Related papers: Window-Dependent Bases for Efficient Representatio…
The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…
We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop…
The second-order dependence structure of purely nondeterministic stationary process is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process.…
Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…
Through the H theorem, Bolzmann attempted to validate the foundations of statistical mechanics. However, it is incompatible with the fundamental laws of mechanics because its deduction requires the introduction of probability. In this paper…
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension.…
This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs,…
Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic…
We extend our statistical mechanical theory of the glass transition from examples consisting of point particles to molecular liquids with internal degrees of freedom. As before, the fundamental assertion is that super-cooled liquids are…
In this paper, $\mathcal{G}(g,L,M,N)$ denotes a $L-$window Gabor system on a periodic set $\mathbb{S}$, where $L,M,M\in \mathbb{N}$ and $g=\{g_l\}_{l\in \mathbb{N}_L}\subset \ell^2(\mathbb{S})$. We characterize which $g$ generates a…
The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function. For signal processing, designing a special…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Stochastic port-Hamiltonian systems represent open dynamical systems with dissipation, inputs, and stochastic forcing in an energy based form. We introduce stochastic port-Hamiltonian neural networks, SPH-NNs, which parameterize the…
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…
Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…
In this work we present the first application of software-defined optoelectronics (SDO) for bidimensional optoacoustic tomography (OAT). The SDO concept refers to optoelectronic systems where the functionality associated with the…
In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use Fast Fourier Transforms (FFT) for calculational efficiency. However, because of the…
The partition function of the directed polymer model on Z^{2+1} undergoes a phase transition in a suitable continuum and weak disorder limit. In this paper, we focus on a window around the critical point. Exploiting local renewal theorems,…
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when…