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Pairing coherent correlation OTDR with low-complexity analysis methods, we investigate the detection of fast temperature changes and vibrations in optical fibers. A localization accuracy of ~2 m and extraction of vibration amplitudes and…
There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the…
The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…
Regular object detection methods output rectangle bounding boxes, which are unable to accurately describe the actual object shapes. Instance segmentation methods output pixel-level labels, which are computationally expensive for real-time…
Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with…
Out-of-Distribution (OoD) detection aims to justify whether a given sample is from the training distribution of the classifier-under-protection, i.e., In-Distribution (InD), or from OoD. Diffusion Models (DMs) are recently utilized in OoD…
The abundance and distribution of solids inside the Hill sphere are central to our understanding of the giant planet dichotomy. Here, we present a three-dimensional characterization of the dust density, mass flux, and mean opacities in the…
Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
A key challenge for LiDAR-based 3D object detection is to capture sufficient features from large scale 3D scenes especially for distant or/and occluded objects. Albeit recent efforts made by Transformers with the long sequence modeling…
Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees $\delta_p(f)$, $1\le p\le {\rm dim}(X)$. We give the definition of the dynamical degrees show how they are…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure…
I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of…
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
The minimum orbital separation of planets in long-stable planetary systems is often modeled as a step function, parameterized with a single value $\Delta_{min}$ (measured in mutual Hill radius of the two neighboring planets). Systems with…