Related papers: V-variable fractals and superfractals
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
We describe a new method that is both physically explicable and quantitatively accurate in describing the multifractal characteristics of intermittent events based on groupings of rank-ordered fluctuations. The generic nature of such…
Concept drift -- the change of the distribution over time -- poses significant challenges for learning systems and is of central interest for monitoring. Understanding drift is thus paramount, and drift localization -- determining which…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
Variational inference transforms posterior inference into parametric optimization thereby enabling the use of latent variable models where otherwise impractical. However, variational inference can be finicky when different variational…
Constructing simpler models, either stochastic or deterministic, for exploring the phenomenon of flow reversals in fluid systems is in vogue across disciplines. Using direct numerical simulations and nonlinear time series analysis, we…
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…