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We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods adopt a Lagrangian perspective by directly treating…
We present EDDY (Exact-marginal Diversification via Divergence-free dYnamics), a guidance mechanism for diffusion and flow matching models that promotes diversity among samples generated while maintaining quality. EDDY exploits symmetries…
The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a…
Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability,…
A generalized form of Wien's displacement law and the blackbody radiation laws of (a) Rayleigh and Jeans, (b) Rayleigh, (c) Wien and Paschen, (d) Thiesen and (e) Planck are derived using principles of dimensional analysis. This kind of…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
Triple Differences (DDD) designs are widely used in empirical work to relax parallel trends assumptions in Difference-in-Differences (DiD) settings. This paper highlights that common DDD implementations -- such as taking the difference…
We investigate in this work some situations where it is possible to estimate or determine the upper and the lower $q$-generalized fractal dimensions $D^{\pm}_{\mu}(q)$, $q\in\mathbb{R}$, of invariant measures associated with continuous…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
This paper explores visual motion-based invariants, resulting in a new instantaneous domain where: a) the stationary environment is perceived as unchanged, even as the 2D images undergo continuous changes due to camera motion, b) obstacles…
Being able to characterise objects at low frequencies, but above the limiting frequency of the eddy current approximation of the Maxwell system, is important for improving current metal detection technologies. Importantly, the upper…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of the straight-line flow on certain translation surfaces, and…
Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum,…
We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…
In this note, we address several issues, including some raised in recent works and commentary, related to bending measures and energies for plates and shells, and certain of their invariance properties. We discuss overlaps and distinctions…
The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the…
This work investigates the self-excited shock wave oscillations in a three-dimensional planar over-expanded nozzle turbulent flow by means of Detached Eddy Simulations. Time resolved wall pressure measurements are used as primary…