@article{464, abstract = {The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on n vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time O(n5/2) and for (2) k-pair Streett objectives in graphs in time O(n2+nklogn). For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Loitzenbauer, Veronika}, issn = {1860-5974}, journal = {Logical Methods in Computer Science}, number = {3}, publisher = {International Federation for Computational Logic}, title = {{Improved algorithms for parity and Streett objectives}}, doi = {10.23638/LMCS-13(3:26)2017}, volume = {13}, year = {2017}, } @article{484, abstract = {We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory.}, author = {Nam, Phan and Napiórkowski, Marcin M}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {3}, pages = {683 -- 738}, publisher = {International Press of Boston}, title = {{Bogoliubov correction to the mean-field dynamics of interacting bosons}}, doi = {10.4310/ATMP.2017.v21.n3.a4}, volume = {21}, year = {2017}, } @article{483, abstract = {We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.}, author = {Bourgade, Paul and Erdös, László and Yau, Horng and Yin, Jun}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {3}, pages = {739 -- 800}, publisher = {International Press of Boston}, title = {{Universality for a class of random band matrices}}, doi = {10.4310/ATMP.2017.v21.n3.a5}, volume = {21}, year = {2017}, } @inproceedings{1000, abstract = {We study probabilistic models of natural images and extend the autoregressive family of PixelCNN models by incorporating latent variables. Subsequently, we describe two new generative image models that exploit different image transformations as latent variables: a quantized grayscale view of the image or a multi-resolution image pyramid. The proposed models tackle two known shortcomings of existing PixelCNN models: 1) their tendency to focus on low-level image details, while largely ignoring high-level image information, such as object shapes, and 2) their computationally costly procedure for image sampling. We experimentally demonstrate benefits of our LatentPixelCNN models, in particular showing that they produce much more realistically looking image samples than previous state-of-the-art probabilistic models. }, author = {Kolesnikov, Alexander and Lampert, Christoph}, booktitle = {34th International Conference on Machine Learning}, isbn = {978-151085514-4}, location = {Sydney, Australia}, pages = {1905 -- 1914}, publisher = {Journal of Machine Learning Research}, title = {{PixelCNN models with auxiliary variables for natural image modeling}}, volume = {70}, year = {2017}, } @article{568, abstract = {We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).}, author = {Franek, Peter and Krcál, Marek}, issn = {1532-0073}, journal = {Homology, Homotopy and Applications}, number = {2}, pages = {313 -- 342}, publisher = {International Press of Boston}, title = {{Persistence of zero sets}}, doi = {10.4310/HHA.2017.v19.n2.a16}, volume = {19}, year = {2017}, } @article{701, abstract = {A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2.}, author = {Kynčl, Jan and Patakova, Zuzana}, issn = {1077-8926}, journal = {The Electronic Journal of Combinatorics}, number = {3}, pages = {1--44}, publisher = {International Press of Boston}, title = {{On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4}}, volume = {24}, year = {2017}, } @article{951, abstract = {Dengue-suppressing Wolbachia strains are promising tools for arbovirus control, particularly as they have the potential to self-spread following local introductions. To test this, we followed the frequency of the transinfected Wolbachia strain wMel through Ae. aegypti in Cairns, Australia, following releases at 3 nonisolated locations within the city in early 2013. Spatial spread was analysed graphically using interpolation and by fitting a statistical model describing the position and width of the wave. For the larger 2 of the 3 releases (covering 0.97 km2 and 0.52 km2), we observed slow but steady spatial spread, at about 100–200 m per year, roughly consistent with theoretical predictions. In contrast, the smallest release (0.11 km2) produced erratic temporal and spatial dynamics, with little evidence of spread after 2 years. This is consistent with the prediction concerning fitness-decreasing Wolbachia transinfections that a minimum release area is needed to achieve stable local establishment and spread in continuous habitats. Our graphical and likelihood analyses produced broadly consistent estimates of wave speed and wave width. Spread at all sites was spatially heterogeneous, suggesting that environmental heterogeneity will affect large-scale Wolbachia transformations of urban mosquito populations. The persistence and spread of Wolbachia in release areas meeting minimum area requirements indicates the promise of successful large-scale population transfo}, author = {Schmidt, Tom and Barton, Nicholas H and Rasic, Gordana and Turley, Andrew and Montgomery, Brian and Iturbe Ormaetxe, Inaki and Cook, Peter and Ryan, Peter and Ritchie, Scott and Hoffmann, Ary and O’Neill, Scott and Turelli, Michael}, issn = {1544-9173}, journal = {PLoS Biology}, number = {5}, publisher = {Public Library of Science}, title = {{Local introduction and heterogeneous spatial spread of dengue-suppressing Wolbachia through an urban population of Aedes Aegypti}}, doi = {10.1371/journal.pbio.2001894}, volume = {15}, year = {2017}, } @misc{9857, author = {Schmidt, Tom and Barton, Nicholas H and Rasic, Gordana and Turley, Andrew and Montgomery, Brian and Iturbe Ormaetxe, Inaki and Cook, Peter and Ryan, Peter and Ritchie, Scott and Hoffmann, Ary and O’Neill, Scott and Turelli, Michael}, publisher = {Public Library of Science}, title = {{Supporting information concerning observed wMel frequencies and analyses of habitat variables}}, doi = {10.1371/journal.pbio.2001894.s015}, year = {2017}, } @inbook{604, abstract = {In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem, based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose–Einstein condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows us not only to greatly simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies.}, author = {Lemeshko, Mikhail and Schmidt, Richard}, booktitle = {Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero }, editor = {Dulieu, Oliver and Osterwalder, Andreas}, issn = {2041-3181}, pages = {444 -- 495}, publisher = {Royal Society of Chemistry}, title = {{Molecular impurities interacting with a many-particle environment: From ultracold gases to helium nanodroplets}}, doi = {10.1039/9781782626800-00444}, volume = {11}, year = {2017}, } @article{823, abstract = {The resolution of a linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density c and the ratio α=N/M between number of variables N and number of constraints M. By means of ensemble calculations we show that the space of feasible solutions endows a Van-Der-Waals phase diagram in the plane (c, α). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region.}, author = {Colabrese, Simona and De Martino, Daniele and Leuzzi, Luca and Marinari, Enzo}, issn = {1742-5468}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, number = {9}, publisher = {IOP Publishing}, title = {{Phase transitions in integer linear problems}}, doi = {10.1088/1742-5468/aa85c3}, volume = {2017}, year = {2017}, } @article{912, abstract = {We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer (BCS) theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals. }, author = {Deuchert, Andreas}, issn = {0022-2488}, journal = {Journal of Mathematical Physics}, number = {8}, publisher = {AIP Publishing}, title = {{A lower bound for the BCS functional with boundary conditions at infinity}}, doi = {10.1063/1.4996580}, volume = {58}, year = {2017}, } @article{744, abstract = {In evolutionary game theory interactions between individuals are often assumed obligatory. However, in many real-life situations, individuals can decide to opt out of an interaction depending on the information they have about the opponent. We consider a simple evolutionary game theoretic model to study such a scenario, where at each encounter between two individuals the type of the opponent (cooperator/defector) is known with some probability, and where each individual either accepts or opts out of the interaction. If the type of the opponent is unknown, a trustful individual accepts the interaction, whereas a suspicious individual opts out of the interaction. If either of the two individuals opt out both individuals remain without an interaction. We show that in the prisoners dilemma optional interactions along with suspicious behaviour facilitates the emergence of trustful cooperation.}, author = {Priklopil, Tadeas and Chatterjee, Krishnendu and Nowak, Martin}, issn = {0022-5193}, journal = {Journal of Theoretical Biology}, pages = {64 -- 72}, publisher = {Elsevier}, title = {{Optional interactions and suspicious behaviour facilitates trustful cooperation in prisoners dilemma}}, doi = {10.1016/j.jtbi.2017.08.025}, volume = {433}, year = {2017}, } @article{1076, abstract = {Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of a one-dimensional problem. A high-order Coulomb-corrected strong-field approximation is applied, where the exact continuum state in the S matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although without high-order corrections our theory coincides with the known analytical R-matrix (ARM) theory, we propose a simplified procedure for the matrix element derivation. Rather than matching the eikonal Coulomb-Volkov wave function with the bound state as in the ARM theory to remove the Coulomb singularity, we calculate the matrix element via the saddle-point integration method by time as well as by coordinate, and in this way avoiding the Coulomb singularity. The momentum shift in the photoelectron momentum distribution with respect to the ARM theory due to high-order corrections is analyzed for tunneling and multiphoton regimes. The relation of the quantum corrections to the tunneling delay time is discussed.}, author = {Klaiber, Michael and Daněk, Jiří and Yakaboylu, Enderalp and Hatsagortsyan, Karen and Keitel, Christoph}, issn = {2469-9926}, journal = {Physical Review A}, number = {2}, publisher = {American Physical Society}, title = {{Strong-field ionization via a high-order Coulomb-corrected strong-field approximation}}, doi = {10.1103/PhysRevA.95.023403}, volume = {95}, year = {2017}, } @inproceedings{6526, abstract = {This paper studies the complexity of estimating Rényi divergences of discrete distributions: p observed from samples and the baseline distribution q known a priori. Extending the results of Acharya et al. (SODA'15) on estimating Rényi entropy, we present improved estimation techniques together with upper and lower bounds on the sample complexity. We show that, contrarily to estimating Rényi entropy where a sublinear (in the alphabet size) number of samples suffices, the sample complexity is heavily dependent on events occurring unlikely in q, and is unbounded in general (no matter what an estimation technique is used). For any divergence of integer order bigger than 1, we provide upper and lower bounds on the number of samples dependent on probabilities of p and q (the lower bounds hold for non-integer orders as well). We conclude that the worst-case sample complexity is polynomial in the alphabet size if and only if the probabilities of q are non-negligible. This gives theoretical insights into heuristics used in the applied literature to handle numerical instability, which occurs for small probabilities of q. Our result shows that they should be handled with care not only because of numerical issues, but also because of a blow up in the sample complexity.}, author = {Skórski, Maciej}, booktitle = {2017 IEEE International Symposium on Information Theory}, isbn = {9781509040964}, location = {Aachen, Germany}, publisher = {IEEE}, title = {{On the complexity of estimating Rènyi divergences}}, doi = {10.1109/isit.2017.8006529}, year = {2017}, } @article{467, abstract = {Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata or in any other known decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata, which makes it possible to express important quantitative properties such as average response time. In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in runtime verification. We establish an almost-complete decidability picture for the basic decision problems about nested weighted automata and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, issn = {1529-3785}, journal = {ACM Transactions on Computational Logic}, number = {4}, publisher = {ACM}, title = {{Nested weighted automata}}, doi = {10.1145/3152769}, volume = {18}, year = {2017}, } @phdthesis{6287, abstract = {The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's.}, author = {Nikitenko, Anton}, issn = {2663-337X}, pages = {86}, publisher = {Institute of Science and Technology Austria}, title = {{Discrete Morse theory for random complexes }}, doi = {10.15479/AT:ISTA:th_873}, year = {2017}, } @phdthesis{1127, abstract = {Plant hormone auxin and its transport between cells belong to the most important mechanisms controlling plant development. Auxin itself could change localization of PINs and thereby control direction of its own flow. We performed an expression profiling experiment in Arabidopsis roots to identify potential regulators of PIN polarity which are transcriptionally regulated by auxin signalling. We identified several novel regulators and performed a detailed characterization of the transcription factor WRKY23 (At2g47260) and its role in auxin feedback on PIN polarity. Gain-of-function and dominant-negative mutants revealed that WRKY23 plays a crucial role in mediating the auxin effect on PIN polarity. In concordance, typical polar auxin transport processes such as gravitropism and leaf vascular pattern formation were disturbed by interfering with WRKY23 function. In order to identify direct targets of WRKY23, we performed consequential expression profiling experiments using a WRKY23 inducible gain-of-function line and dominant-negative WRKY23 line that is defunct in PIN re-arrangement. Among several genes mostly related to the groups of cell wall and defense process regulators, we identified LYSINE-HISTIDINE TRANSPORTER 1 (LHT1; At5g40780), a small amino acid permease gene from the amino acid/auxin permease family (AAAP), we present its detailed characterisation in auxin feedback on PIN repolarization, identified its transcriptional regulation, we propose a potential mechanism of its action. Moreover, we identified also a member of receptor-like protein kinase LRR-RLK (LEUCINE-RICH REPEAT TRANSMEMBRANE PROTEIN KINASE PROTEIN 1; LRRK1; At1g05700), which also affects auxin-dependent PIN re-arrangement. We described its transcriptional behaviour, subcellular localization. Based on global expression data, we tried to identify ligand responsible for mechanism of signalling and suggest signalling partner and interactors. Additionally, we described role of novel phytohormone group, strigolactone, in auxin-dependent PIN re-arrangement, that could be a fundament for future studies in this field. Our results provide first insights into an auxin transcriptional network targeting PIN localization and thus regulating plant development. We highlighted WRKY23 transcriptional network and characterised its mediatory role in plant development. We identified direct effectors of this network, LHT1 and LRRK1, and describe their roles in PIN re-arrangement and PIN-dependent auxin transport processes.}, author = {Prat, Tomas}, issn = {2663-337X}, pages = {131}, publisher = {Institute of Science and Technology Austria}, title = {{Identification of novel regulators of PIN polarity and development of novel auxin sensor}}, year = {2017}, } @phdthesis{839, abstract = {This thesis describes a brittle fracture simulation method for visual effects applications. Building upon a symmetric Galerkin boundary element method, we first compute stress intensity factors following the theory of linear elastic fracture mechanics. We then use these stress intensities to simulate the motion of a propagating crack front at a significantly higher resolution than the overall deformation of the breaking object. Allowing for spatial variations of the material's toughness during crack propagation produces visually realistic, highly-detailed fracture surfaces. Furthermore, we introduce approximations for stress intensities and crack opening displacements, resulting in both practical speed-up and theoretically superior runtime complexity compared to previous methods. While we choose a quasi-static approach to fracture mechanics, ignoring dynamic deformations, we also couple our fracture simulation framework to a standard rigid-body dynamics solver, enabling visual effects artists to simulate both large scale motion, as well as fracturing due to collision forces in a combined system. As fractures inside of an object grow, their geometry must be represented both in the coarse boundary element mesh, as well as at the desired fine output resolution. Using a boundary element method, we avoid complicated volumetric meshing operations. Instead we describe a simple set of surface meshing operations that allow us to progressively add cracks to the mesh of an object and still re-use all previously computed entries of the linear boundary element system matrix. On the high resolution level, we opt for an implicit surface representation. We then describe how to capture fracture surfaces during crack propagation, as well as separate the individual fragments resulting from the fracture process, based on this implicit representation. We show results obtained with our method, either solving the full boundary element system in every time step, or alternatively using our fast approximations. These results demonstrate that both of these methods perform well in basic test cases and produce realistic fracture surfaces. Furthermore we show that our fast approximations substantially out-perform the standard approach in more demanding scenarios. Finally, these two methods naturally combine, using the full solution while the problem size is manageably small and switching to the fast approximations later on. The resulting hybrid method gives the user a direct way to choose between speed and accuracy of the simulation. }, author = {Hahn, David}, issn = {2663-337X}, pages = {124}, publisher = {Institute of Science and Technology Austria}, title = {{Brittle fracture simulation with boundary elements for computer graphics}}, doi = {10.15479/AT:ISTA:th_855}, year = {2017}, } @misc{5568, abstract = {Includes source codes, test cases, and example data used in the thesis Brittle Fracture Simulation with Boundary Elements for Computer Graphics. Also includes pre-built binaries of the HyENA library, but not sources - please contact the HyENA authors to obtain these sources if required (https://mech.tugraz.at/hyena)}, author = {Hahn, David}, keywords = {Boundary elements, brittle fracture, computer graphics, fracture simulation}, publisher = {Institute of Science and Technology Austria}, title = {{Source codes: Brittle fracture simulation with boundary elements for computer graphics}}, doi = {10.15479/AT:ISTA:73}, year = {2017}, } @inproceedings{559, abstract = {Proofs of space (PoS) were suggested as more ecological and economical alternative to proofs of work, which are currently used in blockchain designs like Bitcoin. The existing PoS are based on rather sophisticated graph pebbling lower bounds. Much simpler and in several aspects more efficient schemes based on inverting random functions have been suggested, but they don’t give meaningful security guarantees due to existing time-memory trade-offs. In particular, Hellman showed that any permutation over a domain of size N can be inverted in time T by an algorithm that is given S bits of auxiliary information whenever (Formula presented). For functions Hellman gives a weaker attack with S2· T≈ N2 (e.g., S= T≈ N2/3). To prove lower bounds, one considers an adversary who has access to an oracle f: [ N] → [N] and can make T oracle queries. The best known lower bound is S· T∈ Ω(N) and holds for random functions and permutations. We construct functions that provably require more time and/or space to invert. Specifically, for any constant k we construct a function [N] → [N] that cannot be inverted unless Sk· T∈ Ω(Nk) (in particular, S= T≈ (Formula presented). Our construction does not contradict Hellman’s time-memory trade-off, because it cannot be efficiently evaluated in forward direction. However, its entire function table can be computed in time quasilinear in N, which is sufficient for the PoS application. Our simplest construction is built from a random function oracle g: [N] × [N] → [ N] and a random permutation oracle f: [N] → N] and is defined as h(x) = g(x, x′) where f(x) = π(f(x′)) with π being any involution without a fixed point, e.g. flipping all the bits. For this function we prove that any adversary who gets S bits of auxiliary information, makes at most T oracle queries, and inverts h on an ϵ fraction of outputs must satisfy S2· T∈ Ω(ϵ2N2).}, author = {Abusalah, Hamza M and Alwen, Joel F and Cohen, Bram and Khilko, Danylo and Pietrzak, Krzysztof Z and Reyzin, Leonid}, isbn = {978-331970696-2}, location = {Hong Kong, China}, pages = {357 -- 379}, publisher = {Springer}, title = {{Beyond Hellman’s time-memory trade-offs with applications to proofs of space}}, doi = {10.1007/978-3-319-70697-9_13}, volume = {10625}, year = {2017}, }