Related papers: On linear weak predictability with single point sp…

It is shown that the partial amplitudes of the pure point part of the diffraction spectrum of an aperiodic Delone point pattern of finite local complexity are linked by a set of linear constraints. These relations can be explicitly derived…

Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…

In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary…

Time series forecasting task predicts future trends based on historical information. Transformer-based U-Net architectures, despite their success in medical image segmentation, have limitations in both expressiveness and computation…

Diffractive optical information processors have demonstrated significant promise in delivering high-speed, parallel, and energy efficient inference for scaling machine learning tasks. Training, however, remains a major computational…

We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that…

For a real sequence of length of m = nl, we may deduce its congruence derivative sequence with length of l. The discrete Fourier transform of original sequence can be calculated by the discrete Fourier transform of the congruence derivative…

A novel and efficient end-to-end learning model for automatic modulation classification is proposed for wireless spectrum monitoring applications, which automatically learns from the time domain in-phase and quadrature data without…

We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

Time-series classification is essential across diverse domains, including medical diagnosis, industrial monitoring, financial forecasting, and human activity recognition. The Rocket algorithm has emerged as a simple yet powerful method,…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

Non-destructive weak measurements (WM) made on a quantum particle allow to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate,…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these…

This paper addresses the classical problem of determining the sets of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve…

For a contraction $C_0$-semigroup on a separable Hilbert space, the decay rate is estimated by using the weak Poincar\'e inequalities for the symmetric and anti-symmetric part of the generator. As applications, non-exponential convergence…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…