Related papers: Packing Dimension Profiles and Levy Processes

We prove a new rearrangement inequality for multiple integrals, which partly generalizes a result of Friedberg and Luttinger (1976) and can be interpreted as involving symmetric rearrangements of domains around infinity. As applications, we…

The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…

We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more…

We determine the Hausdorff, packing and box-counting dimension of a family of self-affine sets generalizing Bara\'nski carpets. More specifically, we fix a Bara\'nski system and allow both vertical and horizontal random translations, while…

In 1988 K. Falconer introduced a formula which predicts the value of the Hausdorff dimension of the attractor of an affine iterated function system. The value given by this formula -- sometimes referred to as the affinity dimension -- is…

In this paper using the concept of the extended Hamming code we give a construction for dense packing of points at distance at least one in such unit cubes which dimension are a power of two.

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the analogous results in complex analytic…

The probability distributions, as well as the mean values of stochastic currents and fluxes, associated with a driven Langevin process, provide a good and topologically protected measure of how far a stochastic system is driven out of…

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…

For a (killed) spectrally negative L\'evy process we provide an analytic expression for the distribution of its overshoot over a fixed level in terms of the infinitesimal generator and the scale function of the process. Our identity…

We prove that the packing dimension of any mean porous Radon measure on $\mathbb R^d$ may be estimated from above by a function which depends on mean porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum value. This…

We provide the first known upper bounds for the packing dimension of weighted singular and weighted $\omega$-singular matrices. We also prove upper bounds for these sets when intersected with fractal subsets. The latter results, even in the…

For a one-dimensional L\'{e}vy process, we derive an explicit formula for the probability of first hitting a specified point among a fixed finite set. Moreover, using this formula, we obtain an explicit expression for each entry of the…

We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…

We give upper and lower estimates of densities of convolution semigroups of probability measures under explicit assumptions on the corresponding Levy measure and the Levy--Khinchin exponent. We obtain also estimates of derivatives of…

We relate the notion of dimension expanders to quiver representations and their general subrepresentations, and use this relation to establish sharp existence results.

Computer-based interactive items have become prevalent in recent educational assessments. In such items, the entire human-computer interactive process is recorded in a log file and is known as the response process. This paper aims at…

The aim of this research is to make a step towards providing a tool for model selection for log-density estimation. The author revisits the procedure for local log-density estimation suggested by Clive Loader (1996) and extends the…

Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that…