We study the mixing time of random graphs in the d-dimensional toric unit cube [0, 1] generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights, drawn from s...

We use effective domain theory to introduce a notion of effectivity for test functions and for distributions. We will show that the Fourier transform on S is effective, and that this results lifts to the space of tempered distributions. We also show that convolution is an effective operation on distributions. Finally, as an application of this result we show that it is possible to compute primi...

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson distributed, and the probability of no isolated nodes is equal to the probability the ...

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis & Loukas (1998). The new distribution arises on a latent complementary risks scenarios, where the lifetime associated with a particular risk is not observable, rathe...

Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent conclusions can be more straightly obtained from simple statistics. The different facets of kinetic constants are first classified and clarified with respect to...

OBJECTIVE The common sextant prostate biopsy schema lacks a three-dimensional (3D) geometric definition. The study objective was to determine the influence of the geometric distribution of the cores on the detection probability of prostate cancer (PCa). METHODS The detection probability of significant (>0.5 cm3) and insignificant (<0.2 cm3) tumors was quantified based on a novel 3D capsule mo...