Related papers: Toward a deeper understanding of a basic cascade
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
A feasible model is introduced that manifests phenomena intrinsic to iterative complex analytic maps (such as the Mandelbrot set and Julia sets). The system is composed of two coupled alternately excited oscillators (or self-sustained…
We consider the problems of chaos in disorder and temperature for coupled copies of the mixed p-spin models. Under certain assumptions on the parameters of the models we will first prove a weak form of chaos by showing that the overlap is…
In this paper, to cope with the shortage of sufficient theoretical support resulted from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide…
It has been recently proven that natural images exhibit scaling properties analogue to those of turbulent flows. These properties allow regarding each image as a multifractal object, for which its most singular manifold conveys the most of…
Aeroelastic flutter represents a critical nonlinear instability arising from the coupling between structural elasticity and unsteady aerodynamics. In deterministic settings, flutter onset is associated with bifurcations of invariant sets…
An original experimental setup has been elaborated in order to get a better view of turbulent flows in a von Karman geometry. The availability of a very fast camera allowed to follow in time the evolution of the flows. A surprising finding…
Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical…
While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…
A landmark of out-of-equilibrium physics is Kolmogorov's phenomenological theory of turbulence. However, the past 20 years have provided evidence of a new, universal type of turbulence cascade, which does not abide to Kolmogorov physics. To…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
At present, object recognition studies are mostly conducted in a closed lab setting with classes in test phase typically in training phase. However, real-world problem is far more challenging because: i) new classes unseen in the training…
This investigation presents evidence of the relation between the dynamics of intense events in small-scale turbulence and the energy cascade. We use the generalised (H\"older) means to track the temporal evolution of intense events of the…
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…
A model of a discrete pregeometry on a microscopic scale is introduced. This model is a finite network of finite elementary processes. The mathematical description is a d-graph that is a generalization of a graph. This is the particular…
The coherent dynamics of bubble clusters in liquid are of fundamental and industrial importance and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate unsupervised learning of…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…