142,345 research outputs found
Greedy adaptive walks on a correlated fitness landscape
We study adaptation of a haploid asexual population on a fitness landscape
defined over binary genotype sequences of length . 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 is a
parameter that interpolates between the limits of an uncorrelated random
landscape () and an effectively additive landscape ().
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 , different from its values for and
, if is scaled with in an appropriate combination.Comment: minor change
Coherence effects in Mie scattering
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
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
A regular language is -lookahead deterministic (resp. -block
deterministic) if it is specified by a -lookahead deterministic (resp.
-block deterministic) regular expression. These two subclasses of regular
languages have been respectively introduced by Han and Wood (-lookahead
determinism) and by Giammarresi et al. (-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 -block
deterministic language is the alphabetic image of some one-unambiguous
language. Moreover, we show that the conversion from a minimal DFA of a
-block deterministic regular language to a -block deterministic automaton
not only requires state elimination, and that the proof given by Han and Wood
of a proper hierarchy in -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 -block deterministic regular languages.
We also prove that there is a proper hierarchy in -lookahead deterministic
regular languages by studying particular properties of unary regular
expressions. Finally, using our valid results, we confirm that the family of
-block deterministic regular languages is strictly included into the one of
-lookahead deterministic regular languages by showing that any -block
deterministic unary language is one-unambiguous
The Power of Non-Determinism in Higher-Order Implicit Complexity
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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