Related papers: From configurations to branched configurations and…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to…
A basic arbitrariness in the determination of the topology of a manifold at the Planck length is discussed. An explicit example is given of a `smooth' change in topology from the 2-sphere to the 2-torus through a sequence of noncommuting…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical…
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
This work presents a rigorous statistical and geometric framework for analyzing turbulence-impacted beam propagation and image topology with results obtained using a PMMA slab. The approach models beam intensity distributions as…
In a recent work [1] we consider the topological expansion for the non-mixed observables (including the free energy) for the formal Cauchy matrix model. The only restriction in [1] was the fact that all the branch points have to be simple.…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…
Classical field theories together with the Lagrangian and Eulerian approaches to continuum mechanics are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, space…