Related papers: Window-Dependent Bases for Efficient Representatio…
We develop a new approach for detecting changes in the behavior of stochastic processes and random fields based on tensor product representations such as the Karhunen-Lo\`{e}ve expansion. From the associated eigenspaces of the covariance…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the…
Learned image compression methods have exhibited superior rate-distortion performance than classical image compression standards. Most existing learned image compression models are based on Convolutional Neural Networks (CNNs). Despite…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
Dynamic Fault Trees (DFTs) is a widely used failure modeling technique that allows capturing the dynamic failure characteristics of systems in a very effective manner. Simulation and model checking have been traditionally used for the…
We introduce a framework for studying pathwise time regularity and numerical approximation of $L^0$-valued stochastic evolution equations. At the core of our framework are two Burkholder--Davis--Gundy type inequalities accommodating It\^o…
This paper is dedicated to the study of the orthogonal decomposition of spatially and temporally distributed signals in fluid-structure interaction problems. First application is concerned with the analysis of wall-pressure distributions…
This paper addresses the challenge of Lidar-Inertial Odometry (LIO) in dynamic environments, where conventional methods often fail due to their static-world assumptions. Traditional LIO algorithms perform poorly when dynamic objects…
This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The It\^o or Stratonovich stochastic differential equations with the Wiener…
Any model order reduced dynamical system that evolves a modal decomposition to approximate the discretized solution of a stochastic PDE can be related to a vector field tangent to the manifold of fixed rank matrices. The Dynamically…
We present a practical and computationally effective Ito-Taylor expansion based stochastic simulation framework for modeling rotational optomechanics experiments. By developing a model using this framework, we could capture the nonlinear…
Motion of particles (bodies) in presence of random effects can be considered stochastic process. However, application of widely known stochastic processes used for description of particle motion is reduced to relatively small class of…
We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich--It\^o…
This paper introduces a new tool for time-series analysis: the Sliding Window Discrete Fourier Transform (SWDFT). The SWDFT is especially useful for time-series with local- in-time periodic components. We define a 5-parameter model for…
An important factor which affects performance of solar adaptive optics (AO) systems is the accuracy of tracking an extended object in the wavefront sensor. The accuracy of a centre-ofmass approach to image shift measurement depends on the…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
Stochastic approximation (SA) algorithms have been widely applied in minimization problems when the loss functions and/or the gradient information are only accessible through noisy evaluations. Stochastic gradient (SG) descent---a…
Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In…
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…