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Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. Particularly, the developed methodologies allow the selection of the most…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
It is increasingly common to encounter time-varying random fields on networks (metabolic networks, sensor arrays, distributed computing, etc.). This paper considers the problem of optimal, nonlinear prediction of these fields, showing from…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
A very simple linear signal predictor that uses past predicted values rather than past signal values for prediction is presented. Man-made or natural systems utilizing this predictor would not require a memory of input signal values but…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…
The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…
We study the use of a time series encoder to learn representations that are useful on data set types with which it has not been trained on. The encoder is formed of a convolutional neural network whose temporal output is summarized by a…
The concept of weak invariants has recently been introduced in the context of conserved quantities in finite-time processes in nonequilibrium quantum thermodynamics. A weak invariant itself has a time-dependent spectrum, but its expectation…
We develop a theoretical framework for the exploration of quantum mechanical coherent population transfer phenomena, with the ultimate goal of constructing faithful models of devices for classical and quantum information processing…
Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical…
While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting. However, forecasters based on Transformers are still suffering…
The extraction of information carried by light plays an increasingly important role in optical communication, imaging, and detection. However, the information can only be successfully extracted when the light pulse is comparably strong,…
The signature kernel is a kernel between time series of arbitrary length and comes with strong theoretical guarantees from stochastic analysis. It has found applications in machine learning such as covariance functions for Gaussian…
The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…
Time series forecasting is a critical task in various domains, where accurate predictions can drive informed decision-making. Traditional forecasting methods often rely on current observations of variables to predict future outcomes,…
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out…