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Loss-induced transmission in waveguides, and reversed pump dependence in lasers, are two prominent examples of counter-intuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex…

The eigenvalues of the transfer matrix in a six-vertex model (with periodic boundary conditions) can be written in terms of n constants v1,...,vn, the zeros of the function Q(v). A peculiar class of eigenvalues are those in which two of the…

Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable,…

We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or…

We prove that almost-linear-time high-fidelity state transfer is achievable in a quantum spin chain using loop weights at the second and second-to-last nodes. We provide specific parameter values, and using a careful analysis of the…

The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…

For many years coherent states have been a useful tool for understanding fundamental questions in quantum mechanics. Recently, there has been work on developing a consistent way of including constraints into the phase space path integral…

Feedback is an essential composition operator in many classes of reactive and other systems. This paper studies feedback in the context of compositional theories with refinement. Such theories allow to reason about systems on a…

We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.

We consider a matrix pencil whose coefficients depend on a positive parameter $\epsilon$, and have asymptotic equivalents of the form $a\epsilon^A$ when $\epsilon$ goes to zero, where the leading coefficient $a$ is complex, and the leading…

Sensitivity of eigenvectors and eigenvalues of symmetric matrix estimates to the removal of a single observation have been well documented in the literature. However, a complicating factor can exist in that the rank of the eigenvalues may…

We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain…

In this paper we bring to light an unprecedented property of the eigenvalues of a matrix A with the eigenvalues and eigenvectors of a submatrix of A. This property can be used, through the technique developed here, to determine some of…

In (relativistic) electronic structure methods, the quaternion matrix eigenvalue problem and the linear response (Bethe-Salpeter) eigenvalue problem for excitation energies are two frequently encountered structured eigenvalue problems.…

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…

Despite numerous successes, the field of reinforcement learning (RL) remains far from matching the impressive generalisation power of human behaviour learning. One possible way to help bridge this gap be to provide RL agents with richer,…

Real-time feedback from iterative electronic structure calculations requires to mediate between the inherently unpredictable execution times of the iterative algorithm employed and the necessity to provide data in fixed and short time…

An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations…

This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…

In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…