A Mathematical Model-based Metric of Spatial Disorientation for Use in Triggering Active Countermeasures

Spatial disorientation (SD) is a leading cause of Class A mishaps in aviation. Ground-based SD training has been widely adopted, and resulted in measurable reductions of mishaps attributed to SD. However, most benefits of SD training have been realized for some time, and it remains insufficient as a standalone countermeasure approach. Several active countermeasures have been proposed, however, many can be distracting in nature even during nominal conditions. Thus, there is a need to be able to detect SD, such that countermeasures could be triggered only when SD is likely to be present or posing a risk. Because there is no validated method of objectively measuring SD, particularly for real-time operational environments, previous research has focused on developing SD metrics using mathematical models of human orientation perception. We first review preliminary works proposing an ‘SD-detection-and-aiding-system’. Then we introduce a novel method to combine multiple aspects and dimensions of spatial orientation perception to create a continuous, unidimensional statistic. This metric of SD can be used to trigger active countermeasures for the purpose of reducing the risk of a mishap resulting from SD.

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Simple Prequalification Models

Archives of Civil Engineering ◽

10.2478/v.10169-010-0019-4 ◽

2010 ◽

Vol 56 (4) ◽

pp. 335-351 ◽

Cited By ~ 1

Author(s):

E. Plebankiewicz

Keyword(s):

Mathematical Model ◽

Sensitivity Analysis ◽

Mathematical Models ◽

Fuzzy Sets ◽

Evaluation Criteria ◽

Computer Software ◽

Applied Model ◽

Model Based ◽

Selection Of ◽

Theory Of Fuzzy Sets

AbstractThe selection of a contractor is one of the most important among decisions made by the owner of a construction. The application of the prequalification procedure enables the selection of the most competent tenderers. Various mathematical models are helpful in carrying out prequalification procedure. In the paper, some selected mathematical models are briefly characterized and model based on the theory of fuzzy sets is offered. The applied model takes into consideration the owner’s various objectives, as well as different evaluation criteria. The results of the sensitivity analysis of the model are also presented. Part of a computer software applying an earlier presented prequalification mathematical model is described

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Mathematical model of tumour spheroid experiments with real-time cell cycle imaging

10.1101/2020.12.06.413856 ◽

2020 ◽

Author(s):

Wang Jin ◽

Loredana Spoerri ◽

Nikolas K. Haass ◽

Matthew J. Simpson

Keyword(s):

Mathematical Model ◽

Cell Cycle ◽

Mathematical Models ◽

Real Time ◽

Living Cells ◽

G1 Phase ◽

Tumour Spheroid ◽

Spheroid Growth ◽

M Phase ◽

The Mathematical Model

AbstractThree-dimensional (3D) in vitro tumour spheroid experiments are an important tool for studying cancer progression and potential drug therapies. Standard experiments involve growing and imaging spheroids to explore how different experimental conditions lead to different rates of spheroid growth. These kinds of experiments, however, do not reveal any information about the spatial distribution of the cell cycle within the expanding spheroid. Since 2008, a new experimental technology called fluorescent ubiquitination-based cell cycle indicator (FUCCI), has enabled real time in situ visualisation of the cell cycle progression. FUCCI labelling involves cells in G1 phase of the cell cycle fluorescing red, and cells in the S/G2/M phase of the cell cycle fluorescing green. Experimental observations of 3D tumour spheroids with FUCCI labelling reveal significant intratumoural structure, as the cell cycle status can vary with location. Although many mathematical models of tumour spheroid growth have been developed, none of the existing mathematical models are designed to interpret experimental observations with FUCCI labelling. In this work we extend the mathematical framework originally proposed by Ward and King (1997) to develop a new mathematical model of FUCCI-labelled tumour spheroid growth. The mathematical model treats the spheroid as being composed of three subpopulations: (i) living cells in G1 phase that fluoresce red; (ii) living cells in S/G2/M phase that fluoresce green; and, (iii) dead cells that do not fluoresce. We assume that the rates at which cells pass through different phases of the cell cycle, and the rate of cell death, depend upon the local oxygen concentration in the spheroid. Parameterising the new mathematical model using experimental measurements of cell cycle transition times, we show that the model can capture important experimental observations that cannot be addressed using previous mathematical models. Further, we show that the mathematical model can be used to quantitatively mimic the action of anti-mitotic drugs applied to the spheroid. All software required to solve the nonlinear moving boundary problem associated with the new mathematical model are available on GitHub.

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MODELING OF PHOSPHORUS PRODUCTION PROCESSES AND DEVELOPING A MANAGEMENT STRUCTURE BASED ON GREY SYSTEMS

10.31713/m1016 ◽

2021 ◽

Author(s):

Nigina Toktasynova ◽

◽

Batyrbek Suleimenov ◽

Yelena Kulakova ◽

◽

...

Keyword(s):

Mathematical Model ◽

Predictive Model ◽

Real Time ◽

General Structure ◽

Sinter Machine ◽

Forecast Model ◽

Practical Significance ◽

Time Data ◽

Vacuum Chambers ◽

Model Based

The agglomeration process is one of the complex, multidimensional technological processes; it takes place under conditions of a large number of disturbing influences. As a result, the amount of return during sintering reaches 40-50%. The work is devoted to the development of a mathematical model capable of predicting and controlling the sintering point based on real-time data. As the main parameters for the construction of predictive models, data measured in real time were used – the temperature in the vacuum chambers and the gas velocity determined through the measured pressure (rarefaction) in the vacuum chambers. This paper describes the methodology and basic algorithms for modeling agglomeration processes, starting from the ingress of the charge into the sinter machine and ending with the production of a suitable agglomerate. The obtained curves of the developed mathematical model of temperature in vacuum chambers served as the basis for testing the forecast model based on the use of the theory of gray systems and the optimization algorithm of the "swarm of particles". Based on the developed mathematical model, a system for predicting the sintering point is constructed, which is the basis for determining the quality of the agglomerate, which will reduce the return volume during sintering. The general structure of the sinter control system based on a dynamic predictive model is also proposed. The practical significance of the developed predictive model based on the theory of gray systems is as follows: - forecast of the sintering point value of the agglomerate and synthesis of the control action based on the forecast; - the algorithm for constructing a mathematical model of the forecast can be used for any process that has the character of a "gray exponential law".

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Visual Simulation of Shells Exploding in Virtual Environment

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.756-759.1809 ◽

2013 ◽

Vol 756-759 ◽

pp. 1809-1813

Author(s):

Gong Lin ◽

Da Wei Jiang

Keyword(s):

Mathematical Model ◽

Real Time ◽

Dynamic Model ◽

Virtual Environment ◽

Particle System ◽

Texture Mapping ◽

Visual Simulation ◽

Model Based ◽

Mapping Techniques ◽

The Mathematical Model

The mathematical model of smoke diffusion and dissipation when shells exploding is studied, and the dynamic model based on particle system controlled by the mathematical model and texture mapping techniques is established. The visual simulation of the method is efficient and real-time.

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On the Big-R Notation for Describing Iterative and Recursive Behaviors

Discoveries and Breakthroughs in Cognitive Informatics and Natural Intelligence ◽

10.4018/978-1-60566-902-1.ch015 ◽

2011 ◽

pp. 292-307

Author(s):

Yingxu Wang

Keyword(s):

Mathematical Model ◽

Software Engineering ◽

Mathematical Models ◽

Programming Languages ◽

Real Time ◽

Mathematical Treatment ◽

Time Process ◽

Control Structures ◽

Fundamental Properties ◽

The Mathematical Model

Iterative and recursive control structures are the most fundamental mechanisms of computing that make programming more effective and expressive. However, these constructs are perhaps the most diverse and confusable instructions in programming languages at both syntactic and semantic levels. This article introduces the big-R notation that provides a unifying mathematical treatment of iterations and recursions in computing. Mathematical models of iterations and recursions are developed using logical inductions. Based on the mathematical model of the big-R notation, fundamental properties of iterative and recursive behaviors of software are comparatively analyzed. The big-R notation has been adopted and implemented in Real-Time Process Algebra (RTPA) and its supporting tools. Case studies demonstrate that a convenient notation may dramatically reduce the difficulty and complexity in expressing a frequently used and highly recurring concept and notion in computing and software engineering.

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