@inproceedings{7991, abstract = {We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.}, author = {Avvakumov, Sergey and Nivasch, Gabriel}, booktitle = {36th International Symposium on Computational Geometry}, isbn = {9783959771436}, issn = {18688969}, location = {Zürich, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Homotopic curve shortening and the affine curve-shortening flow}}, doi = {10.4230/LIPIcs.SoCG.2020.12}, volume = {164}, year = {2020}, } @inproceedings{7989, abstract = {We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.}, author = {Patakova, Zuzana}, booktitle = {36th International Symposium on Computational Geometry}, isbn = {9783959771436}, issn = {18688969}, location = {Zürich, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Bounding radon number via Betti numbers}}, doi = {10.4230/LIPIcs.SoCG.2020.61}, volume = {164}, year = {2020}, } @inproceedings{7992, abstract = {Let K be a convex body in ℝⁿ (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K ∩ h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p₀ is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n ≥ 2, there are always at least three distinct barycentric cuts through the point p₀ ∈ K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p₀ are guaranteed if n ≥ 3.}, author = {Patakova, Zuzana and Tancer, Martin and Wagner, Uli}, booktitle = {36th International Symposium on Computational Geometry}, isbn = {9783959771436}, issn = {18688969}, location = {Zürich, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Barycentric cuts through a convex body}}, doi = {10.4230/LIPIcs.SoCG.2020.62}, volume = {164}, year = {2020}, } @inproceedings{7994, abstract = {In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible.}, author = {Arroyo Guevara, Alan M and Bensmail, Julien and Bruce Richter, R.}, booktitle = {36th International Symposium on Computational Geometry}, isbn = {9783959771436}, issn = {18688969}, location = {Zürich, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Extending drawings of graphs to arrangements of pseudolines}}, doi = {10.4230/LIPIcs.SoCG.2020.9}, volume = {164}, year = {2020}, } @article{8011, abstract = {Relaxation to a thermal state is the inevitable fate of nonequilibrium interacting quantum systems without special conservation laws. While thermalization in one-dimensional systems can often be suppressed by integrability mechanisms, in two spatial dimensions thermalization is expected to be far more effective due to the increased phase space. In this work we propose a general framework for escaping or delaying the emergence of the thermal state in two-dimensional arrays of Rydberg atoms via the mechanism of quantum scars, i.e., initial states that fail to thermalize. The suppression of thermalization is achieved in two complementary ways: by adding local perturbations or by adjusting the driving Rabi frequency according to the local connectivity of the lattice. We demonstrate that these mechanisms allow us to realize robust quantum scars in various two-dimensional lattices, including decorated lattices with nonconstant connectivity. In particular, we show that a small decrease of the Rabi frequency at the corners of the lattice is crucial for mitigating the strong boundary effects in two-dimensional systems. Our results identify synchronization as an important tool for future experiments on two-dimensional quantum scars.}, author = {Michailidis, Alexios and Turner, C. J. and Papić, Z. and Abanin, D. A. and Serbyn, Maksym}, issn = {2643-1564}, journal = {Physical Review Research}, number = {2}, publisher = {American Physical Society}, title = {{Stabilizing two-dimensional quantum scars by deformation and synchronization}}, doi = {10.1103/physrevresearch.2.022065}, volume = {2}, year = {2020}, } @unpublished{8063, abstract = {We present a generative model of images that explicitly reasons over the set of objects they show. Our model learns a structured latent representation that separates objects from each other and from the background; unlike prior works, it explicitly represents the 2D position and depth of each object, as well as an embedding of its segmentation mask and appearance. The model can be trained from images alone in a purely unsupervised fashion without the need for object masks or depth information. Moreover, it always generates complete objects, even though a significant fraction of training images contain occlusions. Finally, we show that our model can infer decompositions of novel images into their constituent objects, including accurate prediction of depth ordering and segmentation of occluded parts.}, author = {Anciukevicius, Titas and Lampert, Christoph and Henderson, Paul M}, booktitle = {arXiv}, title = {{Object-centric image generation with factored depths, locations, and appearances}}, year = {2020}, } @unpublished{8081, abstract = {Here, we employ micro- and nanosized cellulose particles, namely paper fines and cellulose nanocrystals, to induce hierarchical organization over a wide length scale. After processing them into carbonaceous materials, we demonstrate that these hierarchically organized materials outperform the best materials for supercapacitors operating with organic electrolytes reported in literature in terms of specific energy/power (Ragone plot) while showing hardly any capacity fade over 4,000 cycles. The highly porous materials feature a specific surface area as high as 2500 m2ˑg-1 and exhibit pore sizes in the range of 0.5 to 200 nm as proven by scanning electron microscopy and N2 physisorption. The carbonaceous materials have been further investigated by X-ray photoelectron spectroscopy and RAMAN spectroscopy. Since paper fines are an underutilized side stream in any paper production process, they are a cheap and highly available feedstock to prepare carbonaceous materials with outstanding performance in electrochemical applications. }, author = {Hobisch, Mathias A. and Mourad, Eléonore and Fischer, Wolfgang J. and Prehal, Christian and Eyley, Samuel and Childress, Anthony and Zankel, Armin and Mautner, Andreas and Breitenbach, Stefan and Rao, Apparao M. and Thielemans, Wim and Freunberger, Stefan Alexander and Eckhart, Rene and Bauer, Wolfgang and Spirk, Stefan }, title = {{High specific capacitance supercapacitors from hierarchically organized all-cellulose composites}}, year = {2020}, } @article{8105, abstract = {Physical and biological systems often exhibit intermittent dynamics with bursts or avalanches (active states) characterized by power-law size and duration distributions. These emergent features are typical of systems at the critical point of continuous phase transitions, and have led to the hypothesis that such systems may self-organize at criticality, i.e. without any fine tuning of parameters. Since the introduction of the Bak-Tang-Wiesenfeld (BTW) model, the paradigm of self-organized criticality (SOC) has been very fruitful for the analysis of emergent collective behaviors in a number of systems, including the brain. Although considerable effort has been devoted in identifying and modeling scaling features of burst and avalanche statistics, dynamical aspects related to the temporal organization of bursts remain often poorly understood or controversial. Of crucial importance to understand the mechanisms responsible for emergent behaviors is the relationship between active and quiet periods, and the nature of the correlations. Here we investigate the dynamics of active (θ-bursts) and quiet states (δ-bursts) in brain activity during the sleep-wake cycle. We show the duality of power-law (θ, active phase) and exponential-like (δ, quiescent phase) duration distributions, typical of SOC, jointly emerge with power-law temporal correlations and anti-correlated coupling between active and quiet states. Importantly, we demonstrate that such temporal organization shares important similarities with earthquake dynamics, and propose that specific power-law correlations and coupling between active and quiet states are distinctive characteristics of a class of systems with self-organization at criticality.}, author = {Lombardi, Fabrizio and Wang, Jilin W.J.L. and Zhang, Xiyun and Ivanov, Plamen Ch}, issn = {2100-014X}, journal = {EPJ Web of Conferences}, publisher = {EDP Sciences}, title = {{Power-law correlations and coupling of active and quiet states underlie a class of complex systems with self-organization at criticality}}, doi = {10.1051/epjconf/202023000005}, volume = {230}, year = {2020}, } @inproceedings{8135, abstract = {Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.}, author = {Edelsbrunner, Herbert and Nikitenko, Anton and Ölsböck, Katharina and Synak, Peter}, booktitle = {Topological Data Analysis}, isbn = {9783030434076}, issn = {21978549}, pages = {181--218}, publisher = {Springer Nature}, title = {{Radius functions on Poisson–Delaunay mosaics and related complexes experimentally}}, doi = {10.1007/978-3-030-43408-3_8}, volume = {15}, year = {2020}, } @misc{8181, author = {Hauschild, Robert}, publisher = {IST Austria}, title = {{Amplified centrosomes in dendritic cells promote immune cell effector functions}}, doi = {10.15479/AT:ISTA:8181}, year = {2020}, } @misc{8294, abstract = {Automated root growth analysis and tracking of root tips. }, author = {Hauschild, Robert}, publisher = {IST Austria}, title = {{RGtracker}}, doi = {10.15479/AT:ISTA:8294}, year = {2020}, } @inproceedings{8322, abstract = {Reverse firewalls were introduced at Eurocrypt 2015 by Miro-nov and Stephens-Davidowitz, as a method for protecting cryptographic protocols against attacks on the devices of the honest parties. In a nutshell: a reverse firewall is placed outside of a device and its goal is to “sanitize” the messages sent by it, in such a way that a malicious device cannot leak its secrets to the outside world. It is typically assumed that the cryptographic devices are attacked in a “functionality-preserving way” (i.e. informally speaking, the functionality of the protocol remains unchanged under this attacks). In their paper, Mironov and Stephens-Davidowitz construct a protocol for passively-secure two-party computations with firewalls, leaving extension of this result to stronger models as an open question. In this paper, we address this problem by constructing a protocol for secure computation with firewalls that has two main advantages over the original protocol from Eurocrypt 2015. Firstly, it is a multiparty computation protocol (i.e. it works for an arbitrary number n of the parties, and not just for 2). Secondly, it is secure in much stronger corruption settings, namely in the active corruption model. More precisely: we consider an adversary that can fully corrupt up to 𝑛−1 parties, while the remaining parties are corrupt in a functionality-preserving way. Our core techniques are: malleable commitments and malleable non-interactive zero-knowledge, which in particular allow us to create a novel protocol for multiparty augmented coin-tossing into the well with reverse firewalls (that is based on a protocol of Lindell from Crypto 2001).}, author = {Chakraborty, Suvradip and Dziembowski, Stefan and Nielsen, Jesper Buus}, booktitle = {Advances in Cryptology – CRYPTO 2020}, isbn = {9783030568795}, issn = {16113349}, location = {Santa Barbara, CA, United States}, pages = {732--762}, publisher = {Springer Nature}, title = {{Reverse firewalls for actively secure MPCs}}, doi = {10.1007/978-3-030-56880-1_26}, volume = {12171}, year = {2020}, } @inproceedings{8339, abstract = {Discrete Gaussian distributions over lattices are central to lattice-based cryptography, and to the computational and mathematical aspects of lattices more broadly. The literature contains a wealth of useful theorems about the behavior of discrete Gaussians under convolutions and related operations. Yet despite their structural similarities, most of these theorems are formally incomparable, and their proofs tend to be monolithic and written nearly “from scratch,” making them unnecessarily hard to verify, understand, and extend. In this work we present a modular framework for analyzing linear operations on discrete Gaussian distributions. The framework abstracts away the particulars of Gaussians, and usually reduces proofs to the choice of appropriate linear transformations and elementary linear algebra. To showcase the approach, we establish several general properties of discrete Gaussians, and show how to obtain all prior convolution theorems (along with some new ones) as straightforward corollaries. As another application, we describe a self-reduction for Learning With Errors (LWE) that uses a fixed number of samples to generate an unlimited number of additional ones (having somewhat larger error). The distinguishing features of our reduction are its simple analysis in our framework, and its exclusive use of discrete Gaussians without any loss in parameters relative to a prior mixed discrete-and-continuous approach. As a contribution of independent interest, for subgaussian random matrices we prove a singular value concentration bound with explicitly stated constants, and we give tighter heuristics for specific distributions that are commonly used for generating lattice trapdoors. These bounds yield improvements in the concrete bit-security estimates for trapdoor lattice cryptosystems.}, author = {Genise, Nicholas and Micciancio, Daniele and Peikert, Chris and Walter, Michael}, booktitle = {23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography}, isbn = {9783030453732}, issn = {16113349}, location = {Edinburgh, United Kingdom}, pages = {623--651}, publisher = {Springer Nature}, title = {{Improved discrete Gaussian and subgaussian analysis for lattice cryptography}}, doi = {10.1007/978-3-030-45374-9_21}, volume = {12110}, year = {2020}, } @inproceedings{8572, abstract = {We present the results of the ARCH 2020 friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. In its fourth edition, eight tools have been applied to solve eight different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, C2E2, HyDRA, Hylaa, Hylaa-Continuous, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.}, author = {Althoff, Matthias and Bak, Stanley and Bao, Zongnan and Forets, Marcelo and Frehse, Goran and Freire, Daniel and Kochdumper, Niklas and Li, Yangge and Mitra, Sayan and Ray, Rajarshi and Schilling, Christian and Schupp, Stefan and Wetzlinger, Mark}, booktitle = {EPiC Series in Computing}, pages = {16--48}, publisher = {EasyChair}, title = {{ARCH-COMP20 Category Report: Continuous and hybrid systems with linear dynamics}}, doi = {10.29007/7dt2}, volume = {74}, year = {2020}, } @inproceedings{8571, abstract = {We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. This year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. These tools are applied to solve reachability analysis problems on six benchmark problems, two of them featuring hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.}, author = {Geretti, Luca and Alexandre Dit Sandretto, Julien and Althoff, Matthias and Benet, Luis and Chapoutot, Alexandre and Chen, Xin and Collins, Pieter and Forets, Marcelo and Freire, Daniel and Immler, Fabian and Kochdumper, Niklas and Sanders, David and Schilling, Christian}, booktitle = {EPiC Series in Computing}, pages = {49--75}, publisher = {EasyChair}, title = {{ARCH-COMP20 Category Report: Continuous and hybrid systems with nonlinear dynamics}}, doi = {10.29007/zkf6}, volume = {74}, year = {2020}, } @inproceedings{8600, abstract = {A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, booktitle = {31st International Conference on Concurrency Theory}, isbn = {9783959771603}, issn = {18688969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Multi-dimensional long-run average problems for vector addition systems with states}}, doi = {10.4230/LIPIcs.CONCUR.2020.23}, volume = {171}, year = {2020}, } @inproceedings{8599, abstract = {A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and study their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We show how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.}, author = {Avni, Guy and Henzinger, Thomas A}, booktitle = {31st International Conference on Concurrency Theory}, isbn = {9783959771603}, issn = {18688969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{A survey of bidding games on graphs}}, doi = {10.4230/LIPIcs.CONCUR.2020.2}, volume = {171}, year = {2020}, } @inproceedings{8725, abstract = {The design and implementation of efficient concurrent data structures have seen significant attention. However, most of this work has focused on concurrent data structures providing good \emph{worst-case} guarantees. In real workloads, objects are often accessed at different rates, since access distributions may be non-uniform. Efficient distribution-adaptive data structures are known in the sequential case, e.g. the splay-trees; however, they often are hard to translate efficiently in the concurrent case. In this paper, we investigate distribution-adaptive concurrent data structures and propose a new design called the splay-list. At a high level, the splay-list is similar to a standard skip-list, with the key distinction that the height of each element adapts dynamically to its access rate: popular elements ``move up,'' whereas rarely-accessed elements decrease in height. We show that the splay-list provides order-optimal amortized complexity bounds for a subset of operations while being amenable to efficient concurrent implementation. Experimental results show that the splay-list can leverage distribution-adaptivity to improve on the performance of classic concurrent designs, and can outperform the only previously-known distribution-adaptive design in certain settings.}, author = {Aksenov, Vitaly and Alistarh, Dan-Adrian and Drozdova, Alexandra and Mohtashami, Amirkeivan}, booktitle = {34th International Symposium on Distributed Computing}, isbn = {9783959771689}, issn = {1868-8969}, location = {Freiburg, Germany}, pages = {3:1--3:18}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The splay-list: A distribution-adaptive concurrent skip-list}}, doi = {10.4230/LIPIcs.DISC.2020.3}, volume = {179}, year = {2020}, } @article{8726, abstract = {Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)⊗SU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling.}, author = {Gotfryd, Dorota and Paerschke, Ekaterina and Wohlfeld, Krzysztof and Oleś, Andrzej M.}, issn = {2410-3896}, journal = {Condensed Matter}, number = {3}, publisher = {MDPI}, title = {{Evolution of spin-orbital entanglement with increasing ising spin-orbit coupling}}, doi = {10.3390/condmat5030053}, volume = {5}, year = {2020}, } @inproceedings{9040, abstract = {Machine learning and formal methods have complimentary benefits and drawbacks. In this work, we address the controller-design problem with a combination of techniques from both fields. The use of black-box neural networks in deep reinforcement learning (deep RL) poses a challenge for such a combination. Instead of reasoning formally about the output of deep RL, which we call the wizard, we extract from it a decision-tree based model, which we refer to as the magic book. Using the extracted model as an intermediary, we are able to handle problems that are infeasible for either deep RL or formal methods by themselves. First, we suggest, for the first time, a synthesis procedure that is based on a magic book. We synthesize a stand-alone correct-by-design controller that enjoys the favorable performance of RL. Second, we incorporate a magic book in a bounded model checking (BMC) procedure. BMC allows us to find numerous traces of the plant under the control of the wizard, which a user can use to increase the trustworthiness of the wizard and direct further training.}, author = {Alamdari, Par Alizadeh and Avni, Guy and Henzinger, Thomas A and Lukina, Anna}, booktitle = {Proceedings of the 20th Conference on Formal Methods in Computer-Aided Design}, isbn = {9783854480426}, issn = {2708-7824}, location = {Online Conference}, pages = {138--147}, publisher = {TU Wien Academic Press}, title = {{Formal methods with a touch of magic}}, doi = {10.34727/2020/isbn.978-3-85448-042-6_21}, year = {2020}, } @article{9249, abstract = {Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.}, author = {Biswas, Ranita and Largeteau-Skapin, Gaëlle and Zrour, Rita and Andres, Eric}, issn = {2353-3390}, journal = {Mathematical Morphology - Theory and Applications}, number = {1}, pages = {143--158}, publisher = {De Gruyter}, title = {{Digital objects in rhombic dodecahedron grid}}, doi = {10.1515/mathm-2020-0106}, volume = {4}, year = {2020}, } @inproceedings{9299, abstract = {We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ .}, author = {Pach, János and Tardos, Gábor and Tóth, Géza}, booktitle = {28th International Symposium on Graph Drawing and Network Visualization}, isbn = {9783030687656}, issn = {1611-3349}, location = {Virtual, Online}, pages = {359--371}, publisher = {Springer Nature}, title = {{Crossings between non-homotopic edges}}, doi = {10.1007/978-3-030-68766-3_28}, volume = {12590}, year = {2020}, } @inproceedings{9632, abstract = {Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this context. Our work examines this question, identifies issues with existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian. Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for oneshot pruning. Further, even when iterative, gradual pruning is allowed, our method results in a gain in test accuracy over the state-of-the-art approaches, for standard image classification datasets such as ImageNet ILSVRC. We examine how our method can be extended to take into account first-order information, as well as illustrate its ability to automatically set layer-wise pruning thresholds and perform compression in the limited-data regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher.}, author = {Singh, Sidak Pal and Alistarh, Dan-Adrian}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713829546}, issn = {10495258}, location = {Vancouver, Canada}, pages = {18098--18109}, publisher = {Curran Associates}, title = {{WoodFisher: Efficient second-order approximation for neural network compression}}, volume = {33}, year = {2020}, } @article{9630, abstract = {Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.}, author = {Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert}, issn = {1920180X}, journal = {Journal of Computational Geometry}, number = {2}, pages = {162--182}, publisher = {Carleton University}, title = {{Topological data analysis in information space}}, doi = {10.20382/jocg.v11i2a7}, volume = {11}, year = {2020}, } @inproceedings{9631, abstract = {The ability to leverage large-scale hardware parallelism has been one of the key enablers of the accelerated recent progress in machine learning. Consequently, there has been considerable effort invested into developing efficient parallel variants of classic machine learning algorithms. However, despite the wealth of knowledge on parallelization, some classic machine learning algorithms often prove hard to parallelize efficiently while maintaining convergence. In this paper, we focus on efficient parallel algorithms for the key machine learning task of inference on graphical models, in particular on the fundamental belief propagation algorithm. We address the challenge of efficiently parallelizing this classic paradigm by showing how to leverage scalable relaxed schedulers in this context. We present an extensive empirical study, showing that our approach outperforms previous parallel belief propagation implementations both in terms of scalability and in terms of wall-clock convergence time, on a range of practical applications.}, author = {Aksenov, Vitaly and Alistarh, Dan-Adrian and Korhonen, Janne}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713829546}, issn = {10495258}, location = {Vancouver, Canada}, pages = {22361--22372}, publisher = {Curran Associates}, title = {{Scalable belief propagation via relaxed scheduling}}, volume = {33}, year = {2020}, } @inproceedings{8533, abstract = {Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Ismael R and Svoboda, Jakub}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959771597}, issn = {18688969}, location = {Prague, Czech Republic}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Simplified game of life: Algorithms and complexity}}, doi = {10.4230/LIPIcs.MFCS.2020.22}, volume = {170}, year = {2020}, } @inproceedings{8534, abstract = {A regular language L of finite words is composite if there are regular languages L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced and studied in [O. Kupferman and J. Mosheiff, 2015], where the complexity of deciding the primality of the language of a given DFA was left open, with a doubly-exponential gap between the upper and lower bounds. We study primality for unary regular languages, namely regular languages with a singleton alphabet. A unary language corresponds to a subset of ℕ, making the study of unary prime languages closer to that of primality in number theory. We show that the setting of languages is richer. In particular, while every composite number is the product of two smaller numbers, the number t of languages necessary to decompose a composite unary language induces a strict hierarchy. In addition, a primality witness for a unary language L, namely a word that is not in L but is in all products of languages that contain L and have an index smaller than L’s, may be of exponential length. Still, we are able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs.}, author = {Jecker, Ismael R and Kupferman, Orna and Mazzocchi, Nicolas}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959771597}, issn = {18688969}, location = {Prague, Czech Republic}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Unary prime languages}}, doi = {10.4230/LIPIcs.MFCS.2020.51}, volume = {170}, year = {2020}, } @article{8538, abstract = {We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.}, author = {Akopyan, Arseniy and Schwartz, Richard and Tabachnikov, Serge}, issn = {2199-6768}, journal = {European Journal of Mathematics}, publisher = {Springer Nature}, title = {{Billiards in ellipses revisited}}, doi = {10.1007/s40879-020-00426-9}, year = {2020}, } @unpublished{8616, abstract = {The brain vasculature supplies neurons with glucose and oxygen, but little is known about how vascular plasticity contributes to brain function. Using longitudinal in vivo imaging, we reported that a substantial proportion of blood vessels in the adult brain sporadically occluded and regressed. Their regression proceeded through sequential stages of blood-flow occlusion, endothelial cell collapse, relocation or loss of pericytes, and retraction of glial endfeet. Regressing vessels were found to be widespread in mouse, monkey and human brains. Both brief occlusions of the middle cerebral artery and lipopolysaccharide-mediated inflammation induced an increase of vessel regression. Blockage of leukocyte adhesion to endothelial cells alleviated LPS-induced vessel regression. We further revealed that blood vessel regression caused a reduction of neuronal activity due to a dysfunction in mitochondrial metabolism and glutamate production. Our results elucidate the mechanism of vessel regression and its role in neuronal function in the adult brain.}, author = {Gao, Xiaofei and Li, Jun-Liszt and Chen, Xingjun and Ci, Bo and Chen, Fei and Lu, Nannan and Shen, Bo and Zheng, Lijun and Jia, Jie-Min and Yi, Yating and Zhang, Shiwen and Shi, Ying-Chao and Shi, Kaibin and Propson, Nicholas E and Huang, Yubin and Poinsatte, Katherine and Zhang, Zhaohuan and Yue, Yuanlei and Bosco, Dale B and Lu, Ying-mei and Yang, Shi-bing and Adams, Ralf H. and Lindner, Volkhard and Huang, Fen and Wu, Long-Jun and Zheng, Hui and Han, Feng and Hippenmeyer, Simon and Stowe, Ann M. and Peng, Bo and Margeta, Marta and Wang, Xiaoqun and Liu, Qiang and Körbelin, Jakob and Trepel, Martin and Lu, Hui and Zhou, Bo O. and Zhao, Hu and Su, Wenzhi and Bachoo, Robert M. and Ge, Woo-ping}, booktitle = {bioRxiv}, publisher = {Cold Spring Harbor Laboratory}, title = {{Reduction of neuronal activity mediated by blood-vessel regression in the brain}}, doi = {10.1101/2020.09.15.262782}, year = {2020}, } @techreport{8695, abstract = {A look at international activities on Open Science reveals a broad spectrum from individual institutional policies to national action plans. The present Recommendations for a National Open Science Strategy in Austria are based on these international initiatives and present practical considerations for their coordinated implementation with regard to strategic developments in research, technology and innovation (RTI) in Austria until 2030. They are addressed to all relevant actors in the RTI system, in particular to Research Performing Organisations, Research Funding Organisations, Research Policy, memory institutions such as Libraries and Researchers. The recommendation paper was developed from 2018 to 2020 by the OANA working group "Open Science Strategy" and published for the first time in spring 2020 for a public consultation. The now available final version of the recommendation document, which contains feedback and comments from the consultation, is intended to provide an impetus for further discussion and implementation of Open Science in Austria and serves as a contribution and basis for a potential national Open Science Strategy in Austria. The document builds on the diverse expertise of the authors (academia, administration, library and archive, information technology, science policy, funding system, etc.) and reflects their personal experiences and opinions.}, author = {Mayer, Katja and Rieck, Katharina and Reichmann, Stefan and Danowski, Patrick and Graschopf, Anton and König, Thomas and Kraker, Peter and Lehner, Patrick and Reckling, Falk and Ross-Hellauer, Tony and Spichtinger, Daniel and Tzatzanis, Michalis and Schürz, Stefanie}, pages = {36}, publisher = {OANA}, title = {{Empfehlungen für eine nationale Open Science Strategie in Österreich / Recommendations for a National Open Science Strategy in Austria}}, doi = {10.5281/ZENODO.4109242}, year = {2020}, } @article{8706, abstract = {As part of the Austrian Transition to Open Access (AT2OA) project, subproject TP1-B is working on designing a monitoring solution for the output of Open Access publications in Austria. This report on a potential Open Access monitoring approach in Austria is one of the results of these efforts and can serve as a basis for discussion on an international level.}, author = {Danowski, Patrick and Ferus, Andreas and Hikl, Anna-Laetitia and McNeill, Gerda and Miniberger, Clemens and Reding, Steve and Zarka, Tobias and Zojer, Michael}, issn = {10222588}, journal = {Mitteilungen der Vereinigung Österreichischer Bibliothekarinnen und Bibliothekare}, number = {2}, pages = {278--284}, publisher = {Vereinigung Osterreichischer Bibliothekarinnen und Bibliothekare}, title = {{„Recommendation“ for the further procedure for open access monitoring. Deliverable of the AT2OA subproject TP1-B}}, doi = {10.31263/voebm.v73i2.3941}, volume = {73}, year = {2020}, } @article{8978, abstract = {Mosaic analysis with double markers (MADM) technology enables concomitant fluorescent cell labeling and induction of uniparental chromosome disomy (UPD) with single-cell resolution. In UPD, imprinted genes are either overexpressed 2-fold or are not expressed. Here, the MADM platform is utilized to probe imprinting phenotypes at the transcriptional level. This protocol highlights major steps for the generation and isolation of projection neurons and astrocytes with MADM-induced UPD from mouse cerebral cortex for downstream single-cell and low-input sample RNA-sequencing experiments. For complete details on the use and execution of this protocol, please refer to Laukoter et al. (2020b).}, author = {Laukoter, Susanne and Amberg, Nicole and Pauler, Florian and Hippenmeyer, Simon}, issn = {2666-1667}, journal = {STAR Protocols}, number = {3}, publisher = {Elsevier}, title = {{Generation and isolation of single cells from mouse brain with mosaic analysis with double markers-induced uniparental chromosome disomy}}, doi = {10.1016/j.xpro.2020.100215}, volume = {1}, year = {2020}, } @inproceedings{9103, abstract = {We introduce LRT-NG, a set of techniques and an associated toolset that computes a reachtube (an over-approximation of the set of reachable states over a given time horizon) of a nonlinear dynamical system. LRT-NG significantly advances the state-of-the-art Langrangian Reachability and its associated tool LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways. First, it uses for the first time an analytically computed metric for the propagated ball which is proven to minimize the ball’s volume. We emphasize that the metric computation is the centerpiece of all bloating-based techniques. Secondly, it computes the next reachset as the intersection of two balls: one based on the Cartesian metric and the other on the new metric. While the two metrics were previously considered opposing approaches, their joint use considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect" associated with the validated integration of the center of the reachset, by optimally absorbing the interval approximation in the radius of the next ball. From a tool-development perspective, LRT-NG is superior to LRT in two ways. First, it is a standalone tool that no longer relies on CAPD. This required the implementation of the Lohner method and a Runge-Kutta time-propagation method. Secondly, it has an improved interface, allowing the input model and initial conditions to be provided as external input files. Our experiments on a comprehensive set of benchmarks, including two Neural ODEs, demonstrates LRT-NG’s superior performance compared to LRT, CAPD, and Flow*.}, author = {Gruenbacher, Sophie and Cyranka, Jacek and Lechner, Mathias and Islam, Md Ariful and Smolka, Scott A. and Grosu, Radu}, booktitle = {Proceedings of the 59th IEEE Conference on Decision and Control}, isbn = {9781728174471}, issn = {07431546}, location = {Jeju Islang, Korea (South)}, pages = {1556--1563}, publisher = {IEEE}, title = {{Lagrangian reachtubes: The next generation}}, doi = {10.1109/CDC42340.2020.9304042}, volume = {2020}, year = {2020}, } @inproceedings{9221, abstract = {Recent works have shown that gradient descent can find a global minimum for over-parameterized neural networks where the widths of all the hidden layers scale polynomially with N (N being the number of training samples). In this paper, we prove that, for deep networks, a single layer of width N following the input layer suffices to ensure a similar guarantee. In particular, all the remaining layers are allowed to have constant widths, and form a pyramidal topology. We show an application of our result to the widely used LeCun’s initialization and obtain an over-parameterization requirement for the single wide layer of order N2. }, author = {Nguyen, Quynh and Mondelli, Marco}, booktitle = {34th Conference on Neural Information Processing Systems}, location = {Vancouver, Canada}, pages = {11961–11972}, publisher = {Curran Associates}, title = {{Global convergence of deep networks with one wide layer followed by pyramidal topology}}, volume = {33}, year = {2020}, } @inproceedings{9415, abstract = {Optimizing convolutional neural networks for fast inference has recently become an extremely active area of research. One of the go-to solutions in this context is weight pruning, which aims to reduce computational and memory footprint by removing large subsets of the connections in a neural network. Surprisingly, much less attention has been given to exploiting sparsity in the activation maps, which tend to be naturally sparse in many settings thanks to the structure of rectified linear (ReLU) activation functions. In this paper, we present an in-depth analysis of methods for maximizing the sparsity of the activations in a trained neural network, and show that, when coupled with an efficient sparse-input convolution algorithm, we can leverage this sparsity for significant performance gains. To induce highly sparse activation maps without accuracy loss, we introduce a new regularization technique, coupled with a new threshold-based sparsification method based on a parameterized activation function called Forced-Activation-Threshold Rectified Linear Unit (FATReLU). We examine the impact of our methods on popular image classification models, showing that most architectures can adapt to significantly sparser activation maps without any accuracy loss. Our second contribution is showing that these these compression gains can be translated into inference speedups: we provide a new algorithm to enable fast convolution operations over networks with sparse activations, and show that it can enable significant speedups for end-to-end inference on a range of popular models on the large-scale ImageNet image classification task on modern Intel CPUs, with little or no retraining cost. }, author = {Kurtz, Mark and Kopinsky, Justin and Gelashvili, Rati and Matveev, Alexander and Carr, John and Goin, Michael and Leiserson, William and Moore, Sage and Nell, Bill and Shavit, Nir and Alistarh, Dan-Adrian}, booktitle = {37th International Conference on Machine Learning, ICML 2020}, issn = {2640-3498}, location = {Online}, pages = {5533--5543}, title = {{Inducing and exploiting activation sparsity for fast neural network inference}}, volume = {119}, year = {2020}, } @inproceedings{10672, abstract = {The family of feedback alignment (FA) algorithms aims to provide a more biologically motivated alternative to backpropagation (BP), by substituting the computations that are unrealistic to be implemented in physical brains. While FA algorithms have been shown to work well in practice, there is a lack of rigorous theory proofing their learning capabilities. Here we introduce the first feedback alignment algorithm with provable learning guarantees. In contrast to existing work, we do not require any assumption about the size or depth of the network except that it has a single output neuron, i.e., such as for binary classification tasks. We show that our FA algorithm can deliver its theoretical promises in practice, surpassing the learning performance of existing FA methods and matching backpropagation in binary classification tasks. Finally, we demonstrate the limits of our FA variant when the number of output neurons grows beyond a certain quantity.}, author = {Lechner, Mathias}, booktitle = {8th International Conference on Learning Representations}, location = {Virtual ; Addis Ababa, Ethiopia}, publisher = {ICLR}, title = {{Learning representations for binary-classification without backpropagation}}, year = {2020}, } @inproceedings{8188, abstract = {A natural approach to generative modeling of videos is to represent them as a composition of moving objects. Recent works model a set of 2D sprites over a slowly-varying background, but without considering the underlying 3D scene that gives rise to them. We instead propose to model a video as the view seen while moving through a scene with multiple 3D objects and a 3D background. Our model is trained from monocular videos without any supervision, yet learns to generate coherent 3D scenes containing several moving objects. We conduct detailed experiments on two datasets, going beyond the visual complexity supported by state-of-the-art generative approaches. We evaluate our method on depth-prediction and 3D object detection---tasks which cannot be addressed by those earlier works---and show it out-performs them even on 2D instance segmentation and tracking.}, author = {Henderson, Paul M and Lampert, Christoph}, booktitle = {34th Conference on Neural Information Processing Systems}, isbn = {9781713829546}, location = {Vancouver, Canada}, pages = {3106–3117}, publisher = {Curran Associates}, title = {{Unsupervised object-centric video generation and decomposition in 3D}}, volume = {33}, year = {2020}, } @book{7474, abstract = {This booklet is a collection of abstracts presented at the AHPC conference.}, editor = {Schlögl, Alois and Kiss, Janos and Elefante, Stefano}, isbn = {978-3-99078-004-6}, location = {Klosterneuburg, Austria}, pages = {72}, publisher = {IST Austria}, title = {{Austrian High-Performance-Computing meeting (AHPC2020)}}, doi = {10.15479/AT:ISTA:7474}, year = {2020}, } @inproceedings{7808, abstract = {Quantization converts neural networks into low-bit fixed-point computations which can be carried out by efficient integer-only hardware, and is standard practice for the deployment of neural networks on real-time embedded devices. However, like their real-numbered counterpart, quantized networks are not immune to malicious misclassification caused by adversarial attacks. We investigate how quantization affects a network’s robustness to adversarial attacks, which is a formal verification question. We show that neither robustness nor non-robustness are monotonic with changing the number of bits for the representation and, also, neither are preserved by quantization from a real-numbered network. For this reason, we introduce a verification method for quantized neural networks which, using SMT solving over bit-vectors, accounts for their exact, bit-precise semantics. We built a tool and analyzed the effect of quantization on a classifier for the MNIST dataset. We demonstrate that, compared to our method, existing methods for the analysis of real-numbered networks often derive false conclusions about their quantizations, both when determining robustness and when detecting attacks, and that existing methods for quantized networks often miss attacks. Furthermore, we applied our method beyond robustness, showing how the number of bits in quantization enlarges the gender bias of a predictor for students’ grades.}, author = {Giacobbe, Mirco and Henzinger, Thomas A and Lechner, Mathias}, booktitle = {International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783030452360}, issn = {16113349}, location = {Dublin, Ireland}, pages = {79--97}, publisher = {Springer Nature}, title = {{How many bits does it take to quantize your neural network?}}, doi = {10.1007/978-3-030-45237-7_5}, volume = {12079}, year = {2020}, } @inproceedings{7952, abstract = {Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary. }, author = {Boissonnat, Jean-Daniel and Wintraecken, Mathijs}, booktitle = {36th International Symposium on Computational Geometry}, isbn = {978-3-95977-143-6}, issn = {1868-8969}, location = {Zürich, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The topological correctness of PL-approximations of isomanifolds}}, doi = {10.4230/LIPIcs.SoCG.2020.20}, volume = {164}, year = {2020}, } @inproceedings{7990, abstract = {Given a finite point set P in general position in the plane, a full triangulation is a maximal straight-line embedded plane graph on P. A partial triangulation on P is a full triangulation of some subset P' of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge, removes a non-extreme point of degree 3, or adds a point in P ⧵ P' as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The goal of this paper is to investigate the structure of this graph, with emphasis on its connectivity. For sets P of n points in general position, we show that the bistellar flip graph is (n-3)-connected, thereby answering, for sets in general position, an open questions raised in a book (by De Loera, Rambau, and Santos) and a survey (by Lee and Santos) on triangulations. This matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points and projecting the lower convex hull), where (n-3)-connectivity has been known since the late 1980s through the secondary polytope (Gelfand, Kapranov, Zelevinsky) and Balinski’s Theorem. Our methods also yield the following results (see the full version [Wagner and Welzl, 2020]): (i) The bistellar flip graph can be covered by graphs of polytopes of dimension n-3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n-3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations are regular iff the trivial subdivision has height n-3 in the partial order of partial subdivisions. (iv) There are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction).}, author = {Wagner, Uli and Welzl, Emo}, booktitle = {36th International Symposium on Computational Geometry}, isbn = {9783959771436}, issn = {18688969}, location = {Zürich, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)}}, doi = {10.4230/LIPIcs.SoCG.2020.67}, volume = {164}, year = {2020}, } @inproceedings{7807, abstract = {In a straight-line embedded triangulation of a point set P in the plane, removing an inner edge and—provided the resulting quadrilateral is convex—adding the other diagonal is called an edge flip. The (edge) flip graph has all triangulations as vertices, and a pair of triangulations is adjacent if they can be obtained from each other by an edge flip. The goal of this paper is to contribute to a better understanding of the flip graph, with an emphasis on its connectivity. For sets in general position, it is known that every triangulation allows at least edge flips (a tight bound) which gives the minimum degree of any flip graph for n points. We show that for every point set P in general position, the flip graph is at least -vertex connected. Somewhat more strongly, we show that the vertex connectivity equals the minimum degree occurring in the flip graph, i.e. the minimum number of flippable edges in any triangulation of P, provided P is large enough. Finally, we exhibit some of the geometry of the flip graph by showing that the flip graph can be covered by 1-skeletons of polytopes of dimension (products of associahedra). A corresponding result ((n – 3)-vertex connectedness) can be shown for the bistellar flip graph of partial triangulations, i.e. the set of all triangulations of subsets of P which contain all extreme points of P. This will be treated separately in a second part.}, author = {Wagner, Uli and Welzl, Emo}, booktitle = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms}, isbn = {9781611975994}, location = {Salt Lake City, UT, United States}, pages = {2823--2841}, publisher = {SIAM}, title = {{Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)}}, doi = {10.1137/1.9781611975994.172}, volume = {2020-January}, year = {2020}, } @misc{13073, abstract = {The Mytilus complex of marine mussel species forms a mosaic of hybrid zones, found across temperate regions of the globe. This allows us to study "replicated" instances of secondary contact between closely-related species. Previous work on this complex has shown that local introgression is both widespread and highly heterogeneous, and has identified SNPs that are outliers of differentiation between lineages. Here, we developed an ancestry-informative panel of such SNPs. We then compared their frequencies in newly-sampled populations, including samples from within the hybrid zones, and parental populations at different distances from the contact. Results show that close to the hybrid zones, some outlier loci are near to fixation for the heterospecific allele, suggesting enhanced local introgression, or the local sweep of a shared ancestral allele. Conversely, genomic cline analyses, treating local parental populations as the reference, reveal a globally high concordance among loci, albeit with a few signals of asymmetric introgression. Enhanced local introgression at specific loci is consistent with the early transfer of adaptive variants after contact, possibly including asymmetric bi-stable variants (Dobzhansky-Muller incompatibilities), or haplotypes loaded with fewer deleterious mutations. Having escaped one barrier, however, these variants can be trapped or delayed at the next barrier, confining the introgression locally. These results shed light on the decay of species barriers during phases of contact.}, author = {Simon, Alexis and Fraisse, Christelle and El Ayari, Tahani and Liautard-Haag, Cathy and Strelkov, Petr and Welch, John and Bierne, Nicolas}, publisher = {Dryad}, title = {{How do species barriers decay? concordance and local introgression in mosaic hybrid zones of mussels}}, doi = {10.5061/DRYAD.R4XGXD29N}, year = {2020}, } @misc{13065, abstract = {Domestication is a human-induced selection process that imprints the genomes of domesticated populations over a short evolutionary time scale, and that occurs in a given demographic context. Reconstructing historical gene flow, effective population size changes and their timing is therefore of fundamental interest to understand how plant demography and human selection jointly shape genomic divergence during domestication. Yet, the comparison under a single statistical framework of independent domestication histories across different crop species has been little evaluated so far. Thus, it is unclear whether domestication leads to convergent demographic changes that similarly affect crop genomes. To address this question, we used existing and new transcriptome data on three crop species of Solanaceae (eggplant, pepper and tomato), together with their close wild relatives. We fitted twelve demographic models of increasing complexity on the unfolded joint allele frequency spectrum for each wild/crop pair, and we found evidence for both shared and species-specific demographic processes between species. A convergent history of domestication with gene-flow was inferred for all three species, along with evidence of strong reduction in the effective population size during the cultivation stage of tomato and pepper. The absence of any reduction in size of the crop in eggplant stands out from the classical view of the domestication process; as does the existence of a “protracted period” of management before cultivation. Our results also suggest divergent management strategies of modern cultivars among species as their current demography substantially differs. Finally, the timing of domestication is species-specific and supported by the few historical records available.}, author = {Arnoux, Stephanie and Fraisse, Christelle and Sauvage, Christopher}, publisher = {Dryad}, title = {{VCF files of synonymous SNPs related to: Genomic inference of complex domestication histories in three Solanaceae species}}, doi = {10.5061/DRYAD.Q2BVQ83HD}, year = {2020}, } @inproceedings{8536, abstract = {This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is O(N 1−1/µ ), where N is the block length and µ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate 0 and 1.}, author = {Mondelli, Marco and Hashemi, Seyyed Ali and Cioffi, John and Goldsmith, Andrea}, booktitle = {IEEE International Symposium on Information Theory - Proceedings}, isbn = {9781728164328}, issn = {21578095}, location = {Los Angeles, CA, United States}, publisher = {IEEE}, title = {{Simplified successive cancellation decoding of polar codes has sublinear latency}}, doi = {10.1109/ISIT44484.2020.9174141}, volume = {2020-June}, year = {2020}, } @article{9308, author = {Avvakumov, Sergey and Wagner, Uli and Mabillard, Isaac and Skopenkov, A. B.}, issn = {0036-0279}, journal = {Russian Mathematical Surveys}, number = {6}, pages = {1156--1158}, publisher = {IOP Publishing}, title = {{Eliminating higher-multiplicity intersections, III. Codimension 2}}, doi = {10.1070/RM9943}, volume = {75}, year = {2020}, } @article{6358, abstract = {We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.}, author = {Carlen, Eric A. and Maas, Jan}, issn = {15729613}, journal = {Journal of Statistical Physics}, number = {2}, pages = {319--378}, publisher = {Springer Nature}, title = {{Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems}}, doi = {10.1007/s10955-019-02434-w}, volume = {178}, year = {2020}, } @inbook{74, abstract = {We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class of compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2. We use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian measures.}, author = {Akopyan, Arseniy and Karasev, Roman}, booktitle = {Geometric Aspects of Functional Analysis}, editor = {Klartag, Bo'az and Milman, Emanuel}, isbn = {9783030360191}, issn = {16179692}, pages = {1--27}, publisher = {Springer Nature}, title = {{Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures}}, doi = {10.1007/978-3-030-36020-7_1}, volume = {2256}, year = {2020}, } @article{177, abstract = {We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.}, author = {Browning, Timothy D and Sawin, Will}, journal = {Annals of Mathematics}, number = {3}, pages = {893--948}, publisher = {Princeton University}, title = {{A geometric version of the circle method}}, doi = {10.4007/annals.2020.191.3.4}, volume = {191}, year = {2020}, } @article{6649, abstract = {While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials. }, author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, pages = {2097–2150}, publisher = {Springer Nature}, title = {{Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime}}, doi = {10.1007/s00220-019-03505-5}, volume = {374}, year = {2020}, }