Level-Based Analysis of the Population-Based Incremental Learning Algorithm

The Population-Based Incremental Learning (PBIL) algorithm uses a convex combination of the current model and the empirical model to construct the next model, which is then sampled to generate offspring. The Univariate Marginal Distribution Algorithm (UMDA) is a special case of the PBIL, where the current model is ignored. Dang and Lehre (GECCO 2015) showed that UMDA can optimise LeadingOnes efficiently. The question still remained open if the PBIL performs equally well. Here, by applying the level-based theorem in addition to Dvoretzky--Kiefer--Wolfowitz inequality, we show that the PBIL optimises function LeadingOnes in expected time $\mathcal{O}(n\lambda \log \lambda + n^2)$ for a population size $\lambda = \Omega(\log n)$, which matches the bound of the UMDA. Finally, we show that the result carries over to BinVal, giving the fist runtime result for the PBIL on the BinVal problem.Comment: To appea

Fourth order indirect integration method for black hole perturbations: even modes

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth order algorithm for non-rotating black hole perturbations in the Regge-Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the $(r^*,t)$ grid cell is obtained by an algebraic sum of i) the preceding node values of the same cell, ii) analytic expressions, related to the jump conditions on the wave function and its derivatives, iii) the values of the wave function at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be object of a forthcoming publication.Comment: This series of papers deals with EMRI for LISA. With the respect to the v1 version, the algorithm has been improved; convergence tests and references have been added; v2 is composed by 23 pages, and 6 figures. Paper accepted by Class. Quantum Gravity for the special issue on Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (Capra and NRDA) at Perimeier Institute in June 201

Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions

Bifinite Chu Spaces

This paper studies colimits of sequences of finite Chu spaces and their ramifications. Besides generic Chu spaces, we consider extensional and biextensional variants. In the corresponding categories we first characterize the monics and then the existence (or the lack thereof) of the desired colimits. In each case, we provide a characterization of the finite objects in terms of monomorphisms/injections. Bifinite Chu spaces are then expressed with respect to the monics of generic Chu spaces, and universal, homogeneous Chu spaces are shown to exist in this category. Unanticipated results driving this development include the fact that while for generic Chu spaces monics consist of an injective first and a surjective second component, in the extensional and biextensional cases the surjectivity requirement can be dropped. Furthermore, the desired colimits are only guaranteed to exist in the extensional case. Finally, not all finite Chu spaces (considered set-theoretically) are finite objects in their categories. This study opens up opportunities for further investigations into recursively defined Chu spaces, as well as constructive models of linear logic

Near-Optimal Scheduling for LTL with Future Discounting

We study the search problem for optimal schedulers for the linear temporal logic (LTL) with future discounting. The logic, introduced by Almagor, Boker and Kupferman, is a quantitative variant of LTL in which an event in the far future has only discounted contribution to a truth value (that is a real number in the unit interval [0, 1]). The precise problem we study---it naturally arises e.g. in search for a scheduler that recovers from an internal error state as soon as possible---is the following: given a Kripke frame, a formula and a number in [0, 1] called a margin, find a path of the Kripke frame that is optimal with respect to the formula up to the prescribed margin (a truly optimal path may not exist). We present an algorithm for the problem; it works even in the extended setting with propositional quality operators, a setting where (threshold) model-checking is known to be undecidable

Evolution of Conventions in Endogenous Social Networks

We analyze the dynamic implications of learning in a large population coordination game where both the actions of the players and the communication network between these players evolve over time. We depart from the conventional models in assuming that the interaction network itself is subject to evolutionary pressure. Cost considerations of social interaction are incorporated by application of a circular model in which all players are located at equal distances along a circle. Although the locations of the players are fixed they can create their own interaction neighborhood by forming and severing links with other players. The spatial structure of the model is then used to determine the costs of establishing a communication link between a pair of players. Namely, we assume that the larger the distance between two players on the circle, the larger the maintenance costs of the mutual link will be. As maintenance costs include invested time and effort, distance should not only be interpreted as physical distance but may also represent social distance. We follow standard evolutionary game theoretic practice to determine the equilibria in this setting. The resulting equilibrium represents the players' medium run behavior if perturbations representing players' mistakes are absent. We find that in this medium run case, the dynamic process converges to an absorbing state. These absorbing states include ones in which there emerge local conventions, i.e., fully connected neighborhoods of players who coordinate on the same strategy. In the ultralong run, i.e., when perturbations representing players' mistakes are taken into account, coexistence of conventions is no longer possible. We show that the risk-dominant convention is the unique stochastically stable convention, meaning that it will be observed almost surely when the mistake probabilities are small but nonvanishing. This confirms the insights obtained in Ellison (1993) for fixed spatial interaction structures.

Integrated Structure and Semantics for Reo Connectors and Petri Nets

In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models. For this purpose, we introduce a notion of connectors which consist of a number of interconnected, user-defined primitives with fixed behavior. While the structure of connectors resembles hypergraphs, their semantics is given in terms of so-called port automata. We define both models in a categorical setting where composition operations can be elegantly defined and integrated. Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks. We then define a semantical functor from the connector to the port automata category which preserves this composition. We further show how to encode Reo connectors and Petri nets into this model and indicate applications to dynamic reconfigurations modeled using double pushout graph transformation

Fragments of the earliest land plants

The earliest fossil evidence for land plants comes from microscopic dispersed spores. These microfossils are abundant and widely distributed in sediments, and the earliest generally accepted reports are from rocks of mid-Ordovician age (Llanvirn, 475 million years ago). Although distribution, morphology and ultrastructure of the spores indicate that they are derived from terrestrial plants, possibly early relatives of the bryophytes, this interpretation remains controversial as there is little in the way of direct evidence for the parent plants. An additional complicating factor is that there is a significant hiatus between the appearance of the first dispersed spores and fossils of relatively complete land plants (megafossils): spores predate the earliest megafossils (Late Silurian, 425 million year ago) by some 50 million years. Here we report the description of spore-containing plant fragments from Ordovician rocks of Oman. These fossils provide direct evidence for the nature of the spore-producing plants. They confirm that the earliest spores developed in large numbers within sporangia, providing strong evidence that they are the fossilized remains of bona fide land plants. Furthermore, analysis of spore wall ultrastructure supports liverwort affinities

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far

Holonomy in the Schwarzschild-Droste Geometry

Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such holonomy in the Schwarzschild-Droste geometry and find a number of interesting features that are not widely known. For example, parallel transport around circular orbits results in a quantized band structure of holonomy invariance. We also examine radial holonomy and extend the analysis to spinors and to the Reissner-Nordstr\"om metric, where we find qualitatively different behavior for the extremal ($Q = M$) case. Our calculations provide a toolbox that will hopefully be useful in the investigation of quantum parallel transport in Hilbert-fibered spacetimes.Comment: 18 Latex pages, 3 figures. Second replacement. This version as published in CQG with some misprints correcte