Consider the problem of calculating the fractal dimension of a set X consisting of all infinite sequences S over a finite alphabet Σ that satisfy some given condition P on the asymptotic frequencies with which various symbols from Σ appear in S. Solutions to this problem are known in cases where (i) the fractal dimension is classical (Hausdorff or packing dimension), or (ii) the fractal dimensi...

Let X = {X(t), t ∈ RN} be a Gaussian random field with values in R defined by X(t) = ( X1(t), . . . , Xd(t) ) , ∀ t ∈ R , where X1, . . . , Xd are independent copies of a centered Gaussian random field X0. Under certain general conditions, Xiao (2007a) defined an upper index α∗ and a lower index α∗ for X0 and showed that the Hausdorff dimensions of the range X ( [0, 1] ) and graph GrX ( [0, 1] ...

This paper is concerned with various combinatorial parameters of classes that can be learned from a small set of examples. We show that the recursive teaching dimension, recently introduced by Zilles et al. (2008), is strongly connected to known complexity notions in machine learning, e.g., the self-directed learning complexity and the VC-dimension. To the best of our knowledge these are the fi...

We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the “global measure formula” for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we ...

We construct a Π1-class X that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective packing dimension. We also examine the relationship between upper box dimension and packing dimension for Π1-classes.

Let χ be a finite Borel measure on [0, 1]. Consider the L-spectrum of χ: τχ(q) = lim infn→∞−n logb P Q∈Gn, χ(Q) 6=0 χ(Q) , where Gn is the set of b-adic cubes of generation n. Let qτ = inf{q : τχ(q) = 0} and Hτ = τ ′ χ(q − τ ). When χ is a mono-dimensional continuous measure of information dimension D, (qτ , Hτ ) = (1, D). When χ is purely discontinuous, its information dimension is D = 0, but ...

The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite sequence CEk(A) formed by concatenating the base-k representations of the elements of A in numerical order. This paper concerns the following four quantities. • The finite-state dimension dimFS(CEk(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. • The finite-state ...

Although the existence of cosmic rays with energies extending well above 1019 eV has been confirmed, their origin remains one of the most important questions in astroparticle physics today. Several source models have been proposed for the observed set of Ultra High Energy Cosmic Rays (UHECRs). Yet none of these models have been conclusively identified as corresponding with all of the available ...

We construct a Π1-class X that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective packing dimension. We also examine the relationship between upper box dimension and packing dimension for Π1-classes.

research has consistently indicated that worker turnover intentions are factors external to an employee; however, little work has investigated turnover intention behavior from personality perspective in a context of a private university in a low resourced country like uganda.  the purpose of this study was to investigate the effect of individual personality dimensions and job turnover intention...