Related papers: An Alternative Parameterization of R-matrix Theory
In this work, we present a new approach for constructing models for correlation matrices with a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of…
For a simple and connected graph, several lower and upper bounds of graph invariants expressed in terms of the eigenvalues of the normalized Laplacian matrix have been proposed in literature. In this paper, through a unified approach based…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Our collective knowledge of nuclear cross sections is recorded as resonance parameters in nuclear data libraries. To evaluate these parameters, campaigns of measurements are fitted with a parametric model of nuclear cross sections called…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…
Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to…
The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of (idealized) markets. The paper addresses the following basic…
Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes adaPG$^{q,r}$, a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds.…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation…
A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…
We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed…