU - Inoue, Tsuyoshi AU - Zhu, Gang AU - Kimura, Naoki AU - Okada, Motohiro AU - Nishimura, Masaki AU - Murayama, Shigeo AU - Kaneko, Sunao AU - Ryuichi Shigemoto AU - Imoto, Keiji AU - Suzuki, Toshiharu ID - 2475 IS - 1 JF - Molecular Neurodegeneration TI - Hyperpolarization-activated cyclic nucleotide gated channels: A potential molecular link between epileptic seizures and Aβ generation in Alzheimer's disease VL - 7 ER - TY - JOUR AB - Dynamic activity of glia has repeatedly been demonstrated, but if such activity is independent from neuronal activity, glia would not have any role in the information processing in the brain or in the generation of animal behavior. Evidence for neurons communicating with glia is solid, but the signaling pathway leading back from glial-to-neuronal activity was often difficult to study. Here, we introduced a transgenic mouse line in which channelrhodopsin-2, a light-gated cation channel, was expressed in astrocytes. Selective photostimulation of these astrocytes in vivo triggered neuronal activation. Using slice preparations, we show that glial photostimulation leads to release of glutamate, which was sufficient to activate AMPA receptors on Purkinje cells and to induce long-term depression of parallel fiber-to-Purkinje cell synapses through activation of metabotropic glutamate receptors. In contrast to neuronal synaptic vesicular release, glial activation likely causes preferential activation of extrasynaptic receptors that appose glial membrane. Finally, we show that neuronal activation by glial stimulation can lead to perturbation of cerebellar modulated motor behavior. These findings demonstrate that glia can modulate the tone of neuronal activity and behavior. This animal model is expected to be a potentially powerful approach to study the role of glia in brain function. AU - Sasaki, Takuya AU - Beppu, Kaoru AU - Tanaka, Kenji F AU - Fukazawa, Yugo AU - Ryuichi Shigemoto AU - Matsui, Ko ID - 2477 IS - 50 JF - PNAS TI - Application of an optogenetic byway for perturbing neuronal activity via glial photostimulation VL - 109 ER - TY - JOUR AB - Interneurons are critical for neuronal circuit function, but how their dendritic morphologies and membrane properties influence information flow within neuronal circuits is largely unknown. We studied the spatiotemporal profile of synaptic integration and short-term plasticity in dendrites of mature cerebellar stellate cells by combining two-photon guided electrical stimulation, glutamate uncaging, electron microscopy, and modeling. Synaptic activation within thin (0.4 μm) dendrites produced somatic responses that became smaller and slower with increasing distance from the soma, sublinear subthreshold input-output relationships, and a somatodendritic gradient of short-term plasticity. Unlike most studies showing that neurons employ active dendritic mechanisms, we found that passive cable properties of thin dendrites determine the sublinear integration and plasticity gradient, which both result from large dendritic depolarizations that reduce synaptic driving force. These integrative properties allow stellate cells to act as spatiotemporal filters of synaptic input patterns, thereby biasing their output in favor of sparse presynaptic activity. Stellate cells are critical sources of inhibition in the cerebellum, but how their dendrites integrate excitatory synaptic inputs is unknown. Abrahamsson et al. show that thin dendrites and passive membrane properties of SCs promote sublinear synaptic summation and distance-dependent short-term plasticity. AU - Abrahamsson, Therese AU - Cathala, Laurence AU - Matsui, Ko AU - Ryuichi Shigemoto AU - DiGregorio, David A ID - 2474 IS - 6 JF - Neuron TI - Thin dendrites of cerebellar interneurons confer sublinear synaptic integration and a gradient of short-term plasticity VL - 73 ER - TY - JOUR AB - We investigated the temporal and spatial expression of SK2 in the developing mouse hippocampus using molecular and biochemical techniques, quantitative immunogold electron microscopy, and electrophysiology. The mRNA encoding SK2 was expressed in the developing and adult hippocampus. Western blotting and immunohistochemistry showed that SK2 protein increased with age. This was accompanied by a shift in subcellular localization. Early in development (P5), SK2 was predominantly localized to the endoplasmic reticulum in the pyramidal cell layer. But by P30 SK2 was almost exclusively expressed in the dendrites and spines. The level of SK2 at the postsynaptic density (PSD) also increased during development. In the adult, SK2 expression on the spine plasma membrane showed a proximal-to-distal gradient. Consistent with this redistribution and gradient of SK2, the selective SK channel blocker apamin increased evoked excitatory postsynaptic potentials (EPSPs) only in CA1 pyramidal neurons from mice older than P15. However, the effect of apamin on EPSPs was not different between synapses in proximal or distal stratum radiatum or stratum lacunosum-moleculare in adult. These results show a developmental increase and gradient in SK2-containing channel surface expression that underlie their influence on neurotransmission, and that may contribute to increased memory acquisition during early development. AU - Ballesteros-Merino, Carmen AU - Lin, Michael AU - Wu, Wendy W AU - Ferrándiz-Huertas, Clotilde AU - Cabañero, María José AU - Watanabe, Masahiko AU - Fukazawa, Yugo AU - Ryuichi Shigemoto AU - Maylie, James G AU - Adelman, John P AU - Luján, Rafael ID - 2515 IS - 6 JF - Hippocampus TI - Developmental profile of SK2 channel expression and function in CA1 neurons VL - 22 ER - TY - JOUR AB - Visual information must be relayed through the lateral geniculate nucleus before it reaches the visual cortex. However, not all spikes created in the retina lead to postsynaptic spikes and properties of the retinogeniculate synapse contribute to this filtering. To understand the mechanisms underlying this filtering process, we conducted electrophysiology to assess the properties of signal transmission in the Long-Evans rat. We also performed SDS-digested freeze-fracture replica labeling to quantify the receptor and transporter distribution, as well as EM reconstruction to describe the 3D structure. To analyze the impact of transmitter diffusion on the activity of the receptors, simulations were integrated. We identified that a large contributor to the filtering is the marked paired-pulse depression at this synapse, which was intensified by the morphological characteristics of the contacts. The broad presynaptic and postsynaptic contact area restricts transmitter diffusion two dimensionally. Additionally, the presence of multiple closely arranged release sites invites intersynaptic spillover, which causes desensitization of AMPA receptors. The presence of AMPA receptors that slowly recover from desensitization along with the high presynaptic release probability and multivesicular release at each synapse also contribute to the depression. These features contrast with many other synapses where spatiotemporal spread of transmitter is limited by rapid transmitter clearance allowing synapses to operate more independently. We propose that the micrometer-order structure can ultimately affect the visual information processing. AU - Budisantoso, Timotheus AU - Matsui, Ko AU - Kamasawa, Naomi AU - Fukazawa, Yugo AU - Ryuichi Shigemoto ID - 2514 IS - 7 JF - Journal of Neuroscience TI - Mechanisms underlying signal filtering at a multisynapse contact VL - 32 ER - TY - JOUR AB - R-type calcium channels (RTCCs) are well known for their role in synaptic plasticity, but little is known about their subcellular distribution across various neuronal compartments. Using subtype-specific antibodies, we characterized the regional and subcellular localization of Ca v2.3 in mice and rats at both light and electron microscopic levels. Ca v2.3 immunogold particles were found to be predominantly presynaptic in the interpeduncular nucleus, but postsynaptic in other brain regions. Serial section analysis of electron microscopic images from the hippocampal CA1 revealed a higher density of immunogold particles in the dendritic shaft plasma membrane compared with the pyramidal cell somata. However, the labeling densities were not significantly different among the apical, oblique, or basal dendrites. Immunogold particles were also observed over the plasma membrane of dendritic spines, including both synaptic and extrasynaptic sites. Individual spine heads contained <20 immunogold particles, with an average density of ~260 immunoparticles per μm 3 spine head volume, in accordance with the density of RTCCs estimated using calcium imaging (Sabatini and Svoboda, 2000). The Ca v2.3 density was variable among similar-sized spine heads and did not correlate with the density in the parent dendrite, implying that spines are individual calcium compartments operating autonomously from their parent dendrites. AU - Parajuli, Laxmi K AU - Nakajima, Chikako AU - Kulik, Ákos AU - Matsui, Ko AU - Schneider, Toni AU - Ryuichi Shigemoto AU - Fukazawa, Yugo ID - 2689 IS - 39 JF - Journal of Neuroscience TI - Quantitative regional and ultra structural localization of the Ca v2 3 subunit of R type calcium channel in mouse brain VL - 32 ER - TY - JOUR AB - Left-right asymmetry of human brain function has been known for a century, although much of molecular and cellular basis of brain laterality remains to be elusive. Recent studies suggest that hippocampal CA3-CA1 excitatory synapses are asymmetrically arranged, however, the functional implication of the asymmetrical circuitry has not been studied at the behavioral level. In order to address the left-right asymmetry of hippocampal function in behaving mice, we analyzed the performance of "split-brain" mice in the Barnes maze. The "split-brain" mice received ventral hippocampal commissure and corpus callosum transection in addition to deprivation of visual input from one eye. In such mice, the hippocampus in the side of visual deprivation receives sensory-driven input. Better spatial task performance was achieved by the mice which were forced to use the right hippocampus than those which were forced to use the left hippocampus. In two-choice spatial maze, forced usage of left hippocampus resulted in a comparable performance to the right counterpart, suggesting that both hippocampal hemispheres are capable of conducting spatial learning. Therefore, the results obtained from the Barnes maze suggest that the usage of the right hippocampus improves the accuracy of spatial memory. Performance of non-spatial yet hippocampus-dependent tasks (e.g. fear conditioning) was not influenced by the laterality of the hippocampus. AU - Shinohara, Yoshiaki AU - Hosoya, Aki AU - Yamasaki, Nobuyuki AU - Ahmed, Hassan AU - Hattori, Satoko AU - Eguchi, Megumi AU - Yamaguchi, Shun AU - Miyakawa, Tsuyoshi AU - Hirase, Hajime AU - Ryuichi Shigemoto ID - 2687 IS - 2 JF - Hippocampus TI - Right-hemispheric dominance of spatial memory in split-brain mice VL - 22 ER - TY - JOUR AB - To gain insights into structure-function relationship of excitatory synapses, we revisit our quantitative analysis of synaptic AMPAR by highly sensitive freeze-fracture replica labeling in eight different connections. All of these connections showed linear correlation between synapse size and AMPAR number indicating a common intra-synapse-type relationship in CNS synapses. On the contrary, inter-synapse-type relationship is unexpected indicating no correlation between averages of synapse size and AMPAR number. Interestingly, connections with large average synapse size and low AMPAR density showed high variability of AMPAR number and mosaic distribution within the postsynaptic membrane. We propose an idea that these connections may quickly exhibit synaptic plasticity by modifying AMPAR density/number whereas those with high AMPAR density change their efficacy by modifying synapse size. AU - Fukazawa, Yugo AU - Ryuichi Shigemoto ID - 2688 IS - 3 JF - Current Opinion in Neurobiology TI - Intra-synapse-type and inter-synapse-type relationships between synaptic size and AMPAR expression VL - 22 ER - TY - GEN AU - László Erdös ID - 2696 T2 - ArXiv TI - Universality for random matrices and log-gases ER - TY - CONF AU - László Erdös ID - 2700 TI - Lecture notes on quantum Brownian motion VL - 95 ER - TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Joglekar, Manas AU - Shah, Nisarg ID - 2715 TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives VL - 18 ER - TY - CONF AB - Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω-regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on VASS (vector addition systems with states). Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts. AU - Chatterjee, Krishnendu AU - Randour, Mickael AU - Raskin, Jean-François ED - Koutny, Maciej ED - Ulidowski, Irek ID - 10904 SN - 0302-9743 T2 - CONCUR 2012 - Concurrency Theory TI - Strategy synthesis for multi-dimensional quantitative objectives VL - 7454 ER - TY - JOUR AB - Consider N×N Hermitian or symmetric random matrices H with independent entries, where the distribution of the (i,j) matrix element is given by the probability measure vij with zero expectation and with variance σ ιj 2. We assume that the variances satisfy the normalization condition Σiσij2=1 for all j and that there is a positive constant c such that c≤Nσ ιj 2 ιc -1. We further assume that the probability distributions νij have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eigenvalue distribution of H is given by the Wigner semicircle law uniformly up to the edges of the spectrum with an error of order (Nη) -1 where η is the imaginary part of the spectral parameter in the Stieltjes transform. There are three corollaries to this strong local semicircle law: (1) Rigidity of eigenvalues: If γj=γj,N denotes the classical location of the j-th eigenvalue under the semicircle law ordered in increasing order, then the j-th eigenvalue λj is close to γj in the sense that for some positive constants C, c P{double-struck}(∃j:|λ j-γ j|≥(logN) CloglogN[min(j,N-j+1)] -1/3N -2/3)≤ C exp[-(logN) cloglogN] for N large enough. (2) The proof of Dyson's conjecture (Dyson, 1962 [15]) which states that the time scale of the Dyson Brownian motion to reach local equilibrium is of order N -1 up to logarithmic corrections. (3) The edge universality holds in the sense that the probability distributions of the largest (and the smallest) eigenvalues of two generalized Wigner ensembles are the same in the large N limit provided that the second moments of the two ensembles are identical. AU - László Erdös AU - Yau, Horng-Tzer AU - Yin, Jun ID - 2770 IS - 3 JF - Advances in Mathematics TI - Rigidity of eigenvalues of generalized Wigner matrices VL - 229 ER - TY - JOUR AB - We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {X J} N j=1 are close to their classical location {y j} N j=1 determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/N, the necessary apriori estimate on the location of eigenvalues requires only to know that E|x j - γ j| 2 ≤ N-1-ε on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for sample covariance matrices. AU - László Erdös AU - Schlein, Benjamin AU - Yau, Horng-Tzer AU - Yin, Jun ID - 2769 IS - 1 JF - Annales de l'institut Henri Poincare (B) Probability and Statistics TI - The local relaxation flow approach to universality of the local statistics for random matrices VL - 48 ER - TY - JOUR AB - Consider N × N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure ν ij with a subexponential decay. Let σ ij 2 be the variance for the probability measure ν ij with the normalization property that Σ iσ i,j 2 = 1 for all j. Under essentially the only condition that c ≤ N σ ij 2 ≤ c -1 for some constant c > 0, we prove that, in the limit N → ∞, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M -1. AU - László Erdös AU - Yau, Horng-Tzer AU - Yin, Jun ID - 2767 IS - 1-2 JF - Probability Theory and Related Fields TI - Bulk universality for generalized Wigner matrices VL - 154 ER - TY - JOUR AB - We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i. e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum. AU - László Erdös AU - Hasler, David G ID - 2768 IS - 2 JF - Communications in Mathematical Physics TI - Wegner estimate and Anderson localization for random magnetic fields VL - 309 ER - TY - JOUR AB - 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. AU - László Erdös AU - Yau, Horng-Tzer ID - 2775 IS - 3 JF - Bulletin of the American Mathematical Society TI - Universality of local spectral statistics of random matrices VL - 49 ER - TY - JOUR AB - 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. AU - László Erdös AU - Fournais, Søren AU - Solovej, Jan P ID - 2777 IS - 9 JF - Journal of Mathematical Physics TI - Relativistic Scott correction in self-generated magnetic fields VL - 53 ER - TY - JOUR AB - We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all magnetic fields. The parameter β effectively determines the strength of the field. We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term vanishes. However for potentials with a Coulomb singularity, the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper (Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated magnetic field, Preprint, 2011) to prove the second order Scott correction to the ground state energy of large atoms and molecules. AU - László Erdös AU - Fournais, Søren AU - Solovej, Jan P ID - 2772 IS - 4 JF - Annales Henri Poincare TI - Second order semiclassics with self generated magnetic fields VL - 13 ER - TY - JOUR AB - 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. AU - László Erdös AU - Knowles, Antti AU - Yau, Horng-Tzer AU - Yin, Jun ID - 2776 IS - 3 JF - Communications in Mathematical Physics TI - Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues VL - 314 ER - TY - JOUR AB - 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. AU - László Erdös AU - Fournais, Søren AU - Solovej, Jan P ID - 2774 IS - 3 JF - Communications in Mathematical Physics TI - Scott correction for large atoms and molecules in a self-generated magnetic field VL - 312 ER - 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 -