TY - JOUR AB - We investigate the relation between Bose-Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder AU - Könenberg, Martin AU - Moser, Thomas AU - Seiringer, Robert AU - Yngvason, Jakob ID - 1880 JF - New Journal of Physics TI - Superfluid behavior of a Bose-Einstein condensate in a random potential VL - 17 ER - TY - CONF AB - We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations. AU - Fahrenberg, Uli AU - Kretinsky, Jan AU - Legay, Axel AU - Traonouez, Louis ID - 1882 TI - Compositionality for quantitative specifications VL - 8997 ER - TY - JOUR AB - We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point. AU - Keller-Schmidt, Stephanie AU - Tugrul, Murat AU - Eguíluz, Víctor AU - Hernandez Garcia, Emilio AU - Klemm, Konstantin ID - 1883 IS - 2 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics TI - Anomalous scaling in an age-dependent branching model VL - 91 ER - TY - JOUR AB - Petrocoptis is a small genus of chasmophytic plants endemic to the Iberian Peninsula, with some localized populations in the French Pyrenees. Within the genus, a dozen species have been recognized based on morphological diversity, most of them with limited distribution area, in small populations and frequently with potential threats to their survival. To date, however, a molecular evaluation of the current systematic treatments has not been carried out. The aim of the present study is to infer phylogenetic relationships among its subordinate taxa by using plastidial rps16 intron and nuclear internal transcribed spacer (ITS) DNA sequences; and evaluate the phylogenetic placement of the genus Petrocoptis within the family Caryophyllaceae. The monophyly of Petrocoptis is supported by both ITS and rps16 intron sequence analyses. Furthermore, time estimates using BEAST analyses indicate a Middle to Late Miocene diversification (10.59 Myr, 6.44–15.26 Myr highest posterior densities [HPD], for ITS; 14.30 Myr, 8.61–21.00 Myr HPD, for rps16 intron). AU - Cires Rodriguez, Eduardo AU - Prieto, José ID - 1878 IS - 2 JF - Journal of Plant Research TI - Phylogenetic relationships of Petrocoptis A. Braun ex Endl. (Caryophyllaceae), a discussed genus from the Iberian Peninsula VL - 128 ER - TY - JOUR AB - The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail. AU - Tkacik, Gasper AU - Dubuis, Julien AU - Petkova, Mariela AU - Gregor, Thomas ID - 1885 IS - 1 JF - Genetics TI - Positional information, positional error, and readout precision in morphogenesis: A mathematical framework VL - 199 ER - TY - JOUR AB - We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the "input") by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively new regulatory strategy emerges where individual cells respond to the input in a nearly step-like fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models. AU - Sokolowski, Thomas R AU - Tkacik, Gasper ID - 1940 IS - 6 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics TI - Optimizing information flow in small genetic networks. IV. Spatial coupling VL - 91 ER - TY - JOUR AB - We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2. AU - Pausinger, Florian AU - Steinerberger, Stefan ID - 1938 IS - 6 JF - Physics Letters, Section A TI - On the distribution of local extrema in quantum chaos VL - 379 ER - TY - JOUR AU - Rakusová, Hana AU - Fendrych, Matyas AU - Friml, Jirí ID - 1944 IS - 2 JF - Current Opinion in Plant Biology TI - Intracellular trafficking and PIN-mediated cell polarity during tropic responses in plants VL - 23 ER - TY - CONF AB - We present a method and a tool for generating succinct representations of sets of concurrent traces. We focus on trace sets that contain all correct or all incorrect permutations of events from a given trace. We represent trace sets as HB-Formulas that are Boolean combinations of happens-before constraints between events. To generate a representation of incorrect interleavings, our method iteratively explores interleavings that violate the specification and gathers generalizations of the discovered interleavings into an HB-Formula; its complement yields a representation of correct interleavings. We claim that our trace set representations can drive diverse verification, fault localization, repair, and synthesis techniques for concurrent programs. We demonstrate this by using our tool in three case studies involving synchronization synthesis, bug summarization, and abstraction refinement based verification. In each case study, our initial experimental results have been promising. In the first case study, we present an algorithm for inferring missing synchronization from an HB-Formula representing correct interleavings of a given trace. The algorithm applies rules to rewrite specific patterns in the HB-Formula into locks, barriers, and wait-notify constructs. In the second case study, we use an HB-Formula representing incorrect interleavings for bug summarization. While the HB-Formula itself is a concise counterexample summary, we present additional inference rules to help identify specific concurrency bugs such as data races, define-use order violations, and two-stage access bugs. In the final case study, we present a novel predicate learning procedure that uses HB-Formulas representing abstract counterexamples to accelerate counterexample-guided abstraction refinement (CEGAR). In each iteration of the CEGAR loop, the procedure refines the abstraction to eliminate multiple spurious abstract counterexamples drawn from the HB-Formula. AU - Gupta, Ashutosh AU - Henzinger, Thomas A AU - Radhakrishna, Arjun AU - Samanta, Roopsha AU - Tarrach, Thorsten ID - 1992 SN - 978-1-4503-3300-9 TI - Succinct representation of concurrent trace sets ER - TY - JOUR AB - We prove that the three-state toric homogeneous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals is generated by quadratic binomials. This was conjectured by Haws, Martin del Campo, Takemura and Yoshida, who proved that they are generated by degree six binomials. AU - Noren, Patrik ID - 1997 IS - May-June JF - Journal of Symbolic Computation TI - The three-state toric homogeneous Markov chain model has Markov degree two VL - 68/Part 2 ER - TY - JOUR AB - The paper describes a generalized iterative proportional fitting procedure that can be used for maximum likelihood estimation in a special class of the general log-linear model. The models in this class, called relational, apply to multivariate discrete sample spaces that do not necessarily have a Cartesian product structure and may not contain an overall effect. When applied to the cell probabilities, the models without the overall effect are curved exponential families and the values of the sufficient statistics are reproduced by the MLE only up to a constant of proportionality. The paper shows that Iterative Proportional Fitting, Generalized Iterative Scaling, and Improved Iterative Scaling fail to work for such models. The algorithm proposed here is based on iterated Bregman projections. As a by-product, estimates of the multiplicative parameters are also obtained. An implementation of the algorithm is available as an R-package. AU - Klimova, Anna AU - Rudas, Tamás ID - 2008 IS - 3 JF - Scandinavian Journal of Statistics TI - Iterative scaling in curved exponential families VL - 42 ER - TY - JOUR AB - The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko). We present some theoretical evidence for this conjecture, as well as computational evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of the phenomena we observed in our data. AU - Hein, Nicolas AU - Hillar, Christopher AU - Martin Del Campo Sanchez, Abraham AU - Sottile, Frank AU - Teitler, Zach ID - 2006 IS - 3 JF - Experimental Mathematics TI - The monotone secant conjecture in the real Schubert calculus VL - 24 ER - TY - JOUR AB - The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-) faithfulness with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association. AU - Klimova, Anna AU - Uhler, Caroline AU - Rudas, Tamás ID - 2014 IS - 7 JF - Computational Statistics & Data Analysis TI - Faithfulness and learning hypergraphs from discrete distributions VL - 87 ER - TY - JOUR AB - Small GTP-binding proteins of the Ras superfamily play diverse roles in intracellular trafficking. Among them, the Rab, Arf, and Rho families function in successive steps of vesicle transport, in forming vesicles from donor membranes, directing vesicle trafficking toward target membranes and docking vesicles onto target membranes. These proteins act as molecular switches that are controlled by a cycle of GTP binding and hydrolysis regulated by guanine nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs). In this study we explored the role of GAPs in the regulation of the endocytic pathway using fluorescently labeled yeast mating pheromone α-factor. Among 25 non-essential GAP mutants, we found that deletion of the GLO3 gene, encoding Arf-GAP protein, caused defective internalization of fluorescently labeled α-factor. Quantitative analysis revealed that glo3Δ cells show defective α-factor binding to the cell surface. Interestingly, Ste2p, the α-factor receptor, was mis-localized from the plasma membrane to the vacuole in glo3Δ cells. Domain deletion mutants of Glo3p revealed that a GAP-independent function, as well as the GAP activity, of Glo3p is important for both α-factor binding and Ste2p localization at the cell surface. Additionally, we found that deletion of the GLO3 gene affects the size and number of Arf1p-residing Golgi compartments and causes a defect in transport from the TGN to the plasma membrane. Furthermore, we demonstrated that glo3Δ cells were defective in the late endosome-to-TGN transport pathway, but not in the early endosome-to-TGN transport pathway. These findings suggest novel roles for Arf-GAP Glo3p in endocytic recycling of cell surface proteins. AU - Kawada, Daiki AU - Kobayashi, Hiromu AU - Tomita, Tsuyoshi AU - Nakata, Eisuke AU - Nagano, Makoto AU - Siekhaus, Daria E AU - Toshima, Junko AU - Toshimaa, Jiro ID - 2025 IS - 1 JF - Biochimica et Biophysica Acta - Molecular Cell Research TI - The yeast Arf-GAP Glo3p is required for the endocytic recycling of cell surface proteins VL - 1853 ER - TY - JOUR AB - A hybrid-parallel direct-numerical-simulation method with application to turbulent Taylor-Couette flow is presented. The Navier-Stokes equations are discretized in cylindrical coordinates with the spectral Fourier-Galerkin method in the axial and azimuthal directions, and high-order finite differences in the radial direction. Time is advanced by a second-order, semi-implicit projection scheme, which requires the solution of five Helmholtz/Poisson equations, avoids staggered grids and renders very small slip velocities. Nonlinear terms are evaluated with the pseudospectral method. The code is parallelized using a hybrid MPI-OpenMP strategy, which, compared with a flat MPI parallelization, is simpler to implement, allows to reduce inter-node communications and MPI overhead that become relevant at high processor-core counts, and helps to contain the memory footprint. A strong scaling study shows that the hybrid code maintains scalability up to more than 20,000 processor cores and thus allows to perform simulations at higher resolutions than previously feasible. In particular, it opens up the possibility to simulate turbulent Taylor-Couette flows at Reynolds numbers up to O(105). This enables to probe hydrodynamic turbulence in Keplerian flows in experimentally relevant regimes. AU - Shi, Liang AU - Rampp, Markus AU - Hof, Björn AU - Avila, Marc ID - 2030 IS - 1 JF - Computers and Fluids TI - A hybrid MPI-OpenMP parallel implementation for pseudospectral simulations with application to Taylor-Couette flow VL - 106 ER - TY - JOUR AB - Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility. AU - Edelsbrunner, Herbert AU - Jablonski, Grzegorz AU - Mrozek, Marian ID - 2035 IS - 5 JF - Foundations of Computational Mathematics TI - The persistent homology of a self-map VL - 15 ER - TY - JOUR AB - Opacity is a generic security property, that has been defined on (non-probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non-deterministicchoice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and ω-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non-opaquebecomes decidable for a restricted class of ω-regular secrets, as well as for all ω-regular secrets under finite-memory schedulers. AU - Bérard, Béatrice AU - Chatterjee, Krishnendu AU - Sznajder, Nathalie ID - 2034 IS - 1 JF - Information Processing Letters TI - Probabilistic opacity for Markov decision processes VL - 115 ER - TY - JOUR AB - We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. AU - Nam, Phan AU - Seiringer, Robert ID - 2085 IS - 2 JF - Archive for Rational Mechanics and Analysis TI - Collective excitations of Bose gases in the mean-field regime VL - 215 ER - TY - JOUR AB - We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). AU - Erdös, László AU - Knowles, Antti ID - 2166 IS - 3 JF - Communications in Mathematical Physics TI - The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case VL - 333 ER - TY - JOUR AB - Linearizability of concurrent data structures is usually proved by monolithic simulation arguments relying on the identification of the so-called linearization points. Regrettably, such proofs, whether manual or automatic, are often complicated and scale poorly to advanced non-blocking concurrency patterns, such as helping and optimistic updates. In response, we propose a more modular way of checking linearizability of concurrent queue algorithms that does not involve identifying linearization points. We reduce the task of proving linearizability with respect to the queue specification to establishing four basic properties, each of which can be proved independently by simpler arguments. As a demonstration of our approach, we verify the Herlihy and Wing queue, an algorithm that is challenging to verify by a simulation proof. AU - Chakraborty, Soham AU - Henzinger, Thomas A AU - Sezgin, Ali AU - Vafeiadis, Viktor ID - 1832 IS - 1 JF - Logical Methods in Computer Science TI - Aspect-oriented linearizability proofs VL - 11 ER -