Three aspects of texture are considered by the fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Fractal Dimension has been well studied; a great number of approaches have been presented to extract it from images. It can be computed from black-white to multi-band image. There are many approaches also, from the simple Box-Dimension to the most complex Hausdorff Dimension. The...

In this paper we present some new properties of the metric dimension defined by Bouligand in 1928 and prove the following new projection theorem: Let dimb(A − A) denote the Bouligand dimension of the set A − A of differences between elements of A. Given any compact set A ⊆ R such that dimb(A−A) < m, then almost every orthogonal projection P of A of rank m is injective on A and P |A has Lipschit...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

Drug molecules consist of a few tens of atoms connected by covalent bonds. How many such molecules are possible in total and what is their structure? This question is of pressing interest in medicinal chemistry to help solve the problems of drug potency, selectivity, and toxicity and reduce attrition rates by pointing to new molecular series. To better define the unknown chemical space, we have...

Despite widely differing methodologies, previous studies on affect (emotion as represented in language) have often obtained what appear to be the same basic dimensions. Whether these similarly named dimensions from different methodologies are actually equivalent was tested here by intercorrelating dimensions obtained from multidimensional scaling, successive-intervals scaling, semantic differen...

The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko’s result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov complexity ≤ α to the case of exact dimension. Th...

Two experiments examined access to the semantic attributes of words that participants failed to retrieve. The results indicated access to all 3 dimensions of the semantic differential--evaluation, potency, and activity, as revealed by attribute judgments and by the nature of the commission errors made. There was no evidence for superior access to the emotional-evaluative dimension, inconsistent...

passiflora species were known by their anticonvulsant, anxiolytic and sedative activities. the aim of this study was to investigate the chemical composition of the most active leaf extract of passiflora caerulea l. grown in egypt. the ethanolic extract of the leaves exhibited higher activity than aqueous extract as anticonvulsant (63% potency relative to carbamazepine), analgesic (70% potency r...

this paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by topsis method. topsis method is technique for order preference by similarity to ideal solution. topsis is one of the renowned methods for classical multi-criteria decision-making (mcdm) problems that defines the positive ideal solution and negative ideal solution...

We analyze ‘Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the L2 risk; also,...