TY - JOUR AB - The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves. AU - Kalinin, Nikita AU - Shkolnikov, Mikhail ID - 303 IS - 6 JF - Discrete and Continuous Dynamical Systems- Series A TI - Introduction to tropical series and wave dynamic on them VL - 38 ER - TY - JOUR AB - Adaptive introgression is common in nature and can be driven by selection acting on multiple, linked genes. We explore the effects of polygenic selection on introgression under the infinitesimal model with linkage. This model assumes that the introgressing block has an effectively infinite number of genes, each with an infinitesimal effect on the trait under selection. The block is assumed to introgress under directional selection within a native population that is genetically homogeneous. We use individual-based simulations and a branching process approximation to compute various statistics of the introgressing block, and explore how these depend on parameters such as the map length and initial trait value associated with the introgressing block, the genetic variability along the block, and the strength of selection. Our results show that the introgression dynamics of a block under infinitesimal selection is qualitatively different from the dynamics of neutral introgression. We also find that in the long run, surviving descendant blocks are likely to have intermediate lengths, and clarify how the length is shaped by the interplay between linkage and infinitesimal selection. Our results suggest that it may be difficult to distinguish introgression of single loci from that of genomic blocks with multiple, tightly linked and weakly selected loci. AU - Sachdeva, Himani AU - Barton, Nicholas H ID - 282 IS - 4 JF - Genetics TI - Introgression of a block of genome under infinitesimal selection VL - 209 ER - TY - CONF AB - Universal hashing found a lot of applications in computer science. In cryptography the most important fact about universal families is the so called Leftover Hash Lemma, proved by Impagliazzo, Levin and Luby. In the language of modern cryptography it states that almost universal families are good extractors. In this work we provide a somewhat surprising characterization in the opposite direction. Namely, every extractor with sufficiently good parameters yields a universal family on a noticeable fraction of its inputs. Our proof technique is based on tools from extremal graph theory applied to the \'collision graph\' induced by the extractor, and may be of independent interest. We discuss possible applications to the theory of randomness extractors and non-malleable codes. AU - Obremski, Marciej AU - Skorski, Maciej ID - 108 TI - Inverted leftover hash lemma VL - 2018 ER - TY - CONF AB - We present layered concurrent programs, a compact and expressive notation for specifying refinement proofs of concurrent programs. A layered concurrent program specifies a sequence of connected concurrent programs, from most concrete to most abstract, such that common parts of different programs are written exactly once. These programs are expressed in the ordinary syntax of imperative concurrent programs using gated atomic actions, sequencing, choice, and (recursive) procedure calls. Each concurrent program is automatically extracted from the layered program. We reduce refinement to the safety of a sequence of concurrent checker programs, one each to justify the connection between every two consecutive concurrent programs. These checker programs are also automatically extracted from the layered program. Layered concurrent programs have been implemented in the CIVL verifier which has been successfully used for the verification of several complex concurrent programs. AU - Kragl, Bernhard AU - Qadeer, Shaz ID - 160 TI - Layered Concurrent Programs VL - 10981 ER - TY - JOUR AB - In experimental cultures, when bacteria are mixed with lytic (virulent) bacteriophage, bacterial cells resistant to the phage commonly emerge and become the dominant population of bacteria. Following the ascent of resistant mutants, the densities of bacteria in these simple communities become limited by resources rather than the phage. Despite the evolution of resistant hosts, upon which the phage cannot replicate, the lytic phage population is most commonly maintained in an apparently stable state with the resistant bacteria. Several mechanisms have been put forward to account for this result. Here we report the results of population dynamic/evolution experiments with a virulent mutant of phage Lambda, λVIR, and Escherichia coli in serial transfer cultures. We show that, following the ascent of λVIR-resistant bacteria, λVIRis maintained in the majority of cases in maltose-limited minimal media and in all cases in nutrient-rich broth. Using mathematical models and experiments, we show that the dominant mechanism responsible for maintenance of λVIRin these resource-limited populations dominated by resistant E. coli is a high rate of either phenotypic or genetic transition from resistance to susceptibility—a hitherto undemonstrated mechanism we term "leaky resistance." We discuss the implications of leaky resistance to our understanding of the conditions for the maintenance of phage in populations of bacteria—their “existence conditions.”. AU - Chaudhry, Waqas AU - Pleska, Maros AU - Shah, Nilang AU - Weiss, Howard AU - Mccall, Ingrid AU - Meyer, Justin AU - Gupta, Animesh AU - Guet, Calin C AU - Levin, Bruce ID - 82 IS - 8 JF - PLoS Biology TI - Leaky resistance and the conditions for the existence of lytic bacteriophage VL - 16 ER - TY - JOUR AB - We present a data-driven technique to instantly predict how fluid flows around various three-dimensional objects. Such simulation is useful for computational fabrication and engineering, but is usually computationally expensive since it requires solving the Navier-Stokes equation for many time steps. To accelerate the process, we propose a machine learning framework which predicts aerodynamic forces and velocity and pressure fields given a threedimensional shape input. Handling detailed free-form three-dimensional shapes in a data-driven framework is challenging because machine learning approaches usually require a consistent parametrization of input and output. We present a novel PolyCube maps-based parametrization that can be computed for three-dimensional shapes at interactive rates. This allows us to efficiently learn the nonlinear response of the flow using a Gaussian process regression. We demonstrate the effectiveness of our approach for the interactive design and optimization of a car body. AU - Umetani, Nobuyuki AU - Bickel, Bernd ID - 4 IS - 4 JF - ACM Trans. Graph. TI - Learning three-dimensional flow for interactive aerodynamic design VL - 37 ER - TY - JOUR AB - We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. [11,12] shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. AU - Alt, Johannes AU - Erdös, László AU - Krüger, Torben H ID - 566 IS - 1 JF - Annals Applied Probability TI - Local inhomogeneous circular law VL - 28 ER - TY - JOUR AB - The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below. AU - Akopyan, Arseniy AU - Petrunin, Anton ID - 106 IS - 3 JF - Mathematical Intelligencer TI - Long geodesics on convex surfaces VL - 40 ER - TY - JOUR AB - Lymphatic endothelial cells (LECs) release extracellular chemokines to guide the migration of dendritic cells. In this study, we report that LECs also release basolateral exosome-rich endothelial vesicles (EEVs) that are secreted in greater numbers in the presence of inflammatory cytokines and accumulate in the perivascular stroma of small lymphatic vessels in human chronic inflammatory diseases. Proteomic analyses of EEV fractions identified > 1,700 cargo proteins and revealed a dominant motility-promoting protein signature. In vitro and ex vivo EEV fractions augmented cellular protrusion formation in a CX3CL1/fractalkine-dependent fashion and enhanced the directional migratory response of human dendritic cells along guidance cues. We conclude that perilymphatic LEC exosomes enhance exploratory behavior and thus promote directional migration of CX3CR1-expressing cells in complex tissue environments. AU - Brown, Markus AU - Johnson, Louise AU - Leone, Dario AU - Májek, Peter AU - Vaahtomeri, Kari AU - Senfter, Daniel AU - Bukosza, Nora AU - Schachner, Helga AU - Asfour, Gabriele AU - Langer, Brigitte AU - Hauschild, Robert AU - Parapatics, Katja AU - Hong, Young AU - Bennett, Keiryn AU - Kain, Renate AU - Detmar, Michael AU - Sixt, Michael K AU - Jackson, David AU - Kerjaschki, Dontscho ID - 275 IS - 6 JF - Journal of Cell Biology TI - Lymphatic exosomes promote dendritic cell migration along guidance cues VL - 217 ER - TY - JOUR AB - The angiosperm seed is composed of three genetically distinct tissues: the diploid embryo that originates from the fertilized egg cell, the triploid endosperm that is produced from the fertilized central cell, and the maternal sporophytic integuments that develop into the seed coat1. At the onset of embryo development in Arabidopsis thaliana, the zygote divides asymmetrically, producing a small apical embryonic cell and a larger basal cell that connects the embryo to the maternal tissue2. The coordinated and synchronous development of the embryo and the surrounding integuments, and the alignment of their growth axes, suggest communication between maternal tissues and the embryo. In contrast to animals, however, where a network of maternal factors that direct embryo patterning have been identified3,4, only a few maternal mutations have been described to affect embryo development in plants5–7. Early embryo patterning in Arabidopsis requires accumulation of the phytohormone auxin in the apical cell by directed transport from the suspensor8–10. However, the origin of this auxin has remained obscure. Here we investigate the source of auxin for early embryogenesis and provide evidence that the mother plant coordinates seed development by supplying auxin to the early embryo from the integuments of the ovule. We show that auxin response increases in ovules after fertilization, due to upregulated auxin biosynthesis in the integuments, and this maternally produced auxin is required for correct embryo development. AU - Robert, Hélène AU - Park, Chulmin AU - Gutièrrez, Carla AU - Wójcikowska, Barbara AU - Pěnčík, Aleš AU - Novák, Ondřej AU - Chen, Junyi AU - Grunewald, Wim AU - Dresselhaus, Thomas AU - Friml, Jirí AU - Laux, Thomas ID - 158 IS - 8 JF - Nature Plants TI - Maternal auxin supply contributes to early embryo patterning in Arabidopsis VL - 4 ER -