435 results
Search Results
202. CasADi: a software framework for nonlinear optimization and optimal control.
- Author
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Andersson, Joel A. E., Gillis, Joris, Horn, Greg, Rawlings, James B., and Diehl, Moritz
- Abstract
We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
203. Linear port-Hamiltonian descriptor systems.
- Author
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Beattie, Christopher, Mehrmann, Volker, Xu, Hongguo, and Zwart, Hans
- Published
- 2018
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204. Balanced truncation for linear switched systems.
- Author
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Gosea, Ion Victor, Petreczky, Mihaly, Antoulas, Athanasios C., and Fiter, Christophe
- Subjects
BALANCED truncation ,LINEAR systems ,REDUCED-order models - Abstract
We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
205. Dynamics of mosaic disease with roguing and delay in Jatropha curcas plantations.
- Author
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Al Basir, Fahad and Roy, Priti Kumar
- Abstract
Jatropha curcas plant is seriously affected by the mosaic disease caused by begomovirus which is carried through infected white-flies. It severely affects the Jatropha plants causing leaf damage, yellowing leaves and sap drainage. Traditionally, the diseased is controlled by roguing or removal of infected plant biomass, using insecticides or increasing resistance to host plant. In this article, a mathematical model is formulated to study mosaic disease dynamics in J. curcas plantations with roguing. Also, time delay has been incorporated in roguing and reformulates the mathematical model using delay differential equations. Sufficient conditions for the stability of the equilibrium points of the system are among the results obtained through qualitative analysis. Using the normal form theory and the center manifold theorem, the stability and direction of the bifurcating periodic solutions of the delayed system are determined. The findings are confirmed by means of numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
206. Global stability analysis and control of leptospirosis
- Author
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Okosun Kazeem Oare, Mukamuri M., and Makinde Daniel Oluwole
- Subjects
leptospirosis ,stability analysis ,optimal control ,cost-effectiveness analaysis ,anova ,92b05 ,93a30 ,93c15 ,Mathematics ,QA1-939 - Abstract
The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.
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- 2016
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207. Parametric models analysed with linear maps
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Matthies, Hermann G. and Ohayon, Roger
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- 2020
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208. pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations.
- Author
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Nicholson, Bethany, Siirola, John D., Watson, Jean-Paul, Zavala, Victor M., and Biegler, Lorenz T.
- Abstract
We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at
http://www.pyomo.org . One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers. [ABSTRACT FROM AUTHOR]- Published
- 2018
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209. Structural damage identification based on modified Artificial Bee Colony algorithm using modal data.
- Author
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Ding, Zhenghao, Yao, Renzhi, Li, Jun, and Lu, Zhongrong
- Subjects
ALGORITHMS ,SIMULATION methods & models ,BEES algorithm ,NUMERICAL analysis ,ROBUST control ,MATHEMATICAL optimization - Abstract
A method for structural damage identification based on a modified Artificial Bee Colony algorithm is presented. A new formula is introduced to the onlooker bee phase to improve the convergence rate and the Tournament Selection Strategy is adopted instead of roulette to enhance global search ability of the algorithm. Test functions are introduced as benchmarks to verify the proposed algorithm. And then two numerical examples, including a supported beam and a plate, are conducted to investigate the efficiency and correctness of the proposed method. Final estimated results show that the present technique can produce more accurate damage identification results, comparing with other evolutionary algorithms, even with a few noise contaminated measurements. [ABSTRACT FROM PUBLISHER]
- Published
- 2018
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210. Implementation of F.W. Lanchester's combat model in a supply chain in duopoly: the case of Coca-Cola and Pepsi in Greece.
- Author
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Chalikias, Miltiadis and Skordoulis, Michalis
- Abstract
The purpose of this study is to investigate the possibility of applying some of the most widely known mathematical theories of war in the case of firms. In this research, Frederick William Lanchester's combat models, that seemed to be particularly useful to the U.S. Army at the Pacific campaign against the Japanese fleet during World War II, were examined. These mathematical models were based on differential equations and their main purpose was to predict the outcome of battles. After the appropriate theoretical assumptions were set, the examined models were applied to the case of Coca-Cola™ and Pepsi™ supply chains in the Greek market. These models have been applied to these firms by other researchers too. The results of the implementations have led to the conclusion that the theoretical models are almost identical to the reality, which means that they are applicable in business under the right conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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211. Multi-objective Geometry Optimization of a Gas Cyclone Using Triple-Fidelity Co-Kriging Surrogate Models.
- Author
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Singh, Prashant, Couckuyt, Ivo, Elsayed, Khairy, Deschrijver, Dirk, and Dhaene, Tom
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MATHEMATICAL optimization ,KRIGING ,GEOLOGICAL statistics ,NONLINEAR theories ,MATHEMATICAL analysis ,ALGORITHMS ,MATHEMATICAL models - Abstract
Cyclone separators are widely used in a variety of industrial applications. A low-mass loading gas cyclone is characterized by two performance parameters, namely the Euler and Stokes numbers. These parameters are highly sensitive to the geometrical design parameters defining the cyclone. Optimizing the cyclone geometry therefore is a complex problem. Testing a large number of cyclone geometries is impractical due to time constraints. Experimental data and even computational fluid dynamics simulations are time-consuming to perform, with a single simulation or experiment taking several weeks. Simpler analytical models are therefore often used to expedite the design process. However, this comes at the cost of model accuracy. Existing techniques used for cyclone shape optimization in literature do not take multiple fidelities into account. This work combines cheap-to-evaluate well-known mathematical models of cyclones, available data from computational fluid dynamics simulations and experimental data to build a triple-fidelity recursive co-Kriging model. This model can be used as a surrogate with a multi-objective optimization algorithm to identify a Pareto set of a finite number of solutions. The proposed scheme is applied to optimize the cyclone geometry, parametrized by seven design variables. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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212. Modeling, optimal control of intervention strategies and cost effectiveness analysis for buruli ulcer model
- Author
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Ali I. Michael, Nurudeen G.A. Abimbola, Harrisu Muhammed Abdullahi, and A. A. Momoh
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Buruli ulcer ,Equilibrium point ,education.field_of_study ,020209 energy ,Population ,General Engineering ,02 engineering and technology ,Cost-effectiveness analysis ,Engineering (General). Civil engineering (General) ,Optimal control ,medicine.disease ,01 natural sciences ,010305 fluids & plasmas ,93A30 ,Maximum principle ,0103 physical sciences ,Statistics ,92D40 ,0202 electrical engineering, electronic engineering, information engineering ,medicine ,Sensitivity (control systems) ,TA1-2040 ,education ,Basic reproduction number ,Mathematics - Abstract
A mathematical model for the transmission of buruli ulcer disease is proposed in this paper, incorporating three control strategies. Using the stability theory of differential equations, optimal control, and computer simulation, a nonlinear mathematical model for the problem is developed and qualitatively analyzed. Buruli ulcer free equilibrium and buruli ulcer present equilibrium were established. Using the next-generation operator method, the basic reproduction number of the model is obtained. It is found that the buruli ulcer-free equilibrium point is asymptotically stable locally and globally when R 0 1 and otherwise when R 0 > 1 . The bifurcation analysis performed in this study indicates that the buruli ulcer model exhibits backward bifurcation. To investigate the parameters that influence the basic reproduction number R 0 , sensitivity analysis is performed. To minimize the transmission dynamics of buruli ulcer in humans and water bugs populations respectively, the buruli ulcer model is updated to include control measures attached to the parameters that affect the R 0 . In particular, the prevention measures covered are health education on the use of protective clothing, treatment of infected humans, and spraying of insecticides. The Pontryagin’s maximum principle is used to characterize the controls’ optimal levels. Using forward and backward sweep techniques in MATLAB, the optimality system was solved numerically. The results of the simulations show that, relative to the case of no control, there is a substantial decrease in the population of infected humans and the total population of water bugs when control measures are implemented. A study of cost-effectiveness shows that the most cost-effective approach is strategy G with the smallest ICER of 33442.44. To mitigate or eliminate buruli ulcer in the population, we conclude that the government should invest in health education on the use of protective clothing, treatment of infected humans, and the use of insecticide spray.
- Published
- 2021
213. Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative
- Author
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Alqudah, Manar A., Abdeljawad, Thabet, Eiman, Shah, Kamal, Jarad, Fahd, and Al-Mdallal, Qasem
- Published
- 2020
- Full Text
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214. Approximately bisimilar symbolic models for incrementally stable switched systems
- Author
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Giordano Pola, Antoine Girard, Paulo Tabuada, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), University of L'Aquila [Italy] (UNIVAQ), Cyber-Physical Systems Laboratory, University of California [Los Angeles] (UCLA), University of California-University of California, Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Electrical Engineering Department [Los Angeles], Dipartimento di Ingegneria industriale e dell'informazione e di economia (DIIIE / UNIVAQ), Università degli Studi dell'Aquila (UNIVAQ), and Magnus Egerstedt, Bud Mishra
- Subjects
Lyapunov function ,Engineering ,0209 industrial biotechnology ,Computer science ,Stability (learning theory) ,02 engineering and technology ,Computer Science (all) ,Theoretical Computer Science ,Dynamical system ,symbols.namesake ,Software ,020901 industrial engineering & automation ,Approximate bisimulation ,Supervisory control ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Software system ,Electrical and Electronic Engineering ,Mathematics - Optimization and Control ,Switched systems ,Bisimulation ,Finite-state machine ,business.industry ,Finite controllers ,Computer Science Applications1707 Computer Vision and Pattern Recognition ,Control engineering ,Construct (python library) ,Control and Systems Engineering ,Computer Science Applications ,Model predictive control ,93A30 ,Optimization and Control (math.OC) ,Control system ,Hybrid system ,Transition system ,symbols ,A priori and a posteriori ,020201 artificial intelligence & image processing ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Constant (mathematics) ,business ,Voltage - Abstract
Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for switched systems. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e. existence of a common Lyapunov function, or multiple Lyapunov functions with dwell time), it is possible to construct a finite symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach, we use symbolic models to synthesize controllers for two examples of switched systems, including the boost DC-DC converter., Comment: 17 pages
- Published
- 2008
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215. Group purchasing organization design: a clustering approach
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Safaei, Abdul Sattar, Heidarpoor, Farnaz, and Paydar, Mohammad Mahdi
- Published
- 2018
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216. Model of Shell Metal Mould Heating in the Automotive Industry
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Mlýnek, Jaroslav and Knobloch, Roman
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- 2018
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217. On a Class of Block Operator Matrices in System Theory.
- Author
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Trostorff, Sascha
- Abstract
We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator matrices considered in (Trostorff in J Funct Anal 267(8):2787-2822, 2014), which can be characterized in terms of an associated boundary relation. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
218. A Velocity-Based Dynamic Model and Its Properties for Differential Drive Mobile Robots.
- Author
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Martins, Felipe, Sarcinelli-Filho, Mário, and Carelli, Ricardo
- Abstract
An important issue in the field of motion control of wheeled mobile robots is that the design of most controllers is based only on the robot's kinematics. However, when high-speed movements and/or heavy load transportation are required, it becomes essential to consider the robot dynamics as well. The control signals generated by most dynamic controllers reported in the literature are torques or voltages for the robot motors, while commercial robots usually accept velocity commands. In this context, we present a velocity-based dynamic model for differential drive mobile robots that also includes the dynamics of the robot actuators. Such model has linear and angular velocities as inputs and has been included in Peter Corke's Robotics Toolbox for MATLAB, therefore it can be easily integrated into simulation systems that have been built for the unicycle kinematics. We demonstrate that the proposed dynamic model has useful mathematical properties. We also present an application of such model on the design of an adaptive dynamic controller and the stability analysis of the complete system, while applying the proposed model properties. Finally, we show some simulation and experimental results and discuss the advantages and limitations of the proposed model. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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219. Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory.
- Author
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Mao, Yawen and Ding, Feng
- Subjects
PARAMETER estimation ,NONLINEAR systems ,INFORMATION filtering systems ,STOCHASTIC processes ,ALGORITHMS ,DECOMPOSITION method ,HAMMERSTEIN equations - Abstract
For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
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220. On modeling of coronavirus-19 disease under Mittag-Leffler power law
- Author
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Kamal Shah, Hussam Alrabaiah, and Samia Bushnaq
- Subjects
Fixed-point theorem ,34A08 ,Type (model theory) ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,0103 physical sciences ,Numerical simulations ,Applied mathematics ,Coronavirus disease model ,Uniqueness ,010306 general physics ,Mathematics ,Algebra and Number Theory ,Partial differential equation ,Computer simulation ,Stability results ,Applied Mathematics ,Research ,lcsh:Mathematics ,Order (ring theory) ,( ABC ) $(\mathcal{ABC})$ derivative ,lcsh:QA1-939 ,93A30 ,Ordinary differential equation ,Fractional Adams–Bashforth (AB) method ,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\mathcal{ABC})$\end{document}(ABC) derivative ,26A33 ,Analysis - Abstract
This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as$(\mathcal{ABC})$(ABC). Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.
- Published
- 2020
221. Variational Networks: An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration
- Author
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Karl Kunisch, Thomas Pock, Alexander Effland, and Erich Kobler
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Statistics and Probability ,Deblurring ,49K15 ,Image quality ,Computer science ,Variational problems ,65L05 ,Image processing ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Article ,Gradient flow ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,Image restoration ,Early stopping ,Variational networks ,business.industry ,Applied Mathematics ,Deep learning ,68T45 ,Condensed Matter Physics ,Optimal control ,93A30 ,Recurrent neural network ,Optimal control theory ,Modeling and Simulation ,34H05 ,020201 artificial intelligence & image processing ,Geometry and Topology ,Computer Vision and Pattern Recognition ,Artificial intelligence ,business ,Algorithm - Abstract
We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox originates from a tradeoff between optimization and modeling errors of the underlying variational model and holds true even if deep learning methods are used to learn highly expressive regularizers from data. In this paper, we take advantage of this paradox and introduce an optimal stopping time into the gradient flow process, which in turn is learned from data by means of an optimal control approach. After a time discretization, we obtain variational networks, which can be interpreted as a particular type of recurrent neural networks. The learned variational networks achieve competitive results for image denoising and image deblurring on a standard benchmark data set. One of the key theoretical results is the development of first- and second-order conditions to verify optimal stopping time. A nonlinear spectral analysis of the gradient of the learned regularizer gives enlightening insights into the different regularization properties.
- Published
- 2020
222. Stepwise modeling with friction/inertia effects separation and velocity control with dynamic compensation of a reaction wheel
- Author
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Lopes, Rafael A. M., Carrara, Valdemir, and Kuga, Hélio K.
- Published
- 2019
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223. A Delayed Model for HIV Infection Incorporating Intracellular Delay
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Sahani, Saroj Kumar
- Published
- 2017
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224. Modelization of the grape marc pyrolysis and combustion based on an extended independent parallel reaction and determination of the optimal kinetic constants
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Brillard, A., Brilhac, J. F., and Valente, M.
- Published
- 2017
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225. A new algorithm in cloud computing of multi-agent fractional differential economical system
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Ibrahim, Rabha W. and Gani, Abdullah
- Published
- 2016
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226. Modelling of Biological Decontamination of a Water Resource in Natural Environment and Related Feedback Strategies.
- Author
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Barbier, S., Rapaport, A., and Rousseau, A.
- Abstract
We show how to combine numerical schemes and calibration of systems of o.d.e. to provide efficient feedback strategies for the biological decontamination of water resources. For natural resources, we retain to introduce any bacteria in the resource and treat it aside preserving a constant volume of the resource at any time. The feedback strategies are derived from the minimal time synthesis of the system of o.d.e. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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- View/download PDF
227. Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model.
- Author
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Dziubek, Andrea, Guidoboni, Giovanna, Harris, Alon, Hirani, Anil, Rusjan, Edmond, and Thistleton, William
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RETINA ,HEMODYNAMICS ,EYE ,BLOOD vessels ,FINITE element method ,MATHEMATICAL models - Abstract
A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
228. An optimal control problem for ovine brucellosis with culling.
- Author
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Nannyonga, B., Mwanga, G.G., and Luboobi, L.S.
- Subjects
OPTIMAL control theory ,BRUCELLOSIS ,CULLING of animals ,MATHEMATICAL models ,SENSITIVITY analysis ,POPULATION dynamics ,CATTLE - Abstract
A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnsebaet al.[A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2–11. Available athttp://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
229. Coordinated Speed Oscillations in Schooling Killifish Enrich Social Communication.
- Author
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Swain, Daniel, Couzin, Iain, and Leonard, Naomi
- Subjects
FISH schooling ,KILLIFISHES ,TIME-varying systems ,FISH industry ,SOCIAL interaction - Abstract
We examine the spatial dynamics of individuals in small schools of banded killifish ( Fundulus diaphanus) that exhibit rhythmic, oscillating speed, typically with sustained, coordinated, out-of-phase speed oscillations as they move around a shallow water tank. We show that the relative motion among the fish yields a periodically time-varying network of social interactions that enriches visually driven social communication. The oscillations lead to the regular making and breaking of occlusions, which we term 'switching.' We show that the rate of convergence to consensus (biologically, the capacity for individuals in groups to achieve effective coordinated motion) governed by the switching outperforms static alternatives, and performs as well as the less practical case of every fish sensing every other fish. We show further that the oscillations in speed yield oscillations in relative bearing between fish over a range that includes the angles previously predicted to be optimal for a fish to detect changes in heading and speed of its neighbors. To investigate systematically, we derive and analyze a dynamic model of interacting agents that move with oscillatory speed. We show that coordinated circular motion of the school leads to systematic cycling of spatial ordering of agents and possibilities for enriched spatial density of measurements of the external environment. Our results highlight the potential benefits of dynamic communication topologies in collective animal behavior, and suggest new, useful control laws for the distributed coordination of mobile robotic networks. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
230. Wind energy in the United Kingdom: modelling the effect of increases in installed capacity on generation efficiency
- Author
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Anthony D Stephens and David Richard Walwyn
- Subjects
Physics - Physics and Society ,Wind power ,Renewable Energy, Sustainability and the Environment ,Natural resource economics ,business.industry ,FOS: Physical sciences ,Physics and Society (physics.soc-ph) ,National Grid ,Nameplate capacity ,Offshore wind power ,93A30 ,Electricity generation ,Base load power plant ,Greenhouse gas ,Environmental science ,Operations management ,Electricity ,business - Abstract
The decision by the United Kingdom (UK) government in 2007 that the country should build a 33GW wind fleet, capable of generating 25 percent of the UK electricity requirement, was controversial. Proponents argued that it was the most attractive means of lowering the UK greenhouse gas emissions, whereas opponents noted that it would result in an unnecessary and burdensome additional expense to industry and households. Subsequently there have been calls for the wind fleet target to be further increased to perhaps 50 percent of demand. Although the National Grid has had little difficulty in accommodating the current output of about 10 percent of the total demand on the grid, this will not be the case for a substantially larger wind fleet. When the wind blows strongly, turbines shed wind which is surplus to demand, leading to significant reductions in generating efficiency. The purpose of the research described in this paper has been to develop a method for investigating the likely performance of future large wind fleets. The method relies on the use of mathematical models based on National Grid records for 2013 to 2015, each year being separately analysed. It was found that the incremental load factor of the wind fleet will be reduced to 63 percent of its current level should the wind fleet increase from its current size of 14GW to 35GW, assuming a base load of 15GW, 24 pages, 15 figures, 4 tables
- Published
- 2018
231. Global stability analysis of the role of multi-therapies and non-pharmaceutical treatment protocols for COVID-19 pandemic
- Author
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Bassey Echeng Bassey and Jeremiah Atsu
- Subjects
Lyapunov function ,65L20 ,Coronavirus disease 2019 (COVID-19) ,General Mathematics ,Population ,Stability (learning theory) ,General Physics and Astronomy ,01 natural sciences ,93C15 ,Article ,010305 fluids & plasmas ,Reduction (complexity) ,symbols.namesake ,Dual-bilinear-control-functions ,0103 physical sciences ,34H15 ,Applied mathematics ,Invariant (mathematics) ,education ,010301 acoustics ,Mathematics ,education.field_of_study ,Applied Mathematics ,Statistical and Nonlinear Physics ,Measure-zero ,Super-spreader ,Dual (category theory) ,Global-stability-conditions ,Coronavirus ,93A30 ,Susceptible individual ,Lyapunov-stable ,symbols - Abstract
In this paper, we sought and presented an 8-Dimensional deterministic mathematical COVID-19 dynamic model that accounted for the global stability analysis of the role of dual-bilinear treatment protocols of COVID-19 infection. The model, which is characterized by human-to-human transmission mode was investigated using dual non-pharmaceutical (face-masking and social distancing) and dual pharmaceutical (hydroxylchloroquine and azithromycin) as control functions following the interplay of susceptible population and varying infectious population. First, we investigated the model state-space and then established and computed the system reproduction number for both off-treatment ℜ 0 ( 1 ) = 10.94 and for onset-treatment ℜ 0 ( 2 ) = 3.224 . We considered the model for off-treatment and thereafter by incorporating the theory of LaSalle's invariant principle into the classical method of Lyapunov functions, we presented an approach for global stability analysis of COVID-19 dynamics. Numerical verification of system theoretical predictions was computed using in-built Runge-Kutta of order of precision 4 in a Mathcad surface. The set approach produces highly significant results in the main text. For example, while rapid population extinction was observed by the susceptible under off-treatment scenario in the first t f ≤ 18 days, the application of non-pharmaceuticals at early stage of infection proved very effective strategy in curtailing the spread of the virus. Moreso, the implementation of dual pharmacotherapies in conjunction with non-pharmaceuticals yields tremendous rejuvenation of susceptible population ( 0.5 ≤ S p ( t ) ≤ 3.143 c e l l s / m l 3 ) with maximal reduction in the rates of isolation, super spreaders and hospitalization of the infectives. Thus, experimental results of investigation affirm the suitability of proposed model for the control and treatment of the deadly disease provided individuals adheres to treatment protocols.
- Published
- 2021
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232. Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses.
- Author
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Guo, Ya and Tan, Jinglu
- Subjects
MATHEMATICAL models ,ESTIMATION theory ,LINEAR systems ,CONDITIONED response ,ORDINARY differential equations - Abstract
Many systems can be represented as linear time-invariant (LTI) systems in state space with ordinary differential equations (ODE). Forced responses are often used for model parameter estimation; however, some models are not uniquely identifiable from the data of forced responses, or experiments with pure forced response may not be the optimal design. It is thus meaningful to look for other types of data for model parameter estimation through redesigning experiments. In this work, we compare the influence of forced and initial condition responses on the deterministic identifiability of LTI systems in state space with ODEs as model structure. It is clearly demonstrated that one initial condition vector is equivalent to one column vector of the control matrix for constraining system eigenvectors. The combination of forced and initial condition responses can improve the identifiability of models that are not identifiable only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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- View/download PDF
233. The impact of self-protective measures in the optimal interventions for controlling infectious diseases of human population.
- Author
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Kassa, Semu and Ouhinou, Aziz
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PREVENTION of communicable diseases ,BIOLOGICAL mathematical modeling ,OPTIMAL control theory ,BEHAVIOR modification ,EPIDEMICS - Abstract
A mathematical model for infectious disease epidemics with behaviour change and treatment is formulated and analysed. It is indicated that behaviour modification by the population has a significant impact on the dynamics of the disease. Moreover, an optimal control theory is applied to propose the best possible combination of efforts in controlling a disease. It is shown that it may not be necessary to continuously apply treatment at a full rate to eradicate the disease, if the effort is supported by effective behaviour modification strategies. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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- View/download PDF
234. Spreading dynamics on complex networks: a general stochastic approach.
- Author
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Noël, Pierre-André, Allard, Antoine, Hébert-Dufresne, Laurent, Marceau, Vincent, and Dubé, Louis
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STOCHASTIC processes ,MARKOV processes ,COMPUTER simulation ,INFORMATION technology ,COMPUTATIONAL complexity - Abstract
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics ( e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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- View/download PDF
235. Modeling the impact of optimal screening on typhoid dynamics
- Author
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Mushayabasa, Steady
- Published
- 2016
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- View/download PDF
236. Measurement of Para-Xylene Diffusivity in Zeolites and Analyzing Desorption Curves Using the Mittag-Leffler Function
- Author
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Zaman, Sharif F., Baleanu, Dumitru, and Petráš, Ivo
- Published
- 2016
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- View/download PDF
237. Modeling peer influence effects on the spread of high-risk alcohol consumption behavior.
- Author
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Buonomo, Bruno and Lacitignola, Deborah
- Abstract
Alcohol dependence is among the main healthy risky behavior due to the high relevance of negative health and social effect. We study a mathematical model, given by nonlinear ordinary differential equations, describing the spread of high-risk alcohol consumption behavior within a community of individuals. We describe the peer-influence effects on alcohol addiction by assuming that susceptibles become heavy drinkers through the mechanism of imitation. We show that the model may exhibit the phenomenon of backward bifurcation. This means that alcohol problems may persist in the population even if the basic reproduction number is less than one. Nonlinear stability analysis of equilibria is also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
238. An Optimal Model Identification for Oscillatory Dynamics with a Stable Limit Cycle.
- Author
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Protas, Bartosz, Noack, Bernd, and Morzyński, Marek
- Subjects
LIMIT cycles ,DYNAMICAL systems ,MATHEMATICAL models ,PARAMETER estimation ,GALERKIN methods ,POLYNOMIALS - Abstract
We propose a general framework for the parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in traditional approaches. The proposed formulation relies on variational data assimilation using measurement data combined with assumptions on the smoothness of the propagator. This approach is illustrated using a generalized dynamic model describing oscillatory transients from an unstable fixed point to a stable limit cycle and arising in nonlinear stability analysis as an example. This 3-state model comprises an evolution equation for the dominant oscillation and an algebraic manifold for the low- and high-frequency components in an autonomous descriptor system. The proposed optimal model identification technique employs mode amplitudes of the transient vortex shedding in a cylinder wake flow as example measurements. The reconstruction obtained with our technique features distinct and systematic improvements over the well-known mean-field (Landau) model of the Hopf bifurcation. The computational aspect of the identification method is thoroughly validated showing that good reconstructions can also be obtained in the absence of accurate initial approximations. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
239. Structured parametric epidemic models.
- Author
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Cantó, B., Coll, C., and Sánchez, E.
- Subjects
EPIDEMICS ,MATHEMATICAL models ,MARKOV processes ,PARAMETERS (Statistics) ,EQUILIBRIUM ,MODEL theory - Abstract
A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton–Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number ℛ0and the stability of the model in the equilibrium is studied using ℛ0in terms of the model parameters. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
240. A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control
- Author
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Abdelfatah Kouidere, Bouchaib Khajji, Omar Balatif, and Mostafa Rachik
- Subjects
Gerontology ,Multi-age ,49J15 ,Population ,030209 endocrinology & metabolism ,93C55 ,Disease ,Pontryagin's minimum principle ,03 medical and health sciences ,0302 clinical medicine ,Mathematical model ,Age groups ,Diabetes mellitus ,medicine ,education ,Psychological treatment ,030304 developmental biology ,Mathematics ,Original Research ,0303 health sciences ,education.field_of_study ,Applied Mathematics ,Diabetes ,65Q10 ,medicine.disease ,Optimal control ,Social relation ,Computational Mathematics ,Diabetics with complication ,93A30 ,Simulation - Abstract
Diabetes is a disease which caused by socio-environmental and / or genetic factors. The negative effect of socio-environmental or lifestyle leads a susceptible individual to become a diabetic. On the one hand, social interaction wields a great deal of influence over lifestyle. On the other hand, genetic factors are the main cause of the birth diabetes genetic disorder. Considering these above mentioned factors. In the present paper, we study a discrete age continuous mathematical model that describes the dynamics of diabetics. We highlight the negative impact of socio-environmental on diabetic patients according to age groups. We also suggest an optimal strategy to implement the best campaigns of rising awareness that aims at protecting diabetic patients from the negative impact of a lifestyle that leads them to complications. In addition to psychological treatment and follow-up of diabetic patients with complications, an awareness campaign will also be carried out for people with potential diabetes that aims at educating them about the dangerous of diabetes and its complications. Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using MATLAB.
- Published
- 2020
241. Modeling COVID-19 in Cape Verde Islands -- An application of SIR model
- Author
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Adilson Da Silva
- Subjects
santiago ,2019-20 coronavirus outbreak ,Coronavirus disease 2019 (COVID-19) ,QC1-999 ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Population ,Biophysics ,boavista ,01 natural sciences ,Cape verde ,93a30 ,010104 statistics & probability ,03 medical and health sciences ,cape verde ,0302 clinical medicine ,FOS: Mathematics ,030212 general & internal medicine ,0101 mathematics ,Quantitative Biology - Populations and Evolution ,education ,Mathematics - Optimization and Control ,Molecular Biology ,sir model ,Mathematical Physics ,education.field_of_study ,Physics ,Applied Mathematics ,Populations and Evolution (q-bio.PE) ,93d99 ,Archaeology ,Computational Mathematics ,Geography ,covid-19 ,Optimization and Control (math.OC) ,FOS: Biological sciences ,92d30 ,TP248.13-248.65 ,Biotechnology - Abstract
The rapid and surprised emergence of COVID-19, having infected three million and killed two hundred thousand people worldwide in less than five months, has led many experts to focus on simulating its propagation dynamics in order to have an estimated outlook for the not too distante future and so supporting the local and national governments in making decisions. In this paper, we apply the SIR model to simulating the propagation dynamics of COVID-19 on the Cape Verde Islands. It will be done firstly for Santiago and Boavista Islands, ant then for Cape Verde in general. The choice of Santiago rests on the fact that it is the largest island, with more than 50% of the Population of the country, whereas Boavista was chosen because it is the island where the first case of COVID-19 in Cape Verde was diagnosed. Observations made after the date of the simulations were carried out corroborates our projections., Comment: 23 pages, 8 figures and 6 tables
- Published
- 2020
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- View/download PDF
242. Novel Corona virus Disease infection in Tunisia: Mathematical model and the impact of the quarantine strategy
- Author
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Haifa Ben Fredj and Farouk Chérif
- Subjects
medicine.medical_specialty ,General Mathematics ,Population ,34C60 ,General Physics and Astronomy ,92Bxx ,Disease ,Dynamical Systems (math.DS) ,Virus diseases ,Biology ,01 natural sciences ,Article ,010305 fluids & plasmas ,law.invention ,law ,0103 physical sciences ,Quarantine ,Pandemic ,Epidemiology ,medicine ,FOS: Mathematics ,Mathematics - Dynamical Systems ,education ,Quantitative Biology - Populations and Evolution ,010301 acoustics ,Estimation ,education.field_of_study ,Actuarial science ,Mathematical modelling ,Applied Mathematics ,Mortality rate ,Populations and Evolution (q-bio.PE) ,Statistical and Nonlinear Physics ,34A34 ,93A30 ,FOS: Biological sciences ,Nonlinear differential systems ,Qualitative study ,Simulation - Abstract
Highlights • We give a model of dynamical behavior of COVID-19 in Tunisia. • We study the qualitative properties of the considered model. • We establish the stability of equilibrium point via R 0. • We prove theoretically and by numerical simulations the effect of quarantine strategy on the spread of the disease., Corona virus disease (COVID-19) is an extremely serious infection with an extremely high death rate worldwide. In March, the disease was declared a ”global pandemic” by the World Health Organization (WHO). Until now, there is no known vaccine or drug, since the unknown things related to the disease are more important than our theoretical and empirical knowledge. However, mathematical modeling and the estimation of the basic number of reproductions can provide clarifications in order to determine the potential and severity of this epidemic and therefore provide essential information to identify the type of measures and interventions to be taken to control the intensity of the spread of the disease. Hence, in this paper, we propose a new deterministic compartmental model based on the clinical progression of the disease, the epidemiological state of the individuals and the intervention for the dynamics of COVID-19 infections. Our approach consists of seven phenotypes: the susceptible humans, exposed humans, infectious humans, the recovered humans, the quarantine population, there recovered-exposed and deceased population. We proved first through mathematical approach the positivity, boundness and existence of a solution to the considered model. We also studied the existence of the disease free equilibrium and corresponding stability. Our work shows, in particular, that the disease will decrease if the number of reproduction R0 was less than one. Moreover, the impact of the quarantine strategies to reduce the spread of this disease is discussed. The theoretical results are validated by some numerical simulations of the system of the epidemic’s differential equations. It should be mentioned that, the error between the considered model and the official data curve is quite small.
- Published
- 2020
- Full Text
- View/download PDF
243. A 2D-Planar Dielectrophoretic Model with Electro-Thermally Induced Fluid Motion and the Stability of Trapping Zones.
- Author
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Simha, H. and Banavar, R. N.
- Subjects
DIELECTROPHORESIS ,ARC-jet rocket engines ,FLUID dynamics ,STABILITY (Mechanics) ,ELECTROKINETICS ,ELECTRIC fields - Abstract
Dielectrophoresis (DEP) is an electrokinetics-based phenomenon that involves the motion of a particle due to the interaction between an applied nonuniform electric field and an induced dipole moment. This technique is very effective in particle manipulation and separation. Earlier studies on control-amenable models to describe the motion of a neutrally buoyant, neutrally charged particle in a chamber with a parallel electrode array have restricted the motion of the particle to one dimension. Here, incorporating the electro-thermal fluid motion as well, we present a 2D-planar DEP model and study the effect of electro-thermal fluid motion on particle trapping. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
244. Diffusion-Chemotaxis Model of Effects of Cortisol on Immune Response to Human Immunodeficiency virus
- Author
-
Shikaa Samuel and Vinod Gill
- Subjects
0301 basic medicine ,92b08 ,Computer Networks and Communications ,General Chemical Engineering ,General Engineering ,Human immunodeficiency virus (HIV) ,65p10 ,Chemotaxis ,radial basis functions ,65p35 ,Biology ,cortisol ,medicine.disease_cause ,Engineering (General). Civil engineering (General) ,03 medical and health sciences ,chemotaxis system ,93a30 ,030104 developmental biology ,0302 clinical medicine ,Immune system ,Modeling and Simulation ,Immunology ,medicine ,TA1-2040 ,030217 neurology & neurosurgery - Abstract
In quest to contain and subsequently eradication Human Immunodeficiency virus (HIV) in the society, mathematical modelling remains an important research tool. In this paper, we formulated a mathematical model to study the effects of cortisol on immune response to HIV capturing the roles played by dendritic cells, T helper cells, regulatory T cells and cytotoxic T cells in the virus replication dynamics. The primary source of concentration of cortisol in this work is through psychological stress. Numerical experiments are performed to examine the effect of cortisol on selective inhibition of antigen presentation activities and up-regulation of naive cytotoxic T cells activation in the case of acute and persistent stressful conditions.
- Published
- 2018
245. TACO: a toolkit for AMPL control optimization.
- Author
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Kirches, Christian and Leyffer, Sven
- Abstract
We describe a set of extensions to the AMPL modeling language to conveniently model mixed-integer optimal control problems for ODE or DAE dynamic processes. These extensions are realized as AMPL user functions and suffixes and do not require intrusive changes to the AMPL language standard or implementation itself. We describe and provide TACO, a Toolkit for AMPL Control Optimization that reads AMPL stub.nl files and detects the structure of the optimal control problem. This toolkit is designed to facilitate the coupling of existing optimal control software packages to AMPL. We discuss requirements, capabilities, and the current implementation. Using the example of the multiple shooting code for optimal control MUSCOD-II, a direct and simultaneous method for DAE-constrained optimal control, we demonstrate how the problem information provided by the TACO toolkit is interfaced to the solver. In addition, we show how the MS-MINTOC algorithm for mixed-integer optimal control can be used to efficiently solve mixed-integer optimal control problems modeled in AMPL. We use the AMPL extensions to model three control problem examples and we discuss how those extensions affect the representation of optimal control problems. Solutions to these problems are obtained by using MUSCOD-II and MS-MINTOC inside the AMPL environment. A collection of further AMPL control models is provided on the web site . MUSCOD-II and MS-MINTOC have been made available on the NEOS Server for Optimization, using the TACO toolkit to enable input of AMPL models. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
246. A practical approach to parameter estimation applied to model predicting heart rate regulation.
- Author
-
Olufsen, Mette and Ottesen, Johnny
- Subjects
HEART beat ,REGULATION of heart contraction ,BIOLOGICAL models ,MATHEMATICAL models ,ANALYSIS of variance ,THEORY of knowledge ,ESTIMATION theory ,SET theory - Abstract
Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The 'best' subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
247. Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems.
- Author
-
Ding, Feng and Gu, Ya
- Subjects
PERFORMANCE evaluation ,LEAST squares ,ALGORITHMS ,DELAY lines ,PARAMETER estimation ,STOCHASTIC processes ,SIMULATION methods & models ,SYSTEM analysis - Abstract
Based on the input–output representation of one-step state-delay systems, we use the auxiliary model-based recursive least-squares algorithm to estimate the parameters of the systems and study the convergence of the proposed algorithm by using the stochastic process theory. A simulation example is provided. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
248. On modeling with multiplicative differential equations.
- Author
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Bashirov, Agamirza, Mısırlı, Emine, Tandoğdu, Yücel, and Özyapıcı, Ali
- Abstract
This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
249. Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models.
- Author
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Wang, Wei, Li, Junhong, and Ding, Ruifeng
- Subjects
MAXIMUM likelihood statistics ,PARAMETER estimation ,ALGORITHMS ,AUTOREGRESSION (Statistics) ,TRANSFER functions ,DATA analysis ,RECURSIVE functions ,LEAST squares ,STOCHASTIC systems - Abstract
A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
- Full Text
- View/download PDF
250. Pyomo: modeling and solving mathematical programs in Python.
- Author
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Hart, William, Watson, Jean-Paul, and Woodruff, David
- Abstract
We describe Pyomo, an open source software package for modeling and solving mathematical programs in Python. Pyomo can be used to define abstract and concrete problems, create problem instances, and solve these instances with standard open-source and commercial solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS. In contrast, Pyomo's modeling objects are embedded within a full-featured high-level programming language with a rich set of supporting libraries. Pyomo leverages the capabilities of the Coopr software library, which together with Pyomo is part of IBM's COIN-OR open-source initiative for operations research software. Coopr integrates Python packages for defining optimizers, modeling optimization applications, and managing computational experiments. Numerous examples illustrating advanced scripting applications are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
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