@inproceedings{1192, abstract = {The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Δ-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Knowing that edge CSP is tractable for even Δ-matroid constraints allows us to extend the tractability result to a larger class of Δ-matroids that includes many classes that were known to be tractable before, namely co-independent, compact, local and binary.}, author = {Kazda, Alexandr and Kolmogorov, Vladimir and Rolinek, Michal}, isbn = {978-161197478-2}, location = {Barcelona, Spain}, pages = {307 -- 326}, publisher = {SIAM}, title = {{Even delta-matroids and the complexity of planar Boolean CSPs}}, doi = {10.1137/1.9781611974782.20}, year = {2017}, } @inproceedings{1194, abstract = {Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples. }, author = {Chatterjee, Krishnendu and Novotny, Petr and Zikelic, Djordje}, issn = {07308566}, location = {Paris, France}, number = {1}, pages = {145 -- 160}, publisher = {ACM}, title = {{Stochastic invariants for probabilistic termination}}, doi = {10.1145/3009837.3009873}, volume = {52}, year = {2017}, } @article{1196, abstract = {We define the . model-measuring problem: given a model . M and specification . ϕ, what is the maximal distance . ρ such that all models . M' within distance . ρ from . M satisfy (or violate) . ϕ. The model-measuring problem presupposes a distance function on models. We concentrate on . automatic distance functions, which are defined by weighted automata. The model-measuring problem subsumes several generalizations of the classical model-checking problem, in particular, quantitative model-checking problems that measure the degree of satisfaction of a specification; robustness problems that measure how much a model can be perturbed without violating the specification; and parameter synthesis for hybrid systems. We show that for automatic distance functions, and (a) . ω-regular linear-time, (b) . ω-regular branching-time, and (c) hybrid specifications, the model-measuring problem can be solved.We use automata-theoretic model-checking methods for model measuring, replacing the emptiness question for word, tree, and hybrid automata by the . optimal-value question for the weighted versions of these automata. For automata over words and trees, we consider weighted automata that accumulate weights by maximizing, summing, discounting, and limit averaging. For hybrid automata, we consider monotonic (parametric) hybrid automata, a hybrid counterpart of (discrete) weighted automata.We give several examples of using the model-measuring problem to compute various notions of robustness and quantitative satisfaction for temporal specifications. Further, we propose the modeling framework for model measuring to ease the specification and reduce the likelihood of errors in modeling.Finally, we present a variant of the model-measuring problem, called the . model-repair problem. The model-repair problem applies to models that do not satisfy the specification; it can be used to derive restrictions, under which the model satisfies the specification, i.e., to repair the model.}, author = {Henzinger, Thomas A and Otop, Jan}, journal = {Nonlinear Analysis: Hybrid Systems}, pages = {166 -- 190}, publisher = {Elsevier}, title = {{Model measuring for discrete and hybrid systems}}, doi = {10.1016/j.nahs.2016.09.001}, volume = {23}, year = {2017}, } @article{11961, abstract = {Flow chemistry involves the use of channels or tubing to conduct a reaction in a continuous stream rather than in a flask. Flow equipment provides chemists with unique control over reaction parameters enhancing reactivity or in some cases enabling new reactions. This relatively young technology has received a remarkable amount of attention in the past decade with many reports on what can be done in flow. Until recently, however, the question, “Should we do this in flow?” has merely been an afterthought. This review introduces readers to the basic principles and fundamentals of flow chemistry and critically discusses recent flow chemistry accounts.}, author = {Plutschack, Matthew B. and Pieber, Bartholomäus and Gilmore, Kerry and Seeberger, Peter H.}, issn = {1520-6890}, journal = {Chemical Reviews}, number = {18}, pages = {11796--11893}, publisher = {American Chemical Society}, title = {{The Hitchhiker’s Guide to flow chemistry}}, doi = {10.1021/acs.chemrev.7b00183}, volume = {117}, year = {2017}, } @article{11976, abstract = {The way organic multistep synthesis is performed is changing due to the adoption of flow chemical techniques, which has enabled the development of improved methods to make complex molecules. The modular nature of the technique provides not only access to target molecules via linear flow approaches but also for the targeting of structural cores with single systems. This perspective article summarizes the state of the art of continuous multistep synthesis and discusses the main challenges and opportunities in this area.}, author = {Pieber, Bartholomäus and Gilmore, Kerry and Seeberger, Peter H.}, issn = {2063-0212}, journal = {Journal of Flow Chemistry}, number = {3-4}, pages = {129--136}, publisher = {AKJournals}, title = {{Integrated flow processing - challenges in continuous multistep synthesis}}, doi = {10.1556/1846.2017.00016}, volume = {7}, year = {2017}, } @article{1198, abstract = {We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.}, author = {Moser, Thomas and Seiringer, Robert}, issn = {03779017}, journal = {Letters in Mathematical Physics}, number = {3}, pages = { 533 -- 552}, publisher = {Springer}, title = {{Triviality of a model of particles with point interactions in the thermodynamic limit}}, doi = {10.1007/s11005-016-0915-x}, volume = {107}, year = {2017}, } @article{1199, abstract = {Much of quantitative genetics is based on the ‘infinitesimal model’, under which selection has a negligible effect on the genetic variance. This is typically justified by assuming a very large number of loci with additive effects. However, it applies even when genes interact, provided that the number of loci is large enough that selection on each of them is weak relative to random drift. In the long term, directional selection will change allele frequencies, but even then, the effects of epistasis on the ultimate change in trait mean due to selection may be modest. Stabilising selection can maintain many traits close to their optima, even when the underlying alleles are weakly selected. However, the number of traits that can be optimised is apparently limited to ~4Ne by the ‘drift load’, and this is hard to reconcile with the apparent complexity of many organisms. Just as for the mutation load, this limit can be evaded by a particular form of negative epistasis. A more robust limit is set by the variance in reproductive success. This suggests that selection accumulates information most efficiently in the infinitesimal regime, when selection on individual alleles is weak, and comparable with random drift. A review of evidence on selection strength suggests that although most variance in fitness may be because of alleles with large Nes, substantial amounts of adaptation may be because of alleles in the infinitesimal regime, in which epistasis has modest effects.}, author = {Barton, Nicholas H}, journal = {Heredity}, pages = {96 -- 109}, publisher = {Nature Publishing Group}, title = {{How does epistasis influence the response to selection?}}, doi = {10.1038/hdy.2016.109}, volume = {118}, year = {2017}, } @article{1207, abstract = {The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.}, author = {Bao, Zhigang and Erdös, László and Schnelli, Kevin}, issn = {00103616}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {947 -- 990}, publisher = {Springer}, title = {{Local law of addition of random matrices on optimal scale}}, doi = {10.1007/s00220-016-2805-6}, volume = {349}, year = {2017}, } @article{1208, abstract = {We study parameter estimation in linear Gaussian covariance models, which are p-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Although we are primarily interested in the case in which n≫p, the proofs of our results utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that, for sample sizes n≃14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem. © 2016 The Royal Statistical Society and Blackwell Publishing Ltd.}, author = {Zwiernik, Piotr and Uhler, Caroline and Richards, Donald}, issn = {13697412}, journal = {Journal of the Royal Statistical Society. Series B: Statistical Methodology}, number = {4}, pages = {1269 -- 1292}, publisher = {Wiley-Blackwell}, title = {{Maximum likelihood estimation for linear Gaussian covariance models}}, doi = {10.1111/rssb.12217}, volume = {79}, year = {2017}, } @article{1211, abstract = {Systems such as fluid flows in channels and pipes or the complex Ginzburg–Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial reflections or complex conjugation. The simplest, and very common symmetry of this type is the equivariance of the defining equations under the orthogonal group O(2). We formulate a novel symmetry reduction scheme for such systems by combining the method of slices with invariant polynomial methods, and show how it works by applying it to the Kuramoto–Sivashinsky system in one spatial dimension. As an example, we track a relative periodic orbit through a sequence of bifurcations to the onset of chaos. Within the symmetry-reduced state space we are able to compute and visualize the unstable manifolds of relative periodic orbits, their torus bifurcations, a transition to chaos via torus breakdown, and heteroclinic connections between various relative periodic orbits. It would be very hard to carry through such analysis in the full state space, without a symmetry reduction such as the one we present here.}, author = {Budanur, Nazmi B and Cvitanović, Predrag}, journal = {Journal of Statistical Physics}, number = {3-4}, pages = {636--655}, publisher = {Springer}, title = {{Unstable manifolds of relative periodic orbits in the symmetry reduced state space of the Kuramoto–Sivashinsky system}}, doi = {10.1007/s10955-016-1672-z}, volume = {167}, year = {2017}, } @inbook{1213, abstract = {Bacterial cytokinesis is commonly initiated by the Z-ring, a dynamic cytoskeletal structure that assembles at the site of division. Its primary component is FtsZ, a tubulin-like GTPase, that like its eukaryotic relative forms protein filaments in the presence of GTP. Since the discovery of the Z-ring 25 years ago, various models for the role of FtsZ have been suggested. However, important information about the architecture and dynamics of FtsZ filaments during cytokinesis is still missing. One reason for this lack of knowledge has been the small size of bacteria, which has made it difficult to resolve the orientation and dynamics of individual FtsZ filaments in the Z-ring. While superresolution microscopy experiments have helped to gain more information about the organization of the Z-ring in the dividing cell, they were not yet able to elucidate a mechanism of how FtsZ filaments reorganize during assembly and disassembly of the Z-ring. In this chapter, we explain how to use an in vitro reconstitution approach to investigate the self-organization of FtsZ filaments recruited to a biomimetic lipid bilayer by its membrane anchor FtsA. We show how to perform single-molecule experiments to study the behavior of individual FtsZ monomers during the constant reorganization of the FtsZ-FtsA filament network. We describe how to analyze the dynamics of single molecules and explain why this information can help to shed light onto possible mechanism of Z-ring constriction. We believe that similar experimental approaches will be useful to study the mechanism of membrane-based polymerization of other cytoskeletal systems, not only from prokaryotic but also eukaryotic origin.}, author = {Baranova, Natalia and Loose, Martin}, booktitle = {Cytokinesis}, editor = {Echard, Arnaud }, issn = {0091679X}, pages = {355 -- 370}, publisher = {Academic Press}, title = {{Single-molecule measurements to study polymerization dynamics of FtsZ-FtsA copolymers}}, doi = {10.1016/bs.mcb.2016.03.036}, volume = {137}, year = {2017}, } @article{256, abstract = {We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over ℝ and over ℚp for all primes p, provided that the form has at least (d - 1/2 √d)2d variables. This improves on a longstanding result of Birch.}, author = {Browning, Timothy D and Prendiville, Sean}, issn = {0075-4102}, journal = {Journal fur die Reine und Angewandte Mathematik}, number = {731}, pages = {122}, publisher = {Walter de Gruyter}, title = {{Improvements in Birch's theorem on forms in many variables}}, doi = {10.1515/crelle-2014-0122}, volume = {2017}, year = {2017}, } @article{265, abstract = {We establish the dimension and irreducibility of the moduli space of rational curves (of fixed degree) on arbitrary smooth hypersurfaces of sufficiently low degree. A spreading out argument reduces the problem to hypersurfaces defined over finite fields of large cardinality, which can then be tackled using a function field version of the Hardy-Littlewood circle method, in which particular care is taken to ensure uniformity in the size of the underlying finite field.}, author = {Browning, Timothy D and Vishe, Pankaj}, issn = {1944-7833}, journal = {Geometric Methods in Algebra and Number Theory}, number = {7}, pages = {1657 -- 1675}, publisher = { Mathematical Sciences Publishers}, title = {{Rational curves on smooth hypersurfaces of low degree}}, doi = {10.2140/ant.2017.11.1657}, volume = {11}, year = {2017}, } @article{266, abstract = {We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.}, author = {Browning, Timothy D and Heath Brown, Roger}, journal = {Journal of the European Mathematical Society}, number = {2}, pages = {357 -- 394}, publisher = {European Mathematical Society Publishing House}, title = {{Forms in many variables and differing degrees}}, doi = {10.4171/JEMS/668}, volume = {19}, year = {2017}, } @article{267, abstract = {Building on recent work of Bhargava, Elkies and Schnidman and of Kriz and Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.}, author = {Browning, Timothy D}, issn = {0025-5793}, journal = {Mathematika}, number = {3}, pages = {818 -- 839}, publisher = {Cambridge University Press}, title = {{Many cubic surfaces contain rational points}}, doi = {10.1112/S0025579317000195}, volume = {63}, year = {2017}, } @article{268, abstract = {We show that any subset of the squares of positive relative upper density contains nontrivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish the partition regularity of any diagonal quadric in five or more variables whose coefficients sum to zero. Unlike previous approaches, which are limited to equations in seven or more variables, we employ transference technology of Green to import bounds from the linear setting.}, author = {Browning, Timothy D and Prendiville, Sean}, issn = {1073-7928}, journal = {International Mathematics Research Notices}, number = {7}, pages = {2219 -- 2248}, publisher = {Oxford University Press}, title = {{A transference approach to a Roth-type theorem in the squares}}, doi = {10.1093/imrn/rnw096}, volume = {2017}, year = {2017}, } @article{269, abstract = {We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.}, author = {Browning, Timothy D and Loughran, Daniel}, journal = {Mathematische Zeitschrift}, number = {3-4}, pages = {1249 -- 1267}, publisher = {Springer}, title = {{Varieties with too many rational points}}, doi = {10.1007/s00209-016-1746-2}, volume = {285}, year = {2017}, } @article{270, abstract = {Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral points on general affine quadrics defined over Q.}, author = {Browning, Timothy D and Gorodnik, Alexander}, issn = {0024-6115}, journal = {Proceedings of the London Mathematical Society}, number = {6}, pages = {1044 -- 1080}, publisher = {Wiley}, title = {{Power-free values of polynomials on symmetric varieties}}, doi = {10.1112/plms.12030}, volume = {114}, year = {2017}, } @article{272, abstract = {Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation NK (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X.}, author = {Browning, Timothy D and Matthiesen, Lilian}, journal = {Annales Scientifiques de l'Ecole Normale Superieure}, number = {6}, pages = {1383 -- 1446}, publisher = {Societe Mathematique de France}, title = {{Norm forms for arbitrary number fields as products of linear polynomials}}, doi = {10.24033/asens.2348}, volume = {50}, year = {2017}, } @inproceedings{274, abstract = {We consider the problem of estimating the partition function Z(β)=∑xexp(−β(H(x)) of a Gibbs distribution with a Hamilton H(⋅), or more precisely the logarithm of the ratio q=lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0,β]. The current best known approach due to Huber [9] uses O(qlnn⋅[lnq+lnlnn+ε−2]) oracle calls on average where ε is the desired accuracy of approximation and H(⋅) is assumed to lie in {0}∪[1,n]. We improve the complexity to O(qlnn⋅ε−2) oracle calls. We also show that the same complexity can be achieved if exact oracles are replaced with approximate sampling oracles that are within O(ε2qlnn) variation distance from exact oracles. Finally, we prove a lower bound of Ω(q⋅ε−2) oracle calls under a natural model of computation.}, author = {Kolmogorov, Vladimir}, booktitle = {Proceedings of the 31st Conference On Learning Theory}, pages = {228--249}, publisher = {ML Research Press}, title = {{A faster approximation algorithm for the Gibbs partition function}}, volume = {75}, year = {2017}, }