142,318 research outputs found

    Greedy adaptive walks on a correlated fitness landscape

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    We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length LL. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached. The landscape is of the rough mount Fuji type, which means that the fitness value assigned to a sequence is the sum of a random and a deterministic component. The random components are independent and identically distributed random variables, and the deterministic component varies linearly with the distance to a reference sequence. The deterministic fitness gradient cc is a parameter that interpolates between the limits of an uncorrelated random landscape (c=0c = 0) and an effectively additive landscape (c→∞c \to \infty). When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence. Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for L→∞L \to \infty, different from its values for c=0c=0 and c=∞c = \infty, if cc is scaled with LL in an appropriate combination.Comment: minor change

    Coherence effects in Mie scattering

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    The scattering of a partially coherent beam by a deterministic, spherical scatterer is studied. In particular, the Mie scattering by a Gaussian Schell-model beam is analyzed. Expressions are derived for (a) the extinguished power, (b) the radiant intensity of the scattered field, and (c) the encircled energy in the far field. It is found that the radiant intensity and the encircled energy in the far field depend on the degree of coherence of the incident beam, whereas the extinguished power does not. (C) 2011 Optical Society of Americ

    Non-Deterministic Kleene Coalgebras

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    In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems such as Mealy and Moore machines

    On the Hierarchy of Block Deterministic Languages

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    A regular language is kk-lookahead deterministic (resp. kk-block deterministic) if it is specified by a kk-lookahead deterministic (resp. kk-block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood (kk-lookahead determinism) and by Giammarresi et al. (kk-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each kk-block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a kk-block deterministic regular language to a kk-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in kk-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in kk-block deterministic regular languages. We also prove that there is a proper hierarchy in kk-lookahead deterministic regular languages by studying particular properties of unary regular expressions. Finally, using our valid results, we confirm that the family of kk-block deterministic regular languages is strictly included into the one of kk-lookahead deterministic regular languages by showing that any kk-block deterministic unary language is one-unambiguous

    The Power of Non-Determinism in Higher-Order Implicit Complexity

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    We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice. Cons-freeness roughly means that data constructors cannot occur in function bodies and all manipulation of storage space thus has to happen indirectly using the call stack. While cons-free programs have previously been used by several authors to characterise complexity classes, the work on non-deterministic programs has almost exclusively considered programs of data order 0. Previous work has shown that adding explicit non-determinism to cons-free programs taking data of order 0 does not increase expressivity; we prove that this - dramatically - is not the case for higher data orders: adding non-determinism to programs with data order at least 1 allows for a characterisation of the entire class of elementary-time decidable sets. Finally we show how, even with non-deterministic choice, the original hierarchy of characterisations is restored by imposing different restrictions.Comment: pre-edition version of a paper accepted for publication at ESOP'1
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