TY - CONF
AB - We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front.
Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation.
Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix.
AU - Hahn, David
AU - Wojtan, Christopher J
ID - 1633
IS - 4
TI - High-resolution brittle fracture simulation with boundary elements
VL - 34
ER -
TY - CONF
AB - Simulating the delightful dynamics of soap films, bubbles, and foams has traditionally required the use of a fully three-dimensional many-phase Navier-Stokes solver, even though their visual appearance is completely dominated by the thin liquid surface. We depart from earlier work on soap bubbles and foams by noting that their dynamics are naturally described by a Lagrangian vortex sheet model in which circulation is the primary variable. This leads us to derive a novel circulation-preserving surface-only discretization of foam dynamics driven by surface tension on a non-manifold triangle mesh. We represent the surface using a mesh-based multimaterial surface tracker which supports complex bubble topology changes, and evolve the surface according to the ambient air flow induced by a scalar circulation field stored on the mesh. Surface tension forces give rise to a simple update rule for circulation, even at non-manifold Plateau borders, based on a discrete measure of signed scalar mean curvature. We further incorporate vertex constraints to enable the interaction of soap films with wires. The result is a method that is at once simple, robust, and efficient, yet able to capture an array of soap films behaviors including foam rearrangement, catenoid collapse, blowing bubbles, and double bubbles being pulled apart.
AU - Da, Fang
AU - Batty, Christopher
AU - Wojtan, Christopher J
AU - Grinspun, Eitan
ID - 1634
IS - 4
TI - Double bubbles sans toil and trouble: discrete circulation-preserving vortex sheets for soap films and foams
VL - 34
ER -
TY - JOUR
AB - We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the n-dimensional discrete cube (the so-called Bernoulli-Laplace model) and the random transposition shuffle of the symmetric group of permutations on n letters.
AU - Erbar, Matthias
AU - Maas, Jan
AU - Tetali, Prasad
ID - 1635
IS - 4
JF - Annales de la faculté des sciences de Toulouse
TI - Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models
VL - 24
ER -
TY - CONF
AB - Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism R→ΓΓ between two relational structures, e.g. between two directed graphs. Analyzing its complexity has been a prominent research direction, especially for the fixed template CSPs where the right side ΓΓ is fixed and the left side R is unconstrained.
Far fewer results are known for the hybrid setting that restricts both sides simultaneously. It assumes that R belongs to a certain class of relational structures (called a structural restriction in this paper). We study which structural restrictions are effective, i.e. there exists a fixed template ΓΓ (from a certain class of languages) for which the problem is tractable when R is restricted, and NP-hard otherwise. We provide a characterization for structural restrictions that are closed under inverse homomorphisms. The criterion is based on the chromatic number of a relational structure defined in this paper; it generalizes the standard chromatic number of a graph.
As our main tool, we use the algebraic machinery developed for fixed template CSPs. To apply it to our case, we introduce a new construction called a “lifted language”. We also give a characterization for structural restrictions corresponding to minor-closed families of graphs, extend results to certain Valued CSPs (namely conservative valued languages), and state implications for (valued) CSPs with ordered variables and for the maximum weight independent set problem on some restricted families of graphs.
AU - Kolmogorov, Vladimir
AU - Rolinek, Michal
AU - Takhanov, Rustem
ID - 1636
TI - Effectiveness of structural restrictions for hybrid CSPs
VL - 9472
ER -
TY - CONF
AB - An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. We study, assuming that P ≠ NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language. The case when all allowed functions take values in {0, ∞} corresponds to ordinary CSPs, where one deals only with the feasibility issue and there is no optimization. This case is the subject of the Algebraic CSP Dichotomy Conjecture predicting for which constraint languages CSPs are tractable (i.e. solvable in polynomial time) and for which NP-hard. The case when all allowed functions take only finite values corresponds to finite-valued CSP, where the feasibility aspect is trivial and one deals only with the optimization issue. The complexity of finite-valued CSPs was fully classified by Thapper and Zivny. An algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language was recently given by Kozik and Ochremiak. As our main result, we prove that if a constraint language satisfies this algebraic necessary condition, and the feasibility CSP (i.e. the problem of deciding whether a given instance has a feasible solution) corresponding to the VCSP with this language is tractable, then the VCSP is tractable. The algorithm is a simple combination of the assumed algorithm for the feasibility CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy for ordinary CSPs would imply a dichotomy for general-valued CSPs.
AU - Kolmogorov, Vladimir
AU - Krokhin, Andrei
AU - Rolinek, Michal
ID - 1637
TI - The complexity of general-valued CSPs
ER -
TY - JOUR
AB - The mitochondrial respiratory chain, also known as the electron transport chain (ETC), is crucial to life, and energy production in the form of ATP is the main mitochondrial function. Three proton-translocating enzymes of the ETC, namely complexes I, III and IV, generate proton motive force, which in turn drives ATP synthase (complex V). The atomic structures and basic mechanisms of most respiratory complexes have previously been established, with the exception of complex I, the largest complex in the ETC. Recently, the crystal structure of the entire complex I was solved using a bacterial enzyme. The structure provided novel insights into the core architecture of the complex, the electron transfer and proton translocation pathways, as well as the mechanism that couples these two processes.
AU - Sazanov, Leonid A
ID - 1638
IS - 6
JF - Nature Reviews Molecular Cell Biology
TI - A giant molecular proton pump: structure and mechanism of respiratory complex I
VL - 16
ER -
TY - JOUR
AB - In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying Riemannian metric measures the rate of transport cost and the rate of viscous dissipation. Furthermore, the model is capable to deal with strongly varying image contrast and explicitly allows for sources and sinks in the transport equations which are incorporated in the metric related to the metamorphosis approach by Trouvé and Younes. In the non-viscous case with source term existence of geodesic paths is proven in the space of measures. The proposed model is explored on the range from merely optimal transport to strongly dissipative dynamics. For this model a robust and effective variational time discretization of geodesic paths is proposed. This requires to minimize a discrete path energy consisting of a sum of consecutive image matching functionals. These functionals are defined on corresponding pairs of intensity functions and on associated pairwise matching deformations. Existence of time discrete geodesics is demonstrated. Furthermore, a finite element implementation is proposed and applied to instructive test cases and to real images. In the non-viscous case this is compared to the algorithm proposed by Benamou and Brenier including a discretization of the source term. Finally, the model is generalized to define discrete weighted barycentres with applications to textures and objects.
AU - Maas, Jan
AU - Rumpf, Martin
AU - Schönlieb, Carola
AU - Simon, Stefan
ID - 1639
IS - 6
JF - ESAIM: Mathematical Modelling and Numerical Analysis
TI - A generalized model for optimal transport of images including dissipation and density modulation
VL - 49
ER -
TY - JOUR
AB - Auxin and cytokinin are key endogenous regulators of plant development. Although cytokinin-mediated modulation of auxin distribution is a developmentally crucial hormonal interaction, its molecular basis is largely unknown. Here we show a direct regulatory link between cytokinin signalling and the auxin transport machinery uncovering a mechanistic framework for cytokinin-auxin cross-talk. We show that the CYTOKININ RESPONSE FACTORS (CRFs), transcription factors downstream of cytokinin perception, transcriptionally control genes encoding PIN-FORMED (PIN) auxin transporters at a specific PIN CYTOKININ RESPONSE ELEMENT (PCRE) domain. Removal of this cis-regulatory element effectively uncouples PIN transcription from the CRF-mediated cytokinin regulation and attenuates plant cytokinin sensitivity. We propose that CRFs represent a missing cross-talk component that fine-tunes auxin transport capacity downstream of cytokinin signalling to control plant development.
AU - Šimášková, Mária
AU - O'Brien, José
AU - Khan-Djamei, Mamoona
AU - Van Noorden, Giel
AU - Ötvös, Krisztina
AU - Vieten, Anne
AU - De Clercq, Inge
AU - Van Haperen, Johanna
AU - Cuesta, Candela
AU - Hoyerová, Klára
AU - Vanneste, Steffen
AU - Marhavy, Peter
AU - Wabnik, Krzysztof T
AU - Van Breusegem, Frank
AU - Nowack, Moritz
AU - Murphy, Angus
AU - Friml, Jiřĺ
AU - Weijers, Dolf
AU - Beeckman, Tom
AU - Benková, Eva
ID - 1640
JF - Nature Communications
TI - Cytokinin response factors regulate PIN-FORMED auxin transporters
VL - 6
ER -
TY - JOUR
AB - The Hanani-Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward extension to flat clustered graphs with three or more disjoint clusters is not possible. For general clustered graphs we show a variant of the Hanani-Tutte theorem in the case when each cluster induces a connected subgraph. Di Battista and Frati proved that clustered planarity of embedded clustered graphs whose every face is incident to at most five vertices can be tested in polynomial time. We give a new and short proof of this result, using the matroid intersection algorithm.
AU - Fulek, Radoslav
AU - Kynčl, Jan
AU - Malinovič, Igor
AU - Pálvölgyi, Dömötör
ID - 1642
IS - 4
JF - Electronic Journal of Combinatorics
TI - Clustered planarity testing revisited
VL - 22
ER -
TY - CONF
AB - Increasing the computational complexity of evaluating a hash function, both for the honest users as well as for an adversary, is a useful technique employed for example in password-based cryptographic schemes to impede brute-force attacks, and also in so-called proofs of work (used in protocols like Bitcoin) to show that a certain amount of computation was performed by a legitimate user. A natural approach to adjust the complexity of a hash function is to iterate it c times, for some parameter c, in the hope that any query to the scheme requires c evaluations of the underlying hash function. However, results by Dodis et al. (Crypto 2012) imply that plain iteration falls short of achieving this goal, and designing schemes which provably have such a desirable property remained an open problem. This paper formalizes explicitly what it means for a given scheme to amplify the query complexity of a hash function. In the random oracle model, the goal of a secure query-complexity amplifier (QCA) scheme is captured as transforming, in the sense of indifferentiability, a random oracle allowing R queries (for the adversary) into one provably allowing only r < R queries. Turned around, this means that making r queries to the scheme requires at least R queries to the actual random oracle. Second, a new scheme, called collision-free iteration, is proposed and proven to achieve c-fold QCA for both the honest parties and the adversary, for any fixed parameter c.
AU - Demay, Grégory
AU - Gazi, Peter
AU - Maurer, Ueli
AU - Tackmann, Björn
ID - 1644
TI - Query-complexity amplification for random oracles
VL - 9063
ER -