Related papers: Distributing points uniformly on the unit sphere u…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We consider a steady-state heat conduction problem in a multidimensional bounded domain Omega for the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion Gamma_1 of…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
A resonant two level atom doped in one dimensional waveguide behaves as a mirror, but this single-atom "mirror" can only reflect single photon perfectly at a specific frequency. For a one dimensional coupled-resonator waveguide, we propose…
Motivated by the central role played by rotationally symmetric distributions in directional statistics, we consider the problem of testing rotational symmetry on the hypersphere. We adopt a semiparametric approach and tackle problems where…
The problem of uniformly placing N points onto a sphere finds applications in many areas. For example, points on the sphere correspond to unit quaternions as well as to the group of rotations SO(3) and the online version of generating…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target…
We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution…
We investigate the photon emission in coupled quantum dots based on symmetry considerations. With the help of a new theorem we proved, we reveal the origin of the various emission patterns, which is the combinative symmetry in the time…
We have studied the configurations of minimal energy of $N$ charges on a curve on the plane, interacting with a repulsive potential $V_{ij} = 1/r_{ij}^s$, with $s \geq 1$ and $i,j=1,\dots, N$. Among the examples considered are ellipses of…
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show…
We propose a geometric framework where dispersion relations are viewed as parametric surfaces in energy-momentum space. Within this picture, the presence and type of critical points of the surface emerge as clear geometric signatures of…
A broad-band reflectionless channel which supports unidirectional wave propagation originating from the interplay between gyrotropic elements and symmetrically placed gain and loss constituents is proposed. Interchange of the active…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…