Related papers: Optimization of quasi-normal eigenvalues for Krein…
In this paper we investigate a minimization problem related to the principal eigenvalue of the $s$-wave Schr\"{o}dinger operator. The operator depends nonlinearly on the eigenparameter. We prove the existence of a solution for the…
The string corrections to the Riemann Curvature tensor are found to first order in the string slope parameter, here proportional to $\g$. This is done for D=10 supergravity, the presumed low energy limit of string theory. We follow the…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
An optimal algorithm is described for solving the deconvolution problem of the form ${\bf k}u:=\int_0^tk(t-s)u(s)ds=f(t)$ given the noisy data $f_\delta$, $||f-f_\delta||\leq \delta.$ The idea of the method consists of the representation…
We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions for the formulation and characterize the…
This paper presents a novel formalization of optimality theory. Unlike previous treatments of optimality in computational linguistics, starting with Ellison (1994), the new approach does not require any explicit marking and counting of…
We investigate string amplitudes by using the partial modular transformation which we introduced in our previous works. This enables us to extract stringy threshold corrections from the full string amplitudes and interpret them in terms of…
We use the factorization constraints of open-closed string field theory to determine the signs and normalizations of general string amplitudes with both open and closed string external states. The normalization of all amplitudes is…
Low-harmonic formulas for closed relativistic strings are given. General parametrizations are presented for the addition of second- and third-harmonic waves to the fundamental wave. The method of determination of the parametrizations is…
The target space of minimal $(2,2m-1)$ strings is embedded into the phase space of an integrable mechanical model. Quantum effects on the target space correspond to quantum corrections on the mechanical model. In particular double scaling…
Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework…
We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimiser both under the…
Consider the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices with fixed degree $d\geq 3$, and denote the eigenvalues as $\lambda_1=d/\sqrt{d-1}\geq \lambda_2\geq\lambda_3\cdots\geq \lambda_N$. We prove that the…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
String theory is a promising candidate for a fundamental quantum theory of all interactions including Einstein gravity. Some solutions in string theory can be interpreted as black holes. Using the semi-analytic method and WKB method,the…
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…
In the first part of this dissertation, we study two different aspects of string phenomenology. First we discuss the complementary signals of low mass superstrings at the proposed electron-positron facilities (ILC and CLIC), in e+e- and…
To resolve the non-convex optimization problem in partial wave analysis, this paper introduces a novel approach that incorporates fraction constraints into the likelihood function. This method offers significant improvements in both the…
We give a new analysis of a tuning problem in music theory, pertaining specifically to the approximation of harmonics on a two-dimensional keyboard. We formulate the question as a linear programming problem on families of constraints and…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…