Related papers: Notes on the mathematical basis of the UK Non-Nati…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
Possible sources of uncertainties in the calculations of the internal conversion coefficients are studied. The uncertainties induced by them are estimated.
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…
Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative…
Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…
The basic formalism of a novel scale invarinat nonlinear analysis is presented. A few analytic number theoretic results are derived independent of standard approaches.
Exact and approximate analytical formulas are derived for the internal structure and global parameters of the spherical non-rotating quasi-incompressible planet. The planet is modeled by a polytrope with a small polytropic index n << 1, and…
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…
In this article, we address the problem of risk assessment of stealthy attacks on uncertain control systems. Considering data injection attacks that aim at maximizing impact while remaining undetected, we use the recently proposed…
Assessing the effects of a policy based on observational data from a different policy is a common problem across several high-stake decision-making domains, and several off-policy evaluation (OPE) techniques have been proposed. However,…
Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We…
Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
This paper addresses different aspects of "coupled" model descriptions in computational electromagnetics. This includes domain decomposition, multiscale problems, multiple or hybrid discrete field formulation and multi-physics problems.…
The situation assessment problem is considered, in terms of object, condition, activity, and plan recognition, based on data coming from the real-word {em via} various sensors. It is shown that uncertainty issues are linked both to the…
Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the…
The mathematical basis motivating the "implication operator" of the polySAT algorithm and its function is examined. Such is not undertaken with onerous rigor of symbolic mathematics; a more intuitive visual appeal being employed to present…
This work is an attempt to develop an approximate scheme for estimating the volume-based truncation errors in the finite volume analysis of laminar flows. The volume-based truncation error is the net flow error across the faces of a control…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Multiple testing problems arise naturally in scientific studies because of the need to capture or convey more information with more variables. The literature is enormous, but the emphasis is primarily methodological, providing numerous…