Related papers: Notes on the mathematical basis of the UK Non-Nati…
Deriving analytical solutions of ordinary differential equations is usually restricted to a small subset of problems and numerical techniques are considered. Inevitably, a numerical simulation of a differential equation will then always be…
Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan…
It is often the case that risk assessment and prognostics are viewed as related but separate tasks. This chapter describes a risk-based approach to prognostics that seeks to provide a tighter coupling between risk assessment and fault…
This paper explores how the modelling of energy systems may lead to undue closure of alternatives by generating an excess of certainty around some of the possible policy options. We exemplify the problem with two cases: first, the…
The pressure on marine renewable resources has rapidly increased over past decades. The resulting scarcity has led to a variety of different control and surveillance instruments. Often they have not improved the current situation, mainly…
This is a note on logistic regression models and logistic kernel machine models. It contains derivations to some of the expressions in a paper -- SNP Set Analysis for Detecting Disease Association Using Exon Sequence Data -- submitted to…
Error estimation is given for a regularized Shannon's sampling formulae, which was found to be accurate and robust for numerically solving partial differential equations.
We discuss some aspects of the approach of the mass parameters by means of the simple cranking model. In particular, it is well known that the numerical application of this formula is often subject to ambiguities or contradictions. It is…
In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, - images, - regularity (recognizability by a…
In this work, we survey skepticism regarding AI risk and show parallels with other types of scientific skepticism. We start by classifying different types of AI Risk skepticism and analyze their root causes. We conclude by suggesting some…
This article first presents two examples of algorithms that extracts information on scheme out of its defining equations. We also give a review on the notion of Castelnuovo-Mumford regularity, its main properties (in particular its relation…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…
An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…
A task of interest in machine learning (ML) is that of ascribing explanations to the predictions made by ML models. Furthermore, in domains deemed high risk, the rigor of explanations is paramount. Indeed, incorrect explanations can and…
Nonlinear evolution equation at small x with impact parameter dependence is analyzed numerically. Saturation scales and the radius of expansion in impact parameter are extracted as functions of rapidity. Running coupling is included in this…
I present a brief overview of observational, modeling and theoretical issues related to ageing calculations based on spectral steepening. These include problems such as inhomogeneous magnetic fields, diffusion of relativistic particles,…
Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…
A method is presented for using the consistent part of inconsistent axiomatic systems.
We study some problems in metric Diophantine approximation over local fields of positive characteristic.