Coupling control and human factors in mathematical models of complex systems

Melnik, Roderick

doi:10.1016/j.engappai.2008.10.015

Cited by 21 publications

(5 citation statements)

References 126 publications

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“…These couplings have to be implemented from the beginning of and alongside with the model development, not a posteriori. Based on the idea of ramifications from initial conditions given approximately (RICA), this approach was developed in a series of earlier papers, offering also a new generalized framework for control problems [105][106][107][108][109]. Another attempt along this direction has been labeled as MOND, the Modified Newtonian Dynamics approach [110][111][112], which is also time-nonlocal.…”

Section: Nonlocality In Timementioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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Section: Nonlocality In Timementioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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“…The integration of machine learning with the coupled models could play a vital role in decision-making processes and the treatment planning stage of such procedures, e.g., by providing a priori information about electrode placement for enhancing treatment efficacy or by the real-time monitoring of the damage to the target tissue and other critical structures. Furthermore, a general framework of incorporating human factors into mathematical models of complex systems with control has been provided in [137,138]. This can be useful in the context of AI and the machine learning algorithms mentioned earlier in Section 2.…”

Section: Coupling Framework and Pain Relief Modelsmentioning

confidence: 99%

Domain Heterogeneity in Radiofrequency Therapies for Pain Relief: A Computational Study with Coupled Models

Singh

Melnik

2020

Bioengineering

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The objective of the current research work is to study the differences between the predicted ablation volume in homogeneous and heterogeneous models of typical radiofrequency (RF) procedures for pain relief. A three-dimensional computational domain comprising of the realistic anatomy of the target tissue was considered in the present study. A comparative analysis was conducted for three different scenarios: (a) a completely homogeneous domain comprising of only muscle tissue, (b) a heterogeneous domain comprising of nerve and muscle tissues, and (c) a heterogeneous domain comprising of bone, nerve and muscle tissues. Finite-element-based simulations were performed to compute the temperature and electrical field distribution during conventional RF procedures for treating pain, and exemplified here for the continuous case. The predicted results reveal that the consideration of heterogeneity within the computational domain results in distorted electric field distribution and leads to a significant reduction in the attained ablation volume during the continuous RF application for pain relief. The findings of this study could provide first-hand quantitative information to clinical practitioners about the impact of such heterogeneities on the efficacy of RF procedures, thereby assisting them in developing standardized optimal protocols for different cases of interest.

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“…It has also been successful in describing the mechanism ascribed to the decision‐making process with limited information available. In addition, this method has shown that it is capable of predicting the timing of state transitions, which can determine whether these are qualitatively good or bad, detecting anomalous behavior, and subsequently taking the necessary remedial actions (Boussemart & Cummings, ; Melnik, ; J. Park & Sloman, ; Sanborn, Griffiths, & Shiffrin, ).…”

Section: Determining the Navigation System's Automatic Interventionmentioning

confidence: 99%

Fuzzy logic system interference in ship accidents

Psarros

2018

Hum Ftrs & Erg Mfg Svc

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Poor lookout, lack of situation awareness, and delayed response have been continuously recognized as contributory causes of navigation accidents (i.e., collisions and groundings). It is claimed that such negative behavioral characteristics can be corrected when the navigation system is equipped with the automation capability to intervene upon their detection. Building on the results of my previous work, this study sets the starting line in exploring this technological innovation under a conceptual framework, where it is attempted to employ simple, quantifiable, and measurable ways to assess the deck officer's (navigator's) complex aspect of mental task reliability. To deal with this challenge, the navigator's behavior when performing navigation tasks is described by the Markov method and the uncertainty, ambiguity, and weakness in perceiving accurately the environment and traffic conditions is determined by fuzzy logic. The proposed concept is demonstrated through its practical application in collision and grounding accidents, where it is argued that further research is required for its validation. K E Y W O R D Sautomation, cognitive/mental performance reliability, fuzzy logic, human factors, maritime accidents, Markov method

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Coupling control and human factors in mathematical models of complex systems

Cited by 21 publications

References 126 publications

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Domain Heterogeneity in Radiofrequency Therapies for Pain Relief: A Computational Study with Coupled Models

Fuzzy logic system interference in ship accidents

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