Anticipatory Neurofuzzy Control

NASA Technical Reports Server (NTRS)

Mccullough, Claire L.

1994-01-01

Technique of feedback control, called "anticipatory neurofuzzy control," developed for use in controlling flexible structures and other dynamic systems for which mathematical models of dynamics poorly known or unknown. Superior ability to act during operation to compensate for, and adapt to, errors in mathematical model of dynamics, changes in dynamics, and noise. Also offers advantage of reduced computing time. Hybrid of two older fuzzy-logic control techniques: standard fuzzy control and predictive fuzzy control.

Teachers' Use of Computational Tools to Construct and Explore Dynamic Mathematical Models

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2011-01-01

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

Mathematical Model Of Nerve/Muscle Interaction

NASA Technical Reports Server (NTRS)

Hannaford, Blake

1990-01-01

Phasic Excitation/Activation (PEA) mathematical model simulates short-term nonlinear dynamics of activation and control of muscle by nerve. Includes electronic and mechanical elements. Is homeomorphic at level of its three major building blocks, which represent motoneuron, dynamics of activation of muscle, and mechanics of muscle.

Differential Equations Models to Study Quorum Sensing.

PubMed

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation.

PubMed

Getto, Philipp; Marciniak-Czochra, Anna

2015-01-01

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...

Population dynamics of Aphis gossypii Glover and in sole and intercropping systems of cotton and cowpea.

PubMed

Fernandes, Francisco S; Godoy, Wesley A C; Ramalho, Francisco S; Garcia, Adriano G; Santos, Bárbara D B; Malaquias, José B

2018-01-01

Population dynamics of aphids have been studied in sole and intercropping systems. These studies have required the use of more precise analytical tools in order to better understand patterns in quantitative data. Mathematical models are among the most important tools to explain the dynamics of insect populations. This study investigated the population dynamics of aphids Aphis gossypii and Aphis craccivora over time, using mathematical models composed of a set of differential equations as a helpful analytical tool to understand the population dynamics of aphids in arrangements of cotton and cowpea. The treatments were sole cotton, sole cowpea, and three arrangements of cotton intercropped with cowpea (t1, t2 and t3). The plants were infested with two aphid species and were evaluated at 7, 14, 28, 35, 42, and 49 days after the infestations. Mathematical models were used to fit the population dynamics of two aphid species. There were good fits for aphid dynamics by mathematical model over time. The highest population peak of both species A. gossypii and A. craccivora was found in the sole crops, and the lowest population peak was found in crop system t2. These results are important for integrated management programs of aphids in cotton and cowpea.

Clinical study and numerical simulation of brain cancer dynamics under radiotherapy

NASA Astrophysics Data System (ADS)

Nawrocki, S.; Zubik-Kowal, B.

2015-05-01

We perform a clinical and numerical study of the progression of brain cancer tumor growth dynamics coupled with the effects of radiotherapy. We obtained clinical data from a sample of brain cancer patients undergoing radiotherapy and compare it to our numerical simulations to a mathematical model of brain tumor cell population growth influenced by radiation treatment. We model how the body biologically receives a physically delivered dose of radiation to the affected tumorous area in the form of a generalized LQ model, modified to account for the conversion process of sublethal lesions into lethal lesions at high radiation doses. We obtain good agreement between our clinical data and our numerical simulations of brain cancer progression given by the mathematical model, which couples tumor growth dynamics and the effect of irradiation. The correlation, spanning a wide dataset, demonstrates the potential of the mathematical model to describe the dynamics of brain tumor growth influenced by radiotherapy.

Mathematical model for adaptive control system of ASEA robot at Kennedy Space Center

NASA Technical Reports Server (NTRS)

Zia, Omar

1989-01-01

The dynamic properties and the mathematical model for the adaptive control of the robotic system presently under investigation at Robotic Application and Development Laboratory at Kennedy Space Center are discussed. NASA is currently investigating the use of robotic manipulators for mating and demating of fuel lines to the Space Shuttle Vehicle prior to launch. The Robotic system used as a testbed for this purpose is an ASEA IRB-90 industrial robot with adaptive control capabilities. The system was tested and it's performance with respect to stability was improved by using an analogue force controller. The objective of this research project is to determine the mathematical model of the system operating under force feedback control with varying dynamic internal perturbation in order to provide continuous stable operation under variable load conditions. A series of lumped parameter models are developed. The models include some effects of robot structural dynamics, sensor compliance, and workpiece dynamics.

Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work

NASA Astrophysics Data System (ADS)

Pedrammehr, Siamak; Nahavandi, Saeid; Abdi, Hamid

2018-04-01

In this research, a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work. For the first time, a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms. An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories. Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Modelling Mathematics Teachers' Intention to Use the Dynamic Geometry Environments in Macau: An SEM Approach

ERIC Educational Resources Information Center

Zhou, Mingming; Chan, Kan Kan; Teo, Timothy

2016-01-01

Dynamic geometry environments (DGEs) provide computer-based environments to construct and manipulate geometric figures with great ease. Research has shown that DGEs has positive impact on student motivation, engagement, and achievement in mathematics learning. However, the adoption of DGEs by mathematics teachers varies substantially worldwide.…

Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

ERIC Educational Resources Information Center

Marshall, Neil; Buteau, Chantal

2014-01-01

As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

Polynomial algebra of discrete models in systems biology.

PubMed

Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2010-07-01

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

Mathematical model of the glucose-insulin regulatory system: From the bursting electrical activity in pancreatic β-cells to the glucose dynamics in the whole body

NASA Astrophysics Data System (ADS)

Han, Kyungreem; Kang, Hyuk; Choi, M. Y.; Kim, Jinwoong; Lee, Myung-Shik

2012-10-01

A theoretical approach to the glucose-insulin regulatory system is presented. By means of integrated mathematical modeling and extensive numerical simulations, we probe the cell-level dynamics of the membrane potential, intracellular Ca2+ concentration, and insulin secretion in pancreatic β-cells, together with the whole-body level glucose-insulin dynamics in the liver, brain, muscle, and adipose tissues. In particular, the three oscillatory modes of insulin secretion are reproduced successfully. Such comprehensive mathematical modeling may provide a theoretical basis for the simultaneous assessment of the β-cell function and insulin resistance in clinical examination.

Effects of intracerebroventricular administration of beta-amyloid on the dynamics of learning in purebred and mongrel rats.

PubMed

Stepanov, I I; Kuznetsova, N N; Klement'ev, B I; Sapronov, N S

2007-07-01

The effects of intracerebroventricular administration of the beta-amyloid peptide fragment Abeta(25-35) on the dynamics of the acquisition of a conditioned reflex in a Y maze were studied in Wistar and mongrel rats. The dynamics of decreases in the number of errors were assessed using an exponential mathematical model describing the transfer function of a first-order system in response to stepped inputs using non-linear regression analysis. This mathematical model provided a good approximation to the learning dynamics in inbred and mongrel mice. In Wistar rats, beta-amyloid impaired learning, with reduced memory between the first and second training sessions, but without complete blockade of learning. As a result, learning dynamics were no longer approximated by the mathematical model. At the same time, comparison of the number of errors in each training sessions between the control group of Wistar rats and the group given beta-amyloid showed no significant differences (Student's t test). This result demonstrates the advantage of regression analysis based on a mathematical model over the traditionally used statistical methods. In mongrel rats, the effect of beta-amyloid was limited to an a slowing of the process of learning as compared with control mongrel rats, with retention of the approximation by the mathematical model. It is suggested that mongrel animals have some kind of innate, genetically determined protective mechanism against the harmful effects of beta-amyloid.

And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

ERIC Educational Resources Information Center

Street, Garrett M.; Laubach, Timothy A.

2013-01-01

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

CADLIVE toolbox for MATLAB: automatic dynamic modeling of biochemical networks with comprehensive system analysis.

PubMed

Inoue, Kentaro; Maeda, Kazuhiro; Miyabe, Takaaki; Matsuoka, Yu; Kurata, Hiroyuki

2014-09-01

Mathematical modeling has become a standard technique to understand the dynamics of complex biochemical systems. To promote the modeling, we had developed the CADLIVE dynamic simulator that automatically converted a biochemical map into its associated mathematical model, simulated its dynamic behaviors and analyzed its robustness. To enhance the feasibility by CADLIVE and extend its functions, we propose the CADLIVE toolbox available for MATLAB, which implements not only the existing functions of the CADLIVE dynamic simulator, but also the latest tools including global parameter search methods with robustness analysis. The seamless, bottom-up processes consisting of biochemical network construction, automatic construction of its dynamic model, simulation, optimization, and S-system analysis greatly facilitate dynamic modeling, contributing to the research of systems biology and synthetic biology. This application can be freely downloaded from http://www.cadlive.jp/CADLIVE_MATLAB/ together with an instruction.

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

NASA Astrophysics Data System (ADS)

Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

2012-06-01

A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

A Mathematical Model of Economic Population Dynamics in a Country That Has Optimal Zakat Management

NASA Astrophysics Data System (ADS)

Subhan, M.

2018-04-01

Zakat is the main tools against two issues in Islamic economy: economic justice and helping the poor. However, no government of Islamic countries can solve the economic disparity today. A mathematical model could give some understanding about this phenomenon. The goal of this research is to obtain a mathematical model that can describe the dynamic of economic group population. The research is theoretical based on relevance references. From the analytical and numerical simulation, we conclude that well-manage zakat and full comitment of the wealthy can achieve wealth equilibrium that represents minimum poverty.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Mathematical modeling of moving boundary problems in thermal energy storage

NASA Technical Reports Server (NTRS)

Solomon, A. D.

1980-01-01

The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

Understanding the Impact of Interventions to Prevent Antimicrobial Resistant Infections in the Long-Term Care Facility: A Review and Practical Guide to Mathematical Modeling.

PubMed

Rosello, Alicia; Horner, Carolyne; Hopkins, Susan; Hayward, Andrew C; Deeny, Sarah R

2017-02-01

OBJECTIVES (1) To systematically search for all dynamic mathematical models of infectious disease transmission in long-term care facilities (LTCFs); (2) to critically evaluate models of interventions against antimicrobial resistance (AMR) in this setting; and (3) to develop a checklist for hospital epidemiologists and policy makers by which to distinguish good quality models of AMR in LTCFs. METHODS The CINAHL, EMBASE, Global Health, MEDLINE, and Scopus databases were systematically searched for studies of dynamic mathematical models set in LTCFs. Models of interventions targeting methicillin-resistant Staphylococcus aureus in LTCFs were critically assessed. Using this analysis, we developed a checklist for good quality mathematical models of AMR in LTCFs. RESULTS AND DISCUSSION Overall, 18 papers described mathematical models that characterized the spread of infectious diseases in LTCFs, but no models of AMR in gram-negative bacteria in this setting were described. Future models of AMR in LTCFs require a more robust methodology (ie, formal model fitting to data and validation), greater transparency regarding model assumptions, setting-specific data, realistic and current setting-specific parameters, and inclusion of movement dynamics between LTCFs and hospitals. CONCLUSIONS Mathematical models of AMR in gram-negative bacteria in the LTCF setting, where these bacteria are increasingly becoming prevalent, are needed to help guide infection prevention and control. Improvements are required to develop outputs of sufficient quality to help guide interventions and policy in the future. We suggest a checklist of criteria to be used as a practical guide to determine whether a model is robust enough to test policy. Infect Control Hosp Epidemiol 2017;38:216-225.

Mathematical Modeling of the Dynamics of Salmonella Cerro Infection in a US Dairy Herd

NASA Astrophysics Data System (ADS)

Chapagain, Prem; van Kessel, Jo Ann; Karns, Jeffrey; Wolfgang, David; Schukken, Ynte; Grohn, Yrjo

2006-03-01

Salmonellosis has been one of the major causes of human foodborne illness in the US. The high prevalence of infections makes transmission dynamics of Salmonella in a farm environment of interest both from animal and human health perspectives. Mathematical modeling approaches are increasingly being applied to understand the dynamics of various infectious diseases in dairy herds. Here, we describe the transmission dynamics of Salmonella infection in a dairy herd with a set of non-linear differential equations. Although the infection dynamics of different serotypes of Salmonella in cattle are likely to be different, we find that a relatively simple SIR-type model can describe the observed dynamics of the Salmonella enterica serotype Cerro infection in the herd.

Predicting Student Academic Performance in an Engineering Dynamics Course: A Comparison of Four Types of Predictive Mathematical Models

ERIC Educational Resources Information Center

Huang, Shaobo; Fang, Ning

2013-01-01

Predicting student academic performance has long been an important research topic in many academic disciplines. The present study is the first study that develops and compares four types of mathematical models to predict student academic performance in engineering dynamics--a high-enrollment, high-impact, and core course that many engineering…

Mathematical Model Development and Simulation Support

NASA Technical Reports Server (NTRS)

Francis, Ronald C.; Tobbe, Patrick A.

2000-01-01

This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.

Emulation of rocket trajectory based on a six degree of freedom model

NASA Astrophysics Data System (ADS)

Zhang, Wenpeng; Li, Fan; Wu, Zhong; Li, Rong

2008-10-01

In this paper, a 6-DOF motion mathematical model is discussed. It is consisted of body dynamics and kinematics block, aero dynamics block and atmosphere block. Based on Simulink, the whole rocket trajectory mathematical model is developed. In this model, dynamic system simulation becomes easy and visual. The method of modularization design gives more convenience to transplant. At last, relevant data is given to be validated by Monte Carlo means. Simulation results show that the flight trajectory of the rocket can be simulated preferably by means of this model, and it also supplies a necessary simulating tool for the development of control system.

Mathematical modeling relevant to closed artificial ecosystems

USGS Publications Warehouse

DeAngelis, D.L.

2003-01-01

The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.

Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

PubMed

Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

2015-02-01

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

The limitations of mathematical modeling in high school physics education

NASA Astrophysics Data System (ADS)

Forjan, Matej

The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems geometrical approach to solving differential equations is appropriate, while in dynamical systems of higher dimensions mathematical constraints are avoided by using a graphical oriented programs for modeling. Because in dealing with dynamical systems with four or more dimensions we may encounter problems in numerical solving, we also show how to overcome them. In the case of electrostatic pendulum we show the process of modeling the real dynamical system and we put a particular emphasize on the different phases of modeling and on the way of overcoming constraints on which we encounter in the development of the model.

Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I.

PubMed

Afenya, Evans K; Ouifki, Rachid; Camara, Baba I; Mundle, Suneel D

2016-04-01

Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture. Copyright © 2016 Elsevier Inc. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua

Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

[Representation and mathematical analysis of human crystalline lens].

PubMed

Tălu, Stefan; Giovanzana, Stefano; Tălu, Mihai

2011-01-01

The surface of human crystalline lens can be described and analyzed using mathematical models based on parametric representations, used in biomechanical studies and 3D solid modeling of the lens. The mathematical models used in lens biomechanics allow the study and the behavior of crystalline lens on variables and complex dynamic loads. Also, the lens biomechanics has the potential to improve the results in the development of intraocular lenses and cataract surgery. The paper presents the most representative mathematical models currently used for the modeling of human crystalline lens, both optically and biomechanically.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Mathematical Modeling of Diverse Phenomena

NASA Technical Reports Server (NTRS)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

Parametric diagnosis of the adaptive gas path in the automatic control system of the aircraft engine

NASA Astrophysics Data System (ADS)

Kuznetsova, T. A.

2017-01-01

The paper dwells on the adaptive multimode mathematical model of the gas-turbine aircraft engine (GTE) embedded in the automatic control system (ACS). The mathematical model is based on the throttle performances, and is characterized by high accuracy of engine parameters identification in stationary and dynamic modes. The proposed on-board engine model is the state space linearized low-level simulation. The engine health is identified by the influence of the coefficient matrix. The influence coefficient is determined by the GTE high-level mathematical model based on measurements of gas-dynamic parameters. In the automatic control algorithm, the sum of squares of the deviation between the parameters of the mathematical model and real GTE is minimized. The proposed mathematical model is effectively used for gas path defects detecting in on-line GTE health monitoring. The accuracy of the on-board mathematical model embedded in ACS determines the quality of adaptive control and reliability of the engine. To improve the accuracy of identification solutions and sustainability provision, the numerical method of Monte Carlo was used. The parametric diagnostic algorithm based on the LPτ - sequence was developed and tested. Analysis of the results suggests that the application of the developed algorithms allows achieving higher identification accuracy and reliability than similar models used in practice.

Non-Lipschitz Dynamics Approach to Discrete Event Systems

NASA Technical Reports Server (NTRS)

Zak, M.; Meyers, R.

1995-01-01

This paper presents and discusses a mathematical formalism for simulation of discrete event dynamics (DED) - a special type of 'man- made' system designed to aid specific areas of information processing. A main objective is to demonstrate that the mathematical formalism for DED can be based upon the terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.

Satellite orbit computation methods

NASA Technical Reports Server (NTRS)

1977-01-01

Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

Transmission dynamics of cholera: Mathematical modeling and control strategies

NASA Astrophysics Data System (ADS)

Sun, Gui-Quan; Xie, Jun-Hui; Huang, Sheng-He; Jin, Zhen; Li, Ming-Tao; Liu, Liqun

2017-04-01

Cholera, as an endemic disease around the world, has generated great threat to human society and caused enormous morbidity and mortality with weak surveillance system. In this paper, we propose a mathematical model to describe the transmission of Cholera. Moreover, basic reproduction number and the global dynamics of the dynamical model are obtained. Then we apply our model to characterize the transmission process of Cholera in China. It was found that, in order to avoid its outbreak in China, it may be better to increase immunization coverage rate and make effort to improve environmental management especially for drinking water. Our results may provide some new insights for elimination of Cholera.

Gamma Ray Observatory (GRO) dynamics simulator requirements and mathematical specifications, revision 1

NASA Technical Reports Server (NTRS)

Harman, R.; Blejer, D.

1990-01-01

The requirements and mathematical specifications for the Gamma Ray Observatory (GRO) Dynamics Simulator are presented. The complete simulator system, which consists of the profie subsystem, simulation control and input/output subsystem, truth model subsystem, onboard computer model subsystem, and postprocessor, is described. The simulator will be used to evaluate and test the attitude determination and control models to be used on board GRO under conditions that simulate the expected in-flight environment.

A dynamic, climate-driven model of Rift Valley fever.

PubMed

Leedale, Joseph; Jones, Anne E; Caminade, Cyril; Morse, Andrew P

2016-03-31

Outbreaks of Rift Valley fever (RVF) in eastern Africa have previously occurred following specific rainfall dynamics and flooding events that appear to support the emergence of large numbers of mosquito vectors. As such, transmission of the virus is considered to be sensitive to environmental conditions and therefore changes in climate can impact the spatiotemporal dynamics of epizootic vulnerability. Epidemiological information describing the methods and parameters of RVF transmission and its dependence on climatic factors are used to develop a new spatio-temporal mathematical model that simulates these dynamics and can predict the impact of changes in climate. The Liverpool RVF (LRVF) model is a new dynamic, process-based model driven by climate data that provides a predictive output of geographical changes in RVF outbreak susceptibility as a result of the climate and local livestock immunity. This description of the multi-disciplinary process of model development is accessible to mathematicians, epidemiological modellers and climate scientists, uniting dynamic mathematical modelling, empirical parameterisation and state-of-the-art climate information.

Mathematical model of the loan portfolio dynamics in the form of Markov chain considering the process of new customers attraction

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana

2017-12-01

Mathematical model of the loan portfolio structure change in the form of Markov chain is explored. This model considers in one scheme both the process of customers attraction, their selection based on the credit score, and loans repayment. The model describes the structure and volume of the loan portfolio dynamics, which allows to make medium-term forecasts of profitability and risk. Within the model corrective actions of bank management in order to increase lending volumes or to reduce the risk are formalized.

An analytical approach to top predator interference on the dynamics of a food chain model

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Vijayalakshmi, T.

2018-04-01

In this paper, a nonlinear mathematical model is proposed and analyzed to study of top predator interference on the dynamics of a food chain model. The mathematical model is formulated using the system of non-linear ordinary differential equations. In this model, there are three state dimensionless variables, viz, size of prey population x, size of intermediate predator y and size of top predator population z. The analytical results are compared with the numerical simulation using MATLAB software and satisfactory results are noticed.

Evaluation of the Thermodynamic Consistency of Closure Approximations in Several Models Proposed for the Description of Liquid Crystalline Dynamics

NASA Astrophysics Data System (ADS)

Edwards, Brian J.

2002-05-01

Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

A magneto-rheological fluid mount featuring squeeze mode: analysis and testing

NASA Astrophysics Data System (ADS)

Chen, Peng; Bai, Xian-Xu; Qian, Li-Jun; Choi, Seung-Bok

2016-05-01

This paper presents a mathematical model for a new semi-active vehicle engine mount utilizing magneto-rheological (MR) fluids in squeeze mode (MR mount in short) and validates the model by comparing analysis results with experimental tests. The proposed MR mount is mainly comprised of a frame for installation, a main rubber, a squeeze plate and a bobbin for coil winding. When the magnetic fields on, MR effect occurs in the upper gap between the squeeze plate and the bobbin, and the dynamic stiffness can be controlled by tuning the applied currents. Employing Bingham model and flow properties between parallel plates of MR fluids, a mathematical model for the squeeze type of MR mount is formulated with consideration of the fluid inertia, MR effect and hysteresis property. The field-dependent dynamic stiffness of the MR mount is then analyzed using the established mathematical model. Subsequently, in order to validate the mathematical model, an appropriate size of MR mount is fabricated and tested. The field-dependent force and dynamic stiffness of the proposed MR mount are evaluated and compared between the model and experimental tests in both time and frequency domains to verify the model efficiency. In addition, it is shown that both the damping property and the stiffness property of the proposed MR mount can be simultaneously controlled.

A MATHEMATICAL MODEL FOR THE ANDROGENIC REGULATION OF THE PROSTATE IN INTACT AND CASTRATE ADULT MALE RATS

EPA Science Inventory

An abstract that provides understanding for a mathematical model by Barton and Anderson, for the dynamics of androgenic synthesis, transport, metabolism, and regulation of the rodent ventral prostate.

MATHEMATICAL MODEL OF STERIODOGENESIS TO PREDICT DYNAMIC RESPONSE TO ENDOCRINE DISRUPTORS

EPA Science Inventory

WE ARE DEVELOPING A MECHANISTIC MATHEMATICAL MODEL OF THE INTRATESTICULAR AND INTRAOVARIAN METABOLIC NETWORK THAT MEDIATES STEROID SYNTHESIS, AND THE KINETICS FOR ENZYME INHIBITION BY EDCs TO PREDICT THE TIME AND DOSE-RESPONSE.

Terminal Dynamics Approach to Discrete Event Systems

NASA Technical Reports Server (NTRS)

Zak, Michail; Meyers, Ronald

1995-01-01

This paper presents and discusses a mathematical formalism for simulation of discrete event dynamic (DED)-a special type of 'man-made' systems to serve specific purposes of information processing. The main objective of this work is to demonstrate that the mathematical formalism for DED can be based upon a terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.!.

Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

NASA Astrophysics Data System (ADS)

Choustova, Olga

2007-02-01

We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

Correlation of AH-1G airframe test data with a NASTRAN mathematical model

NASA Technical Reports Server (NTRS)

Cronkhite, J. D.; Berry, V. L.

1976-01-01

Test data was provided for evaluating a mathematical vibration model of the Bell AH-1G helicopter airframe. The math model was developed and analyzed using the NASTRAN structural analysis computer program. Data from static and dynamic tests were used for comparison with the math model. Static tests of the fuselage and tailboom were conducted to verify the stiffness representation of the NASTRAN model. Dynamic test data were obtained from shake tests of the airframe and were used to evaluate the NASTRAN model for representing the low frequency (below 30 Hz) vibration response of the airframe.

Incorporating heterogeneity into the transmission dynamics of a waterborne disease model.

PubMed

Collins, O C; Govinder, K S

2014-09-07

We formulate a mathematical model that captures the essential dynamics of waterborne disease transmission to study the effects of heterogeneity on the spread of the disease. The effects of heterogeneity on some important mathematical features of the model such as the basic reproduction number, type reproduction number and final outbreak size are analysed accordingly. We conduct a real-world application of this model by using it to investigate the heterogeneity in transmission in the recent cholera outbreak in Haiti. By evaluating the measure of heterogeneity between the administrative departments in Haiti, we discover a significant difference in the dynamics of the cholera outbreak between the departments. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nonlinear and Digital Man-machine Control Systems Modeling

NASA Technical Reports Server (NTRS)

Mekel, R.

1972-01-01

An adaptive modeling technique is examined by which controllers can be synthesized to provide corrective dynamics to a human operator's mathematical model in closed loop control systems. The technique utilizes a class of Liapunov functions formulated for this purpose, Liapunov's stability criterion and a model-reference system configuration. The Liapunov function is formulated to posses variable characteristics to take into consideration the identification dynamics. The time derivative of the Liapunov function generate the identification and control laws for the mathematical model system. These laws permit the realization of a controller which updates the human operator's mathematical model parameters so that model and human operator produce the same response when subjected to the same stimulus. A very useful feature is the development of a digital computer program which is easily implemented and modified concurrent with experimentation. The program permits the modeling process to interact with the experimentation process in a mutually beneficial way.

Students' Conceptions of Congruency through the Use of Dynamic Geometry Software

ERIC Educational Resources Information Center

Gonzalez, Gloriana; Herbst, Patricio G.

2009-01-01

This paper describes students' interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK[cent sign] model of conceptions, suggests that incorporating technology in mathematics classrooms…

The impact of cell regeneration on the dynamics of viral coinfection

NASA Astrophysics Data System (ADS)

Pinky, Lubna; Dobrovolny, Hana M.

2017-06-01

Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ˜40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.

Understanding immunology via engineering design: the role of mathematical prototyping.

PubMed

Klinke, David J; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and "fitness for use," can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2009-01-01

This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Dynamic model of production enterprises based on accounting registers and its identification

NASA Astrophysics Data System (ADS)

Sirazetdinov, R. T.; Samodurov, A. V.; Yenikeev, I. A.; Markov, D. S.

2016-06-01

The report focuses on the mathematical modeling of economic entities based on accounting registers. Developed the dynamic model of financial and economic activity of the enterprise as a system of differential equations. Created algorithms for identification of parameters of the dynamic model. Constructed and identified the model of Russian machine-building enterprises.

3-D Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

DTIC Science & Technology

2014-01-01

resistant mutants [?]. Inspired by experimental findings, researchers have come up with some mathematical models to study biofilm formation and function...develop a full 3D mathematical model to study how quorum sensing regulates biofilm formation and development as well as the pros and cons of quorum...have given an overview of current advances in mathematical modeling of biofilms. Concerning coupling biofilm growth with quorum sensing features

Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can bemore » potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.« less

A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology.

PubMed

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology.

A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology

PubMed Central

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

2017-01-01

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology. PMID:29267315

[Mathematical calculation of strength of the vertebral column in surgical treatment of unstable fractures of the spine].

PubMed

Orlov, S V; Kanykin, A Iu; Moskalev, V P; Shchedrenok, V V; Sedov, R L

2009-01-01

A mathematical model of a three-vertebra complex was developed in order to make an exact calculation of loss of supporting ability of the vertebral column in trauma. Mathematical description of the dynamic processes was based on Lagrange differential equation of the second order. The degree of compression and instability of the three-vertebra complex, established using mathematical modeling, determines the decision on the surgical treatment and might be considered as a prognostic criterion of the course of the compression trauma of the spine. The method of mathematical modeling of supporting ability of the vertebral column was used in 72 patients.

The application of virtual prototyping methods to determine the dynamic parameters of mobile robot

NASA Astrophysics Data System (ADS)

Kurc, Krzysztof; Szybicki, Dariusz; Burghardt, Andrzej; Muszyńska, Magdalena

2016-04-01

The paper presents methods used to determine the parameters necessary to build a mathematical model of an underwater robot with a crawler drive. The parameters present in the dynamics equation will be determined by means of advanced mechatronic design tools, including: CAD/CAE software andMES modules. The virtual prototyping process is described as well as the various possible uses (design adaptability) depending on the optional accessories added to the vehicle. A mathematical model is presented to show the kinematics and dynamics of the underwater crawler robot, essential for the design stage.

Concepts and tools for predictive modeling of microbial dynamics.

PubMed

Bernaerts, Kristel; Dens, Els; Vereecken, Karen; Geeraerd, Annemie H; Standaert, Arnout R; Devlieghere, Frank; Debevere, Johan; Van Impe, Jan F

2004-09-01

Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.

A mathematical simulation model of the CH-47B helicopter, volume 2

NASA Technical Reports Server (NTRS)

Weber, J. M.; Liu, T. Y.; Chung, W.

1984-01-01

A nonlinear simulation model of the CH-47B helicopter, was adapted for use in a simulation facility. The model represents the specific configuration of the variable stability CH-47B helicopter. Modeling of the helicopter uses a total force approach in six rigid body degrees of freedom. Rotor dynamics are simulated using the Wheatley-Bailey equations, steady state flapping dynamics and included in the model of the option for simulation of external suspension, slung load equations of motion. Validation of the model was accomplished by static and dynamic data from the original Boeing Vertol mathematical model and flight test data. The model is appropriate for use in real time piloted simulation and is implemented on the ARC Sigma IX computer where it may be operated with a digital cycle time of 0.03 sec.

Why Don't All Maths Teachers Use Dynamic Geometry Software in Their Classrooms?

ERIC Educational Resources Information Center

Stols, Gerrit; Kriek, Jeanne

2011-01-01

In this exploratory study, we sought to examine the influence of mathematics teachers' beliefs on their intended and actual usage of dynamic mathematics software in their classrooms. The theory of planned behaviour (TPB), the technology acceptance model (TAM) and the innovation diffusion theory (IDT) were used to examine the influence of teachers'…

Numerical simulation of dynamics of brushless dc motors for aerospace and other applications. Volume 1: Model development and applications, part A

NASA Technical Reports Server (NTRS)

Demerdash, N. A. O.; Nehl, T. W.

1979-01-01

The development, fabrication and evaluation of a prototype electromechanical actuator (EMA) is discussed. Application of the EMA as a motor for control surfaces in aerospace flight is examined. A mathematical model of the EMA is developed for design optimization. Nonlinearities which complicate the mathematical model are discussed. The dynamics of the EMA from the underlying physical principles are determined and a discussion of similating the control logic by means of equivalent boolean expressions is presented.

Chancroid transmission dynamics: a mathematical modeling approach.

PubMed

Bhunu, C P; Mushayabasa, S

2011-12-01

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

NASA Technical Reports Server (NTRS)

Austin, F.; Markowitz, J.; Goldenberg, S.; Zetkov, G. A.

1973-01-01

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.

Stability analysis for a delay differential equations model of a hydraulic turbine speed governor

NASA Astrophysics Data System (ADS)

Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.

2017-01-01

The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.

The World According to Malthus and Volterra: The Mathematical Theory of the Struggle for Existence.

ERIC Educational Resources Information Center

Bogdanov, Constantine

1992-01-01

Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

Generalized Adaptive Artificial Neural Networks

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1993-01-01

Mathematical model of supervised learning by artificial neural network provides for simultaneous adjustments of both temperatures of neurons and synaptic weights, and includes feedback as well as feedforward synaptic connections. Extension of mathematical model described in "Adaptive Neurons For Artificial Neural Networks" (NPO-17803). Dynamics of neural network represented in new model by less-restrictive continuous formalism.

Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit.

PubMed

Eriksson, O; Brinne, B; Zhou, Y; Björkegren, J; Tegnér, J

2009-03-01

Complex regulatory dynamics is ubiquitous in molecular networks composed of genes and proteins. Recent progress in computational biology and its application to molecular data generate a growing number of complex networks. Yet, it has been difficult to understand the governing principles of these networks beyond graphical analysis or extensive numerical simulations. Here the authors exploit several simplifying biological circumstances which thereby enable to directly detect the underlying dynamical regularities driving periodic oscillations in a dynamical nonlinear computational model of a protein-protein network. System analysis is performed using the cell cycle, a mathematically well-described complex regulatory circuit driven by external signals. By introducing an explicit time delay and using a 'tearing-and-zooming' approach the authors reduce the system to a piecewise linear system with two variables that capture the dynamics of this complex network. A key step in the analysis is the identification of functional subsystems by identifying the relations between state-variables within the model. These functional subsystems are referred to as dynamical modules operating as sensitive switches in the original complex model. By using reduced mathematical representations of the subsystems the authors derive explicit conditions on how the cell cycle dynamics depends on system parameters, and can, for the first time, analyse and prove global conditions for system stability. The approach which includes utilising biological simplifying conditions, identification of dynamical modules and mathematical reduction of the model complexity may be applicable to other well-characterised biological regulatory circuits. [Includes supplementary material].

Mathematical and Computational Aspects of Multiscale Materials Modeling, Mathematics-Numerical analysis, Section II.A.a.3.4, Conference and symposia organization II.A.2.a

DTIC Science & Technology

2015-02-04

dislocation dynamics models ( DDD ), continuum representations). Coupling of these models is difficult. Coupling of atomistics and DDD models has been...explored to some extent, but the coupling between DDD and continuum models of the evolution of large populations of dislocations is essentially unexplored

Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens.

PubMed

Smith, David L; Battle, Katherine E; Hay, Simon I; Barker, Christopher M; Scott, Thomas W; McKenzie, F Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various "Ross-Macdonald" mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955-1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

PubMed Central

Smith, David L.; Battle, Katherine E.; Hay, Simon I.; Barker, Christopher M.; Scott, Thomas W.; McKenzie, F. Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention. PMID:22496640

A simplified rotor system mathematical model for piloted flight dynamics simulation

NASA Technical Reports Server (NTRS)

Chen, R. T. N.

1979-01-01

The model was developed for real-time pilot-in-the-loop investigation of helicopter flying qualities. The mathematical model included the tip-path plane dynamics and several primary rotor design parameters, such as flapping hinge restraint, flapping hinge offset, blade Lock number, and pitch-flap coupling. The model was used in several exploratory studies of the flying qualities of helicopters with a variety of rotor systems. The basic assumptions used and the major steps involved in the development of the set of equations listed are described. The equations consisted of the tip-path plane dynamic equation, the equations for the main rotor forces and moments, and the equation for control phasing required to achieve decoupling in pitch and roll due to cyclic inputs.

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

PubMed

Smith, Robert W; van Rosmalen, Rik P; Martins Dos Santos, Vitor A P; Fleck, Christian

2018-06-19

Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

PubMed Central

Liao, David; Tlsty, Thea D.

2014-01-01

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

V/STOL tilt rotor aircraft study mathematical model for a real time simulation of a tilt rotor aircraft (Boeing Vertol Model 222), volume 8

NASA Technical Reports Server (NTRS)

Rosenstein, H.; Mcveigh, M. A.; Mollenkof, P. A.

1973-01-01

A mathematical model for a real time simulation of a tilt rotor aircraft was developed. The mathematical model is used for evaluating aircraft performance and handling qualities. The model is based on an eleven degree of freedom total force representation. The rotor is treated as a point source of forces and moments with appropriate response time lags and actuator dynamics. The aerodynamics of the wing, tail, rotors, landing gear, and fuselage are included.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

From the guest editors.

PubMed

Chowell, Gerardo; Feng, Zhilan; Song, Baojun

2013-01-01

Carlos Castilo-Chavez is a Regents Professor, a Joaquin Bustoz Jr. Professor of Mathematical Biology, and a Distinguished Sustainability Scientist at Arizona State University. His research program is at the interface of the mathematical and natural and social sciences with emphasis on (i) the role of dynamic social landscapes on disease dispersal; (ii) the role of environmental and social structures on the dynamics of addiction and disease evolution, and (iii) Dynamics of complex systems at the interphase of ecology, epidemiology and the social sciences. Castillo-Chavez has co-authored over two hundred publications (see goggle scholar citations) that include journal articles and edited research volumes. Specifically, he co-authored a textbook in Mathematical Biology in 2001 (second edition in 2012); a volume (with Harvey Thomas Banks) on the use of mathematical models in homeland security published in SIAM's Frontiers in Applied Mathematics Series (2003); and co-edited volumes in the Series Contemporary Mathematics entitled '' Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges'' (American Mathematical Society, 2006) and Mathematical and Statistical Estimation Approaches in Epidemiology (Springer-Verlag, 2009) highlighting his interests in the applications of mathematics in emerging and re-emerging diseases. Castillo-Chavez is a member of the Santa Fe Institute's external faculty, adjunct professor at Cornell University, and contributor, as a member of the Steering Committee of the '' Committee for the Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials,'' to a 2004 NRC report. The CBMS workshop '' Mathematical Epidemiology with Applications'' lectures delivered by C. Castillo-Chavez and F. Brauer in 2011 have been published by SIAM in 2013.

F-111C Flight Data Reduction and Analysis Procedures

DTIC Science & Technology

1990-12-01

BPHI NO 24 BTHE YES 25 BPSI NO 26 BH YES 27 LVEL NO 28 LBET NO 29 LALP YES 30 LPHI NO 31 LTHE NO 32 LPSI NO 33 LH NO 34 TABLE 2 INPUTS I Ax YES 2 Av NO...03 * 51 IJ Appendix G - A priori Data from Six Degree of Free- dom Flight Dynamic Model The six degree of freedom flight dynamic mathematical model of...Estimated Mathematical mode response - > of aircraft !Gauss- Maximum " Newton --- likelihood 4,computational cost Salgorithm function Maximum

Mathematical modeling of shell configurations made of homogeneous and composite materials experiencing intensive short actions and large displacements

NASA Astrophysics Data System (ADS)

Khairnasov, K. Z.

2018-04-01

The paper presents a mathematical model for solving the problem of behavior of shell configurations under the action of static and dynamic impacts. The problem is solved in geometrically nonlinear statement with regard to the finite element method. The composite structures with different material layers are considered. The obtained equations are used to study the behavior of shell configurations under the action of dynamic loads. The results agree well with the experimental data.

A Mathematical Model for Vertical Attitude Takeoff and Landing (VATOL) Aircraft Simulation. Volume 1; Model Description Application

NASA Technical Reports Server (NTRS)

Fortenbaugh, R. L.

1980-01-01

A mathematical model of a high performance airplane capable of vertical attitude takeoff and landing (VATOL) was developed. An off line digital simulation program incorporating this model was developed to provide trim conditions and dynamic check runs for the piloted simulation studies and support dynamic analyses of proposed VATOL configuration and flight control concepts. Development details for the various simulation component models and the application of the off line simulation program, Vertical Attitude Take-Off and Landing Simulation (VATLAS), to develop a baseline control system for the Vought SF-121 VATOL airplane concept are described.

Paintbrush of Discovery: Using Java Applets to Enhance Mathematics Education

ERIC Educational Resources Information Center

Eason, Ray; Heath, Garrett

2004-01-01

This article addresses the enhancement of the learning environment by using Java applets in the mathematics classroom. Currently, the first year mathematics program at the United States Military Academy involves one semester of modeling with discrete dynamical systems (DDS). Several faculty members from the Academy have integrated Java applets…

Nonlinear differential system applied of a mechanical plan model of the automotives used for the nonlinear stability analysis

NASA Astrophysics Data System (ADS)

Simniceanu, Loreta; Mihaela, Bogdan; Otat, Victor; Trotea, Mario

2017-10-01

This paper proposes a plan mechanical model for the vehicles with two axles, taking into account the lateral deflection of the tire. For this mechanical model are determined two mathematical models under the nonlinear differential equations systems form without taking into account the action of the driver and taking into account. The analysis of driver-vehicle system consists in the mathematical description of vehicle dynamics, coupled with the possibilities and limits of the human factor. Description seeks to emphasize the significant influence of the driver in handling and stability analyzes of vehicles and vehicle-driver system stability until the advent of skidding. These mathematical models are seen as very useful tools to analyzing the vehicles stability. The paper analyzes the influence of some parameters of the vehicle on its behavior in terms of stability of dynamic systems.

A mathematical model for adaptive transport network in path finding by true slime mold.

PubMed

Tero, Atsushi; Kobayashi, Ryo; Nakagaki, Toshiyuki

2007-02-21

We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter.

Mathematical model for dynamic cell formation in fast fashion apparel manufacturing stage

NASA Astrophysics Data System (ADS)

Perera, Gayathri; Ratnayake, Vijitha

2018-05-01

This paper presents a mathematical programming model for dynamic cell formation to minimize changeover-related costs (i.e., machine relocation costs and machine setup cost) and inter-cell material handling cost to cope with the volatile production environments in apparel manufacturing industry. The model is formulated through findings of a comprehensive literature review. Developed model is validated based on data collected from three different factories in apparel industry, manufacturing fast fashion products. A program code is developed using Lingo 16.0 software package to generate optimal cells for developed model and to determine the possible cost-saving percentage when the existing layouts used in three factories are replaced by generated optimal cells. The optimal cells generated by developed mathematical model result in significant cost saving when compared with existing product layouts used in production/assembly department of selected factories in apparel industry. The developed model can be considered as effective in minimizing the considered cost terms in dynamic production environment of fast fashion apparel manufacturing industry. Findings of this paper can be used for further researches on minimizing the changeover-related costs in fast fashion apparel production stage.

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

SSME structural dynamic model development

NASA Technical Reports Server (NTRS)

Foley, M. J.; Tilley, D. M.; Welch, C. T.

1983-01-01

A mathematical model of the Space Shuttle Main Engine (SSME) as a complete assembly, with detailed emphasis on LOX and High Fuel Turbopumps is developed. The advantages of both complete engine dynamics, and high fidelity modeling are incorporated. Development of this model, some results, and projected applications are discussed.

A DYNAMIC MODEL OF AN ESTUARINE INVASION BY A NON-NATIVE SEAGRASS

EPA Science Inventory

Mathematical and simulation models provide an excellent tool for examining and predicting biological invasions in time and space; however, traditional models do not incorporate dynamic rates of population growth, which limits their realism. We developed a spatially explicit simul...

Understanding Immunology via Engineering Design: The Role of Mathematical Prototyping

PubMed Central

Klinke, David J.; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and “fitness for use,” can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans. PMID:22973412

A heuristic mathematical model for the dynamics of sensory conflict and motion sickness

NASA Technical Reports Server (NTRS)

Oman, C. M.

1982-01-01

By consideration of the information processing task faced by the central nervous system in estimating body spatial orientation and in controlling active body movement using an internal model referenced control strategy, a mathematical model for sensory conflict generation is developed. The model postulates a major dynamic functional role for sensory conflict signals in movement control, as well as in sensory-motor adaptation. It accounts for the role of active movement in creating motion sickness symptoms in some experimental circumstance, and in alleviating them in others. The relationship between motion sickness produced by sensory rearrangement and that resulting from external motion disturbances is explicitly defined. A nonlinear conflict averaging model is proposed which describes dynamic aspects of experimentally observed subjective discomfort sensation, and suggests resulting behaviours. The model admits several possibilities for adaptive mechanisms which do not involve internal model updating. Further systematic efforts to experimentally refine and validate the model are indicated.

Formulating a stand-growth model for mathematical programming problems in Appalachian forests

Treesearch

Gary W. Miller; Jay Sullivan

1993-01-01

Some growth and yield simulators applicable to central hardwood forests can be formulated for use in mathematical programming models that are designed to optimize multi-stand, multi-resource management problems. Once in the required format, growth equations serve as model constraints, defining the dynamics of stand development brought about by harvesting decisions. In...

Combat Simulation Using Breach Computer Language

DTIC Science & Technology

1979-09-01

simulation and weapon system analysis computer language Two types of models were constructed: a stochastic duel and a dynamic engagement model The... duel model validates the BREACH approach by comparing results with mathematical solutions. The dynamic model shows the capability of the BREACH...BREACH 2 Background 2 The Language 3 Static Duel 4 Background and Methodology 4 Validation 5 Results 8 Tank Duel Simulation 8 Dynamic Assault Model

Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine.

PubMed

Erdem, Mustafa; Safan, Muntaser; Castillo-Chavez, Carlos

2017-07-01

The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

Evaluation of the lambda model for human postural control during ankle strategy.

PubMed

Micheau, Philippe; Kron, Aymeric; Bourassa, Paul

2003-09-01

An accurate modeling of human stance might be helpful in assessing postural deficit. The objective of this article is to validate a mathematical postural control model for quiet standing posture. The postural dynamics is modeled in the sagittal plane as an inverted pendulum with torque applied at the ankle joint. The torque control system is represented by the physiological lambda model. Two neurophysiological command variables of the central nervous system, designated lambda and micro, establish the dynamic threshold muscle at which motoneuron recruitment begins. Kinematic data and electromyographic signals were collected on four young males in order to measure small voluntary sway and quiet standing posture. Validation of the mathematical model was achieved through comparison of the experimental and simulated results. The mathematical model allows computation of the unmeasurable neurophysiological commands lambda and micro that control the equilibrium position and stability. Furthermore, with the model it is possible to conclude that low-amplitude body sway during quiet stance is commanded by the central nervous system.

Modeling birds on wires.

PubMed

Aydoğdu, A; Frasca, P; D'Apice, C; Manzo, R; Thornton, J M; Gachomo, B; Wilson, T; Cheung, B; Tariq, U; Saidel, W; Piccoli, B

2017-02-21

In this paper we introduce a mathematical model to study the group dynamics of birds resting on wires. The model is agent-based and postulates attraction-repulsion forces between the interacting birds: the interactions are "topological", in the sense that they involve a given number of neighbors irrespective of their distance. The model is first mathematically analyzed and then simulated to study its main properties: we observe that the model predicts birds to be more widely spaced near the borders of each group. We compare the results from the model with experimental data, derived from the analysis of pictures of pigeons and starlings taken in New Jersey: two different image elaboration protocols allow us to establish a good agreement with the model and to quantify its main parameters. We also discuss the potential handedness of the birds, by analyzing the group organization features and the group dynamics at the arrival of new birds. Finally, we propose a more refined mathematical model that describes landing and departing birds by suitable stochastic processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Correlated receptor transport processes buffer single-cell heterogeneity

PubMed Central

Kallenberger, Stefan M.; Unger, Anne L.; Legewie, Stefan; Lymperopoulos, Konstantinos; Eils, Roland

2017-01-01

Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system. PMID:28945754

Numerical bifurcation analysis of immunological models with time delays

NASA Astrophysics Data System (ADS)

Luzyanina, Tatyana; Roose, Dirk; Bocharov, Gennady

2005-12-01

In recent years, a large number of mathematical models that are described by delay differential equations (DDEs) have appeared in the life sciences. To analyze the models' dynamics, numerical methods are necessary, since analytical studies can only give limited results. In turn, the availability of efficient numerical methods and software packages encourages the use of time delays in mathematical modelling, which may lead to more realistic models. We outline recently developed numerical methods for bifurcation analysis of DDEs and illustrate the use of these methods in the analysis of a mathematical model of human hepatitis B virus infection.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

PubMed

Eftimie, Raluca; Gillard, Joseph J; Cantrell, Doreen A

2016-10-01

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

A Comprehensive Fluid Dynamic-Diffusion Model of Blood Microcirculation with Focus on Sickle Cell Disease

NASA Astrophysics Data System (ADS)

Le Floch, Francois; Harris, Wesley L.

2009-11-01

A novel methodology has been developed to address sickle cell disease, based on highly descriptive mathematical models for blood flow in the capillaries. Our investigations focus on the coupling between oxygen delivery and red blood cell dynamics, which is crucial to understanding sickle cell crises and is unique to this blood disease. The main part of our work is an extensive study of blood dynamics through simulations of red cells deforming within the capillary vessels, and relies on the use of a large mathematical system of equations describing oxygen transfer, blood plasma dynamics and red cell membrane mechanics. This model is expected to lead to the development of new research strategies for sickle cell disease. Our simulation model could be used not only to assess current researched remedies, but also to spur innovative research initiatives, based on our study of the physical properties coupled in sickle cell disease.

Study on dynamic performance of SOFC

NASA Astrophysics Data System (ADS)

Zhan, Haiyang; Liang, Qianchao; Wen, Qiang; Zhu, Runkai

2017-05-01

In order to solve the problem of real-time matching of load and fuel cell power, it is urgent to study the dynamic response process of SOFC in the case of load mutation. The mathematical model of SOFC is constructed, and its performance is simulated. The model consider the influence factors such as polarization effect, ohmic loss. It also takes the diffusion effect, thermal effect, energy exchange, mass conservation, momentum conservation. One dimensional dynamic mathematical model of SOFC is constructed by using distributed lumped parameter method. The simulation results show that the I-V characteristic curves are in good agreement with the experimental data, and the accuracy of the model is verified. The voltage response curve, power response curve and the efficiency curve are obtained by this way. It lays a solid foundation for the research of dynamic performance and optimal control in power generation system of high power fuel cell stack.

Creative-Dynamics Approach To Neural Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail A.

1992-01-01

Paper discusses approach to mathematical modeling of artificial neural networks exhibiting complicated behaviors reminiscent of creativity and intelligence of biological neural networks. Neural network treated as non-Lipschitzian dynamical system - as described in "Non-Lipschitzian Dynamics For Modeling Neural Networks" (NPO-17814). System serves as tool for modeling of temporal-pattern memories and recognition of complicated spatial patterns.

Recent literature on structural modeling, identification, and analysis

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1990-01-01

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Predicting Drug Combination Index and Simulating the Network-Regulation Dynamics by Mathematical Modeling of Drug-Targeted EGFR-ERK Signaling Pathway

NASA Astrophysics Data System (ADS)

Huang, Lu; Jiang, Yuyang; Chen, Yuzong

2017-01-01

Synergistic drug combinations enable enhanced therapeutics. Their discovery typically involves the measurement and assessment of drug combination index (CI), which can be facilitated by the development and applications of in-silico CI predictive tools. In this work, we developed and tested the ability of a mathematical model of drug-targeted EGFR-ERK pathway in predicting CIs and in analyzing multiple synergistic drug combinations against observations. Our mathematical model was validated against the literature reported signaling, drug response dynamics, and EGFR-MEK drug combination effect. The predicted CIs and combination therapeutic effects of the EGFR-BRaf, BRaf-MEK, FTI-MEK, and FTI-BRaf inhibitor combinations showed consistent synergism. Our results suggest that existing pathway models may be potentially extended for developing drug-targeted pathway models to predict drug combination CI values, isobolograms, and drug-response surfaces as well as to analyze the dynamics of individual and combinations of drugs. With our model, the efficacy of potential drug combinations can be predicted. Our method complements the developed in-silico methods (e.g. the chemogenomic profile and the statistically-inferenced network models) by predicting drug combination effects from the perspectives of pathway dynamics using experimental or validated molecular kinetic constants, thereby facilitating the collective prediction of drug combination effects in diverse ranges of disease systems.

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Design and Analysis of Precise Pointing Systems

NASA Technical Reports Server (NTRS)

Kim, Young K.

2000-01-01

The mathematical models of Glovebox Integrated Microgravity Isolation Technology (g- LIMIT) dynamics/control system, which include six degrees of freedom (DOF) equations of motion, mathematical models of position sensors, accelerometers and actuators, and acceleration and position controller, were developed using MATLAB and TREETOPS simulations. Optimal control parameters of G-LIMIT control system were determined through sensitivity studies and its performance were evaluated with the TREETOPS model of G-LIMIT dynamics and control system. The functional operation and performance of the Tektronix DTM920 digital thermometer were studied and the inputs to the crew procedures and training of the DTM920 were documented.

Modeling Selection and Extinction Mechanisms of Biological Systems

NASA Astrophysics Data System (ADS)

Amirjanov, Adil

In this paper, the behavior of a genetic algorithm is modeled to enhance its applicability as a modeling tool of biological systems. A new description model for selection mechanism is introduced which operates on a portion of individuals of population. The extinction and recolonization mechanism is modeled, and solving the dynamics analytically shows that the genetic drift in the population with extinction/recolonization is doubled. The mathematical analysis of the interaction between selection and extinction/recolonization processes is carried out to assess the dynamics of motion of the macroscopic statistical properties of population. Computer simulations confirm that the theoretical predictions of described models are in good approximations. A mathematical model of GA dynamics was also examined, which describes the anti-predator vigilance in an animal group with respect to a known analytical solution of the problem, and showed a good agreement between them to find the evolutionarily stable strategies.

GeoGebra in Professional Development: The Experience of Rural Inservice Elementary School (K-8) Teachers

ERIC Educational Resources Information Center

Bu, Ligguo; Mumba, Frackson; Henson, Harvey; Wright, Mary

2013-01-01

GeoGebra is an emergent open-source Dynamic and Interactive Mathematics Learning Environment (DIMLE) (Martinovic & Karadag, 2012) that invites a modeling perspective in mathematics teaching and learning. In springs of 2010 and 2012, GeoGebra was integrated respectively into two online professional development courses on mathematical problem…

Illustrations of mathematical modeling in biology: epigenetics, meiosis, and an outlook.

PubMed

Richards, D; Berry, S; Howard, M

2012-01-01

In the past few years, mathematical modeling approaches in biology have begun to fulfill their promise by assisting in the dissection of complex biological systems. Here, we review two recent examples of predictive mathematical modeling in plant biology. The first involves the quantitative epigenetic silencing of the floral repressor gene FLC in Arabidopsis, mediated by a Polycomb-based system. The second involves the spatiotemporal dynamics of telomere bouquet formation in wheat-rye meiosis. Although both the biology and the modeling framework of the two systems are different, both exemplify how mathematical modeling can help to accelerate discovery of the underlying mechanisms in complex biological systems. In both cases, the models that developed were relatively minimal, including only essential features, but both nevertheless yielded fundamental insights. We also briefly review the current state of mathematical modeling in biology, difficulties inherent in its application, and its potential future development.

Mathematical model of the SH-3G helicopter

NASA Technical Reports Server (NTRS)

Phillips, J. D.

1982-01-01

A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

Keeling, Matt J.; Rohani, Pejman; Grenfell, Bryan T.

2001-01-01

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

Self-Supervised Dynamical Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

1994-01-01

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

It's difficult to build precise mathematical models for complex engineering systems because of the complexity of the structure and dynamics characteristics. Intelligent fault diagnosis introduces artificial intelligence and works in a different way without building the analytical mathematical model of a diagnostic object, so it's a practical approach to solve diagnostic problems of complex systems. This paper presents an intelligent fault diagnosis method, an integrated fault-pattern classifier based on Hidden Markov Model (HMM). This classifier consists of dynamic time warping (DTW) algorithm, self-organizing feature mapping (SOFM) network and Hidden Markov Model. First, after dynamic observation vector in measuring space is processed by DTW, the error vector including the fault feature of being tested system is obtained. Then a SOFM network is used as a feature extractor and vector quantization processor. Finally, fault diagnosis is realized by fault patterns classifying with the Hidden Markov Model classifier. The importing of dynamic time warping solves the problem of feature extracting from dynamic process vectors of complex system such as aeroengine, and makes it come true to diagnose complex system by utilizing dynamic process information. Simulating experiments show that the diagnosis model is easy to extend, and the fault pattern classifier is efficient and is convenient to the detecting and diagnosing of new faults.

Flight test planning and parameter extraction for rotorcraft system identification

NASA Technical Reports Server (NTRS)

Wang, J. C.; Demiroz, M. Y.; Talbot, P. D.

1986-01-01

The present study is concerned with the mathematical modelling of aircraft dynamics on the basis of an investigation conducted with the aid of the Rotor System Research Aircraft (RSRA). The particular characteristics of RSRA make it possible to investigate aircraft properties which cannot be readily studied elsewhere, for example in the wind tunnel. The considered experiment had mainly the objective to develop an improved understanding of the physics of rotor flapping dynamics and rotor loads in maneuvers. The employed approach is based on a utilization of parameter identification methodology (PID) with application to helicopters. A better understanding of the contribution of the main rotor to the overall aircraft forces and moments is also to be obtained. Attention is given to the mathematical model of a rotorcraft system, an integrated identification method, flight data processing, and the identification of RSRA mathematical models.

Analyzing neuronal networks using discrete-time dynamics

NASA Astrophysics Data System (ADS)

Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David

2010-05-01

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.

Pressure Dynamic Characteristics of Pressure Controlled Ventilation System of a Lung Simulator

PubMed Central

Shi, Yan; Ren, Shuai; Cai, Maolin; Xu, Weiqing; Deng, Qiyou

2014-01-01

Mechanical ventilation is an important life support treatment of critically ill patients, and air pressure dynamics of human lung affect ventilation treatment effects. In this paper, in order to obtain the influences of seven key parameters of mechanical ventilation system on the pressure dynamics of human lung, firstly, mechanical ventilation system was considered as a pure pneumatic system, and then its mathematical model was set up. Furthermore, to verify the mathematical model, a prototype mechanical ventilation system of a lung simulator was proposed for experimental study. Last, simulation and experimental studies on the air flow dynamic of the mechanical ventilation system were done, and then the pressure dynamic characteristics of the mechanical system were obtained. The study can be referred to in the pulmonary diagnostics, treatment, and design of various medical devices or diagnostic systems. PMID:25197318

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.

1990-01-01

The development of a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads is examined. In the mathematical model, geometric as well as material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1991-01-01

This report deals with the development of a general mathematical model and solution methodology for analyzing the structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads. In the mathematical model, geometric as well as the material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

VTI Driving Simulator: Mathematical Model of a Four-wheeled Vehicle for Simulation in Real Time. VTI Rapport 267A.

ERIC Educational Resources Information Center

Nordmark, Staffan

1984-01-01

This report contains a theoretical model for describing the motion of a passenger car. The simulation program based on this model is used in conjunction with an advanced driving simulator and run in real time. The mathematical model is complete in the sense that the dynamics of the engine, transmission and steering system is described in some…

Experimental Measurements and Mathematical Modeling of Static and Dynamic Characteristics of Water Flow in a Long Pipe

NASA Astrophysics Data System (ADS)

Jablonska, J.; Kozubkova, M.

2017-08-01

Static and dynamic characteristics of flow in technical practice are very important and serious problem and can be solved by experimental measurement or mathematical modeling. Unsteady flow presents time changes of the flow and water hammer can be an example of this phenomenon. Water hammer is caused by rapid changes in the water flow by means the closure or opening of the control valve. The authors deal with by hydraulic hammer at the multiphase flow (water and air), its one-dimensional modeling (Matlab SimHydraulics) and modeling with the use of the finite volume method (Ansys Fluent) in article. The circuit elements are defined by static and dynamic characteristics. The results are verified with measurements. The article evaluates different approaches, their advantages, disadvantages and specifics in solving of water hammer.

Epidemics Modelings: Some New Challenges

NASA Astrophysics Data System (ADS)

Boatto, Stefanella; Khouri, Renata Stella; Solerman, Lucas; Codeço, Claudia; Bonnet, Catherine

2010-09-01

Epidemics modeling has been particularly growing in the past years. In epidemics studies, mathematical modeling is used in particular to reach a better understanding of some neglected diseases (dengue, malaria, …) and of new emerging ones (SARS, influenza A,….) of big agglomerates. Such studies offer new challenges both from the modeling point of view (searching for simple models which capture the main characteristics of the disease spreading), data analysis and mathematical complexity. We are facing often with complex networks especially when modeling the city dynamics. Such networks can be static (in first approximation) and homogeneous, static and not homogeneous and/or not static (when taking into account the city structure, micro-climates, people circulation, etc.). The objective being studying epidemics dynamics and being able to predict its spreading.

Dynamic deformation of soft soil media: Experimental studies and mathematical modeling

NASA Astrophysics Data System (ADS)

Balandin, V. V.; Bragov, A. M.; Igumnov, L. A.; Konstantinov, A. Yu.; Kotov, V. L.; Lomunov, A. K.

2015-05-01

A complex experimental-theoretical approach to studying the problem of high-rate strain of soft soil media is presented. This approach combines the following contemporary methods of dynamical tests: the modified Hopkinson-Kolsky method applied tomedium specimens contained in holders and the method of plane wave shock experiments. The following dynamic characteristics of sand soils are obtained: shock adiabatic curves, bulk compressibility curves, and shear resistance curves. The obtained experimental data are used to study the high-rate strain process in the system of a split pressure bar, and the constitutive relations of Grigoryan's mathematical model of soft soil medium are verified by comparing the results of computational and natural test experiments of impact and penetration.

A "Kane's Dynamics" Model for the Active Rack Isolation System Part Two: Nonlinear Model Development, Verification, and Simplification

NASA Technical Reports Server (NTRS)

Beech, G. S.; Hampton, R. D.; Rupert, J. K.

2004-01-01

Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

A heuristic mathematical model for the dynamics of sensory conflict and motion sickness

NASA Technical Reports Server (NTRS)

Oman, C. M.

1982-01-01

The etiology of motion sickness is now usually explained in terms of a qualitatively formulated sensory conflict hypothesis. By consideration of the information processing task faced by the central nervous system in estimating body spatial orientation and in controlling active body movement using an internal model referenced control strategy, a mathematical model for sensory conflict generation is developed. The model postulates a major dynamic functional role for sensory conflict signals in movement control, as well as in sensory motor adaptation. It accounts for the role of active movement in creating motion sickness symptoms in some experimental circumstances, and in alleviating them in others. The relationship between motion sickness produced by sensory rearrangement and that resulting from external motion disturbances is explicitly defined. A nonlinear conflict averaging model describes dynamic aspects of experimentally observed subjective discomfort sensation, and suggests resulting behavior.

A heuristic mathematical model for the dynamics of sensory conflict and motion sickness

NASA Technical Reports Server (NTRS)

Oman, C. M.

1980-01-01

The etiology of motion sickness is explained in terms of a qualitatively formulated sensory conflict hypothesis. By consideration of the information processing task faced by the central nervous system in estimating body spatial orientation and in controlling active body movement using an internal model referenced control strategy, a mathematical model for sensory conflict generation is developed. The model postulates a major dynamic functional role for sensory conflict signals in movement control, as well as in sensory-motor adaptation. It accounts for the role of active movement in creating motion sickness symptoms in some experimental circumstances, and in alleviating them in others. The relationship between motion sickness produced by sensory rearrangement and that resulting from external motion disturbances is explicitly defined. A nonlinear conflict averaging model is proposed which describes dynamic aspects of experimentally observed subjective discomfort sensation, and suggests resulting behaviors.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

PubMed Central

Boianelli, Alessandro; Nguyen, Van Kinh; Ebensen, Thomas; Schulze, Kai; Wilk, Esther; Sharma, Niharika; Stegemann-Koniszewski, Sabine; Bruder, Dunja; Toapanta, Franklin R.; Guzmán, Carlos A.; Meyer-Hermann, Michael; Hernandez-Vargas, Esteban A.

2015-01-01

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization. PMID:26473911

Modeling Influenza Virus Infection: A Roadmap for Influenza Research.

PubMed

Boianelli, Alessandro; Nguyen, Van Kinh; Ebensen, Thomas; Schulze, Kai; Wilk, Esther; Sharma, Niharika; Stegemann-Koniszewski, Sabine; Bruder, Dunja; Toapanta, Franklin R; Guzmán, Carlos A; Meyer-Hermann, Michael; Hernandez-Vargas, Esteban A

2015-10-12

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

Dynamic Characteristics of Simple Cylindrical Hydraulic Engine Mount Utilizing Air Compressibility

NASA Astrophysics Data System (ADS)

Nakahara, Kazunari; Nakagawa, Noritoshi; Ohta, Katsutoshi

A cylindrical hydraulic engine mount with simple construction has been developed. This engine mount has a sub chamber formed by utilizing air compressibility without a diaphragm. A mathematical model of the mount is presented to predict non-linear dynamic characteristics in consideration of the effect of the excitation amplitude on the storage stiffness and loss factor. The mathematical model predicts experimental results well for the frequency responses of the storage stiffness and loss factor over the frequency range of 5 Hz to 60Hz. The effect of air volume and internal pressure on the dynamic characteristics is clarified by the analysis and dynamic characterization testing. The effectiveness of the cylindrical hydraulic engine mount on the reduction of engine shake is demonstrated for riding comfort through on-vehicle testing with a chassis dynamometer.

Pre Service Teachers' Usage of Dynamic Mathematics Software

ERIC Educational Resources Information Center

Bulut, Mehmet; Bulut, Neslihan

2011-01-01

Aim of this study is about mathematics education and dynamic mathematics software. Dynamic mathematics software provides new opportunities for using both computer algebra system and dynamic geometry software. GeoGebra selected as dynamic mathematics software in this research. In this study, it is investigated that what is the usage of pre service…

Preliminary Findings from the First Two Waves of a Panel Study of Developing Career Expectations.

ERIC Educational Resources Information Center

Hotchkiss, Lawrence; Chiteji, Lisa

This report is an exploratory application of a dynamic mathematical model to express a theory of changes in youth's career expectations over time. Main content is divided into two focuses: (1) theoretical interpretations of the differential equations which embody the mathematical model and (2) reporting and discussion of the results of preliminary…

[Mathematical models and epidemiological analysis].

PubMed

Gerasimov, A N

2010-01-01

The limited use of mathematical simulation in epidemiology is due not only to the difficulty of monitoring the epidemic process and identifying its parameters but also to the application of oversimplified models. It is shown that realistic reproduction of actual morbidity dynamics requires taking into account heterogeneity and finiteness of the population and seasonal character of pathogen transmission mechanism.

Simulation of dental collisions and occlusal dynamics in the virtual environment.

PubMed

Stavness, I K; Hannam, A G; Tobias, D L; Zhang, X

2016-04-01

Semi-adjustable articulators have often been used to simulate occlusal dynamics, but advances in intra-oral scanning and computer software now enable dynamics to be modelled mathematically. Computer simulation of occlusal dynamics requires accurate virtual casts, records to register them and methods to handle mesh collisions during movement. Here, physical casts in a semi-adjustable articulator were scanned with a conventional clinical intra-oral scanner. A coordinate measuring machine was used to index their positions in intercuspation, protrusion, right and left laterotrusion, and to model features of the articulator. Penetrations between the indexed meshes were identified and resolved using restitution forces, and the final registrations were verified by distance measurements between dental landmarks at multiple sites. These sites were confirmed as closely approximating via measurements made from homologous transilluminated vinylpolysiloxane interocclusal impressions in the mounted casts. Movements between the indexed positions were simulated with two models in a custom biomechanical software platform. In model DENTAL, 6 degree-of-freedom movements were made to minimise deviation from a straight line path and also shaped by dynamic mesh collisions detected and resolved mathematically. In model ARTIC, the paths were further constrained by surfaces matching the control settings of the articulator. Despite these differences, the lower mid-incisor point paths were very similar in both models. The study suggests that mathematical simulation utilising interocclusal 'bite' registrations can closely replicate the primary movements of casts mounted in a semi-adjustable articulator. Additional indexing positions and appropriate software could, in some situations, replace the need for mechanical semi-adjustable articulation and/or its virtual representation. © 2015 John Wiley & Sons Ltd.

Crypt dynamics and colorectal cancer: advances in mathematical modelling.

PubMed

van Leeuwen, I M M; Byrne, H M; Jensen, O E; King, J R

2006-06-01

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

A Mathematical Framework for the Complex System Approach to Group Dynamics: The Case of Recovery House Social Integration.

PubMed

Light, John M; Jason, Leonard A; Stevens, Edward B; Callahan, Sarah; Stone, Ariel

2016-03-01

The complex system conception of group social dynamics often involves not only changing individual characteristics, but also changing within-group relationships. Recent advances in stochastic dynamic network modeling allow these interdependencies to be modeled from data. This methodology is discussed within a context of other mathematical and statistical approaches that have been or could be applied to study the temporal evolution of relationships and behaviors within small- to medium-sized groups. An example model is presented, based on a pilot study of five Oxford House recovery homes, sober living environments for individuals following release from acute substance abuse treatment. This model demonstrates how dynamic network modeling can be applied to such systems, examines and discusses several options for pooling, and shows how results are interpreted in line with complex system concepts. Results suggest that this approach (a) is a credible modeling framework for studying group dynamics even with limited data, (b) improves upon the most common alternatives, and (c) is especially well-suited to complex system conceptions. Continuing improvements in stochastic models and associated software may finally lead to mainstream use of these techniques for the study of group dynamics, a shift already occurring in related fields of behavioral science.

The Characteristics of Middle Eastern Respiratory Syndrome Coronavirus Transmission Dynamics in South Korea.

PubMed

Kim, Yunhwan; Lee, Sunmi; Chu, Chaeshin; Choe, Seoyun; Hong, Saeme; Shin, Youngseo

2016-02-01

The outbreak of Middle Eastern respiratory syndrome coronavirus (MERS-CoV) was one of the major events in South Korea in 2015. In particular, this study pays attention to formulating a mathematical model for MERS transmission dynamics and estimating transmission rates. Incidence data of MERS-CoV from the government authority was analyzed for the first aim and a mathematical model was built and analyzed for the second aim of the study. A mathematical model for MERS-CoV transmission dynamics is used to estimate the transmission rates in two periods due to the implementation of intensive interventions. Using the estimates of the transmission rates, the basic reproduction number was estimated in two periods. Due to the superspreader, the basic reproduction number was very large in the first period; however, the basic reproduction number of the second period has reduced significantly after intensive interventions. It turned out to be the intensive isolation and quarantine interventions that were the most critical factors that prevented the spread of the MERS outbreak. The results are expected to be useful to devise more efficient intervention strategies in the future.

Multiphysics Simulation of Welding-Arc and Nozzle-Arc System: Mathematical-Model, Solution-Methodology and Validation

NASA Astrophysics Data System (ADS)

Pawar, Sumedh; Sharma, Atul

2018-01-01

This work presents mathematical model and solution methodology for a multiphysics engineering problem on arc formation during welding and inside a nozzle. A general-purpose commercial CFD solver ANSYS FLUENT 13.0.0 is used in this work. Arc formation involves strongly coupled gas dynamics and electro-dynamics, simulated by solution of coupled Navier-Stoke equations, Maxwell's equations and radiation heat-transfer equation. Validation of the present numerical methodology is demonstrated with an excellent agreement with the published results. The developed mathematical model and the user defined functions (UDFs) are independent of the geometry and are applicable to any system that involves arc-formation, in 2D axisymmetric coordinates system. The high-pressure flow of SF6 gas in the nozzle-arc system resembles arc chamber of SF6 gas circuit breaker; thus, this methodology can be extended to simulate arcing phenomenon during current interruption.

Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.

Model Of Neural Network With Creative Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail; Barhen, Jacob

1993-01-01

Paper presents analysis of mathematical model of one-neuron/one-synapse neural network featuring coupled activation and learning dynamics and parametrical periodic excitation. Demonstrates self-programming, partly random behavior of suitable designed neural network; believed to be related to spontaneity and creativity of biological neural networks.

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David

2000-01-01

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

Forest forming process and dynamic vegetation models under global change

Treesearch

A. Shvidenko; E. Gustafson

2009-01-01

The paper analyzes mathematical models that are used to project the dynamics of forest ecosystems on different spatial and temporal scales. Landscape disturbance and succession models (LDSMs) are of a particular interest for studying the forest forming process in Northern Eurasia. They have a solid empirical background and are able to model ecological processes under...

Stochastic population dynamic models as probability networks

Treesearch

M.E. and D.C. Lee Borsuk

2009-01-01

The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and...

Dynamical Analysis in the Mathematical Modelling of Human Blood Glucose

ERIC Educational Resources Information Center

Bae, Saebyok; Kang, Byungmin

2012-01-01

We want to apply the geometrical method to a dynamical system of human blood glucose. Due to the educational importance of model building, we show a relatively general modelling process using observational facts. Next, two models of some concrete forms are analysed in the phase plane by means of linear stability, phase portrait and vector…

The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.

PubMed

Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin

2016-07-01

Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.

Mathematical Model of Bone Regeneration in a Porous Implant

NASA Astrophysics Data System (ADS)

Maslov, L. B.

2017-07-01

A mathematical model of the reparative regeneration of bone tissue governed by the law of cell differentiation and action of an external periodic mechanical loading is presented. The model allows one to study the recovery processes of injured human locomotor system elements under a dynamic loading and to theoretically substantiate the choice of an optimum periodic impact on the defective tissues for their fastest and steady healing.

Mathematical Models to Determine Stable Behavior of Complex Systems

NASA Astrophysics Data System (ADS)

Sumin, V. I.; Dushkin, A. V.; Smolentseva, T. E.

2018-05-01

The paper analyzes a possibility to predict functioning of a complex dynamic system with a significant amount of circulating information and a large number of random factors impacting its functioning. Functioning of the complex dynamic system is described as a chaotic state, self-organized criticality and bifurcation. This problem may be resolved by modeling such systems as dynamic ones, without applying stochastic models and taking into account strange attractors.

Casablanca International Workshop in Mathematical Biology: Control and Analysis

DTIC Science & Technology

2012-10-05

Africa such Cholera, Malaria, HIV and within-­host diseases such as cancers . The economic, demographical and environmental changes in Africa require that...mathematical modeling of emerging diseases in Africa, cancer modeling, calcium oscillation, population dynamics, signaling networks, and optimal...INVESTIGATOR(S): Phone Number: 4807275005 Principal: Y Name: Abdessamad Tridane Email: atridan@asu.edu diseases such as cancer , vector-­borne diseases

Mathematical modeling of the aerodynamic characteristics in flight dynamics

NASA Technical Reports Server (NTRS)

Tobak, M.; Chapman, G. T.; Schiff, L. B.

1984-01-01

Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

PREFACE: 3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)

NASA Astrophysics Data System (ADS)

2015-01-01

The third International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Madrid, Spain, from Thursday 28 to Sunday 31 August 2014. The Conference was attended by more than 200 participants and hosted about 350 oral, poster, and virtual presentations. More than 600 pre-registered authors were also counted. The third IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral sessions and one poster session were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

PREFACE: 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare2015)

NASA Astrophysics Data System (ADS)

Vlachos, Dimitrios; Vagenas, Elias C.

2015-09-01

The 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place in Mykonos, Greece, from Friday 5th June to Monday 8th June 2015. The Conference was attended by more than 150 participants and hosted about 200 oral, poster, and virtual presentations. There were more than 600 pre-registered authors. The 4th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather intense as after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with a high quality of talks creating an innovative and productive scientific environment for all attendees. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

Optimal quality control of bakers' yeast fed-batch culture using population dynamics.

PubMed

Dairaku, K; Izumoto, E; Morikawa, H; Shioya, S; Takamatsu, T

1982-12-01

An optimal quality control policy for the overall specific growth rate of bakers' yeast, which maximizes the fermentative activity in the making of bread, was obtained by direct searching based on the mathematical model proposed previously. The mathematical model had described the age distribution of bakers' yeast which had an essential relationship to the ability of fermentation in the making of bread. The mathematical model is a simple aging model with two periods: Nonbudding and budding. Based on the result obtained by direct searching, the quality control of bakers' yeast fed-batch culture was performed and confirmed to be experimentally valid.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Dynamic behavior of a rolling housing

NASA Astrophysics Data System (ADS)

Gentile, A.; Messina, A. M.; Trentadue, Bartolo

1994-09-01

One of the major objectives of industry is to curtail costs. An element, among others, that enables to achieve such goal is the efficiency of the production cycle machines. Such efficiency lies in the reliability of the upkeeping operations. Among maintenance procedures, measuring and analyzing vibrations is a way to detect structure modifications over the machine's lifespan. Further, the availability of a mathematical model describing the influence of each individual part of the machine on the total dynamic behavior of the whole machine may help localizing breakdowns during diagnosis operations. The paper hereof illustrates an analytical-numerical model which can simulate the behavior of a rolling housing. The aforesaid mathematical model has been obtained by FEM techniques, the dynamic response by mode superposition and the synthesis of the vibration time sequence in the frequency versus by FFT numerical techniques.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Some problems of control of dynamical conditions of technological vibrating machines

NASA Astrophysics Data System (ADS)

Kuznetsov, N. K.; Lapshin, V. L.; Eliseev, A. V.

2017-10-01

The possibility of control of dynamical condition of the shakers that are designed for vibration treatment of parts interacting with granular media is discussed. The aim of this article is to develop the methodological basis of technology of creation of mathematical models of shake tables and the development of principles of formation of vibrational fields, estimation of their parameters and control of the structure vibration fields. Approaches to build mathematical models that take into account unilateral constraints, the relationships between elements, with the vibrating surface are developed. Methods intended to construct mathematical model of linear mechanical oscillation systems are used. Small oscillations about the position of static equilibrium are performed. The original method of correction of vibration fields by introduction of the oscillating system additional ties to the structure are proposed. Additional ties are implemented in the form of a mass-inertial device for changing the inertial parameters of the working body of the vibration table by moving the mass-inertial elements. The concept of monitoring the dynamic state of the vibration table based on the original measuring devices is proposed. Estimation for possible changes in dynamic properties is produced. The article is of interest for specialists in the field of creation of vibration technology machines and equipment.

Extension of Liouville Formalism to Postinstability Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Short-term dynamics of intertidal microphytobenthic biomass. Mathematical modelling [La dynamique a court terme de la biomasse du microphytobenthos intertidal. Formalisation mathematique

USGS Publications Warehouse

Guarini, J.-M.; Gros, P.; Blanchard, G.F.; Bacher, C.

1999-01-01

We formulate a deterministic mathematical model to describe the dynamics of the microphytobenthos of intertidal mudflats. It is 'minimal' because it only takes into account the essential processes governing the functioning of the system: the autotrophic production, the active upward and downward migrations of epipelic microalgae, the saturation of the mud surface by a biofilm of diatoms and the global net loss rates of biomass. According to the photic environment of the benthic diatoms inhabiting intertidal mudflats, and to their migration rhythm, the model is composed of two sub-systems of ordinary differential equations; they describe the simultaneous evolution of the biomass 'S' concentrated in the mud surface biofilm - the photic layer - and of the biomass 'F' diluted in the topmost centimetre of the mud - the aphotic layer. Qualitatively, the model solutions agree fairly well with the in situ observed dynamics of the S + F biomass. The study of the mathematical properties of the model, under some simplifying assumptions, shows the convergence of solutions to a stable cyclic equilibrium, whatever the frequencies of the physical synchronizers of the production. The sensitivity analysis reveals the necessity of a better knowledge of the processes of biomass losses, which so far are uncertain, and may further vary in space and time.

Continuous system modeling

NASA Technical Reports Server (NTRS)

Cellier, Francois E.

1991-01-01

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Champredon, David; Earn, David J. D.

2016-09-01

Mechanistic mathematical modelling of the population dynamics of infectious diseases has advanced tremendously over the last few decades [1-6]. Transmission models have been applied to countless diseases of public health importance, including seasonal and pandemic influenza [7], childhood diseases such as measles [8,9] and whooping cough [10], vector transmitted diseases such as malaria [11] and dengue [12], and waterborne diseases such as cholera [13-15]. Much attention in recent years has been directed to emergent diseases such as SARS [16], new subtypes of influenza [17,18], Ebola [19,20], and Zika [21], for which an understanding of early outbreak dynamics is critical.

The Worm Propagation Model with Dual Dynamic Quarantine Strategy

NASA Astrophysics Data System (ADS)

Yao, Yu; Xie, Xiao-Wu; Guo, Hao; Gao, Fu-Xiang; Yu, Ge

Internet worms are becoming more and more harmful with the rapid development of the Internet. Due to the extremely fast spread and great destructive power of network worms, strong dynamic quarantine strategies are necessary. Inspired by the real-world approach to the prevention and treatment of infectious diseases, this paper proposes a quarantine strategy based on dynamic worm propagation model: the SIQRV dual quarantine model. This strategy uses dynamic quarantine method to make the vulnerable host and infected host quarantined, and then release them after a certain period of time, regardless of whether quarantined host security is checked. Through mathematic modeling, it has been found that when the basic reproduction number R0 is less than a critical value, the system will stabilize in the disease-free equilibrium, that is, in theory, the infected hosts will be completely immune. Finally, by comparing the simulation results and numerical analysis, the basic agreement between the two curves supports the validity of the mathematical model. Our future work will be focusing on taking both the delay and double-quarantine strategy into account and further expanding the scale of our simulation work.

Characterizing mercury concentrations and flux dynamics in a coastal plain watershed using multiple models

EPA Science Inventory

The primary goal was to asess Hg cycling within a small coastal plain watershed (McTier Creek) using multiple watershed models with distinct mathematical frameworks that emphasize different system dynamics; a secondary goal was to identify current needs in watershed-scale Hg mode...

UH-60A Black Hawk engineering simulation program. Volume 1: Mathematical model

NASA Technical Reports Server (NTRS)

Howlett, J. J.

1981-01-01

A nonlinear mathematical model of the UR-60A Black Hawk helicopter was developed. This mathematical model, which was based on the Sikorsky General Helicopter (Gen Hel) Flight Dynamics Simulation, provides NASA with an engineering simulation for performance and handling qualities evaluations. This mathematical model is total systems definition of the Black Hawk helicopter represented at a uniform level of sophistication considered necessary for handling qualities evaluations. The model is a total force, large angle representation in six rigid body degrees of freedom. Rotor blade flapping, lagging, and hub rotational degrees of freedom are also represented. In addition to the basic helicopter modules, supportive modules were defined for the landing interface, power unit, ground effects, and gust penetration. Information defining the cockpit environment relevant to pilot in the loop simulation is presented.

The Computer Simulation of Liquids by Molecular Dynamics.

ERIC Educational Resources Information Center

Smith, W.

1987-01-01

Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

Mathematical modeling of atopic dermatitis reveals "double-switch" mechanisms underlying 4 common disease phenotypes.

PubMed

Domínguez-Hüttinger, Elisa; Christodoulides, Panayiotis; Miyauchi, Kosuke; Irvine, Alan D; Okada-Hatakeyama, Mariko; Kubo, Masato; Tanaka, Reiko J

2017-06-01

The skin barrier acts as the first line of defense against constant exposure to biological, microbial, physical, and chemical environmental stressors. Dynamic interplay between defects in the skin barrier, dysfunctional immune responses, and environmental stressors are major factors in the development of atopic dermatitis (AD). A systems biology modeling approach can yield significant insights into these complex and dynamic processes through integration of prior biological data. We sought to develop a multiscale mathematical model of AD pathogenesis that describes the dynamic interplay between the skin barrier, environmental stress, and immune dysregulation and use it to achieve a coherent mechanistic understanding of the onset, progression, and prevention of AD. We mathematically investigated synergistic effects of known genetic and environmental risk factors on the dynamic onset and progression of the AD phenotype, from a mostly asymptomatic mild phenotype to a severe treatment-resistant form. Our model analysis identified a "double switch," with 2 concatenated bistable switches, as a key network motif that dictates AD pathogenesis: the first switch is responsible for the reversible onset of inflammation, and the second switch is triggered by long-lasting or frequent activation of the first switch, causing irreversible onset of systemic T H 2 sensitization and worsening of AD symptoms. Our mathematical analysis of the bistable switch predicts that genetic risk factors decrease the threshold of environmental stressors to trigger systemic T H 2 sensitization. This analysis predicts and explains 4 common clinical AD phenotypes from a mild and reversible phenotype through to severe and recalcitrant disease and provides a mechanistic explanation for clinically demonstrated preventive effects of emollient treatments against development of AD. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Dynamic Modeling for Development and Education: From Concepts to Numbers

ERIC Educational Resources Information Center

Van Geert, Paul

2014-01-01

The general aim of the article is to teach the reader how to transform conceptual models of change, development, and learning into mathematical expressions and how to use these equations to build dynamic models by means of the widely used spreadsheet program Excel. The explanation is supported by a number of Excel files, which the reader can…

Earth and ocean modeling

NASA Technical Reports Server (NTRS)

Knezovich, F. M.

1976-01-01

A modular structured system of computer programs is presented utilizing earth and ocean dynamical data keyed to finitely defined parameters. The model is an assemblage of mathematical algorithms with an inherent capability of maturation with progressive improvements in observational data frequencies, accuracies and scopes. The Eom in its present state is a first-order approach to a geophysical model of the earth's dynamics.

Disorder and Chaos: Developing and Teaching an Interdisciplinary Course on Chemical Dynamics

ERIC Educational Resources Information Center

Desjardins, Steven G.

2008-01-01

In this paper we describe an interdisciplinary course on dynamics that is appropriate for nonscience majors. This course introduces ideas about mathematical modeling using examples based on pendulums, chemical kinetics, and population dynamics. The unique emphasis for a nonmajors course is on chemical reactions as dynamical systems that do more…

Mathematical model for prediction of efficiency indicators of educational activity in high school

NASA Astrophysics Data System (ADS)

Tikhonova, O. M.; Kushnikov, V. A.; Fominykh, D. S.; Rezchikov, A. F.; Ivashchenko, V. A.; Bogomolov, A. S.; Filimonyuk, L. Yu; Dolinina, O. N.; Kushnikov, O. V.; Shulga, T. E.; Tverdokhlebov, V. A.

2018-05-01

The quality of high school is a current problem all over the world. The paper presents the system dedicated to predicting the accreditation indicators of technical universities based on J. Forrester mechanism of system dynamics. The mathematical model is developed for prediction of efficiency indicators of the educational activity and is based on the apparatus of nonlinear differential equations.

A dynamic model of functioning of a bank

NASA Astrophysics Data System (ADS)

Malafeyev, Oleg; Awasthi, Achal; Zaitseva, Irina; Rezenkov, Denis; Bogdanova, Svetlana

2018-04-01

In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of bank's work is described in this paper. The problem is then approached using the method of dynamic programming. Dynamic programming makes sure that the solutions obtained are globally optimal and numerically stable. The optimization process is set up as a discrete multi-stage decision process and solved with the help of dynamic programming.

On the characterization of dynamic supramolecular systems: a general mathematical association model for linear supramolecular copolymers and application on a complex two-component hydrogen-bonding system.

PubMed

Odille, Fabrice G J; Jónsson, Stefán; Stjernqvist, Susann; Rydén, Tobias; Wärnmark, Kenneth

2007-01-01

A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab, and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4n5m as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the DeltaH degrees and DeltaS degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters.

Systems analysis of the vestibulo-ocular system. [mathematical model of vestibularly driven head and eye movements

NASA Technical Reports Server (NTRS)

Schmid, R. M.

1973-01-01

The vestibulo-ocular system is examined from the standpoint of system theory. The evolution of a mathematical model of the vestibulo-ocular system in an attempt to match more and more experimental data is followed step by step. The final model explains many characteristics of the eye movement in vestibularly induced nystagmus. The analysis of the dynamic behavior of the model at the different stages of its development is illustrated in time domain, mainly in a qualitative way.

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

A real success in numerical modeling of dynamics of the Earth can be achieved only by multidisciplinary research teams of experts in geodynamics, applied and pure mathematics, and computer science. The success in numerical modeling is based on the following basic, but simple, rules. (i) People need simplicity most, but they understand intricacies best (B. Pasternak, writer). Start from a simple numerical model, which describes basic physical laws by a set of mathematical equations, and move then to a complex model. Never start from a complex model, because you cannot understand the contribution of each term of the equations to the modeled geophysical phenomenon. (ii) Study the numerical methods behind your computer code. Otherwise it becomes difficult to distinguish true and erroneous solutions to the geodynamic problem, especially when your problem is complex enough. (iii) Test your model versus analytical and asymptotic solutions, simple 2D and 3D model examples. Develop benchmark analysis of different numerical codes and compare numerical results with laboratory experiments. Remember that the numerical tool you employ is not perfect, and there are small bugs in every computer code. Therefore the testing is the most important part of your numerical modeling. (iv) Prove (if possible) or learn relevant statements concerning the existence, uniqueness and stability of the solution to the mathematical and discrete problems. Otherwise you can solve an improperly-posed problem, and the results of the modeling will be far from the true solution of your model problem. (v) Try to analyze numerical models of a geological phenomenon using as less as possible tuning model variables. Already two tuning variables give enough possibilities to constrain your model well enough with respect to observations. The data fitting sometimes is quite attractive and can take you far from a principal aim of your numerical modeling: to understand geophysical phenomena. (vi) If the number of tuning model variables are greater than two, test carefully the effect of each of the variables on the modeled phenomenon. Remember: With four exponents I can fit an elephant (E. Fermi, physicist). (vii) Make your numerical model as accurate as possible, but never put the aim to reach a great accuracy: Undue precision of computations is the first symptom of mathematical illiteracy (N. Krylov, mathematician). How complex should be a numerical model? A model which images any detail of the reality is as useful as a map of scale 1:1 (J. Robinson, economist). This message is quite important for geoscientists, who study numerical models of complex geodynamical processes. I believe that geoscientists will never create a model of the real Earth dynamics, but we should try to model the dynamics such a way to simulate basic geophysical processes and phenomena. Does a particular model have a predictive power? Each numerical model has a predictive power, otherwise the model is useless. The predictability of the model varies with its complexity. Remember that a solution to the numerical model is an approximate solution to the equations, which have been chosen in believe that they describe dynamic processes of the Earth. Hence a numerical model predicts dynamics of the Earth as well as the mathematical equations describe this dynamics. What methodological advances are still needed for testable geodynamic modeling? Inverse (time-reverse) numerical modeling and data assimilation are new methodologies in geodynamics. The inverse modeling can allow to test geodynamic models forward in time using restored (from present-day observations) initial conditions instead of unknown conditions.

A mathematical model of Chagas disease transmission

NASA Astrophysics Data System (ADS)

Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning

2018-03-01

Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.

Infectious diseases in space and time: noise and nonlinearity in epidemiological dynamics

NASA Astrophysics Data System (ADS)

Grenfell, Bryan

2005-03-01

I illustrate the impact of noise and nonlinearity on the spatio-temporal dynamics and evolution of epidemics using mathematical models and analyses of detailed epidemiological data from childhood infections, such as measles.

Dynamic pathway modeling of signal transduction networks: a domain-oriented approach.

PubMed

Conzelmann, Holger; Gilles, Ernst-Dieter

2008-01-01

Mathematical models of biological processes become more and more important in biology. The aim is a holistic understanding of how processes such as cellular communication, cell division, regulation, homeostasis, or adaptation work, how they are regulated, and how they react to perturbations. The great complexity of most of these processes necessitates the generation of mathematical models in order to address these questions. In this chapter we provide an introduction to basic principles of dynamic modeling and highlight both problems and chances of dynamic modeling in biology. The main focus will be on modeling of s transduction pathways, which requires the application of a special modeling approach. A common pattern, especially in eukaryotic signaling systems, is the formation of multi protein signaling complexes. Even for a small number of interacting proteins the number of distinguishable molecular species can be extremely high. This combinatorial complexity is due to the great number of distinct binding domains of many receptors and scaffold proteins involved in signal transduction. However, these problems can be overcome using a new domain-oriented modeling approach, which makes it possible to handle complex and branched signaling pathways.

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

Stem cell transplantation as a dynamical system: are clinical outcomes deterministic?

PubMed

Toor, Amir A; Kobulnicky, Jared D; Salman, Salman; Roberts, Catherine H; Jameson-Lee, Max; Meier, Jeremy; Scalora, Allison; Sheth, Nihar; Koparde, Vishal; Serrano, Myrna; Buck, Gregory A; Clark, William B; McCarty, John M; Chung, Harold M; Manjili, Masoud H; Sabo, Roy T; Neale, Michael C

2014-01-01

Outcomes in stem cell transplantation (SCT) are modeled using probability theory. However, the clinical course following SCT appears to demonstrate many characteristics of dynamical systems, especially when outcomes are considered in the context of immune reconstitution. Dynamical systems tend to evolve over time according to mathematically determined rules. Characteristically, the future states of the system are predicated on the states preceding them, and there is sensitivity to initial conditions. In SCT, the interaction between donor T cells and the recipient may be considered as such a system in which, graft source, conditioning, and early immunosuppression profoundly influence immune reconstitution over time. This eventually determines clinical outcomes, either the emergence of tolerance or the development of graft versus host disease. In this paper, parallels between SCT and dynamical systems are explored and a conceptual framework for developing mathematical models to understand disparate transplant outcomes is proposed.

Stem Cell Transplantation as a Dynamical System: Are Clinical Outcomes Deterministic?

PubMed Central

Toor, Amir A.; Kobulnicky, Jared D.; Salman, Salman; Roberts, Catherine H.; Jameson-Lee, Max; Meier, Jeremy; Scalora, Allison; Sheth, Nihar; Koparde, Vishal; Serrano, Myrna; Buck, Gregory A.; Clark, William B.; McCarty, John M.; Chung, Harold M.; Manjili, Masoud H.; Sabo, Roy T.; Neale, Michael C.

2014-01-01

Outcomes in stem cell transplantation (SCT) are modeled using probability theory. However, the clinical course following SCT appears to demonstrate many characteristics of dynamical systems, especially when outcomes are considered in the context of immune reconstitution. Dynamical systems tend to evolve over time according to mathematically determined rules. Characteristically, the future states of the system are predicated on the states preceding them, and there is sensitivity to initial conditions. In SCT, the interaction between donor T cells and the recipient may be considered as such a system in which, graft source, conditioning, and early immunosuppression profoundly influence immune reconstitution over time. This eventually determines clinical outcomes, either the emergence of tolerance or the development of graft versus host disease. In this paper, parallels between SCT and dynamical systems are explored and a conceptual framework for developing mathematical models to understand disparate transplant outcomes is proposed. PMID:25520720

Investigation of vibration characteristics of electric motors

NASA Technical Reports Server (NTRS)

Bakshis, A. K.; Tamoshyunas, Y. K.

1973-01-01

The vibration characteristics of electric motors were analyzed using mathematical statistics methods. The equipment used and the method of conducting the test are described. Curves are developed to show the visualization of the electric motor vibrations in the vertical direction. Additional curves are included to show the amplitude-phase frequency characteristic of dynamic rotor-housing vibrations at the first lug and the same data for the second lug of the electric motor. Mathematical models were created to show the transmission function of the dynamic rotor housing system.

Quantum Bohmian model for financial market

NASA Astrophysics Data System (ADS)

Choustova, Olga Al.

2007-01-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

Students' Abstraction in Recognizing, Building with and Constructing a Quadrilateral

ERIC Educational Resources Information Center

Budiarto, Mega Teguh; Rahaju, Endah Budi; Hartono, Sugi

2017-01-01

This study aims to implement empirically students' abstraction with socio-cultural background of Indonesia. Abstraction is an activity that involves a vertical reorganization of previously constructed mathematics into a new mathematical structure. The principal components of the model are three dynamic nested epistemic actions: recognizing,…

Dynamic Hyperbolic Geometry: Building Intuition and Understanding Mediated by a Euclidean Model

ERIC Educational Resources Information Center

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-01-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

POEM: PESTICIDE ORCHARD ECOSYSTEM MODEL

EPA Science Inventory

The Pesticide Orchard Ecosystem Model (POEM) is a mathematical model of organophosphate pesticide movement in an apple orchard ecosystem. In addition submodels on invertebrate population dynamics are included. The fate model allows the user to select the pesticide, its applicatio...

The Use of Mathematical Models of Chlamydia Transmission to Address Public Health Policy Questions: A Systematic Review.

PubMed

Rönn, Minttu M; Wolf, Emory E; Chesson, Harrell; Menzies, Nicolas A; Galer, Kara; Gorwitz, Rachel; Gift, Thomas; Hsu, Katherine; Salomon, Joshua A

2017-05-01

Mathematical models of chlamydia transmission can help inform disease control policy decisions when direct empirical evaluation of alternatives is impractical. We reviewed published chlamydia models to understand the range of approaches used for policy analyses and how the studies have responded to developments in the field. We performed a literature review by searching Medline and Google Scholar (up to October 2015) to identify publications describing dynamic chlamydia transmission models used to address public health policy questions. We extracted information on modeling methodology, interventions, and key findings. We identified 47 publications (including two model comparison studies), which reported collectively on 29 distinct mathematical models. Nine models were individual-based, and 20 were deterministic compartmental models. The earliest studies evaluated the benefits of national-level screening programs and predicted potentially large benefits from increased screening. Subsequent trials and further modeling analyses suggested the impact might have been overestimated. Partner notification has been increasingly evaluated in mathematical modeling, whereas behavioral interventions have received relatively limited attention. Our review provides an overview of chlamydia transmission models and gives a perspective on how mathematical modeling has responded to increasing empirical evidence and addressed policy questions related to prevention of chlamydia infection and sequelae.

Modeling human behavior in economics and social science.

PubMed

Dolfin, M; Leonida, L; Outada, N

2017-12-01

The complex interactions between human behaviors and social economic sciences is critically analyzed in this paper in view of possible applications of mathematical modeling as an attainable interdisciplinary approach to understand and simulate the aforementioned dynamics. The quest is developed along three steps: Firstly an overall analysis of social and economic sciences indicates the main requirements that a contribution of mathematical modeling should bring to these sciences; subsequently the focus moves to an overview of mathematical tools and to the selection of those which appear, according to the authors bias, appropriate to the modeling; finally, a survey of applications is presented looking ahead to research perspectives. Copyright © 2017 Elsevier B.V. All rights reserved.

A simple mathematical model of society collapse applied to Easter Island

NASA Astrophysics Data System (ADS)

Bologna, M.; Flores, J. C.

2008-02-01

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.

Dynamic Boolean Mathematics

ERIC Educational Resources Information Center

Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen

2016-01-01

Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

Exploring Classroom Interaction with Dynamic Social Network Analysis

ERIC Educational Resources Information Center

Bokhove, Christian

2018-01-01

This article reports on an exploratory project in which technology and dynamic social network analysis (SNA) are used for modelling classroom interaction. SNA focuses on the links between social actors, draws on graphic imagery to reveal and display the patterning of those links, and develops mathematical and computational models to describe and…

Mathematical modelling and linear stability analysis of laser fusion cutting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg

A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.

Analytical Models for Rotor Test Module, Strut, and Balance Frame Dynamics in the 40 by 80 Ft Wind Tunnel

NASA Technical Reports Server (NTRS)

Johnson, W.

1976-01-01

A mathematical model is developed for the dynamics of a wind tunnel support system consisting of a balance frame, struts, and an aircraft or test module. Data are given for several rotor test modules in the Ames 40 by 80 ft wind tunnel. A model for ground resonance calculations is also described.

Mathematical modeling of heat treatment processes conserving biological activity of plant bioresources

NASA Astrophysics Data System (ADS)

Rodionova, N. S.; Popov, E. S.; Pozhidaeva, E. A.; Pynzar, S. S.; Ryaskina, L. O.

2018-05-01

The aim of this study is to develop a mathematical model of the heat exchange process of LT-processing to estimate the dynamics of temperature field changes and optimize the regime parameters, due to the non-stationarity process, the physicochemical and thermophysical properties of food systems. The application of LT-processing, based on the use of low-temperature modes in thermal culinary processing of raw materials with preliminary vacuum packaging in a polymer heat- resistant film is a promising trend in the development of technics and technology in the catering field. LT-processing application of food raw materials guarantees the preservation of biologically active substances in food environments, which are characterized by a certain thermolability, as well as extend the shelf life and high consumer characteristics of food systems that are capillary-porous bodies. When performing the mathematical modeling of the LT-processing process, the packet of symbolic mathematics “Maple” was used, as well as the mathematical packet flexPDE that uses the finite element method for modeling objects with distributed parameters. The processing of experimental results was evaluated with the help of the developed software in the programming language Python 3.4. To calculate and optimize the parameters of the LT processing process of polycomponent food systems, the differential equation of non-stationary thermal conductivity was used, the solution of which makes it possible to identify the temperature change at any point of the solid at different moments. The present study specifies data on the thermophysical characteristics of the polycomponent food system based on plant raw materials, with the help of which the physico-mathematical model of the LT- processing process has been developed. The obtained mathematical model allows defining of the dynamics of the temperature field in different sections of the LT-processed polycomponent food systems on the basis of calculating the evolution profiles of temperature fields, which enable one to analyze the efficiency of the regime parameters of heat treatment.

Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude.

PubMed

Zamora-Chimal, Criseida; Santillán, Moisés; Rodríguez-González, Jesús

2012-10-07

In this paper we introduce a mathematical model for the tryptophan operon regulatory pathway in Bacillus subtilis. This model considers the transcription-attenuation, and the enzyme-inhibition regulatory mechanisms. Special attention is paid to the estimation of all the model parameters from reported experimental data. With the aid of this model we investigate, from a mathematical-modeling point of view, whether the existing multiplicity of regulatory feedback loops is advantageous in some sense, regarding the dynamic response and the biochemical noise in the system. The tryptophan operon dynamic behavior is studied by means of deterministic numeric simulations, while the biochemical noise is analyzed with the aid of stochastic simulations. The model feasibility is tested comparing its stochastic and deterministic results with experimental reports. Our results for the wildtype and for a couple of mutant bacterial strains suggest that the enzyme-inhibition feedback loop, dynamically accelerates the operon response, and plays a major role in the reduction of biochemical noise. Also, the transcription-attenuation feedback loop makes the trp operon sensitive to changes in the endogenous tryptophan level, and increases the amplitude of the biochemical noise. Copyright © 2012 Elsevier Ltd. All rights reserved.

The Origin of Mathematics and Number Sense in the Cerebellum: with Implications for Finger Counting and Dyscalculia.

PubMed

Vandervert, Larry

2017-01-01

Mathematicians and scientists have struggled to adequately describe the ultimate foundations of mathematics. Nobel laureates Albert Einstein and Eugene Wigner were perplexed by this issue, with Wigner concluding that the workability of mathematics in the real world is a mystery we cannot explain. In response to this classic enigma, the major purpose of this article is to provide a theoretical model of the ultimate origin of mathematics and "number sense" (as defined by S. Dehaene) that is proposed to involve the learning of inverse dynamics models through the collaboration of the cerebellum and the cerebral cortex (but prominently cerebellum-driven). This model is based upon (1) the modern definition of mathematics as the "science of patterns," (2) cerebellar sequence (pattern) detection, and (3) findings that the manipulation of numbers is automated in the cerebellum. This cerebro-cerebellar approach does not necessarily conflict with mathematics or number sense models that focus on brain functions associated with especially the intraparietal sulcus region of the cerebral cortex. A direct corollary purpose of this article is to offer a cerebellar inner speech explanation for difficulty in developing "number sense" in developmental dyscalculia. It is argued that during infancy the cerebellum learns (1) a first tier of internal models for a primitive physics that constitutes the foundations of visual-spatial working memory, and (2) a second (and more abstract) tier of internal models based on (1) that learns "number" and relationships among dimensions across the primitive physics of the first tier. Within this context it is further argued that difficulty in the early development of the second tier of abstraction (and "number sense") is based on the more demanding attentional requirements imposed on cerebellar inner speech executive control during the learning of cerebellar inverse dynamics models. Finally, it is argued that finger counting improves (does not originate) "number sense" by extending focus of attention in executive control of silent cerebellar inner speech. It is suggested that (1) the origin of mathematics has historically been an enigma only because it is learned below the level of conscious awareness in cerebellar internal models, (2) understandings of the development of "number sense" and developmental dyscalculia can be advanced by first understanding the ultimate foundations of number and mathematics do not simply originate in the cerebral cortex, but rather in cerebro-cerebellar collaboration (predominately driven by the cerebellum). It is concluded that difficulty with "number sense" results from the extended demands on executive control in learning inverse dynamics models associated with cerebellar inner speech related to the second tier of abstraction (numbers) of the infant's primitive physics.

Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

USGS Publications Warehouse

Iverson, Richard M.; LeVeque, Randall J.

2009-01-01

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Understanding the dynamics of sustainable social-ecological systems: human behavior, institutions, and regulatory feedback networks.

PubMed

Anderies, John M

2015-02-01

I present a general mathematical modeling framework that can provide a foundation for the study of sustainability in social- ecological systems (SESs). Using basic principles from feedback control and a sequence of specific models from bioeconomics and economic growth, I outline several mathematical and empirical challenges associated with the study of sustainability of SESs. These challenges are categorized into three classes: (1) the social choice of performance measures, (2) uncertainty, and (3) collective action. Finally, I present some opportunities for combining stylized dynamical systems models with empirical data on human behavior and biophysical systems to address practical challenges for the design of effective governance regimes (policy feedbacks) for highly uncertain natural resource systems.

Dynamic Analyses Including Joints Of Truss Structures

NASA Technical Reports Server (NTRS)

Belvin, W. Keith

1991-01-01

Method for mathematically modeling joints to assess influences of joints on dynamic response of truss structures developed in study. Only structures with low-frequency oscillations considered; only Coulomb friction and viscous damping included in analysis. Focus of effort to obtain finite-element mathematical models of joints exhibiting load-vs.-deflection behavior similar to measured load-vs.-deflection behavior of real joints. Experiments performed to determine stiffness and damping nonlinearities typical of joint hardware. Algorithm for computing coefficients of analytical joint models based on test data developed to enable study of linear and nonlinear effects of joints on global structural response. Besides intended application to large space structures, applications in nonaerospace community include ground-based antennas and earthquake-resistant steel-framed buildings.

Avian Influenza spread and transmission dynamics

USGS Publications Warehouse

Bourouiba, Lydia; Gourley, Stephen A.; Liu, Rongsong; Takekawa, John Y.; Wu, Jianhong; Chen, Dongmei; Moulin, Bernard; Wu, Jianhong

2015-01-01

The spread of highly pathogenic avian influenza (HPAI) viruses of type A of subtype H5N1 has been a serious threat to global public health. Understanding the roles of various (migratory, wild, poultry) bird species in the transmission of these viruses is critical for designing and implementing effective control and intervention measures. Developing appropriate models and mathematical techniques to understand these roles and to evaluate the effectiveness of mitigation strategies have been a challenge. Recent development of the global health surveillance (especially satellite tracking and GIS techniques) and the mathematical theory of dynamical systems combined have gradually shown the promise of some cutting-edge methodologies and techniques in mathematical biology to meet this challenge.

Cognitive algorithms: dynamic logic, working of the mind, evolution of consciousness and cultures

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2007-04-01

The paper discusses evolution of consciousness driven by the knowledge instinct, a fundamental mechanism of the mind which determines its higher cognitive functions. Dynamic logic mathematically describes the knowledge instinct. It overcomes past mathematical difficulties encountered in modeling intelligence and relates it to mechanisms of concepts, emotions, instincts, consciousness and unconscious. The two main aspects of the knowledge instinct are differentiation and synthesis. Differentiation is driven by dynamic logic and proceeds from vague and unconscious states to more crisp and conscious states, from less knowledge to more knowledge at each hierarchical level of the mind. Synthesis is driven by dynamic logic operating in a hierarchical organization of the mind; it strives to achieve unity and meaning of knowledge: every concept finds its deeper and more general meaning at a higher level. These mechanisms are in complex relationship of symbiosis and opposition, which leads to complex dynamics of evolution of consciousness and cultures. Modeling this dynamics in a population leads to predictions for the evolution of consciousness, and cultures. Cultural predictive models can be compared to experimental data and used for improvement of human conditions. We discuss existing evidence and future research directions.

The study of thermal processes in control systems of heat consumption of buildings

NASA Astrophysics Data System (ADS)

Tsynaeva, E.; A, Tsynaeva

2017-11-01

The article discusses the main thermal processes in the automated control systems for heat consumption (ACSHC) of buildings, schematic diagrams of these systems, mathematical models used for description of thermal processes in ACSHC. Conducted verification represented by mathematical models. It was found that the efficiency of the operation of ACSHC depend from the external and internal factors. Numerical study of dynamic modes of operation of ACSHC.

Predictive models of forest dynamics.

PubMed

Purves, Drew; Pacala, Stephen

2008-06-13

Dynamic global vegetation models (DGVMs) have shown that forest dynamics could dramatically alter the response of the global climate system to increased atmospheric carbon dioxide over the next century. But there is little agreement between different DGVMs, making forest dynamics one of the greatest sources of uncertainty in predicting future climate. DGVM predictions could be strengthened by integrating the ecological realities of biodiversity and height-structured competition for light, facilitated by recent advances in the mathematics of forest modeling, ecological understanding of diverse forest communities, and the availability of forest inventory data.

PREFACE: 2nd International Conference on Mathematical Modeling in Physical Sciences 2013 (IC-MSQUARE 2013)

NASA Astrophysics Data System (ADS)

2014-03-01

The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013. The Conference was attended by more than 280 participants and hosted about 400 oral, poster, and virtual presentations while counted more than 600 pre-registered authors. The second IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel sessions were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. Further information on the editors, speakers and committees is available in the attached pdf.

Current Results and Proposed Activities in Microgravity Fluid Dynamics

NASA Technical Reports Server (NTRS)

Polezhaev, V. I.

1996-01-01

The Institute for Problems in Mechanics' Laboratory work in mathematical and physical modelling of fluid mechanics develops models, methods, and software for analysis of fluid flow, instability analysis, direct numerical modelling and semi-empirical models of turbulence, as well as experimental research and verification of these models and their applications in technological fluid dynamics, microgravity fluid mechanics, geophysics, and a number of engineering problems. This paper presents an overview of the results in microgravity fluid dynamics research during the last two years. Nonlinear problems of weakly compressible and compressible fluid flows are discussed.

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Physical Invariants of Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective, the mechanism of decision-making is feedback from the mental dynamics to the motor dynamics, and this mechanism provides a quantum-like collapse of a random motion into an appropriate deterministic state, such that entropy undergoes a pronounced decrease. The existence of this mechanism is considered to be an invariant of intelligent behavior of living systems, regardless of the origins and material compositions of the systems.

Quantum-like dynamics applied to cognition: a consideration of available options

NASA Astrophysics Data System (ADS)

Broekaert, Jan; Basieva, Irina; Blasiak, Pawel; Pothos, Emmanuel M.

2017-10-01

Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Integrating System Dynamics and Bayesian Networks with Application to Counter-IED Scenarios

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jarman, Kenneth D.; Brothers, Alan J.; Whitney, Paul D.

2010-06-06

The practice of choosing a single modeling paradigm for predictive analysis can limit the scope and relevance of predictions and their utility to decision-making processes. Considering multiple modeling methods simultaneously may improve this situation, but a better solution provides a framework for directly integrating different, potentially complementary modeling paradigms to enable more comprehensive modeling and predictions, and thus better-informed decisions. The primary challenges of this kind of model integration are to bridge language and conceptual gaps between modeling paradigms, and to determine whether natural and useful linkages can be made in a formal mathematical manner. To address these challenges inmore » the context of two specific modeling paradigms, we explore mathematical and computational options for linking System Dynamics (SD) and Bayesian network (BN) models and incorporating data into the integrated models. We demonstrate that integrated SD/BN models can naturally be described as either state space equations or Dynamic Bayes Nets, which enables the use of many existing computational methods for simulation and data integration. To demonstrate, we apply our model integration approach to techno-social models of insurgent-led attacks and security force counter-measures centered on improvised explosive devices.« less

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

NASA Technical Reports Server (NTRS)

Thompson, David E.

2005-01-01

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Finite-element approach to Brownian dynamics of polymers.

PubMed

Cyron, Christian J; Wall, Wolfgang A

2009-12-01

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

Models of determining deformations

NASA Astrophysics Data System (ADS)

Gladilin, V. N.

2016-12-01

In recent years, a lot of functions designed to determine deformation values that occur mostly as a result of settlement of structures and industrial equipment. Some authors suggest such advanced mathematical functions approximating deformations as general methods for the determination of deformations. The article describes models of deformations as physical processes. When comparing static, cinematic and dynamic models, it was found that the dynamic model reflects the deformation of structures and industrial equipment most reliably.

Dynamics of an HIV-1 infection model with cell mediated immunity

NASA Astrophysics Data System (ADS)

Yu, Pei; Huang, Jianing; Jiang, Jiao

2014-10-01

In this paper, we study the dynamics of an improved mathematical model on HIV-1 virus with cell mediated immunity. This new 5-dimensional model is based on the combination of a basic 3-dimensional HIV-1 model and a 4-dimensional immunity response model, which more realistically describes dynamics between the uninfected cells, infected cells, virus, the CTL response cells and CTL effector cells. Our 5-dimensional model may be reduced to the 4-dimensional model by applying a quasi-steady state assumption on the variable of virus. However, it is shown in this paper that virus is necessary to be involved in the modeling, and that a quasi-steady state assumption should be applied carefully, which may miss some important dynamical behavior of the system. Detailed bifurcation analysis is given to show that the system has three equilibrium solutions, namely the infection-free equilibrium, the infectious equilibrium without CTL, and the infectious equilibrium with CTL, and a series of bifurcations including two transcritical bifurcations and one or two possible Hopf bifurcations occur from these three equilibria as the basic reproduction number is varied. The mathematical methods applied in this paper include characteristic equations, Routh-Hurwitz condition, fluctuation lemma, Lyapunov function and computation of normal forms. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.

Dynamic modeling method for infrared smoke based on enhanced discrete phase model

NASA Astrophysics Data System (ADS)

Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo

2018-03-01

The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.

On the interplay between mathematics and biology. Hallmarks toward a new systems biology

NASA Astrophysics Data System (ADS)

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M.; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach.

Development of the Mathematics of Learning Curve Models for Evaluating Small Modular Reactor Economics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, Thomas J.

2014-03-01

This report documents the efforts to perform dynamic model validation on the Eastern Interconnection (EI) by modeling governor deadband. An on-peak EI dynamic model is modified to represent governor deadband characteristics. Simulation results are compared with synchrophasor measurements collected by the Frequency Monitoring Network (FNET/GridEye). The comparison shows that by modeling governor deadband the simulated frequency response can closely align with the actual system response.

Space-time dynamics of Stem Cell Niches: a unified approach for Plants.

PubMed

Pérez, Maria Del Carmen; López, Alejandro; Padilla, Pablo

2013-06-01

Many complex systems cannot be analyzed using traditional mathematical tools, due to their irreducible nature. This makes it necessary to develop models that can be implemented computationally to simulate their evolution. Examples of these models are cellular automata, evolutionary algorithms, complex networks, agent-based models, symbolic dynamics and dynamical systems techniques. We review some representative approaches to model the stem cell niche in Arabidopsis thaliana and the basic biological mechanisms that underlie its formation and maintenance. We propose a mathematical model based on cellular automata for describing the space-time dynamics of the stem cell niche in the root. By making minimal assumptions on the cell communication process documented in experiments, we classify the basic developmental features of the stem-cell niche, including the basic structural architecture, and suggest that they could be understood as the result of generic mechanisms given by short and long range signals. This could be a first step in understanding why different stem cell niches share similar topologies, not only in plants. Also the fact that this organization is a robust consequence of the way information is being processed by the cells and to some extent independent of the detailed features of the signaling mechanism.

Space-time dynamics of stem cell niches: a unified approach for plants.

PubMed

Pérez, Maria del Carmen; López, Alejandro; Padilla, Pablo

2013-04-02

Many complex systems cannot be analyzed using traditional mathematical tools, due to their irreducible nature. This makes it necessary to develop models that can be implemented computationally to simulate their evolution. Examples of these models are cellular automata, evolutionary algorithms, complex networks, agent-based models, symbolic dynamics and dynamical systems techniques. We review some representative approaches to model the stem cell niche in Arabidopsis thaliana and the basic biological mechanisms that underlie its formation and maintenance. We propose a mathematical model based on cellular automata for describing the space-time dynamics of the stem cell niche in the root. By making minimal assumptions on the cell communication process documented in experiments, we classify the basic developmental features of the stem-cell niche, including the basic structural architecture, and suggest that they could be understood as the result of generic mechanisms given by short and long range signals. This could be a first step in understanding why different stem cell niches share similar topologies, not only in plants. Also the fact that this organization is a robust consequence of the way information is being processed by the cells and to some extent independent of the detailed features of the signaling mechanism.

Model-Based Phenotypic Signatures Governing the Dynamics of the Stem and Semi-differentiated Cell Populations in Dysplastic Colonic Crypts.

PubMed

Nikolov, Svetoslav; Santos, Guido; Wolkenhauer, Olaf; Vera, Julio

2018-02-01

Mathematical modeling of cell differentiated in colonic crypts can contribute to a better understanding of basic mechanisms underlying colonic tissue organization, but also its deregulation during carcinogenesis and tumor progression. Here, we combined bifurcation analysis to assess the effect that time delay has in the complex interplay of stem cells and semi-differentiated cells at the niche of colonic crypts, and systematic model perturbation and simulation to find model-based phenotypes linked to cancer progression. The models suggest that stem cell and semi-differentiated cell population dynamics in colonic crypts can display chaotic behavior. In addition, we found that clinical profiling of colorectal cancer correlates with the in silico phenotypes proposed by the mathematical model. Further, potential therapeutic targets for chemotherapy resistant phenotypes are proposed, which in any case will require experimental validation.

Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.

PubMed

Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz

2016-04-01

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymptotically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth cannot be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor's microenvironment are taken into account.

A survey on hysteresis modeling, identification and control

NASA Astrophysics Data System (ADS)

Hassani, Vahid; Tjahjowidodo, Tegoeh; Do, Thanh Nho

2014-12-01

The various mathematical models for hysteresis such as Preisach, Krasnosel'skii-Pokrovskii (KP), Prandtl-Ishlinskii (PI), Maxwell-Slip, Bouc-Wen and Duhem are surveyed in terms of their applications in modeling, control and identification of dynamical systems. In the first step, the classical formalisms of the models are presented to the reader, and more broadly, the utilization of the classical models is considered for development of more comprehensive models and appropriate controllers for corresponding systems. In addition, the authors attempt to encourage the reader to follow the existing mathematical models of hysteresis to resolve the open problems.

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data.

PubMed

Sriyudthsak, Kansuporn; Shiraishi, Fumihide; Hirai, Masami Yokota

2016-01-01

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although, hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Dynamic testing for shuttle design verification

NASA Technical Reports Server (NTRS)

Green, C. E.; Leadbetter, S. A.; Rheinfurth, M. H.

1972-01-01

Space shuttle design verification requires dynamic data from full scale structural component and assembly tests. Wind tunnel and other scaled model tests are also required early in the development program to support the analytical models used in design verification. Presented is a design philosophy based on mathematical modeling of the structural system strongly supported by a comprehensive test program; some of the types of required tests are outlined.

Using the Dynamic Model to Identify Stages of Teacher Skills in Assessment

ERIC Educational Resources Information Center

Christoforidou, Margarita; Xirafidou, Elisavet

2014-01-01

The article presents the results of two cross-sectional studies that investigate teachers' skills in using various techniques of assessment in mathematics by taking into account the four phases of assessment. The five dimensions of the dynamic model are also taken into account in proposing a framework for measuring teacher skills in assessment.…

Learning How to Construct Models of Dynamic Systems: An Initial Evaluation of the Dragoon Intelligent Tutoring System

ERIC Educational Resources Information Center

VanLehn, Kurt; Wetzel, Jon; Grover, Sachin; van de Sande, Brett

2017-01-01

Constructing models of dynamic systems is an important skill in both mathematics and science instruction. However, it has proved difficult to teach. Dragoon is an intelligent tutoring system intended to quickly and effectively teach this important skill. This paper describes Dragoon and an evaluation of it. The evaluation randomly assigned…

A Dynamic Process Model for Optimizing the Hospital Environment Cash-Flow

NASA Astrophysics Data System (ADS)

Pater, Flavius; Rosu, Serban

2011-09-01

In this article is presented a new approach to some fundamental techniques of solving dynamic programming problems with the use of functional equations. We will analyze the problem of minimizing the cost of treatment in a hospital environment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon.

Optimal control of HIV/AIDS dynamic: Education and treatment

NASA Astrophysics Data System (ADS)

Sule, Amiru; Abdullah, Farah Aini

2014-07-01

A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.

A mathematical model for ethanol fermentation from oil palm trunk sap using Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Sultana, S.; Jamil, Norazaliza Mohd; Saleh, E. A. M.; Yousuf, A.; Faizal, Che Ku M.

2017-09-01

This paper presents a mathematical model and solution strategy of ethanol fermentation for oil palm trunk (OPT) sap by considering the effect of substrate limitation, substrate inhibition product inhibition and cell death. To investigate the effect of cell death rate on the fermentation process we extended and improved the current mathematical model. The kinetic parameters of the model were determined by nonlinear regression using maximum likelihood function. The temporal profiles of sugar, cell and ethanol concentrations were modelled by a set of ordinary differential equations, which were solved numerically by the 4th order Runge-Kutta method. The model was validated by the experimental data and the agreement between the model and experimental results demonstrates that the model is reasonable for prediction of the dynamic behaviour of the fermentation process.

Specific modes of vibratory technological machines: mathematical models, peculiarities of interaction of system elements

NASA Astrophysics Data System (ADS)

Eliseev, A. V.; Sitov, I. S.; Eliseev, S. V.

2018-03-01

The methodological basis of constructing mathematical models of vibratory technological machines is developed in the article. An approach is proposed that makes it possible to introduce a vibration table in a specific mode that provides conditions for the dynamic damping of oscillations for the zone of placement of a vibration exciter while providing specified vibration parameters in the working zone of the vibration table. The aim of the work is to develop methods of mathematical modeling, oriented to technological processes with long cycles. The technologies of structural mathematical modeling are used with structural schemes, transfer functions and amplitude-frequency characteristics. The concept of the work is to test the possibilities of combining the conditions for reducing loads with working components of a vibration exciter while simultaneously maintaining sufficiently wide limits in variating the parameters of the vibrational field.

Existence and characterization of optimal control in mathematics model of diabetics population

NASA Astrophysics Data System (ADS)

Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.

2018-03-01

Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.

Features calibration of the dynamic force transducers

NASA Astrophysics Data System (ADS)

Sc., M. Yu Prilepko D.; Lysenko, V. G.

2018-04-01

The article discusses calibration methods of dynamic forces measuring instruments. The relevance of work is dictated by need to valid definition of the dynamic forces transducers metrological characteristics taking into account their intended application. The aim of this work is choice justification of calibration method, which provides the definition dynamic forces transducers metrological characteristics under simulation operating conditions for determining suitability for using in accordance with its purpose. The following tasks are solved: the mathematical model and the main measurements equation of calibration dynamic forces transducers by load weight, the main budget uncertainty components of calibration are defined. The new method of dynamic forces transducers calibration with use the reference converter “force-deformation” based on the calibrated elastic element and measurement of his deformation by a laser interferometer is offered. The mathematical model and the main measurements equation of the offered method is constructed. It is shown that use of calibration method based on measurements by the laser interferometer of calibrated elastic element deformations allows to exclude or to considerably reduce the uncertainty budget components inherent to method of load weight.

Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin S.; Young, Todd R.; Rabinovich, Mikhail I.

Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in which the number of variables is usually small enough for analysis. The dynamical images of different mental processes depend on their temporal organization and, as a rule, cannot be just simple attractors since cognition is characterized by transient dynamics. The mathematical image for a robust transient is a stable heteroclinic channel consisting of a chain of saddles connected by unstable separatrices. We focus here on hierarchical chunking dynamics that can represent several cognitive activities. Chunking is the dynamical phenomenon that means dividing a long information chain into shorter items. Chunking is known to be important in many processes of perception, learning, memory and cognition. We prove that in the phase space of the model that describes chunking there exists a new mathematical object — heteroclinic sequence of heteroclinic cycles — using the technique of slow-fast approximations. This new object serves as a skeleton of motions reflecting sequential features of hierarchical chunking dynamics and is an adequate image of the chunking processing.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Logic Dynamics for Deductive Inference -- Its Stability and Neural Basis

NASA Astrophysics Data System (ADS)

Tsuda, Ichiro

2014-12-01

We propose a dynamical model that represents a process of deductive inference. We discuss the stability of logic dynamics and a neural basis for the dynamics. We propose a new concept of descriptive stability, thereby enabling a structure of stable descriptions of mathematical models concerning dynamic phenomena to be clarified. The present theory is based on the wider and deeper thoughts of John S. Nicolis. In particular, it is based on our joint paper on the chaos theory of human short-term memories with a magic number of seven plus or minus two.

Web-based dynamic Delphi: a new survey instrument

NASA Astrophysics Data System (ADS)

Yao, JingTao; Liu, Wei-Ning

2006-04-01

We present a mathematical model for a dynamic Delphi survey method which takes advantages of Web technology. A comparative study on the performance of the conventional Delphi method and the dynamic Delphi instrument is conducted. It is suggested that a dynamic Delphi survey may form a consensus quickly. However, the result may not be robust due to the judgement leaking issues.

Multiobjective optimization and multivariable control of the beer fermentation process with the use of evolutionary algorithms.

PubMed

Andrés-Toro, B; Girón-Sierra, J M; Fernández-Blanco, P; López-Orozco, J A; Besada-Portas, E

2004-04-01

This paper describes empirical research on the model, optimization and supervisory control of beer fermentation. Conditions in the laboratory were made as similar as possible to brewery industry conditions. Since mathematical models that consider realistic industrial conditions were not available, a new mathematical model design involving industrial conditions was first developed. Batch fermentations are multiobjective dynamic processes that must be guided along optimal paths to obtain good results. The paper describes a direct way to apply a Pareto set approach with multiobjective evolutionary algorithms (MOEAs). Successful finding of optimal ways to drive these processes were reported. Once obtained, the mathematical fermentation model was used to optimize the fermentation process by using an intelligent control based on certain rules.

The Dynamics of Drug Resistance: A Mathematical Perspective

PubMed Central

Lavi, Orit; Gottesman, Michael M.; Levy, Doron

2012-01-01

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance that is therapy independent, therapy-dependent cellular alterations including induced resistance (dose-dependent) and acquired resistance (dose-independent). In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intra-cellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance. PMID:22387162

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Application of quantum master equation for long-term prognosis of asset-prices

NASA Astrophysics Data System (ADS)

Khrennikova, Polina

2016-05-01

This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a ;financial bath;. The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.

Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility.

PubMed

Devenyi, Ryan A; Ortega, Francis A; Groenendaal, Willemijn; Krogh-Madsen, Trine; Christini, David J; Sobie, Eric A

2017-04-01

Arrhythmias result from disruptions to cardiac electrical activity, although the factors that control cellular action potentials are incompletely understood. We combined mathematical modelling with experiments in heart cells from guinea pigs to determine how cellular electrical activity is regulated. A mismatch between modelling predictions and the experimental results allowed us to construct an improved, more predictive mathematical model. The balance between two particular potassium currents dictates how heart cells respond to perturbations and their susceptibility to arrhythmias. Imbalances of ionic currents can destabilize the cardiac action potential and potentially trigger lethal cardiac arrhythmias. In the present study, we combined mathematical modelling with information-rich dynamic clamp experiments to determine the regulation of action potential morphology in guinea pig ventricular myocytes. Parameter sensitivity analysis was used to predict how changes in ionic currents alter action potential duration, and these were tested experimentally using dynamic clamp, a technique that allows for multiple perturbations to be tested in each cell. Surprisingly, we found that a leading mathematical model, developed with traditional approaches, systematically underestimated experimental responses to dynamic clamp perturbations. We then re-parameterized the model using a genetic algorithm, which allowed us to estimate ionic current levels in each of the cells studied. This unbiased model adjustment consistently predicted an increase in the rapid delayed rectifier K + current and a drastic decrease in the slow delayed rectifier K + current, and this prediction was validated experimentally. Subsequent simulations with the adjusted model generated the clinically relevant prediction that the slow delayed rectifier is better able to stabilize the action potential and suppress pro-arrhythmic events than the rapid delayed rectifier. In summary, iterative coupling of simulations and experiments enabled novel insight into how the balance between cardiac K + currents influences ventricular arrhythmia susceptibility. © 2016 The Authors. The Journal of Physiology © 2016 The Physiological Society.

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

2017-12-01

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.

An algebra-based method for inferring gene regulatory networks.

PubMed

Vera-Licona, Paola; Jarrah, Abdul; Garcia-Puente, Luis David; McGee, John; Laubenbacher, Reinhard

2014-03-26

The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used. This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network. Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.

Cell Surface Mechanochemistry and the Determinants of Bleb Formation, Healing, and Travel Velocity

PubMed Central

Manakova, Kathryn; Yan, Huaming; Lowengrub, John; Allard, Jun

2016-01-01

Blebs are pressure-driven cell protrusions implicated in cellular functions such as cell division, apoptosis, and cell motility, including motility of protease-inhibited cancer cells. Because of their mechanical nature, blebs inform us about general cell-surface mechanics, including membrane dynamics, pressure propagation throughout the cytoplasm, and the architecture and dynamics of the actin cortex. Mathematical models including detailed fluid dynamics have previously been used to understand bleb expansion. Here, we develop mathematical models in two and three dimensions on longer timescales that recapitulate the full bleb life cycle, including both expansion and healing by cortex reformation, in terms of experimentally accessible biophysical parameters such as myosin contractility, osmotic pressure, and turnover of actin and ezrin. The model provides conditions under which blebbing occurs, and naturally gives rise to traveling blebs. The model predicts conditions under which blebs travel or remain stationary, as well as the bleb traveling velocity, a quantity that has remained elusive in previous models. As previous studies have used blebs as reporters of membrane tension and pressure dynamics within the cell, we have used our system to investigate various pressure equilibration models and dynamic, nonuniform membrane tension to account for the shape of a traveling bleb. We also find that traveling blebs tend to expand in all directions unless otherwise constrained. One possible constraint could be provided by spatial heterogeneity in, for example, adhesion density. PMID:27074688

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kengne, Jacques; Kenmogne, Fabien

2014-12-15

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

Mathematical modeling on T-cell mediated adaptive immunity in primary dengue infections.

PubMed

Sasmal, Sourav Kumar; Dong, Yueping; Takeuchi, Yasuhiro

2017-09-21

At present, dengue is the most common mosquito-borne viral disease in the world, and the global dengue incidence is increasing day by day due to climate changing. Here, we present a mathematical model of dengue viruses (DENVs) dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T-cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. From our analysis, we have identified the important model parameters and done the numerical simulation with respect to such important parameters. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment for dengue in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces

NASA Astrophysics Data System (ADS)

Molz, F. J.; Murdoch, L. C.; Faybishenko, B.

2013-12-01

Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the complex dynamics. We found that complex dynamics occur even with a constant food supply maintained at the upstream boundary of the biofilm. Results will be presented along with a description of the model, including 3 coupled partial differential equations and examples of the localized and propagating nonlinear dynamics inherent in the system. Contrary to a common opinion that chaos in many mechanical systems is a type of instability, appearing when energy is added, we hypothesize, based on the results of our modeling, that chaos in biofilm dynamics and other microbial ecosystems is driven by a competitive decrease in the food supply (i.e., chemical energy). We also hypothesize that, somewhat paradoxically, this, in turn, may support a long-term system stability that could cause bioclogging in porous media.

Dynamics of Longitudinal Impact in the Variable Cross-Section Rods

NASA Astrophysics Data System (ADS)

Stepanov, R.; Romenskyi, D.; Tsarenko, S.

2018-03-01

Dynamics of longitudinal impact in rods of variable cross-section is considered. Rods of various configurations are used as elements of power pulse systems. There is no single method to the construction of a mathematical model of longitudinal impact on rods. The creation of a general method for constructing a mathematical model of longitudinal impact for rods of variable cross-section is the goal of the article. An elastic rod is considered with a cross-sectional area varying in powers of law from the longitudinal coordinate. The solution of the wave equation is obtained using the Fourier method. Special functions are introduced on the basis of recurrence relations for Bessel functions for solving boundary value problems. The expression for the square of the norm is obtained taking into account the orthogonality property of the eigen functions with weight. For example, the impact of an inelastic mass along the wide end of a conical rod is considered. The expressions for the displacements, forces and stresses of the rod sections are obtained for the cases of sudden velocity communication and the application of force. The proposed mathematical model makes it possible to carry out investigations of the stress-strain state in rods of variable and constant cross-section for various conditions of dynamic effects.

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

NASA Astrophysics Data System (ADS)

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-05-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks.

PubMed

Deng, Zhimin; Tian, Tianhai

2014-07-29

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions. The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

TRPM8-Dependent Dynamic Response in a Mathematical Model of Cold Thermoreceptor

PubMed Central

Olivares, Erick; Salgado, Simón; Maidana, Jean Paul; Herrera, Gaspar; Campos, Matías; Madrid, Rodolfo; Orio, Patricio

2015-01-01

Cold-sensitive nerve terminals (CSNTs) encode steady temperatures with regular, rhythmic temperature-dependent firing patterns that range from irregular tonic firing to regular bursting (static response). During abrupt temperature changes, CSNTs show a dynamic response, transiently increasing their firing frequency as temperature decreases and silencing when the temperature increases (dynamic response). To date, mathematical models that simulate the static response are based on two depolarizing/repolarizing pairs of membrane ionic conductance (slow and fast kinetics). However, these models fail to reproduce the dynamic response of CSNTs to rapid changes in temperature and notoriously they lack a specific cold-activated conductance such as the TRPM8 channel. We developed a model that includes TRPM8 as a temperature-dependent conductance with a calcium-dependent desensitization. We show by computer simulations that it appropriately reproduces the dynamic response of CSNTs from mouse cornea, while preserving their static response behavior. In this model, the TRPM8 conductance is essential to display a dynamic response. In agreement with experimental results, TRPM8 is also needed for the ongoing activity in the absence of stimulus (i.e. neutral skin temperature). Free parameters of the model were adjusted by an evolutionary optimization algorithm, allowing us to find different solutions. We present a family of possible parameters that reproduce the behavior of CSNTs under different temperature protocols. The detection of temperature gradients is associated to a homeostatic mechanism supported by the calcium-dependent desensitization. PMID:26426259

Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes.

PubMed

Silk, Daniel; Kirk, Paul D W; Barnes, Chris P; Toni, Tina; Rose, Anna; Moon, Simon; Dallman, Margaret J; Stumpf, Michael P H

2011-10-04

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems.

On the intrinsic dynamics of bacteria in waterborne infections.

PubMed

Yang, Chayu; Wang, Jin

2018-02-01

The intrinsic dynamics of bacteria often play an important role in the transmission and spread of waterborne infectious diseases. In this paper, we construct mathematical models for waterborne infections and analyze two types of nontrivial bacterial dynamics: logistic growth, and growth with Allee effects. For the model with logistic growth, we find that regular threshold dynamics take place, and the basic reproduction number can be used to characterize disease extinction and persistence. In contrast, the model with Allee effects exhibits much more complex dynamics, including the existence of multiple endemic equilibria and the presence of backward bifurcation and forward hysteresis. Copyright © 2017 Elsevier Inc. All rights reserved.

Dynamic ambulance reallocation for the reduction of ambulance response times using system status management.

PubMed

Lam, Sean Shao Wei; Zhang, Ji; Zhang, Zhong Cheng; Oh, Hong Choon; Overton, Jerry; Ng, Yih Yng; Ong, Marcus Eng Hock

2015-02-01

Dynamically reassigning ambulance deployment locations throughout a day to balance ambulance availability and demands can be effective in reducing response times. The objectives of this study were to model dynamic ambulance allocation plans in Singapore based on the system status management (SSM) strategy and to evaluate the dynamic deployment plans using a discrete event simulation (DES) model. The geographical information system-based analysis and mathematical programming were used to develop the dynamic ambulance deployment plans for SSM based on ambulance calls data from January 1, 2011, to June 30, 2011. A DES model that incorporated these plans was used to compare the performance of the dynamic SSM strategy against static reallocation policies under various demands and travel time uncertainties. When the deployment plans based on the SSM strategy were followed strictly, the DES model showed that the geographical information system-based plans resulted in approximately 13-second reduction in the median response times compared to the static reallocation policy, whereas the mathematical programming-based plans resulted in approximately a 44-second reduction. The response times and coverage performances were still better than the static policy when reallocations happened for only 60% of all the recommended moves. Dynamically reassigning ambulance deployment locations based on the SSM strategy can result in superior response times and coverage performance compared to static reallocation policies even when the dynamic plans were not followed strictly. Copyright © 2014 Elsevier Inc. All rights reserved.

On dynamics of integrate-and-fire neural networks with conductance based synapses.

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IF models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

Towards predictive models of the human gut microbiome

PubMed Central

2014-01-01

The intestinal microbiota is an ecosystem susceptible to external perturbations such as dietary changes and antibiotic therapies. Mathematical models of microbial communities could be of great value in the rational design of microbiota-tailoring diets and therapies. Here, we discuss how advances in another field, engineering of microbial communities for wastewater treatment bioreactors, could inspire development of mechanistic mathematical models of the gut microbiota. We review the current state-of-the-art in bioreactor modeling and current efforts in modeling the intestinal microbiota. Mathematical modeling could benefit greatly from the deluge of data emerging from metagenomic studies, but data-driven approaches such as network inference that aim to predict microbiome dynamics without explicit mechanistic knowledge seem better suited to model these data. Finally, we discuss how the integration of microbiome shotgun sequencing and metabolic modeling approaches such as flux balance analysis may fulfill the promise of a mechanistic model of the intestinal microbiota. PMID:24727124

Stability analysis and application of a mathematical cholera model.

PubMed

Liao, Shu; Wang, Jin

2011-07-01

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

USAF/SCEEE Summer Faculty Research Program (1982). Management Report.

DTIC Science & Technology

1982-10-01

Patrick J. Sweeney, Ph.D., P.E. Mary Doddy, M.S. ABSTRACT This dynamic simulation computer model demonstrates the affects of C-forces upon the eyeball...Assistant Professor Specialty: Numerical Modeling and University of Lowell Computer Simulation of Mathematics Department Geophysical Problems Lowell...Problems And Promises 25 Modeling And Tracking Saccadic Dr. John D. Enderle Eye Movements 26 Dynamic Response Of Doubly Curved Dr. Fernando E. Fagundo

Building new computational models to support health behavior change and maintenance: new opportunities in behavioral research.

PubMed

Spruijt-Metz, Donna; Hekler, Eric; Saranummi, Niilo; Intille, Stephen; Korhonen, Ilkka; Nilsen, Wendy; Rivera, Daniel E; Spring, Bonnie; Michie, Susan; Asch, David A; Sanna, Alberto; Salcedo, Vicente Traver; Kukakfa, Rita; Pavel, Misha

2015-09-01

Adverse and suboptimal health behaviors and habits are responsible for approximately 40 % of preventable deaths, in addition to their unfavorable effects on quality of life and economics. Our current understanding of human behavior is largely based on static "snapshots" of human behavior, rather than ongoing, dynamic feedback loops of behavior in response to ever-changing biological, social, personal, and environmental states. This paper first discusses how new technologies (i.e., mobile sensors, smartphones, ubiquitous computing, and cloud-enabled processing/computing) and emerging systems modeling techniques enable the development of new, dynamic, and empirical models of human behavior that could facilitate just-in-time adaptive, scalable interventions. The paper then describes concrete steps to the creation of robust dynamic mathematical models of behavior including: (1) establishing "gold standard" measures, (2) the creation of a behavioral ontology for shared language and understanding tools that both enable dynamic theorizing across disciplines, (3) the development of data sharing resources, and (4) facilitating improved sharing of mathematical models and tools to support rapid aggregation of the models. We conclude with the discussion of what might be incorporated into a "knowledge commons," which could help to bring together these disparate activities into a unified system and structure for organizing knowledge about behavior.

Fostering Mathematical Creativity through Problem Posing and Modeling Using Dynamic Geometry: Viviani's Problem in the Classroom

ERIC Educational Resources Information Center

Contreras, José N.

2013-01-01

This paper discusses a classroom experience in which a group of prospective secondary mathematics teachers were asked to create, cooperatively (in class) and individually, problems related to Viviani's problem using a problem-posing framework. When appropriate, students used Sketchpad to explore the problem to better understand its attributes…

Mathematical Modeling: Immune System Dynamics in the Presence of Cancer and Immunodeficiency in vivo

DTIC Science & Technology

2016-05-11

Control 2 Acknowledgments This research was sponsored by the United States Naval Academy’s Trident Scholar Program and the Department of Mathematics... experimental science which relies on qualitative observations; however, in the past decade the need for quantitative analysis has become much more...of Midshipman Research _________________________________________ ___________________________ USNA-1531-2 REPORT

Study on the dynamic recrystallization model and mechanism of nuclear grade 316LN austenitic stainless steel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Shenglong; Zhang, Mingxian; Wu, Huanchun

In this study, the dynamic recrystallization behaviors of a nuclear grade 316LN austenitic stainless steel were researched through hot compression experiment performed on a Gleeble-1500 simulator at temperatures of 900–1250 °C and strain rates of 0.01–1 s{sup −1}. By multiple linear regressions of the flow stress-strain data, the dynamic recrystallization mathematical models of this steel as functions of strain rate, strain and temperature were developed. Then these models were verified in a real experiment. Furthermore, the dynamic recrystallization mechanism of the steel was determined. The results indicated that the subgrains in this steel are formed through dislocations polygonization and thenmore » grow up through subgrain boundaries migration towards high density dislocation areas and subgrain coalescence mechanism. Dynamic recrystallization nucleation performs in grain boundary bulging mechanism and subgrain growth mechanism. The nuclei grow up through high angle grain boundaries migration. - Highlights: •Establish the DRX mathematical models of nuclear grade 316LN stainless steel •Determine the DRX mechanism of this steel •Subgrains are formed through dislocations polygonization. •Subgrains grow up through subgrain boundaries migration and coalescence mechanism. •DRX nucleation performs in grain boundary bulging mechanism and subgrain growth mechanism.« less

Dynamic, stochastic models for congestion pricing and congestion securities.

DOT National Transportation Integrated Search

2010-12-01

This research considers congestion pricing under demand uncertainty. In particular, a robust optimization (RO) approach is applied to optimal congestion pricing problems under user equilibrium. A mathematical model is developed and an analysis perfor...

Do the Teacher and School Factors of the Dynamic Model Affect High- and Low-Achieving Student Groups to the Same Extent? A Cross-Country Study

ERIC Educational Resources Information Center

Vanlaar, Gudrun; Kyriakides, Leonidas; Panayiotou, Anastasia; Vandecandelaere, Machteld; McMahon, Léan; De Fraine, Bieke; Van Damme, Jan

2016-01-01

Background: The dynamic model of educational effectiveness (DMEE) is a comprehensive theoretical framework including factors that are important for school learning, based on consistent findings within educational effectiveness research. Purpose: This study investigates the impact of teacher and school factors of DMEE on mathematics and science…

Forest and Agricultural Sector Optimization Model Greenhouse Gas Version (FASOM-GHG)

EPA Science Inventory

FASOM-GHG is a dynamic, multi-period, intertemporal, price-endogenous, mathematical programming model depicting land transfers and other resource allocations between and within the agricultural and forest sectors in the US. The model solution portrays simultaneous market equilibr...

Estimating Setup of Driven Piles into Louisiana Clayey Soils

DOT National Transportation Integrated Search

2009-11-15

Two types of mathematical models for pile setup prediction, the Skov-Denver model and the newly developed rate-based model, have been established from all the dynamic and static testing data, including restrikes of the production piles, restrikes, st...

Estimating setup of driven piles into Louisiana clayey soils.

DOT National Transportation Integrated Search

2010-11-15

Two types of mathematical models for pile setup prediction, the Skov-Denver model and the newly developed rate-based model, have been established from all the dynamic and static testing data, including restrikes of the production piles, restrikes, st...

Assessing the importance of self-regulating mechanisms in diamondback moth population dynamics: application of discrete mathematical models.

PubMed

Nedorezov, Lev V; Löhr, Bernhard L; Sadykova, Dinara L

2008-10-07

The applicability of discrete mathematical models for the description of diamondback moth (DBM) (Plutella xylostella L.) population dynamics was investigated. The parameter values for several well-known discrete time models (Skellam, Moran-Ricker, Hassell, Maynard Smith-Slatkin, and discrete logistic models) were estimated for an experimental time series from a highland cabbage-growing area in eastern Kenya. For all sets of parameters, boundaries of confidence domains were determined. Maximum calculated birth rates varied between 1.086 and 1.359 when empirical values were used for parameter estimation. After fitting of the models to the empirical trajectory, all birth rate values resulted considerably higher (1.742-3.526). The carrying capacity was determined between 13.0 and 39.9DBM/plant, after fitting of the models these values declined to 6.48-9.3, all values well within the range encountered empirically. The application of the Durbin-Watson criteria for comparison of theoretical and experimental population trajectories produced negative correlations with all models. A test of residual value groupings for randomness showed that their distribution is non-stochastic. In consequence, we conclude that DBM dynamics cannot be explained as a result of intra-population self-regulative mechanisms only (=by any of the models tested) and that more comprehensive models are required for the explanation of DBM population dynamics.

Past and future perspectives on mathematical models of tick-borne pathogens.

PubMed

Norman, R A; Worton, A J; Gilbert, L

2016-06-01

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

Event- and Time-Driven Techniques Using Parallel CPU-GPU Co-processing for Spiking Neural Networks

PubMed Central

Naveros, Francisco; Garrido, Jesus A.; Carrillo, Richard R.; Ros, Eduardo; Luque, Niceto R.

2017-01-01

Modeling and simulating the neural structures which make up our central neural system is instrumental for deciphering the computational neural cues beneath. Higher levels of biological plausibility usually impose higher levels of complexity in mathematical modeling, from neural to behavioral levels. This paper focuses on overcoming the simulation problems (accuracy and performance) derived from using higher levels of mathematical complexity at a neural level. This study proposes different techniques for simulating neural models that hold incremental levels of mathematical complexity: leaky integrate-and-fire (LIF), adaptive exponential integrate-and-fire (AdEx), and Hodgkin-Huxley (HH) neural models (ranged from low to high neural complexity). The studied techniques are classified into two main families depending on how the neural-model dynamic evaluation is computed: the event-driven or the time-driven families. Whilst event-driven techniques pre-compile and store the neural dynamics within look-up tables, time-driven techniques compute the neural dynamics iteratively during the simulation time. We propose two modifications for the event-driven family: a look-up table recombination to better cope with the incremental neural complexity together with a better handling of the synchronous input activity. Regarding the time-driven family, we propose a modification in computing the neural dynamics: the bi-fixed-step integration method. This method automatically adjusts the simulation step size to better cope with the stiffness of the neural model dynamics running in CPU platforms. One version of this method is also implemented for hybrid CPU-GPU platforms. Finally, we analyze how the performance and accuracy of these modifications evolve with increasing levels of neural complexity. We also demonstrate how the proposed modifications which constitute the main contribution of this study systematically outperform the traditional event- and time-driven techniques under increasing levels of neural complexity. PMID:28223930

Dynamics of nonlinear feedback control.

PubMed

Snippe, H P; van Hateren, J H

2007-05-01

Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.

Simulation of Power Collection Dynamics for Simply Supported Power Rail

DOT National Transportation Integrated Search

1972-11-01

The mathematical model of a sprung mass moving along a simply supported beam is used to analyze the dynamics of a power-collection system. A computer simulation of one-dimensional motion is used to demonstrate the phenomenon of collector-power rail i...

Spatial operator algebra for flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Jain, A.; Rodriguez, G.

1993-01-01

This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.

The futility of utility: how market dynamics marginalize Adam Smith

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2000-10-01

Economic theorizing is based on the postulated, nonempiric notion of utility. Economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics I show the following. A utility function generally does not exist mathematically due to nonintegrable dynamics when production/investment are accounted for, resolving Mirowski's thesis. Price as a function of demand does not exist mathematically either. All equilibria are unstable. I then explain how deterministic chaos can be distinguished from random noise at short times. In the generalization to liquid markets and finance theory described by stochastic excess demand dynamics, I also show the following. Market price distributions cannot be rescaled to describe price movements as ‘equilibrium’ fluctuations about a systematic drift in price. Utility maximization does not describe equilibrium. Maximization of the Gibbs entropy of the observed price distribution of an asset would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real, liquid markets (stocks, bonds, foreign exchange). There are three inconsistent definitions of equilibrium used in economics and finance, only one of which is correct. Prices in unregulated free markets are unstable against both noise and rising or falling expectations: Adam Smith's stabilizing invisible hand does not exist, either in mathematical models of liquid market data, or in real market data.

Mathematical Modeling For Control Of A Flexible Manipulator

NASA Technical Reports Server (NTRS)

Hu, Anren

1996-01-01

Improved method of mathematical modeling of dynamics of flexible robotic manipulators developed for use in controlling motions of manipulators. Involves accounting for effect, upon modes of vibration of manipulator, of changes in configuration of manipulator and manipulated payload(s). Flexible manipulator has one or more long, slender articulated link(s), like those used in outer space, method also applicable to terrestrial industrial robotic manipulators with relatively short, stiff links, or to such terrestrial machines as construction cranes.

A flight-dynamic helicopter mathematical model with a single flap-lag-torsion main rotor

NASA Technical Reports Server (NTRS)

Takahashi, Marc D.

1990-01-01

A mathematical model of a helicopter system with a single main rotor that includes rigid, hinge-restrained rotor blades with flap, lag, and torsion degrees of freedom is described. The model allows several hinge sequences and two offsets in the hinges. Quasi-steady Greenberg theory is used to calculate the blade-section aerodynamic forces, and inflow effects are accounted for by using three-state nonlinear dynamic inflow model. The motion of the rigid fuselage is defined by six degrees of freedom, and an optional rotor rpm degree of freedom is available. Empennage surfaces and the tail rotor are modeled, and the effect of main-rotor downwash on these elements is included. Model trim linearization, and time-integration operations are described and can be applied to a subset of the model in the rotating or nonrotating coordinate frame. A preliminary validation of the model is made by comparing its results with those of other analytical and experimental studies. This publication presents the results of research compiled in November 1989.

A Mathematical Model of Marine Diesel Engine Speed Control System

NASA Astrophysics Data System (ADS)

Sinha, Rajendra Prasad; Balaji, Rajoo

2018-02-01

Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

PubMed

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

On the interplay between mathematics and biology: hallmarks toward a new systems biology.

PubMed

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach. Copyright © 2014 Elsevier B.V. All rights reserved.

Mathematical model for HIV dynamics in HIV-specific helper cells

NASA Astrophysics Data System (ADS)

Pinto, Carla M. A.; Carvalho, Ana

2014-03-01

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

PubMed Central

Wiratsudakul, Anuwat; Suparit, Parinya

2018-01-01

Background The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. Survey Methodology In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms “dynamics,” “mathematical model,” “modeling,” and “vector-borne” together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were “compartmental,” “spatial,” “metapopulation,” “network,” “individual-based,” “agent-based” AND “Zika.” All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. Results We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Discussion Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation. PMID:29593941

Mathematical model of microbicidal flow dynamics and optimization of rheological properties for intra-vaginal drug delivery: Role of tissue mechanics and fluid rheology.

PubMed

Anwar, Md Rajib; Camarda, Kyle V; Kieweg, Sarah L

2015-06-25

Topically applied microbicide gels can provide a self-administered and effective strategy to prevent sexually transmitted infections (STIs). We have investigated the interplay between vaginal tissue elasticity and the yield-stress of non-Newtonian fluids during microbicide deployment. We have developed a mathematical model of tissue deformation driven spreading of microbicidal gels based on thin film lubrication approximation and demonstrated the effect of tissue elasticity and fluid yield-stress on the spreading dynamics. Our results show that both elasticity of tissue and yield-stress rheology of gel are strong determinants of the coating behavior. An optimization framework has been demonstrated which leverages the flow dynamics of yield-stress fluid during deployment to maximize retention while reaching target coating length for a given tissue elasticity. Copyright © 2015 Elsevier Ltd. All rights reserved.

A Flight-Dynamic Helicopter Mathematical Model with a Single Flap-Lag- Torsion Main Rotor

DTIC Science & Technology

1990-02-01

allows several hinge sequences and two offsets in the hinges. Quasi-steady Greenberg theory is used to calculate the blade-section aerodynamic forces...steady Greenberg model is used (ref. 3), Unsteady inflow effects are included using the three-state nonlinear Pitt/Peters dynamic inflow model (ref. 4...sectional aerodynamic model is based on quasi-steady Greenberg theory, which is a Theodorsen theory modified to account for lead-lag motions (refs. 3,14). The

Individual-based model for radiation risk assessment

NASA Astrophysics Data System (ADS)

Smirnova, O.

A mathematical model is developed which enables one to predict the life span probability for mammals exposed to radiation. It relates statistical biometric functions with statistical and dynamic characteristics of an organism's critical system. To calculate the dynamics of the latter, the respective mathematical model is used too. This approach is applied to describe the effects of low level chronic irradiation on mice when the hematopoietic system (namely, thrombocytopoiesis) is the critical one. For identification of the joint model, experimental data on hematopoiesis in nonirradiated and irradiated mice, as well as on mortality dynamics of those in the absence of radiation are utilized. The life span probability and life span shortening predicted by the model agree with corresponding experimental data. Modeling results show the significance of ac- counting the variability of the individual radiosensitivity of critical system cells when estimating the radiation risk. These findings are corroborated by clinical data on persons involved in the elimination of the Chernobyl catastrophe after- effects. All this makes it feasible to use the model for radiation risk assessments for cosmonauts and astronauts on long-term missions such as a voyage to Mars or a lunar colony. In this case the model coefficients have to be determined by making use of the available data for humans. Scenarios for the dynamics of dose accumulation during space flights should also be taken into account.

Acute radiation risk models

NASA Astrophysics Data System (ADS)

Smirnova, Olga

Biologically motivated mathematical models, which describe the dynamics of the major hematopoietic lineages (the thrombocytopoietic, lymphocytopoietic, granulocytopoietic, and erythropoietic systems) in acutely/chronically irradiated humans are developed. These models are implemented as systems of nonlinear differential equations, which variables and constant parameters have clear biological meaning. It is shown that the developed models are capable of reproducing clinical data on the dynamics of these systems in humans exposed to acute radiation in the result of incidents and accidents, as well as in humans exposed to low-level chronic radiation. Moreover, the averaged value of the "lethal" dose rates of chronic irradiation evaluated within models of these four major hematopoietic lineages coincides with the real minimal dose rate of lethal chronic irradiation. The demonstrated ability of the models of the human thrombocytopoietic, lymphocytopoietic, granulocytopoietic, and erythropoietic systems to predict the dynamical response of these systems to acute/chronic irradiation in wide ranges of doses and dose rates implies that these mathematical models form an universal tool for the investigation and prediction of the dynamics of the major human hematopoietic lineages for a vast pattern of irradiation scenarios. In particular, these models could be applied for the radiation risk assessment for health of astronauts exposed to space radiation during long-term space missions, such as voyages to Mars or Lunar colonies, as well as for health of people exposed to acute/chronic irradiation due to environmental radiological events.

Explaining formation of Astronomical Jets using Dynamic Universe Model

NASA Astrophysics Data System (ADS)

Naga Parameswara Gupta, Satyavarapu

2016-07-01

Astronomical jets are observed from the centres of many Galaxies including our own Milkyway. The formation of such jet is explained using SITA simulations of Dynamic Universe Model. For this purpose the path traced by a test neutron is calculated and depicted using a set up of one densemass of the mass equivalent to mass of Galaxy center, 90 stars with similar masses of stars near Galaxy center, mass equivalents of 23 Globular Cluster groups, 16 Milkyway parts, Andromeda and Triangulum Galaxies at appropriate distances. Five different kinds of theoretical simulations gave positive results The path travelled by this test neutron was found to be an astronomical jet emerging from Galaxy center. This is another result from Dynamic Universe Model. It solves new problems like a. Variable Mass Rocket Trajectory Problem b. Explaining Very long baseline interferometry (VLBI) observations c. Astronomical jets observed from Milkyway Center d. Prediction of Blue shifted Galaxies e. Explaining Pioneer Anomaly f. Prediction of New Horizons satellite trajectory etc. Dynamic Universe Model never reduces to General relativity on any condition. It uses a different type of mathematics based on Newtonian physics. This mathematics used here is simple and straightforward. As there are no differential equations present in Dynamic Universe Model, the set of equations give single solution in x y z Cartesian coordinates for every point mass for every time step

The knowledge instinct, cognitive algorithms, modeling of language and cultural evolution

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2008-04-01

The talk discusses mechanisms of the mind and their engineering applications. The past attempts at designing "intelligent systems" encountered mathematical difficulties related to algorithmic complexity. The culprit turned out to be logic, which in one way or another was used not only in logic rule systems, but also in statistical, neural, and fuzzy systems. Algorithmic complexity is related to Godel's theory, a most fundamental mathematical result. These difficulties were overcome by replacing logic with a dynamic process "from vague to crisp," dynamic logic. It leads to algorithms overcoming combinatorial complexity, and resulting in orders of magnitude improvement in classical problems of detection, tracking, fusion, and prediction in noise. I present engineering applications to pattern recognition, detection, tracking, fusion, financial predictions, and Internet search engines. Mathematical and engineering efficiency of dynamic logic can also be understood as cognitive algorithm, which describes fundamental property of the mind, the knowledge instinct responsible for all our higher cognitive functions: concepts, perception, cognition, instincts, imaginations, intuitions, emotions, including emotions of the beautiful. I present our latest results in modeling evolution of languages and cultures, their interactions in these processes, and role of music in cultural evolution. Experimental data is presented that support the theory. Future directions are outlined.

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes.

PubMed

Handy, Gregory; Taheri, Marsa; White, John A; Borisyuk, Alla

2017-06-01

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

A discrete mathematical model of the dynamic evolution of a transportation network

NASA Astrophysics Data System (ADS)

Malinetskii, G. G.; Stepantsov, M. E.

2009-09-01

A dynamic model of the evolution of a transportation network is proposed. The main feature of this model is that the evolution of the transportation network is not a process of centralized transportation optimization. Rather, its dynamic behavior is a result of the system self-organization that occurs in the course of the satisfaction of needs in goods transportation and the evolution of the infrastructure of the network nodes. Nonetheless, the possibility of soft control of the network evolution direction is taken into account.

Modelling and control system of multi motor conveyor

NASA Astrophysics Data System (ADS)

Kovalchuk, M. S.; Baburin, S. V.

2018-03-01

The paper deals with the actual problem of developing the mathematical model of electromechanical system: conveyor – multimotor electric drive with a frequency converter, with the implementation in Simulink/MatLab, which allows one to perform studies of conveyor operation modes, taking into account the specifics of the mechanism with different electric drives control algorithms. The authors designed the mathematical models of the conveyor and its control system that provides increased uniformity of load distribution between drive motors and restriction of dynamic loads on the belt (over-regulation until 15%).

Mathematical modeling of the MHD stability dependence on the interpole distance in the multianode aluminium electrolyser

NASA Astrophysics Data System (ADS)

Kuzmin, R. N.; Savenkova, N. P.; Shobukhov, A. V.; Kalmykov, A. V.

2018-03-01

The paper deals with investigation of the MHD-stability dependence on the depth of the anode immersion in the process of aluminium electrolysis. The proposed 3D three-phase mathematical model is based on the Navier-Stokes and Maxwell equation systems. This model makes it possible to simulate the distributions of the main physical fields both in horizontal and vertical planes. The suggested approach also allows to study the dynamics of the border between aluminium and electrolyte and the shape of the back oxidation zone.

[A dynamic model of the extravehicular (correction of extravehicuar) activity space suit].

PubMed

Yang, Feng; Yuan, Xiu-gan

2002-12-01

Objective. To establish a dynamic model of the space suit base on the particular configuration of the space suit. Method. The mass of the space suit components, moment of inertia, mobility of the joints of space suit, as well as the suit-generated torques, were considered in this model. The expressions to calculate the moment of inertia were developed by simplifying the geometry of the space suit. A modified Preisach model was used to mathematically describe the hysteretic torque characteristics of joints in a pressurized space suit, and it was implemented numerically basing on the observed suit parameters. Result. A dynamic model considering mass, moment of inertia and suit-generated torques was established. Conclusion. This dynamic model provides some elements for the dynamic simulation of the astronaut extravehicular activity.

Dynamic design and control of a high-speed pneumatic jet actuator

NASA Astrophysics Data System (ADS)

Misyurin, S. Yu; Ivlev, V. I.; Kreinin, G. V.

2017-12-01

Mathematical model of an actuator, consisting of a pneumatic (gas) high-speed jet engine, transfer mechanism, and a control device used for switching the ball valve is worked out. The specific attention was paid to the transition (normalization) of the dynamic model into the dimensionless form. Its dynamic simulation criteria are determined, and dynamics study of an actuator was carried out. The simple control algorithm of relay action with a velocity feedback enabling the valve plug to be turned with a smooth nonstop and continuous approach to the final position is demonstrated

Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

PubMed

Clément, Frédérique

2016-07-01

Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of the (neuro-) hormonal signals at play within the HPG axis and detect complex, possibly hidden rhythms, in experimental time series. Copyright © 2016 Elsevier Inc. All rights reserved.

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.

PubMed

Millat, Thomas; Winzer, Klaus

2017-03-01

Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

System Identification Methods for Aircraft Flight Control Development and Validation

DOT National Transportation Integrated Search

1995-10-01

System-identification methods compose a mathematical model, or series of models, : from measurements of inputs and outputs of dynamic systems. This paper : discusses the use of frequency-domain system-identification methods for the : development and ...

Some aspects on kinetic modeling of evacuation dynamics. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Calvo, Juan; Nieto, Juanjo

2016-09-01

The management of human crowds in extreme situations is a complex subject which requires to take into account a variety of factors. To name a few, the understanding of human behaviour, the psychological and behavioural features of individuals, the quality of the venue and the stress level of the pedestrian need to be addressed in order to select the most appropriate action during an evacuation process on a complex venue. In this sense, the mathematical modeling of such complex phenomena can be regarded as a very useful tool to understand and predict these situations. As presented in [4], mathematical models can provide guidance to the personnel in charge of managing evacuation processes, by means of helping to design a set of protocols, among which the most appropriate during a given critical situation is then chosen.

Mathematical analysis of a lymphatic filariasis model with quarantine and treatment.

PubMed

Mwamtobe, Peter M; Simelane, Simphiwe M; Abelman, Shirley; Tchuenche, Jean M

2017-03-16

Lymphatic filariasis is a globally neglected tropical parasitic disease which affects individuals of all ages and leads to an altered lymphatic system and abnormal enlargement of body parts. A mathematical model of lymphatic filariaris with intervention strategies is developed and analyzed. Control of infections is analyzed within the model through medical treatment of infected-acute individuals and quarantine of infected-chronic individuals. We derive the effective reproduction number, [Formula: see text] and its interpretation/investigation suggests that treatment contributes to a reduction in lymphatic filariasis cases faster than quarantine. However, this reduction is greater when the two intervention approaches are applied concurrently. Numerical simulations are carried out to monitor the dynamics of the filariasis model sub-populations for various parameter values of the associated reproduction threshold. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance on the disease transmission.

Mathematical Model of Three Species Food Chain Interaction with Mixed Functional Response

NASA Astrophysics Data System (ADS)

Ws, Mada Sanjaya; Mohd, Ismail Bin; Mamat, Mustafa; Salleh, Zabidin

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

Designing a mathematical model for integrating dynamic cellular manufacturing into supply chain system

NASA Astrophysics Data System (ADS)

Aalaei, Amin; Davoudpour, Hamid

2012-11-01

This article presents designing a new mathematical model for integrating dynamic cellular manufacturing into supply chain system with an extensive coverage of important manufacturing features consideration of multiple plants location, multi-markets allocation, multi-period planning horizons with demand and part mix variation, machine capacity, and the main constraints are demand of markets satisfaction in each period, machine availability, machine time-capacity, worker assignment, available time of worker, production volume for each plant and the amounts allocated to each market. The aim of the proposed model is to minimize holding and outsourcing costs, inter-cell material handling cost, external transportation cost, procurement & maintenance and overhead cost of machines, setup cost, reconfiguration cost of machines installation and removal, hiring, firing and salary worker costs. Aimed to prove the potential benefits of such a design, presented an example is shown using a proposed model.

Conformal mapping in optical biosensor applications.

PubMed

Zumbrum, Matthew E; Edwards, David A

2015-09-01

Optical biosensors are devices used to investigate surface-volume reaction kinetics. Current mathematical models for reaction dynamics rely on the assumption of unidirectional flow within these devices. However, new devices, such as the Flexchip, include a geometry that introduces two-dimensional flow, complicating the depletion of the volume reactant. To account for this, a previous mathematical model is extended to include two-dimensional flow, and the Schwarz-Christoffel mapping is used to relate the physical device geometry to that for a device with unidirectional flow. Mappings for several Flexchip dimensions are considered, and the ligand depletion effect is investigated for one of these mappings. Estimated rate constants are produced for simulated data to quantify the inclusion of two-dimensional flow in the mathematical model.

Mathematical modelling of prostate cancer growth and its application to hormone therapy.

PubMed

Tanaka, Gouhei; Hirata, Yoshito; Goldenberg, S Larry; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-11-13

Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on- and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

A control theoretical approach to crowd management. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Borzí, Alfio; Caponigro, Marco

2016-09-01

The formulation of mathematical models for crowd dynamics is one current challenge in many fields of applied sciences. It involves the modelization of the complex behavior of a large number of individuals. In particular, the difficulty lays in describing emerging collective behaviors by means of a relatively small number of local interaction rules between individuals in a crowd. Clearly, the individual's free will involved in decision making processes and in the management of the social interactions cannot be described by a finite number of deterministic rules. On the other hand, in large crowds, this individual indeterminacy can be considered as a local fluctuation averaged to zero by the size of the crowd. While at the microscopic scale, using a system of coupled ODEs, the free will should be included in the mathematical description (e.g. with a stochastic term), the mesoscopic and macroscopic scales, modeled by PDEs, represent a powerful modelling tool that allows to neglect this feature and provide a reliable description. In this sense, the work by Bellomo, Clarke, Gibelli, Townsend, and Vreugdenhil [2] represents a mathematical-epistemological contribution towards the design of a reliable model of human behavior.

Modelling and analysis of gene regulatory network using feedback control theory

NASA Astrophysics Data System (ADS)

El-Samad, H.; Khammash, M.

2010-01-01

Molecular pathways are a part of a remarkable hierarchy of regulatory networks that operate at all levels of organisation. These regulatory networks are responsible for much of the biological complexity within the cell. The dynamic character of these pathways and the prevalence of feedback regulation strategies in their operation make them amenable to systematic mathematical analysis using the same tools that have been used with success in analysing and designing engineering control systems. In this article, we aim at establishing this strong connection through various examples where the behaviour exhibited by gene networks is explained in terms of their underlying control strategies. We complement our analysis by a survey of mathematical techniques commonly used to model gene regulatory networks and analyse their dynamic behaviour.

Structural Stability of Mathematical Models of National Economy

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar A.; Sultanov, Bahyt T.; Borovskiy, Yuriy V.; Adilov, Zheksenbek M.; Ashimov, Askar A.

2011-12-01

In the paper we test robustness of particular dynamic systems in a compact regions of a plane and a weak structural stability of one dynamic system of high order in a compact region of its phase space. The test was carried out based on the fundamental theory of dynamical systems on a plane and based on the conditions for weak structural stability of high order dynamic systems. A numerical algorithm for testing the weak structural stability of high order dynamic systems has been proposed. Based on this algorithm we assess the weak structural stability of one computable general equilibrium model.

COLD-SAT dynamic model

NASA Technical Reports Server (NTRS)

Adams, Neil S.; Bollenbacher, Gary

1992-01-01

This report discusses the development and underlying mathematics of a rigid-body computer model of a proposed cryogenic on-orbit liquid depot storage, acquisition, and transfer spacecraft (COLD-SAT). This model, referred to in this report as the COLD-SAT dynamic model, consists of both a trajectory model and an attitudinal model. All disturbance forces and torques expected to be significant for the actual COLD-SAT spacecraft are modeled to the required degree of accuracy. Control and experimental thrusters are modeled, as well as fluid slosh. The model also computes microgravity disturbance accelerations at any specified point in the spacecraft. The model was developed by using the Boeing EASY5 dynamic analysis package and will run on Apollo, Cray, and other computing platforms.

Transport theory and fluid dynamics

NASA Astrophysics Data System (ADS)

Greenberg, W.; Zweifel, P. F.

We report progress in various areas of applied mathematics relevant to transport theory under the subjects: abstract transport theory, explicit transport models and computation, and fluid dynamics. We present a brief review of progress during the past year and personnel supported, and we indicate the direction of our future research.

A cost-effectiveness model to personalize antiviral therapy in naive patients with genotype 1 chronic hepatitis C.

PubMed

Iannazzo, Sergio; Colombatto, Piero; Ricco, Gabriele; Oliveri, Filippo; Bonino, Ferruccio; Brunetto, Maurizia R

2015-03-01

Rapid virologic response is the best predictor of sustained virologic response with dual therapy in genotype-1 chronic hepatitis C, and its evaluation was proposed to tailor triple therapy in F0-F2 patients. Bio-mathematical modelling of viral dynamics during dual therapy has potentially higher accuracy than rapid virologic in the identification of patients who will eventually achieve sustained response. Study's objective was the cost-effectiveness analysis of a personalized therapy in naïve F0-F2 patients with chronic hepatitis C based on a bio-mathematical model (model-guided strategy) rather than on rapid virologic response (guideline-guided strategy). A deterministic bio-mathematical model of the infected cell dynamics was validated in a cohort of 135 patients treated with dual therapy. A decision-analytic economic model was then developed to compare model-guided and guideline-guided strategies in the Italian setting. The outcomes of the cost-effectiveness analysis with model-guided and guideline-guided strategy were 19.1-19.4 and 18.9-19.3 quality-adjusted-life-years. Total per-patient lifetime costs were €25,200-€26,000 with model-guided strategy and €28,800-€29,900 with guideline-guided strategy. When comparing model-guided with guideline-guided strategy the former resulted more effective and less costly. The adoption of the bio-mathematical predictive criterion has the potential to improve the cost-effectiveness of a personalized therapy for chronic hepatitis C, reserving triple therapy for those patients who really need it. Copyright © 2014 Editrice Gastroenterologica Italiana S.r.l. Published by Elsevier Ltd. All rights reserved.

Modelling fungal growth in heterogeneous soil: analyses of the effect of soil physical structure on fungal community dynamics

NASA Astrophysics Data System (ADS)

Falconer, R.; Radoslow, P.; Grinev, D.; Otten, W.

2009-04-01

Fungi play a pivital role in soil ecosystems contributing to plant productivity. The underlying soil physical and biological processes responsible for community dynamics are interrelated and, at present, poorly understood. If these complex processes can be understood then this knowledge can be managed with an aim to providing more sustainable agriculture. Our understanding of microbial dynamics in soil has long been hampered by a lack of a theoretical framework and difficulties in observation and quantification. We will demonstrate how the spatial and temporal dynamics of fungi in soil can be understood by linking mathematical modelling with novel techniques that visualise the complex structure of the soil. The combination of these techniques and mathematical models opens up new possibilities to understand how the physical structure of soil affects fungal colony dynamics and also how fungal dynamics affect soil structure. We will quantify, using X ray tomography, soil structure for a range of artificially prepared microcosms. We characterise the soil structures using soil metrics such as porosity, fractal dimension, and the connectivity of the pore volume. Furthermore we will use the individual based fungal colony growth model of Falconer et al. 2005, which is based on the physiological processes of fungi, to assess the effect of soil structure on microbial dynamics by qualifying biomass abundances and distributions. We demonstrate how soil structure can critically affect fungal species interactions with consequences for biological control and fungal biodiversity.

Cocaine addiction and personality: a mathematical model.

PubMed

Caselles, Antonio; Micó, Joan C; Amigó, Salvador

2010-05-01

The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Study on the tumor-induced angiogenesis using mathematical models.

PubMed

Suzuki, Takashi; Minerva, Dhisa; Nishiyama, Koichi; Koshikawa, Naohiko; Chaplain, Mark Andrew Joseph

2018-01-01

We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables. © 2017 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.

Stability and bifurcation in a model for the dynamics of stem-like cells in leukemia under treatment

NASA Astrophysics Data System (ADS)

Rǎdulescu, I. R.; Cândea, D.; Halanay, A.

2012-11-01

A mathematical model for the dynamics of leukemic cells during treatment is introduced. Delay differential equations are used to model cells' evolution and are based on the Mackey-Glass approach, incorporating Goldie-Coldman law. Since resistance is propagated by cells that have the capacity of self-renewal, a population of stem-like cells is studied. Equilibrium points are calculated and their stability properties are investigated.

SensA: web-based sensitivity analysis of SBML models.

PubMed

Floettmann, Max; Uhlendorf, Jannis; Scharp, Till; Klipp, Edda; Spiesser, Thomas W

2014-10-01

SensA is a web-based application for sensitivity analysis of mathematical models. The sensitivity analysis is based on metabolic control analysis, computing the local, global and time-dependent properties of model components. Interactive visualization facilitates interpretation of usually complex results. SensA can contribute to the analysis, adjustment and understanding of mathematical models for dynamic systems. SensA is available at http://gofid.biologie.hu-berlin.de/ and can be used with any modern browser. The source code can be found at https://bitbucket.org/floettma/sensa/ (MIT license) © The Author 2014. Published by Oxford University Press.

Mathematical modeling of a class of multibody flexible spacecraft structures

NASA Technical Reports Server (NTRS)

Kelkar, Atul, G.

1994-01-01

A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.

Hierarchical analytical and simulation modelling of human-machine systems with interference

NASA Astrophysics Data System (ADS)

Braginsky, M. Ya; Tarakanov, D. V.; Tsapko, S. G.; Tsapko, I. V.; Baglaeva, E. A.

2017-01-01

The article considers the principles of building the analytical and simulation model of the human operator and the industrial control system hardware and software. E-networks as the extension of Petri nets are used as the mathematical apparatus. This approach allows simulating complex parallel distributed processes in human-machine systems. The structural and hierarchical approach is used as the building method for the mathematical model of the human operator. The upper level of the human operator is represented by the logical dynamic model of decision making based on E-networks. The lower level reflects psychophysiological characteristics of the human-operator.

Computational Methods for Structural Mechanics and Dynamics, part 1

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

What should be considered if you decide to build your own mathematical model for predicting the development of bacterial resistance? Recommendations based on a systematic review of the literature

PubMed Central

Arepeva, Maria; Kolbin, Alexey; Kurylev, Alexey; Balykina, Julia; Sidorenko, Sergey

2015-01-01

Acquired bacterial resistance is one of the causes of mortality and morbidity from infectious diseases. Mathematical modeling allows us to predict the spread of resistance and to some extent to control its dynamics. The purpose of this review was to examine existing mathematical models in order to understand the pros and cons of currently used approaches and to build our own model. During the analysis, seven articles on mathematical approaches to studying resistance that satisfied the inclusion/exclusion criteria were selected. All models were classified according to the approach used to study resistance in the presence of an antibiotic and were analyzed in terms of our research. Some models require modifications due to the specifics of the research. The plan for further work on model building is as follows: modify some models, according to our research, check all obtained models against our data, and select the optimal model or models with the best quality of prediction. After that we would be able to build a model for the development of resistance using the obtained results. PMID:25972847

Modeling Zika plasma viral dynamics in non-human primates: insights into viral pathogenesis and antiviral strategies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Best, Katharine; Guedj, Jeremie; Madelain, Vincent

2016-10-24

The recent outbreak of Zika virus (ZIKV) has been associated with fetal abnormalities and neurological complications, prompting global concern. Here we present the first mathematical analysis of the within-host dynamics of plasma ZiKV burden in a non-human primate model, allowing for characterization of the growth and clearance of ZIKV within an individual macaque.

Dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gravitational waves

NASA Astrophysics Data System (ADS)

Rabinovich, B. I.

2006-01-01

The model problem of the dynamics of a planar plasma ring rotating in the dipole magnetic field of a central body is considered. A finite-dimensional mathematical model of the system is synthesized by the Boubnov-Galerkin method. The class of solutions corresponding to magneto-gravitational waves associated with deformations of the ring boundaries is investigated.

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review.

PubMed

Herzog, Sereina A; Blaizot, Stéphanie; Hens, Niel

2017-12-18

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals. We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design. We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6). Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

A mathematical model for computer image tracking.

PubMed

Legters, G R; Young, T Y

1982-06-01

A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.

Mathematical modeling in biological populations through branching processes. Application to salmonid populations.

PubMed

Molina, Manuel; Mota, Manuel; Ramos, Alfonso

2015-01-01

This work deals with mathematical modeling through branching processes. We consider sexually reproducing animal populations where, in each generation, the number of progenitor couples is determined in a non-predictable environment. By using a class of two-sex branching processes, we describe their demographic dynamics and provide several probabilistic and inferential contributions. They include results about the extinction of the population and the estimation of the offspring distribution and its main moments. We also present an application to salmonid populations.

Mathematic Model of Digital Control System with PID Regulator and Regular Step of Quantization with Information Transfer via the Channel of Plural Access

NASA Astrophysics Data System (ADS)

Abramov, G. V.; Emeljanov, A. E.; Ivashin, A. L.

Theoretical bases for modeling a digital control system with information transfer via the channel of plural access and a regular quantization cycle are submitted. The theory of dynamic systems with random changes of the structure including elements of the Markov random processes theory is used for a mathematical description of a network control system. The characteristics of similar control systems are received. Experimental research of the given control systems is carried out.

A new ODE tumor growth modeling based on tumor population dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oroji, Amin; Omar, Mohd bin; Yarahmadian, Shantia

2015-10-22

In this paper a new mathematical model for the population of tumor growth treated by radiation is proposed. The cells dynamics population in each state and the dynamics of whole tumor population are studied. Furthermore, a new definition of tumor lifespan is presented. Finally, the effects of two main parameters, treatment parameter (q), and repair mechanism parameter (r) on tumor lifespan are probed, and it is showed that the change in treatment parameter (q) highly affects the tumor lifespan.

Control of Supercavitation Flow and Stability of Supercavitating Motion of Bodies

DTIC Science & Technology

2001-02-01

sign opposite to a sign of angle Vf - accidental deflection of the model Sgn M = -Sgn i. 4.3. EQUATIONS OF THE SCM DYNAMICS The most effective method of...the motion stability in interactive regime "researcher - computer" [ 16]. The complete mathematical model of the SCM motion includes a set of equations ...of solid body dynamics, equations to calculate the unsteady cavity shape and relations to calculate the acting forces. A set of dynamic equations of

Swarm Counter-Asymmetric-Threat (CAT) 6-DOF Dynamics Simulation

DTIC Science & Technology

2005-07-01

NAWCWD TP 8593 Swarm Counter-Asymmetric-Threat ( CAT ) 6-DOF Dynamics Simulation by James Bobinchak Weapons and Energetics...mathematical models used in the swarm counter- asymmetric-threat ( CAT ) simulation and the results of extensive Monte Carlo simulations. The swarm CAT ...Asymmetric-Threat ( CAT ) 6-DOF Dynamics Simulation (U) 6. AUTHOR(S) James Bobinchak and Gary Hewer 7. PERFORMING ORGANIZATION NAME(S) AND

Ground Reaction Forces Generated During Rhythmical Squats as a Dynamic Loads of the Structure

NASA Astrophysics Data System (ADS)

Pantak, Marek

2017-10-01

Dynamic forces generated by moving persons can lead to excessive vibration of the long span, slender and lightweight structure such as floors, stairs, stadium stands and footbridges. These dynamic forces are generated during walking, running, jumping and rhythmical body swaying in vertical or horizontal direction etc. In the paper the mathematical models of the Ground Reaction Forces (GRFs) generated during squats have been presented. Elaborated models was compared to the GRFs measured during laboratory tests carried out by author in wide range of frequency using force platform. Moreover, the GRFs models were evaluated during dynamic numerical analyses and dynamic field tests of the exemplary structure (steel footbridge).

Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

PubMed Central

Noecker, Cecilia; Schaefer, Krista; Zaccheo, Kelly; Yang, Yiding; Day, Judy; Ganusov, Vitaly V.

2015-01-01

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available. PMID:25781919

Sensory neural pathways revisited to unravel the temporal dynamics of the Simon effect: A model-based cognitive neuroscience approach.

PubMed

Salzer, Yael; de Hollander, Gilles; Forstmann, Birte U

2017-06-01

The Simon task is one of the most prominent interference tasks and has been extensively studied in experimental psychology and cognitive neuroscience. Despite years of research, the underlying mechanism driving the phenomenon and its temporal dynamics are still disputed. Within the framework of the review, we adopt a model-based cognitive neuroscience approach. We first go over key findings in the literature of the Simon task, discuss competing qualitative cognitive theories and the difficulty of testing them empirically. We then introduce sequential sampling models, a particular class of mathematical cognitive process models. Finally, we argue that the brain architecture accountable for the processing of spatial ('where') and non-spatial ('what') information, could constrain these models. We conclude that there is a clear need to bridge neural and behavioral measures, and that mathematical cognitive models may facilitate the construction of this bridge and work towards revealing the underlying mechanisms of the Simon effect. Copyright © 2017 Elsevier Ltd. All rights reserved.

A dynamic subgrid scale model for Large Eddy Simulations based on the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric J.; Duraisamy, Karthik

2017-11-01

The development of reduced models for complex multiscale problems remains one of the principal challenges in computational physics. The optimal prediction framework of Chorin et al. [1], which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived reduced models of dynamical systems. Several promising models have emerged from the optimal prediction community and have found application in molecular dynamics and turbulent flows. In this work, a new M-Z-based closure model that addresses some of the deficiencies of existing methods is developed. The model is constructed by exploiting similarities between two levels of coarse-graining via the Germano identity of fluid mechanics and by assuming that memory effects have a finite temporal support. The appeal of the proposed model, which will be referred to as the 'dynamic-MZ-τ' model, is that it is parameter-free and has a structural form imposed by the mathematics of the coarse-graining process (rather than the phenomenological assumptions made by the modeler, such as in classical subgrid scale models). To promote the applicability of M-Z models in general, two procedures are presented to compute the resulting model form, helping to bypass the tedious error-prone algebra that has proven to be a hindrance to the construction of M-Z-based models for complex dynamical systems. While the new formulation is applicable to the solution of general partial differential equations, demonstrations are presented in the context of Large Eddy Simulation closures for the Burgers equation, decaying homogeneous turbulence, and turbulent channel flow. The performance of the model and validity of the underlying assumptions are investigated in detail.

Proceedings of the 3rd Annual SCOLE Workshop

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr. (Compiler)

1987-01-01

Topics addressed include: modeling and controlling the Spacecraft Control Laboratory Experiment (SCOLE) configurations; slewing maneuvers; mathematical models; vibration damping; gravitational effects; structural dynamics; finite element method; distributed parameter system; on-line pulse control; stability augmentation; and stochastic processes.

Rotor-to-stator Partial Rubbing and Its Effects on Rotor Dynamic Response

NASA Technical Reports Server (NTRS)

Muszynska, Agnes; Franklin, Wesley D.; Hayashida, Robert D.

1991-01-01

Results from experimental and analytical studies on rotor to stationary element partial rubbings at several locations and their effects on rotor dynamic responses are presented. The mathematical model of a rubbing rotor is given. The computer program provides numerical results which agree with experimentally obtained rotor responses.

The Rangeland Hydrology and Erosion Model: A dynamic approach for predicting soil loss on rangelands

USDA-ARS?s Scientific Manuscript database

In this study we present the improved Rangeland Hydrology and Erosion Model (RHEM V2.3), a process-based erosion prediction tool specific for rangeland application. The article provides the mathematical formulation of the model and parameter estimation equations. Model performance is assessed agains...

Spacecraft Dynamics Should be Considered in Kalman Filter Attitude Estimation

NASA Technical Reports Server (NTRS)

Yang, Yaguang; Zhou, Zhiqiang

2016-01-01

Kalman filter based spacecraft attitude estimation has been used in some high-profile missions and has been widely discussed in literature. While some models in spacecraft attitude estimation include spacecraft dynamics, most do not. To our best knowledge, there is no comparison on which model is a better choice. In this paper, we discuss the reasons why spacecraft dynamics should be considered in the Kalman filter based spacecraft attitude estimation problem. We also propose a reduced quaternion spacecraft dynamics model which admits additive noise. Geometry of the reduced quaternion model and the additive noise are discussed. This treatment is more elegant in mathematics and easier in computation. We use some simulation example to verify our claims.

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib

PubMed Central

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J.; Wolf, Stephanie; Mueller, Nikola S.; D'Alessandro, Lorenza A.; Mueller-Bohl, Stephanie; Boehm, Martin E.; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D.; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J.; Ehlting, Christian; Bode, Johannes G.; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines. PMID:29062282

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib.

PubMed

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J; Wolf, Stephanie; Mueller, Nikola S; D'Alessandro, Lorenza A; Mueller-Bohl, Stephanie; Boehm, Martin E; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J; Ehlting, Christian; Bode, Johannes G; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines.

Informations in Models of Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Rivoire, Olivier

2016-03-01

Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of evolutionary dynamics and show how explicit results are obtained for a solvable subclass of these models. In several limits, the results coincide with those obtained in studies of information processing for communication, gambling or thermodynamics. In the most general case, however, information processing by biological populations shows unique features that motivate the analysis of specific models.

Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

NASA Astrophysics Data System (ADS)

Huang, Qingdao; Qian, Hong

2009-09-01

We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells.

Engineering model of the electric drives of separation device for simulation of automatic control systems of reactive power compensation by means of serially connected capacitors

NASA Astrophysics Data System (ADS)

Juromskiy, V. M.

2016-09-01

It is developed a mathematical model for an electric drive of high-speed separation device in terms of the modeling dynamic systems Simulink, MATLAB. The model is focused on the study of the automatic control systems of the power factor (Cosφ) of an actuator by compensating the reactive component of the total power by switching a capacitor bank in series with the actuator. The model is based on the methodology of the structural modeling of dynamic processes.

Between timelessness and historiality: on the dynamics of the epistemic objects of mathematics.

PubMed

Epple, Moritz

2011-09-01

In order to discuss the temporal structure of mathematical research, this essay offers four related definitions of a mathematical object from different times and places. It is argued that in order to appreciate the differences between these definitions, the historian needs to understand that none of them made sense in mathematical practice without a technical framework, referred to but not explained in the definitions themselves (an "epistemic configuration of research"); that the dynamics of the epistemic objects of mathematical research are secondary to the dynamics of these epistemic configurations as a whole; and that the dynamics of epistemic configurations of mathematical research do not follow law-like processes. Very different types of change may happen, and some of them link the dynamics of epistemic configurations with events and developments far beyond the bounds of the research field in question. These insights have historiographical consequences that require us to rethink the kind of temporality ascribed to mathematics.

Dynamic Fuzzy Model Development for a Drum-type Boiler-turbine Plant Through GK Clustering

NASA Astrophysics Data System (ADS)

Habbi, Ahcène; Zelmat, Mimoun

2008-10-01

This paper discusses a TS fuzzy model identification method for an industrial drum-type boiler plant using the GK fuzzy clustering approach. The fuzzy model is constructed from a set of input-output data that covers a wide operating range of the physical plant. The reference data is generated using a complex first-principle-based mathematical model that describes the key dynamical properties of the boiler-turbine dynamics. The proposed fuzzy model is derived by means of fuzzy clustering method with particular attention on structure flexibility and model interpretability issues. This may provide a basement of a new way to design model based control and diagnosis mechanisms for the complex nonlinear plant.

A lateral dynamics of a wheelchair: identification and analysis of tire parameters.

PubMed

Silva, L C A; Corrêa, F C; Eckert, J J; Santiciolli, F M; Dedini, F G

2017-02-01

In vehicle dynamics studies, the tire behaviour plays an important role in planar motion of the vehicle. Therefore, a correct representation of tire is a necessity. This paper describes a mathematical model for wheelchair tire based on the Magic Formula model. This model is widely used to represent forces and moments between the tire and the ground; however some experimental parameters must be determined. The purpose of this work is to identify the tire parameters for the wheelchair tire model, implementing them in a dynamic model of the wheelchair. For this, we developed an experimental test rig to measure the tires parameters for the lateral dynamics of a wheelchair. This dynamic model was made using a multi-body software and the wheelchair behaviour was analysed and discussed according to the tire parameters. The result of this work is one step further towards the understanding of wheelchair dynamics.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study.

PubMed

Mercader, Jessica; Miranda, Ana; Presentación, M Jesús; Siegenthaler, Rebeca; Rosel, Jesús F

2017-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

PubMed Central

Mercader, Jessica; Miranda, Ana; Presentación, M. Jesús; Siegenthaler, Rebeca; Rosel, Jesús F.

2018-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5–6 and 7–8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed. PMID:29379462

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

The effects of psammophilous plants on sand dune dynamics

NASA Astrophysics Data System (ADS)

Bel, Golan; Ashkenazy, Yosef

2014-07-01

Mathematical models of sand dune dynamics have considered different types of sand dune cover. However, despite the important role of psammophilous plants (plants that flourish in moving-sand environments) in dune dynamics, the incorporation of their effects into mathematical models of sand dunes remains a challenging task. Here we propose a nonlinear physical model for the role of psammophilous plants in the stabilization and destabilization of sand dunes. There are two main mechanisms by which the wind affects these plants: (i) sand drift results in the burial and exposure of plants, a process that is known to result in an enhanced growth rate, and (ii) strong winds remove shoots and rhizomes and seed them in nearby locations, enhancing their growth rate. Our model describes the temporal evolution of the fractions of surface cover of regular vegetation, biogenic soil crust, and psammophilous plants. The latter reach their optimal growth under either (i) specific sand drift or (ii) specific wind power. The model exhibits complex bifurcation diagrams and dynamics, which explain observed phenomena, and it predicts new dune stabilization scenarios. Depending on the climatological conditions, it is possible to obtain one, two, or, predicted here for the first time, three stable dune states. Our model shows that the development of the different cover types depends on the precipitation rate and the wind power and that the psammophilous plants are not always the first to grow and stabilize the dunes.

Slow [Na+]i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model.

PubMed

Krogh-Madsen, Trine; Christini, David J

2017-09-01

Accumulation of intracellular Na + is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na + concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na + concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na + ] i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na + ] i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na + ] i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na + ] i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na + ] i may play complex roles in cellular and tissue-level cardiac dynamics.

Slow [Na+]i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model

NASA Astrophysics Data System (ADS)

Krogh-Madsen, Trine; Christini, David J.

2017-09-01

Accumulation of intracellular Na+ is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na+ concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na+ concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na+]i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na+]i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na+]i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na+]i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na+]i may play complex roles in cellular and tissue-level cardiac dynamics.

Modelling the evolution of drug resistance in the presence of antiviral drugs

PubMed Central

Wu, Jianhong; Yan, Ping; Archibald, Chris

2007-01-01

Background The emergence of drug resistance in treated populations and the transmission of drug resistant strains to newly infected individuals are important public health concerns in the prevention and control of infectious diseases such as HIV and influenza. Mathematical modelling may help guide the design of treatment programs and also may help us better understand the potential benefits and limitations of prevention strategies. Methods To explore further the potential synergies between modelling of drug resistance in HIV and in pandemic influenza, the Public Health Agency of Canada and the Mathematics for Information Technology and Complex Systems brought together selected scientists and public health experts for a workshop in Ottawa in January 2007, to discuss the emergence and transmission of HIV antiviral drug resistance, to report on progress in the use of mathematical models to study the emergence and spread of drug resistant influenza viral strains, and to recommend future research priorities. Results General lectures and round-table discussions were organized around the issues on HIV drug resistance at the population level, HIV drug resistance in Western Canada, HIV drug resistance at the host level (with focus on optimal treatment strategies), and drug resistance for pandemic influenza planning. Conclusion Some of the issues related to drug resistance in HIV and pandemic influenza can possibly be addressed using existing mathematical models, with a special focus on linking the existing models to the data obtained through the Canadian HIV Strain and DR Surveillance Program. Preliminary statistical analysis of these data carried out at PHAC, together with the general model framework developed by Dr. Blower and her collaborators, should provide further insights into the mechanisms behind the observed trends and thus could help with the prediction and analysis of future trends in the aforementioned items. Remarkable similarity between dynamic, compartmental models for the evolution of wild and drug resistance strains of both HIV and pandemic influenza may provide sufficient common ground to create synergies between modellers working in these two areas. One of the key contributions of mathematical modeling to the control of infectious diseases is the quantification and design of optimal strategies, combining techniques of operations research with dynamic modeling would enhance the contribution of mathematical modeling to the prevention and control of infectious diseases. PMID:17953775

Modelling the evolution of drug resistance in the presence of antiviral drugs.

PubMed

Wu, Jianhong; Yan, Ping; Archibald, Chris

2007-10-23

The emergence of drug resistance in treated populations and the transmission of drug resistant strains to newly infected individuals are important public health concerns in the prevention and control of infectious diseases such as HIV and influenza. Mathematical modelling may help guide the design of treatment programs and also may help us better understand the potential benefits and limitations of prevention strategies. To explore further the potential synergies between modelling of drug resistance in HIV and in pandemic influenza, the Public Health Agency of Canada and the Mathematics for Information Technology and Complex Systems brought together selected scientists and public health experts for a workshop in Ottawa in January 2007, to discuss the emergence and transmission of HIV antiviral drug resistance, to report on progress in the use of mathematical models to study the emergence and spread of drug resistant influenza viral strains, and to recommend future research priorities. General lectures and round-table discussions were organized around the issues on HIV drug resistance at the population level, HIV drug resistance in Western Canada, HIV drug resistance at the host level (with focus on optimal treatment strategies), and drug resistance for pandemic influenza planning. Some of the issues related to drug resistance in HIV and pandemic influenza can possibly be addressed using existing mathematical models, with a special focus on linking the existing models to the data obtained through the Canadian HIV Strain and DR Surveillance Program. Preliminary statistical analysis of these data carried out at PHAC, together with the general model framework developed by Dr. Blower and her collaborators, should provide further insights into the mechanisms behind the observed trends and thus could help with the prediction and analysis of future trends in the aforementioned items. Remarkable similarity between dynamic, compartmental models for the evolution of wild and drug resistance strains of both HIV and pandemic influenza may provide sufficient common ground to create synergies between modellers working in these two areas. One of the key contributions of mathematical modeling to the control of infectious diseases is the quantification and design of optimal strategies, combining techniques of operations research with dynamic modeling would enhance the contribution of mathematical modeling to the prevention and control of infectious diseases.

Mathematical modeling the radiation effects on humoral immunity

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

A mathematical model of humoral immune response in nonirradiated and irradiated mammals is developed. It is based on conventional theories and experimental facts in this field. The model is a system of nonlinear differential equations which describe the dynamics of concentrations of antibody and antigen molecules, immunocompetent B lymphocytes, and the rest blood lymphocytes, as well as the bone-marrow lymphocyte precursors. The interaction of antigen molecules with antibodies and with antibody-like receptors on immunocompetent cells is also incorporated. The model quantitatively reproduces the dynamics of the humoral immune response to the T-independent antigen (capsular antigen of plague microbe) in nonirradiated mammals (CBA mice). It describes the peculiarities of the humoral immune response in CBA mice exposed to acute radiation before or after introducing antigen. The model predicts an adaptation of humoral immune system to low dose rate chronic irradiation in the result of which the intensity of immune response relaxes to a new, lower than normal, stable level. The mechanisms of this phenomenon are revealed. The results obtained show that the developed model, after the appropriate identification, can be used to predict the effects of acute and low-level long-term irradiation on the system of humoral immunity in humans. Employment of the mathematical model identified in the proper way should be important in estimating the radiation risk for cosmonauts and astronauts on long space missions such as a voyage to Mars or a lunar colony.

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

2014-07-01

Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

An adaptive drug delivery design using neural networks for effective treatment of infectious diseases: a simulation study.

PubMed

Padhi, Radhakant; Bhardhwaj, Jayender R

2009-06-01

An adaptive drug delivery design is presented in this paper using neural networks for effective treatment of infectious diseases. The generic mathematical model used describes the coupled evolution of concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of a damaged organ due to the disease under the influence of external drugs. From a system theoretic point of view, the external drugs can be interpreted as control inputs, which can be designed based on control theoretic concepts. In this study, assuming a set of nominal parameters in the mathematical model, first a nonlinear controller (drug administration) is designed based on the principle of dynamic inversion. This nominal drug administration plan was found to be effective in curing "nominal model patients" (patients whose immunological dynamics conform to the mathematical model used for the control design exactly. However, it was found to be ineffective in curing "realistic model patients" (patients whose immunological dynamics may have off-nominal parameter values and possibly unwanted inputs) in general. Hence, to make the drug delivery dosage design more effective for realistic model patients, a model-following adaptive control design is carried out next by taking the help of neural networks, that are trained online. Simulation studies indicate that the adaptive controller proposed in this paper holds promise in killing the invading pathogens and healing the damaged organ even in the presence of parameter uncertainties and continued pathogen attack. Note that the computational requirements for computing the control are very minimal and all associated computations (including the training of neural networks) can be carried out online. However it assumes that the required diagnosis process can be carried out at a sufficient faster rate so that all the states are available for control computation.

Pest control through viral disease: mathematical modeling and analysis.

PubMed

Bhattacharyya, S; Bhattacharya, D K

2006-01-07

This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'kappa' viruses per host, kappain(1,infinity), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value kappa(0) beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing kappa values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented.

Method and system for dynamic probabilistic risk assessment

NASA Technical Reports Server (NTRS)

Dugan, Joanne Bechta (Inventor); Xu, Hong (Inventor)

2013-01-01

The DEFT methodology, system and computer readable medium extends the applicability of the PRA (Probabilistic Risk Assessment) methodology to computer-based systems, by allowing DFT (Dynamic Fault Tree) nodes as pivot nodes in the Event Tree (ET) model. DEFT includes a mathematical model and solution algorithm, supports all common PRA analysis functions and cutsets. Additional capabilities enabled by the DFT include modularization, phased mission analysis, sequence dependencies, and imperfect coverage.

Dynamic Decision Making in Complex Task Environments: Principles and Neural Mechanisms

DTIC Science & Technology

2013-03-01

Dynamical models of cognition . Mathematical models of mental processes. Human performance optimization. U U U U Dr. Jay Myung 703-696-8487 Reset 1...we have continued to develop a neurodynamic theory of decision making, using a combination of computational and experimental approaches, to address...a long history in the field of human cognitive psychology. The theoretical foundations of this research can be traced back to signal detection

Quality by design: scale-up of freeze-drying cycles in pharmaceutical industry.

PubMed

Pisano, Roberto; Fissore, Davide; Barresi, Antonello A; Rastelli, Massimo

2013-09-01

This paper shows the application of mathematical modeling to scale-up a cycle developed with lab-scale equipment on two different production units. The above method is based on a simplified model of the process parameterized with experimentally determined heat and mass transfer coefficients. In this study, the overall heat transfer coefficient between product and shelf was determined by using the gravimetric procedure, while the dried product resistance to vapor flow was determined through the pressure rise test technique. Once model parameters were determined, the freeze-drying cycle of a parenteral product was developed via dynamic design space for a lab-scale unit. Then, mathematical modeling was used to scale-up the above cycle in the production equipment. In this way, appropriate values were determined for processing conditions, which allow the replication, in the industrial unit, of the product dynamics observed in the small scale freeze-dryer. This study also showed how inter-vial variability, as well as model parameter uncertainty, can be taken into account during scale-up calculations.

A Long-Term Mathematical Model for Mining Industries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Giraud, Pierre-Noel; Lasry, Jean-Michel

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In somemore » cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.« less

Mathematical model for rhythmic protoplasmic movement in the true slime mold.

PubMed

Kobayashi, Ryo; Tero, Atsushi; Nakagaki, Toshiyuki

2006-08-01

The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays "smart" behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporating both these aspects, we constructed a mathematical model for the dynamics of the organism as a first step towards understanding the relation between protoplasmic movement and its unusual abilities. We tested the validity of the model by comparing it with physiological observation. Our model reproduces fundamental characteristics of the spatio-temporal pattern of the rhythmic movement: (1) the antiphase oscillation between frontal tip and rear when the front is freely extending; (2) the asynchronous oscillation pattern when the front is not freely extending; and (3) the formation of protoplasmic mounds over a longer time scale. Both our model and physiological observation suggest that cell stiffness plays a primary role in plasmodial behaviors, in contrast to the conventional theory of coupled oscillator systems.

Examples of Mathematical Modeling

PubMed Central

Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan

2008-01-01

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.

NASA Astrophysics Data System (ADS)

Velichkin, Vladimir A.; Zavyalov, Vladimir A.

2018-03-01

This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.

Application of Decision Making and Team Training Research to Operational Training. A Translative Technique.

DTIC Science & Technology

DECISION MAKING , * GROUP DYNAMICS, NAVAL TRAINING, TRANSFER OF TRAINING, SCIENTIFIC RESEARCH, CLASSIFICATION, PROBLEM SOLVING, MATHEMATICAL MODELS, SUBMARINES, SIMULATORS, PERFORMANCE(HUMAN), UNDERSEA WARFARE.

An algebra-based method for inferring gene regulatory networks

PubMed Central

2014-01-01

Background The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used. Results This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network. Conclusions Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html. PMID:24669835

Research on modeling and motion simulation of a spherical space robot with telescopic manipulator based on virtual prototype technology

NASA Astrophysics Data System (ADS)

Shi, Chengkun; Sun, Hanxu; Jia, Qingxuan; Zhao, Kailiang

2009-05-01

For realizing omni-directional movement and operating task of spherical space robot system, this paper describes an innovated prototype and analyzes dynamic characteristics of a spherical rolling robot with telescopic manipulator. Based on the Newton-Euler equations, the kinematics and dynamic equations of the spherical robot's motion are instructed detailedly. Then the motion simulations of the robot in different environments are developed with ADAMS. The simulation results validate the mathematics model of the system. And the dynamic model establishes theoretical basis for the latter job.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Dynamic electrical response of solar cells

NASA Technical Reports Server (NTRS)

Catani, J. P.

1981-01-01

The dynamic response of a solar generator is of primary importance as much for the design and development of electrical power conditioning hardware as for the analysis of electromagnetic compatibility. A mathematical model of photo-batteries was developed on the basis of impedance measurements performed under differing conditions of temperature, light intensity, before and after irradiation. This model was compared with that derived from PN junction theory and to static measurements. These dynamic measurements enabled the refinement of an integration method capable of determining, under normal laboratory conditions, the dynamic response of a generator to operational lighting conditions.

A discrete mathematical model for the aggregation of β-Amyloid.

PubMed

Dayeh, Maher A; Livadiotis, George; Elaydi, Saber

2018-01-01

Dementia associated with the Alzheimer's disease is thought to be correlated with the conversion of the β - Amyloid (Aβ) peptides from soluble monomers to aggregated oligomers and insoluble fibrils. We present a discrete-time mathematical model for the aggregation of Aβ monomers into oligomers using concepts from chemical kinetics and population dynamics. Conditions for the stability and instability of the equilibria of the model are established. A formula for the number of monomers that is required for producing oligomers is also given. This may provide compound designers a mechanism to inhibit the Aβ aggregation.

Traffic Flow Density Distribution Based on FEM

NASA Astrophysics Data System (ADS)

Ma, Jing; Cui, Jianming

In analysis of normal traffic flow, it usually uses the static or dynamic model to numerical analyze based on fluid mechanics. However, in such handling process, the problem of massive modeling and data handling exist, and the accuracy is not high. Finite Element Method (FEM) is a production which is developed from the combination of a modern mathematics, mathematics and computer technology, and it has been widely applied in various domain such as engineering. Based on existing theory of traffic flow, ITS and the development of FEM, a simulation theory of the FEM that solves the problems existing in traffic flow is put forward. Based on this theory, using the existing Finite Element Analysis (FEA) software, the traffic flow is simulated analyzed with fluid mechanics and the dynamics. Massive data processing problem of manually modeling and numerical analysis is solved, and the authenticity of simulation is enhanced.

Robust Fuzzy Logic Stabilization with Disturbance Elimination

PubMed Central

Danapalasingam, Kumeresan A.

2014-01-01

A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design. PMID:25177713

Whole-body mathematical model for simulating intracranial pressure dynamics

NASA Technical Reports Server (NTRS)

Lakin, William D. (Inventor); Penar, Paul L. (Inventor); Stevens, Scott A. (Inventor); Tranmer, Bruce I. (Inventor)

2007-01-01

A whole-body mathematical model (10) for simulating intracranial pressure dynamics. In one embodiment, model (10) includes 17 interacting compartments, of which nine lie entirely outside of intracranial vault (14). Compartments (F) and (T) are defined to distinguish ventricular from extraventricular CSF. The vasculature of the intracranial system within cranial vault (14) is also subdivided into five compartments (A, C, P, V, and S, respectively) representing the intracranial arteries, capillaries, choroid plexus, veins, and venous sinus. The body's extracranial systemic vasculature is divided into six compartments (I, J, O, Z, D, and X, respectively) representing the arteries, capillaries, and veins of the central body and the lower body. Compartments (G) and (B) include tissue and the associated interstitial fluid in the intracranial and lower regions. Compartment (Y) is a composite involving the tissues, organs, and pulmonary circulation of the central body and compartment (M) represents the external environment.

Development of a mathematical model for the growth associated Polyhydroxybutyrate fermentation by Azohydromonas australica and its use for the design of fed-batch cultivation strategies.

PubMed

Gahlawat, Geeta; Srivastava, Ashok K

2013-06-01

In the present investigation, batch cultivation of Azohydromonas australica DSM 1124 was carried out in a bioreactor for growth associated PHB production. The observed batch PHB production kinetics data was then used for the development of a mathematical model which adequately described the substrate limitation and inhibition during the cultivation. The statistical validity test demonstrated that the proposed mathematical model predictions were significant at 99% confidence level. The model was thereafter extrapolated to fed-batch to identify various nutrients feeding regimes during the bioreactor cultivation to improve the PHB accumulation. The distinct capability of the mathematical model to predict highly dynamic fed-batch cultivation strategies was demonstrated by experimental implementation of two fed-batch cultivation strategies. A significantly high PHB concentration of 22.65 g/L & an overall PHB content of 76% was achieved during constant feed rate fed-batch cultivation which is the highest PHB content reported so far using A. australica. Copyright © 2013 Elsevier Ltd. All rights reserved.

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

NASA Astrophysics Data System (ADS)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Modelling of thermal field and point defect dynamics during silicon single crystal growth using CZ technique

NASA Astrophysics Data System (ADS)

Sabanskis, A.; Virbulis, J.

2018-05-01

Mathematical modelling is employed to numerically analyse the dynamics of the Czochralski (CZ) silicon single crystal growth. The model is axisymmetric, its thermal part describes heat transfer by conduction and thermal radiation, and allows to predict the time-dependent shape of the crystal-melt interface. Besides the thermal field, the point defect dynamics is modelled using the finite element method. The considered process consists of cone growth and cylindrical phases, including a short period of a reduced crystal pull rate, and a power jump to avoid large diameter changes. The influence of the thermal stresses on the point defects is also investigated.

Exponential Models of Legislative Turnover. [and] The Dynamics of Political Mobilization, I: A Model of the Mobilization Process, II: Deductive Consequences and Empirical Application of the Model. Applications of Calculus to American Politics. [and] Public Support for Presidents. Applications of Algebra to American Politics. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 296-300.

ERIC Educational Resources Information Center

Casstevens, Thomas W.; And Others

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

Kinetic modeling of plant metabolism and its predictive power: peppermint essential oil biosynthesis as an example.

PubMed

Lange, Bernd Markus; Rios-Estepa, Rigoberto

2014-01-01

The integration of mathematical modeling with analytical experimentation in an iterative fashion is a powerful approach to advance our understanding of the architecture and regulation of metabolic networks. Ultimately, such knowledge is highly valuable to support efforts aimed at modulating flux through target pathways by molecular breeding and/or metabolic engineering. In this article we describe a kinetic mathematical model of peppermint essential oil biosynthesis, a pathway that has been studied extensively for more than two decades. Modeling assumptions and approximations are described in detail. We provide step-by-step instructions on how to run simulations of dynamic changes in pathway metabolites concentrations.

Neurodynamics With Spatial Self-Organization

NASA Technical Reports Server (NTRS)

Zak, Michail A.

1993-01-01

Report presents theoretical study of dynamics of neural network organizing own response in both phase space and in position space. Postulates several mathematical models of dynamics including spatial derivatives representing local interconnections among neurons. Shows how neural responses propagate via these interconnections and how spatial pattern of neural responses formed in homogeneous biological neural network.

Modeling Spring Mass System with System Dynamics Approach in Middle School Education

ERIC Educational Resources Information Center

Nuhoglu, Hasret

2008-01-01

System Dynamics is a well formulated methodology for analyzing the components of a system including causeeffect relationships and their underlying mathematics and logic, time delays, and feedback loops. It began in the business and manufacturing world, but is now affecting education and many other disciplines. Having inspired by successful policy…

Modeling Spring Mass System with System Dynamics Approach in Middle School Education

ERIC Educational Resources Information Center

Nuhoglu, Hasret

2008-01-01

System Dynamics is a well formulated methodology for analyzing the components of a system including cause-effect relationships and their underlying mathematics and logic, time delays, and feedback loops. It began in the business and manufacturing world, but is now affecting education and many other disciplines. Having inspired by successful policy…

Modelling and Analysis of a New Piezoelectric Dynamic Balance Regulator

PubMed Central

Du, Zhe; Mei, Xue-Song; Xu, Mu-Xun

2012-01-01

In this paper, a new piezoelectric dynamic balance regulator, which can be used in motorised spindle systems, is presented. The dynamic balancing adjustment mechanism is driven by an in-plane bending vibration from an annular piezoelectric stator excited by a high-frequency sinusoidal input voltage. This device has different construction, characteristics and operating principles than a conventional balance regulator. In this work, a dynamic model of the regulator is first developed using a detailed analytical method. Thereafter, MATLAB is employed to numerically simulate the relations between the dominant parameters and the characteristics of the regulator based on thedynamic model. Finally, experimental measurements are used to certify the validity of the dynamic model. Consequently, the mathematical model presented and analysed in this paper can be used as a tool for optimising the design of a piezoelectric dynamic balance regulator during steady state operation. PMID:23202182

Standard representation and unified stability analysis for dynamic artificial neural network models.

PubMed

Kim, Kwang-Ki K; Patrón, Ernesto Ríos; Braatz, Richard D

2018-02-01

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. Copyright © 2017. Published by Elsevier Ltd.

A multidimensional model of the effect of gravity on the spatial orientation of the monkey

NASA Technical Reports Server (NTRS)

Merfeld, D. M.; Young, L. R.; Oman, C. M.; Shelhamer, M. J.

1993-01-01

A "sensory conflict" model of spatial orientation was developed. This mathematical model was based on concepts derived from observer theory, optimal observer theory, and the mathematical properties of coordinate rotations. The primary hypothesis is that the central nervous system of the squirrel monkey incorporates information about body dynamics and sensory dynamics to develop an internal model. The output of this central model (expected sensory afference) is compared to the actual sensory afference, with the difference defined as "sensory conflict." The sensory conflict information is, in turn, used to drive central estimates of angular velocity ("velocity storage"), gravity ("gravity storage"), and linear acceleration ("acceleration storage") toward more accurate values. The model successfully predicts "velocity storage" during rotation about an earth-vertical axis. The model also successfully predicts that the time constant of the horizontal vestibulo-ocular reflex is reduced and that the axis of eye rotation shifts toward alignment with gravity following postrotatory tilt. Finally, the model predicts the bias, modulation, and decay components that have been observed during off-vertical axis rotations (OVAR).

Buckling of circular cylindrical shells under dynamically applied axial loads

NASA Technical Reports Server (NTRS)

Tulk, J. D.

1972-01-01

A theoretical and experimental study was made of the buckling characteristics of perfect and imperfect circular cylindrical shells subjected to dynamic axial loading. Experimental data included dynamic buckling loads (124 data points), high speed photographs of buckling mode shapes and observations of the dynamic stability of shells subjected to rapidly applied sub-critical loads. A mathematical model was developed to describe the dynamic behavior of perfect and imperfect shells. This model was based on the Donnell-Von Karman compatibility and equilibrium equations and had a wall deflection function incorporating five separate modes of deflection. Close agreement between theory and experiment was found for both dynamic buckling strength and buckling mode shapes.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Optimal harvesting for a predator-prey agent-based model using difference equations.

PubMed

Oremland, Matthew; Laubenbacher, Reinhard

2015-03-01

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

The mathematical model of dynamic stabilization system for autonomous car

NASA Astrophysics Data System (ADS)

Saikin, A. M.; Buznikov, S. E.; Shabanov, N. S.; Elkin, D. S.

2018-02-01

Leading foreign companies and domestic enterprises carry out extensive researches and developments in the field of control systems for autonomous cars and in the field of improving driver assistance systems. The search for technical solutions, as a rule, is based on heuristic methods and does not always lead to satisfactory results. The purpose of this research is to formalize the road safety problem in the terms of modern control theory, to construct the adequate mathematical model for solving it, including the choice of software and hardware environment. For automatic control of the object, it is necessary to solve the problem of dynamic stabilization in the most complete formulation. The solution quality of the problem on a finite time interval is estimated by the value of the quadratic functional. Car speed, turn angle and additional yaw rate (during car drift or skidding) measurements are performed programmatically by the original virtual sensors. The limit speeds at which drift, skidding or rollover begins are calculated programmatically taking into account the friction coefficient identified in motion. The analysis of the results confirms both the adequacy of the mathematical models and the algorithms and the possibility of implementing the system in the minimal technical configuration.

Concurrent processing simulation of the space station

NASA Technical Reports Server (NTRS)

Gluck, R.; Hale, A. L.; Sunkel, John W.

1989-01-01

The development of a new capability for the time-domain simulation of multibody dynamic systems and its application to the study of a large angle rotational maneuvers of the Space Station is described. The effort was divided into three sequential tasks, which required significant advancements of the state-of-the art to accomplish. These were: (1) the development of an explicit mathematical model via symbol manipulation of a flexible, multibody dynamic system; (2) the development of a methodology for balancing the computational load of an explicit mathematical model for concurrent processing; and (3) the implementation and successful simulation of the above on a prototype Custom Architectured Parallel Processing System (CAPPS) containing eight processors. The throughput rate achieved by the CAPPS operating at only 70 percent efficiency, was 3.9 times greater than that obtained sequentially by the IBM 3090 supercomputer simulating the same problem. More significantly, analysis of the results leads to the conclusion that the relative cost effectiveness of concurrent vs. sequential digital computation will grow substantially as the computational load is increased. This is a welcomed development in an era when very complex and cumbersome mathematical models of large space vehicles must be used as substitutes for full scale testing which has become impractical.

Planetary rings - Theory

NASA Technical Reports Server (NTRS)

Borderies, Nicole

1989-01-01

Theoretical models of planetary-ring dynamics are examined in a brief analytical review. The mathematical description of streamlines and streamline interactions is outlined; the redistribution of angular momentum due to collisions between particles is explained; and problems in the modeling of broad, narrow, and arc rings are discussed.

Use of the mathematical modelling method for the investigation of dynamic characteristics of acoustical measuring instruments

NASA Technical Reports Server (NTRS)

Vasilyev, Y. M.; Lagunov, L. F.

1973-01-01

The schematic diagram of a noise measuring device is presented that uses pulse expansion modeling according to the peak or any other measured values, to obtain instrument readings at a very low noise error.

Mathematical Modeling and Nonlinear Dynamical Analysis of Cell Growth in Response to Antibiotics

NASA Astrophysics Data System (ADS)

Jin, Suoqin; Niu, Lili; Wang, Gang; Zou, Xiufen

2015-06-01

This study is devoted to the revelation of the dynamical mechanisms of cell growth in response to antibiotics. We establish a mathematical model of ordinary differential equations for an antibiotic-resistant growth system with one positive feedback loop. We perform a dynamical analysis of the behavior of this model system. We present adequate sets of conditions that can guarantee the existence and stability of biologically-reasonable steady states. Using bifurcation analysis and numerical simulation, we show that the relative growth rate, which is defined as the ratio of the cell growth rate to the basal cell growth rate in the absence of antibiotics, can exhibit bistable behavior in an extensive range of parameters that correspond to a growth state and a nongrowth state in biology. We discover that both antibiotic and antibiotic resistance genes can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to the onset of bistability. These results would contribute to a better understanding of not only the evolution of antibiotics but also the emergence of drug resistance in other diseases.

Preface.

PubMed

Friedman, Avner; Lachowicz, Mirosław; Ledzewicz, Urszula; Piotrowska, Monika Joanna; Szymanska, Zuzanna

2017-02-01

This volume was inspired by the topics presented at the international conference "Micro and Macro Systems in Life Sciences" which was held on Jun 8-12, 2015 in Będlewo, Poland. System biology is an approach which tries to understand how micro systems, at the molecular and cellular levels, affect macro systems such as organs, tissue and populations. Thus it is not surprising that a major theme of this volume evolves around cancer and its treatment. Articles on this topic include models for tumor induced angiogenesis, without and with delays, metastatic niche of the bone marrow, drug resistance and metronomic chemotherapy, and virotherapy of glioma. Methods range from dynamical systems to optimal control. Another well represented topic of this volume is mathematical modeling in epidemiology. Mathematical approaches to modeling and control of more specific diseases like malaria, Ebola or human papillomavirus are discussed as well as a more general approaches to the SEIR, and even more general class of models in epidemiology, by using the tools of optimal control and optimization. The volume also brings up challenges in mathematical modeling of other diseases such as tuberculosis. Partial differential equations combined with numerical approaches are becoming important tools in modeling not only tumor growth and treatment, but also other diseases, such as fibrosis of the liver, and atherosclerosis and its associated blood flow dynamics, and our volume presents a state of the art approach on these topics. Understanding mathematics behind the cell motion, appearance of the special patterns in various cell populations, and age structured mutations are among topics addressed inour volume. A spatio-temporal models of synthetic genetic oscillators brings the analysis to the gene level which is the focus of much of current biological research. Mathematics can help biologists to explain the collective behavior of bacterial, a topic that is also presented here. Finally some more across the discipline topics are being addresses, which can appear as a challenge in studying problems in systems biology on all, macro, meso and micro levels. They include numerical approaches to stochastic wave equation arising in modeling Brownian motion, discrete velocity models, many particle approximations as well as very important aspect on the connection between discrete measurement and the construction of the models for various phenomena, particularly the one involving delays. With the variety of biological topics and their mathematical approaches we very much hope that the reader of the Mathematical Biosciences and Engineering will find this volume interesting and inspirational for their own research.

Optimized planning methodologies of ASON implementation

NASA Astrophysics Data System (ADS)

Zhou, Michael M.; Tamil, Lakshman S.

2005-02-01

Advanced network planning concerns effective network-resource allocation for dynamic and open business environment. Planning methodologies of ASON implementation based on qualitative analysis and mathematical modeling are presented in this paper. The methodology includes method of rationalizing technology and architecture, building network and nodal models, and developing dynamic programming for multi-period deployment. The multi-layered nodal architecture proposed here can accommodate various nodal configurations for a multi-plane optical network and the network modeling presented here computes the required network elements for optimizing resource allocation.

How students learn to coordinate knowledge of physical and mathematical models in cellular physiology

NASA Astrophysics Data System (ADS)

Lira, Matthew

This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students shift from recognizing one influence to recognizing both the chemical and the electrical gradients as responsible for a cell's membrane potential reaching dynamic equilibrium. Together, the studies illustrate that to coordinate knowledge, students need opportunities to reflect upon relations between representations of mathematical and physical models as well as distinguish between physical quantities such as molarities for ions and transmembrane voltages.

The motion behind the symbols: a vital role for dynamism in the conceptualization of limits and continuity in expert mathematics.

PubMed

Marghetis, Tyler; Núñez, Rafael

2013-04-01

The canonical history of mathematics suggests that the late 19th-century "arithmetization" of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice. Copyright © 2013 Cognitive Science Society, Inc.

Teaching Strategies Mediated by Technologies in the EduLab Model: The Case of Mathematics and Natural Sciences

ERIC Educational Resources Information Center

Oliveira, Ana; Pombo, Lúcia

2017-01-01

The EduLab model is a "new" educational model that integrates technologies in educational contexts comprising full equipped classrooms with attractive and easy-to-use technological resources. This model tries to promote a dynamic and more effective teaching and learning process. For this purpose, the model provides teachers training and…

Discrete dynamic modeling of cellular signaling networks.

PubMed

Albert, Réka; Wang, Rui-Sheng

2009-01-01

Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

NASA Technical Reports Server (NTRS)

Ozguven, H. Nevzat

1991-01-01

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

Modeling in the quality by design environment: Regulatory requirements and recommendations for design space and control strategy appointment.

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

Mathematical models can be used as an integral part of the quality by design (QbD) concept throughout the product lifecycle for variety of purposes, including appointment of the design space and control strategy, continual improvement and risk assessment. Examples of different mathematical modeling techniques (mechanistic, empirical and hybrid) in the pharmaceutical development and process monitoring or control are provided in the presented review. In the QbD context, mathematical models are predominantly used to support design space and/or control strategies. Considering their impact to the final product quality, models can be divided into the following categories: high, medium and low impact models. Although there are regulatory guidelines on the topic of modeling applications, review of QbD-based submission containing modeling elements revealed concerns regarding the scale-dependency of design spaces and verification of models predictions at commercial scale of manufacturing, especially regarding real-time release (RTR) models. Authors provide critical overview on the good modeling practices and introduce concepts of multiple-unit, adaptive and dynamic design space, multivariate specifications and methods for process uncertainty analysis. RTR specification with mathematical model and different approaches to multivariate statistical process control supporting process analytical technologies are also presented. Copyright © 2017 Elsevier B.V. All rights reserved.

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Calculation and Analysis of Dynamic Characteristics of Multilink Permanent Magnetic Actuator in Vacuum Circuit Breaker

NASA Astrophysics Data System (ADS)

Liu, Yingyi; Yuan, Haiwen; Zhang, Qingjie; Chen, Degui; Yuan, Haibin

The dynamic characteristics are the key issues in the optimum design of a permanent magnetic actuator (PMA). A new approach to forecast the dynamic characteristics of the multilink PMA is proposed. By carrying out further developments of ADAMS and ANSOFT, a mathematic calculation model describing the coupling of mechanical movement, electric circuit and magnetic field considering eddy current effect, is constructed. With this model, the dynamic characteristics of the multilink PMA are calculated and compared with the experimental results. Factors that affect the opening time of the multilink PMA are analyzed with the model as well. The method is capable of providing a reference for the design of the PMA.

Interdisciplinary education - a predator-prey model for developing a skill set in mathematics, biology and technology

NASA Astrophysics Data System (ADS)

van der Hoff, Quay

2017-08-01

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in biological phenomena, find it difficult to master the complex systems encountered in biology. In short, the biologists do not have enough mathematics and the mathematicians are not being taught enough biology. The need for interdisciplinary curricula that includes disciplines such as biology, physical science, and mathematics is widely recognized, but has not been widely implemented. In this paper, it is suggested that students develop a skill set of ecology, mathematics and technology to encourage working across disciplinary boundaries. To illustrate such a skill set, a predator-prey model that contains self-limiting factors for both predator and prey is suggested. The general idea of dynamics, is introduced and students are encouraged to discover the applicability of this approach to more complex biological systems. The level of mathematics and technology required is not advanced; therefore, it is ideal for inclusion in a senior-level or introductory graduate-level course for students interested in mathematical biology.

A general consumer-resource population model

USGS Publications Warehouse

Lafferty, Kevin D.; DeLeo, Giulio; Briggs, Cheryl J.; Dobson, Andrew P.; Gross, Thilo; Kuris, Armand M.

2015-01-01

Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

PubMed Central

Jenness, Samuel M.; Goodreau, Steven M.; Morris, Martina

2018-01-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers. PMID:29731699

Generating self-organizing collective behavior using separation dynamics from experimental data

NASA Astrophysics Data System (ADS)

Dieck Kattas, Graciano; Xu, Xiao-Ke; Small, Michael

2012-09-01

Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena, and later tuned or verified to simulate desired dynamics. In contrast to this approach, we propose using a model that attempts to follow an averaged rule of the essential distance-dependent collective behavior of real pigeon flocks, which was abstracted from experimental data. By using a simple model to follow the behavioral tendencies of real data, we show that our model can exhibit a wide range of emergent self-organizing dynamics such as flocking, pattern formation, and counter-rotating vortices.

Generating self-organizing collective behavior using separation dynamics from experimental data.

PubMed

Dieck Kattas, Graciano; Xu, Xiao-Ke; Small, Michael

2012-09-01

Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena, and later tuned or verified to simulate desired dynamics. In contrast to this approach, we propose using a model that attempts to follow an averaged rule of the essential distance-dependent collective behavior of real pigeon flocks, which was abstracted from experimental data. By using a simple model to follow the behavioral tendencies of real data, we show that our model can exhibit a wide range of emergent self-organizing dynamics such as flocking, pattern formation, and counter-rotating vortices.

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition.

PubMed

Simeoni, Chiara; Dinicola, Simona; Cucina, Alessandra; Mascia, Corrado; Bizzarri, Mariano

2018-01-01

In this report, we aim at presenting a viable strategy for the study of Epithelial-Mesenchymal Transition (EMT) and its opposite Mesenchymal-Epithelial Transition (MET) by means of a Systems Biology approach combined with a suitable Mathematical Modeling analysis. Precisely, it is shown how the presence of a metastable state, that is identified at a mesoscopic level of description, is crucial for making possible the appearance of a phase transition mechanism in the framework of fast-slow dynamics for Ordinary Differential Equations (ODEs).

On the Effects of Artificial Feeding on Bee Colony Dynamics: A Mathematical Model

PubMed Central

Paiva, Juliana Pereira Lisboa Mohallem; Paiva, Henrique Mohallem; Esposito, Elisa; Morais, Michelle Manfrini

2016-01-01

This paper proposes a new mathematical model to evaluate the effects of artificial feeding on bee colony population dynamics. The proposed model is based on a classical framework and contains differential equations that describe the changes in the number of hive bees, forager bees, and brood cells, as a function of amounts of natural and artificial food. The model includes the following elements to characterize the artificial feeding scenario: a function to model the preference of the bees for natural food over artificial food; parameters to quantify the quality and palatability of artificial diets; a function to account for the efficiency of the foragers in gathering food under different environmental conditions; and a function to represent different approaches used by the beekeeper to feed the hive with artificial food. Simulated results are presented to illustrate the main characteristics of the model and its behavior under different scenarios. The model results are validated with experimental data from the literature involving four different artificial diets. A good match between simulated and experimental results was achieved. PMID:27875589

Mathematical modeling of control subsystems for CELSS: Application to diet

NASA Technical Reports Server (NTRS)

Waleh, Ahmad; Nguyen, Thoi K.; Kanevsky, Valery

1991-01-01

The dynamic control of a Closed Ecological Life Support System (CELSS) in a closed space habitat is of critical importance. The development of a practical method of control is also a necessary step for the selection and design of realistic subsystems and processors for a CELSS. Diet is one of the dynamic factors that strongly influences, and is influenced, by the operational states of all major CELSS subsystems. The problems of design and maintenance of a stable diet must be obtained from well characterized expert subsystems. The general description of a mathematical model that forms the basis of an expert control program for a CELSS is described. The formulation is expressed in terms of a complete set of time dependent canonical variables. System representation is dynamic and includes time dependent storage buffers. The details of the algorithm are described. The steady state results of the application of the method for representative diets made from wheat, potato, and soybean are presented.

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

NASA Astrophysics Data System (ADS)

Dockendorff, Monika; Solar, Horacio

2018-01-01

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers' conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets - designed and used in an exploratory manner - promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.

Helicopter mathematical models and control law development for handling qualities research

NASA Technical Reports Server (NTRS)

Chen, Robert T. N.; Lebacqz, J. Victor; Aiken, Edwin W.; Tischler, Mark B.

1988-01-01

Progress made in joint NASA/Army research concerning rotorcraft flight-dynamics modeling, design methodologies for rotorcraft flight-control laws, and rotorcraft parameter identification is reviewed. Research into these interactive disciplines is needed to develop the analytical tools necessary to conduct flying qualities investigations using both the ground-based and in-flight simulators, and to permit an efficient means of performing flight test evaluation of rotorcraft flying qualities for specification compliance. The need for the research is particularly acute for rotorcraft because of their mathematical complexity, high order dynamic characteristics, and demanding mission requirements. The research in rotorcraft flight-dynamics modeling is pursued along two general directions: generic nonlinear models and nonlinear models for specific rotorcraft. In addition, linear models are generated that extend their utilization from 1-g flight to high-g maneuvers and expand their frequency range of validity for the design analysis of high-gain flight control systems. A variety of methods ranging from classical frequency-domain approaches to modern time-domain control methodology that are used in the design of rotorcraft flight control laws is reviewed. Also reviewed is a study conducted to investigate the design details associated with high-gain, digital flight control systems for combat rotorcraft. Parameter identification techniques developed for rotorcraft applications are reviewed.

Numerical modeling and preliminary validation of drag-based vertical axis wind turbine

NASA Astrophysics Data System (ADS)

Krysiński, Tomasz; Buliński, Zbigniew; Nowak, Andrzej J.

2015-03-01

The main purpose of this article is to verify and validate the mathematical description of the airflow around a wind turbine with vertical axis of rotation, which could be considered as representative for this type of devices. Mathematical modeling of the airflow around wind turbines in particular those with the vertical axis is a problematic matter due to the complex nature of this highly swirled flow. Moreover, it is turbulent flow accompanied by a rotation of the rotor and the dynamic boundary layer separation. In such conditions, the key aspects of the mathematical model are accurate turbulence description, definition of circular motion as well as accompanying effects like centrifugal force or the Coriolis force and parameters of spatial and temporal discretization. The paper presents the impact of the different simulation parameters on the obtained results of the wind turbine simulation. Analysed models have been validated against experimental data published in the literature.

Experimental and mathematical model of the interactions in the mixed culture of links in the “producer-consumer” cycle

NASA Astrophysics Data System (ADS)

Pisman, T. I.

2009-07-01

The paper presents a experimental and mathematical model of interactions between invertebrates (the ciliates Paramecium caudatum and the rotifers Brachionus plicatilis) in the "producer-consumer" aquatic biotic cycle with spatially separated components. The model describes the dynamics of the mixed culture of ciliates and rotifers in the "consumer" component, feeding on the mixed algal culture of the "producer" component. It has been found that metabolites of the algae Scenedesmus produce an adverse effect on the reproduction of the ciliates P. caudatum. Taking into account this effect, the results of investigation of the mathematical model were in qualitative agreement with the experimental results. In the "producer-consumer" biotic cycle it was shown that coexistence is impossible in the mixed culture of invertebrates of the "consumer" component. The ciliates P. caudatum are driven out by the rotifers B. plicatilis.

Modeling of Semiconductor Optical Amplifier Gain Characteristics for Amplification and Switching

NASA Astrophysics Data System (ADS)

Mahad, Farah Diana; Sahmah, Abu; Supa'at, M.; Idrus, Sevia Mahdaliza; Forsyth, David

2011-05-01

The Semiconductor Optical Amplifier (SOA) is presently commonly used as a booster or pre-amplifier in some communication networks. However, SOAs are also a strong candidate for utilization as multi-functional elements in future all-optical switching, regeneration and also wavelength conversion schemes. With this in mind, the purpose of this paper is to simulate the performance of the SOA for improved amplification and switching functions. The SOA is modeled and simulated using OptSim software. In order to verify the simulated results, a MATLAB mathematical model is also used to aid the design of the SOA. Using the model, the gain difference between simulated and mathematical results in the unsaturated region is <1dB. The mathematical analysis is in good agreement with the simulation result, with only a small offset due to inherent software limitations in matching the gain dynamics of the SOA.

Molecular Mechanics and Dynamics Characterization of an "in silico" Mutated Protein: A Stand-Alone Lab Module or Support Activity for "in vivo" and "in vitro" Analyses of Targeted Proteins

ERIC Educational Resources Information Center

Chiang, Harry; Robinson, Lucy C.; Brame, Cynthia J.; Messina, Troy C.

2013-01-01

Over the past 20 years, the biological sciences have increasingly incorporated chemistry, physics, computer science, and mathematics to aid in the development and use of mathematical models. Such combined approaches have been used to address problems from protein structure-function relationships to the workings of complex biological systems.…

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression.

PubMed

Saitou, Takashi; Imamura, Takeshi

2016-01-01

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation. © 2015 Japanese Society of Developmental Biologists.

Numerical modeling of dynamics of heart rate and arterial pressure during passive orthostatic test

NASA Astrophysics Data System (ADS)

Ishbulatov, Yu. M.; Kiselev, A. R.; Karavaev, A. S.

2018-04-01

A model of human cardiovascular system is proposed to describe the main heart rhythm, influence of autonomous regulation on frequency and strength of heart contractions and resistance of arterial vessels; process of formation of arterial pressure during systolic and diastolic phases; influence of respiration; synchronization between loops of autonomous regulation. The proposed model is used to simulate the dynamics of heart rate and arterial pressure during passive transition from supine to upright position. Results of mathematical modeling are compared to original experimental data.

Model-based calculations of surface mass balance of mountain glaciers for the purpose of water consumption planning: focus on Djankuat Glacier (Central Caucasus)

NASA Astrophysics Data System (ADS)

Rybak, O. O.; Rybak, E. A.

2018-01-01

Mountain glaciers act as regulators of run-off in the summer period, which is very crucial for economy especially in dynamically developing regions with rapidly growing population, such as Central Asia or the Northern Caucasus in Russia. In overall, glaciers stabilize water consumption in comparatively arid areas and provide conditions for sustainable development of the economy in mountainous regions and in the surrounding territories. A proper prediction of the glacial run-off is required to elaborate strategies of the regional development. This goal can be achieved by implementation of mathematical modeling methods into planning methodologies. In the paper, we consider one of the first steps in glacier dynamical modeling - surface mass balance simulation. We focus on the Djankuat Glacier in the Central Caucasus, where regular observations have been conducted during the last fifty years providing an exceptional opportunity to calibrate and to validate a mathematical model.

Analysis of the impact of trap-neuter-return programs on populations of feral cats.

PubMed

Foley, Patrick; Foley, Janet E; Levy, Julie K; Paik, Terry

2005-12-01

To evaluate 2 county trap-neuter-return (TNR) programs for feral cat population management via mathematical modeling. Theoretical population model. Feral cats assessed from 1992 to 2003 in San Diego County, California (n = 14,452), and from 1998 to 2004 in Alachua County, Florida (11,822). Data were analyzed with a mathematical Ricker model to describe population dynamics of the feral cats and modifications to the dynamics that occurred as a result of the TNR programs. In both counties, results of analyses did not indicate a consistent reduction in per capita growth, the population multiplier, or the proportion of female cats that were pregnant. Success of feral cat management programs that use TNR can be monitored with an easily collected set of data and statistical analyses facilitated by population modeling techniques. Results may be used to suggest possible future monitoring and modification of TNR programs, which could result in greater success controlling and reducing feral cat populations.

Opportunities and constraints of presently used thermal manikins for thermo-physiological simulation of the human body.

PubMed

Psikuta, Agnes; Kuklane, Kalev; Bogdan, Anna; Havenith, George; Annaheim, Simon; Rossi, René M

2016-03-01

Combining the strengths of an advanced mathematical model of human physiology and a thermal manikin is a new paradigm for simulating thermal behaviour of humans. However, the forerunners of such adaptive manikins showed some substantial limitations. This project aimed to determine the opportunities and constraints of the existing thermal manikins when dynamically controlled by a mathematical model of human thermal physiology. Four thermal manikins were selected and evaluated for their heat flux measurement uncertainty including lateral heat flows between manikin body parts and the response of each sector to the frequent change of the set-point temperature typical when using a physiological model for control. In general, all evaluated manikins are suitable for coupling with a physiological model with some recommendations for further improvement of manikin dynamic performance. The proposed methodology is useful to improve the performance of the adaptive manikins and help to provide a reliable and versatile tool for the broad research and development domain of clothing, automotive and building engineering.

Dynamic cardiac PET imaging: extraction of time-activity curves using ICA and a generalized Gaussian distribution model.

PubMed

Mabrouk, Rostom; Dubeau, François; Bentabet, Layachi

2013-01-01

Kinetic modeling of metabolic and physiologic cardiac processes in small animals requires an input function (IF) and a tissue time-activity curves (TACs). In this paper, we present a mathematical method based on independent component analysis (ICA) to extract the IF and the myocardium's TACs directly from dynamic positron emission tomography (PET) images. The method assumes a super-Gaussian distribution model for the blood activity, and a sub-Gaussian distribution model for the tissue activity. Our appreach was applied on 22 PET measurement sets of small animals, which were obtained from the three most frequently used cardiac radiotracers, namely: desoxy-fluoro-glucose ((18)F-FDG), [(13)N]-ammonia, and [(11)C]-acetate. Our study was extended to PET human measurements obtained with the Rubidium-82 ((82) Rb) radiotracer. The resolved mathematical IF values compare favorably to those derived from curves extracted from regions of interest (ROI), suggesting that the procedure presents a reliable alternative to serial blood sampling for small-animal cardiac PET studies.

Train Control and Operations

DOT National Transportation Integrated Search

1971-06-01

ATO (automatic train operation) and ATC (automatic train control) systems are evaluated relative to available technology and cost-benefit. The technological evaluation shows that suitable mathematical models of the dynamics of long trains are require...

PASMet: a web-based platform for prediction, modelling and analyses of metabolic systems

PubMed Central

Sriyudthsak, Kansuporn; Mejia, Ramon Francisco; Arita, Masanori; Hirai, Masami Yokota

2016-01-01

PASMet (Prediction, Analysis and Simulation of Metabolic networks) is a web-based platform for proposing and verifying mathematical models to understand the dynamics of metabolism. The advantages of PASMet include user-friendliness and accessibility, which enable biologists and biochemists to easily perform mathematical modelling. PASMet offers a series of user-functions to handle the time-series data of metabolite concentrations. The functions are organised into four steps: (i) Prediction of a probable metabolic pathway and its regulation; (ii) Construction of mathematical models; (iii) Simulation of metabolic behaviours; and (iv) Analysis of metabolic system characteristics. Each function contains various statistical and mathematical methods that can be used independently. Users who may not have enough knowledge of computing or programming can easily and quickly analyse their local data without software downloads, updates or installations. Users only need to upload their files in comma-separated values (CSV) format or enter their model equations directly into the website. Once the time-series data or mathematical equations are uploaded, PASMet automatically performs computation on server-side. Then, users can interactively view their results and directly download them to their local computers. PASMet is freely available with no login requirement at http://pasmet.riken.jp/ from major web browsers on Windows, Mac and Linux operating systems. PMID:27174940

Bifurcation phenomena in an impulsive model of non-basal testosterone regulation

NASA Astrophysics Data System (ADS)

Zhusubaliyev, Zhanybai T.; Churilov, Alexander N.; Medvedev, Alexander

2012-03-01

Complex nonlinear dynamics in a recent mathematical model of non-basal testosterone regulation are investigated. In agreement with biological evidence, the pulsatile (non-basal) secretion of testosterone is modeled by frequency and amplitude modulated feedback. It is shown that, in addition to already known periodic motions with one and two pulses in the least period of a closed-loop system solution, cycles of higher periodicity and chaos are present in the model in hand. The broad range of exhibited dynamic behaviors makes the model highly promising in model-based signal processing of hormone data.

Predicting disease progression from short biomarker series using expert advice algorithm

NASA Astrophysics Data System (ADS)

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-01

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of ``prediction with expert advice'' to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

Predicting disease progression from short biomarker series using expert advice algorithm.

PubMed

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-20

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of "prediction with expert advice" to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

An analytically linearized helicopter model with improved modeling accuracy

NASA Technical Reports Server (NTRS)

Jensen, Patrick T.; Curtiss, H. C., Jr.; Mckillip, Robert M., Jr.

1991-01-01

An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.

Mathematical modelling of powder material motion and transportation in high-temperature flow core during plasma coatings application

NASA Astrophysics Data System (ADS)

Bogdanovich, V. I.; Giorbelidze, M. G.

2018-03-01

A problem of mathematical modelling of powder material motion and transportation in gas thermal flow core has been addressed. Undertaken studies indicate significant impact on dynamics of motion of sprayed particles of phenomenological law for drag coefficient and accounting momentum loss of a plasma jet upon acceleration of these particles and their diameter. It is determined that at great dispersion of spraying particles, they reach detail surface at different velocity and significant particles separation takes place at spraying spot. According to the results of mathematical modelling, requirements for admissible dispersion of diameters of particles used for spraying have been formulated. Research has also allowed reducing separation of particles at the spraying spot due to the selection of the method of powder feed to the anode channel of the plasma torch.

An inverse problem for a mathematical model of aquaponic agriculture

NASA Astrophysics Data System (ADS)

Bobak, Carly; Kunze, Herb

2017-01-01

Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

Switching moving boundary models for two-phase flow evaporators and condensers

NASA Astrophysics Data System (ADS)

Bonilla, Javier; Dormido, Sebastián; Cellier, François E.

2015-03-01

The moving boundary method is an appealing approach for the design, testing and validation of advanced control schemes for evaporators and condensers. When it comes to advanced control strategies, not only accurate but fast dynamic models are required. Moving boundary models are fast low-order dynamic models, and they can describe the dynamic behavior with high accuracy. This paper presents a mathematical formulation based on physical principles for two-phase flow moving boundary evaporator and condenser models which support dynamic switching between all possible flow configurations. The models were implemented in a library using the equation-based object-oriented Modelica language. Several integrity tests in steady-state and transient predictions together with stability tests verified the models. Experimental data from a direct steam generation parabolic-trough solar thermal power plant is used to validate and compare the developed moving boundary models against finite volume models.

Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings

PubMed Central

2012-01-01

Background To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana. Results In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study. Conclusions In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots. PMID:22409965

Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings.

PubMed

Otaki, Joji M

2012-03-13

To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana. In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study. In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots.

Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

On bifurcation in dynamics of hemispherical resonator gyroscope

NASA Astrophysics Data System (ADS)

Volkov, D. Yu.; Galunova, K. V.

2018-05-01

A mathematical model of wave solid-state gyro (HRG) are constructed. Wave pattern of resonant oscillations was studied applying normal form method. We calculate the Birkhoff-Gustavson normal form of unterturbed system.

Mathematical modeling of growth of Salmonella in raw ground beef under isothermal conditions from 10 to 45 Degree C

USDA-ARS?s Scientific Manuscript database

The objective of this study was to develop primary and secondary models to describe the growth of Salmonella in raw ground beef. Primary and secondary models can be integrated into a dynamic model that can predict the microbial growth under varying environmental conditions. Growth data of Salmonel...

Effects of rotor model degradation on the accuracy of rotorcraft real time simulation

NASA Technical Reports Server (NTRS)

Houck, J. A.; Bowles, R. L.

1976-01-01

The effects are studied of degrading a rotating blade element rotor mathematical model to meet various real-time simulation requirements of rotorcraft. Three methods of degradation were studied: reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments, (2) reduction of number of blades, and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which the rotating blade element rotor mathematical model should not be used.

Handling qualities of large flexible control-configured aircraft

NASA Technical Reports Server (NTRS)

Swaim, R. L.

1980-01-01

The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task.

A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

PubMed

Guiver, Chris; Packman, David; Townley, Stuart

2017-07-07

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

A Computer Code for Dynamic Stress Analysis of Media-Structure Problems with Nonlinearities (SAMSON). Volume III. User’s Manual.

DTIC Science & Technology

NONLINEAR SYSTEMS, LINEAR SYSTEMS, SUBROUTINES , SOIL MECHANICS, INTERFACES, DYNAMICS, LOADS(FORCES), FORCE(MECHANICS), DAMPING, ACCELERATION, ELASTIC...PROPERTIES, PLASTIC PROPERTIES, CRACKS , REINFORCING MATERIALS , COMPOSITE MATERIALS , FAILURE(MECHANICS), MECHANICAL PROPERTIES, INSTRUCTION MANUALS, DIGITAL COMPUTERS...STRESSES, *COMPUTER PROGRAMS), (*STRUCTURES, STRESSES), (*DATA PROCESSING, STRUCTURAL PROPERTIES), SOILS , STRAIN(MECHANICS), MATHEMATICAL MODELS

Cooperative Team Networks

DTIC Science & Technology

2016-06-01

team processes, such as identifying motifs of dynamic communication exchanges which goes well beyond simple dyadic and triadic configurations; as well...new metrics and ways to formulate team processes, such as identifying motifs of dynamic communication exchanges which goes well beyond simple dyadic ...sensing, communication , information, and decision networks - Darryl Ahner (AFIT: Air Force Inst Tech) Panel Session: Mathematical Models of

A Model for Task Design with Focus on Exploration, Explanation, and Generalization in a Dynamic Geometry Environment

ERIC Educational Resources Information Center

Fahlgren, Maria; Brunström, Mats

2014-01-01

The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…

Methods of Technological Forecasting,

DTIC Science & Technology

1977-05-01

Trend Extrapolation Progress Curve Analogy Trend Correlation Substitution Analysis or Substitution Growth Curves Envelope Curve Advances in the State of...the Art Technological Mapping Contextual Mapping Matrix Input-Output Analysis Mathematical Models Simulation Models Dynamic Modelling. CHAPTER IV...Generation Interaction between Needs and Possibilities Map of the Technological Future — (‘ross- Impact Matri x Discovery Matrix Morphological Analysis

Introduction to Population Modeling.

ERIC Educational Resources Information Center

Frauenthal, James C.

The focus is on the formulation and solution of mathematical models with the idea of a population employed mainly as a pedogogical tool. If the biological setting is stripped away, the material can be interpreted as topics or the qualitative behavior of differential and difference equations. The first group of models investigate the dynamics of a…

Boolean Dynamic Modeling Approaches to Study Plant Gene Regulatory Networks: Integration, Validation, and Prediction.

PubMed

Velderraín, José Dávila; Martínez-García, Juan Carlos; Álvarez-Buylla, Elena R

2017-01-01

Mathematical models based on dynamical systems theory are well-suited tools for the integration of available molecular experimental data into coherent frameworks in order to propose hypotheses about the cooperative regulatory mechanisms driving developmental processes. Computational analysis of the proposed models using well-established methods enables testing the hypotheses by contrasting predictions with observations. Within such framework, Boolean gene regulatory network dynamical models have been extensively used in modeling plant development. Boolean models are simple and intuitively appealing, ideal tools for collaborative efforts between theorists and experimentalists. In this chapter we present protocols used in our group for the study of diverse plant developmental processes. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature.

A new standard model for milk yield in dairy cows based on udder physiology at the milking-session level.

PubMed

Gasqui, Patrick; Trommenschlager, Jean-Marie

2017-08-21

Milk production in dairy cow udders is a complex and dynamic physiological process that has resisted explanatory modelling thus far. The current standard model, Wood's model, is empirical in nature, represents yield in daily terms, and was published in 1967. Here, we have developed a dynamic and integrated explanatory model that describes milk yield at the scale of the milking session. Our approach allowed us to formally represent and mathematically relate biological features of known relevance while accounting for stochasticity and conditional elements in the form of explicit hypotheses, which could then be tested and validated using real-life data. Using an explanatory mathematical and biological model to explore a physiological process and pinpoint potential problems (i.e., "problem finding"), it is possible to filter out unimportant variables that can be ignored, retaining only those essential to generating the most realistic model possible. Such modelling efforts are multidisciplinary by necessity. It is also helpful downstream because model results can be compared with observed data, via parameter estimation using maximum likelihood and statistical testing using model residuals. The process in its entirety yields a coherent, robust, and thus repeatable, model.

Introduction to a special section on ecohydrology of semiarid environments: Confronting mathematical models with ecosystem complexity

NASA Astrophysics Data System (ADS)

Svoray, Tal; Assouline, Shmuel; Katul, Gabriel

2015-11-01

Current literature provides large number of publications about ecohydrological processes and their effect on the biota in drylands. Given the limited laboratory and field experiments in such systems, many of these publications are based on mathematical models of varying complexity. The underlying implicit assumption is that the data set used to evaluate these models covers the parameter space of conditions that characterize drylands and that the models represent the actual processes with acceptable certainty. However, a question raised is to what extent these mathematical models are valid when confronted with observed ecosystem complexity? This Introduction reviews the 16 papers that comprise the Special Section on Eco-hydrology of Semiarid Environments: Confronting Mathematical Models with Ecosystem Complexity. The subjects studied in these papers include rainfall regime, infiltration and preferential flow, evaporation and evapotranspiration, annual net primary production, dispersal and invasion, and vegetation greening. The findings in the papers published in this Special Section show that innovative mathematical modeling approaches can represent actual field measurements. Hence, there are strong grounds for suggesting that mathematical models can contribute to greater understanding of ecosystem complexity through characterization of space-time dynamics of biomass and water storage as well as their multiscale interactions. However, the generality of the models and their low-dimensional representation of many processes may also be a "curse" that results in failures when particulars of an ecosystem are required. It is envisaged that the search for a unifying "general" model, while seductive, may remain elusive in the foreseeable future. It is for this reason that improving the merger between experiments and models of various degrees of complexity continues to shape the future research agenda.

Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Rodríguez, Nancy

2015-03-01

The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].

Prediction of inspiratory flow shapes during sleep with a mathematic model of upper airway forces.

PubMed

Aittokallio, Tero; Gyllenberg, Mats; Saaresranta, Tarja; Polo, Olli

2003-11-01

To predict the airflow dynamics during sleep using a mathematic model that incorporates a number of static and dynamic upper airway forces, and to compare the numerical results to clinical flow data recorded from patients with sleep-disordered breathing on and off various treatment options. Upper airway performance was modeled in virtual subjects characterized by parameter settings that describe common combinations of risk factors predisposing to upper airway collapse during sleep. The treatments effect were induced by relevant changes of the initial parameter values. Computer simulations at our website (http://www.utu.fi/ml/sovmat/bio/). Risk factors considered in the simulation settings were sex, obesity, pharyngeal collapsibility, and decreased phasic activity of pharyngeal muscles. The effects of weight loss, pharyngeal surgery, nasal continuous positive airway pressure, and respiratory stimulation on the inspiratory flow characteristics were tested with the model. Numerical predictions were investigated by means of 3 measurable inspiratory airflow characteristics: initial slope, total volume, and flow shape. The model was able to reproduce the inspiratory flow shape characteristics that have previously been described in the literature. Simulation results also supported the observations that a multitude of factors underlie the pharyngeal collapse and, therefore, certain medical therapies that are effective in some conditions may prove ineffective in others. A mathematic model integrating the current knowledge of upper airway physiology is able to predict individual treatment responses. The model provides a framework for designing novel and potentially feasible treatment alternatives for sleep-disordered breathing.

Large Variations in HIV-1 Viral Load Explained by Shifting-Mosaic Metapopulation Dynamics

PubMed Central

Lythgoe, Katrina A.; Blanquart, François

2016-01-01

The viral population of HIV-1, like many pathogens that cause systemic infection, is structured and differentiated within the body. The dynamics of cellular immune trafficking through the blood and within compartments of the body has also received wide attention. Despite these advances, mathematical models, which are widely used to interpret and predict viral and immune dynamics in infection, typically treat the infected host as a well-mixed homogeneous environment. Here, we present mathematical, analytical, and computational results that demonstrate that consideration of the spatial structure of the viral population within the host radically alters predictions of previous models. We study the dynamics of virus replication and cytotoxic T lymphocytes (CTLs) within a metapopulation of spatially segregated patches, representing T cell areas connected by circulating blood and lymph. The dynamics of the system depend critically on the interaction between CTLs and infected cells at the within-patch level. We show that for a wide range of parameters, the system admits an unexpected outcome called the shifting-mosaic steady state. In this state, the whole body’s viral population is stable over time, but the equilibrium results from an underlying, highly dynamic process of local infection and clearance within T-cell centers. Notably, and in contrast to previous models, this new model can explain the large differences in set-point viral load (SPVL) observed between patients and their distribution, as well as the relatively low proportion of cells infected at any one time, and alters the predicted determinants of viral load variation. PMID:27706164

Mathematical models of bipolar disorder

NASA Astrophysics Data System (ADS)

Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

2009-07-01

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

Nanoscale dynamics of Joule heating and bubble nucleation in a solid-state nanopore.

PubMed

Levine, Edlyn V; Burns, Michael M; Golovchenko, Jene A

2016-01-01

We present a mathematical model for Joule heating of an electrolytic solution in a nanopore. The model couples the electrical and thermal dynamics responsible for rapid and extreme superheating of the electrolyte within the nanopore. The model is implemented numerically with a finite element calculation, yielding a time and spatially resolved temperature distribution in the nanopore region. Temperatures near the thermodynamic limit of superheat are predicted to be attained just before the explosive nucleation of a vapor bubble is observed experimentally. Knowledge of this temperature distribution enables the evaluation of related phenomena including bubble nucleation kinetics, relaxation oscillation, and bubble dynamics.

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

PubMed Central

Schaffer, Evan S.; Ostojic, Srdjan; Abbott, L. F.

2013-01-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons. PMID:24204236

The dynamics of insight: mathematical discovery as a phase transition.

PubMed

Stephen, Damian G; Boncoddo, Rebecca A; Magnuson, James S; Dixon, James A

2009-12-01

In recent work in cognitive science, it has been proposed that cognition is a self-organizing, dynamical system. However, capturing the real-time dynamics of cognition has been a formidable challenge. Furthermore, it has been unclear whether dynamics could effectively address the emergence of abstract concepts (e.g., language, mathematics). Here, we provide evidence that a quintessentially cognitive phenomenon-the spontaneous discovery of a mathematical relation-emerges through self-organization. Participants solved a series of gear-system problems while we tracked their eye movements. They initially solved the problems by manually simulating the forces of the gears but then spontaneously discovered a mathematical solution. We show that the discovery of the mathematical relation was predicted by changes in entropy and changes in power-law behavior, two hallmarks of phase transitions. Thus, the present study demonstrates the emergence of higher order cognitive phenomena through the nonlinear dynamics of self-organization.

Dynamic load-sharing characteristic analysis of face gear power-split gear system based on tooth contact characteristics

NASA Astrophysics Data System (ADS)

Dong, Hao; Hu, Yahui

2018-04-01

The bend-torsion coupling dynamics load-sharing model of the helicopter face gear split torque transmission system is established by using concentrated quality standard, to analyzing the dynamic load-sharing characteristic. The mathematical models include nonlinear support stiffness, time-varying meshing stiffness, damping, gear backlash. The results showed that the errors collectively influenced the load sharing characteristics, only reduce a certain error, it is never fully reached the perfect loading sharing characteristics. The system load-sharing performance can be improved through floating shaft support. The above-method will provide a theoretical basis and data support for its dynamic performance optimization design.

Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals.

PubMed

Cen, Xiuli; Feng, Zhilan; Zheng, Yiqiang; Zhao, Yulin

2017-12-01

Antibiotic-resistant bacteria have posed a grave threat to public health by causing a number of nosocomial infections in hospitals. Mathematical models have been used to study transmission dynamics of antibiotic-resistant bacteria within a hospital and the measures to control antibiotic resistance in nosocomial pathogens. Studies presented in Lipstich et al. (Proc Natl Acad Sci 97(4):1938-1943, 2000) and Lipstich and Bergstrom (Infection control in the ICU environment. Kluwer, Boston, 2002) have provided valuable insights in understanding the transmission of antibiotic-resistant bacteria in a hospital. However, their results are limited to numerical simulations of a few different scenarios without analytical analyses of the models in broader parameter regions that are biologically feasible. Bifurcation analysis and identification of the global stability conditions can be very helpful for assessing interventions that are aimed at limiting nosocomial infections and stemming the spread of antibiotic-resistant bacteria. In this paper we study the global dynamics of the mathematical model of antibiotic resistance in hospitals considered in Lipstich et al. (2000) and Lipstich and Bergstrom (2002). The invasion reproduction number [Formula: see text] of antibiotic-resistant bacteria is derived, and the relationship between [Formula: see text] and two control reproduction numbers of sensitive bacteria and resistant bacteria ([Formula: see text] and [Formula: see text]) is established. More importantly, we prove that a backward bifurcation may occur at [Formula: see text] when the model includes superinfection, which is not mentioned in Lipstich and Bergstrom (2002). More specifically, there exists a new threshold [Formula: see text], such that if [Formula: see text], then the system can have two positive interior equilibria, which leads to an interesting bistable phenomenon. This may have critical implications for controlling the antibiotic-resistance in a hospital.

PREFACE: IC-MSQUARE 2012: International Conference on Mathematical Modelling in Physical Sciences

NASA Astrophysics Data System (ADS)

Kosmas, Theocharis; Vagenas, Elias; Vlachos, Dimitrios

2013-02-01

The first International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE) took place in Budapest, Hungary, from Monday 3 to Friday 7 September 2012. The conference was attended by more than 130 participants, and hosted about 290 oral, poster and virtual papers by more than 460 pre-registered authors. The first IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields in which mathematical modelling is used, such as theoretical/mathematical physics, neutrino physics, non-integrable systems, dynamical systems, computational nanoscience, biological physics, computational biomechanics, complex networks, stochastic modelling, fractional statistics, DNA dynamics, and macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, two parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The mounting question is whether this occurred accidentally, or whether IC-MSQUARE is a necessity in the field of physical and mathematical modelling. For all of us working in the field, the existing and established conferences in this particular field suffer from two distinguished and recognized drawbacks: the first is the increasing orientation, while the second refers to the extreme specialization of the meetings. Therefore, a conference which aims to promote the knowledge and development of high-quality research in mathematical fields concerned with applications of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology, environmental sciences etc., appears to be a necessity. This is the key role that IC-MSQUARE will play. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contributions to IC-MSQUARE. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. Conference Chairmen Theocharis Kosmas Department of Physics, University of Ioannina Elias Vagenas RCAAM, Academy of Athens Dimitrios Vlachos Department of Computer Science and Technology, University of Peloponnese The PDF also contains a list of members of the International Scientific Committes and details of the Keynote and Invited Speakers.

Mathematical model of depolarization mechanism of conducted vasoreactivity

NASA Astrophysics Data System (ADS)

Neganova, Anastasiia Y.; Stiukhina, Elena S.; Postnov, Dmitry E.

2015-03-01

We address the problem of conducted vasodilation, the phenomenon which is also known as functional hyperemia. Specifically, we test the mechanism of nondecremental propagation of electric signals along endothelial cell layer recently hypothesized by Figueroa et al. By means of functional modeling we focus on possible nonlinear mechanisms that can underlie such regenerative pulse transmission (RPT). Since endothelial cells (EC) are generally known as electrically inexcitable, the possible role of ECs in RPT mechanisms is not evident. By means of mathematical modeling we check the dynamical self-consistency of Figueroa's hypothesis, as well as estimate the possible contribution of specific ionic currents to the suggested RPT mechanism.

Markov model of the loan portfolio dynamics considering influence of management and external economic factors

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana; Timofeeva, Galina

2016-12-01

Mathematical model of loan portfolio in the form of a controlled Markov chain with discrete time is considered. It is assumed that coefficients of migration matrix depend on corrective actions and external factors. Corrective actions include process of receiving applications, interaction with existing solvent and insolvent clients. External factors are macroeconomic indicators, such as inflation and unemployment rates, exchange rates, consumer price indices, etc. Changes in corrective actions adjust the intensity of transitions in the migration matrix. The mathematical model for forecasting the credit portfolio structure taking into account a cumulative impact of internal and external changes is obtained.

Attitude dynamics and control of spacecraft with a partially filled liquid tank and flexible panels

NASA Astrophysics Data System (ADS)

Liu, Feng; Yue, Baozeng; Zhao, Liangyu

2018-02-01

A liquid-filled flexible spacecraft is essentially a time-variant fully-coupled system, whose dynamics characteristics are closely associated with its motion features. This paper focuses on the mathematical modelling and attitude control of the spacecraft coupled with fuel sloshing dynamics and flexible solar panels vibration. The slosh motion is represented by a spherical pendulum, whose motion description method is improved by using split variable operation. Benefiting from this improvement, the nonlinear lateral sloshing and the rotary sloshing as well as the rigid motion of a liquid respect to the spacecraft can be approximately described. The assumed modes discretization method has been adopted to approximate the elastic displacements of the attached panels, and the coupled dynamics is derived by using the Lagrangian formulation. A variable substitution method is proposed to obtain the apparently-uncoupled mathematical model of the rigid-flexible-liquid spacecraft. After linearization, this model can be directly used for designing Lyapunov output-feedback attitude controller (OFAC). With only torque actuators, and attitude and rate sensors installed, this kind of attitude controller, as simulation results show, is capable of not only bringing the spacecraft to the desired orientation, but also suppressing the effect of flex and slosh on the attitude motion of the spacecraft.

A mathematical model of liver metabolism: from steady state to dynamic

NASA Astrophysics Data System (ADS)

Calvetti, D.; Kuceyeski, A.; Somersalo, E.

2008-07-01

The increase in Type 2 diabetes and other metabolic disorders has led to an intense focus on the areas of research related to metabolism. Because the liver is essential in regulating metabolite concentrations that maintain life, it is especially important to have good knowledge of the functions within this organ. In silico mathematical models that can adequately describe metabolite concentrations, flux and transport rates in the liver in vivo can be a useful predictive tool. Fully dynamic models, which contain expressions for Michaelis-Menten reaction kinetics can be utilized to investigate different metabolic states, for example exercise, fed or starved state. In this paper we describe a two compartment (blood and tissue) spatially lumped liver metabolism model. First, we use Bayesian Flux Balance Analysis (BFBA) to estimate the values of flux and transport rates at steady state, which agree closely with values from the literature. These values are then used to find a set of Michaelis-Menten parameters and initial concentrations which identify a dynamic model that can be used for exploring different metabolic states. In particular, we investigate the effect of doubling the concentration of lactate entering the system via the hepatic artery and portal vein. This change in lactate concentration forces the system to a new steady state, where glucose production is increased.

Fuzzy differential inclusions in atmospheric and medical cybernetics.

PubMed

Majumdar, Kausik Kumar; Majumder, Dwijesh Dutta

2004-04-01

Uncertainty management in dynamical systems is receiving attention in artificial intelligence, particularly in the fields of qualitative and model based reasoning. Fuzzy dynamical systems occupy a very important position in the class of uncertain systems. It is well established that the fuzzy dynamical systems represented by a set of fuzzy differential inclusions (FDI) are very convenient tools for modeling and simulation of various uncertain systems. In this paper, we discuss about the mathematical modeling of two very complex natural phenomena by means of FDIs. One of them belongs to the atmospheric cybernetics (the term has been used in a broad sense) of the genesis of a cyclonic storm (cyclogenesis), and the other belongs to the bio-medical cybernetics of the evolution of tumor in a human body. Since a discussion of the former already appears in a previous paper by the first author, here, we present very briefly a theoretical formalism of cyclone formation. On the other hand, we treat the latter system more elaborately. We solve the FDIs with the help of an algorithm developed in this paper to numerically simulate the mathematical models. From the simulation results thus obtained, we have drawn a number of interesting conclusions, which have been verified, and this vindicates the validity of our models.

A complete dynamic model of primary sedimentation.

PubMed

Paraskevas, P; Kolokithas, G; Lekkas, T

1993-11-01

A dynamic mathematical model for the primary clarifier of a wastewater treatment plant is described, which is represented by a general tanks-in-series model, to simulate insufficient mixing. The model quantifies successfully the diurnal response of both the suspended and dissolved species. It is general enough, so that the values of the parameters can be replaced with those applicable to a specific case. The model was verified through data from the Biological Centre of Metamorfosi, in Athens, Greece, and can be used to assist in the design of new plants or in the analysis and output predictions of existing ones.

Modelling and extraction technique for micro-doppler signature of aircraft rotor blades

NASA Astrophysics Data System (ADS)

Praveen, N.; Valarmathi, J.

2017-11-01

The process of detecting and distinguishing between different aircrafts has been a major point of interest in Defence applications. Micro-Doppler effect is one such phenomenon unique for aircrafts with different rotor dynamics and design. In this paper, we focus on deducing a mathematical model for micro-Doppler signature, of aircraft rotor blades assumed to be rotating in a plane perpendicular to the flying direction, induced on the incident radar signal. Also, we use the Wigner-Ville Distribution (WVD) to extract this signature from the radar return. This mathematical model is compared with the simulation results obtained from MATLAB, to validate the results and show the accurateness of the developed model.

Flight dynamics simulation modeling and control of a large flexible tiltrotor aircraft

NASA Astrophysics Data System (ADS)

Juhasz, Ondrej

A high order rotorcraft mathematical model is developed and validated against the XV-15 and a Large Civil Tiltrotor (LCTR) concept. The mathematical model is generic and allows for any rotorcraft configuration, from single main rotor helicopters to coaxial and tiltrotor aircraft. Rigid-body and inflow states, as well as flexible wing and blade states are used in the analysis. The separate modeling of each rotorcraft component allows for structural flexibility to be included, which is important when modeling large aircraft where structural modes affect the flight dynamics frequency ranges of interest, generally 1 to 20 rad/sec. Details of the formulation of the mathematical model are given, including derivations of structural, aerodynamic, and inertial loads. The linking of the components of the aircraft is developed using an approach similar to multibody analyses by exploiting a tree topology, but without equations of constraints. Assessments of the effects of wing flexibility are given. Flexibility effects are evaluated by looking at the nature of the couplings between rigid-body modes and wing structural modes and vice versa. The effects of various different forms of structural feedback on aircraft dynamics are analyzed. A proportional-integral feedback on the structural acceleration is deemed to be most effective at both improving the damping and reducing the overall excitation of a structural mode. A model following control architecture is then implemented on full order flexible LCTR models. For this aircraft, the four lowest frequency structural modes are below 20 rad/sec, and are thus needed for control law development and analysis. The impact of structural feedback on both Attitude-Command, Attitude-Hold (ACAH) and Translational Rate Command (TRC) response types are investigated. A rigid aircraft model has optimistic performance characteristics, and a control system designed for a rigid aircraft could potentially destabilize a flexible one. The various control systems are flown in a fixed-base simulator. Pilot inputs and aircraft performance are recorded and analyzed.

Mathematical modeling of climate change and malaria transmission dynamics: a historical review.

PubMed

Eikenberry, Steffen E; Gumel, Abba B

2018-04-24

Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease's geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the "million-murdering Death" of malaria.

Using Dynamic Software in Mathematics: The Case of Reflection Symmetry

ERIC Educational Resources Information Center

Tatar, Enver; Akkaya, Adnan; Kagizmanli, Türkan Berrin

2014-01-01

This study was carried out to examine the effects of computer-assisted instruction (CAI) using dynamic software on the achievement of students in mathematics in the topic of reflection symmetry. The study also aimed to ascertain the pre-service mathematics teachers' opinions on the use of CAI in mathematics lessons. In the study, a mixed research…