In this paper, we adapt the very effective Berry–Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point process. We illustrate the use of our theorems in three examples; in a rather general model of the ...

Appreciation of stochastic Loewner evolution (SLE_{kappa}) , as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model are numerically shown to be conformally invariant and can be described by SLE with ...

In this manuscript, a Genetic Algorithm is applied on a filter in order to optimize the selection of clusters having a high probability to represent protein complexes. The filter was applied on the results (obtained by experiments made on five different yeast datasets) of three different algorithms known for their efficiency on protein complex detection through protein interaction graphs. The d...

The method of evolutionary programming is used to search for the optimal solution in fuzzy clustering of images and in fuzzy boundary detection. In fuzzy evolutionary clustering, the Gibb's probability distribution is employed to model the evolution of object clusters, and the total fuzzy distance is used as a measurement of fitness. In image boundary detection, both geometrical shape and arbit...

The Müller-Lyer effect, the apparent difference in the length of a line as the result of its adornment with arrowheads or arrow tails, is the best known and most controversial of the classical geometrical illusions. By sampling a range-image database of natural scenes, we show that the perceptual effects elicited by the Müller-Lyer stimulus and its major variants are correctly predicted by the ...

Hough proposed an algorithm for detecting lines in pictures. His algorithm, based on a slope-intercept parameterization of lines, was improved by Duda and Hart through the use of angle-radius parameterization. When pictures contain random noise that cannot be removed, the Duda-Hart procedure can yield unsatisfactory results. This paper presents two modifications of that procedure which compensa...

Visual stimuli that entail the intersection of two or more straight lines elicit a variety of well known perceptual anomalies. Preeminent among these anomalies are the systematic overestimation of acute angles, the underestimation of obtuse angles, and the misperceptions of line orientation exemplified in the classical tilt, Zollner, and Hering illusions. Here we show that the probability distr...

We consider a weak version of the cosmological principle. The large scale mass distribution associated to this principle must have the geometrical structures known as regular honeycombs. We give the most important parameters that characterize the honeycombs associated to the closed, open, and flat Robertson-Walker models. These parameters can be used to determinate by observations which is the ...

In this paper, we introduce a novel algorithm for segmentation of imperfect boundary probability maps (BPM) in connectomics. Our algorithm can be a considered as an extension of spectral clustering. Instead of clustering the diffusion maps with traditional clustering algorithms, we learn the manifold and compute an estimate of the minimum normalized cut. We proceed by divide and conquer. We als...

We study directed percolation on a 2D triangular lattice where the forward direction is perpendicular to one of the lattice axes. In addition to the geometrical description, an equivalent dynamic description of the model is presented. Simulations are performed based on an algorithm from the dynamic description to obtain the critical probability of bond occupation as pc ≈ 0.522. A mean field the...