Related papers: High dimensional Schwarzian derivatives and Painle…

We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schr\"odinger eigenvalue equation $H\Psi \equiv (\Delta_2 +V)\Psi=E\Psi$ on any 2D Riemannian…

We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic…

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…

In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…

In this paper, we study the possible second order Lax operators for all the possible (1+1)-dimensional models with Schwarz variants and some special types of high dimensional models. It is shown that for every (1+1)-dimensional model and…

Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…

We modify the Schr\"{o}dinger equation in a way that preserves its main properties but makes use of higher order derivative terms. Although the modification represents an analogy to the Doebner-Goldin modification, it can differ from it…

A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons…

Discrete Painlev\'e equations constitute a famous class of integrable non-autonomous second order difference equations. A classification scheme proposed by Sakai interprets a discrete Painlev\'e equation as a birational map between…

A study of the noncommutative Schwinger model is presented. It is shown that the Schwinger mass is not modified by the noncommutativity of spacetime till the first nontrivial order in the noncommutative parameter. Instead, a higher…

Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…

In this paper, we present a unified approach to constructing continuous and discrete $\mathrm{PGL}(3)$-invariant integrable systems, formulated in terms of the common dependent variables $z_1,z_2$, from linear spectral problems and their…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…

In the study of properties within one dimensional dynamics, the assumption of a negative Schwarzian derivative has been shown to be very useful. However, this condition may seem somewhat arbitrary, as it is not inherently a dynamical…

Variational inference in Bayesian deep learning often involves computing the gradient of an expectation that lacks a closed-form solution. In these cases, pathwise and score-function gradient estimators are the most common approaches. The…

Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…