TY - CONF AB - In this paper, we address the problem of synthesizing periodic switching controllers for stabilizing a family of linear systems. Our broad approach consists of constructing a finite game graph based on the family of linear systems such that every winning strategy on the game graph corresponds to a stabilizing switching controller for the family of linear systems. The construction of a (finite) game graph, the synthesis of a winning strategy and the extraction of a stabilizing controller are all computationally feasible. We illustrate our method on an example. AU - Kundu, Atreyee AU - Garcia Soto, Miriam AU - Prabhakar, Pavithra ID - 6565 SN - 978-153866246-5 T2 - 5th Indian Control Conference Proceedings TI - Formal synthesis of stabilizing controllers for periodically controlled linear switched systems ER - TY - CONF AB - Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space. AU - Vegter, Gert AU - Wintraecken, Mathijs ID - 6628 T2 - The 31st Canadian Conference in Computational Geometry TI - The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds ER - TY - CONF AB - 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. AU - Edelsbrunner, Herbert AU - Virk, Ziga AU - Wagner, Hubert ID - 6648 SN - 9783959771047 T2 - 35th International Symposium on Computational Geometry TI - Topological data analysis in information space VL - 129 ER - TY - JOUR AB - Chemical labeling of proteins with synthetic molecular probes offers the possibility to probe the functions of proteins of interest in living cells. However, the methods for covalently labeling targeted proteins using complementary peptide tag-probe pairs are still limited, irrespective of the versatility of such pairs in biological research. Herein, we report the new CysHis tag-Ni(II) probe pair for the specific covalent labeling of proteins. A broad-range evaluation of the reactivity profiles of the probe and the CysHis peptide tag afforded a tag-probe pair with an optimized and high labeling selectivity and reactivity. In particular, the labeling specificity of this pair was notably improved compared to the previously reported one. This pair was successfully utilized for the fluorescence imaging of membrane proteins on the surfaces of living cells, demonstrating its potential utility in biological research. AU - Zenmyo, Naoki AU - Tokumaru, Hiroki AU - Uchinomiya, Shohei AU - Fuchida, Hirokazu AU - Tabata, Shigekazu AU - Hamachi, Itaru AU - Shigemoto, Ryuichi AU - Ojida, Akio ID - 6659 IS - 5 JF - Bulletin of the Chemical Society of Japan SN - 00092673 TI - Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins VL - 92 ER - TY - JOUR AB - In phase retrieval, we want to recover an unknown signal 𝑥∈ℂ𝑑 from n quadratic measurements of the form 𝑦𝑖=|⟨𝑎𝑖,𝑥⟩|2+𝑤𝑖, where 𝑎𝑖∈ℂ𝑑 are known sensing vectors and 𝑤𝑖 is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n needed to produce an estimator 𝑥^(𝑦) that is positively correlated with the signal 𝑥? We consider the case of Gaussian vectors 𝑎𝑎𝑖. We prove that—in the high-dimensional limit—a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For 𝑛≤𝑑−𝑜(𝑑), no estimator can do significantly better than random and achieve a strictly positive correlation. For 𝑛≥𝑑+𝑜(𝑑), a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theoretic arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper bound and lower bound generalize beyond phase retrieval to measurements 𝑦𝑖 produced according to a generalized linear model. As a by-product of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm. AU - Mondelli, Marco AU - Montanari, Andrea ID - 6662 IS - 3 JF - Foundations of Computational Mathematics TI - Fundamental limits of weak recovery with applications to phase retrieval VL - 19 ER - TY - JOUR AB - The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure that approximates the Riemannian Voronoi diagram. This structure has been implemented and was shown to lead to good triangulations in $\mathbb{R}^2$ and on surfaces embedded in $\mathbb{R}^3$ as detailed in our experimental companion paper. In this paper, we study theoretical aspects of our structure. Given a finite set of points $\mathcal{P}$ in a domain $\Omega$ equipped with a Riemannian metric, we compare the discrete Riemannian Voronoi diagram of $\mathcal{P}$ to its Riemannian Voronoi diagram. Both diagrams have dual structures called the discrete Riemannian Delaunay and the Riemannian Delaunay complex. We provide conditions that guarantee that these dual structures are identical. It then follows from previous results that the discrete Riemannian Delaunay complex can be embedded in $\Omega$ under sufficient conditions, leading to an anisotropic triangulation with curved simplices. Furthermore, we show that, under similar conditions, the simplices of this triangulation can be straightened. AU - Boissonnat, Jean-Daniel AU - Rouxel-Labbé, Mael AU - Wintraecken, Mathijs ID - 6672 IS - 3 JF - SIAM Journal on Computing SN - 0097-5397 TI - Anisotropic triangulations via discrete Riemannian Voronoi diagrams VL - 48 ER - TY - CONF AB - A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language. Recent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds. AU - Kolmogorov, Vladimir ID - 6725 SN - 1868-8969 T2 - 46th International Colloquium on Automata, Languages and Programming TI - Testing the complexity of a valued CSP language VL - 132 ER - TY - CHAP AB - Randomness is an essential part of any secure cryptosystem, but many constructions rely on distributions that are not uniform. This is particularly true for lattice based cryptosystems, which more often than not make use of discrete Gaussian distributions over the integers. For practical purposes it is crucial to evaluate the impact that approximation errors have on the security of a scheme to provide the best possible trade-off between security and performance. Recent years have seen surprising results allowing to use relatively low precision while maintaining high levels of security. A key insight in these results is that sampling a distribution with low relative error can provide very strong security guarantees. Since floating point numbers provide guarantees on the relative approximation error, they seem a suitable tool in this setting, but it is not obvious which sampling algorithms can actually profit from them. While previous works have shown that inversion sampling can be adapted to provide a low relative error (Pöppelmann et al., CHES 2014; Prest, ASIACRYPT 2017), other works have called into question if this is possible for other sampling techniques (Zheng et al., Eprint report 2018/309). In this work, we consider all sampling algorithms that are popular in the cryptographic setting and analyze the relationship of floating point precision and the resulting relative error. We show that all of the algorithms either natively achieve a low relative error or can be adapted to do so. AU - Walter, Michael ED - Buchmann, J ED - Nitaj, A ED - Rachidi, T ID - 6726 SN - 0302-9743 T2 - Progress in Cryptology – AFRICACRYPT 2019 TI - Sampling the integers with low relative error VL - 11627 ER - TY - JOUR AB - Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, we know from two independent works by Schürch and by Bardet et al. that the synthetic channels are partially ordered with respect to degradation. Hence, it is natural to ask whether the partial order can be exploited to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order, we can construct a polar code by computing the reliability of roughly a fraction 1/ log 3/2 N of the synthetic channels. In particular, we prove that N/ log 3/2 N is a lower bound on the number of synthetic channels to be considered and such a bound is tight up to a multiplicative factor log log N. This set of roughly N/ log 3/2 N synthetic channels is universal, in the sense that it allows one to construct polar codes for any W, and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists of reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general, and it can be used to further improve the complexity of the construction problem, in case a refined partial order on the synthetic channels of polar codes is discovered. AU - Mondelli, Marco AU - Hassani, Hamed AU - Urbanke, Rudiger ID - 6663 IS - 5 JF - IEEE TI - Construction of polar codes with sublinear complexity VL - 65 ER - TY - CONF AB - We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors x∈ℝd, r hidden units with weights {wi}1≤i≤r and output y∈ℝ, i.e., y=∑ri=1σ(w𝖳ix), with activation functions given by low-degree polynomials. In particular, if σ(x)=a0+a1x+a3x3, we prove that no polynomial-time learning algorithm can outperform the trivial predictor that assigns to each example the response variable 𝔼(y), when d3/2≪r≪d2. Our conclusion holds for a `natural data distribution', namely standard Gaussian feature vectors x, and output distributed according to a two-layer neural network with random isotropic weights, and under a certain complexity-theoretic assumption on tensor decomposition. Roughly speaking, we assume that no polynomial-time algorithm can substantially outperform current methods for tensor decomposition based on the sum-of-squares hierarchy. We also prove generalizations of this statement for higher degree polynomial activations, and non-random weight vectors. Remarkably, several existing algorithms for learning two-layer networks with rigorous guarantees are based on tensor decomposition. Our results support the idea that this is indeed the core computational difficulty in learning such networks, under the stated generative model for the data. As a side result, we show that under this model learning the network requires accurate learning of its weights, a property that does not hold in a more general setting. AU - Mondelli, Marco AU - Montanari, Andrea ID - 6747 T2 - Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics TI - On the connection between learning two-layers neural networks and tensor decomposition VL - 89 ER - TY - JOUR AB - Polar codes have gained extensive attention during the past few years and recently they have been selected for the next generation of wireless communications standards (5G). Successive-cancellation-based (SC-based) decoders, such as SC list (SCL) and SC flip (SCF), provide a reasonable error performance for polar codes at the cost of low decoding speed. Fast SC-based decoders, such as Fast-SSC, Fast-SSCL, and Fast-SSCF, identify the special constituent codes in a polar code graph off-line, produce a list of operations, store the list in memory, and feed the list to the decoder to decode the constituent codes in order efficiently, thus increasing the decoding speed. However, the list of operations is dependent on the code rate and as the rate changes, a new list is produced, making fast SC-based decoders not rate-flexible. In this paper, we propose a completely rate-flexible fast SC-based decoder by creating the list of operations directly in hardware, with low implementation complexity. We further propose a hardware architecture implementing the proposed method and show that the area occupation of the rate-flexible fast SC-based decoder in this paper is only 38% of the total area of the memory-based base-line decoder when 5G code rates are supported. AU - Hashemi, Seyyed Ali AU - Condo, Carlo AU - Mondelli, Marco AU - Gross, Warren J ID - 6750 IS - 22 JF - IEEE Transactions on Signal Processing SN - 1053587X TI - Rate-flexible fast polar decoders VL - 67 ER - TY - JOUR AB - We consider the graph class Grounded-L corresponding to graphs that admit an intersection representation by L-shaped curves, where additionally the topmost points of each curve are assumed to belong to a common horizontal line. We prove that Grounded-L graphs admit an equivalent characterisation in terms of vertex ordering with forbidden patterns. We also compare this class to related intersection classes, such as the grounded segment graphs, the monotone L-graphs (a.k.a. max point-tolerance graphs), or the outer-1-string graphs. We give constructions showing that these classes are all distinct and satisfy only trivial or previously known inclusions. AU - Jelínek, Vít AU - Töpfer, Martin ID - 6759 IS - 3 JF - Electronic Journal of Combinatorics TI - On grounded L-graphs and their relatives VL - 26 ER - TY - CONF AB - In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the qualitative winner or quantitative payoff of the game. In bidding games, in each turn, we hold an auction between the two players to determine which player moves the token. Bidding games have largely been studied with concrete bidding mechanisms that are variants of a first-price auction: in each turn both players simultaneously submit bids, the higher bidder moves the token, and pays his bid to the lower bidder in Richman bidding, to the bank in poorman bidding, and in taxman bidding, the bid is split between the other player and the bank according to a predefined constant factor. Bidding games are deterministic games. They have an intriguing connection with a fragment of stochastic games called randomturn games. We study, for the first time, a combination of bidding games with probabilistic behavior; namely, we study bidding games that are played on Markov decision processes, where the players bid for the right to choose the next action, which determines the probability distribution according to which the next vertex is chosen. We study parity and meanpayoff bidding games on MDPs and extend results from the deterministic bidding setting to the probabilistic one. AU - Avni, Guy AU - Henzinger, Thomas A AU - Ibsen-Jensen, Rasmus AU - Novotny, Petr ID - 6822 SN - 0302-9743 T2 - Proceedings of the 13th International Conference of Reachability Problems TI - Bidding games on Markov decision processes VL - 11674 ER - TY - CONF AB - The fundamental model-checking problem, given as input a model and a specification, asks for the algorithmic verification of whether the model satisfies the specification. Two classical models for reactive systems are graphs and Markov decision processes (MDPs). A basic specification formalism in the verification of reactive systems is the strong fairness (aka Streett) objective, where given different types of requests and corresponding grants, the requirement is that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All omega-regular objectives can be expressed as Streett objectives and hence they are canonical in verification. Consider graphs/MDPs with n vertices, m edges, and a Streett objectives with k pairs, and let b denote the size of the description of the Streett objective for the sets of requests and grants. The current best-known algorithm for the problem requires time O(min(n^2, m sqrt{m log n}) + b log n). In this work we present randomized near-linear time algorithms, with expected running time O~(m + b), where the O~ notation hides poly-log factors. Our randomized algorithms are near-linear in the size of the input, and hence optimal up to poly-log factors. AU - Chatterjee, Krishnendu AU - Dvorák, Wolfgang AU - Henzinger, Monika H AU - Svozil, Alexander ID - 6887 T2 - Leibniz International Proceedings in Informatics TI - Near-linear time algorithms for Streett objectives in graphs and MDPs VL - 140 ER - TY - CONF AB - In this paper, we design novel liquid time-constant recurrent neural networks for robotic control, inspired by the brain of the nematode, C. elegans. In the worm's nervous system, neurons communicate through nonlinear time-varying synaptic links established amongst them by their particular wiring structure. This property enables neurons to express liquid time-constants dynamics and therefore allows the network to originate complex behaviors with a small number of neurons. We identify neuron-pair communication motifs as design operators and use them to configure compact neuronal network structures to govern sequential robotic tasks. The networks are systematically designed to map the environmental observations to motor actions, by their hierarchical topology from sensory neurons, through recurrently-wired interneurons, to motor neurons. The networks are then parametrized in a supervised-learning scheme by a search-based algorithm. We demonstrate that obtained networks realize interpretable dynamics. We evaluate their performance in controlling mobile and arm robots, and compare their attributes to other artificial neural network-based control agents. Finally, we experimentally show their superior resilience to environmental noise, compared to the existing machine learning-based methods. AU - Lechner, Mathias AU - Hasani, Ramin AU - Zimmer, Manuel AU - Henzinger, Thomas A AU - Grosu, Radu ID - 6888 SN - 9781538660270 T2 - Proceedings - IEEE International Conference on Robotics and Automation TI - Designing worm-inspired neural networks for interpretable robotic control VL - 2019-May ER - TY - CONF AB - In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a non-terminating system and its environment. In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Bidding games are known to have a clean and elegant mathematical structure that relies on the ability of the players to submit arbitrarily small bids. Many applications, however, require a fixed granularity for the bids, which can represent, for example, the monetary value expressed in cents. We study, for the first time, the combination of discrete-bidding and infinite-duration games. Our most important result proves that these games form a large determined subclass of concurrent games, where determinacy is the strong property that there always exists exactly one player who can guarantee winning the game. In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games. We study several natural tie-breaking mechanisms and show that, while some do not admit determinacy, most natural mechanisms imply determinacy for every pair of initial budgets. AU - Aghajohari, Milad AU - Avni, Guy AU - Henzinger, Thomas A ID - 6886 TI - Determinacy in discrete-bidding infinite-duration games VL - 140 ER - TY - CONF AB - A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open. AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Otop, Jan ID - 6885 TI - Long-run average behavior of vector addition systems with states VL - 140 ER - TY - CONF AB - We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths to satisfy the condition, almost-sure winning, which requires the condition to be satisfied with probability 1, and limit-sure winning, which requires the condition to be satisfied with probability arbitrarily close to 1. We study the combination of two of these criteria for parity conditions, e.g., there are two parity conditions one of which must be won surely, and the other almost-surely. The problem has been studied recently by Berthon et al. for MDPs with combination of sure and almost-sure winning, under infinite-memory strategies, and the problem has been established to be in NP cap co-NP. Even in MDPs there is a difference between finite-memory and infinite-memory strategies. Our main results for combination of sure and almost-sure winning are as follows: (a) we show that for MDPs with finite-memory strategies the problem is in NP cap co-NP; (b) we show that for turn-based stochastic games the problem is co-NP-complete, both for finite-memory and infinite-memory strategies; and (c) we present algorithmic results for the finite-memory case, both for MDPs and turn-based stochastic games, by reduction to non-stochastic parity games. In addition we show that all the above complexity results also carry over to combination of sure and limit-sure winning, and results for all other combinations can be derived from existing results in the literature. Thus we present a complete picture for the study of combinations of two qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games. AU - Chatterjee, Krishnendu AU - Piterman, Nir ID - 6889 TI - Combinations of Qualitative Winning for Stochastic Parity Games VL - 140 ER - TY - CONF AB - Consider a distributed system with n processors out of which f can be Byzantine faulty. In the approximate agreement task, each processor i receives an input value xi and has to decide on an output value yi such that 1. the output values are in the convex hull of the non-faulty processors’ input values, 2. the output values are within distance d of each other. Classically, the values are assumed to be from an m-dimensional Euclidean space, where m ≥ 1. In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to output vertices that are within distance d of each other in G, but still remain in the graph-induced convex hull of the input values. For d = 0, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any d ≥ 1, we show that the task is solvable in asynchronous systems when G is chordal and n > (ω + 1)f, where ω is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures. AU - Nowak, Thomas AU - Rybicki, Joel ID - 6931 KW - consensus KW - approximate agreement KW - Byzantine faults KW - chordal graphs KW - lattice agreement T2 - 33rd International Symposium on Distributed Computing TI - Byzantine approximate agreement on graphs VL - 146 ER - TY - CONF AB - In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked contribution of individual cells to the network's output is computed by analyzing a set of interpretable metrics of their decoupled step and sinusoidal responses. As a result, our method is able to uniquely identify neurons with insightful dynamics, quantify relationships between dynamical properties and test accuracy through ablation analysis, and interpret the impact of network capacity on a network's dynamical distribution. Finally, we demonstrate the generalizability and scalability of our method by evaluating a series of different benchmark sequential datasets. AU - Hasani, Ramin AU - Amini, Alexander AU - Lechner, Mathias AU - Naser, Felix AU - Grosu, Radu AU - Rus, Daniela ID - 6985 SN - 9781728119854 T2 - Proceedings of the International Joint Conference on Neural Networks TI - Response characterization for auditing cell dynamics in long short-term memory networks ER -