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Anomaly detection in random fields is an important problem in many applications including the detection of cancerous cells in medicine, obstacles in autonomous driving and cracks in the construction material of buildings. Such anomalies are…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
Living organisms have developed a wide range of appearances from iridescent to matt textures. Interestingly, angular independent structural colors, where isotropy in the scattering structure is present, only produce coloration in the blue…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric.…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
Structural colors are a result of the scattering of certain frequencies of the incident light on micro- or nanoscale features in a material. This is a quite different phenomenon from that of colors produced by absorption of different…
Colorizing a given gray-level image is an important task in the media and advertising industry. Due to the ambiguity inherent to colorization (many shades are often plausible), recent approaches started to explicitly model diversity.…
Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently…
The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The…
Colors observed in nature are very important to form our perception of an object as well as its design. The desire to reproduce vivid colors such as those found in birds, fishes, flowers and insects has driven extensive research into…
Random noise plays a beneficial role in cognitive processing and produces measurable improvement in simulations and biological agents' task performance. Stochastic facilitation, the phenomenon of additive noise improving signal transmission…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random,…
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
Using light to control the movement of nano-structured objects is a great challenge. This challenge involves fields like optical tweezing, Casimir forces, integrated optics, bio-physics, and many others. Photonic "robots" could have…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…