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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…
We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the…
We propose using smeared boundary states $e^{-\tau H}|\cal B\rangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches…
Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization…
This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
The essence of the potential algebra concept [3] is that quantum mechanical free motions of scalar particles on curved surfaces of given isometry algebras can be mapped on 1D Schroedinger equations with particular potentials. As long as the…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to…
The spectral stability of liquid metal differentially rotating in transverse magnetic field is studied numerically by solving the eigenvalue problem with rigid-wall boundary conditions. The equilibrium velocity profile used in calculations…
Standard methods in computer model calibration treat the calibration parameters as constant throughout the domain of control inputs. In many applications, systematic variation may cause the best values for the calibration parameters to…
Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
The conformal mapping method is used to study the problem of flux line interaction with surface cavities having cylindrical profile and characteristic size much less than the penetration length, i.e, within mesoscopic scale. It is shown…
Considering the radial nonlinear Schrodinger equation - \Delta u + V(x)u = g(x,u) in R^N, N \geq 3 we aim to find a radial nontrivial solution for it, where V changes sign ensuring this problem is indefinite and g is an asymptotically…
Substances such as chemical compounds are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Though spectra of pure chemicals can be identified by visual inspection, the spectra of…
As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…