TY - JOUR
AB - We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.
AU - Akopyan, Arseniy
AU - Plakhov, Alexander
ID - 1710
IS - 4
JF - Society for Industrial and Applied Mathematics
TI - Minimal resistance of curves under the single impact assumption
VL - 47
ER -
TY - JOUR
AB - The majority of immune cells in Drosophila melanogaster are plasmatocytes; they carry out similar functions to vertebrate macrophages, influencing development as well as protecting against infection and cancer. Plasmatocytes, sometimes referred to with the broader term of hemocytes, migrate widely during embryonic development and cycle in the larvae between sessile and circulating positions. Here we discuss the similarities of plasmatocyte developmental migration and its functions to that of vertebrate macrophages, considering the recent controversy regarding the functions of Drosophila PDGF/VEGF related ligands. We also examine recent findings on the significance of adhesion for plasmatocyte migration in the embryo, as well as proliferation, trans-differentiation, and tumor responses in the larva. We spotlight parallels throughout to vertebrate immune responses.
AU - Ratheesh, Aparna
AU - Belyaeva, Vera
AU - Siekhaus, Daria E
ID - 1712
IS - 10
JF - Current Opinion in Cell Biology
TI - Drosophila immune cell migration and adhesion during embryonic development and larval immune responses
VL - 36
ER -
TY - CONF
AB - We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm-deadline real-time tasks based on multi-objective graphs: Given a task set and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. A clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including Dover, that have been proposed in the past, for various task sets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are task sets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 1714
IS - January
T2 - Real-Time Systems Symposium
TI - A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks
VL - 2015
ER -
TY - JOUR
AB - How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given combinatorial map in triangulated combinatorial surfaces (or their dual cross-metric counterpart). Our work builds upon Riemannian systolic inequalities, which bound the minimum length of non-trivial closed curves in terms of the genus and the area of the surface. We first describe a systematic way to translate Riemannian systolic inequalities to a discrete setting, and vice-versa. This implies a conjecture by Przytycka and Przytycki (Graph structure theory. Contemporary Mathematics, vol. 147, 1993), a number of new systolic inequalities in the discrete setting, and the fact that a theorem of Hutchinson on the edge-width of triangulated surfaces and Gromov’s systolic inequality for surfaces are essentially equivalent. We also discuss how these proofs generalize to higher dimensions. Then we focus on topological decompositions of surfaces. Relying on ideas of Buser, we prove the existence of pants decompositions of length O(g^(3/2)n^(1/2)) for any triangulated combinatorial surface of genus g with n triangles, and describe an O(gn)-time algorithm to compute such a decomposition. Finally, we consider the problem of embedding a cut graph (or more generally a cellular graph) with a given combinatorial map on a given surface. Using random triangulations, we prove (essentially) that, for any choice of a combinatorial map, there are some surfaces on which any cellular embedding with that combinatorial map has length superlinear in the number of triangles of the triangulated combinatorial surface. There is also a similar result for graphs embedded on polyhedral triangulations.
AU - Colin De Verdière, Éric
AU - Hubard, Alfredo
AU - De Mesmay, Arnaud N
ID - 1730
IS - 3
JF - Discrete & Computational Geometry
TI - Discrete systolic inequalities and decompositions of triangulated surfaces
VL - 53
ER -
TY - JOUR
AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 1731
IS - 12
JF - Information and Computation
TI - Randomness for free
VL - 245
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1732
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - JOUR
AB - Facial appearance capture is now firmly established within academic research and used extensively across various application domains, perhaps most prominently in the entertainment industry through the design of virtual characters in video games and films. While significant progress has occurred over the last two decades, no single survey currently exists that discusses the similarities, differences, and practical considerations of the available appearance capture techniques as applied to human faces. A central difficulty of facial appearance capture is the way light interacts with skin-which has a complex multi-layered structure-and the interactions that occur below the skin surface can, by definition, only be observed indirectly. In this report, we distinguish between two broad strategies for dealing with this complexity. "Image-based methods" try to exhaustively capture the exact face appearance under different lighting and viewing conditions, and then render the face through weighted image combinations. "Parametric methods" instead fit the captured reflectance data to some parametric appearance model used during rendering, allowing for a more lightweight and flexible representation but at the cost of potentially increased rendering complexity or inexact reproduction. The goal of this report is to provide an overview that can guide practitioners and researchers in assessing the tradeoffs between current approaches and identifying directions for future advances in facial appearance capture.
AU - Klehm, Oliver
AU - Rousselle, Fabrice
AU - Papas, Marios
AU - Bradley, Derek
AU - Hery, Christophe
AU - Bickel, Bernd
AU - Jarosz, Wojciech
AU - Beeler, Thabo
ID - 1734
IS - 2
JF - Computer Graphics Forum
TI - Recent advances in facial appearance capture
VL - 34
ER -
TY - JOUR
AB - This work presents a method for efficiently simplifying the pressure projection step in a liquid simulation. We first devise a straightforward dimension reduction technique that dramatically reduces the cost of solving the pressure projection. Next, we introduce a novel change of basis that satisfies free-surface boundary conditions exactly, regardless of the accuracy of the pressure solve. When combined, these ideas greatly reduce the computational complexity of the pressure solve without compromising free surface boundary conditions at the highest level of detail. Our techniques are easy to parallelize, and they effectively eliminate the computational bottleneck for large liquid simulations.
AU - Ando, Ryoichi
AU - Thürey, Nils
AU - Wojtan, Christopher J
ID - 1735
IS - 2
JF - Computer Graphics Forum
TI - A dimension-reduced pressure solver for liquid simulations
VL - 34
ER -
TY - JOUR
AB - Intellectual disability (ID) has an estimated prevalence of 2-3%. Due to its extreme heterogeneity, the genetic basis of ID remains elusive in many cases. Recently, whole exome sequencing (WES) studies revealed that a large proportion of sporadic cases are caused by de novo gene variants. To identify further genes involved in ID, we performed WES in 250 patients with unexplained ID and their unaffected parents and included exomes of 51 previously sequenced child-parents trios in the analysis. Exome analysis revealed de novo intragenic variants in SET domain-containing 5 (SETD5) in two patients. One patient carried a nonsense variant, and the other an 81 bp deletion located across a splice-donor site. Chromosomal microarray diagnostics further identified four de novo non-recurrent microdeletions encompassing SETD5. CRISPR/Cas9 mutation modelling of the two intragenic variants demonstrated nonsense-mediated decay of the resulting transcripts, pointing to a loss-of-function (LoF) and haploinsufficiency as the common disease-causing mechanism of intragenic SETD5 sequence variants and SETD5-containing microdeletions. In silico domain prediction of SETD5, a predicted SET domain-containing histone methyltransferase (HMT), substantiated the presence of a SET domain and identified a novel putative PHD domain, strengthening a functional link to well-known histone-modifying ID genes. All six patients presented with ID and certain facial dysmorphisms, suggesting that SETD5 sequence variants contribute substantially to the microdeletion 3p25.3 phenotype. The present report of two SETD5 LoF variants in 301 patients demonstrates a prevalence of 0.7% and thus SETD5 variants as a relatively frequent cause of ID.
AU - Kuechler, Alma
AU - Zink, Alexander
AU - Wieland, Thomas
AU - Lüdecke, Hermann
AU - Cremer, Kirsten
AU - Salviati, Leonardo
AU - Magini, Pamela
AU - Najafi, Kimia
AU - Zweier, Christiane
AU - Czeschik, Johanna
AU - Aretz, Stefan
AU - Endele, Sabine
AU - Tamburrino, Federica
AU - Pinato, Claudia
AU - Clementi, Maurizio
AU - Gundlach, Jasmin
AU - Maylahn, Carina
AU - Mazzanti, Laura
AU - Wohlleber, Eva
AU - Schwarzmayr, Thomas
AU - Kariminejad, Roxana
AU - Schlessinger, Avner
AU - Wieczorek, Dagmar
AU - Strom, Tim
AU - Novarino, Gaia
AU - Engels, Hartmut
ID - 1789
IS - 6
JF - European Journal of Human Genetics
TI - Loss-of-function variants of SETD5 cause intellectual disability and the core phenotype of microdeletion 3p25.3 syndrome
VL - 23
ER -
TY - JOUR
AB - Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology.
AU - Pausinger, Florian
AU - Svane, Anne
ID - 1792
IS - 6
JF - Journal of Complexity
TI - A Koksma-Hlawka inequality for general discrepancy systems
VL - 31
ER -