Related papers: Notes on the mathematical basis of the UK Non-Nati…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
An error analysis is presented for explicit partitioned Runge-Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes.…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
This paper discusses the properties of certain risk estimators recently proposed to choose regularization parameters in ill-posed problems. A simple approach is Stein's unbiased risk estimator (SURE), which estimates the risk in the data…
Polygenic risk score (PRS) analysis is a powerful method been used to estimate an individual's genetic risk towards targeted traits. PRS analysis could be used to obtain evidence of a genetic effect beyond Genome-Wide Association Studies…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
I discuss the issue of uncertainties in parton distributions and in the physical quantities which are determined in terms of them. While there has been significant progress on the uncertainties associated with errors on experimental data,…
In this work, we consider the problem of estimating a behaviour policy for use in Off-Policy Policy Evaluation (OPE) when the true behaviour policy is unknown. Via a series of empirical studies, we demonstrate how accurate OPE is strongly…
The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment…
We present some new mathematical tools which help to derive information about the quark mass matrices directly from experimental data and to elucidate the structure of these mass matrices.
In ecological studies niche overlap is often used to quantify species interaction and dynamics. This paper develops a robust, nonparametric statistical framework for quantifying and analyzing multivariate niche overlap. Parametric methods…
Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax…
The computational modeling of genetic regulatory networks is now common place, either by fitting a system to experimental data or by exploring the behaviour of abstract systems with the aim of identifying underlying principles. This paper…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
These are notes from a basic course in Several Complex Variables
Natural computing offers new opportunities to understand, model and analyze the complexity of the physical and human-created environment. This paper examines the application of natural computing in environmental informatics, by…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
Understanding the landscape of potential harms from algorithmic systems enables practitioners to better anticipate consequences of the systems they build. It also supports the prospect of incorporating controls to help minimize harms that…