Related papers: On the Optical Role of Randomness for Structured S…
Naive scale invariance is not a true property of natural images. Natural monochrome images posses a much richer geometrical structure, that is particularly well described in terms of multiscaling relations. This means that the pixels of a…
Under white light illumination, gratings produce an angular distribution of wavelengths dependent on the diffraction order and geometric parameters. However, previous studies of gratings are limited to at least one geometric parameter…
Arbitrary distributions of radiant exposure may be written by transversely scanning a single known spatially-random screen that is normally illuminated by spatially but not necessarily temporally uniform radiation or matter wave fields. The…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…
This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions.…
Speckled images of a binary broad band light source (600-670 nm), generated by randomized reflections or transmissions, were used to reconstruct a binary image by use of multi-frame blind deconvolution algorithms. Craft store glitter was…
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global…
Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably…
We introduce a characteristic function for laws of random surfaces $\mathbf{X}: [0,s] \times [0,t] \to \mathbb{R}^d$, in the spirit of expected path developments for one-dimensional stochastic processes into matrix groups. A key property is…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
Light beams can be symmetric under different transformations: translations, rotations, mirror symmetries, duality transformations, etc. In this thesis, a systematic way of characterizing these symmetries is presented. Then, it is shown that…
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian…