Related papers: An invariant analytic orthonormalization procedure…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order…
The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented.…
We study integrable lattice regularizations of the sine-Gordon model with the help of the separation of variables method of Sklyanin and the Baxter Q-operators. This leads us to the complete characterization of the spectrum (eigenvalues and…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
Non-perturbative renormalization of lattice composite operators plays a crucial role in many applications of lattice field theory. We sketch the general problems involved in this task and the methods which are currently used to cope with…
The process $e^+e^-\rightarrow \bar \nu_e e^-W^+ \rightarrow\bar\nu_e e^-u\bar d$ is considered as an example of the problems associated with maintaining gauge invariance in matrix elements involving unstable particles. It is shown how to…
For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation…
We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in such datasets requires performing statistics on Lie groups,…
In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be…
In this paper, we investigate the robustness of structured frames to measurement noise and erasures, with the focus on Gabor frames $(g, \Lambda)$ with arbitrary sets of time-frequency shifts $\Lambda$. This property of frames is important…
We construct a uniformly discrete sequence $\{\lambda_1 < \lambda_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) =…
The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…
We prove stability results for a class of Gabor frames in $ L^2(\R)$. We consider window functions in the Sobolev spaces $H^1_0(\R)$ and B-splines of order $p\ge 1$. Our results can be used to describe the effect of the timing jitters in…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
The paper presents a new generalized integer orthogonal transformation which consists of a well known orthogonal transform followed by stretching the basis vectors maintaining the asymptotic behavior of the number of integer solutions for…
We give a survey of recent joint work with E. M. Stein (Princeton University) concerning the application of suitable versions of the T(1)-theorem technique to the study of orthogonal projections onto the Hardy and Bergman spaces of…
We report in a series of papers two types of generalized Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. In this first part the symmetrical operation of half length bonds on translational invariant…