TY - CONF AB - 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. AU - Avvakumov, Sergey AU - Nivasch, Gabriel ID - 7991 SN - 18688969 T2 - 36th International Symposium on Computational Geometry TI - Homotopic curve shortening and the affine curve-shortening flow VL - 164 ER - TY - CONF AB - 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. AU - Patakova, Zuzana ID - 7989 SN - 18688969 T2 - 36th International Symposium on Computational Geometry TI - Bounding radon number via Betti numbers VL - 164 ER - TY - CONF AB - 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. AU - Patakova, Zuzana AU - Tancer, Martin AU - Wagner, Uli ID - 7992 SN - 18688969 T2 - 36th International Symposium on Computational Geometry TI - Barycentric cuts through a convex body VL - 164 ER - TY - CONF AB - 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. AU - Arroyo Guevara, Alan M AU - Bensmail, Julien AU - Bruce Richter, R. ID - 7994 SN - 18688969 T2 - 36th International Symposium on Computational Geometry TI - Extending drawings of graphs to arrangements of pseudolines VL - 164 ER - TY - JOUR AB - 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. AU - Michailidis, Alexios AU - Turner, C. J. AU - Papić, Z. AU - Abanin, D. A. AU - Serbyn, Maksym ID - 8011 IS - 2 JF - Physical Review Research SN - 2643-1564 TI - Stabilizing two-dimensional quantum scars by deformation and synchronization VL - 2 ER - TY - GEN AB - 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. AU - Anciukevicius, Titas AU - Lampert, Christoph AU - Henderson, Paul M ID - 8063 T2 - arXiv TI - Object-centric image generation with factored depths, locations, and appearances ER - TY - GEN AB - 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. AU - Hobisch, Mathias A. AU - Mourad, Eléonore AU - Fischer, Wolfgang J. AU - Prehal, Christian AU - Eyley, Samuel AU - Childress, Anthony AU - Zankel, Armin AU - Mautner, Andreas AU - Breitenbach, Stefan AU - Rao, Apparao M. AU - Thielemans, Wim AU - Freunberger, Stefan Alexander AU - Eckhart, Rene AU - Bauer, Wolfgang AU - Spirk, Stefan ID - 8081 TI - High specific capacitance supercapacitors from hierarchically organized all-cellulose composites ER - TY - JOUR AB - 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. AU - Lombardi, Fabrizio AU - Wang, Jilin W.J.L. AU - Zhang, Xiyun AU - Ivanov, Plamen Ch ID - 8105 JF - EPJ Web of Conferences SN - 2100-014X TI - Power-law correlations and coupling of active and quiet states underlie a class of complex systems with self-organization at criticality VL - 230 ER - TY - CONF AB - 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. AU - Edelsbrunner, Herbert AU - Nikitenko, Anton AU - Ölsböck, Katharina AU - Synak, Peter ID - 8135 SN - 21932808 T2 - Topological Data Analysis TI - Radius functions on Poisson–Delaunay mosaics and related complexes experimentally VL - 15 ER - TY - COMP AU - Hauschild, Robert ID - 8181 TI - Amplified centrosomes in dendritic cells promote immune cell effector functions ER - TY - COMP AB - Automated root growth analysis and tracking of root tips. AU - Hauschild, Robert ID - 8294 TI - RGtracker ER - TY - CONF AB - 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). AU - Chakraborty, Suvradip AU - Dziembowski, Stefan AU - Nielsen, Jesper Buus ID - 8322 SN - 03029743 T2 - Advances in Cryptology – CRYPTO 2020 TI - Reverse firewalls for actively secure MPCs VL - 12171 ER - TY - CONF AB - 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. AU - Genise, Nicholas AU - Micciancio, Daniele AU - Peikert, Chris AU - Walter, Michael ID - 8339 SN - 03029743 T2 - 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography TI - Improved discrete Gaussian and subgaussian analysis for lattice cryptography VL - 12110 ER - TY - CONF AB - 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. AU - Althoff, Matthias AU - Bak, Stanley AU - Bao, Zongnan AU - Forets, Marcelo AU - Frehse, Goran AU - Freire, Daniel AU - Kochdumper, Niklas AU - Li, Yangge AU - Mitra, Sayan AU - Ray, Rajarshi AU - Schilling, Christian AU - Schupp, Stefan AU - Wetzlinger, Mark ID - 8572 T2 - EPiC Series in Computing TI - ARCH-COMP20 Category Report: Continuous and hybrid systems with linear dynamics VL - 74 ER - TY - CONF AB - 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. AU - Geretti, Luca AU - Alexandre Dit Sandretto, Julien AU - Althoff, Matthias AU - Benet, Luis AU - Chapoutot, Alexandre AU - Chen, Xin AU - Collins, Pieter AU - Forets, Marcelo AU - Freire, Daniel AU - Immler, Fabian AU - Kochdumper, Niklas AU - Sanders, David AU - Schilling, Christian ID - 8571 T2 - EPiC Series in Computing TI - ARCH-COMP20 Category Report: Continuous and hybrid systems with nonlinear dynamics VL - 74 ER - TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Otop, Jan ID - 8600 SN - 18688969 T2 - 31st International Conference on Concurrency Theory TI - Multi-dimensional long-run average problems for vector addition systems with states VL - 171 ER - TY - CONF AB - 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. AU - Avni, Guy AU - Henzinger, Thomas A ID - 8599 SN - 18688969 T2 - 31st International Conference on Concurrency Theory TI - A survey of bidding games on graphs VL - 171 ER - TY - CONF AB - 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. AU - Aksenov, Vitaly AU - Alistarh, Dan-Adrian AU - Drozdova, Alexandra AU - Mohtashami, Amirkeivan ID - 8725 SN - 1868-8969 T2 - 34th International Symposium on Distributed Computing TI - The splay-list: A distribution-adaptive concurrent skip-list VL - 179 ER - TY - JOUR AB - 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. AU - Gotfryd, Dorota AU - Paerschke, Ekaterina AU - Wohlfeld, Krzysztof AU - Oleś, Andrzej M. ID - 8726 IS - 3 JF - Condensed Matter SN - 2410-3896 TI - Evolution of spin-orbital entanglement with increasing ising spin-orbit coupling VL - 5 ER - TY - CONF AB - 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. AU - Alamdari, Par Alizadeh AU - Avni, Guy AU - Henzinger, Thomas A AU - Lukina, Anna ID - 9040 SN - 9783854480426 T2 - Proceedings of the 20th Conference on Formal Methods in Computer-Aided Design TI - Formal methods with a touch of magic ER -