相关论文: On signal and extraneous roots in Singular Spectru…

How to handle time features shall be the core question of any time series forecasting model. Ironically, it is often ignored or misunderstood by deep-learning based models, even those baselines which are state-of-the-art. This behavior…

In this paper, we explore how different selections of basis functions impact the efficacy of frequency domain techniques in statistical independence tests, and study different algorithms for extracting low-dimensional algebraic relations…

The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random…

In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…

The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…

Random forest (RF) stands out as a highly favored machine learning approach for classification problems. The effectiveness of RF hinges on two key factors: the accuracy of individual trees and the diversity among them. In this study, we…

We develop two algorithms, based on maximum likelihood (ML) inference, for estimating the parameters of polarized radio sources which emit at a single rotation measure (RM), e.g., pulsars. These algorithms incorporate the flux density…

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…

The paper focuses on the adaptation of local polynomial filters at the end of the sample period. We show that for real time estimation of signals (i.e., exactly at the boundary of the time support) we cannot rely on the automatic adaptation…

A rooted phylogenetic network is a directed acyclic graph with a single root, whose sinks correspond to a set of species. As such networks are useful for representing the evolution of species that have undergone reticulate evolution, there…

We study a relation between roots of characteristic polynomials and intersection points of line arrangements. Using these results, we obtain a lot of applications for line arrangements. Namely, we give (i) a generalized addition theorem for…

A characteristic polynomial is an important invariant in the field of hyperplane arrangement. For the Linial arrangement of any irreducible root system, Postnikov and Stanley conjectured that all roots of the characteristic polynomial have…

We study monitoring of linear-time arithmetic properties against finite traces generated by an unknown dynamic system. The monitoring state is determined by considering at once the trace prefix seen so far, and all its possible…

Individualization-Refinement (IR) algorithms form the standard method and currently the only practical method for symmetry computations of graphs and combinatorial objects in general. Through backtracking, on each graph an IR-algorithm…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…

In this paper we derive aggregate separation bounds, named after Davenport-Mahler-Mignotte (\dmm), on the isolated roots of polynomial systems, specifically on the minimum distance between any two such roots. The bounds exploit the…

We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix…

Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…

This paper introduces a novel periodogram-like function, called the expectile periodogram, for modeling spectral features of time series and detecting hidden periodicities. The expectile periodogram is constructed from trigonometric…