Search results for "Descriptive set theory"
showing 10 items of 94 documents
Complex ecological models with simple dynamics: From individuals to populations
1994
The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for food of different types. The degree of competition as well as the predation pressure are dependent upon these activities. Preys are more vulnerable when doing some activities during which they are …
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
The small-world of 'Le Petit Prince': Revisiting the word frequency distribution
2016
[EN] Many complex systems are naturally described through graph theory, and different kinds of systems described as networks present certain important characteristics in common. One of these features is the so-called scale-free distribution for its node s connectivity, which means that the degree distribution for the network s nodes follows a power law. Scale-free networks are usually referred to as small-world because the average distance between their nodes do not scale linearly with the size of the network, but logarithmically. Here we present a mathematical analysis on linguistics: the word frequency effect for different translations of the Le Petit Prince in different languages. Compar…
Loop-free Gray code algorithm for the e-restricted growth functions
2011
The subject of Gray codes algorithms for the set partitions of {1,2,...,n} had been covered in several works. The first Gray code for that set was introduced by Knuth (1975) [5], later, Ruskey presented a modified version of [email protected]?s algorithm with distance two, Ehrlich (1973) [3] introduced a loop-free algorithm for the set of partitions of {1,2,...,n}, Ruskey and Savage (1994) [9] generalized [email protected]?s results and give two Gray codes for the set of partitions of {1,2,...,n}, and recently, Mansour et al. (2008) [7] gave another Gray code and loop-free generating algorithm for that set by adopting plane tree techniques. In this paper, we introduce the set of e-restricte…
Any AND-OR Formula of Size N Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
2007
Consider the problem of evaluating an AND-OR formula on an $N$-bit black-box input. We present a bounded-error quantum algorithm that solves this problem in time $N^{1/2+o(1)}$. In particular, approximately balanced formulas can be evaluated in $O(\sqrt{N})$ queries, which is optimal. The idea of the algorithm is to apply phase estimation to a discrete-time quantum walk on a weighted tree whose spectrum encodes the value of the formula.
A Note on Algebraic Sums of Subsets of the Real Line
2002
AbstractWe investigate the algebraic sums of sets for a large class of invari-ant ˙-ideals and ˙- elds of subsets of the real line. We give a simpleexample of two Borel subsets of the real line such that its algebraicsum is not a Borel set. Next we show a similar result to Proposition 2from A. Kharazishvili paper [4]. Our results are obtained for ideals withcoanalytical bases. 1 Introduction We shall work in ZFC set theory. By !we denote natural numbers. By 4wedenote the symmetric di erence of sets. The cardinality of a set Xwe denoteby jXj. By R we denote the real line and by Q we denote rational numbers. IfAand Bare subsets of R n and b2R , then A+B= fa+b: a2A^b2Bgand A+ b= A+ fbg. Simila…
Circular sturmian words and Hopcroft’s algorithm
2009
AbstractIn order to analyze some extremal cases of Hopcroft’s algorithm, we investigate the relationships between the combinatorial properties of a circular sturmian word (x) and the run of the algorithm on the cyclic automaton Ax associated to (x). The combinatorial properties of words taken into account make use of sturmian morphisms and give rise to the notion of reduction tree of a circular sturmian word. We prove that the shape of this tree uniquely characterizes the word itself. The properties of the run of Hopcroft’s algorithm are expressed in terms of the derivation tree of the automaton, which is a tree that represents the refinement process that, in the execution of Hopcroft’s alg…
Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property
2010
Abstract Let X be a Banach space. For describing the space P ( C [ 0 , 1 ] , X ) of absolutely summing operators from C [ 0 , 1 ] to X in terms of the space X itself, we construct a tree space l 1 tree ( X ) on X. It consists of special trees in X which we call two-trunk trees. We prove that P ( C [ 0 , 1 ] , X ) is isometrically isomorphic to l 1 tree ( X ) . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X ∗ -valued sequence spaces.
A two-scale approach to electron correlation in multiconfigurational perturbation theory.
2014
We present a new approach for the calculation of dynamic electron correlation effects in large molecular systems using multiconfigurational second-order perturbation theory (CASPT2). The method is restricted to cases where partitioning of the molecular system into an active site and an environment is meaningful. Only dynamic correlation effects derived from orbitals extending over the active site are included at the CASPT2 level of theory, whereas the correlation effects of the environment are retrieved at lower computational costs. For sufficiently large systems, the small errors introduced by this approximation are contrasted by the substantial savings in both storage and computational de…
New Flexible Probability Distributions for Ranking Data
2015
Recently, several models have been proposed in literature for analyzing ranks assigned by people to some object. These models summarize the liking feeling for this object, possibly also with respect to a set of explanatory variables. Some recent works have suggested the use of the Shifted Binomial and of the Inverse Hypergeometric distribution for modelling the approval rate, while mixture models have been developed for taking into account the uncertainty of the ranking process. We propose two new probabilistic models, based on the Discrete Beta and the Shifted-Beta Binomial distributions, that ensure much flexibility and allow the joint modelling of the scale (approval rate) and the shape …