Models of Individual Trajectories in Computer-Assisted Instruction for Deaf Students. Technical Report No. 214.

ERIC Educational Resources Information Center

Suppes, P.; And Others

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1975-01-01

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Load influence on gear noise. [mathematical model for determining acoustic pressure level as function of load

NASA Technical Reports Server (NTRS)

Merticaru, V.

1974-01-01

An original mathematical model is proposed to derive equations for calculation of gear noise. These equations permit the acoustic pressure level to be determined as a function of load. Application of this method to three parallel gears is reported. The logical calculation scheme is given, as well as the results obtained.

Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study

ERIC Educational Resources Information Center

Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat

2015-01-01

The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

On the stochastic dissemination of faults in an admissible network

NASA Technical Reports Server (NTRS)

Kyrala, A.

1987-01-01

The dynamic distribution of faults in a general type network is discussed. The starting point is a uniquely branched network in which each pair of nodes is connected by a single branch. Mathematical expressions for the uniquely branched network transition matrix are derived to show that sufficient stationarity exists to ensure the validity of the use of the Markov Chain model to analyze networks. In addition the conditions for the use of Semi-Markov models are discussed. General mathematical expressions are derived in an examination of branch redundancy techniques commonly used to increase reliability.

Mathematical modeling of synthetic unit hydrograph case study: Citarum watershed

NASA Astrophysics Data System (ADS)

Islahuddin, Muhammad; Sukrainingtyas, Adiska L. A.; Kusuma, M. Syahril B.; Soewono, Edy

2015-09-01

Deriving unit hydrograph is very important in analyzing watershed's hydrologic response of a rainfall event. In most cases, hourly measures of stream flow data needed in deriving unit hydrograph are not always available. Hence, one needs to develop methods for deriving unit hydrograph for ungagged watershed. Methods that have evolved are based on theoretical or empirical formulas relating hydrograph peak discharge and timing to watershed characteristics. These are usually referred to Synthetic Unit Hydrograph. In this paper, a gamma probability density function and its variant are used as mathematical approximations of a unit hydrograph for Citarum Watershed. The model is adjusted with real field condition by translation and scaling. Optimal parameters are determined by using Particle Swarm Optimization method with weighted objective function. With these models, a synthetic unit hydrograph can be developed and hydrologic parameters can be well predicted.

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.

Comparison of actual oxygen delivery kinetics to those predicted by mathematical modeling following stage 1 palliation just prior to superior cavopulmonary anastomosis.

PubMed

Yuki, Koichi; DiNardo, James A

2015-02-01

Optimizing systemic oxygen delivery (DO2) and hemodynamics in children with hypoplastic left heart syndrome (HLHS) is a clinical challenge. Mathematical modeling of the HLHS circulation has been used to determine the relationship between oxygen kinetic parameters and DO2 and to determine how DO2 might be optimized. The model demonstrates that neither arterial oxygen saturation (SaO2) nor mixed venous oxygen saturation (SvO2) alone accurately predicts DO2. Oxygen delivery kinetics predicted by previously described mathematical modeling were compared with actual patients' hemodynamic data. We sought to determine which patient derived parameters correlated best with DO2. Patients with HLHS who underwent cardiac catheterization prior to surgery to create a superior cavopulmonary anastomosis from 2007 to 2011 were identified. Hemodynamic data obtained were compared with the data derived from the mathematical model. Correlations between SaO2, SvO2, SaO2-SvO2, SaO2/(SaO2-SvO2), pulmonary-to-systemic blood flow ratio (Qp/Qs), and DO2 were evaluated using both linear and nonlinear analyses, and R(2) was calculated. Patients' data fit most aspects of the mathematical model. DO2 had the best correlation with SaO2/(SaO2-SvO2; R(2) = 0.8755) followed by SaO2 -SvO2 (R(2) = 0.8063), while SaO2 or SvO2 alone did not demonstrate a significant correlation as predicated by the mathematical model (R(2) = 0.09564 and 0.4831, respectively). SaO2/(SaO2 -SvO2) would be useful clinically to track changes in DO2 that occur with changes in patient condition or with interventions. © 2014 John Wiley & Sons Ltd.

Validation of an instrument for mathematics enhancement teaching efficacy of Pacific Northwest agricultural educators

NASA Astrophysics Data System (ADS)

Jansen, Daniel J.

Teacher efficacy continues to be an important area of study in educational research. This study tested an instrument designed to assess the perceived efficacy of agricultural education teachers when engaged in lessons involving mathematics instruction. The study population of Oregon and Washington agricultural educators utilized in the validation of the instrument revealed important demographic findings and specific results related to teacher efficacy for the study population. An instrument was developed from the assimilation of three scales previously used and validated in efficacy research. Participants' mathematics teaching efficacy was assessed using a portion of the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and personal mathematics efficacy was evaluated by the mathematics self-belief instrument which was derived from the Betz and Hackett's Mathematics Self-Efficacy Scale. The final scale, the Teachers' Sense of Efficacy Scale (TSES) created by Tschannen-Moran and Woolfolk Hoy, examined perceived personal teaching efficacy. Structural equation modeling was used as the statistical analyses tool to validate the instrument and examine correlations between efficacy constructs used to determine potential professional development needs of the survey population. As part of the data required for validation of the Mathematics Enhancement Teaching Efficacy instrument, demographic information defining the population of Oregon and Washington agricultural educators was obtained and reported. A hypothetical model derived from teacher efficacy literature was found to be an acceptable model to verify construct validity and determine strength of correlations between the scales that defined the instrument. The instrument produced an alpha coefficient of .905 for reliability. Both exploratory and confirmatory factor analyses were used to verify construct and discriminate validity. Specifics results related to the survey population of agricultural educators concluded that personal mathematics efficacy has a stronger correlation with mathematics teaching efficacy than personal teaching efficacy of teachers for this population. The implications of such findings suggest that professional development and pre-service preparation should be more focused on mathematics content knowledge rather than pedagogical knowledge when the objective is to enhance mathematics in interdisciplinary lessons.

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952

Mathematical manipulative models: in defense of "beanbag biology".

PubMed

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Modeling of the dolphin's clicking sound source: The influence of the critical parameters

NASA Astrophysics Data System (ADS)

Dubrovsky, N. A.; Gladilin, A.; Møhl, B.; Wahlberg, M.

2004-07-01

A physical and a mathematical models of the dolphin’s source of echolocation clicks have been recently proposed. The physical model includes a bottle of pressurized air connected to the atmosphere with an underwater rubber tube. A compressing rubber ring is placed on the underwater portion of the tube. The ring blocks the air jet passing through the tube from the bottle. This ring can be brought into self-oscillation by the air jet. In the simplest case, the ring displacement follows a repeated triangular waveform. Because the acoustic pressure gradient is proportional to the second time derivative of the displacement, clicks arise at the bends of the displacement waveform. The mathematical model describes the dipole oscillations of a sphere “frozen” in the ring and calculates the waveform and the sound pressure of the generated clicks. The critical parameters of the mathematical model are the radius of the sphere and the peak value and duration of the triangular displacement curve. This model allows one to solve both the forward (deriving the properties of acoustic clicks from the known source parameters) and the inverse (calculating the source parameters from the acoustic data) problems. Data from click records of Odontocetes were used to derive both the displacement waveforms and the size of the “frozen sphere” or a structure functionally similar to it. The mathematical model predicts a maximum source level of up to 235 dB re 1 μPa at 1-m range when using a 5-cm radius of the “frozen” sphere and a 4-mm maximal displacement. The predicted sound pressure level is similar to that of the clicks produced by Odontocetest.

Reverse engineering of aircraft wing data using a partial differential equation surface model

NASA Astrophysics Data System (ADS)

Huband, Jacalyn Mann

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing. The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab. There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions. The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Determination of Flow Direction with Pressure Probes.

DTIC Science & Technology

1979-07-01

SECTION NUMBER I INTRODUCTION .......... .. ...................... 1 II A MATHEMATICAL MODEL OF PROBE AERODYNAMIC BEHAVIOR . . 4 2.1 Objectives...also postulated. 3 SECTION II A MATHEMATICAL MODEL OF PROBE AERODYNAMIC BEHAVIOR 2. 1 Objectives The objective of an aerodynamic probe - in the present...characLerizaLion of prode behavior , they are not capable of replacing individual probe caiibrarions. Tis is due to the limitations of the derivation itself, i.e

Mathematical modeling of silica deposition in Tongonan-I reinjection wells, Philippines

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

Malate, R.C.M.; O`Sullivan, M.J.

1993-10-01

Mathematical models of silica deposition are derived using the method of characteristics for the problem of variable rate injection into a well producing radially symmetric flow. Solutions are developed using the first order rate equation of silica deposition suggested by Rimstidt and Barnes (1980). The changes in porosity and permeability resulting from deposition are included in the models. The models developed are successfully applied in simulating the changes in injection capacity in some of the reinjection wells in Tongonan geothermal field, Philippines.

Maneuverability Estimation of High-Speed Craft

DTIC Science & Technology

2015-06-01

derived based on equations by Lewandowski and Denny- Hubble in order to find the fundamental maneuvering characteristics. The model is developed in...characteristic of high- speed craft. A mathematical model is derived based on equations by Lewandowski and Denny- Hubble in order to find the fundamental...33 C. EQUATIONS BY DENNY AND HUBBLE ................................................43 D. NOMOTO

A mathematical simulation model of a 1985-era tilt-rotor passenger aircraft

NASA Technical Reports Server (NTRS)

Mcveigh, M. A.; Widdison, C. A.

1976-01-01

A mathematical model for use in real-time piloted simulation of a 1985-era tilt rotor passenger aircraft is presented. The model comprises the basic six degrees-of-freedom equations of motion, and a large angle of attack representation of the airframe and rotor aerodynamics, together with equations and functions used to model turbine engine performance, aircraft control system and stability augmentation system. A complete derivation of the primary equations is given together with a description of the modeling techniques used. Data for the model is included in an appendix.

Mathematical neuroscience: from neurons to circuits to systems.

PubMed

Gutkin, Boris; Pinto, David; Ermentrout, Bard

2003-01-01

Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.

Mathematical models for Isoptera (Insecta) mound growth.

PubMed

Buschini, M L T; Abuabara, M A P; Petrere, Miguel

2008-08-01

In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.

Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

NASA Astrophysics Data System (ADS)

Morén, B.; Larsson, T.; Carlsson Tedgren, Å.

2018-03-01

High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.

PubMed

Sardar, Tridip; Saha, Bapi

2017-06-01

In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R 0 ). It is shown that if R 0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. Copyright © 2017 Elsevier Inc. All rights reserved.

Rigorous mathematical modelling for a Fast Corrector Power Supply in TPS

NASA Astrophysics Data System (ADS)

Liu, K.-B.; Liu, C.-Y.; Chien, Y.-C.; Wang, B.-S.; Wong, Y. S.

2017-04-01

To enhance the stability of beam orbit, a Fast Orbit Feedback System (FOFB) eliminating undesired disturbances was installed and tested in the 3rd generation synchrotron light source of Taiwan Photon Source (TPS) of National Synchrotron Radiation Research Center (NSRRC). The effectiveness of the FOFB greatly depends on the output performance of Fast Corrector Power Supply (FCPS); therefore, the design and implementation of an accurate FCPS is essential. A rigorous mathematical modelling is very useful to shorten design time and improve design performance of a FCPS. A rigorous mathematical modelling derived by the state-space averaging method for a FCPS in the FOFB of TPS composed of a full-bridge topology is therefore proposed in this paper. The MATLAB/SIMULINK software is used to construct the proposed mathematical modelling and to conduct the simulations of the FCPS. Simulations for the effects of the different resolutions of ADC on the output accuracy of the FCPS are investigated. A FCPS prototype is realized to demonstrate the effectiveness of the proposed rigorous mathematical modelling for the FCPS. Simulation and experimental results show that the proposed mathematical modelling is helpful for selecting the appropriate components to meet the accuracy requirements of a FCPS.

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

Several mathematical equations have been proposed to modeling nutrient-response curve for animal and human justified on the goodness of fit and/or on the biological mechanism. In this paper, a functional form of a generalized quantitative model based on Rayleigh distribution principle for description of nutrient-response phenomena is derived. The three parameters governing the curve a) has biological interpretation, b) may be used to calculate reliable estimates of nutrient response relationships, and c) provide the basis for deriving relationships between nutrient and physiological responses. The new function was successfully applied to fit the nutritional data obtained from 6 experiments including a wide range of nutrients and responses. An evaluation and comparison were also done based simulated data sets to check the suitability of new model and four-parameter logistic model for describing nutrient responses. This study indicates the usefulness and wide applicability of the new introduced, simple and flexible model when applied as a quantitative approach to characterizing nutrient-response curve. This new mathematical way to describe nutritional-response data, with some useful biological interpretations, has potential to be used as an alternative approach in modeling nutritional responses curve to estimate nutrient efficiency and requirements. PMID:29161271

Study of Adaptive Mathematical Models for Deriving Automated Pilot Performance Measurement Techniques. Volume I. Model Development.

ERIC Educational Resources Information Center

Connelly, Edward A.; And Others

A new approach to deriving human performance measures and criteria for use in automatically evaluating trainee performance is documented in this report. The ultimate application of the research is to provide methods for automatically measuring pilot performance in a flight simulator or from recorded in-flight data. An efficient method of…

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 mathematical techniques for the assimilation of remote sensing data into atmospheric models

NASA Technical Reports Server (NTRS)

Seinfeld, J. H. (Principal Investigator)

1982-01-01

The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The data assimilation problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three-dimensional concentration fields from atmospheric diffusion models. General conditions were derived for the reconstructability of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data was developed.

Development of mathematical techniques for the assimilation of remote sensing data into atmospheric models

NASA Technical Reports Server (NTRS)

Seinfeld, J. H. (Principal Investigator)

1982-01-01

The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three dimensional concentration fields from atmospheric diffusion models. General conditions are derived for the "reconstructability' of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data is developed.

Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment.

PubMed

Pirbodaghi, Tohid

2017-08-01

Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin-water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

A mathematical model of physiological processes and its application to the study of aging

NASA Technical Reports Server (NTRS)

Hibbs, A. R.; Walford, R. L.

1989-01-01

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

On Theoretical Limits of Dynamic Model Updating Using a Sensitivity-Based Approach

NASA Astrophysics Data System (ADS)

GOLA, M. M.; SOMÀ, A.; BOTTO, D.

2001-07-01

The present work deals with the determination of the newly discovered conditions necessary for model updating with the eigensensitivity approach. The treatment concerns the maximum number of identifiable parameters regarding the structure of the eigenvectors derivatives. A mathematical demonstration is based on the evaluation of the rank of the least-squares matrix and produces the algebraic limiting conditions. Numerical application to a lumped parameter structure is employed to validate the mathematical limits taking into account different subsets of mode shapes. The demonstration is extended to the calculation of the eigenvector derivatives with both the Fox and Kapoor, and Nelson methods. III conditioning of the least-squares sensitivity matrix is revealed through the covariance jump.

Irrigation water demand: A meta-analysis of price elasticities

NASA Astrophysics Data System (ADS)

Scheierling, Susanne M.; Loomis, John B.; Young, Robert A.

2006-01-01

Metaregression models are estimated to investigate sources of variation in empirical estimates of the price elasticity of irrigation water demand. Elasticity estimates are drawn from 24 studies reported in the United States since 1963, including mathematical programming, field experiments, and econometric studies. The mean price elasticity is 0.48. Long-run elasticities, those that are most useful for policy purposes, are likely larger than the mean estimate. Empirical results suggest that estimates may be more elastic if they are derived from mathematical programming or econometric studies and calculated at a higher irrigation water price. Less elastic estimates are found to be derived from models based on field experiments and in the presence of high-valued crops.

Optimal policies of non-cross-resistant chemotherapy on Goldie and Coldman's cancer model.

PubMed

Chen, Jeng-Huei; Kuo, Ya-Hui; Luh, Hsing Paul

2013-10-01

Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman's analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas' model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas' work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman's work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work. Copyright © 2013 Elsevier Inc. All rights reserved.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

2003-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

Calculating degree-based topological indices of dominating David derived networks

NASA Astrophysics Data System (ADS)

Ahmad, Muhammad Saeed; Nazeer, Waqas; Kang, Shin Min; Imran, Muhammad; Gao, Wei

2017-12-01

An important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the dominating David derived networks [1, 2, 3, 4, 5].

Integrative approaches for modeling regulation and function of the respiratory system.

PubMed

Ben-Tal, Alona; Tawhai, Merryn H

2013-01-01

Mathematical models have been central to understanding the interaction between neural control and breathing. Models of the entire respiratory system-which comprises the lungs and the neural circuitry that controls their ventilation-have been derived using simplifying assumptions to compartmentalize each component of the system and to define the interactions between components. These full system models often rely-through necessity-on empirically derived relationships or parameters, in addition to physiological values. In parallel with the development of whole respiratory system models are mathematical models that focus on furthering a detailed understanding of the neural control network, or of the several functions that contribute to gas exchange within the lung. These models are biophysically based, and rely on physiological parameters. They include single-unit models for a breathing lung or neural circuit, through to spatially distributed models of ventilation and perfusion, or multicircuit models for neural control. The challenge is to bring together these more recent advances in models of neural control with models of lung function, into a full simulation for the respiratory system that builds upon the more detailed models but remains computationally tractable. This requires first understanding the mathematical models that have been developed for the respiratory system at different levels, and which could be used to study how physiological levels of O2 and CO2 in the blood are maintained. Copyright © 2013 Wiley Periodicals, Inc.

The (Mathematical) Modeling Process in Biosciences.

PubMed

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

Mathematical modeling of tomographic scanning of cylindrically shaped test objects

NASA Astrophysics Data System (ADS)

Kapranov, B. I.; Vavilova, G. V.; Volchkova, A. V.; Kuznetsova, I. S.

2018-05-01

The paper formulates mathematical relationships that describe the length of the radiation absorption band in the test object for the first generation tomographic scan scheme. A cylindrically shaped test object containing an arbitrary number of standard circular irregularities is used to perform mathematical modeling. The obtained mathematical relationships are corrected with respect to chemical composition and density of the test object material. The equations are derived to calculate the resulting attenuation radiation from cobalt-60 isotope when passing through the test object. An algorithm to calculate the radiation flux intensity is provided. The presented graphs describe the dependence of the change in the γ-quantum flux intensity on the change in the radiation source position and the scanning angle of the test object.

Mathematical 3D modelling and sensitivity analysis of multipolar radiofrequency ablation in the spine.

PubMed

Matschek, Janine; Bullinger, Eric; von Haeseler, Friedrich; Skalej, Martin; Findeisen, Rolf

2017-02-01

Radiofrequency ablation is a valuable tool in the treatment of many diseases, especially cancer. However, controlled heating up to apoptosis of the desired target tissue in complex situations, e.g. in the spine, is challenging and requires experienced interventionalists. For such challenging situations a mathematical model of radiofrequency ablation allows to understand, improve and optimise the outcome of the medical therapy. The main contribution of this work is the derivation of a tailored, yet expandable mathematical model, for the simulation, analysis, planning and control of radiofrequency ablation in complex situations. The dynamic model consists of partial differential equations that describe the potential and temperature distribution during intervention. To account for multipolar operation, time-dependent boundary conditions are introduced. Spatially distributed parameters, like tissue conductivity and blood perfusion, allow to describe the complex 3D environment representing diverse involved tissue types in the spine. To identify the key parameters affecting the prediction quality of the model, the influence of the parameters on the temperature distribution is investigated via a sensitivity analysis. Simulations underpin the quality of the derived model and the analysis approach. The proposed modelling and analysis schemes set the basis for intervention planning, state- and parameter estimation, and control. Copyright © 2016. Published by Elsevier Inc.

Computing Linear Mathematical Models Of Aircraft

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1991-01-01

Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways.

PubMed

Alves, Rui; Vilaprinyo, Ester; Hernádez-Bermejo, Benito; Sorribas, Albert

2008-01-01

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

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.

A new mathematical model and control of a three-phase AC-DC voltage source converter

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

Blasko, V.; Kaura, V.

1997-01-01

A new mathematical model of the power circuit of a three-phase voltage source converter (VSC) was developed in the stationary and synchronous reference frames. The mathematical model was then used to analyze and synthesize the voltage and current control loops for the VSC. Analytical expressions were derived for calculating the gains and time constants of the current and voltage regulators. The mathematical model was used to control a 140-kW regenerative VSC. The synchronous reference frame model was used to define feedforward signals in the current regulators to eliminate the cross coupling between the d and q phases. It allowed themore » reduction of the current control loop to first-order plants and improved their tracking capability. The bandwidths of the current and voltage-control loops were found to be approximately 20 and 60 times (respectively) smaller than the sampling frequency. All control algorithms were implemented in a digital-signal processor. All results of the analysis were experimentally verified.« less

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.

Respiratory protective device design using control system techniques

NASA Technical Reports Server (NTRS)

Burgess, W. A.; Yankovich, D.

1972-01-01

The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.

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.

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

NASA Astrophysics Data System (ADS)

Falcke, Martin; Moein, Mahsa; TilÅ«naitÄ--, Agne; Thul, Rüdiger; Skupin, Alexander

2018-04-01

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system's general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Error enhancement in geomagnetic models derived from scalar data

NASA Technical Reports Server (NTRS)

Stern, D. P.; Bredekamp, J. H.

1975-01-01

An investigation conducted by Backus (1970) regarding the possible existence of two harmonic functions of certain characteristics in three-dimensional space is considered. The derivation of a model of the main geomagnetic field from scalar data is discussed along with a numerical simulation study. It is found that experimental discrepancies between vector field observations and the predictions of the model may have a mathematical origin, related to the work of Backus.

Objective estimation of tropical cyclone innercore surface wind structure using infrared satellite images

NASA Astrophysics Data System (ADS)

Zhang, Changjiang; Dai, Lijie; Ma, Leiming; Qian, Jinfang; Yang, Bo

2017-10-01

An objective technique is presented for estimating tropical cyclone (TC) innercore two-dimensional (2-D) surface wind field structure using infrared satellite imagery and machine learning. For a TC with eye, the eye contour is first segmented by a geodesic active contour model, based on which the eye circumference is obtained as the TC eye size. A mathematical model is then established between the eye size and the radius of maximum wind obtained from the past official TC report to derive the 2-D surface wind field within the TC eye. Meanwhile, the composite information about the latitude of TC center, surface maximum wind speed, TC age, and critical wind radii of 34- and 50-kt winds can be combined to build another mathematical model for deriving the innercore wind structure. After that, least squares support vector machine (LSSVM), radial basis function neural network (RBFNN), and linear regression are introduced, respectively, in the two mathematical models, which are then tested with sensitivity experiments on real TC cases. Verification shows that the innercore 2-D surface wind field structure estimated by LSSVM is better than that of RBFNN and linear regression.

Computing maximum-likelihood estimates for parameters of the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

Donato, David I.

2012-01-01

This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.

General existence principles for Stieltjes differential equations with applications to mathematical biology

NASA Astrophysics Data System (ADS)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

An evidential reasoning extension to quantitative model-based failure diagnosis

NASA Technical Reports Server (NTRS)

Gertler, Janos J.; Anderson, Kenneth C.

1992-01-01

The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied. A quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system. On the basis of the latter, diagnostic models are derived each of which comprises a set of orthogonal parity equations. To improve the robustness of the algorithm, several models may be used in parallel, providing potentially incomplete and/or conflicting inferences. Dempster's rule of combination is used to integrate evidence from the different models. The basic probability measures are assigned utilizing quantitative information extracted from the mathematical model and from online computation performed therewith.

Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

NASA Astrophysics Data System (ADS)

Kolev, M.; Nawrocki, S.; Zubik-Kowal, B.

2013-06-01

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.

VERTICAL INTEGRATION OF THREE-PHASE FLOW EQUATIONS FOR ANALYSIS OF LIGHT HYDROCARBON PLUME MOVEMENT

EPA Science Inventory

A mathematical model is derived for areal flow of water and light hydrocarbon in the presence of gas at atmospheric pressure. Closed-form expressions for the vertically integrated constitutive relations are derived based on a three-phase extension of the Brooks-Corey saturation-...

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.

A mathematical model for describing the mechanical behaviour of root canal instruments.

PubMed

Zhang, E W; Cheung, G S P; Zheng, Y F

2011-01-01

The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

Point spread function and depth-invariant focal sweep point spread function for plenoptic camera 2.0.

PubMed

Jin, Xin; Liu, Li; Chen, Yanqin; Dai, Qionghai

2017-05-01

This paper derives a mathematical point spread function (PSF) and a depth-invariant focal sweep point spread function (FSPSF) for plenoptic camera 2.0. Derivation of PSF is based on the Fresnel diffraction equation and image formation analysis of a self-built imaging system which is divided into two sub-systems to reflect the relay imaging properties of plenoptic camera 2.0. The variations in PSF, which are caused by changes of object's depth and sensor position variation, are analyzed. A mathematical model of FSPSF is further derived, which is verified to be depth-invariant. Experiments on the real imaging systems demonstrate the consistency between the proposed PSF and the actual imaging results.

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

The (Mathematical) Modeling Process in Biosciences

PubMed Central

Torres, Nestor V.; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063

Illness-death model: statistical perspective and differential equations.

PubMed

Brinks, Ralph; Hoyer, Annika

2018-01-27

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Spatially homogeneous rotating world models.

NASA Technical Reports Server (NTRS)

Ozsvath, I.

1971-01-01

The mathematical problem encountered when looking for the simplest expanding and rotating model of the universe without the compactness condition for the space sections is formulated. The Lagrangian function is derived for four different rotating universes simultaneously. These models correspond in a certain sense to Godel's (1950) ?symmetric case.'

Approaching mathematical model of the immune network based DNA Strand Displacement system.

PubMed

Mardian, Rizki; Sekiyama, Kosuke; Fukuda, Toshio

2013-12-01

One biggest obstacle in molecular programming is that there is still no direct method to compile any existed mathematical model into biochemical reaction in order to solve a computational problem. In this paper, the implementation of DNA Strand Displacement system based on nature-inspired computation is observed. By using the Immune Network Theory and Chemical Reaction Network, the compilation of DNA-based operation is defined and the formulation of its mathematical model is derived. Furthermore, the implementation on this system is compared with the conventional implementation by using silicon-based programming. From the obtained results, we can see a positive correlation between both. One possible application from this DNA-based model is for a decision making scheme of intelligent computer or molecular robot. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

NASA Astrophysics Data System (ADS)

Rodríguez, Clara Rojas; Fernández Calvo, Gabriel; Ramis-Conde, Ignacio; Belmonte-Beitia, Juan

2017-08-01

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

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.

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

Receptors as a master key for synchronization of rhythms

NASA Astrophysics Data System (ADS)

Nagano, Seido

2004-03-01

A simple, but general scheme to achieve synchronization of rhythms was derived. The scheme has been inductively generalized from the modelling study of cellular slime mold. It was clarified that biological receptors work as apparatuses that can convert external stimulus to the form of nonlinear interaction within individual oscillators. Namely, the mathematical model receptor works as a nonlinear coupling apparatus between nonlinear oscillators. Thus, synchronization is achieved as a result of competition between two kinds of non-linearities, and to achieve synchronization, even a small external stimulation via model receptors can change the characteristics of individual oscillators significantly. The derived scheme is very simple mathematically, but it is a very powerful scheme as numerically demonstrated. The biological receptor scheme should significantly help understanding of synchronization phenomena in biology since groups of limit cycle oscillators and receptors are ubiquitous in biological systems. Reference: S. Nagano, Phys Rev. E67, 056215(2003)

Mathematical concepts for modeling human behavior in complex man-machine systems

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1979-01-01

Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.

Mathematical model of one-man air revitalization system

NASA Technical Reports Server (NTRS)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

Full nonlinear treatment of the global thermospheric wind system. Part 1: Mathematical method and analysis of forces

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1973-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all the nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In part 1 the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analysed.

Mathematics in Marine Botany: Examples of the Modelling Process. Part II: Continuous Models.

ERIC Educational Resources Information Center

Nyman, Melvin A.; Brown, Murray T.

1996-01-01

Describes some continuous models for growth of the seaweed Macrocystis pyrifera. Uses observed growth rates over several months to derive first-order differential equations as models for growth rates of individual fronds. The nature of the solutions is analyzed and comparison between these theoretical results and documented characteristics of…

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

Theoretical Modelling of Sound Radiation from Plate

NASA Astrophysics Data System (ADS)

Zaman, I.; Rozlan, S. A. M.; Yusoff, A.; Madlan, M. A.; Chan, S. W.

2017-01-01

Recently the development of aerospace, automotive and building industries demands the use of lightweight materials such as thin plates. However, the plates can possibly add to significant vibration and sound radiation, which eventually lead to increased noise in the community. So, in this study, the fundamental concept of sound pressure radiated from a simply-supported thin plate (SSP) was analyzed using the derivation of mathematical equations and numerical simulation of ANSYS®. The solution to mathematical equations of sound radiated from a SSP was visualized using MATLAB®. The responses of sound pressure level were measured at far field as well as near field in the frequency range of 0-200 Hz. Result shows that there are four resonance frequencies; 12 Hz, 60 Hz, 106 Hz and 158 Hz were identified which represented by the total number of the peaks in the frequency response function graph. The outcome also indicates that the mathematical derivation correlated well with the simulation model of ANSYS® in which the error found is less than 10%. It can be concluded that the obtained model is reliable and can be applied for further analysis such as to reduce noise emitted from a vibrating thin plate.

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.

A variational data assimilation system for the range dependent acoustic model using the representer method: Theoretical derivations.

PubMed

Ngodock, Hans; Carrier, Matthew; Fabre, Josette; Zingarelli, Robert; Souopgui, Innocent

2017-07-01

This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.

A Gravitational, Mathematical Model for the Energy, Emitted Power and Longevity of the Sun and Stars that does not use E=mc^2

NASA Astrophysics Data System (ADS)

Morse Kingsley, James

2017-08-01

A gravitational mathematical model for the energy, radiated power and lifetime of the sun and stars is derived that does not use E=mc^2. The speed of solar flares, 200 to 1000km/sec is used to derive the surface temperature of the sun as 1.4(10^6)degrees K. Optical radiation results as gamma rays leave the sun's surface and traverse and lose energy to the ~10^6km of the sun's corona. The corona is a result of solar flares with a speed component of 424km/sec parallel to the sun's surface placing their atoms into gravitational orbit about the sun. The temperature, density, and pressure of the sun are derived as a function of r, i.e. the distance from the center of the sun. The complete article is chapter 11 of my text that can be found on my website www.jmkingsleyiii.info

Optimization of CW Fiber Lasers With Strong Nonlinear Cavity Dynamics

NASA Astrophysics Data System (ADS)

Shtyrina, O. V.; Efremov, S. A.; Yarutkina, I. A.; Skidin, A. S.; Fedoruk, M. P.

2018-04-01

In present work the equation for the saturated gain is derived from one-level gain equations describing the energy evolution inside the laser cavity. It is shown how to derive the parameters of the mathematical model from the experimental results. The numerically-estimated energy and spectrum of the signal are in good agreement with the experiment. Also, the optimization of the output energy is performed for a given set of model parameters.

Scaling Limit for a Generalization of the Nelson Model and its Application to Nuclear Physics

NASA Astrophysics Data System (ADS)

Suzuki, Akito

We study a mathematically rigorous derivation of a quantum mechanical Hamiltonian in a general framework. We derive such a Hamiltonian by taking a scaling limit for a generalization of the Nelson model, which is an abstract interaction model between particles and a Bose field with some internal degrees of freedom. Applying it to a model for the field of the nuclear force with isospins, we obtain a Schrödinger Hamiltonian with a matrix-valued potential, the one pion exchange potential, describing an effective interaction between nucleons.

Air Force Journal of Logistics. Volume 34, Numbers 3 and 4, 2011

DTIC Science & Technology

2011-01-01

best value. Since these scores are mathematically derived, they violate some agencies* procurement policies (those that require qualitative ratings...the trust fund assets will be exhausted and Social Security will lack the resources to pay all promised benefits. According to SSA actuaries ...education programs (masters degrees) than either the Air Force or the Army. This was quite surprising. Mathematical Model to Determine Senior Officers

A mathematical model for the deformation of the eyeball by an elastic band.

PubMed

Keeling, Stephen L; Propst, Georg; Stadler, Georg; Wackernagel, Werner

2009-06-01

In a certain kind of eye surgery, the human eyeball is deformed sustainably by the application of an elastic band. This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given.

The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations

ERIC Educational Resources Information Center

Tristanti, Lia Budi; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muskar, Makbul

2016-01-01

This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…

Study of Adaptive Mathematical Models for Deriving Automated Pilot Performance Measurement Techniques. Volume II. Appendices. Final Report.

ERIC Educational Resources Information Center

Connelly, E. M.; And Others

A new approach to deriving human performance measures and criteria for use in automatically evaluating trainee performance is described. Ultimately, this approach will allow automatic measurement of pilot performance in a flight simulator or from recorded in-flight data. An efficient method of representing performance data within a computer is…

Flight instrument and telemetry response and its inversion

NASA Technical Reports Server (NTRS)

Weinberger, M. R.

1971-01-01

Mathematical models of rate gyros, servo accelerometers, pressure transducers, and telemetry systems were derived and their parameters were obtained from laboratory tests. Analog computer simulations were used extensively for verification of the validity for fast and large input signals. An optimal inversion method was derived to reconstruct input signals from noisy output signals and a computer program was prepared.

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.

Simulation model for the Boeing 720B aircraft-flight control system in continuous flight.

DOT National Transportation Integrated Search

1971-08-01

A mathematical model of the Boeing 720B aircraft and autopilot has been derived. The model is representative of the 720B aircraft for continuous flight within a flight envelope defined by a Mach number of .4 at 20,000 feet altitude in a cruise config...

10 CFR 431.445 - Determination of small electric motor efficiency.

Code of Federal Regulations, 2010 CFR

2010-01-01

... determined either by testing in accordance with § 431.444 of this subpart, or by application of an... method. An AEDM applied to a basic model must be: (i) Derived from a mathematical model that represents... statistical analysis, computer simulation or modeling, or other analytic evaluation of performance data. (3...

Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology.

PubMed

Lei, Chon Lok; Wang, Ken; Clerx, Michael; Johnstone, Ross H; Hortigon-Vinagre, Maria P; Zamora, Victor; Allan, Andrew; Smith, Godfrey L; Gavaghan, David J; Mirams, Gary R; Polonchuk, Liudmila

2017-01-01

Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.

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.

Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

NASA Astrophysics Data System (ADS)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

On the validity of the arithmetic-geometric mean method to locate the optimal solution in a supply chain system

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2012-08-01

Cardenas-Barron [Cardenas-Barron, L.E. (2010) 'A Simple Method to Compute Economic order Quantities: Some Observations', Applied Mathematical Modelling, 34, 1684-1688] indicates that there are several functions in which the arithmetic-geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), 'A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives', Applied Mathematical Modelling, 33, 4388-4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), 'Comment on 'Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives', International Journal of Systems Science, 40, 1095-1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), 'A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage', Production Planning and Control, 19, 601-604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic-geometric mean method of Teng et al. (2009), Teng and Goyal (2009) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.

Modeling breath-enhanced jet nebulizers to estimate pulmonary drug deposition.

PubMed

Wee, Wallace B; Leung, Kitty; Coates, Allan L

2013-12-01

Predictable delivery of aerosol medication for a given patient and drug-device combination is crucial, both for therapeutic effect and to avoid toxicity. The gold standard for measuring pulmonary drug deposition (PDD) is gamma scintigraphy. However, these techniques expose patients to radiation, are complicated, and are relevant for only one patient and drug-device combination, making them less available. Alternatively, in vitro experiments have been used as a surrogate to estimate in vivo performance, but this is time-consuming and has few "in vitro to in vivo" correlations for therapeutics delivered by inhalation. An alternative method for determining inhaled mass and PDD is proposed by deriving and validating a mathematical model, for the individual breathing patterns of normal subjects and drug-device operating parameters. This model was evaluated for patients with cystic fibrosis (CF). This study is comprised of three stages: mathematical model derivation, in vitro testing, and in vivo validation. The model was derived from an idealized patient's respiration cycle and the steady-state operating characteristics of a drug-device combination. The model was tested under in vitro dynamic conditions that varied tidal volume, inspiration-to-expiration time, and breaths per minute. This approach was then extended to incorporate additional physiological parameters (dead space, aerodynamic particle size distribution) and validated against in vivo nuclear medicine data in predicting PDD in both normal subjects and those with CF. The model shows strong agreement with in vitro testing. In vivo testing with normal subjects yielded good agreement, but less agreement for patients with chronic obstructive lung disease and bronchiectasis from CF. The mathematical model was successful in accommodating a wide range of breathing patterns and drug-device combinations. Furthermore, the model has demonstrated its effectiveness in predicting the amount of aerosol delivered to "normal" subjects. However, challenges remain in predicting deposition in obstructive lung disease.

Curved-flow, rolling-flow, and oscillatory pure-yawing wind-tunnel test methods for determination of dynamic stability derivatives

NASA Technical Reports Server (NTRS)

Chambers, J. R.; Grafton, S. B.; Lutze, F. H.

1981-01-01

Dynamic stability derivatives are evaluated on the basis of rolling-flow, curved-flow and snaking tests. Attention is given to the hardware associated with curved-flow, rolling-flow and oscillatory pure-yawing wind-tunnel tests. It is found that the snaking technique, when combined with linear- and forced-oscillation methods, yields an important method for evaluating beta derivatives for current configurations at high angles of attack. Since the rolling flow model is fixed during testing, forced oscillations may be imparted to the model, permitting the measurement of damping and cross-derivatives. These results, when coupled with basic rolling-flow or rotary-balance data, yield a highly accurate mathematical model for studies of incipient spin and spin entry.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

System and method for anomaly detection

DOEpatents

Scherrer, Chad

2010-06-15

A system and method for detecting one or more anomalies in a plurality of observations is provided. In one illustrative embodiment, the observations are real-time network observations collected from a stream of network traffic. The method includes performing a discrete decomposition of the observations, and introducing derived variables to increase storage and query efficiencies. A mathematical model, such as a conditional independence model, is then generated from the formatted data. The formatted data is also used to construct frequency tables which maintain an accurate count of specific variable occurrence as indicated by the model generation process. The formatted data is then applied to the mathematical model to generate scored data. The scored data is then analyzed to detect anomalies.

Wind laws for shockless initialization. [numerical forecasting model

NASA Technical Reports Server (NTRS)

Ghil, M.; Shkoller, B.

1976-01-01

A system of diagnostic equations for the velocity field, or wind laws, was derived for each of a number of models of large-scale atmospheric flow. The derivation in each case is mathematically exact and does not involve any physical assumptions not already present in the prognostic equations, such as nondivergence or vanishing of derivatives of the divergence. Therefore, initial states computed by solving these diagnostic equations should be compatible with the type of motion described by the prognostic equations of the model and should not generate initialization shocks when inserted into the model. Numerical solutions of the diagnostic system corresponding to a barotropic model are exhibited. Some problems concerning the possibility of implementing such a system in operational numerical weather prediction are discussed.

Factor Analysis for Clustered Observations.

ERIC Educational Resources Information Center

Longford, N. T.; Muthen, B. O.

1992-01-01

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

Angular motion equations for a satellite with hinged flexible solar panel

NASA Astrophysics Data System (ADS)

Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

2016-11-01

Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

Adaptive Control Of Remote Manipulator

NASA Technical Reports Server (NTRS)

Seraji, Homayoun

1989-01-01

Robotic control system causes remote manipulator to follow closely reference trajectory in Cartesian reference frame in work space, without resort to computationally intensive mathematical model of robot dynamics and without knowledge of robot and load parameters. System, derived from linear multivariable theory, uses relatively simple feedforward and feedback controllers with model-reference adaptive control.

Derivation of an applied nonlinear Schroedinger equation

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

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

System identification of propagating wave segments in excitable media and its application to advanced control

NASA Astrophysics Data System (ADS)

Katsumata, Hisatoshi; Konishi, Keiji; Hara, Naoyuki

2018-04-01

The present paper proposes a scheme for controlling wave segments in excitable media. This scheme consists of two phases: in the first phase, a simple mathematical model for wave segments is derived using only the time series data of input and output signals for the media; in the second phase, the model derived in the first phase is used in an advanced control technique. We demonstrate with numerical simulations of the Oregonator model that this scheme performs better than a conventional control scheme.

Mathematical prediction of core body temperature from environment, activity, and clothing: The heat strain decision aid (HSDA).

PubMed

Potter, Adam W; Blanchard, Laurie A; Friedl, Karl E; Cadarette, Bruce S; Hoyt, Reed W

2017-02-01

Physiological models provide useful summaries of complex interrelated regulatory functions. These can often be reduced to simple input requirements and simple predictions for pragmatic applications. This paper demonstrates this modeling efficiency by tracing the development of one such simple model, the Heat Strain Decision Aid (HSDA), originally developed to address Army needs. The HSDA, which derives from the Givoni-Goldman equilibrium body core temperature prediction model, uses 16 inputs from four elements: individual characteristics, physical activity, clothing biophysics, and environmental conditions. These inputs are used to mathematically predict core temperature (T c ) rise over time and can estimate water turnover from sweat loss. Based on a history of military applications such as derivation of training and mission planning tools, we conclude that the HSDA model is a robust integration of physiological rules that can guide a variety of useful predictions. The HSDA model is limited to generalized predictions of thermal strain and does not provide individualized predictions that could be obtained from physiological sensor data-driven predictive models. This fully transparent physiological model should be improved and extended with new findings and new challenging scenarios. Published by Elsevier Ltd.

The experience of mathematical beauty and its neural correlates

PubMed Central

Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F.

2014-01-01

Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art. This makes it interesting to learn whether the experience of beauty derived from such a highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources. To determine this, we used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources. PMID:24592230

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

NASA Astrophysics Data System (ADS)

Muntean, S.; Ciocan, T.; Susan-Resiga, R. F.; Cervantes, M.; Nilsson, H.

2012-11-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Exploration of cellular reaction systems.

PubMed

Kirkilionis, Markus

2010-01-01

We discuss and review different ways to map cellular components and their temporal interaction with other such components to different non-spatially explicit mathematical models. The essential choices made in the literature are between discrete and continuous state spaces, between rule and event-based state updates and between deterministic and stochastic series of such updates. The temporal modelling of cellular regulatory networks (dynamic network theory) is compared with static network approaches in two first introductory sections on general network modelling. We concentrate next on deterministic rate-based dynamic regulatory networks and their derivation. In the derivation, we include methods from multiscale analysis and also look at structured large particles, here called macromolecular machines. It is clear that mass-action systems and their derivatives, i.e. networks based on enzyme kinetics, play the most dominant role in the literature. The tools to analyse cellular reaction networks are without doubt most complete for mass-action systems. We devote a long section at the end of the review to make a comprehensive review of related tools and mathematical methods. The emphasis is to show how cellular reaction networks can be analysed with the help of different associated graphs and the dissection into modules, i.e. sub-networks.

Development of guidelines for the definition of the relavant information content in data classes

NASA Technical Reports Server (NTRS)

Schmitt, E.

1973-01-01

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Prospects of a mathematical theory of human behavior in complex man-machine systems tasks. [time sharing computer analogy of automobile driving

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1978-01-01

A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.

A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new Belehdradek-type model for evaluating the effect of temperature on growth rate

USDA-ARS?s Scientific Manuscript database

A new mechanistic growth model was developed to describe microbial growth under isothermal conditions. The new mathematical model was derived from the basic observation of bacterial growth that may include lag, exponential, and stationary phases. With this model, the lag phase duration and exponen...

Lateral-Torsional Buckling Instability Caused by Individuals Walking on Wood Composite I-Joists

NASA Astrophysics Data System (ADS)

Villasenor Aguilar, Jose Maria

Recent research has shown that a significant number of the falls from elevation occur when laborers are working on unfinished structures. Workers walking on wood I-joists on roofs and floors are prone to fall hazards. Wood I-joists have been replacing dimension lumber for many floor systems and a substantial number of roof systems in light-frame construction. Wood I-joists are designed to resist axial stresses on the flanges and shear stresses on the web while minimizing material used. However, wood I-joists have poor resistance to applied lateral and torsional loads and are susceptible to lateral-torsional buckling instability. Workers walking on unbraced or partially braced wood I-joists can induce axial and lateral forces as well as twist. Experimental testing demonstrated that workers cause lateral-torsional buckling instability in wood I-joists. However, no research was found related to the lateral-torsional buckling instability induced by individuals walking on the wood I-joists. Furthermore, no research was found considering the effects of the supported end conditions and partial bracing in the lateral-torsional buckling instability of wood I-joists. The goal of this research was to derive mathematical models to predict the dynamic lateral-torsional buckling instability of wood composite I-joists loaded by individuals walking considering different supported end conditions and bracing system configurations. The dynamic lateral-torsional buckling instability was analyzed by linearly combining the static lateral-torsional buckling instability with the lateral bending motion of the wood Ijoists. Mathematical models were derived to calculate the static critical loads for the simply supported end condition and four wood I-joist hanger supported end conditions. Additionally, mathematical models were derived to calculate the dynamic maximum lateral displacements and positions of the individual walking on the wood Ijoists for the same five different supported end conditions. Three different lean-on bracing systems were investigated, non-bracing, one-bracing, and two-bracing systems. Mathematical models were derived to calculate the amount of constraint due to the lean-on bracing system. The derived mathematical models were validated by comparison to data from testing for all supported end conditions and bracing systems. The predicted critical loads using the static buckling theoretical models for the non-bracing system and the static buckling theoretical models combined with the bracing theoretical models for the simply and hanger supported end conditions agreed well with the critical loads obtained from testing for the two wood I-joist sizes investigated. The predicted maximum lateral displacements and individual positions using the bending motion theoretical models for the simply and hanger supported end conditions agreed well with the corresponding maximum lateral displacements and individual positions obtained from testing for both wood I-joist sizes. Results showed that; a) the supported end condition influenced the critical loads, maximum lateral displacements and individual positions, b) the bracing system increased the critical loads and reduced the maximum lateral displacements, c) the critical load increased as the load position displaced away from the wood I-joist mid-span, d) the critical load reduced as the initial lateral displacement of the wood I-joist increased and e) the wood I-joist mid-span was the critical point in the dynamic lateral-torsional buckling instability.

Nonlinear ARMA models for the D(st) index and their physical interpretation

NASA Technical Reports Server (NTRS)

Vassiliadis, D.; Klimas, A. J.; Baker, D. N.

1996-01-01

Time series models successfully reproduce or predict geomagnetic activity indices from solar wind parameters. A method is presented that converts a type of nonlinear filter, the nonlinear Autoregressive Moving Average (ARMA) model to the nonlinear damped oscillator physical model. The oscillator parameters, the growth and decay, the oscillation frequencies and the coupling strength to the input are derived from the filter coefficients. Mathematical methods are derived to obtain unique and consistent filter coefficients while keeping the prediction error low. These methods are applied to an oscillator model for the Dst geomagnetic index driven by the solar wind input. A data set is examined in two ways: the model parameters are calculated as averages over short time intervals, and a nonlinear ARMA model is calculated and the model parameters are derived as a function of the phase space.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

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

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Dose- and time-dependence of the host-mediated response to paclitaxel therapy: a mathematical modeling approach.

PubMed

Benguigui, Madeleine; Alishekevitz, Dror; Timaner, Michael; Shechter, Dvir; Raviv, Ziv; Benzekry, Sebastien; Shaked, Yuval

2018-01-05

It has recently been suggested that pro-tumorigenic host-mediated processes induced in response to chemotherapy counteract the anti-tumor activity of therapy, and thereby decrease net therapeutic outcome. Here we use experimental data to formulate a mathematical model describing the host response to different doses of paclitaxel (PTX) chemotherapy as well as the duration of the response. Three previously described host-mediated effects are used as readouts for the host response to therapy. These include the levels of circulating endothelial progenitor cells in peripheral blood and the effect of plasma derived from PTX-treated mice on migratory and invasive properties of tumor cells in vitro . A first set of mathematical models, based on basic principles of pharmacokinetics/pharmacodynamics, did not appropriately describe the dose-dependence and duration of the host response regarding the effects on invasion. We therefore provide an alternative mathematical model with a dose-dependent threshold, instead of a concentration-dependent one, that describes better the data. This model is integrated into a global model defining all three host-mediated effects. It not only precisely describes the data, but also correctly predicts host-mediated effects at different doses as well as the duration of the host response. This mathematical model may serve as a tool to predict the host response to chemotherapy in cancer patients, and therefore may be used to design chemotherapy regimens with improved therapeutic outcome by minimizing host mediated effects.

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

USGS Publications Warehouse

Iverson, R.M.

1993-01-01

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data. ?? 1993 International Association for Mathematical Geology.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

The role of mathematics for physics teaching and understanding

NASA Astrophysics Data System (ADS)

Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

2016-05-01

-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

Conditions for duality between fluxes and concentrations in biochemical networks

PubMed Central

Fleming, Ronan M.T.; Vlassis, Nikos; Thiele, Ines; Saunders, Michael A.

2016-01-01

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality. The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes. PMID:27345817

Conditions for duality between fluxes and concentrations in biochemical networks

DOE PAGES

Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines; ...

2016-06-23

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We alsomore » provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes« less

Conditions for duality between fluxes and concentrations in biochemical networks

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

Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We alsomore » provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes« less

On the Concept of Random Orientation in Far-Field Electromagnetic Scattering by Nonspherical Particles

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2017-01-01

Although the model of randomly oriented nonspherical particles has been used in a great variety of applications of far-field electromagnetic scattering, it has never been defined in strict mathematical terms. In this Letter we use the formalism of Euler rigid-body rotations to clarify the concept of statistically random particle orientations and derive its immediate corollaries in the form of most general mathematical properties of the orientation-averaged extinction and scattering matrices. Our results serve to provide a rigorous mathematical foundation for numerous publications in which the notion of randomly oriented particles and its light-scattering implications have been considered intuitively obvious.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Modeling Flow in Porous Media with Double Porosity/Permeability.

NASA Astrophysics Data System (ADS)

Seyed Joodat, S. H.; Nakshatrala, K. B.; Ballarini, R.

2016-12-01

Although several continuum models are available to study the flow of fluids in porous media with two pore-networks [1], they lack a firm theoretical basis. In this poster presentation, we will present a mathematical model with firm thermodynamic basis and a robust computational framework for studying flow in porous media that exhibit double porosity/permeability. The mathematical model will be derived by appealing to the maximization of rate of dissipation hypothesis, which ensures that the model is in accord with the second law of thermodynamics. We will also present important properties that the solutions under the model satisfy, along with an analytical solution procedure based on the Green's function method. On the computational front, a stabilized mixed finite element formulation will be derived based on the variational multi-scale formalism. The equal-order interpolation, which is computationally the most convenient, is stable under this formulation. The performance of this formulation will be demonstrated using patch tests, numerical convergence study, and representative problems. It will be shown that the pressure and velocity profiles under the double porosity/permeability model are qualitatively and quantitatively different from the corresponding ones under the classical Darcy equations. Finally, it will be illustrated that the surface pore-structure is not sufficient in characterizing the flow through a complex porous medium, which pitches a case for using advanced characterization tools like micro-CT. References [1] G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]," Journal of Applied Mathematics and Mechanics, vol. 24, pp. 1286-1303, 1960.

Formulation of a General Technique for Predicting Pneumatic Attenuation Errors in Airborne Pressure Sensing Devices

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.

1988-01-01

Presented is a mathematical model derived from the Navier-Stokes equations of momentum and continuity, which may be accurately used to predict the behavior of conventionally mounted pneumatic sensing systems subject to arbitrary pressure inputs. Numerical techniques for solving the general model are developed. Both step and frequency response lab tests were performed. These data are compared with solutions of the mathematical model and show excellent agreement. The procedures used to obtain the lab data are described. In-flight step and frequency response data were obtained. Comparisons with numerical solutions of the math model show good agreement. Procedures used to obtain the flight data are described. Difficulties encountered with obtaining the flight data are discussed.

Development of an Underactuated 2-DOF Wrist Joint using McKibben PAMs

NASA Astrophysics Data System (ADS)

Rajagopal, S. P.; Jain, S.; Ramasubramanian, S. N.; Johnson, B. V.; Dwivedy, S. K.

2014-10-01

In this work, model of an underactuated 2-DOF wrist joint with pneumatically actuated muscles is proposed. For the joint, McKibben-type artificial muscles are used in parallel configuration for the actuation. For each Degree of Freedom (DOF) one agonist-antagonist pair arrangement is usually used with a pulley mechanism. A mathematical model of wrist joint is derived using conventional forward kinematic analysis. The static model relating pressure in the muscle with the orientation of the wrist joint is obtained by combining the experimental data and mathematical model. Regulation of pressure can be achieved by pulse width modulation control of on/off solenoid valves. A set of free vibration experiments are done for the dynamic identification of the muscle characteristics.

Model verification of large structural systems

NASA Technical Reports Server (NTRS)

Lee, L. T.; Hasselman, T. K.

1977-01-01

A methodology was formulated, and a general computer code implemented for processing sinusoidal vibration test data to simultaneously make adjustments to a prior mathematical model of a large structural system, and resolve measured response data to obtain a set of orthogonal modes representative of the test model. The derivation of estimator equations is shown along with example problems. A method for improving the prior analytic model is included.

The Bean model in suprconductivity: Variational formulation and numerical solution

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

Prigozhin, L.

The Bean critical-state model describes the penetration of magnetic field into type-II superconductors. Mathematically, this is a free boundary problem and its solution is of interest in applied superconductivity. We derive a variational formulation for the Bean model and use it to solve two-dimensional and axially symmetric critical-state problems numerically. 25 refs., 9 figs., 1 tab.

Automating FEA programming

NASA Technical Reports Server (NTRS)

Sharma, Naveen

1992-01-01

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer.

Electrochemical carbon dioxide concentrator: Math model

NASA Technical Reports Server (NTRS)

Marshall, R. D.; Schubert, F. H.; Carlson, J. N.

1973-01-01

A steady state computer simulation model of an Electrochemical Depolarized Carbon Dioxide Concentrator (EDC) has been developed. The mathematical model combines EDC heat and mass balance equations with empirical correlations derived from experimental data to describe EDC performance as a function of the operating parameters involved. The model is capable of accurately predicting performance over EDC operating ranges. Model simulation results agree with the experimental data obtained over the prediction range.

A mathematical model for simulating noise suppression of lined ejectors

NASA Technical Reports Server (NTRS)

Watson, Willie R.

1994-01-01

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

Application of the Refined Integral Method in the mathematical modeling of drug delivery from one-layer torus-shaped devices.

PubMed

Helbling, Ignacio M; Ibarra, Juan C D; Luna, Julio A

2012-02-28

A mathematical modeling of controlled release of drug from one-layer torus-shaped devices is presented. Analytical solutions based on Refined Integral Method (RIM) are derived. The validity and utility of the model are ascertained by comparison of the simulation results with matrix-type vaginal rings experimental release data reported in the literature. For the comparisons, the pair-wise procedure is used to measure quantitatively the fit of the theoretical predictions to the experimental data. A good agreement between the model prediction and the experimental data is observed. A comparison with a previously reported model is also presented. More accurate results are achieved for small A/C(s) ratios. Copyright © 2011 Elsevier B.V. All rights reserved.

Laser Atmospheric Propagation Kinetics

DTIC Science & Technology

1975-07-01

the available data. Section III also describes the mathematical model used to calculate the relaxation of the vibrational degrees of freedom in...has been used. This relation is derived in Appendix C, 11 -30- ---— ^^^^UM^ MUfi L^^MAamMMWaaMbAaMMMMMAMÜMMMM MMUMfa*,«« M^Mi mmm \\i •s T...is when the change in the optical path length is of the order of \\/2-n. Mathematically , this is expressed by the formula t vf (n - l)4jrdx = O

QSAR modeling of cumulative environmental end-points for the prioritization of hazardous chemicals.

PubMed

Gramatica, Paola; Papa, Ester; Sangion, Alessandro

2018-01-24

The hazard of chemicals in the environment is inherently related to the molecular structure and derives simultaneously from various chemical properties/activities/reactivities. Models based on Quantitative Structure Activity Relationships (QSARs) are useful to screen, rank and prioritize chemicals that may have an adverse impact on humans and the environment. This paper reviews a selection of QSAR models (based on theoretical molecular descriptors) developed for cumulative multivariate endpoints, which were derived by mathematical combination of multiple effects and properties. The cumulative end-points provide an integrated holistic point of view to address environmentally relevant properties of chemicals.

The contribution of executive functions to emergent mathematic skills in preschool children.

PubMed

Espy, Kimberly Andrews; McDiarmid, Melanie M; Cwik, Mary F; Stalets, Melissa Meade; Hamby, Arlena; Senn, Theresa E

2004-01-01

Mathematical ability is related to both activation of the prefrontal cortex in neuroimaging studies of adults and to executive functions in school-age children. The purpose of this study was to determine whether executive functions were related to emergent mathematical proficiency in preschool children. Preschool children (N = 96) were administered an executive function battery that was reduced empirically to working memory (WM), inhibitory control (IC), and shifting abilities by calculating composite scores derived from principal component analysis. Both WM and IC predicted early arithmetic competency, with the observed relations robust after controlling statistically for child age, maternal education, and child vocabulary. Only IC accounted for unique variance in mathematical skills, after the contribution of other executive functions were controlled statistically as well. Specific executive functions are related to emergent mathematical proficiency in this age range. Longitudinal studies using structural equation modeling are necessary to better characterize these ontogenetic relations.

A Mixed Methods Analysis of Students' Understanding of Slope and Derivative Concepts and Students' Mathematical Dispositions

ERIC Educational Resources Information Center

Patel, Rita Manubhai

2013-01-01

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

The prediction of the flash point for binary aqueous-organic solutions.

PubMed

Liaw, Horng-Jang; Chiu, Yi-Yu

2003-07-18

A mathematical model, which may be used for predicting the flash point of aqueous-organic solutions, has been proposed and subsequently verified by experimentally-derived data. The results reveal that this model is able to precisely predict the flash point over the entire composition range of binary aqueous-organic solutions by way of utilizing the flash point data pertaining to the flammable component. The derivative of flash point with respect to composition (solution composition effect upon flash point) can be applied to process safety design/operation in order to identify as to whether the dilution of a flammable liquid solution with water is effective in reducing the fire and explosion hazard of the solution at a specified composition. Such a derivative equation was thus derived based upon the flash point prediction model referred to above and then verified by the application of experimentally-derived data.

Modeling of Two-Wheeled Self-Balancing Robot Driven by DC Gearmotors

NASA Astrophysics Data System (ADS)

Frankovský, P.; Dominik, L.; Gmiterko, A.; Virgala, I.; Kurylo, P.; Perminova, O.

2017-08-01

This paper is aimed at modelling a two-wheeled self-balancing robot driven by the geared DC motors. A mathematical model consists of two main parts, the model of robot's mechanical structure and the model of the actuator. Linearized equations of motion are derived and the overall model of the two-wheeled self-balancing robot is represented in state-space realization for the purpose of state feedback controller design.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions.

PubMed

Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji

2018-06-01

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Workshop Physics Activity Guide, Module 3: Heat Temperature and Nuclear Radiation, Thermodynamics, Kinetic Theory, Heat Engines, Nuclear Decay, and Random Monitoring (Units 16 - 18 & 28)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research.

Subsonic stability and control derivatives for an unpowered, remotely piloted 3/8-scale F-15 airplane model obtained from flight test

NASA Technical Reports Server (NTRS)

Iliff, K. W.; Maine, R. E.; Shafer, M. F.

1976-01-01

In response to the interest in airplane configuration characteristics at high angles of attack, an unpowered remotely piloted 3/8-scale F-15 airplane model was flight tested. The subsonic stability and control characteristics of this airplane model over an angle of attack range of -20 to 53 deg are documented. The remotely piloted technique for obtaining flight test data was found to provide adequate stability and control derivatives. The remotely piloted technique provided an opportunity to test the aircraft mathematical model in an angle of attack regime not previously examined in flight test. The variation of most of the derivative estimates with angle of attack was found to be consistent, particularly when the data were supplemented by uncertainty levels.

Investigation of approximate models of experimental temperature characteristics of machines

NASA Astrophysics Data System (ADS)

Parfenov, I. V.; Polyakov, A. N.

2018-05-01

This work is devoted to the investigation of various approaches to the approximation of experimental data and the creation of simulation mathematical models of thermal processes in machines with the aim of finding ways to reduce the time of their field tests and reducing the temperature error of the treatments. The main methods of research which the authors used in this work are: the full-scale thermal testing of machines; realization of various approaches at approximation of experimental temperature characteristics of machine tools by polynomial models; analysis and evaluation of modelling results (model quality) of the temperature characteristics of machines and their derivatives up to the third order in time. As a result of the performed researches, rational methods, type, parameters and complexity of simulation mathematical models of thermal processes in machine tools are proposed.

Estimation of dynamic rotor loads for the rotor systems research aircraft: Methodology development and validation

NASA Technical Reports Server (NTRS)

Duval, R. W.; Bahrami, M.

1985-01-01

The Rotor Systems Research Aircraft uses load cells to isolate the rotor/transmission systm from the fuselage. A mathematical model relating applied rotor loads and inertial loads of the rotor/transmission system to the load cell response is required to allow the load cells to be used to estimate rotor loads from flight data. Such a model is derived analytically by applying a force and moment balance to the isolated rotor/transmission system. The model is tested by comparing its estimated values of applied rotor loads with measured values obtained from a ground based shake test. Discrepancies in the comparison are used to isolate sources of unmodeled external loads. Once the structure of the mathematical model has been validated by comparison with experimental data, the parameters must be identified. Since the parameters may vary with flight condition it is desirable to identify the parameters directly from the flight data. A Maximum Likelihood identification algorithm is derived for this purpose and tested using a computer simulation of load cell data. The identification is found to converge within 10 samples. The rapid convergence facilitates tracking of time varying parameters of the load cell model in flight.

Engineering Students' Conceptions of the Derivative and Some Implications for Their Mathematical Education

ERIC Educational Resources Information Center

Bingolbali, E.; Monaghan, J.; Roper, T.

2007-01-01

This paper explores Mechanical Engineering students' conceptions of and preferences for conceptions of the derivative, and their views on mathematics. Data comes from pre-, post- and delayed post-tests, a preference test, interviews with students and an analysis of calculus courses. Data from Mathematics students is used to make comparisons with…

Analytical derivation: An epistemic game for solving mathematically based physics problems

NASA Astrophysics Data System (ADS)

Bajracharya, Rabindra R.; Thompson, John R.

2016-06-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Reliability model derivation of a fault-tolerant, dual, spare-switching, digital computer system

NASA Technical Reports Server (NTRS)

1974-01-01

A computer based reliability projection aid, tailored specifically for application in the design of fault-tolerant computer systems, is described. Its more pronounced characteristics include the facility for modeling systems with two distinct operational modes, measuring the effect of both permanent and transient faults, and calculating conditional system coverage factors. The underlying conceptual principles, mathematical models, and computer program implementation are presented.

Linearized mathematical models for De Havilland Canada "Buffalo & Twin Otter" STOL transports.

DOT National Transportation Integrated Search

1971-06-01

Linearized six degree of freedom rigid body aircraft equations of motion are presented in a stability axes system. Values of stability derivatives are estimated for two representative STOL aircraft - the DeHavilland of Canada 'Buffalo' and 'Twin Otte...

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Improving Odometric Accuracy for an Autonomous Electric Cart.

PubMed

Toledo, Jonay; Piñeiro, Jose D; Arnay, Rafael; Acosta, Daniel; Acosta, Leopoldo

2018-01-12

In this paper, a study of the odometric system for the autonomous cart Verdino, which is an electric vehicle based on a golf cart, is presented. A mathematical model of the odometric system is derived from cart movement equations, and is used to compute the vehicle position and orientation. The inputs of the system are the odometry encoders, and the model uses the wheels diameter and distance between wheels as parameters. With this model, a least square minimization is made in order to get the nominal best parameters. This model is updated, including a real time wheel diameter measurement improving the accuracy of the results. A neural network model is used in order to learn the odometric model from data. Tests are made using this neural network in several configurations and the results are compared to the mathematical model, showing that the neural network can outperform the first proposed model.

Model of Fluidized Bed Containing Reacting Solids and Gases

NASA Technical Reports Server (NTRS)

Bellan, Josette; Lathouwers, Danny

2003-01-01

A mathematical model has been developed for describing the thermofluid dynamics of a dense, chemically reacting mixture of solid particles and gases. As used here, "dense" signifies having a large volume fraction of particles, as for example in a bubbling fluidized bed. The model is intended especially for application to fluidized beds that contain mixtures of carrier gases, biomass undergoing pyrolysis, and sand. So far, the design of fluidized beds and other gas/solid industrial processing equipment has been based on empirical correlations derived from laboratory- and pilot-scale units. The present mathematical model is a product of continuing efforts to develop a computational capability for optimizing the designs of fluidized beds and related equipment on the basis of first principles. Such a capability could eliminate the need for expensive, time-consuming predesign testing.

Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management

NASA Astrophysics Data System (ADS)

Bellomo, N.; Clarke, D.; Gibelli, L.; Townsend, P.; Vreugdenhil, B. J.

2016-09-01

This paper proposes an essay concerning the understanding of human behaviours and crisis management of crowds in extreme situations, such as evacuation through complex venues. The first part focuses on the understanding of the main features of the crowd viewed as a living, hence complex system. The main concepts are subsequently addressed, in the second part, to a critical analysis of mathematical models suitable to capture them, as far as it is possible. Then, the third part focuses on the use, toward safety problems, of a model derived by the methods of the mathematical kinetic theory and theoretical tools of evolutionary game theory. It is shown how this model can depict critical situations and how these can be managed with the aim of minimizing the risk of catastrophic events.

Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

2018-04-01

In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

The S factor--a new derived hemodynamic oxygenation parameter--a useful tool for simplified mathematical modeling of global problems of oxygen transport.

PubMed

Farrell, K; Wasser, T

1997-01-01

We describe a new derived hemodynamic oxygenation parameter, the S factor (S). The factor is based on oxygen delivery and oxygen consumption and can range from -3 to 1. It allows simplified mathematical modeling of clinical problems of oxygen transport and can be applied to many clinical situations. A new hemodynamic oxygenation parameter, the S factor (S), is introduced as an aid to mathematical modeling. It is defined as follows: [formula: see text] (DO2 = oxygen delivery, VO2 = oxygen consumption) S can theoretically vary from -3 (DO2 = VO2) to +1 (VO2 = 0). When DO2/VO2 = 4 (ie. OER = 0.25), S = 0. An S < 0 implies utilization of reserve oxygen transport capacity. An S > 0 implies increased oxygen delivery in relation to oxygen consumption (ie. "shunted oxygen delivery"). By algebraic manipulation and substitution of the components of DO2 into Equation 1: DO2 = Q x Ca x 10 DO2 = Q [(Hb)(Sat)(1.36) + PaO2(.0031)] 10 (2) the following equations can be derived: [formula: see text] [formula: see text] Ca - Cv (Ca = arterial content, Cv = venous content) can be determined by substituting components of oxygen consumption: VO2 = Q (Ca - Cv) x 10 (5) into equation 1 and solving for Ca - Cv. [formula: see text] Equation 6 can be simplified to: [formula: see text] A previously defined relationship between mixed venous PO2 (PvO2) and DO2/VO2 (where calculated P50 is 26.6 +/- 1.0) can be used to modify S in a clinically relevant manner. PvO2 = 5.44D O2/VO2 + 18.16 (8) The relationship between S and PvO2 can be defined by substituting Equation 4 into Equation 1 and solving for PvO2 PvO2 = [21.76/(1-S)] + 18.16 (9) As an example, at a PvO2 of 28 torr (anaerobic threshold), S = -1.2. The relationship between PvO2 and S is shown in Figure 1. S, which can also be defined as 1-4(VO2/DO2) or 1-4(OER), is a useful tool for mathematical modeling of global problems of oxygen transport because the previously derived equations with the S value allow the components of oxygen transport to be interrelated in a clinically relevant manner. Additional advantages of using S in mathematical modeling are: 1. Conceptually it 'fits' in that in regards to the sign (+ or -), as a -S implies utilization of reserve oxygen transport capacity and a +S implies wasted or excess oxygen delivery (shunted). 2. These concepts are easily quantified using the S factor. 3. It 'spreads out' the difference between values for parameters (OER or S) integrating components of oxygen transport, ie. in the 'normal state' regarding oxygen transport, OER = 0.25 and S = 0. At the anaerobic threshold (PvO2 = 28 torr), OER = 0.55 and S = -1.2. Thus, the change in OER from 'normal state' to anaerobic threshold is 0.3 (0.55-0.25) and the change in S is 1.2. This represents a four-fold increase. Four examples of mathematical modeling of global problems of oxygen transport using the S factor are described below.

A Highly Similar Mathematical Model for Cerebral Blood Flow Velocity in Geriatric Patients with Suspected Cerebrovascular Disease

NASA Astrophysics Data System (ADS)

Liu, Bo; Li, Qi; Wang, Jisheng; Xiang, Hu; Ge, Hong; Wang, Hui; Xie, Peng

2015-10-01

Cerebral blood flow velocity(CBFV) is an important parameter for study of cerebral hemodynamics. However, a simple and highly similar mathematical model has not yet been established for analyzing CBFV. To alleviate this issue, through TCD examination in 100 geriatric patients with suspected cerebrovascular disease (46 males and 54 females), we established a representative eighth-order Fourier function Vx(t) that simulates the CBFV. The measured TCD waveforms were compared to those derived from Vx(t), an illustrative Kolmogorov-Smirnov test was employed to determine the validity. The results showed that the TCD waves could been reconstructed for patients with different CBFVs by implementing their variable heart rates and the formulated maximum/minimum of Vx(t). Comparisons between derived and measured TCD waveforms suggest that the two waveforms are very similar. The results confirm that CBFV can be well-modeled through an eighth-order Fourier function. This function Vx(t) can be used extensively for a prospective study of cerebral hemodynamics in geriatric patients with suspected cerebrovascular disease.

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Bouncing Balls and Graphing Derivatives

ERIC Educational Resources Information Center

Cory, Beth

2010-01-01

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

Control of thermal balance by a liquid circulating garment based on a mathematical representation of the human thermoregulatory system. Ph.D. Thesis - California Univ., Berkeley

NASA Technical Reports Server (NTRS)

Kuznetz, L. H.

1976-01-01

Test data and a mathematical model of the human thermoregulatory system were used to investigate control of thermal balance by means of a liquid circulating garment (LCG). The test data were derived from five series of experiments in which environmental and metabolic conditions were varied parametrically as a function of several independent variables, including LCG flowrate, LCG inlet temperature, net environmental heat exchange, surrounding gas ventilation rate, ambient pressure, metabolic rate, and subjective/obligatory cooling control. The resultant data were used to relate skin temperature to LCG water temperature and flowrate, to assess a thermal comfort band, to demonstrate the relationship between metabolic rate and LCG heat dissipation, and so forth. The usefulness of the mathematical model as a tool for data interpretation and for generation of trends and relationships among the various physiological parameters was also investigated and verified.

Semianalytical Solutions for Transport in Aquifer and Fractured Clay Matrix System

EPA Science Inventory

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of analytical solutions is derived based on specific initial and boundary conditions as well as ...

Towing Tank Tests on a Ram Wing in a Rectangular Guideway

DOT National Transportation Integrated Search

1973-07-01

The object of the study was to set the theoretical and experimental basis for a preliminary design of a ram wing vehicle. A simplified one-dimensional mathematical model is developed in an attempt to estimate the stability derivatives of this type of...

Computer-Generated Feedback on Student Writing

ERIC Educational Resources Information Center

Ware, Paige

2011-01-01

A distinction must be made between "computer-generated scoring" and "computer-generated feedback". Computer-generated scoring refers to the provision of automated scores derived from mathematical models built on organizational, syntactic, and mechanical aspects of writing. In contrast, computer-generated feedback, the focus of this article, refers…

BioModels: expanding horizons to include more modelling approaches and formats

PubMed Central

Nguyen, Tung V N; Graesslin, Martin; Hälke, Robert; Ali, Raza; Schramm, Jochen; Wimalaratne, Sarala M; Kothamachu, Varun B; Rodriguez, Nicolas; Swat, Maciej J; Eils, Jurgen; Eils, Roland; Laibe, Camille; Chelliah, Vijayalakshmi

2018-01-01

Abstract BioModels serves as a central repository of mathematical models representing biological processes. It offers a platform to make mathematical models easily shareable across the systems modelling community, thereby supporting model reuse. To facilitate hosting a broader range of model formats derived from diverse modelling approaches and tools, a new infrastructure for BioModels has been developed that is available at http://www.ebi.ac.uk/biomodels. This new system allows submitting and sharing of a wide range of models with improved support for formats other than SBML. It also offers a version-control backed environment in which authors and curators can work collaboratively to curate models. This article summarises the features available in the current system and discusses the potential benefit they offer to the users over the previous system. In summary, the new portal broadens the scope of models accepted in BioModels and supports collaborative model curation which is crucial for model reproducibility and sharing. PMID:29106614

The Erroneous Derivative Examples of Eleventh Grade Students

ERIC Educational Resources Information Center

Gur, Hulya; Barak, Basak

2007-01-01

The derivative is not only an important subject for mathematics but also is an important subject for engineering, physics, economy, chemistry, and statistics. Especially, mathematics depends on strongly preceding learning and the subject of derivative will be used in university education by all students. Therefore, it is one of the most important…

Analytical Derivation: An Epistemic Game for Solving Mathematically Based Physics Problems

ERIC Educational Resources Information Center

Bajracharya, Rabindra R.; Thompson, John R.

2016-01-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the "analytical derivation" game. This game involves deriving an…

Model-Based Policymaking: A Framework to Promote Ethical "Good Practice" in Mathematical Modeling for Public Health Policymaking.

PubMed

Boden, Lisa A; McKendrick, Iain J

2017-01-01

Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical "good practice" and are thus "fit for purpose" as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science-policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy.

Mathematical Modeling in Support of Military Operational Medicine

DTIC Science & Technology

2006-07-01

of PBPK models in toxicol- ogy research and chemical risk assessment today is pri- marily related to their ability to make more quantitative ...derived earlier. The biomechanical basis of SFC is established by its correlation with strain. (a) Pretest Scan (b) Posttest Fracture...Three-Dimensional Reconstruction of Pretest and Posttest CT Scans Cited References Vander Vorst, M., Stuhmiller, J., et al., (2003). Biomechanically

Constructing Ebola transmission chains from West Africa and estimating model parameters using internet sources.

PubMed

Pettey, W B P; Carter, M E; Toth, D J A; Samore, M H; Gundlapalli, A V

2017-07-01

During the recent Ebola crisis in West Africa, individual person-level details of disease onset, transmissions, and outcomes such as survival or death were reported in online news media. We set out to document disease transmission chains for Ebola, with the goal of generating a timely account that could be used for surveillance, mathematical modeling, and public health decision-making. By accessing public web pages only, such as locally produced newspapers and blogs, we created a transmission chain involving two Ebola clusters in West Africa that compared favorably with other published transmission chains, and derived parameters for a mathematical model of Ebola disease transmission that were not statistically different from those derived from published sources. We present a protocol for responsibly gleaning epidemiological facts, transmission model parameters, and useful details from affected communities using mostly indigenously produced sources. After comparing our transmission parameters to published parameters, we discuss additional benefits of our method, such as gaining practical information about the affected community, its infrastructure, politics, and culture. We also briefly compare our method to similar efforts that used mostly non-indigenous online sources to generate epidemiological information.

Temporal Subtraction of Digital Breast Tomosynthesis Images for Improved Mass Detection

DTIC Science & Technology

2009-11-01

imaging using two distinct methods7-15: mathematically based models defined by geometric primitives and voxelized models derived from real human...trees to complete them. We also plan to add further detail by defining the Cooper’s ligaments using geometrical NURBS surfaces. Realistic...generated model for the coronary arterial tree based on multislice CT and morphometric data," Medical Imaging 2006: Physics of Medical Imaging 6142

Biological control via "ecological" damping: An approach that attenuates non-target effects.

PubMed

Parshad, Rana D; Quansah, Emmanuel; Black, Kelly; Beauregard, Matthew

2016-03-01

In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population, that functions as a top predator, in a three-species food chain. We allow for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous", and uncontrollable population levels, in a finite time. We next improve the mathematical model and incorporate controls that are shown to drive down the invasive population growth and, in certain cases, eliminate blow-up. Hence, the population does not reach an uncontrollable level. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in Parshad et al. (2014). Lastly, we confirm the existence of spatiotemporal chaos. Copyright © 2016 Elsevier Inc. All rights reserved.

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

NASA Astrophysics Data System (ADS)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

A Quantitative Risk Analysis of Deficient Contractor Business System

DTIC Science & Technology

2012-04-30

Mathematically , Jorion’s concept of VaR looks like this: ( > ) ≤ 1 − (2) where, = ^Åèìáëáíáçå=oÉëÉ~êÅÜ=éêçÖê~ãW= `êÉ~íáåÖ=póåÉêÖó=Ñçê=fåÑçêãÉÇ=ÅÜ...presents three models for calculating VaR. The local-valuation method determines the value of a portfolio once and uses mathematical derivatives...management. In the insurance industry, actuarial data is applied to model risk and risk capital reserves are “held” to cover the expected values for

Mathematical modeling of tumor-induced immunosuppression by myeloid-derived suppressor cells: Implications for therapeutic targeting strategies.

PubMed

Shariatpanahi, Seyed Peyman; Shariatpanahi, Seyed Pooya; Madjidzadeh, Keivan; Hassan, Moustapha; Abedi-Valugerdi, Manuchehr

2018-04-07

Myeloid-derived suppressor cells (MDSCs) belong to immature myeloid cells that are generated and accumulated during the tumor development. MDSCs strongly suppress the anti-tumor immunity and provide conditions for tumor progression and metastasis. In this study, we present a mathematical model based on ordinary differential equations (ODE) to describe tumor-induced immunosuppression caused by MDSCs. The model consists of four equations and incorporates tumor cells, cytotoxic T cells (CTLs), natural killer (NK) cells and MDSCs. We also provide simulation models that evaluate or predict the effects of anti-MDSC drugs (e.g., l-arginine and 5-Fluorouracil (5-FU)) on the tumor growth and the restoration of anti-tumor immunity. The simulated results obtained using our model were in good agreement with the corresponding experimental findings on the expansion of splenic MDSCs, immunosuppressive effects of these cells at the tumor site and effectiveness of l-arginine and 5-FU on the re-establishment of antitumor immunity. Regarding this latter issue, our predictive simulation results demonstrated that intermittent therapy with low-dose 5-FU alone could eradicate the tumors irrespective of their origins and types. Furthermore, at the time of tumor eradication, the number of CTLs prevailed over that of cancer cells and the number of splenic MDSCs returned to the normal levels. Finally, our predictive simulation results also showed that the addition of l-arginine supplementation to the intermittent 5-FU therapy reduced the time of the tumor eradication and the number of iterations for 5-FU treatment. Thus, the present mathematical model provides important implications for designing new therapeutic strategies that aim to restore antitumor immunity by targeting MDSCs. Copyright © 2018 Elsevier Ltd. All rights reserved.

Pressure oscillation delivery to the lung: Computer simulation of neonatal breathing parameters.

PubMed

Al-Jumaily, Ahmed M; Reddy, Prasika I; Bold, Geoff T; Pillow, J Jane

2011-10-13

Preterm newborn infants may develop respiratory distress syndrome (RDS) due to functional and structural immaturity. A lack of surfactant promotes collapse of alveolar regions and airways such that newborns with RDS are subject to increased inspiratory effort and non-homogeneous ventilation. Pressure oscillation has been incorporated into one form of RDS treatment; however, how far it reaches various parts of the lung is still questionable. Since in-vivo measurement is very difficult if not impossible, mathematical modeling may be used as one way of assessment. Whereas many models of the respiratory system have been developed for adults, the neonatal lung remains essentially ill-described in mathematical models. A mathematical model is developed, which represents the first few generations of the tracheo-bronchial tree and the 5 lobes that make up the premature ovine lung. The elements of the model are derived using the lumped parameter approach and formulated in Simulink™ within the Matlab™ environment. The respiratory parameters at the airway opening compare well with those measured from experiments. The model demonstrates the ability to predict pressures, flows and volumes in the alveolar regions of a premature ovine lung. Copyright © 2011 Elsevier Ltd. All rights reserved.

A Conceptual and Procedural Research on the Hierarchical Structure of Mathematics Emerging in the Minds of University Students: An Example of Limit-Continuity-Integral-Derivative

ERIC Educational Resources Information Center

Dane, Arif; Çetin, Ömer Faruk; Bas, Fatih; Sagirli, Meryem Özturan

2016-01-01

In this present study, it was aimed to investigate whether the hierarchical structure of mathematics emerged in university students' minds or not, considering the concepts of limit, continuity derivative and integral from the perspective of students in the department of secondary school mathematics teacher training and the department of…

Lacosamide derivatives with anticonvulsant activity as carbonic anhydrase inhibitors. Molecular modeling, docking and QSAR analysis.

PubMed

Garro Martinez, Juan C; Vega-Hissi, Esteban G; Andrada, Matías F; Duchowicz, Pablo R; Torrens, Francisco; Estrada, Mario R

2014-01-01

Lacosamide is an anticonvulsant drug which presents carbonic anhydrase inhibition. In this paper, we analyzed the apparent relationship between both activities performing a molecular modeling, docking and QSAR studies on 18 lacosamide derivatives with known anticonvulsant activity. Docking results suggested the zinc-binding site of carbonic anhydrase is a possible target of lacosamide and lacosamide derivatives making favorable Van der Waals interactions with Asn67, Gln92, Phe131 and Thr200. The mathematical models revealed a poor relationship between the anticonvulsant activity and molecular descriptors obtained from DFT and docking calculations. However, a QSAR model was developed using Dragon software descriptors. The statistic parameters of the model are: correlation coefficient, R=0.957 and standard deviation, S=0.162. Our results provide new valuable information regarding the relationship between both activities and contribute important insights into the essential molecular requirements for the anticonvulsant activity.

Development of a mathematical model for the dissolution of uranium dioxide. II. Statistical model for the dissolution of uranium dioxide tablets in nitric acid

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

Zhukovskii, Yu.M.; Luksha, O.P.; Nenarokomov, E.A.

1988-03-01

We have derived a statistical model for the dissolution of uranium dioxide tablets for the 6 to 12 M concentration range and temperatures from 80/sup 0/C to the boiling point. The model differs qualitatively from the dissolution model for ground uranium dioxide. In the indicated range of experimental conditions, the mean-square deviation of the curves for the model from the experimental curves is not greater than 6%.

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

PubMed

Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

2011-08-01

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

A poroelastic medium saturated by a two-phase capillary fluid

NASA Astrophysics Data System (ADS)

Shelukhin, V. V.

2014-09-01

By Landau's approach developed for description of superfluidity of 2He, we derive a mathematical model for a poroelastic medium saturated with a two-phase capillary fluid. The model describes a three-velocity continuum with conservation laws which obey the basic principles of thermodynamics and which are consistent with the Galilean transformations. In contrast to Biot' linear theory, the equations derived allow for finite deformations. As the acoustic analysis reveals, there is one more longitudinal wave in comparison with the poroelastic medium saturated with a one-phase fluid. We prove that such a result is due to surface tension.

Ecological quality boundary-setting procedures: the Gulf of Riga case study.

PubMed

Aigars, Juris; Müller-Karulis, Bärbel; Martin, Georg; Jermakovs, Vadims

2008-03-01

Two approaches for setting ecological class boundaries, response curves and a simplified mathematical boundary-setting protocol, were tested for coastal, transitional and open waters in the Gulf of Riga, Baltic Sea. The simplified mathematical boundary-setting protocol defines acceptable ecological status based on expert judgment by a uniform relative deviation from reference conditions. In contrast, response curves derive class boundary definitions from observed changes in biological quality elements along environmental pressure gradients for class boundary definitions. Identification of relevant environmental pressures for the construction of response curves was based on a conceptual model of eutrophication in the Gulf of Riga. Response curves were successfully established for summer chlorophyll a and transparency, as well as for macrozoobenthos abundance in the Central Gulf, macrozoobenthos biotic coefficient in the Southern Gulf, and maximum depth of phytobenthos in the Northern Gulf. In the Gulf of Riga response curves almost always permitted a larger deviation from reference conditions than the 50% deviation applied for the simplified mathematical boundary-setting protocol. The case study clearly demonstrated that class boundary definitions should take into account the sensitivity of the target water body. Also, the class boundaries for different ecological quality elements were internally more consistent than those derived by the simplified mathematical boundary-setting protocol.

Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

NASA Astrophysics Data System (ADS)

Ekici, Can

2016-05-01

Fanger's predicted mean vote (PMV) equation is the result of the combined quantitative effects of the air temperature, mean radiant temperature, air velocity, humidity activity level and clothing thermal resistance. PMV is a mathematical model of thermal comfort which was developed by Fanger. The uncertainty budget of the PMV equation was developed according to GUM in this study. An example is given for the uncertainty model of PMV in the exemplification section of the study. Sensitivity coefficients were derived from the PMV equation. Uncertainty budgets can be seen in the tables. A mathematical model of the sensitivity coefficients of Ta, hc, T_{mrt}, T_{cl}, and Pa is given in this study. And the uncertainty budgets for hc, T_{cl}, and Pa are given in this study.

Mathematical Model Relating Uniaxial Compressive Behavior of Manufactured Sand Mortar to MIP-Derived Pore Structure Parameters

PubMed Central

Tian, Zhenghong; Bu, Jingwu

2014-01-01

The uniaxial compression response of manufactured sand mortars proportioned using different water-cement ratio and sand-cement ratio is examined. Pore structure parameters such as porosity, threshold diameter, mean diameter, and total amounts of macropores, as well as shape and size of micropores are quantified by using mercury intrusion porosimetry (MIP) technique. Test results indicate that strains at peak stress and compressive strength decreased with the increasing sand-cement ratio due to insufficient binders to wrap up entire sand. A compression stress-strain model of normal concrete extending to predict the stress-strain relationships of manufactured sand mortar is verified and agreed well with experimental data. Furthermore, the stress-strain model constant is found to be influenced by threshold diameter, mean diameter, shape, and size of micropores. A mathematical model relating stress-strain model constants to the relevant pore structure parameters of manufactured sand mortar is developed. PMID:25133257

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Toda hierarchies and their applications

NASA Astrophysics Data System (ADS)

Takasaki, Kanehisa

2018-05-01

The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz–Ladik (aka relativistic Toda) hierarchy can be derived from the 2D Toda hierarchy as reductions. These integrable hierarchies have been applied to various problems of mathematics and mathematical physics since 1990s. A recent example is a series of studies on models of statistical mechanics called the melting crystal model. This research has revealed that the aforementioned two reductions of the 2D Toda hierarchy underlie two different melting crystal models. Technical clues are a fermionic realization of the quantum torus algebra, special algebraic relations therein called shift symmetries, and a matrix factorization problem. The two melting crystal models thus exhibit remarkable similarity with the Hermitian and unitary matrix models for which the two reductions of the 2D Toda hierarchy play the role of fundamental integrable structures.

From puddles to planet: modeling approaches to vector-borne diseases at varying resolution and scale.

PubMed

Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A; Smith, David L

2015-08-01

Since the original Ross-Macdonald formulations of vector-borne disease transmission, there has been a broad proliferation of mathematical models of vector-borne disease, but many of these models retain most to all of the simplifying assumptions of the original formulations. Recently, there has been a new expansion of mathematical frameworks that contain explicit representations of the vector life cycle including aquatic stages, multiple vector species, host heterogeneity in biting rate, realistic vector feeding behavior, and spatial heterogeneity. In particular, there are now multiple frameworks for spatially explicit dynamics with movements of vector, host, or both. These frameworks are flexible and powerful, but require additional data to take advantage of these features. For a given question posed, utilizing a range of models with varying complexity and assumptions can provide a deeper understanding of the answers derived from models. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Mathematical model relating uniaxial compressive behavior of manufactured sand mortar to MIP-derived pore structure parameters.

PubMed

Tian, Zhenghong; Bu, Jingwu

2014-01-01

The uniaxial compression response of manufactured sand mortars proportioned using different water-cement ratio and sand-cement ratio is examined. Pore structure parameters such as porosity, threshold diameter, mean diameter, and total amounts of macropores, as well as shape and size of micropores are quantified by using mercury intrusion porosimetry (MIP) technique. Test results indicate that strains at peak stress and compressive strength decreased with the increasing sand-cement ratio due to insufficient binders to wrap up entire sand. A compression stress-strain model of normal concrete extending to predict the stress-strain relationships of manufactured sand mortar is verified and agreed well with experimental data. Furthermore, the stress-strain model constant is found to be influenced by threshold diameter, mean diameter, shape, and size of micropores. A mathematical model relating stress-strain model constants to the relevant pore structure parameters of manufactured sand mortar is developed.

A stochastic model for optimizing composite predictors based on gene expression profiles.

PubMed

Ramanathan, Murali

2003-07-01

This project was done to develop a mathematical model for optimizing composite predictors based on gene expression profiles from DNA arrays and proteomics. The problem was amenable to a formulation and solution analogous to the portfolio optimization problem in mathematical finance: it requires the optimization of a quadratic function subject to linear constraints. The performance of the approach was compared to that of neighborhood analysis using a data set containing cDNA array-derived gene expression profiles from 14 multiple sclerosis patients receiving intramuscular inteferon-beta1a. The Markowitz portfolio model predicts that the covariance between genes can be exploited to construct an efficient composite. The model predicts that a composite is not needed for maximizing the mean value of a treatment effect: only a single gene is needed, but the usefulness of the effect measure may be compromised by high variability. The model optimized the composite to yield the highest mean for a given level of variability or the least variability for a given mean level. The choices that meet this optimization criteria lie on a curve of composite mean vs. composite variability plot referred to as the "efficient frontier." When a composite is constructed using the model, it outperforms the composite constructed using the neighborhood analysis method. The Markowitz portfolio model may find potential applications in constructing composite biomarkers and in the pharmacogenomic modeling of treatment effects derived from gene expression endpoints.

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.

The Discriminating Power of Items that Measure More than One Dimension.

ERIC Educational Resources Information Center

Reckase, Mark D.

The work presented in this paper defined conceptually the concepts of multidimensional discrimination and information, derived mathematical expressions for the concepts for a particular multidimensional item response theory (IRT) model, and applied the concepts to actual test data. Multidimensional discrimination was defined as a function of the…

Synthetic tsunamis along the Israeli coast.

PubMed

Tobias, Joshua; Stiassnie, Michael

2012-04-13

The new mathematical model for tsunami evolution by Tobias & Stiassnie (Tobias & Stiassnie 2011 J. Geophys. Res. Oceans 116, C06026) is used to derive a synthetic tsunami database for the southern part of the Eastern Mediterranean coast. Information about coastal tsunami amplitudes, half-periods, currents and inundation levels is presented.

Deriving Differential Equations from Process Algebra Models in Reagent-Centric Style

NASA Astrophysics Data System (ADS)

Hillston, Jane; Duguid, Adam

The reagent-centric style of modeling allows stochastic process algebra models of biochemical signaling pathways to be developed in an intuitive way. Furthermore, once constructed, the models are amenable to analysis by a number of different mathematical approaches including both stochastic simulation and coupled ordinary differential equations. In this chapter, we give a tutorial introduction to the reagent-centric style, in PEPA and Bio-PEPA, and the way in which such models can be used to generate systems of ordinary differential equations.

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

Quantitative modelling in cognitive ergonomics: predicting signals passed at danger.

PubMed

Moray, Neville; Groeger, John; Stanton, Neville

2017-02-01

This paper shows how to combine field observations, experimental data and mathematical modelling to produce quantitative explanations and predictions of complex events in human-machine interaction. As an example, we consider a major railway accident. In 1999, a commuter train passed a red signal near Ladbroke Grove, UK, into the path of an express. We use the Public Inquiry Report, 'black box' data, and accident and engineering reports to construct a case history of the accident. We show how to combine field data with mathematical modelling to estimate the probability that the driver observed and identified the state of the signals, and checked their status. Our methodology can explain the SPAD ('Signal Passed At Danger'), generate recommendations about signal design and placement and provide quantitative guidance for the design of safer railway systems' speed limits and the location of signals. Practitioner Summary: Detailed ergonomic analysis of railway signals and rail infrastructure reveals problems of signal identification at this location. A record of driver eye movements measures attention, from which a quantitative model for out signal placement and permitted speeds can be derived. The paper is an example of how to combine field data, basic research and mathematical modelling to solve ergonomic design problems.

Study on the Influence of Building Materials on Indoor Pollutants and Pollution Sources

NASA Astrophysics Data System (ADS)

Wang, Yao

2018-01-01

The paper summarizes the achievements and problems of indoor air quality research at home and abroad. The pollutants and pollution sources in the room are analyzed systematically. The types of building materials and pollutants are also discussed. The physical and chemical properties and health effects of main pollutants were analyzed and studied. According to the principle of mass balance, the basic mathematical model of indoor air quality is established. Considering the release rate of pollutants and indoor ventilation, a mathematical model for predicting the concentration of indoor air pollutants is derived. The model can be used to analyze and describe the variation of pollutant concentration in indoor air, and to predict and calculate the concentration of pollutants in indoor air at a certain time. The results show that the mathematical model established in this study can be used to analyze and predict the variation law of pollutant concentration in indoor air. The evaluation model can be used to evaluate the impact of indoor air quality and evaluation of current situation. Especially in the process of building and interior decoration, through pre-evaluation, it can provide reliable design parameters for selecting building materials and determining ventilation volume.

Control of Stirling engine. Simplified, compressible model

NASA Astrophysics Data System (ADS)

Plotnikov, P. I.; Sokołowski, J.; Żochowski, A.

2016-06-01

A one-dimensional free boundary problem on a motion of a heavy piston in a tube filled with viscous gas is considered. The system of governing equations and boundary conditions is derived. The obtained system of differential equations can be regarded as a mathematical model of an exterior combustion engine. The existence of a weak solution to this model is proved. The problem of maximization of the total work of the engine is considered.

Model-Based Policymaking: A Framework to Promote Ethical “Good Practice” in Mathematical Modeling for Public Health Policymaking

PubMed Central

Boden, Lisa A.; McKendrick, Iain J.

2017-01-01

Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical “good practice” and are thus “fit for purpose” as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science–policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy. PMID:28424768

Modeling duckweed growth in wastewater treatment systems

USGS Publications Warehouse

Landesman, L.; Parker, N.C.; Fedler, C.B.; Konikoff, M.

2005-01-01

Species of the genera Lemnaceae, or duckweeds, are floating aquatic plants that show great promise for both wastewater treatment and livestock feed production. Research conducted in the Southern High Plains of Texas has shown that Lemna obscura grew well in cattle feedlot runoff water and produced leaf tissue with a high protein content. A model or mathematical expression derived from duckweed growth data was used to fit data from experiments conducted in a greenhouse in Lubbock, Texas. The relationship between duckweed growth and the total nitrogen concentration in the mediium follows the Mitscherlich Function and is similar to that of other plants. Empirically derived model equations have successfully predicted the growth response of Lemna obscura.

Threshold for extinction and survival in stochastic tumor immune system

NASA Astrophysics Data System (ADS)

Li, Dongxi; Cheng, Fangjuan

2017-10-01

This paper mainly investigates the stochastic character of tumor growth and extinction in the presence of immune response of a host organism. Firstly, the mathematical model describing the interaction and competition between the tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Then, the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells are derived by the rigorous theoretical proofs. Finally, stochastic simulation are taken to substantiate and illustrate the conclusion we have derived. The modeling results will be beneficial to understand to concept of immunoediting, and develop the cancer immunotherapy. Besides, our simple theoretical model can help to obtain new insight into the complexity of tumor growth.

On the mathematical analysis of Ebola hemorrhagic fever: deathly infection disease in West African countries.

PubMed

Atangana, Abdon; Goufo, Emile Franc Doungmo

2014-01-01

For a given West African country, we constructed a model describing the spread of the deathly disease called Ebola hemorrhagic fever. The model was first constructed using the classical derivative and then converted to the generalized version using the beta-derivative. We studied in detail the endemic equilibrium points and provided the Eigen values associated using the Jacobian method. We furthered our investigation by solving the model numerically using an iteration method. The simulations were done in terms of time and beta. The study showed that, for small portion of infected individuals, the whole country could die out in a very short period of time in case there is not good prevention.

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice.

PubMed

Whitcomb, David C; Ermentrout, G Bard

2004-08-01

To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation. A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT. This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion. A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

Measuring Near-Infrared Spectroscopy Derived Cerebral Autoregulation in Neonates: From Research Tool Toward Bedside Multimodal Monitoring

PubMed Central

Thewissen, Liesbeth; Caicedo, Alexander; Lemmers, Petra; Van Bel, Frank; Van Huffel, Sabine; Naulaers, Gunnar

2018-01-01

Introduction: Cerebral autoregulation (CAR), the ability of the human body to maintain cerebral blood flow (CBF) in a wide range of perfusion pressures, can be calculated by describing the relation between arterial blood pressure (ABP) and cerebral oxygen saturation measured by near-infrared spectroscopy (NIRS). In literature, disturbed CAR is described in different patient groups, using multiple measurement techniques and mathematical models. Furthermore, it is unclear to what extent cerebral pathology and outcome can be explained by impaired CAR. Aim and methods: In order to summarize CAR studies using NIRS in neonates, a systematic review was performed in the PUBMED and EMBASE database. To provide a general overview of the clinical framework used to study CAR, the different preprocessing methods and mathematical models are described and explained. Furthermore, patient characteristics, definition of impaired CAR and the outcome according to this definition is described organized for the different patient groups. Results: Forty-six articles were included in this review. Four patient groups were established: preterm infants during the transitional period, neonates receiving specific medication/treatment, neonates with congenital heart disease and neonates with hypoxic-ischemic encephalopathy (HIE) treated with therapeutic hypothermia. Correlation, coherence and transfer function (TF) gain are the mathematical models most frequently used to describe CAR. The definition of impaired CAR is depending on the mathematical model used. The incidence of intraventricular hemorrhage in preterm infants is the outcome variable most frequently correlated with impaired CAR. Hypotension, disease severity, dopamine treatment, injury on magnetic resonance imaging (MRI) and long term outcome are associated with impaired CAR. Prospective interventional studies are lacking in all research areas. Discussion and conclusion: NIRS derived CAR measurement is an important research tool to improve knowledge about central hemodynamic fluctuations during the transitional period, cerebral pharmacodynamics of frequently used medication (sedatives-inotropes) and cerebral effects of specific therapies in neonatology. Uniformity regarding measurement techniques and mathematical models is needed. Multimodal monitoring databases of neonatal intensive care patients of multiple centers, together with identical outcome parameters are needed to compare different techniques and make progress in this field. Real-time bedside monitoring of CAR, together with conventional monitoring, seems a promising technique to improve individual patient care. PMID:29868521

Estimating the Uncertain Mathematical Structure of Hydrological Model via Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Bulygina, N.; Gupta, H.; O'Donell, G.; Wheater, H.

2008-12-01

The structure of hydrological model at macro scale (e.g. watershed) is inherently uncertain due to many factors, including the lack of a robust hydrological theory at the macro scale. In this work, we assume that a suitable conceptual model for the hydrologic system has already been determined - i.e., the system boundaries have been specified, the important state variables and input and output fluxes to be included have been selected, and the major hydrological processes and geometries of their interconnections have been identified. The structural identification problem then is to specify the mathematical form of the relationships between the inputs, state variables and outputs, so that a computational model can be constructed for making simulations and/or predictions of system input-state-output behaviour. We show how Bayesian data assimilation can be used to merge both prior beliefs in the form of pre-assumed model equations with information derived from the data to construct a posterior model. The approach, entitled Bayesian Estimation of Structure (BESt), is used to estimate a hydrological model for a small basin in England, at hourly time scales, conditioned on the assumption of 3-dimensional state - soil moisture storage, fast and slow flow stores - conceptual model structure. Inputs to the system are precipitation and potential evapotranspiration, and outputs are actual evapotranspiration and streamflow discharge. Results show the difference between prior and posterior mathematical structures, as well as provide prediction confidence intervals that reflect three types of uncertainty: due to initial conditions, due to input and due to mathematical structure.

Preliminary study of TEC application in cooling system

NASA Astrophysics Data System (ADS)

Sulaiman, A. C.; Amin, N. A. M.; Saidon, M. S.; Majid, M. S. A.; Rahman, M. T. A.; Kazim, M. N. F. M.

2017-10-01

Integration of thermoelectric cooling (TEC) within a space cooling system in the lecturer room is studied. The studied area (air conditioned surrounding) is encapsulated with wall, floor, roof, and glass window. TEC module is placed on the glass window. The prototype of the studied compartment is designed using cabin container. The type and number of TEC module are studied and the effects on the cooling performance are analyzed as it is assumed to be tested within an air conditioned lecturer room. The experimental and mathematical modeling of the cooling system developed. It is expected that the mathematical modeling derived from this study will be used to estimate the use of the number of TEC module to be integrated with air conditioner unit where possible.

Using a mathematical model to evaluate the efficacy of TB control measures.

PubMed Central

Gammaitoni, L.; Nucci, M. C.

1997-01-01

We evaluated the efficacy of recommended tuberculosis (TB) infection control measures by using a deterministic mathematical model for airborne contagion. We examined the percentage of purified protein derivative conversions under various exposure conditions, environmental controlstrategies, and respiratory protective devices. We conclude that environmental control cannot eliminate the risk for TB transmission during high-risk procedures; respiratory protective devices, and particularly high-efficiency particulate air masks, may provide nearly complete protection if used with air filtration or ultraviolet irradiation. Nevertheless, the efficiency of these control measures decreases as the infectivity of the source case increases. Therefore, administrative control measures (e.g., indentifying and isolating patients with infectious TB) are the most effective because they substantially reduce the rate of infection. PMID:9284378

A hybrid model for traffic flow and crowd dynamics with random individual properties.

PubMed

Schleper, Veronika

2015-04-01

Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Quantitative reconstructions in multi-modal photoacoustic and optical coherence tomography imaging

NASA Astrophysics Data System (ADS)

Elbau, P.; Mindrinos, L.; Scherzer, O.

2018-01-01

In this paper we perform quantitative reconstruction of the electric susceptibility and the Grüneisen parameter of a non-magnetic linear dielectric medium using measurement of a multi-modal photoacoustic and optical coherence tomography system. We consider the mathematical model presented in Elbau et al (2015 Handbook of Mathematical Methods in Imaging ed O Scherzer (New York: Springer) pp 1169-204), where a Fredholm integral equation of the first kind for the Grüneisen parameter was derived. For the numerical solution of the integral equation we consider a Galerkin type method.

Soliton-type solutions for two models in mathematical physics

NASA Astrophysics Data System (ADS)

Al-Ghafri, K. S.

2018-04-01

In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.

Improving Mathematics Instruction Using Technology: A Vygotskian Perspective.

ERIC Educational Resources Information Center

Harvey, Francis A.; Charnitski, Christina Wotell

Strategies and programs for improving mathematics instruction should be derived from sound educational theory. The sociocultural learning theories of Vygotsky may offer guidance in developing technology-based mathematics curriculum materials consonant with the NCTM (National Council of Teachers of Mathematics) goals and objectives. Vygotsky's…

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 modeling of electrical activity of uterine muscle cells.

PubMed

Rihana, Sandy; Terrien, Jeremy; Germain, Guy; Marque, Catherine

2009-06-01

The uterine electrical activity is an efficient parameter to study the uterine contractility. In order to understand the ionic mechanisms responsible for its generation, we aimed at building a mathematical model of the uterine cell electrical activity based upon the physiological mechanisms. First, based on the voltage clamp experiments found in the literature, we focus on the principal ionic channels and their cognate currents involved in the generation of this electrical activity. Second, we provide the methodology of formulations of uterine ionic currents derived from a wide range of electrophysiological data. The model is validated step by step by comparing simulated voltage-clamp results with the experimental ones. The model reproduces successfully the generation of single spikes or trains of action potentials that fit with the experimental data. It allows analyzing ionic channels implications. Likewise, the calcium-dependent conductance influences significantly the cellular oscillatory behavior.

Mathematical description of drug-target interactions: application to biologics that bind to targets with two binding sites.

PubMed

Gibiansky, Leonid; Gibiansky, Ekaterina

2018-02-01

The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

Bipotential continuum models for granular mechanics

NASA Astrophysics Data System (ADS)

Goddard, Joe

2014-03-01

Most currently popular continuum models for granular media are special cases of a generalized Maxwell fluid model, which describes the evolution of stress and internal variables such as granular particle fraction and fabric,in terms of imposed strain rate. It is shown how such models can be obtained from two scalar potentials, a standard elastic free energy and a ``dissipation potential'' given rigorously by the mathematical theory of Edelen. This allows for a relatively easy derivation of properly invariant continuum models for granular media and fluid-particle suspensions within a thermodynamically consistent framework. The resulting continuum models encompass all the prominent regimes of granular flow, ranging from the quasi-static to rapidly sheared, and are readily extended to include higher-gradient or Cosserat effects. Models involving stress diffusion, such as that proposed recently by Kamrin and Koval (PRL 108 178301), provide an alternative approach that is mentioned in passing. This paper provides a brief overview of a forthcoming review articles by the speaker (The Princeton Companion to Applied Mathematics, and Appl. Mech. Rev.,in the press, 2013).

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

An advanced model framework for solid electrolyte intercalation batteries.

PubMed

Landstorfer, Manuel; Funken, Stefan; Jacob, Timo

2011-07-28

Recent developments of solid electrolytes, especially lithium ion conductors, led to all solid state batteries for various applications. In addition, mathematical models sprout for different electrode materials and battery types, but are missing for solid electrolyte cells. We present a mathematical model for ion flux in solid electrolytes, based on non-equilibrium thermodynamics and functional derivatives. Intercalated ion diffusion within the electrodes is further considered, allowing the computation of the ion concentration at the electrode/electrolyte interface. A generalized Frumkin-Butler-Volmer equation describes the kinetics of (de-)intercalation reactions and is here extended to non-blocking electrodes. Using this approach, numerical simulations were carried out to investigate the space charge region at the interface. Finally, discharge simulations were performed to study different limitations of an all solid state battery cell. This journal is © the Owner Societies 2011

Linear Sigma Model Toolshed for D-brane Physics

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

Hellerman, Simeon

Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physic complementary to that of recent work of Douglas.

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

A Formal Theory of Perception. Technical Report No. 161.

ERIC Educational Resources Information Center

Rottmayer, William Arthur

An attempt to build a mathematical model of a device that could learn geometry is discussed. The report discusses the background and motivation of the study, the coding problem, the derivation of Suppes "Stimulus-Response Theory of Finite Automata" used in the work in learning theory, and a summary of the technical work. (DB)

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.

Biofiltration of methanol vapor

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

Shareefdeen, Z.; Baltzis, B.C.; Oh, Youngsook

1993-03-05

Biofiltration of solvent and fuel vapors may offer a cost-effective way to comply with increasingly strict air emission standards. An important step in the development of this technology is to derive and validate mathematical models of the biofiltration process for predictive and scaleup calculations. For the study of methanol vapor biofiltration, an 8-membered bacterial consortium was obtained from methanol-exposed soil. The bacteria were immobilized on solid support and packed into a 5-cm diameter, 60-cm-high column provided with appropriate flowmeters and sampling ports. The solid support was prepared by mixing two volumes of peat with three volumes of perlite particles. Twomore » series of experiments were performed. In the first, the inlet methanol concentration was kept constant while the superficial air velocity was varied from run to run. In the second series, the air flow rate (velocity) was kept constant while the inlet methanol concentration was varied. The unit proved effective in removing methanol at rates up to 112.8 g h[sup [minus]1] m[sup [minus]3] packing. A mathematical model has been derived and validated. The model described and predicted experimental results closely. Both experimental data and model predictions suggest that the methanol biofiltration process was limited by oxygen diffusion and methanol degradation kinetics.« less

Comparison of mathematic models for assessment of glomerular filtration rate with electron-beam CT in pigs.

PubMed

Daghini, Elena; Juillard, Laurent; Haas, John A; Krier, James D; Romero, Juan C; Lerman, Lilach O

2007-02-01

To prospectively compare in pigs three mathematic models for assessment of glomerular filtration rate (GFR) on electron-beam (EB) computed tomographic (CT) images, with concurrent inulin clearance serving as the reference standard. This study was approved by the institutional animal care and use committee. Inulin clearance was measured in nine pigs (18 kidneys) and compared with single-kidney GFR assessed from renal time-attenuation curves (TACs) obtained with EB CT before and after infusion of the vasodilator acetylcholine. CT-derived GFR was calculated with the original and modified Patlak methods and with previously validated extended gamma variate modeling of first-pass cortical TACs. Statistical analysis was performed to assess correlation between CT methods and inulin clearance for estimation of GFR with least-squares regression analysis and Bland-Altman graphical representation. Comparisons within groups were performed with a paired t test. GFR assessed with the original Patlak method indicated poor correlation with inulin clearance, whereas GFR assessed with the modified Patlak method (P < .001, r = 0.75) and with gamma variate modeling (P < .001, r = 0.79) correlated significantly with inulin clearance and indicated an increase in response to acetylcholine. CT-derived estimates of GFR can be significantly improved by modifications in image analysis methods (eg, use of a cortical region of interest). (c) RSNA, 2007.

Dynamic Creep Buckling: Analysis of Shell Structures Subjected to Time-dependent Mechanical and Thermal Loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1985-01-01

The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.

Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach.

PubMed

Mahasa, Khaphetsi Joseph; Eladdadi, Amina; de Pillis, Lisette; Ouifki, Rachid

2017-01-01

In the present paper, we address by means of mathematical modeling the following main question: How can oncolytic virus infection of some normal cells in the vicinity of tumor cells enhance oncolytic virotherapy? We formulate a mathematical model describing the interactions between the oncolytic virus, the tumor cells, the normal cells, and the antitumoral and antiviral immune responses. The model consists of a system of delay differential equations with one (discrete) delay. We derive the model's basic reproductive number within tumor and normal cell populations and use their ratio as a metric for virus tumor-specificity. Numerical simulations are performed for different values of the basic reproduction numbers and their ratios to investigate potential trade-offs between tumor reduction and normal cells losses. A fundamental feature unravelled by the model simulations is its great sensitivity to parameters that account for most variation in the early or late stages of oncolytic virotherapy. From a clinical point of view, our findings indicate that designing an oncolytic virus that is not 100% tumor-specific can increase virus particles, which in turn, can further infect tumor cells. Moreover, our findings indicate that when infected tissues can be regenerated, oncolytic viral infection of normal cells could improve cancer treatment.

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

NASA Astrophysics Data System (ADS)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

Study on the Mathematical Model of Dielectric Recovery Characteristics in High Voltage SF6 Circuit Breaker

NASA Astrophysics Data System (ADS)

Lin, Xin; Wang, Feiming; Xu, Jianyuan; Xia, Yalong; Liu, Weidong

2016-03-01

According to the stream theory, this paper proposes a mathematical model of the dielectric recovery characteristic based on the two-temperature ionization equilibrium equation. Taking the dynamic variation of charged particle's ionization and attachment into account, this model can be used in collaboration with the Coulomb collision model, which gives the relationship of the heavy particle temperature and electron temperature to calculate the electron density and temperature under different pressure and electric field conditions, so as to deliver the breakdown electric field strength under different pressure conditions. Meanwhile an experiment loop of the circuit breaker has been built to measure the breakdown voltage. It is shown that calculated results are in conformity with experiment results on the whole while results based on the stream criterion are larger than experiment results. This indicates that the mathematical model proposed here is more accurate for calculating the dielectric recovery characteristic, it is derived from the stream model with some improvement and refinement and has great significance for increasing the simulation accuracy of circuit breaker's interruption characteristic. supported by Science and Technology Project of State Grid Corporation of China (No. GY17201200063), National Natural Science Foundation of China (No. 51277123), Basic Research Project of Liaoning Key Laboratory of Education Department (LZ2015055)

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes

PubMed Central

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-01-01

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed. PMID:28335425

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes.

PubMed

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-03-14

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed.

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

PubMed

Ross, E W; Taub, I A; Doona, C J; Feeherry, F E; Kustin, K

2005-03-15

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

DRS: Derivational Reasoning System

NASA Technical Reports Server (NTRS)

Bose, Bhaskar

1995-01-01

The high reliability requirements for airborne systems requires fault-tolerant architectures to address failures in the presence of physical faults, and the elimination of design flaws during the specification and validation phase of the design cycle. Although much progress has been made in developing methods to address physical faults, design flaws remain a serious problem. Formal methods provides a mathematical basis for removing design flaws from digital systems. DRS (Derivational Reasoning System) is a formal design tool based on advanced research in mathematical modeling and formal synthesis. The system implements a basic design algebra for synthesizing digital circuit descriptions from high level functional specifications. DRS incorporates an executable specification language, a set of correctness preserving transformations, verification interface, and a logic synthesis interface, making it a powerful tool for realizing hardware from abstract specifications. DRS integrates recent advances in transformational reasoning, automated theorem proving and high-level CAD synthesis systems in order to provide enhanced reliability in designs with reduced time and cost.

Quantum Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-09-01

Foreword; Preface; Acknowledgements; 1. Synopsis; Part I. Fundamental Concepts of Finance: 2. Introduction to finance; 3. Derivative securities; Part II. Systems with Finite Number of Degrees of Freedom: 4. Hamiltonians and stock options; 5. Path integrals and stock options; 6. Stochastic interest rates' Hamiltonians and path integrals; Part III. Quantum Field Theory of Interest Rates Models: 7. Quantum field theory of forward interest rates; 8. Empirical forward interest rates and field theory models; 9. Field theory of Treasury Bonds' derivatives and hedging; 10. Field theory Hamiltonian of forward interest rates; 11. Conclusions; Appendix A: mathematical background; Brief glossary of financial terms; Brief glossary of physics terms; List of main symbols; References; Index.

Immunological self-tolerance: Lessons from mathematical modeling

NASA Astrophysics Data System (ADS)

Carneiro, Jorge; Paixao, Tiago; Milutinovic, Dejan; Sousa, Joao; Leon, Kalet; Gardner, Rui; Faro, Jose

2005-12-01

One of the fundamental properties of the immune system is its capacity to avoid autoimmune diseases. The mechanism underlying this process, known as self-tolerance, is hitherto unresolved but seems to involve the control of clonal expansion of autoreactive lymphocytes. This article reviews mathematical modeling of self-tolerance, addressing two specific hypotheses. The first hypothesis posits that self-tolerance is mediated by tuning of activation thresholds, which makes autoreactive T lymphocytes reversibly "anergic" and unable to proliferate. The second hypothesis posits that the proliferation of autoreactive T lymphocytes is instead controlled by specific regulatory T lymphocytes. Models representing the population dynamics of autoreactive T lymphocytes according to these two hypotheses were derived. For each model we identified how cell density affects tolerance, and predicted the corresponding phase spaces and bifurcations. We show that the simple induction of proliferative anergy, as modeled here, has a density dependence that is only partially compatible with adoptive transfers of tolerance, and that the models of tolerance mediated by specific regulatory T cells are closer to the observations.

A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone.

PubMed

Hurford, Amy; Hebblewhite, Mark; Lewis, Mark A

2006-11-01

A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.

Mathematical modeling on obligate mutualism: Interactions between leaf-cutter ants and their fungus garden.

PubMed

Kang, Yun; Clark, Rebecca; Makiyama, Michael; Fewell, Jennifer

2011-11-21

We propose a simple mathematical model by applying Michaelis-Menton equations of enzyme kinetics to study the mutualistic interaction between the leaf cutter ant and its fungus garden at the early stage of colony expansion. We derive sufficient conditions on the extinction and coexistence of these two species. In addition, we give a region of initial condition that leads to the extinction of two species when the model has an interior attractor. Our global analysis indicates that the division of labor by worker ants and initial conditions are two important factors that determine whether leaf cutter ants' colonies and their fungus garden can survive and grow or not. We validate the model by comparing model simulations and data on fungal and ant colony growth rates under laboratory conditions. We perform sensitive analysis of the model based on the experimental data to gain more biological insights on ecological interactions between leaf-cutter ants and their fungus garden. Finally, we give conclusions and discuss potential future work. Published by Elsevier Ltd.

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

Innovative model to simulate exhalation phase in human respiratory system.

PubMed

Sbrana, Tommaso; Landi, Alberto; Catapano, Giosuè Angelo

2011-11-01

In this paper, we present a mathematical model, which mimics the bronchial resistances of human's lung in an expiratory act. The model is implemented in Matlab. The inputs that are used in this model derive from spirometry test. This model is able to study a physiologic condition, a pathologic one and the patient's follow up after drug treatment. We split our study into two parts. The first one focuses the analysis on the gas fluido dynamic inside of the respiratory pathways. The second part takes care of the pressure equilibrium in the exchange zone. We use the outputs that derive from the second subsystem to solve the Bernoulli's equation of the first part. The model was validated with data provided from "Clinical Physiology Institute" of CNR and G. Monasterio Foundation of Pisa. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Mathematical modeling of tetrahydroimidazole benzodiazepine-1-one derivatives as an anti HIV agent

NASA Astrophysics Data System (ADS)

Ojha, Lokendra Kumar

2017-07-01

The goal of the present work is the study of drug receptor interaction via QSAR (Quantitative Structure-Activity Relationship) analysis for 89 set of TIBO (Tetrahydroimidazole Benzodiazepine-1-one) derivatives. MLR (Multiple Linear Regression) method is utilized to generate predictive models of quantitative structure-activity relationships between a set of molecular descriptors and biological activity (IC50). The best QSAR model was selected having a correlation coefficient (r) of 0.9299 and Standard Error of Estimation (SEE) of 0.5022, Fisher Ratio (F) of 159.822 and Quality factor (Q) of 1.852. This model is statistically significant and strongly favours the substitution of sulphur atom, IS i.e. indicator parameter for -Z position of the TIBO derivatives. Two other parameter logP (octanol-water partition coefficient) and SAG (Surface Area Grid) also played a vital role in the generation of best QSAR model. All three descriptor shows very good stability towards data variation in leave-one-out (LOO).

Tuning and performance evaluation of PID controller for superheater steam temperature control of 200 MW boiler using gain phase assignment algorithm

NASA Astrophysics Data System (ADS)

Begum, A. Yasmine; Gireesh, N.

2018-04-01

In superheater, steam temperature is controlled in a cascade control loop. The cascade control loop consists of PI and PID controllers. To improve the superheater steam temperature control the controller's gains in a cascade control loop has to be tuned efficiently. The mathematical model of the superheater is derived by sets of nonlinear partial differential equations. The tuning methods taken for study here are designed for delay plus first order transfer function model. Hence from the dynamical model of the superheater, a FOPTD model is derived using frequency response method. Then by using Chien-Hrones-Reswick Tuning Algorithm and Gain-Phase Assignment Algorithm optimum controller gains has been found out based on the least value of integral time weighted absolute error.

Shedding light on El Farol

NASA Astrophysics Data System (ADS)

Challet, Damien; Marsili, M.; Ottino, Gabriele

2004-02-01

We mathematize El Farol bar problem and transform it into a workable model. We find general conditions on the predictor space under which the convergence of the average attendance to the resource level does not require any intelligence on the side of the agents. Secondly, specializing to a particular ensemble of continuous strategies yields a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.

Controlled release drug delivery via polymeric microspheres: a neat application of the spherical diffusion equation

NASA Astrophysics Data System (ADS)

Ormerod, C. S.; Nelson, M.

2017-11-01

Various applied mathematics undergraduate skills are demonstrated via an adaptation of Crank's axisymmetric spherical diffusion model. By the introduction of a one-parameter Heaviside initial condition, the pharmaceutically problematic initial mass flux is attenuated. Quantities germane to the pharmaceutical industry are examined and the model is tested with data derived from industry journals. A binomial algorithm for the acceleration of alternating sequences is demonstrated. The model is accompanied by a MAPLE worksheet for further student exploration.

Collective learning modeling based on the kinetic theory of active particles

NASA Astrophysics Data System (ADS)

Burini, D.; De Lillo, S.; Gibelli, L.

2016-03-01

This paper proposes a systems approach to the theory of perception and learning in populations composed of many living entities. Starting from a phenomenological description of these processes, a mathematical structure is derived which is deemed to incorporate their complexity features. The modeling is based on a generalization of kinetic theory methods where interactions are described by theoretical tools of game theory. As an application, the proposed approach is used to model the learning processes that take place in a classroom.

Mathematical modeling of PDC bit drilling process based on a single-cutter mechanics

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

Wojtanowicz, A.K.; Kuru, E.

1993-12-01

An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter`s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verificationsmore » of the model. Qualitative verification shows that the model`s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model`s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.« less

Mathematical modeling and fuzzy availability analysis for serial processes in the crystallization system of a sugar plant

NASA Astrophysics Data System (ADS)

Aggarwal, Anil Kr.; Kumar, Sanjeev; Singh, Vikram

2017-03-01

The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability has been used for reliability analysis of the system, and the effect of coverage factor, failure and repair rates of subsystems on fuzzy availability for fault-tolerant crystallization system of sugar plant is analyzed. Mathematical modeling of the system is carried out using the mnemonic rule to derive Chapman-Kolmogorov differential equations. These governing differential equations are solved with Runge-Kutta fourth-order method.

Analysing of critical force effects of aircraft seat belt using truss elements

NASA Astrophysics Data System (ADS)

Klemenc, Marek; Markopoulos, Alexandros; Maršálek, Pavel

2017-07-01

This paper deals with the mathematical modelling of an aircraft seat belt crash test. The main goal is determination of a time course of the reactions in a lap belt anchoring points and their maximum values. This work was created on the basis of practical requirements from industry. Results are going to be reflected in developing a new type of aircraft seats. We mainly focus on the mathematical modelling of dynamic problems using the finite element method (FEM). Derived procedures are implemented in the Python programming language and are verified by several examples. A final calculation algorithm is applied on the analysis of the safety belt. We consider that a seat belt bending stiffness is very small compared to a tensile stiffness, therefore we used a 2D plane truss element.

Safety in Numbers: Mathematics Support Centres and Their Derivatives as Social Learning Spaces

ERIC Educational Resources Information Center

Solomon, Yvette; Croft, Tony; Lawson, Duncan

2010-01-01

This article reports on data gathered from second and third year mathematics undergraduates at two British universities which have developed Mathematics Support Centres, primarily with a view to supporting skills development for engineering students. However, an unforeseen consequence of the support centres was the mathematics students'…

An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

Simulation of Electrical Characteristics of a Solar Panel

NASA Astrophysics Data System (ADS)

Obukhov, S.; Plotnikov, I.; Kryuchkova, M.

2016-06-01

The fast-growing photovoltaic system market leads to the necessity of the informed choice of major energy components and optimization of operating conditions in order to improve energy efficiency. Development of mathematical models of the main components of photovoltaic systems to ensure their comprehensive study is an urgent problem of improving and practical using of the technology of electrical energy production. The paper presents a mathematical model of the solar module implemented in the popular software MATLAB/Simulink. Equivalent circuit of the solar cell with a diode parallel without derived resistance is used for modelling. The serie8s resistance of the solar module is calculated by Newton's iterative method using the data of its technical specifications. It ensures high precision of simulation. Model validity was evaluated by the well-known technical characteristics of the module Solarex MSX 60. The calculation results of the experiment showed that the obtained current-voltage and current-watt characteristics of the model are compatible with those of the manufacturer.

Gender and Course Selection in Upper Secondary Education: Effects of Academic Self-Concept and Intrinsic Value

ERIC Educational Resources Information Center

Nagy, Gabriel; Trautwein, Ulrich; Baumert, Jurgen; Koller, Olaf; Garrett, Jessica

2006-01-01

Predictions about processes linking gender to students' choices of advanced courses were derived from the internal/external frame of reference (I/E) model and expectancy value (EV) theory. The predictions were tested for the domains of mathematics and biology using data from 1,148 students attending academically oriented secondary schools in…

Catastrophe modelling in the biological sciences.

PubMed

Deakin, M A

1990-03-01

Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional "physical" way, it could also be applied in a new "metaphysical" way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology. Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to have been fully realised. This paper will document and classify the work that has been done. It will be argued that, like other applied Mathematics, applied Catastrophe Theory works best where the underlying laws are securely known and precisely quantified, requiring those same guarantees as does any other branch of Mathematics when it confronts a real-life situation.

Predictability and preparedness in influenza control.

PubMed

Smith, Derek J

2006-04-21

The threat of pandemic human influenza looms as we survey the ongoing avian influenza pandemic and wonder if and when it will jump species. What are the risks and how can we plan? The nub of the problem lies in the inherent variability of the virus, which makes prediction difficult. However, it is not impossible; mathematical models can help determine and quantify critical parameters and thresholds in the relationships of those parameters, even if the relationships are nonlinear and obscure to simple reasoning. Mathematical models can derive estimates for the levels of drug stockpiles needed to buy time, how and when to modify vaccines, whom to target with vaccines and drugs, and when to enforce quarantine measures. Regardless, the models used for pandemic planning must be tested, and for this we must continue to gather data, not just for exceptional scenarios but also for seasonal influenza.

Effect of bandage thickness on interface pressure applied by compression bandages.

PubMed

Al Khaburi, Jawad; Dehghani-Sanij, Abbas A; Nelson, E Andrea; Hutchinson, Jerry

2012-04-01

Medical compression bandages are widely used in the treatment of chronic venous disorder. In order to design effective compression bandages, researchers have attempted to describe the interface pressure applied by these bandages using mathematical models. This paper reports on the work carried out to derive the mathematical model used to describe the interface pressure applied by single-layer bandage using two different approaches. The first assumes that the bandage thickness is negligible, whereas the second model includes the bandage thickness. The estimated pressures using the two formulae are then compared, simulated over a 3D representation of a real leg and validated experimentally. Both theoretical and experimental results have shown that taking bandage thickness into consideration while estimating the pressures applied by a medical compression bandage will result in more accurate estimation. However, the additional accuracy is clinically insignificant. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Cardiomyocytes from late embryos and neonates do optimal work and striate best on substrates with tissue-level elasticity: metrics and mathematics.

PubMed

Majkut, Stephanie F; Discher, Dennis E

2012-11-01

In this review, we discuss recent studies on the mechanosensitive morphology and function of cardiomyocytes derived from embryos and neonates. For early cardiomyocytes cultured on substrates of various stiffnesses, contractile function as measured by force production, work output and calcium handling is optimized when the culture substrate stiffness mimics that of the tissue from which the cells were obtained. This optimal contractile function corresponds to changes in sarcomeric protein conformation and organization that promote contractile ability. In light of current models for myofibillogenesis, a recent mathematical model of striation and alignment on elastic substrates helps to illuminate how substrate stiffness modulates early myofibril formation and organization. During embryonic heart formation and maturation, cardiac tissue mechanics change dynamically. Experiments and models highlighted here have important implications for understanding cardiomyocyte differentiation and function in development and perhaps in regeneration processes.

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1975-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Mathematical modeling provides kinetic details of the human immune response to vaccination

PubMed Central

Le, Dustin; Miller, Joseph D.; Ganusov, Vitaly V.

2015-01-01

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data. PMID:25621280

Mathematical modeling provides kinetic details of the human immune response to vaccination.

PubMed

Le, Dustin; Miller, Joseph D; Ganusov, Vitaly V

2014-01-01

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data.

Mathematical models of real geometrical factors in restricted blood vessels for the analysis of CAD (coronary artery diseases) using Legendre, Boubaker and Bessel polynomials.

PubMed

Awojoyogbe, O B; Faromika, O P; Dada, M; Boubaker, Karem; Ojambati, O S

2011-12-01

Most cardiovascular emergencies are directly caused by coronary artery disease. Coronary arteries can become clogged or occluded, leading to damage to the heart muscle supplied by the artery. Modem cardiovascular medicine can certainly be improved by meticulous analysis of geometrical factors closely associated with the degenerative disease that results in narrowing of the coronary arteries. There are, however, inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries that are very critical in plaque formation and thickening of the vessel wall. Neither the mathematical models of the blood vessels with arthrosclerosis generated by the heart and blood flow or the NMR/MRI data to construct them are available. In this study, a mathematical formulation for the geometrical factors that are very critical for the understanding of coronary artery disease is presented. Based on the Bloch NMR flow equations, we derive analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in restricted blood vessels. The procedure would apply to the situations in which the geometry of the fatty deposits, (plague) on the interior walls of the coronary arteries is spherical. The boundary conditions are introduced based on Bessel, Boubaker and Legendre polynomials.

A Standard Kinematic Model for Flight Simulation at NASA Ames

NASA Technical Reports Server (NTRS)

Mcfarland, R. E.

1975-01-01

A standard kinematic model for aircraft simulation exists at NASA-Ames on a variety of computer systems, one of which is used to control the flight simulator for advanced aircraft (FSAA). The derivation of the kinematic model is given and various mathematical relationships are presented as a guide. These include descriptions of standardized simulation subsystems such as the atmospheric turbulence model and the generalized six-degrees-of-freedom trim routine, as well as an introduction to the emulative batch-processing system which enables this facility to optimize its real-time environment.

Coke formation in the thermal cracking of hydrocarbons. 4: Modeling of coke formation in naphtha cracking

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

Reyniers, G.C.; Froment, G.F.; Kopinke, F.D.

1994-11-01

An extensive experimental program has been carried out in a pilot unit for the thermal cracking of hydrocarbons. On the basis of the experimental information and the insight in the mechanisms for coke formation in pyrolysis reactors, a mathematical model describing the coke formation has been derived. This model has been incorporated in the existing simulation tools at the Laboratorium voor Petrochemische Techniek, and the run length of an industrial naphtha cracking furnace has been accurately simulated. In this way the coking model has been validated.

Mathematical model for self-propelled droplets driven by interfacial tension

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

Nagai, Ken H.; Tachibana, Kunihito; Tobe, Yuta

2016-03-21

We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically.

Manual of phosphoric acid fuel cell power plant optimization model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Search algorithm complexity modeling with application to image alignment and matching

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2014-05-01

Search algorithm complexity modeling, in the form of penetration rate estimation, provides a useful way to estimate search efficiency in application domains which involve searching over a hypothesis space of reference templates or models, as in model-based object recognition, automatic target recognition, and biometric recognition. The penetration rate quantifies the expected portion of the database that must be searched, and is useful for estimating search algorithm computational requirements. In this paper we perform mathematical modeling to derive general equations for penetration rate estimates that are applicable to a wide range of recognition problems. We extend previous penetration rate analyses to use more general probabilistic modeling assumptions. In particular we provide penetration rate equations within the framework of a model-based image alignment application domain in which a prioritized hierarchical grid search is used to rank subspace bins based on matching probability. We derive general equations, and provide special cases based on simplifying assumptions. We show how previously-derived penetration rate equations are special cases of the general formulation. We apply the analysis to model-based logo image alignment in which a hierarchical grid search is used over a geometric misalignment transform hypothesis space. We present numerical results validating the modeling assumptions and derived formulation.

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).

The relationship between a deformation-based eddy parameterization and the LANS-α turbulence model

NASA Astrophysics Data System (ADS)

Bachman, Scott D.; Anstey, James A.; Zanna, Laure

2018-06-01

A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier-Stokes-α model (LANS-α, e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS-α models which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ.

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Rosenzweig instability in a thin layer of a magnetic fluid

NASA Astrophysics Data System (ADS)

Korovin, V. M.

2013-12-01

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.

Students’ epistemic understanding of mathematical derivations in physics

NASA Astrophysics Data System (ADS)

Sirnoorkar, Amogh; Mazumdar, Anwesh; Kumar, Arvind

2017-01-01

We propose an epistemic measure of physics in terms of the ability to discriminate between the purely mathematical, physical (i.e. dependent on empirical inputs) and nominal (i.e. empty of mathematical or physical content) propositions appearing in a typical derivation in physics. The measure can be relevant in understanding the maths-physics link hurdles among college students. To illustrate the idea, we construct a tool for a familiar derivation (involving specific heats of an ideal gas), and use it for a sample of students from three different institutes. The reliability of the tool is examined. The results indicate, as intuitively expected, that epistemic clarity correlates with content clarity. Data yield several significant trends on the extent and kinds of epistemic pitfalls prevalent among physics undergraduates.

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Tan, H. Q.; Dong, X.

1989-01-01

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Evolution of social versus individual learning in a subdivided population revisited: comparative analysis of three coexistence mechanisms using the inclusive-fitness method.

PubMed

Kobayashi, Yutaka; Ohtsuki, Hisashi

2014-03-01

Learning abilities are categorized into social (learning from others) and individual learning (learning on one's own). Despite the typically higher cost of individual learning, there are mechanisms that allow stable coexistence of both learning modes in a single population. In this paper, we investigate by means of mathematical modeling how the effect of spatial structure on evolutionary outcomes of pure social and individual learning strategies depends on the mechanisms for coexistence. We model a spatially structured population based on the infinite-island framework and consider three scenarios that differ in coexistence mechanisms. Using the inclusive-fitness method, we derive the equilibrium frequency of social learners and the genetic load of social learning (defined as average fecundity reduction caused by the presence of social learning) in terms of some summary statistics, such as relatedness, for each of the three scenarios and compare the results. This comparative analysis not only reconciles previous models that made contradictory predictions as to the effect of spatial structure on the equilibrium frequency of social learners but also derives a simple mathematical rule that determines the sign of the genetic load (i.e. whether or not social learning contributes to the mean fecundity of the population). Copyright © 2013 Elsevier Inc. All rights reserved.

Automatic Parametrization of Somatosensory Evoked Potentials With Chirp Modeling.

PubMed

Vayrynen, Eero; Noponen, Kai; Vipin, Ashwati; Thow, X Y; Al-Nashash, Hasan; Kortelainen, Jukka; All, Angelo

2016-09-01

In this paper, an approach using polynomial phase chirp signals to model somatosensory evoked potentials (SEPs) is proposed. SEP waveforms are assumed as impulses undergoing group velocity dispersion while propagating along a multipath neural connection. Mathematical analysis of pulse dispersion resulting in chirp signals is performed. An automatic parameterization of SEPs is proposed using chirp models. A Particle Swarm Optimization algorithm is used to optimize the model parameters. Features describing the latencies and amplitudes of SEPs are automatically derived. A rat model is then used to evaluate the automatic parameterization of SEPs in two experimental cases, i.e., anesthesia level and spinal cord injury (SCI). Experimental results show that chirp-based model parameters and the derived SEP features are significant in describing both anesthesia level and SCI changes. The proposed automatic optimization based approach for extracting chirp parameters offers potential for detailed SEP analysis in future studies. The method implementation in Matlab technical computing language is provided online.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Novel mathematical algorithm for pupillometric data analysis.

PubMed

Canver, Matthew C; Canver, Adam C; Revere, Karen E; Amado, Defne; Bennett, Jean; Chung, Daniel C

2014-01-01

Pupillometry is used clinically to evaluate retinal and optic nerve function by measuring pupillary response to light stimuli. We have developed a mathematical algorithm to automate and expedite the analysis of non-filtered, non-calculated pupillometric data obtained from mouse pupillary light reflex recordings, obtained from dynamic pupillary diameter recordings following exposure of varying light intensities. The non-filtered, non-calculated pupillometric data is filtered through a low pass finite impulse response (FIR) filter. Thresholding is used to remove data caused by eye blinking, loss of pupil tracking, and/or head movement. Twelve physiologically relevant parameters were extracted from the collected data: (1) baseline diameter, (2) minimum diameter, (3) response amplitude, (4) re-dilation amplitude, (5) percent of baseline diameter, (6) response time, (7) re-dilation time, (8) average constriction velocity, (9) average re-dilation velocity, (10) maximum constriction velocity, (11) maximum re-dilation velocity, and (12) onset latency. No significant differences were noted between parameters derived from algorithm calculated values and manually derived results (p ≥ 0.05). This mathematical algorithm will expedite endpoint data derivation and eliminate human error in the manual calculation of pupillometric parameters from non-filtered, non-calculated pupillometric values. Subsequently, these values can be used as reference metrics for characterizing the natural history of retinal disease. Furthermore, it will be instrumental in the assessment of functional visual recovery in humans and pre-clinical models of retinal degeneration and optic nerve disease following pharmacological or gene-based therapies. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Exploring Dietary Kilocalories: An Activity Exemplifying the Personal Value of Science and Mathematics.

ERIC Educational Resources Information Center

Rye, James A.

1999-01-01

Presents an activity that integrates mathematics and science and focuses on estimation, percent, proportionality, ratio, interconverting units, deriving algorithms mathematically, energy transformation, interactions of energy and matter, bioavailability, composition, density, inferring, and data gathering through scientific interpretation.…

Discrete Mathematics Re "Tooled."

ERIC Educational Resources Information Center

Grassl, Richard M.; Mingus, Tabitha T. Y.

1999-01-01

Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

Mathematical Graphic Organizers

ERIC Educational Resources Information Center

Zollman, Alan

2009-01-01

As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…

Analysis of the cable equation with non-local and non-singular kernel fractional derivative

NASA Astrophysics Data System (ADS)

Karaagac, Berat

2018-02-01

Recently a new concept of differentiation was introduced in the literature where the kernel was converted from non-local singular to non-local and non-singular. One of the great advantages of this new kernel is its ability to portray fading memory and also well defined memory of the system under investigation. In this paper the cable equation which is used to develop mathematical models of signal decay in submarine or underwater telegraphic cables will be analysed using the Atangana-Baleanu fractional derivative due to the ability of the new fractional derivative to describe non-local fading memory. The existence and uniqueness of the more generalized model is presented in detail via the fixed point theorem. A new numerical scheme is used to solve the new equation. In addition, stability, convergence and numerical simulations are presented.

A computer code for calculations in the algebraic collective model of the atomic nucleus

NASA Astrophysics Data System (ADS)

Welsh, T. A.; Rowe, D. J.

2016-03-01

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

SIMO optical wireless links with nonzero boresight pointing errors over M modeled turbulence channels

NASA Astrophysics Data System (ADS)

Varotsos, G. K.; Nistazakis, H. E.; Petkovic, M. I.; Djordjevic, G. T.; Tombras, G. S.

2017-11-01

Over the last years terrestrial free-space optical (FSO) communication systems have demonstrated an increasing scientific and commercial interest in response to the growing demands for ultra high bandwidth, cost-effective and secure wireless data transmissions. However, due the signal propagation through the atmosphere, the performance of such links depends strongly on the atmospheric conditions such as weather phenomena and turbulence effect. Additionally, their operation is affected significantly by the pointing errors effect which is caused by the misalignment of the optical beam between the transmitter and the receiver. In order to address this significant performance degradation, several statistical models have been proposed, while particular attention has been also given to diversity methods. Here, the turbulence-induced fading of the received optical signal irradiance is studied through the M (alaga) distribution, which is an accurate model suitable for weak to strong turbulence conditions and unifies most of the well-known, previously emerged models. Thus, taking into account the atmospheric turbulence conditions along with the pointing errors effect with nonzero boresight and the modulation technique that is used, we derive mathematical expressions for the estimation of the average bit error rate performance for SIMO FSO links. Finally, proper numerical results are given to verify our derived expressions and Monte Carlo simulations are also provided to further validate the accuracy of the analysis proposed and the obtained mathematical expressions.

Analytical expressions for noise and crosstalk voltages of the High Energy Silicon Particle Detector

NASA Astrophysics Data System (ADS)

Yadav, I.; Shrimali, H.; Liberali, V.; Andreazza, A.

2018-01-01

The paper presents design and implementation of a silicon particle detector array with the derived closed form equations of signal-to-noise ratio (SNR) and crosstalk voltages. The noise analysis demonstrates the effect of interpixel capacitances (IPC) between center pixel (where particle hits) and its neighbouring pixels, resulting as a capacitive crosstalk. The pixel array has been designed and simulated in a 180 nm BCD technology of STMicroelectronics. The technology uses the supply voltage (VDD) of 1.8 V and the substrate potential of -50 V. The area of unit pixel is 250×50 μm2 with the substrate resistivity of 125 Ωcm and the depletion depth of 30 μm. The mathematical model includes the effects of various types of noise viz. the shot noise, flicker noise, thermal noise and the capacitive crosstalk. This work compares the results of noise and crosstalk analysis from the proposed mathematical model with the circuit simulation results for a given simulation environment. The results show excellent agreement with the circuit simulations and the mathematical model. The average relative error (AVR) generated for the noise spectral densities with respect to the simulations and the model is 12% whereas the comparison gives the errors of 3% and 11.5% for the crosstalk voltages and the SNR results respectively.

Examining spectral properties of Landsat 8 OLI for predicting above-ground carbon of Labanan Forest, Berau

NASA Astrophysics Data System (ADS)

Suhardiman, A.; Tampubolon, B. A.; Sumaryono, M.

2018-04-01

Many studies revealed significant correlation between satellite image properties and forest data attributes such as stand volume, biomass or carbon stock. However, further study is still relevant due to advancement of remote sensing technology as well as improvement on methods of data analysis. In this study, the properties of three vegetation indices derived from Landsat 8 OLI were tested upon above-ground carbon stock data from 50 circular sample plots (30-meter radius) from ground survey in PT. Inhutani I forest concession in Labanan, Berau, East Kalimantan. Correlation analysis using Pearson method exhibited a promising results when the coefficient of correlation (r-value) was higher than 0.5. Further regression analysis was carried out to develop mathematical model describing the correlation between sample plots data and vegetation index image using various mathematical models.Power and exponential model were demonstrated a good result for all vegetation indices. In order to choose the most adequate mathematical model for predicting Above-ground Carbon (AGC), the Bayesian Information Criterion (BIC) was applied. The lowest BIC value (i.e. -376.41) shown by Transformed Vegetation Index (TVI) indicates this formula, AGC = 9.608*TVI21.54, is the best predictor of AGC of study area.

Methodology of Thermodynamics

ERIC Educational Resources Information Center

Mohan, Gyan

1969-01-01

Presents a systematization of the mathematical formulae in thermodynamics. From the set of thermodynamic variables, four equations are derived which contain the total mathematical jargon of thermodynamics. (LC)

On continuous and discontinuous approaches for modeling groundwater flow in heterogeneous media using the Numerical Manifold Method: Model development and comparison

NASA Astrophysics Data System (ADS)

Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny

2015-06-01

One major challenge in modeling groundwater flow within heterogeneous geological media is that of modeling arbitrarily oriented or intersected boundaries and inner material interfaces. The Numerical Manifold Method (NMM) has recently emerged as a promising method for such modeling, in its ability to handle boundaries, its flexibility in constructing physical cover functions (continuous or with gradient jump), its meshing efficiency with a fixed mathematical mesh (covers), its convenience for enhancing approximation precision, and its integration precision, achieved by simplex integration. In this paper, we report on developing and comparing two new approaches for boundary constraints using the NMM, namely a continuous approach with jump functions and a discontinuous approach with Lagrange multipliers. In the discontinuous Lagrange multiplier method (LMM), the material interfaces are regarded as discontinuities which divide mathematical covers into different physical covers. We define and derive stringent forms of Lagrange multipliers to link the divided physical covers, thus satisfying the continuity requirement of the refraction law. In the continuous Jump Function Method (JFM), the material interfaces are regarded as inner interfaces contained within physical covers. We briefly define jump terms to represent the discontinuity of the head gradient across an interface to satisfy the refraction law. We then make a theoretical comparison between the two approaches in terms of global degrees of freedom, treatment of multiple material interfaces, treatment of small area, treatment of moving interfaces, the feasibility of coupling with mechanical analysis and applicability to other numerical methods. The newly derived boundary-constraint approaches are coded into a NMM model for groundwater flow analysis, and tested for precision and efficiency on different simulation examples. We first test the LMM for a Dirichlet boundary and then test both LMM and JFM for an idealized heterogeneous model, comparing the numerical results with analytical solutions. Then we test both approaches for a heterogeneous model and compare the results of hydraulic head and specific discharge. We show that both approaches are suitable for modeling material boundaries, considering high accuracy for the boundary constraints, the capability to deal with arbitrarily oriented or complexly intersected boundaries, and their efficiency using a fixed mathematical mesh.

Geometrical and quantum mechanical aspects in observers' mathematics

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2013-10-01

When we create mathematical models for Quantum Mechanics we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We prove that Euclidean Geometry works in sufficiently small neighborhood of the given line, but when we enlarge the neighborhood, non-euclidean Geometry takes over. We prove that the physical speed is a random variable, cannot exceed some constant, and this constant does not depend on an inertial coordinate system. We proved the following theorems: Theorem A (Lagrangian). Let L be a Lagrange function of free material point with mass m and speed v. Then the probability P of L = m 2 v2 is less than 1: P(L = m 2 v2) < 1. Theorem B (Nadezhda effect). On the plane (x, y) on every line y = kx there is a point (x0, y0) with no existing Euclidean distance between origin (0, 0) and this point. Conjecture (Black Hole). Our space-time nature is a black hole: light cannot go out infinitely far from origin.

Fitting a Structured Juvenile-Adult Model for Green Tree Frogs to Population Estimates from Capture-Mark-Recapture Field Data

USGS Publications Warehouse

Ackleh, A.S.; Carter, J.; Deng, K.; Huang, Q.; Pal, N.; Yang, X.

2012-01-01

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation. ?? 2011 Society for Mathematical Biology.

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.

Effects of SKF-83566 and haloperidol on performance on progressive ratio schedules maintained by sucrose and corn oil reinforcement: quantitative analysis using a new model derived from the Mathematical Principles of Reinforcement (MPR).

PubMed

Olarte-Sánchez, C M; Valencia-Torres, L; Cassaday, H J; Bradshaw, C M; Szabadi, E

2013-12-01

Mathematical models can assist the interpretation of the effects of interventions on schedule-controlled behaviour and help to differentiate between processes that may be confounded in traditional performance measures such as response rate and the breakpoint in progressive ratio (PR) schedules. The effects of a D1-like dopamine receptor antagonist, 8-bromo-2,3,4,5-tetrahydro-3-methyl-5-phenyl-1H-3-benzazepin-7-ol hydrobromide (SKF-83566), and a D2-like receptor antagonist, haloperidol, on rats' performance on PR schedules maintained by sucrose and corn oil reinforcers were assessed using a new model derived from Killeen's (Behav Brain Sci 17:105-172, 1994) Mathematical Principles of Reinforcement. Separate groups of rats were trained under a PR schedule using sucrose or corn oil reinforcers. SKF-83566 (0.015 and 0.03 mg kg(-1)) and haloperidol (0.05 and 0.1 mg kg(-1)) were administered intraperitoneally (five administrations of each treatment). Running and overall response rates in successive ratios were analysed using the new model, and estimates of the model's parameters were compared between treatments. Haloperidol reduced a (the parameter expressing incentive value) in the case of both reinforcers, but did not affect the parameters related to response time and post-reinforcement pausing. SKF-83566 reduced a and k (the parameter expressing sensitivity of post-reinforcement pausing to the prior inter-reinforcement interval) in the case of sucrose, but did not affect any of the parameters in the case of corn oil. The results are consistent with the hypothesis that blockade of both D1-like and D2-like receptors reduces the incentive value of sucrose, whereas the incentive value of corn oil is more sensitive to blockade of D2-like than D1-like receptors.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

PubMed

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-04-08

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals

PubMed Central

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-01-01

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems. DOI: http://dx.doi.org/10.7554/eLife.14022.001 PMID:27058171

Physical Activity and Bone Density in Women

NASA Technical Reports Server (NTRS)

Bowley, Susan M.; Whalen, R. T.

2000-01-01

A mathematical model of bone density regulation as a function of the daily tissue "effective" stress has been derived. Using the model, the influence of daily activity in the form of a daily loading history has been related to bone density of the calcaneus. The theory incorporates a stress exponent m to account for differences in the importance of magnitude and number of load cycles experienced during daily activity. We have derived a parameter from the model, the "Bone Density Index" (BDI). We have developed a method of collecting daily habitual loading histories using an insole force sensor interfaced to a portable digital data logger carried in a fanny pack. Our goal for this study was to determine a stress exponent, m, relating GRFz history to Calcaneal Bone Mineral Density (CBMD).

Mental Models of Software Forecasting

NASA Technical Reports Server (NTRS)

Hihn, J.; Griesel, A.; Bruno, K.; Fouser, T.; Tausworthe, R.

1993-01-01

The majority of software engineers resist the use of the currently available cost models. One problem is that the mathematical and statistical models that are currently available do not correspond with the mental models of the software engineers. In an earlier JPL funded study (Hihn and Habib-agahi, 1991) it was found that software engineers prefer to use analogical or analogy-like techniques to derive size and cost estimates, whereas curren CER's hide any analogy in the regression equations. In addition, the currently available models depend upon information which is not available during early planning when the most important forecasts must be made.

Physical Models for Particle Tracking Simulations in the RF Gap

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

Shishlo, Andrei P.; Holmes, Jeffrey A.

2015-06-01

This document describes the algorithms that are used in the PyORBIT code to track the particles accelerated in the Radio-Frequency cavities. It gives the mathematical description of the algorithms and the assumptions made in each case. The derived formulas have been implemented in the PyORBIT code. The necessary data for each algorithm are described in detail.

Probabilistic assessment methodology for continuous-type petroleum accumulations

USGS Publications Warehouse

Crovelli, R.A.

2003-01-01

The analytic resource assessment method, called ACCESS (Analytic Cell-based Continuous Energy Spreadsheet System), was developed to calculate estimates of petroleum resources for the geologic assessment model, called FORSPAN, in continuous-type petroleum accumulations. The ACCESS method is based upon mathematical equations derived from probability theory in the form of a computer spreadsheet system. ?? 2003 Elsevier B.V. All rights reserved.

A Theoretical Analysis of the Influence of Electroosmosis on the Effective Ionic Mobility in Capillary Zone Electrophoresis

ERIC Educational Resources Information Center

Hijnen, Hens

2009-01-01

A theoretical description of the influence of electroosmosis on the effective mobility of simple ions in capillary zone electrophoresis is presented. The mathematical equations derived from the space-charge model contain the pK[subscript a] value and the density of the weak acid surface groups as parameters characterizing the capillary. It is…

Updating the limit efficiency of silicon solar cells

NASA Technical Reports Server (NTRS)

Wolf, M.

1979-01-01

Evaluation of the limit efficiency based on the simplest, most basic mathematical method that is appropriate for the conditions imposed by the cell model is discussed. The methodology, the solar cell structure, and the selection of the material parameters used in the evaluation are described. The results are discussed including a set of design goals derived from the limit efficiency.

Estimability of geodetic parameters from space VLBI observables

NASA Technical Reports Server (NTRS)

Adam, Jozsef

1990-01-01

The feasibility of space very long base interferometry (VLBI) observables for geodesy and geodynamics is investigated. A brief review of space VLBI systems from the point of view of potential geodetic application is given. A selected notational convention is used to jointly treat the VLBI observables of different types of baselines within a combined ground/space VLBI network. The basic equations of the space VLBI observables appropriate for convariance analysis are derived and included. The corresponding equations for the ground-to-ground baseline VLBI observables are also given for a comparison. The simplified expression of the mathematical models for both space VLBI observables (time delay and delay rate) include the ground station coordinates, the satellite orbital elements, the earth rotation parameters, the radio source coordinates, and clock parameters. The observation equations with these parameters were examined in order to determine which of them are separable or nonseparable. Singularity problems arising from coordinate system definition and critical configuration are studied. Linear dependencies between partials are analytically derived. The mathematical models for ground-space baseline VLBI observables were tested with simulation data in the frame of some numerical experiments. Singularity due to datum defect is confirmed.

Application of recursive Gibbs-Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko Beam Theory

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Shafei, A. M.

2013-02-01

The goal of this paper is to describe the application of Gibbs-Appell (G-A) formulation and the assumed modes method to the mathematical modeling of N-viscoelastic link manipulators. The paper's focus is on obtaining accurate and complete equations of motion which encompass the most related structural properties of lightweight elastic manipulators. In this study, two important damping mechanisms, namely, the structural viscoelasticity (Kelvin-Voigt) effect (as internal damping) and the viscous air effect (as external damping) have been considered. To include the effects of shear and rotational inertia, the assumption of Timoshenko beam (TB) theory (TBT) has been applied. Gravity, torsion, and longitudinal elongation effects have also been included in the formulations. To systematically derive the equations of motion and improve the computational efficiency, a recursive algorithm has been used in the modeling of the system. In this algorithm, all the mathematical operations are carried out by only 3×3 and 3×1 matrices. Finally, a computational simulation for a manipulator with two elastic links is performed in order to verify the proposed method.

An Analytical Model for the Performance Analysis of Concurrent Transmission in IEEE 802.15.4

PubMed Central

Gezer, Cengiz; Zanella, Alberto; Verdone, Roberto

2014-01-01

Interference is a serious cause of performance degradation for IEEE802.15.4 devices. The effect of concurrent transmissions in IEEE 802.15.4 has been generally investigated by means of simulation or experimental activities. In this paper, a mathematical framework for the derivation of chip, symbol and packet error probability of a typical IEEE 802.15.4 receiver in the presence of interference is proposed. Both non-coherent and coherent demodulation schemes are considered by our model under the assumption of the absence of thermal noise. Simulation results are also added to assess the validity of the mathematical framework when the effect of thermal noise cannot be neglected. Numerical results show that the proposed analysis is in agreement with the measurement results on the literature under realistic working conditions. PMID:24658624

An analytical model for the performance analysis of concurrent transmission in IEEE 802.15.4.

PubMed

Gezer, Cengiz; Zanella, Alberto; Verdone, Roberto

2014-03-20

Interference is a serious cause of performance degradation for IEEE802.15.4 devices. The effect of concurrent transmissions in IEEE 802.15.4 has been generally investigated by means of simulation or experimental activities. In this paper, a mathematical framework for the derivation of chip, symbol and packet error probability of a typical IEEE 802.15.4 receiver in the presence of interference is proposed. Both non-coherent and coherent demodulation schemes are considered by our model under the assumption of the absence of thermal noise. Simulation results are also added to assess the validity of the mathematical framework when the effect of thermal noise cannot be neglected. Numerical results show that the proposed analysis is in agreement with the measurement results on the literature under realistic working conditions.

Locality of the Thomas-Fermi-von Weizsäcker Equations

NASA Astrophysics Data System (ADS)

Nazar, F. Q.; Ortner, C.

2017-06-01

We establish a pointwise stability estimate for the Thomas-Fermi-von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

PubMed

Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

2005-05-01

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

Reconstructing Mathematics Pedagogy from a Constructivist Perspective.

ERIC Educational Resources Information Center

Simon, Martin A.

1995-01-01

Begins with an overview of the constructivist perspective and the pedagogical theory development upon which a constructivist teaching experiment with 20 prospective elementary teachers was based. Derives a theoretical framework for mathematics pedagogy with a focus on decisions about content and mathematical tasks. (49 references) (Author/DDD)

Kinetic models of controllable pore growth of anodic aluminum oxide membrane

NASA Astrophysics Data System (ADS)

Huang, Yan; Zeng, Hong-yan; Zhao, Ce; Qu, Ye-qing; Zhang, Pin

2012-06-01

An anodized Al2O3 (AAO) membrane with apertures about 72 nm in diameter was prepared by two-step anodic oxidation. The appearance and pore arrangement of the AAO membrane were characterized by energy dispersive x-ray spectroscopy and scanning electron microscopy. It was confirmed that the pores with high pore aspect ratio were parallel, well-ordered, and uniform. The kinetics of pores growth in the AAO membrane was derived, and the kinetic models showed that pores stopped developing when the pressure ( σ) trended to equal the surface tension at the end of anodic oxidation. During pore expansion, the effects of the oxalic acid concentration and expansion time on the pore size were investigated, and the kinetic behaviors were explained with two kinetic models derived in this study. They showed that the pore size increased with extended time ( r= G· t+ G'), but decreased with increased concentration ( r = - K·ln c- K') through the derived mathematic formula. Also, the values of G, G', K, and K' were derived from our experimental data.

Kinetic model development for biogas production from cattle dung

NASA Astrophysics Data System (ADS)

Ghatak, Manjula Das; Mahanta, P.

2017-07-01

Biogas is a mixture of methane, carbon dioxide and traces of numerous trace of elements. It is produced by anaerobic digestion of organic matters including cattle dung which depend upon various factors affecting the population and activity of microorganisms producing biogas. Among the various factors temperature is one of them which play a significant role in biogas production from cattle dung. Biogas production from cattle dung was studied at temperatures 35°C to 55°C at a step of 5°C to study the effect of temperature on biogas production from cattle dung. In this work a mathematical model is developed for evaluating the effect of temperature on the rate of biogas production from cattle dung. The new mathematical model is derived by adding the effect of temperature on the modified Gompertz model. The new model is found to be suitable for predicting the biogas production from cattle dung in the temperature range 35°C to 55°C. The results from the new model are found to be highly correlated to the experimental data of present study.

Inclusion of unsteady aerodynamics in longitudinal parameter estimation from flight data. [use of vortices and mathematical models for parameterization from flight characteristics

NASA Technical Reports Server (NTRS)

Queijo, M. J.; Wells, W. R.; Keskar, D. A.

1979-01-01

A simple vortex system, used to model unsteady aerodynamic effects into the rigid body longitudinal equations of motion of an aircraft, is described. The equations are used in the development of a parameter extraction algorithm. Use of the two parameter-estimation modes, one including and the other omitting unsteady aerodynamic modeling, is discussed as a means of estimating some acceleration derivatives. Computer generated data and flight data, used to demonstrate the use of the parameter-extraction algorithm are studied.

Discussion on "Modeling karst spring hydrograph recession based on head drop at sinkholes" by Guangquan, Li, Nico Goldscheider, Malcom S. Field

NASA Astrophysics Data System (ADS)

Şen, Zekâi

2018-02-01

Groundwater movement model development in karstic aquifers is very difficult due to the complexity of the solution cavities. The authors (Li et al., 2016) have proposed a square law model for expressing the discharge ratio in terms of hydraulic head ratio, with an exponent equal to 0.5. They have also provided the mathematical derivation in detail with application. It is noticed that the methodology can be expanded towards a better and refined solutions by consideration of the following explanations.

Collective learning modeling based on the kinetic theory of active particles.

PubMed

Burini, D; De Lillo, S; Gibelli, L

2016-03-01

This paper proposes a systems approach to the theory of perception and learning in populations composed of many living entities. Starting from a phenomenological description of these processes, a mathematical structure is derived which is deemed to incorporate their complexity features. The modeling is based on a generalization of kinetic theory methods where interactions are described by theoretical tools of game theory. As an application, the proposed approach is used to model the learning processes that take place in a classroom. Copyright © 2015 Elsevier B.V. All rights reserved.

The basic science and mathematics of random mutation and natural selection.

PubMed

Kleinman, Alan

2014-12-20

The mutation and natural selection phenomenon can and often does cause the failure of antimicrobial, herbicidal, pesticide and cancer treatments selection pressures. This phenomenon operates in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures. The mathematical behavior of mutation and selection is derived using the principles given by probability theory. The derivation of the equations describing the mutation and selection phenomenon is carried out in the context of an empirical example. Copyright © 2014 John Wiley & Sons, Ltd.

Local models of astrophysical discs

NASA Astrophysics Data System (ADS)

Latter, Henrik N.; Papaloizou, John

2017-12-01

Local models of gaseous accretion discs have been successfully employed for decades to describe an assortment of small-scale phenomena, from instabilities and turbulence, to dust dynamics and planet formation. For the most part, they have been derived in a physically motivated but essentially ad hoc fashion, with some of the mathematical assumptions never made explicit nor checked for consistency. This approach is susceptible to error, and it is easy to derive local models that support spurious instabilities or fail to conserve key quantities. In this paper we present rigorous derivations, based on an asympototic ordering, and formulate a hierarchy of local models (incompressible, Boussinesq and compressible), making clear which is best suited for a particular flow or phenomenon, while spelling out explicitly the assumptions and approximations of each. We also discuss the merits of the anelastic approximation, emphasizing that anelastic systems struggle to conserve energy unless strong restrictions are imposed on the flow. The problems encountered by the anelastic approximation are exacerbated by the disc's differential rotation, but also attend non-rotating systems such as stellar interiors. We conclude with a defence of local models and their continued utility in astrophysical research.

A mathematical model of the passage of an asteroid-comet body through the Earth’s atmosphere

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

Shaydurov, V., E-mail: shaidurov04@mail.ru; Siberian Federal University, 79 Svobodny pr., 660041 Krasnoyarsk; Shchepanovskaya, G.

In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth’s atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) andmore » the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.« less

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise

PubMed Central

Lau, Kevin D.; Asrress, Kaleab N.; Redwood, Simon R.; Figueroa, C. Alberto

2016-01-01

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit. PMID:26945076

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise.

PubMed

Arthurs, Christopher J; Lau, Kevin D; Asrress, Kaleab N; Redwood, Simon R; Figueroa, C Alberto

2016-05-01

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit. Copyright © 2016 the American Physiological Society.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

The Alberta K-9 Mathematics Program of Studies with Achievement Indicators

ERIC Educational Resources Information Center

Alberta Education, 2007

2007-01-01

The "Alberta K-9 Mathematics Program of Studies with Achievement Indicators" has been derived from "The Common Curriculum Framework for K-9 Mathematics: Western and Northern Canadian Protocol," May 2006 (the Common Curriculum Framework). The program of studies incorporates the conceptual framework for Kindergarten to Grade 9…

Mathematics and Living Things. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Faber, Norman J.; And Others

This document is designed for grade eight to enrich and supplement the usual courses of instruction. Mathematics and Living Things (MALT) utilizes exercises in biological science to derive data through which mathematical concepts and principles may be introduced and expanded. Chapters included are: (1) Leaves and Natural Variation: Measurement of…

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

PubMed Central

Schwartz, Benjamin L.; Yin, Ziying; Yaşar, Temel K.; Liu, Yifei; Khan, Altaf A.; Ye, Allen Q.; Royston, Thomas J.; Magin, Richard L.

2016-01-01

Aim The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elasography (MRE)–an imaging technique that allows for the non-invasive visualization of the displacement field throughout an object from externally driven harmonic motion–as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles. Methods Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multi-step process for which custom scaffolding was designed and built. A customized spin-echo based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite element method. Results Both complex shear moduli show a significant frequency dependence (p < 0.001) in keeping with previous work. Conclusion The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies. Significance On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g. a cylinder representing a blood vessel. This work demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies. PMID:26886963

On higher order discrete phase-locked loops.

NASA Technical Reports Server (NTRS)

Gill, G. S.; Gupta, S. C.

1972-01-01

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.

Atomistic full-quantum transport model for zigzag graphene nanoribbon-based structures: Complex energy-band method

NASA Astrophysics Data System (ADS)

Chen, Chun-Nan; Luo, Win-Jet; Shyu, Feng-Lin; Chung, Hsien-Ching; Lin, Chiun-Yan; Wu, Jhao-Ying

2018-01-01

Using a non-equilibrium Green’s function framework in combination with the complex energy-band method, an atomistic full-quantum model for solving quantum transport problems for a zigzag-edge graphene nanoribbon (zGNR) structure is proposed. For transport calculations, the mathematical expressions from the theory for zGNR-based device structures are derived in detail. The transport properties of zGNR-based devices are calculated and studied in detail using the proposed method.

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Analysis of Wind Tunnel Oscillatory Data of the X-31A Aircraft

NASA Technical Reports Server (NTRS)

Smith, Mark S.

1999-01-01

Wind tunnel oscillatory tests in pitch, roll, and yaw were performed on a 19%-scale model of the X-31A aircraft. These tests were used to study the aerodynamic characteristics of the X-31A in response to harmonic oscillations at six frequencies. In-phase and out-of-phase components of the aerodynamic coefficients were obtained over a range of angles of attack from 0 to 90 deg. To account for the effect of frequency on the data, mathematical models with unsteady terms were formulated by use of two different indicial functions. Data from a reduced set of frequencies were used to estimate model parameters, including steady-state static and dynamic stability derivatives. Both models showed good prediction capability and the ability to accurately fit the measured data. Estimated static stability derivatives compared well with those obtained from static wind tunnel tests. The roll and yaw rate derivative estimates were compared with rotary-balanced wind tunnel data and theoretical predictions. The estimates and theoretical predictions were in agreement at small angles of attack. The rotary-balance data showed, in general, acceptable agreement with the steady-state derivative estimates.

RF multicoupler design techniques to minimize problems of corona, multipaction, and stability

NASA Technical Reports Server (NTRS)

Hurley, H. S.; Kozakoff, D. J.

1971-01-01

A mathematical expression was derived describing multipacting and corona effects in a coaxial cavity. Both mechanical and electrical design techniques were investigated to minimize the susceptibility of coaxial cavity to corona and multipacting-type breakdown. To assist in the design of a multicoupler free from corona and multipactor breakdown, a flow chart obtained from the derived mathematical expression is included.

A theoretical study of microwave beam absorption by a rectenna

NASA Technical Reports Server (NTRS)

Ott, J. H.; Rice, J. S.; Thorn, D. C.

1980-01-01

The rectenna's microwave power beam absorption limit was theoretically confirmed by two mathematical models descriptive of the microwave absorption process; first one model was based on the current sheet equivalency of a large planar array above a reflector and the second model, which was based on the properties of a waveguide with special imaging characteristics, quantified the electromagnetic modes (field configurations) in the immediate vicinity of a Rectenna element spacing which permit total power beam absorption by preventing unwanted modes from propagating (scattering) were derived using these models. Several factors causing unwanted scattering are discussed.

In defense of derivations

NASA Astrophysics Data System (ADS)

Mungan, Carl E.

2016-05-01

At the 2015 AAPT Summer Meeting, I presented four derivations of the formula for motional emf. Such physics derivations involve the construction of explanatory frameworks involving diagrams and mathematical models. Although textbooks devote considerable space to such explanations, many teachers and students spend their time on worksheets, end-of-chapter problems, and the like. The book is reduced to a bank of solved (i.e., example) and unsolved (i.e., homework) questions, along with equations in colored boxes that presumably are to be used to answer those questions. Such an approach encourages fragmentation of knowledge, the view that there is only one right answer to a problem with the goal of physics being to find that answer (neatly boxed of course), and the inability to reason about even a slightly different (much less a novel) situation. If we are to develop scientific literacy, significant course time must be devoted to explaining the structure of and support for the models and equations we use.

Neonatal MRI is associated with future cognition and academic achievement in preterm children

PubMed Central

Spencer-Smith, Megan; Thompson, Deanne K.; Doyle, Lex W.; Inder, Terrie E.; Anderson, Peter J.; Klingberg, Torkel

2015-01-01

School-age children born preterm are particularly at risk for low mathematical achievement, associated with reduced working memory and number skills. Early identification of preterm children at risk for future impairments using brain markers might assist in referral for early intervention. This study aimed to examine the use of neonatal magnetic resonance imaging measures derived from automated methods (Jacobian maps from deformation-based morphometry; fractional anisotropy maps from diffusion tensor images) to predict skills important for mathematical achievement (working memory, early mathematical skills) at 5 and 7 years in a cohort of preterm children using both univariable (general linear model) and multivariable models (support vector regression). Participants were preterm children born <30 weeks’ gestational age and healthy control children born ≥37 weeks’ gestational age at the Royal Women’s Hospital in Melbourne, Australia between July 2001 and December 2003 and recruited into a prospective longitudinal cohort study. At term-equivalent age ( ±2 weeks) 224 preterm and 46 control infants were recruited for magnetic resonance imaging. Working memory and early mathematics skills were assessed at 5 years (n = 195 preterm; n = 40 controls) and 7 years (n = 197 preterm; n = 43 controls). In the preterm group, results identified localized regions around the insula and putamen in the neonatal Jacobian map that were positively associated with early mathematics at 5 and 7 years (both P < 0.05), even after covarying for important perinatal clinical factors using general linear model but not support vector regression. The neonatal Jacobian map showed the same trend for association with working memory at 7 years (models ranging from P = 0.07 to P = 0.05). Neonatal fractional anisotropy was positively associated with working memory and early mathematics at 5 years (both P < 0.001) even after covarying for clinical factors using support vector regression but not general linear model. These significant relationships were not observed in the control group. In summary, we identified, in the preterm brain, regions around the insula and putamen using neonatal deformation-based morphometry, and brain microstructural organization using neonatal diffusion tensor imaging, associated with skills important for childhood mathematical achievement. Results contribute to the growing evidence for the clinical utility of neonatal magnetic resonance imaging for early identification of preterm infants at risk for childhood cognitive and academic impairment. PMID:26329284

Electro-magneto interaction in fractional Green-Naghdi thermoelastic solid with a cylindrical cavity

NASA Astrophysics Data System (ADS)

Ezzat, M. A.; El-Bary, A. A.

2018-01-01

A unified mathematical model of Green-Naghdi's thermoelasticty theories (GN), based on fractional time-derivative of heat transfer is constructed. The model is applied to solve a one-dimensional problem of a perfect conducting unbounded body with a cylindrical cavity subjected to sinusoidal pulse heating in the presence of an axial uniform magnetic field. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Comparisons are made with the results predicted by the two theories. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.

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

On a PCA-based lung motion model

NASA Astrophysics Data System (ADS)

Li, Ruijiang; Lewis, John H.; Jia, Xun; Zhao, Tianyu; Liu, Weifeng; Wuenschel, Sara; Lamb, James; Yang, Deshan; Low, Daniel A.; Jiang, Steve B.

2011-09-01

Respiration-induced organ motion is one of the major uncertainties in lung cancer radiotherapy and is crucial to be able to accurately model the lung motion. Most work so far has focused on the study of the motion of a single point (usually the tumor center of mass), and much less work has been done to model the motion of the entire lung. Inspired by the work of Zhang et al (2007 Med. Phys. 34 4772-81), we believe that the spatiotemporal relationship of the entire lung motion can be accurately modeled based on principle component analysis (PCA) and then a sparse subset of the entire lung, such as an implanted marker, can be used to drive the motion of the entire lung (including the tumor). The goal of this work is twofold. First, we aim to understand the underlying reason why PCA is effective for modeling lung motion and find the optimal number of PCA coefficients for accurate lung motion modeling. We attempt to address the above important problems both in a theoretical framework and in the context of real clinical data. Second, we propose a new method to derive the entire lung motion using a single internal marker based on the PCA model. The main results of this work are as follows. We derived an important property which reveals the implicit regularization imposed by the PCA model. We then studied the model using two mathematical respiratory phantoms and 11 clinical 4DCT scans for eight lung cancer patients. For the mathematical phantoms with cosine and an even power (2n) of cosine motion, we proved that 2 and 2n PCA coefficients and eigenvectors will completely represent the lung motion, respectively. Moreover, for the cosine phantom, we derived the equivalence conditions for the PCA motion model and the physiological 5D lung motion model (Low et al 2005 Int. J. Radiat. Oncol. Biol. Phys. 63 921-9). For the clinical 4DCT data, we demonstrated the modeling power and generalization performance of the PCA model. The average 3D modeling error using PCA was within 1 mm (0.7 ± 0.1 mm). When a single artificial internal marker was used to derive the lung motion, the average 3D error was found to be within 2 mm (1.8 ± 0.3 mm) through comprehensive statistical analysis. The optimal number of PCA coefficients needs to be determined on a patient-by-patient basis and two PCA coefficients seem to be sufficient for accurate modeling of the lung motion for most patients. In conclusion, we have presented thorough theoretical analysis and clinical validation of the PCA lung motion model. The feasibility of deriving the entire lung motion using a single marker has also been demonstrated on clinical data using a simulation approach.

Laminar flow effects in the coil planet centrifuge

NASA Technical Reports Server (NTRS)

Herrmann, F. T.

1984-01-01

The coil planet centrifuge designed by Ito employs flow of a single liquid phase, through a rotating coiled tube in a centrifugal force field, to provide a separation of particles based on sedimentation rates. Mathematical solutions are derived for the linear differential equations governing particle behavior in the coil planet centrifuge device. These solutions are then applied as the basis of a model for optimizing particle separations.

Cyber Signal/Noise Characteristics and Sensor Models for Early Cyber Indications and Warning

DTIC Science & Technology

2005-09-01

investigating and simulating attack scenarios. The sensors are, in effect , mathematical functions. These functions range from simple functions of...172 8.1.2 Examine each attack scenario or case to derive the cause- effect network for the attack scenario...threat profiles............................ 174 8.1.4 Develop attack profiles by enlarging the cause- effect network of each attack scenario with

A Solution to the Cosmic Conundrum including Cosmological Constant and Dark Energy Problems

NASA Astrophysics Data System (ADS)

Singh, A.

2009-12-01

A comprehensive solution to the cosmic conundrum is presented that also resolves key paradoxes of quantum mechanics and relativity. A simple mathematical model, the Gravity Nullification model (GNM), is proposed that integrates the missing physics of the spontaneous relativistic conversion of mass to energy into the existing physics theories, specifically a simplified general theory of relativity. Mechanistic mathematical expressions are derived for a relativistic universe expansion, which predict both the observed linear Hubble expansion in the nearby universe and the accelerating expansion exhibited by the supernova observations. The integrated model addresses the key questions haunting physics and Big Bang cosmology. It also provides a fresh perspective on the misconceived birth and evolution of the universe, especially the creation and dissolution of matter. The proposed model eliminates singularities from existing models and the need for the incredible and unverifiable assumptions including the superluminous inflation scenario, multiple universes, multiple dimensions, Anthropic principle, and quantum gravity. GNM predicts the observed features of the universe without any explicit consideration of time as a governing parameter.

Optimisation of near-infrared reflectance model in measuring protein and amylose content of rice flour.

PubMed

Xie, L H; Tang, S Q; Chen, N; Luo, J; Jiao, G A; Shao, G N; Wei, X J; Hu, P S

2014-01-01

Near-infrared reflectance spectroscopy (NIRS) has been used to predict the cooking quality parameters of rice, such as the protein (PC) and amylose content (AC). Using brown and milled flours from 519 rice samples representing a wide range of grain qualities, this study was to compare the calibration models generated by different mathematical, preprocessing treatments, and combinations of different regression algorithm. A modified partial least squares model (MPLS) with the mathematic treatment "2, 8, 8, 2" (2nd order derivative computed based on 8 data points, and 8 and 2 data points in the 1st and 2nd smoothing, respectively) and inverse multiplicative scattering correction preprocessing treatment was identified as the best model for simultaneously measurement of PC and AC in brown flours. MPLS/"2, 8, 8, 2"/detrend preprocessing was identified as the best model for milled flours. The results indicated that NIRS could be useful in estimation of PC and AC of breeding lines in early generations of the breeding programs, and for the purposes of quality control in the food industry. Copyright © 2013 Elsevier Ltd. All rights reserved.

Atmospheric mold spore counts in relation to meteorological parameters

NASA Astrophysics Data System (ADS)

Katial, R. K.; Zhang, Yiming; Jones, Richard H.; Dyer, Philip D.

Fungal spore counts of Cladosporium, Alternaria, and Epicoccum were studied during 8 years in Denver, Colorado. Fungal spore counts were obtained daily during the pollinating season by a Rotorod sampler. Weather data were obtained from the National Climatic Data Center. Daily averages of temperature, relative humidity, daily precipitation, barometric pressure, and wind speed were studied. A time series analysis was performed on the data to mathematically model the spore counts in relation to weather parameters. Using SAS PROC ARIMA software, a regression analysis was performed, regressing the spore counts on the weather variables assuming an autoregressive moving average (ARMA) error structure. Cladosporium was found to be positively correlated (P<0.02) with average daily temperature, relative humidity, and negatively correlated with precipitation. Alternaria and Epicoccum did not show increased predictability with weather variables. A mathematical model was derived for Cladosporium spore counts using the annual seasonal cycle and significant weather variables. The model for Alternaria and Epicoccum incorporated the annual seasonal cycle. Fungal spore counts can be modeled by time series analysis and related to meteorological parameters controlling for seasonallity; this modeling can provide estimates of exposure to fungal aeroallergens.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model.

PubMed

Chao, Anne; Jost, Lou; Hsieh, T C; Ma, K H; Sherwin, William B; Rollins, Lee Ann

2015-01-01

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

Multi-factor energy price models and exotic derivatives pricing

NASA Astrophysics Data System (ADS)

Hikspoors, Samuel

The high pace at which many of the world's energy markets have gradually been opened to competition have generated a significant amount of new financial activity. Both academicians and practitioners alike recently started to develop the tools of energy derivatives pricing/hedging as a quantitative topic of its own. The energy contract structures as well as their underlying asset properties set the energy risk management industry apart from its more standard equity and fixed income counterparts. This thesis naturally contributes to these broad market developments in participating to the advances of the mathematical tools aiming at a better theory of energy contingent claim pricing/hedging. We propose many realistic two-factor and three-factor models for spot and forward price processes that generalize some well known and standard modeling assumptions. We develop the associated pricing methodologies and propose stable calibration algorithms that motivate the application of the relevant modeling schemes.

Molecular Descriptors

NASA Astrophysics Data System (ADS)

Consonni, Viviana; Todeschini, Roberto

In the last decades, several scientific researches have been focused on studying how to encompass and convert - by a theoretical pathway - the information encoded in the molecular structure into one or more numbers used to establish quantitative relationships between structures and properties, biological activities, or other experimental properties. Molecular descriptors are formally mathematical representations of a molecule obtained by a well-specified algorithm applied to a defined molecular representation or a well-specified experimental procedure. They play a fundamental role in chemistry, pharmaceutical sciences, environmental protection policy, toxicology, ecotoxicology, health research, and quality control. Evidence of the interest of the scientific community in the molecular descriptors is provided by the huge number of descriptors proposed up today: more than 5000 descriptors derived from different theories and approaches are defined in the literature and most of them can be calculated by means of dedicated software applications. Molecular descriptors are of outstanding importance in the research fields of quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs), where they are the independent chemical information used to predict the properties of interest. Along with the definition of appropriate molecular descriptors, the molecular structure representation and the mathematical tools for deriving and assessing models are other fundamental components of the QSAR/QSPR approach. The remarkable progress during the last few years in chemometrics and chemoinformatics has led to new strategies for finding mathematical meaningful relationships between the molecular structure and biological activities, physico-chemical, toxicological, and environmental properties of chemicals. Different approaches for deriving molecular descriptors here reviewed and some of the most relevant descriptors are presented in detail with numerical examples.

Model-Based Sensor-Augmented Pump Therapy

PubMed Central

Grosman, Benyamin; Voskanyan, Gayane; Loutseiko, Mikhail; Roy, Anirban; Mehta, Aloke; Kurtz, Natalie; Parikh, Neha; Kaufman, Francine R.; Mastrototaro, John J.; Keenan, Barry

2013-01-01

Background In insulin pump therapy, optimization of bolus and basal insulin dose settings is a challenge. We introduce a new algorithm that provides individualized basal rates and new carbohydrate ratio and correction factor recommendations. The algorithm utilizes a mathematical model of blood glucose (BG) as a function of carbohydrate intake and delivered insulin, which includes individualized parameters derived from sensor BG and insulin delivery data downloaded from a patient’s pump. Methods A mathematical model of BG as a function of carbohydrate intake and delivered insulin was developed. The model includes fixed parameters and several individualized parameters derived from the subject’s BG measurements and pump data. Performance of the new algorithm was assessed using n = 4 diabetic canine experiments over a 32 h duration. In addition, 10 in silico adults from the University of Virginia/Padova type 1 diabetes mellitus metabolic simulator were tested. Results The percentage of time in glucose range 80–180 mg/dl was 86%, 85%, 61%, and 30% using model-based therapy and [78%, 100%] (brackets denote multiple experiments conducted under the same therapy and animal model), [75%, 67%], 47%, and 86% for the control experiments for dogs 1 to 4, respectively. The BG measurements obtained in the simulation using our individualized algorithm were in 61–231 mg/dl min–max envelope, whereas use of the simulator’s default treatment resulted in BG measurements 90–210 mg/dl min–max envelope. Conclusions The study results demonstrate the potential of this method, which could serve as a platform for improving, facilitating, and standardizing insulin pump therapy based on a single download of data. PMID:23567006

The dynamics and control of large-flexible space structures, part 10

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R.

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

The beta Burr type X distribution properties with application.

PubMed

Merovci, Faton; Khaleel, Mundher Abdullah; Ibrahim, Noor Akma; Shitan, Mahendran

2016-01-01

We develop a new continuous distribution called the beta-Burr type X distribution that extends the Burr type X distribution. The properties provide a comprehensive mathematical treatment of this distribution. Further more, various structural properties of the new distribution are derived, that includes moment generating function and the rth moment thus generalizing some results in the literature. We also obtain expressions for the density, moment generating function and rth moment of the order statistics. We consider the maximum likelihood estimation to estimate the parameters. Additionally, the asymptotic confidence intervals for the parameters are derived from the Fisher information matrix. Finally, simulation study is carried at under varying sample size to assess the performance of this model. Illustration the real dataset indicates that this new distribution can serve as a good alternative model to model positive real data in many areas.

Why were Matrix Mechanics and Wave Mechanics considered equivalent?

NASA Astrophysics Data System (ADS)

Perovic, Slobodan

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence ("Schrödinger-equivalence") of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it.

The Effect of Geogebra on Students' Conceptual and Procedural Knowledge: The Case of Applications of Derivative

ERIC Educational Resources Information Center

Ocal, Mehmet Fatih

2017-01-01

Integrating the properties of computer algebra systems and dynamic geometry environments, Geogebra became an effective and powerful tool for teaching and learning mathematics. One of the reasons that teachers use Geogebra in mathematics classrooms is to make students learn mathematics meaningfully and conceptually. From this perspective, the…

Working for Learning: Teaching Assistants Developing Mathematics for Teaching

ERIC Educational Resources Information Center

Drake, Pat

2009-01-01

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken…

A Phenomenological Exploration of Mathematical Engagement: Approaching an Old Metaphor Anew.

ERIC Educational Resources Information Center

Handa, Yuichi

2003-01-01

Investigates the heart of the experience of mathematical engagement and the meaning derived from such activities. Analyzes dialogue between five people, two of whom are professional mathematicians, another two who are graduate students in either engineering or education, and one who lacks advanced mathematical training but maintains a positive…

Making Mathematics Relevant for Students in Bali

ERIC Educational Resources Information Center

Sema, Pryde Nubea

2008-01-01

The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…

Teachers, Equity, and Computers for Secondary Mathematics Learning

ERIC Educational Resources Information Center

Forgasz, Helen

2006-01-01

The findings presented in this article were derived from a 3-year study aimed at examining issues associated with the use of computers for secondary mathematics learning in Victorian (Australia) schools. Gender and other equity factors were of particular interest. In this article, the focus is on the participating mathematics teachers. Data on…

A Bionic Polarization Navigation Sensor and Its Calibration Method.

PubMed

Zhao, Huijie; Xu, Wujian

2016-08-03

The polarization patterns of skylight which arise due to the scattering of sunlight in the atmosphere can be used by many insects for deriving compass information. Inspired by insects' polarized light compass, scientists have developed a new kind of navigation method. One of the key techniques in this method is the polarimetric sensor which is used to acquire direction information from skylight. In this paper, a polarization navigation sensor is proposed which imitates the working principles of the polarization vision systems of insects. We introduce the optical design and mathematical model of the sensor. In addition, a calibration method based on variable substitution and non-linear curve fitting is proposed. The results obtained from the outdoor experiments provide support for the feasibility and precision of the sensor. The sensor's signal processing can be well described using our mathematical model. A relatively high degree of accuracy in polarization measurement can be obtained without any error compensation.

Imbedded-Fracture Formulation of THMC Processes in Fractured Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.; Sung, R.

2016-12-01

Fractured media consist of porous materials and fracture networks. There exist four approaches to mathematically formulating THMC (Thermal-Hydrology-Mechanics-Chemistry) processes models in the system: (1) Equivalent Porous Media, (2) Dual Porosity or Dual Continuum, (3) Heterogeneous Media, and (4) Discrete Fracture Network. The first approach cannot explicitly explore the interactions between porous materials and fracture networks. The second approach introduces too many extra parameters (namely, exchange coefficients) between two media. The third approach may make the problems too stiff because the order of material heterogeneity may be too much. The fourth approach ignore the interaction between porous materials and fracture networks. This talk presents an alternative approach in which fracture networks are modeled with a lower dimension than the surrounding porous materials. Theoretical derivation of mathematical formulations will be given. An example will be illustrated to show the feasibility of this approach.

Theoretical analysis of ozone generation by pulsed dielectric barrier discharge in oxygen

NASA Astrophysics Data System (ADS)

Wei, L. S.; Zhou, J. H.; Wang, Z. H.; Cen, K. F.

2007-08-01

The use of very short high-voltage pulses combined with a dielectric layer results in high-energy electrons that dissociate oxygen molecules into atoms, which are a prerequisite for the subsequent production of ozone by collisions with oxygen molecules and third particles. The production of ozone depends on both the electrical and the physical parameters. For ozone generation by pulsed dielectric barrier discharge in oxygen, a mathematical model, which describes the relation between ozone concentration and these parameters that are of importance in its design, is developed according to dimensional analysis theory. A formula considering the ozone destruction factor is derived for predicting the characteristics of the ozone generation, within the range of the corona inception voltage to the gap breakdown voltage. The trend showing the dependence of the concentration of ozone in oxygen on these parameters generally agrees with the experimental results, thus confirming the validity of the mathematical model.

A Bionic Polarization Navigation Sensor and Its Calibration Method

PubMed Central

Zhao, Huijie; Xu, Wujian

2016-01-01

The polarization patterns of skylight which arise due to the scattering of sunlight in the atmosphere can be used by many insects for deriving compass information. Inspired by insects’ polarized light compass, scientists have developed a new kind of navigation method. One of the key techniques in this method is the polarimetric sensor which is used to acquire direction information from skylight. In this paper, a polarization navigation sensor is proposed which imitates the working principles of the polarization vision systems of insects. We introduce the optical design and mathematical model of the sensor. In addition, a calibration method based on variable substitution and non-linear curve fitting is proposed. The results obtained from the outdoor experiments provide support for the feasibility and precision of the sensor. The sensor’s signal processing can be well described using our mathematical model. A relatively high degree of accuracy in polarization measurement can be obtained without any error compensation. PMID:27527171

A mathematical analysis of the Janus combat simulation weather effects models and sensitivity analysis of sky-to-ground brightness ratio on target detection

NASA Astrophysics Data System (ADS)

Shorts, Vincient F.

1994-09-01

The Janus combat simulation offers the user a wide variety of weather effects options to employ during the execution of any simulation run, which can directly influence detection of opposing forces. Realistic weather effects are required if the simulation is to accurately reproduce 'real world' results. This thesis examines the mathematics of the Janus weather effects models. A weather effect option in Janus is the sky-to-ground brightness ratio (SGR). SGR affects an optical sensor's ability to detect targets. It is a measure of the sun angle in relation to the horizon. A review of the derivation of SGR is performed and an analysis of SGR's affect on the number of optical detections and detection ranges is performed using an unmanned aerial vehicle (UAV) search scenario. For comparison, the UAV's are equipped with a combination of optical and thermal sensors.

The effect of gas and fluid flows on nonlinear lateral vibrations of rotating drill strings

NASA Astrophysics Data System (ADS)

Khajiyeva, Lelya; Kudaibergenov, Askar; Kudaibergenov, Askat

2018-06-01

In this work we develop nonlinear mathematical models describing coupled lateral vibrations of a rotating drill string under the effect of external supersonic gas and internal fluid flows. An axial compressive load and a torque also affect the drill string. The mathematical models are derived by the use of Novozhilov's nonlinear theory of elasticity with implementation of Hamilton's variation principle. Expressions for the gas flow pressure are determined according to the piston theory. The fluid flow is considered as added mass inside the curved tube of the drill string. Using an algorithm developed in the Mathematica computation program on the basis of the Galerkin approach and the stiffness switching method the numerical solution of the obtained approximate differential equations is found. Influences of the external loads, drill string angular speed of rotation, parameters of the gas and fluid flows on the drill string vibrations are shown.

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system.

PubMed

Wang, Bin; Xue, Jianyi; Wu, Fengjiao; Zhu, Delan

2016-11-01

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

The fractional diffusion limit of a kinetic model with biochemical pathway

NASA Astrophysics Data System (ADS)

Perthame, Benoît; Sun, Weiran; Tang, Min

2018-06-01

Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.

On Modeling and Analysis of MIMO Wireless Mesh Networks with Triangular Overlay Topology

DOE PAGES

Cao, Zhanmao; Wu, Chase Q.; Zhang, Yuanping; ...

2015-01-01

Multiple input multiple output (MIMO) wireless mesh networks (WMNs) aim to provide the last-mile broadband wireless access to the Internet. Along with the algorithmic development for WMNs, some fundamental mathematical problems also emerge in various aspects such as routing, scheduling, and channel assignment, all of which require an effective mathematical model and rigorous analysis of network properties. In this paper, we propose to employ Cartesian product of graphs (CPG) as a multichannel modeling approach and explore a set of unique properties of triangular WMNs. In each layer of CPG with a single channel, we design a node coordinate scheme thatmore » retains the symmetric property of triangular meshes and develop a function for the assignment of node identity numbers based on their coordinates. We also derive a necessary-sufficient condition for interference-free links and combinatorial formulas to determine the number of the shortest paths for channel realization in triangular WMNs.« less

Quantitative dual-probe microdialysis: mathematical model and analysis.

PubMed

Chen, Kevin C; Höistad, Malin; Kehr, Jan; Fuxe, Kjell; Nicholson, Charles

2002-04-01

Steady-state microdialysis is a widely used technique to monitor the concentration changes and distributions of substances in tissues. To obtain more information about brain tissue properties from microdialysis, a dual-probe approach was applied to infuse and sample the radiotracer, [3H]mannitol, simultaneously both in agar gel and in the rat striatum. Because the molecules released by one probe and collected by the other must diffuse through the interstitial space, the concentration profile exhibits dynamic behavior that permits the assessment of the diffusion characteristics in the brain extracellular space and the clearance characteristics. In this paper a mathematical model for dual-probe microdialysis was developed to study brain interstitial diffusion and clearance processes. Theoretical expressions for the spatial distribution of the infused tracer in the brain extracellular space and the temporal concentration at the probe outlet were derived. A fitting program was developed using the simplex algorithm, which finds local minima of the standard deviations between experiments and theory by adjusting the relevant parameters. The theoretical curves accurately fitted the experimental data and generated realistic diffusion parameters, implying that the mathematical model is capable of predicting the interstitial diffusion behavior of [3H]mannitol and that it will be a valuable quantitative tool in dual-probe microdialysis.

Discerning apical and basolateral properties of HT-29/B6 and IPEC-J2 cell layers by impedance spectroscopy, mathematical modeling and machine learning.

PubMed

Schmid, Thomas; Bogdan, Martin; Günzel, Dorothee

2013-01-01

Quantifying changes in partial resistances of epithelial barriers in vitro is a challenging and time-consuming task in physiology and pathophysiology. Here, we demonstrate that electrical properties of epithelial barriers can be estimated reliably by combining impedance spectroscopy measurements, mathematical modeling and machine learning algorithms. Conventional impedance spectroscopy is often used to estimate epithelial capacitance as well as epithelial and subepithelial resistance. Based on this, the more refined two-path impedance spectroscopy makes it possible to further distinguish transcellular and paracellular resistances. In a next step, transcellular properties may be further divided into their apical and basolateral components. The accuracy of these derived values, however, strongly depends on the accuracy of the initial estimates. To obtain adequate accuracy in estimating subepithelial and epithelial resistance, artificial neural networks were trained to estimate these parameters from model impedance spectra. Spectra that reflect behavior of either HT-29/B6 or IPEC-J2 cells as well as the data scatter intrinsic to the used experimental setup were created computationally. To prove the proposed approach, reliability of the estimations was assessed with both modeled and measured impedance spectra. Transcellular and paracellular resistances obtained by such neural network-enhanced two-path impedance spectroscopy are shown to be sufficiently reliable to derive the underlying apical and basolateral resistances and capacitances. As an exemplary perturbation of pathophysiological importance, the effect of forskolin on the apical resistance of HT-29/B6 cells was quantified.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Strategic development in exact calculation: group and individual differences in four achievement subtypes.

PubMed

Wylie, Judith; Jordan, Julie-Ann; Mulhern, Gerry

2012-09-01

This longitudinal study sought to identify developmental changes in strategy use between 5 and 7 years of age when solving exact calculation problems. Four mathematics and reading achievement subtypes were examined at four time points. Five strategies were considered: finger counting, verbal counting, delayed retrieval, automatic retrieval, and derived fact retrieval. Results provided unique insights into children's strategic development in exact calculation at this early stage. Group analysis revealed relationships between mathematical and/or reading difficulties and strategy choice, shift, and adaptiveness. Use of derived fact retrieval by 7 years of age distinguished children with mathematical difficulties from other achievement subtypes. Analysis of individual differences revealed marked heterogeneity within all subtypes, suggesting (inter alia) no marked qualitative distinction between our two mathematical difficulty subtypes. Copyright © 2012 Elsevier Inc. All rights reserved.

Spatial panorama of malaria prevalence in Africa under climate change and interventions scenarios.

PubMed

Moukam Kakmeni, Francois M; Guimapi, Ritter Y A; Ndjomatchoua, Frank T; Pedro, Sansoa A; Mutunga, James; Tonnang, Henri E Z

2018-01-16

Malaria is highly sensitive to climatic variables and is strongly influenced by the presence of vectors in a region that further contribute to parasite development and sustained disease transmission. Mathematical analysis of malaria transmission through the use and application of the value of the basic reproduction number (R 0 ) threshold is an important and useful tool for the understanding of disease patterns. Temperature dependence aspect of R 0 obtained from dynamical mathematical network model was used to derive the spatial distribution maps for malaria transmission under different climatic and intervention scenarios. Model validation was conducted using MARA map and the Annual Plasmodium falciparum Entomological Inoculation Rates for Africa. The inclusion of the coupling between patches in dynamical model seems to have no effects on the estimate of the optimal temperature (about 25 °C) for malaria transmission. In patches environment, we were able to establish a threshold value (about α = 5) representing the ratio between the migration rates from one patch to another that has no effect on the magnitude of R 0 . Such findings allow us to limit the production of the spatial distribution map of R 0 to a single patch model. Future projections using temperature changes indicated a shift in malaria transmission areas towards the southern and northern areas of Africa and the application of the interventions scenario yielded a considerable reduction in transmission within malaria endemic areas of the continent. The approach employed here is a sole study that defined the limits of contemporary malaria transmission, using R 0 derived from a dynamical mathematical model. It has offered a unique prospect for measuring the impacts of interventions through simple manipulation of model parameters. Projections at scale provide options to visualize and query the results, when linked to the human population could potentially deliver adequate highlight on the number of individuals at risk of malaria infection across Africa. The findings provide a reasonable basis for understanding the fundamental effects of malaria control and could contribute towards disease elimination, which is considered as a challenge especially in the context of climate change.

The stabilizing role of the Sabbath in pre-monarchic Israel: a mathematical model.

PubMed

Livni, Joseph; Stone, Lewi

2015-03-01

The three monotheistic cultures have many common institutions and some of them germinated in pre-monarchic Israel. Reasonably, the essential institutions were in place at that starting point; this work explores the possibility that the Sabbath is one of these institutions. Our mathematical examination points to the potential cultural, civic, and social role of the weekly Sabbath, that is, the Sabbath institution, in controlling deviation from social norms. It begins with an analogy between spread of transgression (defined as lack of conformity with social norms) and of biological infection. Borrowing well-known mathematical methods, we derive solution sets of social equilibrium and study their social stability. The work shows how a weekly Sabbath could in theory enhance social resilience in comparison with a similar assembly with a more natural and longer period, say between New Moon and Full Moon. The examination reveals that an efficient Sabbath institution has the potential to ensure a stable organization and suppress occasional appearances of transgression from cultural norms and boundaries. The work suggests the existence of a sharp threshold governed by the "Basic Sabbath Number ש0"-a critical observance of the Sabbath, or large enough ש0, is required to ensure suppression of transgression. Subsequently, the model is used to explore an interesting question: how old is the Sabbath? The work is interdisciplinary, combining anthropological concepts with mathematical analysis and with archaeological parallels in regards to the findings.

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

PubMed

Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2017-01-01

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

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.

Intra-Mathematical Connections Made by High School Students in Performing Calculus Tasks

ERIC Educational Resources Information Center

García-García, Javier; Dolores-Flores, Crisólogo

2018-01-01

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

Young, Black, and Anxious: Describing the Black Student Mathematics Anxiety Research Using Confidence Intervals

ERIC Educational Resources Information Center

Young, Jamaal Rashad; Young, Jemimah Lea

2016-01-01

In this article, the authors provide a single group summary using the Mathematics Anxiety Rating Scale (MARS) to characterize and delineate the measurement of mathematics anxiety (MA) reported among Black students. Two research questions are explored: (a) What are the characteristics of studies administering the MARS and its derivatives to…

Degrees in Science and Mathematics: National Trends and State-by-State Data.

ERIC Educational Resources Information Center

Harworth, Irene

This compilation of recent statistical information on science and mathematics degrees in the United States also describes the larger environment of employment of individuals with science and mathematics degrees and provides some information on non-U.S. citizens receiving degrees in these areas. Data are derived from four survey programs of the…

Polytechnic Engineering Mathematics: Assessing Its Relevance to the Productivity of Industries in Uganda

ERIC Educational Resources Information Center

Jehopio, Peter J.; Wesonga, Ronald

2017-01-01

Background: The main objective of the study was to examine the relevance of engineering mathematics to the emerging industries. The level of abstraction, the standard of rigor, and the depth of theoretical treatment are necessary skills expected of a graduate engineering technician to be derived from mathematical knowledge. The question of whether…

Thermodynamic work from operational principles

NASA Astrophysics Data System (ADS)

Gallego, R.; Eisert, J.; Wilming, H.

2016-10-01

In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines, in an analogous way to the role played, for macroscopic machines, by the energy stored in the idealisation of a lifted weight. Despite several attempts to resolve this issue by putting forward specific models, these are far from realistically capturing the transitions that a quantum machine is expected to perform. In this work, we adopt a novel strategy by considering arbitrary kinds of systems that one can attach to a quantum thermal machine and defining work quantifiers. These are functions that measure the value of a transition and generalise the concept of work beyond those models familiar from phenomenological thermodynamics. We do so by imposing simple operational axioms that any reasonable work quantifier must fulfil and by deriving from them stringent mathematical condition with a clear physical interpretation. Our approach allows us to derive much of the structure of the theory of thermodynamics without taking the definition of work as a primitive. We can derive, for any work quantifier, a quantitative second law in the sense of bounding the work that can be performed using some non-equilibrium resource by the work that is needed to create it. We also discuss in detail the role of reversibility and correlations in connection with the second law. Furthermore, we recover the usual identification of work with energy in degrees of freedom with vanishing entropy as a particular case of our formalism. Our mathematical results can be formulated abstractly and are general enough to carry over to other resource theories than quantum thermodynamics.

Replica Approach for Minimal Investment Risk with Cost

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-06-01

In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where an objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the mathematical similarity between the Hamiltonian in the mean-variance model and the Hamiltonians in the Hopfield model and the Sherrington-Kirkpatrick model, show that we can analyze this portfolio optimization problem by using replica analysis, and derive the minimal investment risk with cost and the investment concentration of the optimal portfolio. Furthermore, we validate our proposed method through numerical simulations.

3D model of filler melting with micro-beam plasma arc based on additive manufacturing technology

NASA Astrophysics Data System (ADS)

Chen, Weilin; Yang, Tao; Yang, Ruixin

2017-07-01

Additive manufacturing technology is a systematic process based on discrete-accumulation principle, which is derived by the dimension of parts. Aiming at the dimension mathematical model and slicing problems in additive manufacturing process, the constitutive relations between micro-beam plasma welding parameters and the dimension of part were investigated. The slicing algorithm and slicing were also studied based on the dimension characteristics. By using the direct slicing algorithm according to the geometric characteristics of model, a hollow thin-wall spherical part was fabricated by 3D additive manufacturing technology using micro-beam plasma.

Vision, healing brush, and fiber bundles

NASA Astrophysics Data System (ADS)

Georgiev, Todor

2005-03-01

The Healing Brush is a tool introduced for the first time in Adobe Photoshop (2002) that removes defects in images by seamless cloning (gradient domain fusion). The Healing Brush algorithms are built on a new mathematical approach that uses Fibre Bundles and Connections to model the representation of images in the visual system. Our mathematical results are derived from first principles of human vision, related to adaptation transforms of von Kries type and Retinex theory. In this paper we present the new result of Healing in arbitrary color space. In addition to supporting image repair and seamless cloning, our approach also produces the exact solution to the problem of high dynamic range compression of17 and can be applied to other image processing algorithms.

Steady state phosphorus mass balance model during hemodialysis based on a pseudo one-compartment kinetic model.

PubMed

Leypoldt, John K; Agar, Baris U; Akonur, Alp; Gellens, Mary E; Culleton, Bruce F

2012-11-01

Mathematical models of phosphorus kinetics and mass balance during hemodialysis are in early development. We describe a theoretical phosphorus steady state mass balance model during hemodialysis based on a novel pseudo one-compartment kinetic model. The steady state mass balance model accounted for net intestinal absorption of phosphorus and phosphorus removal by both dialysis and residual kidney function. Analytical mathematical solutions were derived to describe time-dependent intradialytic and interdialytic serum phosphorus concentrations assuming hemodialysis treatments were performed symmetrically throughout a week. Results from the steady state phosphorus mass balance model are described for thrice weekly hemodialysis treatment prescriptions only. The analysis predicts 1) a minimal impact of dialyzer phosphorus clearance on predialysis serum phosphorus concentration using modern, conventional hemodialysis technology, 2) variability in the postdialysis-to-predialysis phosphorus concentration ratio due to differences in patient-specific phosphorus mobilization, and 3) the importance of treatment time in determining the predialysis serum phosphorus concentration. We conclude that a steady state phosphorus mass balance model can be developed based on a pseudo one-compartment kinetic model and that predictions from this model are consistent with previous clinical observations. The predictions from this mass balance model are theoretical and hypothesis-generating only; additional prospective clinical studies will be required for model confirmation.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.

PubMed

Zana, F; Klein, J C

2001-01-01

This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.

Effects of global climate change on the US forest sector: response functions derived from a dynamic resource and market simulator.

Treesearch

Bruce A. McCarl; Darius M. Adams; Ralph J. Alig; Diana Burton; Chi-Chung. Chen

2000-01-01

A multiperiod, regional, mathematical programming economic model is used to evaluate the potential economic impacts of global climatic change on the US forest sector. A wide range of scenarios for the biological response of forests to climate change are developed, ranging from small to large changes in forest growth rates. These scenarios are simulated in the economic...

Exact solutions for sporadic acceleration of cosmic rays

NASA Technical Reports Server (NTRS)

Cowsik, R.

1985-01-01

The steady state spectra of cosmic rays which are subject to a sporadic acceleration process, wherein the gain in energy in each encounter is a finite fraction of the particle energy are discussed. They are derived from a mathematical model which includes the possibility of energy dependent leakage of cosmic rays from the galaxy. Comparison with observations allows limits to be placed on the frequency and efficiency of such encounters.

Passive Optical Detection of a Vibrating Surface

DTIC Science & Technology

2014-01-01

modulation from any given surface? Clearly a detailed mathematical model of light scattering (i.e., BRDF ) is needed, so that we may take the partial...reflectance distribution function ( BRDF ): “The BRDF is a derivative, a distri- bution function, relating the irradiance incident from one given...direction to its contribution to the reflected radiance in another direction.” In other words, the BRDF is a multidimensional surface: the relevant variables

Relay-aided free-space optical communications using α - μ distribution over atmospheric turbulence channels with misalignment errors

NASA Astrophysics Data System (ADS)

Upadhya, Abhijeet; Dwivedi, Vivek K.; Singh, G.

2018-06-01

In this paper, we have analyzed the performance of dual hop radio frequency (RF)/free-space optical (FSO) fixed gain relay environment confined by atmospheric turbulence induced fading channel over FSO link and modeled using α - μ distribution. The RF hop of the amplify-and-forward scheme undergoes the Rayleigh fading and the proposed system model also considers the pointing error effect on the FSO link. A novel and accurate mathematical expression of the probability density function for a FSO link experiencing α - μ distributed atmospheric turbulence in the presence of pointing error is derived. Further, we have presented analytical expressions of outage probability and bit error rate in terms of Meijer-G function. In addition to this, a useful and mathematically tractable closed-form expression for the end-to-end ergodic capacity of the dual hop scheme in terms of bivariate Fox's H function is derived. The atmospheric turbulence, misalignment errors and various binary modulation schemes for intensity modulation on optical wireless link are considered to yield the results. Finally, we have analyzed each of the three performance metrics for high SNR in order to represent them in terms of elementary functions and the achieved analytical results are supported by computer-based simulations.

Tumor-Specific Chromosome Mis-Segregation Controls Cancer Plasticity by Maintaining Tumor Heterogeneity

PubMed Central

Hu, Yuanjie; Ru, Ning; Xiao, Huasheng; Chaturbedi, Abhishek; Hoa, Neil T.; Tian, Xiao-Jun; Zhang, Hang; Ke, Chao; Yan, Fengrong; Nelson, Jodi; Li, Zhenzhi; Gramer, Robert; Yu, Liping; Siegel, Eric; Zhang, Xiaona; Jia, Zhenyu; Jadus, Martin R.; Limoli, Charles L.; Linskey, Mark E.; Xing, Jianhua; Zhou, Yi-Hong

2013-01-01

Aneuploidy with chromosome instability is a cancer hallmark. We studied chromosome 7 (Chr7) copy number variation (CNV) in gliomas and in primary cultures derived from them. We found tumor heterogeneity with cells having Chr7-CNV commonly occurs in gliomas, with a higher percentage of cells in high-grade gliomas carrying more than 2 copies of Chr7, as compared to low-grade gliomas. Interestingly, all Chr7-aneuploid cell types in the parental culture of established glioma cell lines reappeared in single-cell-derived subcultures. We then characterized the biology of three syngeneic glioma cultures dominated by different Chr7-aneuploid cell types. We found phenotypic divergence for cells following Chr7 mis-segregation, which benefited overall tumor growth in vitro and in vivo. Mathematical modeling suggested the involvement of chromosome instability and interactions among cell subpopulations in restoring the optimal equilibrium of tumor cell types. Both our experimental data and mathematical modeling demonstrated that the complexity of tumor heterogeneity could be enhanced by the existence of chromosomes with structural abnormality, in addition to their mis-segregations. Overall, our findings show, for the first time, the involvement of chromosome instability in maintaining tumor heterogeneity, which underlies the enhanced growth, persistence and treatment resistance of cancers. PMID:24282558

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

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

He, Jin-zhong, E-mail: viewsino@163.com; Yao, Shu-zhen; Zhang, Zhong-ping

2013-03-15

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seenmore » as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.« less

Mathematical model of salt cavern leaching for gas storage in high-insoluble salt formations.

PubMed

Li, Jinlong; Shi, Xilin; Yang, Chunhe; Li, Yinping; Wang, Tongtao; Ma, Hongling

2018-01-10

A mathematical model is established to predict the salt cavern development during leaching in high-insoluble salt formations. The salt-brine mass transfer rate is introduced, and the effects of the insoluble sediments on the development of the cavern are included. Considering the salt mass conservation in the cavern, the couple equations of the cavern shape, brine concentration and brine velocity are derived. According to the falling and accumulating rules of the insoluble particles, the governing equations of the insoluble sediments are deduced. A computer program using VC++ language is developed to obtain the numerical solution of these equations. To verify the proposed model, the leaching processes of two salt caverns of Jintan underground gas storage are simulated by the program, using the actual geological and technological parameters. The same simulation is performed by the current mainstream leaching software in China. The simulation results of the two programs are compared with the available field data. It shows that the proposed software is more accurate on the shape prediction of the cavern bottom and roof, which demonstrates the reliability and applicability of the model.

Mathematical Modeling of the Pituitary–Thyroid Feedback Loop: Role of a TSH-T3-Shunt and Sensitivity Analysis

PubMed Central

Berberich, Julian; Dietrich, Johannes W.; Hoermann, Rudolf; Müller, Matthias A.

2018-01-01

Despite significant progress in assay technology, diagnosis of functional thyroid disorders may still be a challenge, as illustrated by the vague upper limit of the reference range for serum thyrotropin (TSH). Diagnostical problems also apply to subjects affected by syndrome T, i.e., those 10% of hypothyroid patients who continue to suffer from poor quality of life despite normal TSH concentrations under substitution therapy with levothyroxine (L-T4). In this paper, we extend a mathematical model of the pituitary–thyroid feedback loop in order to improve the understanding of thyroid hormone homeostasis. In particular, we incorporate a TSH-T3-shunt inside the thyroid, whose existence has recently been demonstrated in several clinical studies. The resulting extended model shows good accordance with various clinical observations, such as a circadian rhythm in free peripheral triiodothyronine (FT3). Furthermore, we perform a sensitivity analysis of the derived model, revealing the dependence of TSH and hormone concentrations on different system parameters. The results have implications for clinical interpretation of thyroid tests, e.g., in the differential diagnosis of subclinical hypothyroidism. PMID:29619006

Mathematical Modeling of the Pituitary-Thyroid Feedback Loop: Role of a TSH-T3-Shunt and Sensitivity Analysis.

PubMed

Berberich, Julian; Dietrich, Johannes W; Hoermann, Rudolf; Müller, Matthias A

2018-01-01

Despite significant progress in assay technology, diagnosis of functional thyroid disorders may still be a challenge, as illustrated by the vague upper limit of the reference range for serum thyrotropin ( TSH ). Diagnostical problems also apply to subjects affected by syndrome T, i.e., those 10% of hypothyroid patients who continue to suffer from poor quality of life despite normal TSH concentrations under substitution therapy with levothyroxine ( L - T 4 ). In this paper, we extend a mathematical model of the pituitary-thyroid feedback loop in order to improve the understanding of thyroid hormone homeostasis. In particular, we incorporate a TSH - T 3 -shunt inside the thyroid, whose existence has recently been demonstrated in several clinical studies. The resulting extended model shows good accordance with various clinical observations, such as a circadian rhythm in free peripheral triiodothyronine ( FT 3 ). Furthermore, we perform a sensitivity analysis of the derived model, revealing the dependence of TSH and hormone concentrations on different system parameters. The results have implications for clinical interpretation of thyroid tests, e.g., in the differential diagnosis of subclinical hypothyroidism.

Coexistence trend contingent to Mediterranean oaks with different leaf habits.

PubMed

Di Paola, Arianna; Paquette, Alain; Trabucco, Antonio; Mereu, Simone; Valentini, Riccardo; Paparella, Francesco

2017-05-01

In a previous work we developed a mathematical model to explain the co-occurrence of evergreen and deciduous oak groups in the Mediterranean region, regarded as one of the distinctive features of Mediterranean biodiversity. The mathematical analysis showed that a stabilizing mechanism resulting from niche difference (i.e. different water use and water stress tolerance) between groups allows their coexistence at intermediate values of suitable soil water content. A simple formal derivation of the model expresses this hypothesis in a testable form linked uniquely to the actual evapotranspiration of forests community. In the present work we ascertain whether this simplified conclusion possesses some degree of explanatory power by comparing available data on oaks distributions and remotely sensed evapotranspiration (MODIS product) in a large-scale survey embracing the western Mediterranean area. Our findings confirmed the basic assumptions of model addressed on large scale, but also revealed asymmetric responses to water use and water stress tolerance between evergreen and deciduous oaks that should be taken into account to increase the understating of species interactions and, ultimately, improve the modeling capacity to explain co-occurrence.

Mathematical study of the effects of different intrahepatic cooling on thermal ablation zones.

PubMed

Peng, Tingying; O'Neill, David; Payne, Stephen

2011-01-01

Thermal ablation of a tumour in the liver with Radio Frequency energy can be accomplished by using a probe inserted into the tissue under the guidance of medical imaging. The extent of ablation can be significantly affected by heat loss due to the high blood perfusion in the liver, especially when the tumour is located close to large vessels. A mathematical model is thus presented here to investigate the heat sinking effects of large vessels, combining a 3D two-equation coupled bio-heat model and a 1D model of convective heat transport across the blood vessel surface. The model simulation is able to recover the experimentally observed different intrahepatic cooling on thermal ablation zones: hepatic veins showed a focal indentation whereas portal veins showed broad flattening of the ablation zones. Moreover, this study also illustrates that this shape derivation can largely be attributed to the temperature variations between the microvascular branches of portal vein as compared with hepatic vein. In contrast, different amount of surface heat convection on the vessel wall between these two types of veins, however, has a minor effect.

Mathematical modeling and design of a novel 2-DOF micro attraction actuator for a micro optical switch

NASA Astrophysics Data System (ADS)

Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

2004-08-01

Many studies on optical switches have been performed in an attempt to develop optical information networks to speed information technology. In reality, however, mirror manipulators cannot be applied to multiple input and output systems due to both insufficient output displacements by the mirror parts inside the manipulator, and the difficulty of designing structures and mechanisms suitable for multi-dimensional manipulation. The principal reasons for insufficient displacement are the high rigidity of the elastic parts compared to the available driving forces and the pull-in effect. Therefore, in order to develop optical switches capable of multiple input and output switching, we suggest a novel 2-DOF(degree of freedom) electrostatic microactuator. The actuator is composed of one mirror with four beams laid about it in a corkscrew pattern, with four corkscrew electrodes on the substrate below and one mirror support pyramid situated under the mirror. Using electrostatic force, one or more of the beams are attracted from their outer ends toward the substrate. The mirror is then tilted by an angle proportional to the attracted length along the beam. The inclination and direction of the mirror are determined by the combined attracted length of the four beams. In this work we derive the mathematical model for the corkscrew beam microactuator for optical switches and show that this mathematical model accurately simulates the device by comparison with finite element analysis results. We use this mathematical model for design of the microactuator. Further we show that the designed optical switch microactuator is capable of rotating the mirror from +32 to -32 degrees about two axes with a maximum operating voltage of 163 volts. Finally, stress analysis of the actuator shows that the generated stress in the structure is at most 369 MPa.

A new mathematical model for nitrogen gas production with special emphasis on the role of attached growth media in anammox hybrid reactor.

PubMed

Tomar, Swati; Gupta, Sunil Kumar

2015-11-01

The present study emphasised on the development of new mathematical models based on mass balance and stoichiometry of nitrogen removal in anammox hybrid reactor (AHR). The performance of AHR at varying hydraulic retention times (HRTs) and nitrogen loading rates (NLRs) revealed that nitrogen removal efficiency (NRE) increases with increase in HRT and was found optimal (89 %) at HRT of 2 days. Mass balance of nitrogen revealed that major fraction (74.1 %) of input nitrogen is converted into N2 gas followed by 11.2 % utilised in biomass synthesis. Attached growth media (AGM) in AHR contributed to an additional 15.4 % ammonium removal and reduced the sludge washout rate by 29 %. This also enhanced the sludge retention capacity of AHR and thus minimised the formation of nitrate in the treated effluent, which is one of the bottlenecks of anammox process. Process kinetics was also studied using various mathematical models. The mass balance model derived from total nitrogen was found most precise and predicted N2 gas with least error (1.68 ± 4.44 %). Model validation for substrate removal kinetics dictated comparatively higher correlation for Grau second-order model (0.952) than modified Stover-Kincannon model (0.920). The study concluded that owing to features of high biomass retention, less nitrate formation and consistently higher nitrogen removal efficiency, this reactor configuration is techno-economically most efficient and viable. The study opens the door for researchers and scientists for pilot-scale testing of AHR leading to its wide industrial application.

Mathematical Models for the Apparent Mass of the Seated Human Body Exposed to Vertical Vibration

NASA Astrophysics Data System (ADS)

Wei, L.; Griffin, M. J.

1998-05-01

Alternative mathematical models of the vertical apparent mass of the seated human body are developed. The optimum parameters of four models (two single-degree-of-freedom models and two two-degree-of-freedom models) are derived from the mean measured apparent masses of 60 subjects (24 men, 24 women, 12 children) previously reported. The best fits were obtained by fitting the phase data with single-degree-of-freedom and two-degree-of-freedom models having rigid support structures. For these two models, curve fitting was performed on each of the 60 subjects (so as to obtain optimum model parameters for each subject), for the averages of each of the three groups of subjects, and for the entire group of subjects. The values obtained are tabulated. Use of a two-degree-of-freedom model provided a better fit to the phase of the apparent mass at frequencies greater than about 8 Hz and an improved fit to the modulus of the apparent mass at frequencies around 5 Hz. It is concluded that the two-degree-of-freedom model provides an apparent mass similar to that of the human body, but this does not imply that the body moves in the same manner as the masses in this optimized two-degree-of-freedom model.

Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

NASA Astrophysics Data System (ADS)

Hendzel, Z.; Rykała, Ł.

2017-02-01

The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

Gaussian decomposition of high-resolution melt curve derivatives for measuring genome-editing efficiency

PubMed Central

Zaboikin, Michail; Freter, Carl

2018-01-01

We describe a method for measuring genome editing efficiency from in silico analysis of high-resolution melt curve data. The melt curve data derived from amplicons of genome-edited or unmodified target sites were processed to remove the background fluorescent signal emanating from free fluorophore and then corrected for temperature-dependent quenching of fluorescence of double-stranded DNA-bound fluorophore. Corrected data were normalized and numerically differentiated to obtain the first derivatives of the melt curves. These were then mathematically modeled as a sum or superposition of minimal number of Gaussian components. Using Gaussian parameters determined by modeling of melt curve derivatives of unedited samples, we were able to model melt curve derivatives from genetically altered target sites where the mutant population could be accommodated using an additional Gaussian component. From this, the proportion contributed by the mutant component in the target region amplicon could be accurately determined. Mutant component computations compared well with the mutant frequency determination from next generation sequencing data. The results were also consistent with our earlier studies that used difference curve areas from high-resolution melt curves for determining the efficiency of genome-editing reagents. The advantage of the described method is that it does not require calibration curves to estimate proportion of mutants in amplicons of genome-edited target sites. PMID:29300734

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

Spread of Ebola disease with susceptible exposed infected isolated recovered (SEIIhR) model

NASA Astrophysics Data System (ADS)

Azizah, Afina; Widyaningsih, Purnami; Retno Sari Saputro, Dewi

2017-06-01

Ebola is a deadly infectious disease and has caused an epidemic on several countries in West Africa. Mathematical modeling to study the spread of Ebola disease has been developed, including through models susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR). Furthermore, susceptible exposed infected isolated recovered (SEIIhR) model has been derived. The aims of this research are to derive SEIIhR model for Ebola disease, to determine the patterns of its spread, to determine the equilibrium point and stability of the equilibrium point using phase plane analysis, and also to apply the SEIIhR model on Ebola epidemic in Sierra Leone in 2014. The SEIIhR model is a differential equation system. Pattern of ebola disease spread with SEIIhR model is solution of the differential equation system. The equilibrium point of SEIIhR model is unique and it is a disease-free equilibrium point that stable. Application of the model is based on the data Ebola epidemic in Sierra Leone. The free-disease equilibrium point (Se; Ee; Ie; Ihe; Re )=(5743865, 0, 0, 0, 0) is stable.

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

When to Renew Software Licences at HPC Centres? A Mathematical Analysis

NASA Astrophysics Data System (ADS)

Baolai, Ge; MacIsaac, Allan B.

2010-11-01

In this paper we study a common problem faced by many high performance computing (HPC) centres: When and how to renew commercial software licences. Software vendors often sell perpetual licences along with forward update and support contracts at an additional, annual cost. Every year or so, software support personnel and the budget units of HPC centres are required to make the decision of whether or not to renew such support, and usually such decisions are made intuitively. The total cost for a continuing support contract can, however, be costly. One might therefore want a rational answer to the question of whether the option for a renewal should be exercised and when. In an attempt to study this problem within a market framework, we present the mathematical problem derived for the day to day operation of a hypothetical HPC centre that charges for the use of software packages. In the mathematical model, we assume that the uncertainty comes from the demand, number of users using the packages, as well as the price. Further we assume the availability of up to date software versions may also affect the demand. We develop a renewal strategy that aims to maximize the expected profit from the use the software under consideration. The derived problem involves a decision tree, which constitutes a numerical procedure that can be processed in parallel.

Line integral on engineering mathematics

NASA Astrophysics Data System (ADS)

Wiryanto, L. H.

2018-01-01

Definite integral is a basic material in studying mathematics. At the level of calculus, calculating of definite integral is based on fundamental theorem of calculus, related to anti-derivative, as the inverse operation of derivative. At the higher level such as engineering mathematics, the definite integral is used as one of the calculating tools of line integral. the purpose of this is to identify if there is a question related to line integral, we can use definite integral as one of the calculating experience. The conclusion of this research says that the teaching experience in introducing the relation between both integrals through the engineer way of thinking can motivate and improve students in understanding the material.

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1993-01-01

A new release rate equation to model the phase change of water to steam in composite materials was derived from the theory of molecular diffusion and equilibrium moisture concentration. The new model is dependent on internal pressure, the microstructure of the voids and channels in the composite materials, and the diffusion properties of the matrix material. Hence, it is more fundamental and accurate than the empirical Arrhenius rate equation currently in use. The model was mathematically formalized and integrated into the thermostructural analysis code CHAR. Parametric studies on variation of several parameters have been done. Comparisons to Arrhenius and straight-line models show that the new model produces physically realistic results under all conditions.

Effect of temperature on microbial growth rate-mathematical analysis: the Arrhenius and Eyring-Polanyi connections.

PubMed

Huang, Lihan; Hwang, Andy; Phillips, John

2011-10-01

The objective of this work is to develop a mathematical model for evaluating the effect of temperature on the rate of microbial growth. The new mathematical model is derived by combination and modification of the Arrhenius equation and the Eyring-Polanyi transition theory. The new model, suitable for both suboptimal and the entire growth temperature ranges, was validated using a collection of 23 selected temperature-growth rate curves belonging to 5 groups of microorganisms, including Pseudomonas spp., Listeria monocytogenes, Salmonella spp., Clostridium perfringens, and Escherichia coli, from the published literature. The curve fitting is accomplished by nonlinear regression using the Levenberg-Marquardt algorithm. The resulting estimated growth rate (μ) values are highly correlated to the data collected from the literature (R(2) = 0.985, slope = 1.0, intercept = 0.0). The bias factor (B(f) ) of the new model is very close to 1.0, while the accuracy factor (A(f) ) ranges from 1.0 to 1.22 for most data sets. The new model is compared favorably with the Ratkowsky square root model and the Eyring equation. Even with more parameters, the Akaike information criterion, Bayesian information criterion, and mean square errors of the new model are not statistically different from the square root model and the Eyring equation, suggesting that the model can be used to describe the inherent relationship between temperature and microbial growth rates. The results of this work show that the new growth rate model is suitable for describing the effect of temperature on microbial growth rate. Practical Application:  Temperature is one of the most significant factors affecting the growth of microorganisms in foods. This study attempts to develop and validate a mathematical model to describe the temperature dependence of microbial growth rate. The findings show that the new model is accurate and can be used to describe the effect of temperature on microbial growth rate in foods. Journal of Food Science © 2011 Institute of Food Technologists® No claim to original US government works.

National geodetic satellite program, part 2

NASA Technical Reports Server (NTRS)

Schmid, H.

1977-01-01

Satellite geodesy and the creation of worldwide geodetic reference systems is discussed. The geometric description of the surface and the analytical description of the gravity field of the earth by means of worldwide reference systems, with the aid of satellite geodesy, are presented. A triangulation method based on photogrammetric principles is described in detail. Results are derived in the form of three dimensional models. These mathematical models represent the frame of reference into which one can fit the existing geodetic results from the various local datums, as well as future measurements.

Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

NASA Technical Reports Server (NTRS)

Librescu, L.; Stein, M.

1990-01-01

The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

WKB analysis of relativistic Stern–Gerlach measurements

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

Palmer, Matthew C., E-mail: m.palmer@physics.usyd.edu.au; Takahashi, Maki, E-mail: m.takahashi@physics.usyd.edu.au; Westman, Hans F., E-mail: hwestman74@gmail.com

2013-09-15

Spin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern–Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern–Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern–Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle wemore » show that the +1 and −1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern–Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern–Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are considered. -- Highlights: •Derivation of the spin observable for a relativistic Stern–Gerlach measurement. •Relativistic model of spin measurement using WKB approximation of Dirac equation. •The derived spin operator is distinct from two other commonly used operators. •Consequences for quantum tomography are considered.« less

Higher-Order Hamiltonian Model for Unidirectional Water Waves

NASA Astrophysics Data System (ADS)

Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.

2018-04-01

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS.

USGS Publications Warehouse

Cooley, Richard L.; Vecchia, Aldo V.

1987-01-01

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

A Membrane Model from Implicit Elasticity Theory

PubMed Central

Freed, A. D.; Liao, J.; Einstein, D. R.

2014-01-01

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079

Does the Budyko curve reflect a maximum power state of hydrological systems? A backward analysis

NASA Astrophysics Data System (ADS)

Westhoff, M.; Zehe, E.; Archambeau, P.; Dewals, B.

2015-08-01

Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving runoff and evaporation for a simple one-box model. We did this in such a way that when the conductances are optimized with the maximum power principle, the steady state behaviour of the model leads exactly to a point on the Budyko curve. Subsequently we derived gradients that, under constant forcing, resulted in a Budyko curve following the asymptotes closely. With these gradients we explored the sensitivity of dry spells and dynamics in actual evaporation. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves derived with dynamics in rainfall and evaporation. This indicates that the maximum power principle may be used (i) to derive the Budyko curve and (ii) to move away from the empiricism in free parameters present in many Budyko functions. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

Careers in Applied Mathematics and Computational Sciences.

ERIC Educational Resources Information Center

Society for Industrial and Applied Mathematics, Philadelphia, PA.

This booklet provides some answers to questions on how mathematics is used in the world of work, what kinds of problems it solves, and why it is the key to so many careers, particularly to the jobs of the 21st century. Part of that preparation is mathematical knowledge, tools such as derivatives, probability, and matrices as well as central themes…

Assessing Key Epistemic Features of Didactic-Mathematical Knowledge of Prospective Teachers: The Case of The Derivative

ERIC Educational Resources Information Center

Pino-Fan, Luis R.; Godino, Juan D.; Font, Vicenç

2018-01-01

In recent years, there has been a growing interest in studying the knowledge that mathematics teachers require in order for their teaching to be effective. However, only a few studies have focused on the design and application of instruments that are capable of exploring different aspects of teachers' didactic-mathematical knowledge about specific…

Effect of membranes on oxygen transfer rate and consumption within a newly developed three-compartment bioartificial liver device: Advanced experimental and theoretical studies.

PubMed

Hilal-Alnaqbi, Ali; Mourad, Abdel-Hamid I; Yousef, Basem F

2014-01-01

A mathematical model is developed to predict oxygen transfer in the fiber-in-fiber (FIF) bioartificial liver device. The model parameters are taken from the constructed and tested FIF modules. We extended the Krogh cylinder model by including one more zone for oxygen transfer. Cellular oxygen uptake was based on Michaelis-Menten kinetics. The effect of varying a number of important model parameters is investigated, including (1) oxygen partial pressure at the inlet, (2) the hydraulic permeability of compartment B (cell region), (3) the hydraulic permeability of the inner membrane, and (4) the oxygen diffusivity of the outer membrane. The mathematical model is validated by comparing its output against the experimentally acquired values of an oxygen transfer rate and the hydrostatic pressure drop. Three governing simultaneous linear differential equations are derived to predict and validate the experimental measurements, e.g., the flow rate and the hydrostatic pressure drop. The model output simulated the experimental measurements to a high degree of accuracy. The model predictions show that the cells in the annulus can be oxygenated well even at high cell density or at a low level of gas phase PG if the value of the oxygen diffusion coefficient Dm is 16 × 10(-5) . The mathematical model also shows that the performance of the FIF improves by increasing the permeability of polypropylene membrane (inner fiber). Moreover, the model predicted that 60% of plasma has access to the cells in the annulus within the first 10% of the FIF bioreactor axial length for a specific polypropylene membrane permeability and can reach 95% within the first 30% of its axial length. © 2013 International Union of Biochemistry and Molecular Biology, Inc.

Agent-Based Phytoplankton Models of Cellular and Population Processes: Fostering Individual-Based Learning in Undergraduate Research

NASA Astrophysics Data System (ADS)

Berges, J. A.; Raphael, T.; Rafa Todd, C. S.; Bate, T. C.; Hellweger, F. L.

2016-02-01

Engaging undergraduate students in research projects that require expertise in multiple disciplines (e.g. cell biology, population ecology, and mathematical modeling) can be challenging because they have often not developed the expertise that allows them to participate at a satisfying level. Use of agent-based modeling can allow exploration of concepts at more intuitive levels, and encourage experimentation that emphasizes processes over computational skills. Over the past several years, we have involved undergraduate students in projects examining both ecological and cell biological aspects of aquatic microbial biology, using the freely-downloadable, agent-based modeling environment NetLogo (https://ccl.northwestern.edu/netlogo/). In Netlogo, actions of large numbers of individuals can be simulated, leading to complex systems with emergent behavior. The interface features appealing graphics, monitors, and control structures. In one example, a group of sophomores in a BioMathematics program developed an agent-based model of phytoplankton population dynamics in a pond ecosystem, motivated by observed macroscopic changes in cell numbers (due to growth and death), and driven by responses to irradiance, temperature and a limiting nutrient. In a second example, junior and senior undergraduates conducting Independent Studies created a model of the intracellular processes governing stress and cell death for individual phytoplankton cells (based on parameters derived from experiments using single-cell culturing and flow cytometry), and then this model was embedded in the agents in the pond ecosystem model. In our experience, students with a range of mathematical abilities learned to code quickly and could use the software with varying degrees of sophistication, for example, creation of spatially-explicit two and three-dimensional models. Skills developed quickly and transferred readily to other platforms (e.g. Matlab).

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

A model for estimating pathogen variability in shellfish and predicting minimum depuration times.

PubMed

McMenemy, Paul; Kleczkowski, Adam; Lees, David N; Lowther, James; Taylor, Nick

2018-01-01

Norovirus is a major cause of viral gastroenteritis, with shellfish consumption being identified as one potential norovirus entry point into the human population. Minimising shellfish norovirus levels is therefore important for both the consumer's protection and the shellfish industry's reputation. One method used to reduce microbiological risks in shellfish is depuration; however, this process also presents additional costs to industry. Providing a mechanism to estimate norovirus levels during depuration would therefore be useful to stakeholders. This paper presents a mathematical model of the depuration process and its impact on norovirus levels found in shellfish. Two fundamental stages of norovirus depuration are considered: (i) the initial distribution of norovirus loads within a shellfish population and (ii) the way in which the initial norovirus loads evolve during depuration. Realistic assumptions are made about the dynamics of norovirus during depuration, and mathematical descriptions of both stages are derived and combined into a single model. Parameters to describe the depuration effect and norovirus load values are derived from existing norovirus data obtained from U.K. harvest sites. However, obtaining population estimates of norovirus variability is time-consuming and expensive; this model addresses the issue by assuming a 'worst case scenario' for variability of pathogens, which is independent of mean pathogen levels. The model is then used to predict minimum depuration times required to achieve norovirus levels which fall within possible risk management levels, as well as predictions of minimum depuration times for other water-borne pathogens found in shellfish. Times for Escherichia coli predicted by the model all fall within the minimum 42 hours required for class B harvest sites, whereas minimum depuration times for norovirus and FRNA+ bacteriophage are substantially longer. Thus this study provides relevant information and tools to assist norovirus risk managers with future control strategies.

The mathematics textbook at tertiary level as curriculum material - exploring the teacher's decision-making process

NASA Astrophysics Data System (ADS)

Randahl, Mira

2016-08-01

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative concept. Data were collected during observations of lectures and an interview, and informal talks with the teacher. The introduction and the treatment of the derivative as proposed by the teacher during the lectures were analysed in relation to the results of the content text analysis of the textbook. The teacher's decisions were explored through the lens of intended learning goals for engineering students taking the mathematics course. The results showed that the sequence of concepts and the formal introduction of the derivative as proposed by the textbook were closely followed during the lectures. The examples and tasks offered to the students focused strongly on procedural knowledge. Although the textbook proposes both examples and exercises that promote conceptual knowledge, these opportunities were not fully utilized during the observed lectures. Possible reasons for the teacher's choices and decisions are discussed.

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

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

Dai, Heng; Ye, Ming; Walker, Anthony P.

Hydrological models are always composed of multiple components that represent processes key to intended model applications. When a process can be simulated by multiple conceptual-mathematical models (process models), model uncertainty in representing the process arises. While global sensitivity analysis methods have been widely used for identifying important processes in hydrologic modeling, the existing methods consider only parametric uncertainty but ignore the model uncertainty for process representation. To address this problem, this study develops a new method to probe multimodel process sensitivity by integrating the model averaging methods into the framework of variance-based global sensitivity analysis, given that the model averagingmore » methods quantify both parametric and model uncertainty. A new process sensitivity index is derived as a metric of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and model parameters. For demonstration, the new index is used to evaluate the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that converting precipitation to recharge, and the geology process is also simulated by two models of different parameterizations of hydraulic conductivity; each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.« less

On a PCA-based lung motion model

PubMed Central

Li, Ruijiang; Lewis, John H; Jia, Xun; Zhao, Tianyu; Liu, Weifeng; Wuenschel, Sara; Lamb, James; Yang, Deshan; Low, Daniel A; Jiang, Steve B

2014-01-01

Respiration-induced organ motion is one of the major uncertainties in lung cancer radiotherapy and is crucial to be able to accurately model the lung motion. Most work so far has focused on the study of the motion of a single point (usually the tumor center of mass), and much less work has been done to model the motion of the entire lung. Inspired by the work of Zhang et al (2007 Med. Phys. 34 4772–81), we believe that the spatiotemporal relationship of the entire lung motion can be accurately modeled based on principle component analysis (PCA) and then a sparse subset of the entire lung, such as an implanted marker, can be used to drive the motion of the entire lung (including the tumor). The goal of this work is twofold. First, we aim to understand the underlying reason why PCA is effective for modeling lung motion and find the optimal number of PCA coefficients for accurate lung motion modeling. We attempt to address the above important problems both in a theoretical framework and in the context of real clinical data. Second, we propose a new method to derive the entire lung motion using a single internal marker based on the PCA model. The main results of this work are as follows. We derived an important property which reveals the implicit regularization imposed by the PCA model. We then studied the model using two mathematical respiratory phantoms and 11 clinical 4DCT scans for eight lung cancer patients. For the mathematical phantoms with cosine and an even power (2n) of cosine motion, we proved that 2 and 2n PCA coefficients and eigenvectors will completely represent the lung motion, respectively. Moreover, for the cosine phantom, we derived the equivalence conditions for the PCA motion model and the physiological 5D lung motion model (Low et al 2005 Int. J. Radiat. Oncol. Biol. Phys. 63 921–9). For the clinical 4DCT data, we demonstrated the modeling power and generalization performance of the PCA model. The average 3D modeling error using PCA was within 1 mm (0.7 ± 0.1 mm). When a single artificial internal marker was used to derive the lung motion, the average 3D error was found to be within 2 mm (1.8 ± 0.3 mm) through comprehensive statistical analysis. The optimal number of PCA coefficients needs to be determined on a patient-by-patient basis and two PCA coefficients seem to be sufficient for accurate modeling of the lung motion for most patients. In conclusion, we have presented thorough theoretical analysis and clinical validation of the PCA lung motion model. The feasibility of deriving the entire lung motion using a single marker has also been demonstrated on clinical data using a simulation approach. PMID:21865624

Modeling and controlling a robotic convoy using guidance laws strategies.

PubMed

Belkhouche, Fethi; Belkhouche, Boumediene

2005-08-01

This paper deals with the problem of modeling and controlling a robotic convoy. Guidance laws techniques are used to provide a mathematical formulation of the problem. The guidance laws used for this purpose are the velocity pursuit, the deviated pursuit, and the proportional navigation. The velocity pursuit equations model the robot's path under various sensors based control laws. A systematic study of the tracking problem based on this technique is undertaken. These guidance laws are applied to derive decentralized control laws for the angular and linear velocities. For the angular velocity, the control law is directly derived from the guidance laws after considering the relative kinematics equations between successive robots. The second control law maintains the distance between successive robots constant by controlling the linear velocity. This control law is derived by considering the kinematics equations between successive robots under the considered guidance law. Properties of the method are discussed and proven. Simulation results confirm the validity of our approach, as well as the validity of the properties of the method. Index Terms-Guidance laws, relative kinematics equations, robotic convoy, tracking.

Quantum Sheaf Cohomology on Grassmannians

NASA Astrophysics Data System (ADS)

Guo, Jirui; Lu, Zhentao; Sharpe, Eric

2017-05-01

In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.

40 CFR 211.207 - Computation of the noise -reduction rating (NRR).

Code of Federal Regulations, 2012 CFR

2012-07-01

... mathematics to determine the combined value of protected ear levels (Step #8) which is used in Step #9 to exactly derive the NRR; or use the following table as a substitute for logarithmic mathematics to...

40 CFR 211.207 - Computation of the noise -reduction rating (NRR).

Code of Federal Regulations, 2014 CFR

2014-07-01

... mathematics to determine the combined value of protected ear levels (Step #8) which is used in Step #9 to exactly derive the NRR; or use the following table as a substitute for logarithmic mathematics to...

40 CFR 211.207 - Computation of the noise -reduction rating (NRR).

Code of Federal Regulations, 2013 CFR

2013-07-01

... mathematics to determine the combined value of protected ear levels (Step #8) which is used in Step #9 to exactly derive the NRR; or use the following table as a substitute for logarithmic mathematics to...

40 CFR 211.207 - Computation of the noise -reduction rating (NRR).

Code of Federal Regulations, 2010 CFR

2010-07-01

... mathematics to determine the combined value of protected ear levels (Step #8) which is used in Step #9 to exactly derive the NRR; or use the following table as a substitute for logarithmic mathematics to...

Modeling the effect of topical oxygen therapy on wound healing

NASA Astrophysics Data System (ADS)

Agyingi, Ephraim; Ross, David; Maggelakis, Sophia

2011-11-01

Oxygen supply is a critical element for the healing of wounds. Clinical investigations have shown that topical oxygen therapy (TOT) increases the healing rate of wounds. The reason behind TOT increasing the healing rate of a wound remains unclear and hence current protocols are empirical. In this paper we present a mathematical model of wound healing that we use to simulate the application of TOT in the treatment of cutaneous wounds. At the core of our model is an account of the initiation of angiogenesis by macrophage-derived growth factors. The model is expressed as a system of reaction-diffusion equations. We present results of simulations for a version of the model with one spatial dimension.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

ERIC Educational Resources Information Center

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Modifications to give HOPE/MDC 2.0 the capability to solve for or consider vent forces: Mission planning, mission analysis, and software formulation

NASA Technical Reports Server (NTRS)

Zyla, L. V.

1979-01-01

The modifications are described as necessary to give the Houston Operations Predictor/Estimator (HOPE) program the capability to solve for or consider vent forces for orbit determination. The model implemented in solving for vent forces is described along with the integrator problems encountered. A summary derivation of the mathematical principles applicable to solve/consider methodology is provided.

Surface conservation laws at microscopically diffuse interfaces.

PubMed

Chu, Kevin T; Bazant, Martin Z

2007-11-01

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities are often coupled via surface conservation laws of excess surface quantities. While this approach is easily justified for microscopically sharp interfaces, its applicability in the context of microscopically diffuse interfaces is less theoretically well-established. Furthermore, surface conservation laws (and interfacial models in general) are often derived phenomenologically rather than systematically. In this article, we first provide a mathematically rigorous justification for surface conservation laws at diffuse interfaces based on an asymptotic analysis of transport processes in the boundary layer and derive general formulae for the surface and normal fluxes that appear in surface conservation laws. Next, we use nonequilibrium thermodynamics to formulate surface conservation laws in terms of chemical potentials and provide a method for systematically deriving the structure of the interfacial layer. Finally, we derive surface conservation laws for a few examples from diffusive and electrochemical transport.

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Modelling the dynamics of polar auxin transport in inflorescence stems of Arabidopsis thaliana

PubMed Central

Boot, Kees J.M.; Hille, Sander C.; Libbenga, Kees R.; Peletier, Lambertus A.; van Spronsen, Paulina C.; van Duijn, Bert; Offringa, Remko

2016-01-01

The polar transport of the plant hormone auxin has been the subject of many studies, several involving mathematical modelling. Unfortunately, most of these models have not been experimentally verified. Here we present experimental measurements of long-distance polar auxin transport (PAT) in segments of inflorescence stems of Arabidopsis thaliana together with a descriptive mathematical model that was developed from these data. It is based on a general advection–diffusion equation for auxin density, as suggested by the chemiosmotic theory, but is extended to incorporate both immobilization of auxin and exchange with the surrounding tissue of cells involved in PAT, in order to account for crucial observations. We found that development of the present model assisted effectively in the analysis of experimental observations. As an example, we discuss the analysis of a quadruple mutant for all four AUX1/LAX1–LAX3 influx carriers genes. We found a drastic change in the parameters governing the exchange of PAT channels with the surrounding tissue, whereas the velocity was still of the order of magnitude of the wild type. In addition, the steady-state flux of auxin through the PAT system of the mutant did not exhibit a saturable component, as we found for the wild type, suggesting that the import carriers are responsible for the saturable component in the wild type. In the accompanying Supplementary data available at JXB online, we describe in more detail the data-driven development of the model, review and derive predictions from a mathematical model of the chemiosmotic theory, and explore relationships between parameters in our model and processes and parameters at the cellular level. PMID:26531101

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Physics of mind: Experimental confirmations of theoretical predictions.

PubMed

Schoeller, Félix; Perlovsky, Leonid; Arseniev, Dmitry

2018-02-02

What is common among Newtonian mechanics, statistical physics, thermodynamics, quantum physics, the theory of relativity, astrophysics and the theory of superstrings? All these areas of physics have in common a methodology, which is discussed in the first few lines of the review. Is a physics of the mind possible? Is it possible to describe how a mind adapts in real time to changes in the physical world through a theory based on a few basic laws? From perception and elementary cognition to emotions and abstract ideas allowing high-level cognition and executive functioning, at nearly all levels of study, the mind shows variability and uncertainties. Is it possible to turn psychology and neuroscience into so-called "hard" sciences? This review discusses several established first principles for the description of mind and their mathematical formulations. A mathematical model of mind is derived from these principles. This model includes mechanisms of instincts, emotions, behavior, cognition, concepts, language, intuitions, and imagination. We clarify fundamental notions such as the opposition between the conscious and the unconscious, the knowledge instinct and aesthetic emotions, as well as humans' universal abilities for symbols and meaning. In particular, the review discusses in length evolutionary and cognitive functions of aesthetic emotions and musical emotions. Several theoretical predictions are derived from the model, some of which have been experimentally confirmed. These empirical results are summarized and we introduce new theoretical developments. Several unsolved theoretical problems are proposed, as well as new experimental challenges for future research. Copyright © 2017. Published by Elsevier B.V.

(Chemotaxonomic) Implications of Postharvest/Storage-Induced Changes in Plant Volatile Profiles--the Case of Artemisia absinthium L. Essential Oil.

PubMed

Blagojević, Polina D; Radulović, Niko S; Skropeta, Danielle

2015-08-01

The plant volatile profile and the essential-oil chemical composition change during the storage of plant material. The objective of this study was to develop a mathematical model able to predict, explain, and quantify these changes. Mathematical equations, derived under the assumption that the essential oil contained within plant material could be treated as an ideal solution (Raoult's law), were applied for tracking of postharvest changes in the volatile profile of Artemisia absinthium L. (the essential oils were analyzed by GC-FID and GC/MS). Starting from a specific chemical composition of an essential-oil sample obtained from plant material after a short drying period (typically 5-10 d), and by using the equations derived from this model, one could easily predict evaporation-induced changes in the volatile profile of the plant material. Based on the composition of the essential-oil sample obtained after a given storage time t, it is possible to identify those components that were involved in chemical reactions, both as reactants and possible products. The established model even allowed the recognition of pairs of transformation, i.e., 'daughter' products and their 'parent' compounds. The obtained results highlight that the essential-oil composition is highly dependent on the storage period of any plant material and urges caution in different types of phytochemical studies, especially chemotaxonomic ones, or practical application. Copyright © 2015 Verlag Helvetica Chimica Acta AG, Zürich.

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].

Discerning Apical and Basolateral Properties of HT-29/B6 and IPEC-J2 Cell Layers by Impedance Spectroscopy, Mathematical Modeling and Machine Learning

PubMed Central

Schmid, Thomas; Bogdan, Martin; Günzel, Dorothee

2013-01-01

Quantifying changes in partial resistances of epithelial barriers in vitro is a challenging and time-consuming task in physiology and pathophysiology. Here, we demonstrate that electrical properties of epithelial barriers can be estimated reliably by combining impedance spectroscopy measurements, mathematical modeling and machine learning algorithms. Conventional impedance spectroscopy is often used to estimate epithelial capacitance as well as epithelial and subepithelial resistance. Based on this, the more refined two-path impedance spectroscopy makes it possible to further distinguish transcellular and paracellular resistances. In a next step, transcellular properties may be further divided into their apical and basolateral components. The accuracy of these derived values, however, strongly depends on the accuracy of the initial estimates. To obtain adequate accuracy in estimating subepithelial and epithelial resistance, artificial neural networks were trained to estimate these parameters from model impedance spectra. Spectra that reflect behavior of either HT-29/B6 or IPEC-J2 cells as well as the data scatter intrinsic to the used experimental setup were created computationally. To prove the proposed approach, reliability of the estimations was assessed with both modeled and measured impedance spectra. Transcellular and paracellular resistances obtained by such neural network-enhanced two-path impedance spectroscopy are shown to be sufficiently reliable to derive the underlying apical and basolateral resistances and capacitances. As an exemplary perturbation of pathophysiological importance, the effect of forskolin on the apical resistance of HT-29/B6 cells was quantified. PMID:23840862

A review of Reynolds stress models for turbulent shear flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.

1995-01-01

A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear flows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent flows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such flows. However, substantial problems remain for the description of more complex turbulent flows where there are large departures from equilibrium. Recent efforts to extend Reynolds stress models to nonequilibrium turbulent flows are discussed briefly along with the major modeling issues relevant to practical naval hydrodynamics applications.

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

Formal methods in computer system design

NASA Astrophysics Data System (ADS)

Hoare, C. A. R.

1989-12-01

This note expounds a philosophy of engineering design which is stimulated, guided and checked by mathematical calculations and proofs. Its application to software engineering promises the same benifits as those derived from the use of mathematics in all other branches of modern science.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Response function of a moving contact line

NASA Astrophysics Data System (ADS)

Perrin, H.; Belardinelli, D.; Sbragaglia, M.; Andreotti, B.

2018-04-01

The hydrodynamics of a liquid-vapor interface in contact with a heterogeneous surface is largely impacted by the presence of defects at the smaller scales. Such defects introduce morphological disturbances on the contact line and ultimately determine the force exerted on the wedge of liquid in contact with the surface. From the mathematical point of view, defects introduce perturbation modes, whose space-time evolution is governed by the interfacial hydrodynamic equations of the contact line. In this paper we derive the response function of the contact line to such generic perturbations. The contact line response may be used to design simplified one-dimensional time-dependent models accounting for the complexity of interfacial flows coupled to nanoscale defects, yet offering a more tractable mathematical framework to explore contact line motion through a disordered energy landscape.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Ray Tracing and Modal Methods for Modeling Radio Propagation in Tunnels With Rough Walls

PubMed Central

Zhou, Chenming

2017-01-01

At the ultrahigh frequencies common to portable radios, tunnels such as mine entries are often modeled by hollow dielectric waveguides. The roughness condition of the tunnel walls has an influence on radio propagation, and therefore should be taken into account when an accurate power prediction is needed. This paper investigates how wall roughness affects radio propagation in tunnels, and presents a unified ray tracing and modal method for modeling radio propagation in tunnels with rough walls. First, general analytical formulas for modeling the influence of the wall roughness are derived, based on the modal method and the ray tracing method, respectively. Second, the equivalence of the ray tracing and modal methods in the presence of wall roughnesses is mathematically proved, by showing that the ray tracing-based analytical formula can converge to the modal-based formula through the Poisson summation formula. The derivation and findings are verified by simulation results based on ray tracing and modal methods. PMID:28935995

A generalized preferential attachment model for business firms growth rates. II. Mathematical treatment

NASA Astrophysics Data System (ADS)

Buldyrev, S. V.; Pammolli, F.; Riccaboni, M.; Yamasaki, K.; Fu, D.-F.; Matia, K.; Stanley, H. E.

2007-05-01

We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent ϕ = 2+b/(1-b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent ζ = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.

Discrete-time model reduction in limited frequency ranges

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Dynamical behavior of susceptible-infected-recovered-susceptible epidemic model on weighted networks

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Zhang, Fei

2018-02-01

We study susceptible-infected-recovered-susceptible epidemic model in weighted, regular, and random complex networks. We institute a pairwise-type mathematical model with a general transmission rate to evaluate the influence of the link-weight distribution on the spreading process. Furthermore, we develop a dimensionality reduction approach to derive the condition for the contagion outbreak. Finally, we analyze the influence of the heterogeneity of weight distribution on the outbreak condition for the scenario with a linear transmission rate. Our theoretical analysis is in agreement with stochastic simulations, showing that the heterogeneity of link-weight distribution can have a significant effect on the epidemic dynamics.

An information theory model for dissipation in open quantum systems

NASA Astrophysics Data System (ADS)

Rogers, David M.

2017-08-01

This work presents a general model for open quantum systems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

The Cockroft and Gault formula for estimation of creatinine clearance: a friendly deconstruction.

PubMed

Millar, J Alasdair

2012-02-24

To review the derivation of the Cockroft and Gault formula for estimating creatinine clearance from serum creatinine in a historical context. The derivation described by Cockroft and Gault was reviewed, and an alternative formula was sought using the data reported in the paper. Cockroft and Gault used 24 hour urine creatinine data expressed as mg/kg body weight and mathematical manipulation of a linear regression equation which introduced body weight as an independent variable into the formula. This involved a circular logic and may have been mathematically invalid. A more logical equation not containing body weight was derived from the data. The Cockcroft and Gault formula has been validated by long usage but the derivation appears logically insecure. Nevertheless, its role in estimating renal function at the bedside is established.

Bridging different perspectives of the physiological and mathematical disciplines.

PubMed

Batzel, Jerry Joseph; Hinghofer-Szalkay, Helmut; Kappel, Franz; Schneditz, Daniel; Kenner, Thomas; Goswami, Nandu

2012-12-01

The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research. While physiology education incorporates mathematics, via equations and formulas, it does not typically provide a foundation for interdisciplinary research linking mathematics and physiology. Here, we provide insights and ideas derived from interdisciplinary seminars involving mathematicians and physiologists that have been conducted over the last decade. The approaches described here can be used as templates for giving physiology and medical students insights into how sophisticated tools from mathematics can be applied and how the disciplines of mathematics and physiology can be integrated in research, thereby fostering a foundation for interdisciplinary collaboration. These templates are equally applicable to linking mathematical methods with other life and health sciences in the educational process.

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

A mathematical approach to molecular organization and proteolytic disintegration of bacterial inclusion bodies.

PubMed

Cubarsi, R; Carrió, M M; Villaverde, A

2005-09-01

The in vivo proteolytic digestion of bacterial inclusion bodies (IBs) and the kinetic analysis of the resulting protein fragments is an interesting approach to investigate the molecular organization of these unconventional protein aggregates. In this work, we describe a set of mathematical instruments useful for such analysis and interpretation of observed data. These methods combine numerical estimation of digestion rate and approximation of its high-order derivatives, modelling of fragmentation events from a mixture of Poisson processes associated with differentiated protein species, differential equations techniques in order to estimate the mixture parameters, an iterative predictor-corrector algorithm for describing the flow diagram along the cascade process, as well as least squares procedures with minimum variance estimates. The models are formulated and compared with data, and successively refined to better match experimental observations. By applying such procedures as well as newer improved algorithms of formerly developed equations, it has been possible to model, for two kinds of bacterially produced aggregation prone recombinant proteins, their cascade digestion process that has revealed intriguing features of the IB-forming polypeptides.

The probability of monophyly of a sample of gene lineages on a species tree

PubMed Central

Mehta, Rohan S.; Bryant, David; Rosenberg, Noah A.

2016-01-01

Monophyletic groups—groups that consist of all of the descendants of a most recent common ancestor—arise naturally as a consequence of descent processes that result in meaningful distinctions between organisms. Aspects of monophyly are therefore central to fields that examine and use genealogical descent. In particular, studies in conservation genetics, phylogeography, population genetics, species delimitation, and systematics can all make use of mathematical predictions under evolutionary models about features of monophyly. One important calculation, the probability that a set of gene lineages is monophyletic under a two-species neutral coalescent model, has been used in many studies. Here, we extend this calculation for a species tree model that contains arbitrarily many species. We study the effects of species tree topology and branch lengths on the monophyly probability. These analyses reveal new behavior, including the maintenance of nontrivial monophyly probabilities for gene lineage samples that span multiple species and even for lineages that do not derive from a monophyletic species group. We illustrate the mathematical results using an example application to data from maize and teosinte. PMID:27432988

Modelling dynamics and aerodynamic tests of a sport parachute jumper during flight in sitfly position.

PubMed

Moniuszko, Justyna; Maryniak, Jerzy; Ladyżyńska-Kozdraś, Edyta

2010-01-01

Based on a model of a parachute jumper, for various body configurations in a sitting position, tests were carried out in an aerodynamic tunnel. Aerodynamic characteristics and dimensionless aerodynamic forces' coefficients were calculated. The tests were carried out for various configurations of the jumper's body. A universal mathematical model of a parachute jumper's body was prepared, thus enabling the analysis of the jumper's movement with a closed parachute in any position. In order to build the model, a digitized model of a jumper allowing changing the body configuration, making appropriate changes of the moment of inertia, distribution of the center of mass and the aerodynamic characteristics was adopted. Dynamic movement equations were derived for a jumper in a relative reference system. The mathematical model was formulated for a jumper with a variable body configuration during the flight, which can be realized through a change of the position and the speed of the parachute jumper's limbs. The model allows analyzing the motion of the jumper with a closed parachute. It is an important jump phase during an assault with delayed parachute opening in sports type jumping, e.g., Skydiving and in emergency jumps from higher altitudes for the parachute's opening to be safe.

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

Turbulent eddy diffusion models in exposure assessment - Determination of the eddy diffusion coefficient.

PubMed

Shao, Yuan; Ramachandran, Sandhya; Arnold, Susan; Ramachandran, Gurumurthy

2017-03-01

The use of the turbulent eddy diffusion model and its variants in exposure assessment is limited due to the lack of knowledge regarding the isotropic eddy diffusion coefficient, D T . But some studies have suggested a possible relationship between D T and the air changes per hour (ACH) through a room. The main goal of this study was to accurately estimate D T for a range of ACH values by minimizing the difference between the concentrations measured and predicted by eddy diffusion model. We constructed an experimental chamber with a spatial concentration gradient away from the contaminant source, and conducted 27 3-hr long experiments using toluene and acetone under different air flow conditions (0.43-2.89 ACHs). An eddy diffusion model accounting for chamber boundary, general ventilation, and advection was developed. A mathematical expression for the slope based on the geometrical parameters of the ventilation system was also derived. There is a strong linear relationship between D T and ACH, providing a surrogate parameter for estimating D T in real-life settings. For the first time, a mathematical expression for the relationship between D T and ACH has been derived that also corrects for non-ideal conditions, and the calculated value of the slope between these two parameters is very close to the experimentally determined value. The values of D T obtained from the experiments are generally consistent with values reported in the literature. They are also independent of averaging time of measurements, allowing for comparison of values obtained from different measurement settings. These findings make the use of turbulent eddy diffusion models for exposure assessment in workplace/indoor environments more practical.

Optimum load distribution between heat sources based on the Cournot model

NASA Astrophysics Data System (ADS)

Penkovskii, A. V.; Stennikov, V. A.; Khamisov, O. V.

2015-08-01

One of the widespread models of the heat supply of consumers, which is represented in the "Single buyer" format, is considered. The methodological base proposed for its description and investigation presents the use of principles of the theory of games, basic propositions of microeconomics, and models and methods of the theory of hydraulic circuits. The original mathematical model of the heat supply system operating under conditions of the "Single buyer" organizational structure provides the derivation of a solution satisfying the market Nash equilibrium. The distinctive feature of the developed mathematical model is that, along with problems solved traditionally within the bounds of bilateral relations of heat energy sources-heat consumer, it considers a network component with its inherent physicotechnical properties of the heat network and business factors connected with costs of the production and transportation of heat energy. This approach gives the possibility to determine optimum levels of load of heat energy sources. These levels provide the given heat energy demand of consumers subject to the maximum profit earning of heat energy sources and the fulfillment of conditions for formation of minimum heat network costs for a specified time. The practical realization of the search of market equilibrium is considered by the example of a heat supply system with two heat energy sources operating on integrated heat networks. The mathematical approach to the solution search is represented in the graphical form and illustrates computations based on the stepwise iteration procedure for optimization of levels of loading of heat energy sources (groping procedure by Cournot) with the corresponding computation of the heat energy price for consumers.

Modelling short channel mosfets for use in VLSI

NASA Technical Reports Server (NTRS)

Klafter, Alex; Pilorz, Stuart; Polosa, Rosa Loguercio; Ruddock, Guy; Smith, Andrew

1986-01-01

In an investigation of metal oxide semiconductor field effect transistor (MOFSET) devices, a one-dimensional mathematical model of device dynamics was prepared, from which an accurate and computationally efficient drain current expression could be derived for subsequent parameter extraction. While a critical review revealed weaknesses in existing 1-D models (Pao-Sah, Pierret-Shields, Brews, and Van de Wiele), this new model in contrast was found to allow all the charge distributions to be continuous, to retain the inversion layer structure, and to include the contribution of current from the pinched-off part of the device. The model allows the source and drain to operate in different regimes. Numerical algorithms used for the evaluation of surface potentials in the various models are presented.

Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

PubMed

Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

2016-01-01

A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively.

Determination of Material Constitutive Laws for Inconel 718 Superalloy Under Different Strain Rates and Working Temperatures

NASA Astrophysics Data System (ADS)

Grzesik, W.; Niesłony, P.; Laskowski, P.

2017-12-01

In this paper, a special procedure for the prediction of parameters of the Johnson-Cook constitutive material models is proposed based on the experimental data and specially developed MATLAB scripts which allow advanced modeling of complex 3D response surfaces. Experimental investigations concern two various strain rates of 10-3 and 101 1/s and the testing temperature ranging from the ambient up to 700 °C. As a result, a set of mathematical equations which fit the experimental data is determined. The applicability of the experimentally derived constitutive models to the FEM modeling of real machining processes of Inconel 718 alloy is verified.

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

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

Design of a robust fuzzy controller for the arc stability of CO(2) welding process using the Taguchi method.

PubMed

Kim, Dongcheol; Rhee, Sehun

2002-01-01

CO(2) welding is a complex process. Weld quality is dependent on arc stability and minimizing the effects of disturbances or changes in the operating condition commonly occurring during the welding process. In order to minimize these effects, a controller can be used. In this study, a fuzzy controller was used in order to stabilize the arc during CO(2) welding. The input variable of the controller was the Mita index. This index estimates quantitatively the arc stability that is influenced by many welding process parameters. Because the welding process is complex, a mathematical model of the Mita index was difficult to derive. Therefore, the parameter settings of the fuzzy controller were determined by performing actual control experiments without using a mathematical model of the controlled process. The solution, the Taguchi method was used to determine the optimal control parameter settings of the fuzzy controller to make the control performance robust and insensitive to the changes in the operating conditions.

Data-driven heterogeneity in mathematical learning disabilities based on the triple code model.

PubMed

Peake, Christian; Jiménez, Juan E; Rodríguez, Cristina

2017-12-01

Many classifications of heterogeneity in mathematical learning disabilities (MLD) have been proposed over the past four decades, however no empirical research has been conducted until recently, and none of the classifications are derived from Triple Code Model (TCM) postulates. The TCM proposes MLD as a heterogeneous disorder, with two distinguishable profiles: a representational subtype and a verbal subtype. A sample of elementary school 3rd to 6th graders was divided into two age cohorts (3rd - 4th grades, and 5th - 6th grades). Using data-driven strategies, based on the cognitive classification variables predicted by the TCM, our sample of children with MLD clustered as expected: a group with representational deficits and a group with number-fact retrieval deficits. In the younger group, a spatial subtype also emerged, while in both cohorts a non-specific cluster was produced whose profile could not be explained by this theoretical approach. Copyright © 2017 Elsevier Ltd. All rights reserved.

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor.

PubMed

Xiu, G H; Jiang, L; Li, P

2001-07-05

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor. Copyright 2001 John Wiley & Sons, Inc.

Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks

NASA Astrophysics Data System (ADS)

Eli, Jennifer A.; Mohr-Schroeder, Margaret J.; Lee, Carl W.

2011-09-01

Prospective teachers are expected to construct, emphasise, integrate, and make use of mathematical connections; in doing so, they acquire an understanding of mathematics that is fluid, supple, and interconnected (Evitts Dissertation Abstracts International, 65(12), 4500, 2005). Given the importance of mathematical connection making, an exploratory study was conducted to consider the ability of prospective middle-grades teachers to make mathematical connections while engaging in card-sorting activities. Twenty-eight prospective middle-grades teachers participated in both an open and closed card sort. Data were analysed using constant comparative methods to extract meta themes to describe the types of connections made. Findings indicate that these prospective teachers tended to make more procedural- and categorical-type mathematical connections and far fewer derivational or curricular mathematical connections.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Flow discharge prediction in compound channels using linear genetic programming

NASA Astrophysics Data System (ADS)

Azamathulla, H. Md.; Zahiri, A.

2012-08-01

SummaryFlow discharge determination in rivers is one of the key elements in mathematical modelling in the design of river engineering projects. Because of the inundation of floodplains and sudden changes in river geometry, flow resistance equations are not applicable for compound channels. Therefore, many approaches have been developed for modification of flow discharge computations. Most of these methods have satisfactory results only in laboratory flumes. Due to the ability to model complex phenomena, the artificial intelligence methods have recently been employed for wide applications in various fields of water engineering. Linear genetic programming (LGP), a branch of artificial intelligence methods, is able to optimise the model structure and its components and to derive an explicit equation based on the variables of the phenomena. In this paper, a precise dimensionless equation has been derived for prediction of flood discharge using LGP. The proposed model was developed using published data compiled for stage-discharge data sets for 394 laboratories, and field of 30 compound channels. The results indicate that the LGP model has a better performance than the existing models.

The first international workshop on the role and impact of mathematics in medicine: A collective account

PubMed Central

Artzrouni, Marc; Begg, Colin; Chabiniok, Radomir; Clairambault, Jean; Foss, AJE; Hargrove, John; Lee, Eva K; Siggers, Jennifer H; Tindall, Marcus

2011-01-01

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for interdisciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining high quality data and seeing things through “by the bedside” are some of the issues discussed by the participants.

Throw Away Your Mathematical Handbook! Undergraduate Physics with Wolfram|Alpha, a FREE(!) Internet-Based Mathematical Engine

NASA Astrophysics Data System (ADS)

Looney, Craig W.

2009-10-01

Wolfram|Alpha (http://www.wolframalpha.com/), a free internet-based mathematical engine released earlier this year, represents an orders-of magnitude advance in mathematical power freely available - without money, passwords, or downloads - on the web. Wolfram|Alpha is based on Mathematica, so it can plot functions, take derivatives, solve systems of equations, perform symbolic and numerical integration, and more. These capabilities (especially plotting and integration) will be explored in the context of topics covered in upper level undergraduate physics courses.

Nonstandard Analysis and Jump Conditions for Converging Shock Waves

NASA Technical Reports Server (NTRS)

Baty, Roy S.; Farassat, Fereidoun; Tucker, Don H.

2008-01-01

Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.

Local and Global Gestalt Laws: A Neurally Based Spectral Approach.

PubMed

Favali, Marta; Citti, Giovanna; Sarti, Alessandro

2017-02-01

This letter presents a mathematical model of figure-ground articulation that takes into account both local and global gestalt laws and is compatible with the functional architecture of the primary visual cortex (V1). The local gestalt law of good continuation is described by means of suitable connectivity kernels that are derived from Lie group theory and quantitatively compared with long-range connectivity in V1. Global gestalt constraints are then introduced in terms of spectral analysis of a connectivity matrix derived from these kernels. This analysis performs grouping of local features and individuates perceptual units with the highest salience. Numerical simulations are performed, and results are obtained by applying the technique to a number of stimuli.

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…