Nonlocal Dynamics for Non-Gaussian Systems Arising in Biophysical Modeling

The aim of this article is to review our recent work on nonlocal dynamics of non-Gaussian systems arising in a gene regulatory network.We have used the mean exit time,escape probability and maximal likely trajectory to quantify dynamical behaviors of a stochastic diferential system with non-Gaussianα-stable Lévy motions,to examine how the nonGaussianity index and noise intensity afect the gene transcription processes.

Exploiting Virtual Elasticity of Production Systems to Respect OTD—Part 3: Basic Considerations for Modelling CPPS Characterized by Non-Ergodic Order Entry and Non-Deterministic Product-Mix for Fully Flexible Addressable Workstations

The recently experienced hype concerning the so-called “4th Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.

On the Mean Exit Time for Compact Symmetric Spaces

Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain the mean exit time flmction of a tube of radius r around special totally geodesic submanifolds P of M. Finally we give a comparison result for the mean exit time function of tubes around submanifolds in Riemannian manifolds, using these totally geodesic submanifolds in compact symmetric spaces as a model.

Design optimisation of mean room surface exitance and total corneal illuminance using Monte Carlo simulation

In lighting design,mean room surface exitance(MRSE)has been known as an indicator of the adequacy of illumination in an indoor space.Recent studies have suggested an exponential model relating MRSE and the observer’s retinal response.This is particularly applicable in a room with homogenous room surface reflectance and a constant total corneal illuminance,which is the total illuminance received at the eye.However,accuracy of the exponential model is yet to be assessed in detail.Furthermore,the implication on interior lighting design is also yet to be quantified.This study thus aims to assess the accuracy of the exponential model and to optimise the output variables.Random computations using Monte Carlo simulation are performed for various input variables,followed with sensitivity and uncertainty analyses and optimisation.Prediction errors of the exponential model are found between-10%and 6%.The MRSE is highly influenced by surface reflectance,whereas the total corneal illuminance is influenced by the source luminous flux.Optimum design parameters are obtained by minimising the ratio between total corneal illuminance and MRSE.Overall,this study provides guidelines in lighting design practice for enhancing room spatial brightness while minimising energy use.

Variational Principles for Asymptotic Variance of General Markov Processes

A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reversible and non-reversible diffusion processes.