TY - JOUR
AB - Opacity is a generic security property, that has been defined on (non-probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non-deterministicchoice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and ω-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non-opaquebecomes decidable for a restricted class of ω-regular secrets, as well as for all ω-regular secrets under finite-memory schedulers.
AU - Bérard, Béatrice
AU - Chatterjee, Krishnendu
AU - Sznajder, Nathalie
ID - 2034
IS - 1
JF - Information Processing Letters
TI - Probabilistic opacity for Markov decision processes
VL - 115
ER -
TY - JOUR
AB - Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.
AU - Edelsbrunner, Herbert
AU - Jablonski, Grzegorz
AU - Mrozek, Marian
ID - 2035
IS - 5
JF - Foundations of Computational Mathematics
TI - The persistent homology of a self-map
VL - 15
ER -
TY - JOUR
AB - We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer.
AU - Nam, Phan
AU - Seiringer, Robert
ID - 2085
IS - 2
JF - Archive for Rational Mechanics and Analysis
TI - Collective excitations of Bose gases in the mean-field regime
VL - 215
ER -
TY - JOUR
AB - We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014).
AU - Erdös, László
AU - Knowles, Antti
ID - 2166
IS - 3
JF - Communications in Mathematical Physics
TI - The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case
VL - 333
ER -
TY - JOUR
AB - Currently, there is much debate on the genetic architecture of quantitative traits in wild populations. Is trait variation influenced by many genes of small effect or by a few genes of major effect? Where is additive genetic variation located in the genome? Do the same loci cause similar phenotypic variation in different populations? Great tits (Parus major) have been studied extensively in long‐term studies across Europe and consequently are considered an ecological ‘model organism’. Recently, genomic resources have been developed for the great tit, including a custom SNP chip and genetic linkage map. In this study, we used a suite of approaches to investigate the genetic architecture of eight quantitative traits in two long‐term study populations of great tits—one in the Netherlands and the other in the United Kingdom. Overall, we found little evidence for the presence of genes of large effects in either population. Instead, traits appeared to be influenced by many genes of small effect, with conservative estimates of the number of contributing loci ranging from 31 to 310. Despite concordance between population‐specific heritabilities, we found no evidence for the presence of loci having similar effects in both populations. While population‐specific genetic architectures are possible, an undetected shared architecture cannot be rejected because of limited power to map loci of small and moderate effects. This study is one of few examples of genetic architecture analysis in replicated wild populations and highlights some of the challenges and limitations researchers will face when attempting similar molecular quantitative genetic studies in free‐living populations.
AU - Santure, Anna W.
AU - Poissant, Jocelyn
AU - De Cauwer, Isabelle
AU - van Oers, Kees
AU - Robinson, Matthew Richard
AU - Quinn, John L.
AU - Groenen, Martien A. M.
AU - Visser, Marcel E.
AU - Sheldon, Ben C.
AU - Slate, Jon
ID - 7739
JF - Molecular Ecology
SN - 0962-1083
TI - Replicated analysis of the genetic architecture of quantitative traits in two wild great tit populations
VL - 24
ER -
TY - JOUR
AB - Phenotypes expressed in a social context are not only a function of the individual, but can also be shaped by the phenotypes of social partners. These social effects may play a major role in the evolution of cooperative breeding if social partners differ in the quality of care they provide and if individual carers adjust their effort in relation to that of other carers. When applying social effects models to wild study systems, it is also important to explore sources of individual plasticity that could masquerade as social effects. We studied offspring provisioning rates of parents and helpers in a wild population of long-tailed tits Aegithalos caudatus using a quantitative genetic framework to identify these social effects and partition them into genetic, permanent environment and current environment components. Controlling for other effects, individuals were consistent in their provisioning effort at a given nest, but adjusted their effort based on who was in their social group, indicating the presence of social effects. However, these social effects differed between years and social contexts, indicating a current environment effect, rather than indicating a genetic or permanent environment effect. While this study reveals the importance of examining environmental and genetic sources of social effects, the framework we present is entirely general, enabling a greater understanding of potentially important social effects within any ecological population.
AU - Adams, Mark James
AU - Robinson, Matthew Richard
AU - Mannarelli, Maria-Elena
AU - Hatchwell, Ben J.
ID - 7741
IS - 1810
JF - Proceedings of the Royal Society B: Biological Sciences
SN - 0962-8452
TI - Social genetic and social environment effects on parental and helper care in a cooperatively breeding bird
VL - 282
ER -
TY - GEN
AB - The fact that a disordered material is not constrained in its properties in
the same way as a crystal presents significant and yet largely untapped
potential for novel material design. However, unlike their crystalline
counterparts, disordered solids are not well understood. One of the primary
obstacles is the lack of a theoretical framework for thinking about disorder
and its relation to mechanical properties. To this end, we study an idealized
system of frictionless athermal soft spheres that, when compressed, undergoes a
jamming phase transition with diverging length scales and clean power-law
signatures. This critical point is the cornerstone of a much larger "jamming
scenario" that has the potential to provide the essential theoretical
foundation necessary for a unified understanding of the mechanics of disordered
solids. We begin by showing that jammed sphere packings have a valid linear
regime despite the presence of "contact nonlinearities." We then investigate
the critical nature of the transition, focusing on diverging length scales and
finite-size effects. Next, we argue that jamming plays the same role for
disordered solids as the perfect crystal plays for crystalline solids. Not only
can it be considered an idealized starting point for understanding disordered
materials, but it can even influence systems that have a relatively high amount
of crystalline order. The behavior of solids can thus be thought of as existing
on a spectrum, with the perfect crystal and the jamming transition at opposing
ends. Finally, we introduce a new principle wherein the contribution of an
individual bond to one global property is independent of its contribution to
another. This principle allows the different global responses of a disordered
system to be manipulated independently and provides a great deal of flexibility
in designing materials with unique, textured and tunable properties.
AU - Goodrich, Carl Peter
ID - 7779
T2 - arXiv:1510.08820
TI - Unearthing the anticrystal: Criticality in the linear response of disordered solids
ER -
TY - CONF
AB - Several Hybrid Transactional Memory (HyTM) schemes have recently been proposed to complement the fast, but best-effort nature of Hardware Transactional Memory (HTM) with a slow, reliable software backup. However, the costs of providing concurrency between hardware and software transactions in HyTM are still not well understood. In this paper, we propose a general model for HyTM implementations, which captures the ability of hardware transactions to buffer memory accesses. The model allows us to formally quantify and analyze the amount of overhead (instrumentation) caused by the potential presence of software transactions.We prove that (1) it is impossible to build a strictly serializable HyTM implementation that has both uninstrumented reads and writes, even for very weak progress guarantees, and (2) the instrumentation cost incurred by a hardware transaction in any progressive opaque HyTM is linear in the size of the transaction’s data set.We further describe two implementations which exhibit optimal instrumentation costs for two different progress conditions. In sum, this paper proposes the first formal HyTM model and captures for the first time the trade-off between the degree of hardware-software TM concurrency and the amount of instrumentation overhead.
AU - Alistarh, Dan-Adrian
AU - Kopinsky, Justin
AU - Kuznetsov, Petr
AU - Ravi, Srivatsan
AU - Shavit, Nir
ID - 778
TI - Inherent limitations of hybrid transactional memory
VL - 9363
ER -
TY - CONF
AB - Population protocols are networks of finite-state agents, interacting randomly, and updating their states using simple rules. Despite their extreme simplicity, these systems have been shown to cooperatively perform complex computational tasks, such as simulating register machines to compute standard arithmetic functions. The election of a unique leader agent is a key requirement in such computational constructions. Yet, the fastest currently known population protocol for electing a leader only has linear convergence time, and it has recently been shown that no population protocol using a constant number of states per node may overcome this linear bound. In this paper, we give the first population protocol for leader election with polylogarithmic convergence time, using polylogarithmic memory states per node. The protocol structure is quite simple: each node has an associated value, and is either a leader (still in contention) or a minion (following some leader). A leader keeps incrementing its value and “defeats” other leaders in one-to-one interactions, and will drop from contention and become a minion if it meets a leader with higher value. Importantly, a leader also drops out if it meets a minion with higher absolute value. While these rules are quite simple, the proof that this algorithm achieves polylogarithmic convergence time is non-trivial. In particular, the argument combines careful use of concentration inequalities with anti-concentration bounds, showing that the leaders’ values become spread apart as the execution progresses, which in turn implies that straggling leaders get quickly eliminated. We complement our analysis with empirical results, showing that our protocol converges extremely fast, even for large network sizes.
AU - Alistarh, Dan-Adrian
AU - Gelashvili, Rati
ID - 780
TI - Polylogarithmic-time leader election in population protocols
VL - 9135
ER -
TY - CONF
AB - The problem of electing a leader from among n contenders is one of the fundamental questions in distributed computing. In its simplest formulation, the task is as follows: given n processors, all participants must eventually return a win or lose indication, such that a single contender may win. Despite a considerable amount of work on leader election, the following question is still open: can we elect a leader in an asynchronous fault-prone system faster than just running a Θ(log n)-time tournament, against a strong adaptive adversary? In this paper, we answer this question in the affirmative, improving on a decades-old upper bound. We introduce two new algorithmic ideas to reduce the time complexity of electing a leader to O(log∗ n), using O(n2) point-to-point messages. A non-trivial application of our algorithm is a new upper bound for the tight renaming problem, assigning n items to the n participants in expected O(log2 n) time and O(n2) messages. We complement our results with lower bound of Ω(n2) messages for solving these two problems, closing the question of their message complexity.
AU - Alistarh, Dan-Adrian
AU - Gelashvili, Rati
AU - Vladu, Adrian
ID - 783
TI - How to elect a leader faster than a tournament
VL - 2015-July
ER -
TY - JOUR
AB - We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrödinger functional on a finite interval, as well as smoother interactions in dimensions d 2.
AU - Lewin, Mathieu
AU - Phan Thanh, Nam
AU - Rougerie, Nicolas
ID - 473
JF - Journal de l'Ecole Polytechnique - Mathematiques
TI - Derivation of nonlinear gibbs measures from many-body quantum mechanics
VL - 2
ER -
TY - JOUR
AB - We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Randour, Mickael
AU - Raskin, Jean
ID - 523
IS - 6
JF - Information and Computation
TI - Looking at mean-payoff and total-payoff through windows
VL - 242
ER -
TY - JOUR
AB - We consider concurrent games played by two players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 524
IS - 6
JF - Information and Computation
TI - Qualitative analysis of concurrent mean payoff games
VL - 242
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics.
Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions.
Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5429
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - GEN
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5430
SN - 2664-1690
TI - Faster algorithms for quantitative verification in constant treewidth graphs
ER -
TY - GEN
AB - We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. We consider reachability objectives that given a target set of states require that some state in the target set is visited, and the dual safety objectives that given a target set require that only states in the target set are visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed.
Our main results are as follows: We show that in two-player zero-sum concurrent stochastic games (with reachability objective for one player and the complementary safety objective for the other player): (i) the optimal bound on the patience of optimal and epsilon-optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. In general we study the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that if there is at least one player with reachability objective, then doubly-exponential patience is needed in general for epsilon-Nash equilibrium strategies, whereas in contrast if all players have safety objectives, then the optimal bound on patience for epsilon-Nash equilibrium strategies is only exponential.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Hansen, Kristoffer
ID - 5431
SN - 2664-1690
TI - The patience of concurrent stochastic games with safety and reachability objectives
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction.
The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability.
Our main results are:
(1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure).
(2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5432
SN - 2664-1690
TI - The complexity of evolutionary games on graphs
ER -
TY - GEN
AB - DEC-POMDPs extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. DEC-POMDPs have been studied with finite-horizon and infinite-horizon discounted-sum objectives, and there exist solvers both for exact and approximate solutions. In this work we consider Goal-DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost. We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new method to solve the problem that extends methods for finite-horizon DEC- POMDPs and the RTDP-Bel approach for POMDPs. We present experimental results on several examples, and show our approach presents promising results.
AU - Anonymous, 1
AU - Anonymous, 2
ID - 5434
SN - 2664-1690
TI - Optimal cost indefinite-horizon reachability in goal DEC-POMDPs
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP.
We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5435
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - GEN
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time.
In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5436
SN - 2664-1690
TI - Nested weighted automata
ER -