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Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical definitions--via power series, spectral calculus, or Jordan…
In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization, given in terms of the all-pass divisors of a certain…
We consider a stochastic sequence $\xi(m)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. The filtering…
For a class of semilinear elliptic equations, we establish criteria that guarantee that the linearized operator associated with a solution satisfies certain spectral assumptions that are widely used in the analysis of the stability of…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that…
Hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators. Here we show that hermitian symplectic spaces may also be used to describe the solution to the factorisation problem for the scattering…
An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of…
We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…
We consider a statistical model for matrix factorization in a regime where the rank of the two hidden matrix factors grows linearly with their dimension and their product is corrupted by additive noise. Despite various approaches,…
Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by…
The recently established spectral Favard theorem for bounded banded matrices admitting a positive bidiagonal factorization is applied to a broader class of Markov chains with bounded banded transition matrices, extending beyond the…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
Most particles in nature are unstable, manifesting as resonances in scattering processes. Using analyticity and unitarity, we show nonperturbatively that resonances, defined as poles on higher Riemann sheets of scattering amplitudes, share…
For a given Laurent polynomial matrix function $S$, which is positive definite on the unit circle in the complex plane, we consider all possible polynomial spectral factors of $S$ which are not necessarily invertible inside the unit circle.
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
The calculation of crystal structure from X-ray diffraction data requires that the phases of the ``structure factors'' (Fourier coefficients) determined by scattering be deduced from the absolute values of those structure factors. Motivated…
We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The…
We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…