In this paper some reflections on the concept of transition are presented: groupoids introduced as models for construction a “generalized logic” whose basic statements involve pairs propositions which can be conditioned. We could distinguish between classical probability theory where conditioned if they have non-zero intersection, from cases “non-local” conditioning allowed. The algebraic and g...

In this work, we focus on the centered Hausdorff measure, packing and Hewitt–Stromberg measure that determines modified lower box dimension Moran fractal sets. The equivalence of these measures for a class is shown by having strong separation condition. We give sufficient condition equality dimension, dimensions. As an application, obtain some relevant conclusions about dimensions image τ-invar...

The goal of the present study was to find evidence for a multisensory generalization effect (i.e., generalization from one sensory modality to another sensory modality). The authors used an innovative paradigm (adapted from Brunel, Labeye, Lesourd, & Versace, 2009) involving three phases: a learning phase, consisting in the categorization of geometrical shapes, which manipulated the rules of as...

A non-parametric and scale-independent method for cluster analysis II: the multivariate case Received ; accepted – 2 – ABSTRACT A general method is described for detecting and analysing galaxy systems. The multivariate geometrical structure of the sample is studied by using an extension of the method which we introduced in a previous paper. The method is based on an estimate of the probability ...

The main goal of this paper is to explore latent topic analysis (LTA), in the context of quantum information retrieval. LTA is a valuable technique for document analysis and representation, which has been extensively used in information retrieval and machine learning. Different LTA techniques have been proposed, some based on geometrical modeling (such as latent semantic analysis, LSA) and othe...

We call our approach geometrical as instead of considering 6-fold integral in abstract space we consider random triangle (RT) inside the plane rectangle when all possible cases are explicitly apparent. Area of triangle with vertices p1=(x1,y1), p2=(x2,y2), p3=(x3,y3) is equal to s = 1 2 (x1(y2− y3) + x2 (−y1 + y3) + x3 (y1− y2)). (1) Let points p1, p2, p3 are randomly (with constant differentia...

The generalized spherical Radon transform associates the mean values over spherical tori to a function f defined on S ⊂ H, where the elements of S are considered as quaternions representing rotations. It is introduced into the analysis of crystallographic preferred orientation and identified with the probability density function corresponding to the angle distribution function W . Eventually, t...

Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is based on the Wasserstein distance of optimal transportation, which reflects the structure of the distance between random variables. Here, we propose a new i...

This paper introduces a new consistency-test for a class of codes, referred to as geometric-codes, and proves the test to be of small error-probability. This consistency-test enables us to conclude a strong characterization of NP in terms of PCP. Speciically, our theorem states that, for any given > 0, membership in any NP language can be veriied with O(1) accesses, each reading logarithmic num...

The topic of the paper is the probabilistic analysis of the ultimate limit state of a steel strut loaded by permanent and long-time single variation action. The failure probability misalignment according to the EN 1990 concept of a structure designed according to the EUROCODE 3 is analyzed here. In the stochastic model, material and geometrical characteristics of a hot-rolled steel cross-sectio...