Related papers: Matrix operators for complex interferometer analys…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct…
Quantum optics plays a crucial role in developing quantum computers on different platforms. In photonics, precise control over light's degrees of freedom, including discrete variables (polarization, photon number, orbital angular momentum)…
The effects of the polarization characteristics of beam trains in optical long-baseline interferometers are well known and have led to difficulties in measuring the spatial coherence of astronomical sources in the past. This has been…
Polarizers are key components in optical science and technology. Thus, understanding the action of a polarizer beyond oversimplifying approximations is crucial. In this work, we study the interaction of a polarizing interface with an…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…
Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…
With the wave interferometric approach, we study how extrinsically multiple coherent waves excitation can dramatically alter the overall scattering states, resulting in tailoring the energy assignment among radiation and dissipation. To…
We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use…
In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…
A simple imaging system together with complex semidefinite programming is used to generate the transmission matrix of a multimode fiber. Once the transmission matrix is acquired, we can modulate the phase of the input signal to induce…
Intensity interferometry removes the stringent requirements on mechanical precision and atmospheric corrections that plague all amplitude interferometry techniques at the cost of severely limited sensitivity. A new idea we recently…
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…