Related papers: Lacunary wavelet series on Cantor sets
Large language models (LLMs) often generate fluent but factually incorrect outputs, known as hallucinations, which undermine their reliability in real-world applications. While uncertainty estimation has emerged as a promising strategy for…
In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
Associated Legendre functions of fractional degree appear in the solution of boundary value problems in wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer,…
This paper focuses on solving a fault detection problem using multivariate time series of vibration signals collected from planetary gearboxes in a test rig. Various traditional machine learning and deep learning methods have been proposed…
Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive…
Identifying the causal structure of systems with multiple dynamic elements is critical to several scientific disciplines. The conventional approach is to conduct statistical tests of causality, for example with Granger Causality, between…
Continuous wavelet transform (CWT) based time-scale and multi-fractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain…
We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and…
We introduce DafnyCOMP, a benchmark for evaluating large language models (LLMs) on compositional specification generation in Dafny. Unlike prior benchmarks that focus on single-function tasks, DafnyCOMP targets programs composed of multiple…
We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
Multifractal formalisms provide an apt framework to study random cascades in which multifractal spectrum width $\Delta\alpha$ fluctuates depending on the number of estimable power-law relationships. Then again, multifractality without…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
Wavelet families arise by scaling and translations of a prototype function, called the {\em {mother wavelet}}. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis…
We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate…
We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…
The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the…