Related papers: From configurations to branched configurations and…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
Context-dependent nature of biological phenomena are well documented in every branch of biology. While there have been few previous attempts to (implicitly) model various facets of biological context-dependence, a formal and general…
With respect to the question of supersymmetry breaking, there are three branches of the flux landscape. On one of these, if one requires small cosmological constant, supersymmetry breaking is predominantly at the fundamental scale; on…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. Many mechanisms have been used to show the emergence of fat tails. Here we…
The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these…
We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory.…
Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the…
A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of…
Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence…
We examine a model of network formation in single-layer and multiplex networks in which individuals have positive incentives for social ties, closed triangles, and spillover edges. In particular, we investigate the influence of shocks to…