Qualitative investigation into students' use of divergence and curl in electromagnetism

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; De Cock, Mieke

2016-12-01

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector calculus. To gain insight into student reasoning when solving problems involving divergence and curl, we conducted eight semistructured individual student interviews. During these interviews, students discussed the divergence and curl of electromagnetic fields using graphical representations, mathematical calculations, and the differential form of Maxwell's equations. We observed that while many students attempt to clarify the problem by making a sketch of the electromagnetic field, they struggle to interpret graphical representations of vector fields in terms of divergence and curl. In addition, some students confuse the characteristics of field line diagrams and field vector plots. By interpreting our results within the conceptual blending framework, we show how a lack of conceptual understanding of the vector operators and difficulties with graphical representations can account for an improper understanding of Maxwell's equations in differential form. Consequently, specific learning materials based on a multiple representation approach are required to clarify Maxwell's equations.

Optimization of Control Strategies for Non-Domiciliated Triatoma dimidiata, Chagas Disease Vector in the Yucatán Peninsula, Mexico

PubMed Central

Barbu, Corentin; Dumonteil, Eric; Gourbière, Sébastien

2009-01-01

Background Chagas disease is the most important vector-borne disease in Latin America. Regional initiatives based on residual insecticide spraying have successfully controlled domiciliated vectors in many regions. Non-domiciliated vectors remain responsible for a significant transmission risk, and their control is now a key challenge for disease control. Methodology/Principal Findings A mathematical model was developed to predict the temporal variations in abundance of non-domiciliated vectors inside houses. Demographic parameters were estimated by fitting the model to two years of field data from the Yucatan peninsula, Mexico. The predictive value of the model was tested on an independent data set before simulations examined the efficacy of control strategies based on residual insecticide spraying, insect screens, and bednets. The model accurately fitted and predicted field data in the absence and presence of insecticide spraying. Pyrethroid spraying was found effective when 50 mg/m2 were applied yearly within a two-month period matching the immigration season. The >80% reduction in bug abundance was not improved by larger doses or more frequent interventions, and it decreased drastically for different timing and lower frequencies of intervention. Alternatively, the use of insect screens consistently reduced bug abundance proportionally to the reduction of the vector immigration rate. Conclusion/Significance Control of non-domiciliated vectors can hardly be achieved by insecticide spraying, because it would require yearly application and an accurate understanding of the temporal pattern of immigration. Insect screens appear to offer an effective and sustainable alternative, which may be part of multi-disease interventions for the integrated control of neglected vector-borne diseases. PMID:19365542

POlarized Light Angle Reflectance Instrument I Polarized Incidence (POLAR:I)

NASA Technical Reports Server (NTRS)

Sarto, Anthony W.; Woldemar, Christopher M.; Vanderbilt, V. C.

1989-01-01

The light scattering properties of leaves are used as input data for models which mathematically describe the transport of photons within plant canopies. Polarization measurements may aid in the investigation of these properties. This paper describes an instrument for rapidly determining the bidirectional light scattering properties of leaves illuminated by linearly polarized light. Results for one species, magnolia, show large differences in the bidirectional light scattering properties depending whether or not the electric vector E is parallel to the foliage surface.

The Vector Space as a Unifying Concept in School Mathematics.

ERIC Educational Resources Information Center

Riggle, Timothy Andrew

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

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

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.

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

PubMed Central

Wiratsudakul, Anuwat; Suparit, Parinya

2018-01-01

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

The human body metabolism process mathematical simulation based on Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur

2017-08-01

The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.

Modeling the impact of global warming on vector-borne infections

NASA Astrophysics Data System (ADS)

Massad, Eduardo; Coutinho, Francisco Antonio Bezerra; Lopez, Luis Fernandez; da Silva, Daniel Rodrigues

2011-06-01

Global warming will certainly affect the abundance and distribution of disease vectors. The effect of global warming, however, depends on the complex interaction between the human host population and the causative infectious agent. In this work we review some mathematical models that were proposed to study the impact of the increase in ambient temperature on the spread and gravity of some insect-transmitted diseases.

Age- and bite-structured models for vector-borne diseases.

PubMed

Rock, K S; Wood, D A; Keeling, M J

2015-09-01

The biology and behaviour of biting insects is a vitally important aspect in the spread of vector-borne diseases. This paper aims to determine, through the use of mathematical models, what effect incorporating vector senescence and realistic feeding patterns has on disease. A novel model is developed to enable the effects of age- and bite-structure to be examined in detail. This original PDE framework extends previous age-structured models into a further dimension to give a new insight into the role of vector biting and its interaction with vector mortality and spread of disease. Through the PDE model, the roles of the vector death and bite rates are examined in a way which is impossible under the traditional ODE formulation. It is demonstrated that incorporating more realistic functions for vector biting and mortality in a model may give rise to different dynamics than those seen under a more simple ODE formulation. The numerical results indicate that the efficacy of control methods that increase vector mortality may not be as great as predicted under a standard host-vector model, whereas other controls including treatment of humans may be more effective than previously thought. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Mathematical modeling of fluxgate magnetic gradiometers

NASA Astrophysics Data System (ADS)

Milovzorov, D. G.; Yasoveev, V. Kh.

2017-07-01

Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

The range of attraction for light traps catching Culicoides biting midges (Diptera: Ceratopogonidae)

PubMed Central

2013-01-01

Background Culicoides are vectors of e.g. bluetongue virus and Schmallenberg virus in northern Europe. Light trapping is an important tool for detecting the presence and quantifying the abundance of vectors in the field. Until now, few studies have investigated the range of attraction of light traps. Methods Here we test a previously described mathematical model (Model I) and two novel models for the attraction of vectors to light traps (Model II and III). In Model I, Culicoides fly to the nearest trap from within a fixed range of attraction. In Model II Culicoides fly towards areas with greater light intensity, and in Model III Culicoides evaluate light sources in the field of view and fly towards the strongest. Model II and III incorporated the directionally dependent light field created around light traps with fluorescent light tubes. All three models were fitted to light trap collections obtained from two novel experimental setups in the field where traps were placed in different configurations. Results Results showed that overlapping ranges of attraction of neighboring traps extended the shared range of attraction. Model I did not fit data from any of the experimental setups. Model II could only fit data from one of the setups, while Model III fitted data from both experimental setups. Conclusions The model with the best fit, Model III, indicates that Culicoides continuously evaluate the light source direction and intensity. The maximum range of attraction of a single 4W CDC light trap was estimated to be approximately 15.25 meters. The attraction towards light traps is different from the attraction to host animals and thus light trap catches may not represent the vector species and numbers attracted to hosts. PMID:23497628

The range of attraction for light traps catching Culicoides biting midges (Diptera: Ceratopogonidae).

PubMed

Kirkeby, Carsten; Græsbøll, Kaare; Stockmarr, Anders; Christiansen, Lasse E; Bødker, René

2013-03-15

Culicoides are vectors of e.g. bluetongue virus and Schmallenberg virus in northern Europe. Light trapping is an important tool for detecting the presence and quantifying the abundance of vectors in the field. Until now, few studies have investigated the range of attraction of light traps. Here we test a previously described mathematical model (Model I) and two novel models for the attraction of vectors to light traps (Model II and III). In Model I, Culicoides fly to the nearest trap from within a fixed range of attraction. In Model II Culicoides fly towards areas with greater light intensity, and in Model III Culicoides evaluate light sources in the field of view and fly towards the strongest. Model II and III incorporated the directionally dependent light field created around light traps with fluorescent light tubes. All three models were fitted to light trap collections obtained from two novel experimental setups in the field where traps were placed in different configurations. Results showed that overlapping ranges of attraction of neighboring traps extended the shared range of attraction. Model I did not fit data from any of the experimental setups. Model II could only fit data from one of the setups, while Model III fitted data from both experimental setups. The model with the best fit, Model III, indicates that Culicoides continuously evaluate the light source direction and intensity. The maximum range of attraction of a single 4W CDC light trap was estimated to be approximately 15.25 meters. The attraction towards light traps is different from the attraction to host animals and thus light trap catches may not represent the vector species and numbers attracted to hosts.

Redundancy management of electrohydraulic servoactuators by mathematical model referencing

NASA Technical Reports Server (NTRS)

Campbell, R. A.

1971-01-01

A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

Recombinant Enaction: Manipulatives Generate New Procedures in the Imagination, by Extending and Recombining Action Spaces

ERIC Educational Resources Information Center

Rahaman, Jeenath; Agrawal, Harshit; Srivastava, Nisheeth; Chandrasekharan, Sanjay

2018-01-01

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based…

Decomposition-aggregation stability analysis. [for large scale dynamic systems with application to spinning Skylab control system

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Weissenberger, S.; Cuk, S. M.

1973-01-01

This report presents the development and description of the decomposition aggregation approach to stability investigations of high dimension mathematical models of dynamic systems. The high dimension vector differential equation describing a large dynamic system is decomposed into a number of lower dimension vector differential equations which represent interconnected subsystems. Then a method is described by which the stability properties of each subsystem are aggregated into a single vector Liapunov function, representing the aggregate system model, consisting of subsystem Liapunov functions as components. A linear vector differential inequality is then formed in terms of the vector Liapunov function. The matrix of the model, which reflects the stability properties of the subsystems and the nature of their interconnections, is analyzed to conclude over-all system stability characteristics. The technique is applied in detail to investigate the stability characteristics of a dynamic model of a hypothetical spinning Skylab.

Unsymmetric Lanczos model reduction and linear state function observer for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1991-01-01

This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures.

Epidemic spreading and global stability of an SIS model with an infective vector on complex networks

NASA Astrophysics Data System (ADS)

Kang, Huiyan; Fu, Xinchu

2015-10-01

In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization.

Recent Developments In Theory Of Balanced Linear Systems

NASA Technical Reports Server (NTRS)

Gawronski, Wodek

1994-01-01

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

Comparison study of vector control of induction motor with and without saturation and iron loss fed by three level inverter

NASA Astrophysics Data System (ADS)

Bougherara, Salim; Golea, Amar; Benchouia, M. Toufik

2018-05-01

This paper is addressed to a comparative study of the vector control of a three phase induction motor based on two mathematical models. The first one is the conventional model based on the assumptions that the saturation and the iron losses are neglected; the second model fully accounts for both the fundamental iron loss and main flux saturation with and without compensation. A rotor resistance identifier is developed, so the compensation of its variation is achieved. The induction motor should be fed through a three levels inverter. The simulation results show the performances of the vector control based on the both models.

Modeling the impact of global warming on vector-borne infections.

PubMed

Massad, Eduardo; Coutinho, Francisco Antonio Bezerra; Lopez, Luis Fernandez; da Silva, Daniel Rodrigues

2011-06-01

Global warming will certainly affect the abundance and distribution of disease vectors. The effect of global warming, however, depends on the complex interaction between the human host population and the causative infectious agent. In this work we review some mathematical models that were proposed to study the impact of the increase in ambient temperature on the spread and gravity of some insect-transmitted diseases. Copyright © 2011 Elsevier B.V. All rights reserved.

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

Pulse Vector-Excitation Speech Encoder

NASA Technical Reports Server (NTRS)

Davidson, Grant; Gersho, Allen

1989-01-01

Proposed pulse vector-excitation speech encoder (PVXC) encodes analog speech signals into digital representation for transmission or storage at rates below 5 kilobits per second. Produces high quality of reconstructed speech, but with less computation than required by comparable speech-encoding systems. Has some characteristics of multipulse linear predictive coding (MPLPC) and of code-excited linear prediction (CELP). System uses mathematical model of vocal tract in conjunction with set of excitation vectors and perceptually-based error criterion to synthesize natural-sounding speech.

Vectorized Monte Carlo methods for reactor lattice analysis

NASA Technical Reports Server (NTRS)

Brown, F. B.

1984-01-01

Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.

Stability Analysis Susceptible, Exposed, Infected, Recovered (SEIR) Model for Spread Model for Spread of Dengue Fever in Medan

NASA Astrophysics Data System (ADS)

Side, Syafruddin; Molliq Rangkuti, Yulita; Gerhana Pane, Dian; Setia Sinaga, Marlina

2018-01-01

Dengue fever is endemic disease which spread through vector, Aedes Aegypty. This disease is found more than 100 countries, such as, United State, Africa as well Asia, especially in country that have tropic climate. Mathematical modeling in this paper, discusses the speed of the spread of dengue fever. The model adopting divided over four classes, such as Susceptible (S), Exposed (E), Infected (I) and Recovered (R). SEIR model further analyzed to detect the re-breeding value based on the number reported case by dengue in Medan city. Analysis of the stability of the system in this study is asymptotically stable indicating a case of endemic and unstable that show cases the endemic cases. Simulation on the mathematical model of SEIR showed that require a very long time to produce infected humans will be free of dengue virus infection. This happens because of dengue virus infection that occurs continuously between human and vector populations.

A mathematical model of the impact of present and future malaria vaccines.

PubMed

Wenger, Edward A; Eckhoff, Philip A

2013-04-15

With the encouraging advent of new malaria vaccine candidates, mathematical modelling of expected impacts of present and future vaccines as part of multi-intervention strategies is especially relevant. The impact of potential malaria vaccines is presented utilizing the EMOD model, a comprehensive model of the vector life cycle coupled to a detailed mechanistic representation of intra-host parasite and immune dynamics. Values of baseline transmission and vector feeding behaviour parameters are identified, for which local elimination is enabled by layering pre-erythrocytic vaccines of various efficacies on top of high and sustained insecticide-treated net coverage. The expected reduction in clinical cases is further explored in a scenario that targets children by adding a pre-erythrocytic vaccine to the EPI programme for newborns. At high transmission, there is a minimal reduction in clinical disease cases, as the time to infection is only slightly delayed. At lower transmission, there is an accelerating community-level protection that has subtle dependences on heterogeneities in vector behaviour, ecology, and intervention coverage. At very low transmission, the trend reverses as many children are vaccinated to prevent few cases. The maximum-impact setting is one in which the impact of increasing bed net coverage has saturated, vector feeding is primarily outdoors, and transmission is just above the threshold where small perturbations from a vaccine intervention result in large community benefits.

Agent-based mathematical modeling as a tool for estimating Trypanosoma cruzi vector-host contact rates.

PubMed

Yong, Kamuela E; Mubayi, Anuj; Kribs, Christopher M

2015-11-01

The parasite Trypanosoma cruzi, spread by triatomine vectors, affects over 100 mammalian species throughout the Americas, including humans, in whom it causes Chagas' disease. In the U.S., only a few autochthonous cases have been documented in humans, but prevalence is high in sylvatic hosts (primarily raccoons in the southeast and woodrats in Texas). The sylvatic transmission of T. cruzi is spread by the vector species Triatoma sanguisuga and Triatoma gerstaeckeri biting their preferred hosts and thus creating multiple interacting vector-host cycles. The goal of this study is to quantify the rate of contacts between different host and vector species native to Texas using an agent-based model framework. The contact rates, which represent bites, are required to estimate transmission coefficients, which can be applied to models of infection dynamics. In addition to quantitative estimates, results confirm host irritability (in conjunction with host density) and vector starvation thresholds and dispersal as determining factors for vector density as well as host-vector contact rates. Copyright © 2015 Elsevier B.V. All rights reserved.

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

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

A New Paradigm for Satellite Retrieval of Hydrologic Variables: The CDRD Methodology

NASA Astrophysics Data System (ADS)

Smith, E. A.; Mugnai, A.; Tripoli, G. J.

2009-09-01

Historically, retrieval of thermodynamically active geophysical variables in the atmosphere (e.g., temperature, moisture, precipitation) involved some time of inversion scheme - embedded within the retrieval algorithm - to transform radiometric observations (a vector) to the desired geophysical parameter(s) (either a scalar or a vector). Inversion is fundamentally a mathematical operation involving some type of integral-differential radiative transfer equation - often resisting a straightforward algebraic solution - in which the integral side of the equation (typically the right-hand side) contains the desired geophysical vector, while the left-hand side contains the radiative measurement vector often free of operators. Inversion was considered more desirable than forward modeling because the forward model solution had to be selected from a generally unmanageable set of parameter-observation relationships. However, in the classical inversion problem for retrieval of temperature using multiple radiative frequencies along the wing of an absorption band (or line) of a well-mixed radiatively active gas, in either the infrared or microwave spectrums, the inversion equation to be solved consists of a Fredholm integral equation of the 2nd kind - a specific type of transform problem in which there are an infinite number of solutions. This meant that special treatment of the transform process was required in order to obtain a single solution. Inversion had become the method of choice for retrieval in the 1950s because it appealed to the use of mathematical elegance, and because the numerical approaches used to solve the problems (typically some type of relaxation or perturbation scheme) were computationally fast in an age when computers speeds were slow. Like many solution schemes, inversion has lingered on regardless of the fact that computer speeds have increased many orders of magnitude and forward modeling itself has become far more elegant in combination with Bayesian averaging procedures given that the a priori probabilities of occurrence in the true environment of the parameter(s) in question can be approximated (or are actually known). In this presentation, the theory of the more modern retrieval approach using a combination of cloud, radiation and other specialized forward models in conjunction with Bayesian weighted averaging will be reviewed in light of a brief history of inversion. The application of the theory will be cast in the framework of what we call the Cloud-Dynamics-Radiation-Database (CDRD) methodology - which we now use for the retrieval of precipitation from spaceborne passive microwave radiometers. In a companion presentation, we will specifically describe the CDRD methodology and present results for its application within the Mediterranean basin.

Population density, water supply, and the risk of dengue fever in Vietnam: cohort study and spatial analysis.

PubMed

Schmidt, Wolf-Peter; Suzuki, Motoi; Thiem, Vu Dinh; White, Richard G; Tsuzuki, Ataru; Yoshida, Lay-Myint; Yanai, Hideki; Haque, Ubydul; Tho, Le Huu; Anh, Dang Duc; Ariyoshi, Koya

2011-08-01

Aedes aegypti, the major vector of dengue viruses, often breeds in water storage containers used by households without tap water supply, and occurs in high numbers even in dense urban areas. We analysed the interaction between human population density and lack of tap water as a cause of dengue fever outbreaks with the aim of identifying geographic areas at highest risk. We conducted an individual-level cohort study in a population of 75,000 geo-referenced households in Vietnam over the course of two epidemics, on the basis of dengue hospital admissions (n = 3,013). We applied space-time scan statistics and mathematical models to confirm the findings. We identified a surprisingly narrow range of critical human population densities between around 3,000 to 7,000 people/km² prone to dengue outbreaks. In the study area, this population density was typical of villages and some peri-urban areas. Scan statistics showed that areas with a high population density or adequate water supply did not experience severe outbreaks. The risk of dengue was higher in rural than in urban areas, largely explained by lack of piped water supply, and in human population densities more often falling within the critical range. Mathematical modeling suggests that simple assumptions regarding area-level vector/host ratios may explain the occurrence of outbreaks. Rural areas may contribute at least as much to the dissemination of dengue fever as cities. Improving water supply and vector control in areas with a human population density critical for dengue transmission could increase the efficiency of control efforts. Please see later in the article for the Editors' Summary.

Population Density, Water Supply, and the Risk of Dengue Fever in Vietnam: Cohort Study and Spatial Analysis

PubMed Central

Schmidt, Wolf-Peter; Suzuki, Motoi; Dinh Thiem, Vu; White, Richard G.; Tsuzuki, Ataru; Yoshida, Lay-Myint; Yanai, Hideki; Haque, Ubydul; Huu Tho, Le; Anh, Dang Duc; Ariyoshi, Koya

2011-01-01

Background Aedes aegypti, the major vector of dengue viruses, often breeds in water storage containers used by households without tap water supply, and occurs in high numbers even in dense urban areas. We analysed the interaction between human population density and lack of tap water as a cause of dengue fever outbreaks with the aim of identifying geographic areas at highest risk. Methods and Findings We conducted an individual-level cohort study in a population of 75,000 geo-referenced households in Vietnam over the course of two epidemics, on the basis of dengue hospital admissions (n = 3,013). We applied space-time scan statistics and mathematical models to confirm the findings. We identified a surprisingly narrow range of critical human population densities between around 3,000 to 7,000 people/km2 prone to dengue outbreaks. In the study area, this population density was typical of villages and some peri-urban areas. Scan statistics showed that areas with a high population density or adequate water supply did not experience severe outbreaks. The risk of dengue was higher in rural than in urban areas, largely explained by lack of piped water supply, and in human population densities more often falling within the critical range. Mathematical modeling suggests that simple assumptions regarding area-level vector/host ratios may explain the occurrence of outbreaks. Conclusions Rural areas may contribute at least as much to the dissemination of dengue fever as cities. Improving water supply and vector control in areas with a human population density critical for dengue transmission could increase the efficiency of control efforts. Please see later in the article for the Editors' Summary PMID:21918642

Identification of cardiac rhythm features by mathematical analysis of vector fields.

PubMed

Fitzgerald, Tamara N; Brooks, Dana H; Triedman, John K

2005-01-01

Automated techniques for locating cardiac arrhythmia features are limited, and cardiologists generally rely on isochronal maps to infer patterns in the cardiac activation sequence during an ablation procedure. Velocity vector mapping has been proposed as an alternative method to study cardiac activation in both clinical and research environments. In addition to the visual cues that vector maps can provide, vector fields can be analyzed using mathematical operators such as the divergence and curl. In the current study, conduction features were extracted from velocity vector fields computed from cardiac mapping data. The divergence was used to locate ectopic foci and wavefront collisions, and the curl to identify central obstacles in reentrant circuits. Both operators were applied to simulated rhythms created from a two-dimensional cellular automaton model, to measured data from an in situ experimental canine model, and to complex three-dimensional human cardiac mapping data sets. Analysis of simulated vector fields indicated that the divergence is useful in identifying ectopic foci, with a relatively small number of vectors and with errors of up to 30 degrees in the angle measurements. The curl was useful for identifying central obstacles in reentrant circuits, and the number of velocity vectors needed increased as the rhythm became more complex. The divergence was able to accurately identify canine in situ pacing sites, areas of breakthrough activation, and wavefront collisions. In data from human arrhythmias, the divergence reliably estimated origins of electrical activity and wavefront collisions, but the curl was less reliable at locating central obstacles in reentrant circuits, possibly due to the retrospective nature of data collection. The results indicate that the curl and divergence operators applied to velocity vector maps have the potential to add valuable information in cardiac mapping and can be used to supplement human pattern recognition.

Observables of QCD diffraction

NASA Astrophysics Data System (ADS)

Mieskolainen, Mikael; Orava, Risto

2017-03-01

A new combinatorial vector space measurement model is introduced for soft QCD diffraction. The model independent mathematical construction resolves experimental complications; the theoretical framework of the approach includes the Good-Walker view of diffraction, Regge phenomenology together with AGK cutting rules and random fluctuations.

Application of Vectors to Relative Velocity

ERIC Educational Resources Information Center

Tin-Lam, Toh

2004-01-01

The topic 'relative velocity' has recently been introduced into the Cambridge Ordinary Level Additional Mathematics syllabus under the application of Vectors. In this note, the results of relative velocity and the 'reduction to rest' technique of teaching relative velocity are derived mathematically from vector algebra, in the hope of providing…

Mathematical model of temephos resistance in Aedes aegypti mosquito population

NASA Astrophysics Data System (ADS)

Aldila, D.; Nuraini, N.; Soewono, E.; Supriatna, A. K.

2014-03-01

Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical countries. Dengue became major public concern in these countries due to the unavailability of vaccine or drugs for dengue disease in the market. Hence, the only way to control the spread of DF and DHF is by controlling the vectors carrying the disease, for instance with fumigation, temephos or genetic manipulation. Many previous studies conclude that Aedes aegypti may develop resistance to many kind of insecticide, including temephos. Mathematical model for transmission of temephos resistance in Aedes aegypti population is discussed in this paper. Nontrivial equilibrium point of the system and the corresponding existence are shown analytically. The model analysis have shown epidemiological trends condition that permits the coexistence of nontrivial equilibrium is given analytically. Numerical results are given to show parameter sensitivity and some cases of worsening effect values for illustrating possible conditions in the field.

MIST: An Open Source Environmental Modelling Programming Language Incorporating Easy to Use Data Parallelism.

NASA Astrophysics Data System (ADS)

Bellerby, Tim

2014-05-01

Model Integration System (MIST) is open-source environmental modelling programming language that directly incorporates data parallelism. The language is designed to enable straightforward programming structures, such as nested loops and conditional statements to be directly translated into sequences of whole-array (or more generally whole data-structure) operations. MIST thus enables the programmer to use well-understood constructs, directly relating to the mathematical structure of the model, without having to explicitly vectorize code or worry about details of parallelization. A range of common modelling operations are supported by dedicated language structures operating on cell neighbourhoods rather than individual cells (e.g.: the 3x3 local neighbourhood needed to implement an averaging image filter can be simply accessed from within a simple loop traversing all image pixels). This facility hides details of inter-process communication behind more mathematically relevant descriptions of model dynamics. The MIST automatic vectorization/parallelization process serves both to distribute work among available nodes and separately to control storage requirements for intermediate expressions - enabling operations on very large domains for which memory availability may be an issue. MIST is designed to facilitate efficient interpreter based implementations. A prototype open source interpreter is available, coded in standard FORTRAN 95, with tools to rapidly integrate existing FORTRAN 77 or 95 code libraries. The language is formally specified and thus not limited to FORTRAN implementation or to an interpreter-based approach. A MIST to FORTRAN compiler is under development and volunteers are sought to create an ANSI-C implementation. Parallel processing is currently implemented using OpenMP. However, parallelization code is fully modularised and could be replaced with implementations using other libraries. GPU implementation is potentially possible.

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1987-01-01

The research goal was a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. This presents a formidable mathematical problem. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity are defined. Each model is summarized.

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.

Ecology of Yersinia pestis and the Epidemiology of Plague.

PubMed

Dubyanskiy, Vladimir M; Yeszhanov, Aidyn B

2016-01-01

This chapter summarizes information about the natural foci of plague in the world. We describe the location, main hosts, and vectors of Yersinia pestis. The ecological features of the hosts and vectors of plague are listed, including predators - birds and mammals and their role in the epizootic. The epizootic process in plague and the factors affecting the dynamics of epizootic activity of natural foci of Y. pestis are described in detail. The mathematical models of the epizootic process in plague and predictive models are briefly described. The most comprehensive list of the hosts and vectors of Y. pestis in the world is presented as well.

Impact of combined vector-control and vaccination strategies on transmission dynamics of dengue fever: a model-based analysis.

PubMed

Knerer, Gerhart; Currie, Christine S M; Brailsford, Sally C

2015-06-01

Dengue fever is a vector-borne disease prevalent in tropical and subtropical regions. It is an important public health problem with a considerable and often under-valued disease burden in terms of frequency, cost and quality-of-life. Recent literature reviews have documented the development of mathematical models of dengue fever both to identify important characteristics for future model development as well as to assess the impact of dengue control interventions. Such reviews highlight the importance of short-term cross-protection; antibody-dependent enhancement; and seasonality (in terms of both favourable and unfavourable conditions for mosquitoes). The compartmental model extends work by Bartley (2002) and combines the following factors: seasonality, age-structure, consecutive infection by all four serotypes, cross-protection and immune enhancement, as well as combined vector-host transmission. The model is used to represent dengue transmission dynamics using parameters appropriate for Thailand and to assess the potential impact of combined vector-control and vaccination strategies including routine and catch-up vaccination strategies on disease dynamics. When seasonality and temporary cross-protection between serotypes are included, the model is able to approximate the observed incidence of dengue fever in Thailand. We find vaccination to be the most effective single intervention, albeit with imperfect efficacy (30.2 %) and limited duration of protection. However, in combination, control interventions and vaccination exhibit a marked impact on dengue fever transmission. This study shows that an imperfect vaccine can be a useful weapon in reducing disease spread within the community, although it will be most effective when promoted as one of several strategies for combating dengue fever transmission.

Numerical modeling of heat transfer in the fuel oil storage tank at thermal power plant

NASA Astrophysics Data System (ADS)

Kuznetsova, Svetlana A.

2015-01-01

Presents results of mathematical modeling of convection of a viscous incompressible fluid in a rectangular cavity with conducting walls of finite thickness in the presence of a local source of heat in the bottom of the field in terms of convective heat exchange with the environment. A mathematical model is formulated in terms of dimensionless variables "stream function - vorticity vector speed - temperature" in the Cartesian coordinate system. As the results show the distributions of hydrodynamic parameters and temperatures using different boundary conditions on the local heat source.

Dynamical generation of a repulsive vector contribution to the quark pressure

NASA Astrophysics Data System (ADS)

Restrepo, Tulio E.; Macias, Juan Camilo; Pinto, Marcus Benghi; Ferrari, Gabriel N.

2015-03-01

Lattice QCD results for the coefficient c2 appearing in the Taylor expansion of the pressure show that this quantity increases with the temperature towards the Stefan-Boltzmann limit. On the other hand, model approximations predict that when a vector repulsion, parametrized by GV, is present this coefficient reaches a maximum just after Tc and then deviates from the lattice predictions. Recently, this discrepancy has been used as a guide to constrain the (presently unknown) value of GV within the framework of effective models at large Nc (LN). In the present investigation we show that, due to finite Nc effects, c2 may also develop a maximum even when GV=0 since a vector repulsive term can be dynamically generated by exchange-type radiative corrections. Here we apply the optimized perturbation theory (OPT) method to the two-flavor Polyakov-Nambu-Jona-Lasinio model (at GV=0 ) and compare the results with those furnished by lattice simulations and by the LN approximation at GV=0 and also at GV≠0 . The OPT numerical results for c2 are impressively accurate for T ≲1.2 Tc but, as expected, they predict that this quantity develops a maximum at high T . After identifying the mathematical origin of this extremum we argue that such a discrepant behavior may naturally arise within this type of effective quark theories (at GV=0 ) whenever the first 1 /Nc corrections are taken into account. We then interpret this hypothesis as an indication that beyond the large-Nc limit the correct high-temperature (perturbative) behavior of c2 will be faithfully described by effective models only if they also mimic the asymptotic freedom phenomenon.

A system-level mathematical model of Basal Ganglia motor-circuit for kinematic planning of arm movements.

PubMed

Salimi-Badr, Armin; Ebadzadeh, Mohammad Mehdi; Darlot, Christian

2018-01-01

In this paper, a novel system-level mathematical model of the Basal Ganglia (BG) for kinematic planning, is proposed. An arm composed of several segments presents a geometric redundancy. Thus, selecting one trajectory among an infinite number of possible ones requires overcoming redundancy, according to some kinds of optimization. Solving this optimization is assumed to be the function of BG in planning. In the proposed model, first, a mathematical solution of kinematic planning is proposed for movements of a redundant arm in a plane, based on minimizing energy consumption. Next, the function of each part in the model is interpreted as a possible role of a nucleus of BG. Since the kinematic variables are considered as vectors, the proposed model is presented based on the vector calculus. This vector model predicts different neuronal populations in BG which is in accordance with some recent experimental studies. According to the proposed model, the function of the direct pathway is to calculate the necessary rotation of each joint, and the function of the indirect pathway is to control each joint rotation considering the movement of the other joints. In the proposed model, the local feedback loop between Subthalamic Nucleus and Globus Pallidus externus is interpreted as a local memory to store the previous amounts of movements of the other joints, which are utilized by the indirect pathway. In this model, activities of dopaminergic neurons would encode, at short-term, the error between the desired and actual positions of the end-effector. The short-term modulating effect of dopamine on Striatum is also modeled as cross product. The model is simulated to generate the commands of a redundant manipulator. The performance of the model is studied for different reaching movements between 8 points in a plane. Finally, some symptoms of Parkinson's disease such as bradykinesia and akinesia are simulated by modifying the model parameters, inspired by the dopamine depletion. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematical modeling of a class of multibody flexible spacecraft structures

NASA Technical Reports Server (NTRS)

Kelkar, Atul, G.

1994-01-01

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

Biological Control of the Chagas Disease Vector Triatoma infestans with the Entomopathogenic Fungus Beauveria bassiana Combined with an Aggregation Cue: Field, Laboratory and Mathematical Modeling Assessment

PubMed Central

Forlani, Lucas; Pedrini, Nicolás; Girotti, Juan R.; Mijailovsky, Sergio J.; Cardozo, Rubén M.; Gentile, Alberto G.; Hernández-Suárez, Carlos M.; Rabinovich, Jorge E.; Juárez, M. Patricia

2015-01-01

Background Current Chagas disease vector control strategies, based on chemical insecticide spraying, are growingly threatened by the emergence of pyrethroid-resistant Triatoma infestans populations in the Gran Chaco region of South America. Methodology and findings We have already shown that the entomopathogenic fungus Beauveria bassiana has the ability to breach the insect cuticle and is effective both against pyrethroid-susceptible and pyrethroid-resistant T. infestans, in laboratory as well as field assays. It is also known that T. infestans cuticle lipids play a major role as contact aggregation pheromones. We estimated the effectiveness of pheromone-based infection boxes containing B. bassiana spores to kill indoor bugs, and its effect on the vector population dynamics. Laboratory assays were performed to estimate the effect of fungal infection on female reproductive parameters. The effect of insect exuviae as an aggregation signal in the performance of the infection boxes was estimated both in the laboratory and in the field. We developed a stage-specific matrix model of T. infestans to describe the fungal infection effects on insect population dynamics, and to analyze the performance of the biopesticide device in vector biological control. Conclusions The pheromone-containing infective box is a promising new tool against indoor populations of this Chagas disease vector, with the number of boxes per house being the main driver of the reduction of the total domestic bug population. This ecologically safe approach is the first proven alternative to chemical insecticides in the control of T. infestans. The advantageous reduction in vector population by delayed-action fungal biopesticides in a contained environment is here shown supported by mathematical modeling. PMID:25969989

R0 for vector-borne diseases: impact of the assumption for the duration of the extrinsic incubation period.

PubMed

Hartemink, Nienke; Cianci, Daniela; Reiter, Paul

2015-03-01

Mathematical modeling and notably the basic reproduction number R0 have become popular tools for the description of vector-borne disease dynamics. We compare two widely used methods to calculate the probability of a vector to survive the extrinsic incubation period. The two methods are based on different assumptions for the duration of the extrinsic incubation period; one method assumes a fixed period and the other method assumes a fixed daily rate of becoming infectious. We conclude that the outcomes differ substantially between the methods when the average life span of the vector is short compared to the extrinsic incubation period.

Assessing the impact of model and climate uncertainty in malaria simulations for the Kenyan Highlands.

NASA Astrophysics Data System (ADS)

Tompkins, A. M.; Thomson, M. C.

2017-12-01

Simulations of the impact of climate variations on a vector-bornedisease such as malaria are subject to a number of sources ofuncertainty. These include the model structure and parameter settingsin addition to errors in the climate data and the neglect of theirspatial heterogeneity, especially over complex terrain. We use aconstrained genetic algorithm to confront these two sources ofuncertainty for malaria transmission in the highlands of Kenya. Thetechnique calibrates the parameter settings of a process-based,mathematical model of malaria transmission to vary within theirassessed level of uncertainty and also allows the calibration of thedriving climate data. The simulations show that in highland settingsclose to the threshold for sustained transmission, the uncertainty inclimate is more important to address than the malaria modeluncertainty. Applications of the coupled climate-malaria modelling system are briefly presented.

Effect of difference of cupula and endolymph densities on the dynamics of semicircular canal.

PubMed

Kondrachuk, A V; Sirenko, S P; Boyle, R

2008-01-01

The effect of different densities of a cupula and endolymph on the dynamics of the semicircular canals is considered within the framework of a simplified one-dimensional mathematical model where the canal is approximated by a torus. If the densities are equal, the model is represented by Steinhausen's phenomenological equation. The difference of densities results in the complex dynamics of the cupulo-endolymphatic system, and leads to a dependence on the orientation of both the gravity vector relative to the canal plane and the axis of rotation, as well as on the distance between the axis of rotation and the center of the semicircular canal. Our analysis focused on two cases of canal stimulation: rotation with a constant velocity and a time-dependent (harmonically oscillating) angular velocity. Two types of spatial orientation of the axis of rotation, the axis of canal symmetry, and the vector of gravity were considered: i) the gravity vector and axis of rotation lie in the canal plane, and ii) the axis of rotation and gravity vector are normal to the canal plane. The difference of the cupula and endolymph densities reveals new features of cupula dynamics, for instance--a shift of the cupula to a new position of equilibrium that depends on the gravity vector and the parameters of head rotation, and the onset of cupula oscillations with multiple frequencies that results in the distortion of cupula dynamics relative to harmonic stimulation. Factors that might influence the density difference effects and the conditions under which these effects occur are discussed.

Multi-agent systems in epidemiology: a first step for computational biology in the study of vector-borne disease transmission.

PubMed

Roche, Benjamin; Guégan, Jean-François; Bousquet, François

2008-10-15

Computational biology is often associated with genetic or genomic studies only. However, thanks to the increase of computational resources, computational models are appreciated as useful tools in many other scientific fields. Such modeling systems are particularly relevant for the study of complex systems, like the epidemiology of emerging infectious diseases. So far, mathematical models remain the main tool for the epidemiological and ecological analysis of infectious diseases, with SIR models could be seen as an implicit standard in epidemiology. Unfortunately, these models are based on differential equations and, therefore, can become very rapidly unmanageable due to the too many parameters which need to be taken into consideration. For instance, in the case of zoonotic and vector-borne diseases in wildlife many different potential host species could be involved in the life-cycle of disease transmission, and SIR models might not be the most suitable tool to truly capture the overall disease circulation within that environment. This limitation underlines the necessity to develop a standard spatial model that can cope with the transmission of disease in realistic ecosystems. Computational biology may prove to be flexible enough to take into account the natural complexity observed in both natural and man-made ecosystems. In this paper, we propose a new computational model to study the transmission of infectious diseases in a spatially explicit context. We developed a multi-agent system model for vector-borne disease transmission in a realistic spatial environment. Here we describe in detail the general behavior of this model that we hope will become a standard reference for the study of vector-borne disease transmission in wildlife. To conclude, we show how this simple model could be easily adapted and modified to be used as a common framework for further research developments in this field.

Mathematical modeling of climate change and malaria transmission dynamics: a historical review.

PubMed

Eikenberry, Steffen E; Gumel, Abba B

2018-04-24

Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease's geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the "million-murdering Death" of malaria.

Development of 4D mathematical observer models for the task-based evaluation of gated myocardial perfusion SPECT

NASA Astrophysics Data System (ADS)

Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.

2015-04-01

This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the performance of human observers in detecting regional motion defects in 4D gated MP SPECT images. The result supports the use of the observer model in the optimization and evaluation of 4D image reconstruction and compensation methods for improving the detection of motion abnormalities in 4D gated MP SPECT images.

The application of vector concepts on two skew lines

NASA Astrophysics Data System (ADS)

Alghadari, F.; Turmudi; Herman, T.

2018-01-01

The purpose of this study is knowing how to apply vector concepts on two skew lines in three-dimensional (3D) coordinate and its utilization. Several mathematical concepts have a related function for the other, but the related between the concept of vector and 3D have not applied in learning classroom. In fact, there are studies show that female students have difficulties in learning of 3D than male. It is because of personal spatial intelligence. The relevance of vector concepts creates both learning achievement and mathematical ability of male and female students enables to be balanced. The distance like on a cube, cuboid, or pyramid whose are drawn on the rectangular coordinates of a point in space. Two coordinate points of the lines can be created a vector. The vector of two skew lines has the shortest distance and the angle. Calculating of the shortest distance is started to create two vectors as a representation of line by vector position concept, next to determining a norm-vector of two vector which was obtained by cross-product, and then to create a vector from two combination of pair-points which was passed by two skew line, the shortest distance is scalar orthogonal projection of norm-vector on a vector which is a combination of pair-points. While calculating the angle are used two vectors as a representation of line to dot-product, and the inverse of cosine is yield. The utilization of its application on mathematics learning and orthographic projection method.

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Mathematical modelling of vector-borne diseases and insecticide resistance evolution.

PubMed

Gabriel Kuniyoshi, Maria Laura; Pio Dos Santos, Fernando Luiz

2017-01-01

Vector-borne diseases are important public health issues and, consequently, in silico models that simulate them can be useful. The susceptible-infected-recovered (SIR) model simulates the population dynamics of an epidemic and can be easily adapted to vector-borne diseases, whereas the Hardy-Weinberg model simulates allele frequencies and can be used to study insecticide resistance evolution. The aim of the present study is to develop a coupled system that unifies both models, therefore enabling the analysis of the effects of vector population genetics on the population dynamics of an epidemic. Our model consists of an ordinary differential equation system. We considered the populations of susceptible, infected and recovered humans, as well as susceptible and infected vectors. Concerning these vectors, we considered a pair of alleles, with complete dominance interaction that determined the rate of mortality induced by insecticides. Thus, we were able to separate the vectors according to the genotype. We performed three numerical simulations of the model. In simulation one, both alleles conferred the same mortality rate values, therefore there was no resistant strain. In simulations two and three, the recessive and dominant alleles, respectively, conferred a lower mortality. Our numerical results show that the genetic composition of the vector population affects the dynamics of human diseases. We found that the absolute number of vectors and the proportion of infected vectors are smaller when there is no resistant strain, whilst the ratio of infected people is larger in the presence of insecticide-resistant vectors. The dynamics observed for infected humans in all simulations has a very similar shape to real epidemiological data. The population genetics of vectors can affect epidemiological dynamics, and the presence of insecticide-resistant strains can increase the number of infected people. Based on the present results, the model is a basis for development of other models and for investigating population dynamics.

A malaria transmission-directed model of mosquito life cycle and ecology

PubMed Central

2011-01-01

Background Malaria is a major public health issue in much of the world, and the mosquito vectors which drive transmission are key targets for interventions. Mathematical models for planning malaria eradication benefit from detailed representations of local mosquito populations, their natural dynamics and their response to campaign pressures. Methods A new model is presented for mosquito population dynamics, effects of weather, and impacts of multiple simultaneous interventions. This model is then embedded in a large-scale individual-based simulation and results for local elimination of malaria are discussed. Mosquito population behaviours, such as anthropophily and indoor feeding, are included to study their effect upon the efficacy of vector control-based elimination campaigns. Results Results for vector control tools, such as bed nets, indoor spraying, larval control and space spraying, both alone and in combination, are displayed for a single-location simulation with vector species and seasonality characteristic of central Tanzania, varying baseline transmission intensity and vector bionomics. The sensitivities to habitat type, anthropophily, indoor feeding, and baseline transmission intensity are explored. Conclusions The ability to model a spectrum of local vector species with different ecologies and behaviours allows local customization of packages of interventions and exploration of the effect of proposed new tools. PMID:21999664

Vector and Axial-Vector Current Correlators Within the Instanton Model of QCD Vacuum

NASA Astrophysics Data System (ADS)

Dorokhov, A. E.

2005-08-01

The pion electric polarizability, α {π ^ ± }E , the leading order hadronic contribution to the muon anomalous magnetic moment, aμ hvp(1) , and the ratio of the V - A and V + A correlators are found within the instanton model of QCD vacuum. The results are compared with phenomenological estimates of these quantities from the ALEPH and OPAL data on vector and axial-vector spectral densities.

Application of Lanczos vectors to control design of flexible structures

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Su, Tzu-Jeng

1990-01-01

This report covers research conducted during the first year of the two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to obtain reduced-order mathematical models for use in dynamic response analyses and in control design studies. This report summarizes research described in several reports and papers that were written under this contract. Extended abstracts are presented for technical papers covering the following topics: controller reduction by preserving impulse response energy; substructuring decomposition and controller synthesis; model reduction methods for structural control design; and recent literature on structural modeling, identification, and analysis.

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…

Single Vector Calibration System for Multi-Axis Load Cells and Method for Calibrating a Multi-Axis Load Cell

NASA Technical Reports Server (NTRS)

Parker, Peter A. (Inventor)

2003-01-01

A single vector calibration system is provided which facilitates the calibration of multi-axis load cells, including wind tunnel force balances. The single vector system provides the capability to calibrate a multi-axis load cell using a single directional load, for example loading solely in the gravitational direction. The system manipulates the load cell in three-dimensional space, while keeping the uni-directional calibration load aligned. The use of a single vector calibration load reduces the set-up time for the multi-axis load combinations needed to generate a complete calibration mathematical model. The system also reduces load application inaccuracies caused by the conventional requirement to generate multiple force vectors. The simplicity of the system reduces calibration time and cost, while simultaneously increasing calibration accuracy.

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

PubMed

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

2012-01-01

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

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

PubMed Central

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

2012-01-01

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

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System.

PubMed

Gulbudak, Hayriye; Cannataro, Vincent L; Tuncer, Necibe; Martcheva, Maia

2017-02-01

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission trade-offs and evolution in vector-borne pathogen-host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the [Formula: see text] maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen [Formula: see text], but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.

A Vector Representation for Thermodynamic Relationships

ERIC Educational Resources Information Center

Pogliani, Lionello

2006-01-01

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

Geometric and computer-aided spline hob modeling

NASA Astrophysics Data System (ADS)

Brailov, I. G.; Myasoedova, T. M.; Panchuk, K. L.; Krysova, I. V.; Rogoza, YU A.

2018-03-01

The paper considers acquiring the spline hob geometric model. The objective of the research is the development of a mathematical model of spline hob for spline shaft machining. The structure of the spline hob is described taking into consideration the motion in parameters of the machine tool system of cutting edge positioning and orientation. Computer-aided study is performed with the use of CAD and on the basis of 3D modeling methods. Vector representation of cutting edge geometry is accepted as the principal method of spline hob mathematical model development. The paper defines the correlations described by parametric vector functions representing helical cutting edges designed for spline shaft machining with consideration for helical movement in two dimensions. An application for acquiring the 3D model of spline hob is developed on the basis of AutoLISP for AutoCAD environment. The application presents the opportunity for the use of the acquired model for milling process imitation. An example of evaluation, analytical representation and computer modeling of the proposed geometrical model is reviewed. In the mentioned example, a calculation of key spline hob parameters assuring the capability of hobbing a spline shaft of standard design is performed. The polygonal and solid spline hob 3D models are acquired by the use of imitational computer modeling.

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…

A Guided Tour of Mathematical Methods - 2nd Edition

NASA Astrophysics Data System (ADS)

Snieder, Roel

2004-09-01

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. All the material is presented in the form of problems Mathematical insights are gained by getting the reader to develop answers themselves Many applications of the mathematics are given

A survey of basic reproductive ratios in vector-borne disease transmission modeling

NASA Astrophysics Data System (ADS)

Soewono, E.; Aldila, D.

2015-03-01

Vector-borne diseases are commonly known in tropical and subtropical countries. These diseases have contributed to more than 10% of world infectious disease cases. Among the vectors responsible for transmitting the diseases are mosquitoes, ticks, fleas, flies, bugs and worms. Several of the diseases are known to contribute to the increasing threat to human health such as malaria, dengue, filariasis, chikungunya, west nile fever, yellow fever, encephalistis, and anthrax. It is necessary to understand the real process of infection, factors which contribute to the complication of the transmission in order to come up with a good and sound mathematical model. Although it is not easy to simulate the real transmission process of the infection, we could say that almost all models have been developed from the already long known Host-Vector model. It constitutes the main transmission processes i.e. birth, death, infection and recovery. From this simple model, the basic concepts of Disease Free and Endemic Equilibria and Basic Reproductive Ratio can be well explained and understood. Theoretical, modeling, control and treatment aspects of disease transmission problems have then been developed for various related diseases. General construction as well as specific forms of basic reproductive ratios for vector-borne diseases are discusses here.

Application of Lanczos vectors to control design of flexible structures, part 2

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Su, Tzu-Jeng

1992-01-01

This report covers the period of the grant from January 1991 until its expiration in June 1992. Together with an Interim Report (Ref. 9), it summarizes the research conducted under NASA Grant NAG9-357 on the topic 'Application of Lanczos Vectors to Control Design of Flexible Structures.' The research concerns various ways to obtain reduced-order mathematical models of complex structures for use in dynamics analysis and in the design of control systems for these structures. This report summarizes the research.

Application of three controls optimally in a vector-borne disease - a mathematical study

NASA Astrophysics Data System (ADS)

Kar, T. K.; Jana, Soovoojeet

2013-10-01

We have proposed and analyzed a vector-borne disease model with three types of controls for the eradication of the disease. Four different classes for the human population namely susceptible, infected, recovered and vaccinated and two different classes for the vector populations namely susceptible and infected are considered. In the first part of our analysis the disease dynamics are described for fixed controls and some inferences have been drawn regarding the spread of the disease. Next the optimal control problem is formulated and solved considering control parameters as time dependent. Different possible combination of controls are used and their effectiveness are compared by numerical simulation.

Peer Instruction and Secondary School Students' Achievement in Vectors

ERIC Educational Resources Information Center

Ouko, Susan; Aurah, Catherine; Amadalo, Maurice

2015-01-01

The importance of raising students' competence in mathematics in a developing country such as Kenya cannot be overstated. This is because to produce professionals in areas such as engineering, medicine and accounting requires a good score in mathematics. Students that will further their studies in these areas will find that vectors is prerequisite…

Novel Approach on the Optimisation of Mid-Course Corrections Along Interplanetary Trajectories

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

The primer vector theory, firstly proposed by Lawden, defines a set of necessary conditions to characterise whether an impulsive thrust trajectory is optimal with respect to propellant usage, within a two-body problem context. If the conditions are not satisfied, one or more potential intermediate impulses are performed along the transfer arc, in order to lower the overall cost. The method is based on the propagation of the state transition matrix and on the solution of a boundary value problem, which leads to a mathematical and computational complexity.In this paper, a different approach is introduced. It is based on a polar coordinates transformation of the primer vector which allows the decoupling between its in-plane and out-of-plane components. The out-of-plane component is solved analytically while for the in-plane ones a Hamiltonian approximation is made.The novel procedure reduces the mathematical complexity and the computational cost of Lawden's problem and gives also a different perspective about the optimisation of a transfer trajectory.

A low-cost vector processor boosting compute-intensive image processing operations

NASA Technical Reports Server (NTRS)

Adorf, Hans-Martin

1992-01-01

Low-cost vector processing (VP) is within reach of everyone seriously engaged in scientific computing. The advent of affordable add-on VP-boards for standard workstations complemented by mathematical/statistical libraries is beginning to impact compute-intensive tasks such as image processing. A case in point in the restoration of distorted images from the Hubble Space Telescope. A low-cost implementation is presented of the standard Tarasko-Richardson-Lucy restoration algorithm on an Intel i860-based VP-board which is seamlessly interfaced to a commercial, interactive image processing system. First experience is reported (including some benchmarks for standalone FFT's) and some conclusions are drawn.

Numerical Simulations of Plasma Based Flow Control Applications

NASA Technical Reports Server (NTRS)

Suzen, Y. B.; Huang, P. G.; Jacob, J. D.; Ashpis, D. E.

2005-01-01

A mathematical model was developed to simulate flow control applications using plasma actuators. The effects of the plasma actuators on the external flow are incorporated into Navier Stokes computations as a body force vector. In order to compute this body force vector, the model solves two additional equations: one for the electric field due to the applied AC voltage at the electrodes and the other for the charge density representing the ionized air. The model is calibrated against an experiment having plasma-driven flow in a quiescent environment and is then applied to simulate a low pressure turbine flow with large flow separation. The effects of the plasma actuator on control of flow separation are demonstrated numerically.

Research and simulation of the decoupling transformation in AC motor vector control

NASA Astrophysics Data System (ADS)

He, Jiaojiao; Zhao, Zhongjie; Liu, Ken; Zhang, Yongping; Yao, Tuozhong

2018-04-01

Permanent magnet synchronous motor (PMSM) is a nonlinear, strong coupling, multivariable complex object, and transformation decoupling can solve the coupling problem of permanent magnet synchronous motor. This paper gives a permanent magnet synchronous motor (PMSM) mathematical model, introduces the permanent magnet synchronous motor vector control coordinate transformation in the process of modal matrix inductance matrix transform through the matrix related knowledge of different coordinates of diagonalization, which makes the coupling between the independent, realize the control of motor current and excitation the torque current coupling separation, and derived the coordinate transformation matrix, the thought to solve the coupling problem of AC motor. Finally, in the Matlab/Simulink environment, through the establishment and combination between the PMSM ontology, coordinate conversion module, built the simulation model of permanent magnet synchronous motor vector control, introduces the model of each part, and analyzed the simulation results.

Can antibodies against flies alter malaria transmission in birds by changing vector behavior?

PubMed

Ghosh, Suma; Waite, Jessica L; Clayton, Dale H; Adler, Frederick R

2014-10-07

Transmission of insect-borne diseases is shaped by the interactions among parasites, vectors, and hosts. Any factor that alters movement of infected vectors from infected to uninfeced hosts will in turn alter pathogen spread. In this paper, we study one such pathogen-vector-host system, avian malaria in pigeons transmitted by fly ectoparasites, where both two-way and three-way interactions play a key role in shaping disease spread. Bird immune defenses against flies can decrease malaria prevalence by reducing fly residence time on infected birds or increase disease prevalence by enhancing fly movement and thus infection transmission. We develop a mathematical model that illustrates how these changes in vector behavior influence pathogen transmission and show that malaria prevalence is maximized at an intermediate level of defense avoidance by the flies. Understanding how host immune defenses indirectly alter disease transmission by influencing vector behavior has implications for reducing the transmission of human malaria and other vectored pathogens. Published by Elsevier Ltd.

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

NASA Astrophysics Data System (ADS)

Champredon, David; Earn, David J. D.

2016-09-01

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

Student difficulties regarding symbolic and graphical representations of vector fields

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke

2017-12-01

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.

Shoelace Formula: Connecting the Area of a Polygon and the Vector Cross Product

ERIC Educational Resources Information Center

Lee, Younhee; Lim, Woong

2017-01-01

Understanding how one representation connects to another and how the essential ideas in that relationship are generalized can result in a mathematical theorem or a formula. In this article, the authors demonstrate this process by connecting a vector cross product in algebraic form to a geometric representation and applying a key mathematical idea…

Angry Birds Mathematics: Parabolas and Vectors

ERIC Educational Resources Information Center

Lamb, John H.

2013-01-01

John Lamb, a professor of mathematics education and a teacher of high school precalculus, describes how he developed a way to use the elements of the game Angry Birds® as a platform to engage his students with the concepts of parabolas and vectors. The game could be categorized as a type of microworld game in which students interact with the…

Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

DOE PAGES

Carlberg, Kevin T.

2014-11-05

Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operationsmore » or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.« less

A mathematical model of Chagas disease transmission

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Hyperbolic and semi-parametric models in finance

NASA Astrophysics Data System (ADS)

Bingham, N. H.; Kiesel, Rüdiger

2001-02-01

The benchmark Black-Scholes-Merton model of mathematical finance is parametric, based on the normal/Gaussian distribution. Its principal parametric competitor, the hyperbolic model of Barndorff-Nielsen, Eberlein and others, is briefly discussed. Our main theme is the use of semi-parametric models, incorporating the mean vector and covariance matrix as in the Markowitz approach, plus a non-parametric part, a scalar function incorporating features such as tail-decay. Implementation is also briefly discussed.

Comparison between sparsely distributed memory and Hopfield-type neural network models

NASA Technical Reports Server (NTRS)

Keeler, James D.

1986-01-01

The Sparsely Distributed Memory (SDM) model (Kanerva, 1984) is compared to Hopfield-type neural-network models. A mathematical framework for comparing the two is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independently of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. However, the total number of stored bits per matrix element is the same in the two models, as well as for extended models with higher order interactions. The models are also compared in their ability to store sequences of patterns. The SDM is extended to include time delays so that contextual information can be used to cover sequences. Finally, it is shown how a generalization of the SDM allows storage of correlated input pattern vectors.

Modelling mid-course corrections for optimality conditions along interplanetary transfers

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

2014-12-01

Within the field of trajectory optimisation, Lawden developed the primer vector theory, which defines a set of necessary conditions to characterise whether a transfer trajectory, in the two-body problem context, is optimum with respect to propellant usage. If the conditions are not satisfied, a region of the transfer trajectory is identified in which one or more potential intermediate impulses are performed in order to lower the overall cost. The method is computationally complex owing to having to solve a boundary value problem. In this paper is presented a new propagator that reduces the mathematical complexity and the computational cost of the problem, in particular it exploits a separation between the in-plane and out-of-plane components of the primer vector along the transfer trajectory. Using this propagator, the optimality of the transfer arc has been investigated, varying the departure and arrival orbits. In particular, keeping fixed the transfer trajectory, the optimality has been extensively analysed varying both the initial and final positions on the orbit, together with the directions of the initial and final thrust impulses.

Electric current locator

DOEpatents

King, Paul E [Corvallis, OR; Woodside, Charles Rigel [Corvallis, OR

2012-02-07

The disclosure herein provides an apparatus for location of a quantity of current vectors in an electrical device, where the current vector has a known direction and a known relative magnitude to an input current supplied to the electrical device. Mathematical constants used in Biot-Savart superposition equations are determined for the electrical device, the orientation of the apparatus, and relative magnitude of the current vector and the input current, and the apparatus utilizes magnetic field sensors oriented to a sensing plane to provide current vector location based on the solution of the Biot-Savart superposition equations. Description of required orientations between the apparatus and the electrical device are disclosed and various methods of determining the mathematical constants are presented.

Combining indoor and outdoor methods for controlling malaria vectors: an ecological model of endectocide-treated livestock and insecticidal bed nets.

PubMed

Yakob, Laith; Cameron, Mary; Lines, Jo

2017-03-13

Malaria is spread by mosquitoes that are increasingly recognised to have diverse biting behaviours. How a mosquito in a specific environment responds to differing availability of blood-host species is largely unknown and yet critical to vector control efficacy. A parsimonious mathematical model is proposed that accounts for a diverse range of host-biting behaviours and assesses their impact on combining long-lasting insecticidal nets (LLINs) with a novel approach to malaria control: livestock treated with insecticidal compounds ('endectocides') that kill biting mosquitoes. Simulations of a malaria control programme showed marked differences across biting ecologies in the efficacy of both LLINs as a stand-alone tool and the combination of LLINs with endectocide-treated cattle. During the intervals between LLIN mass campaigns, concordant use of endectocides is projected to reduce the bounce-back in malaria prevalence that can occur as LLIN efficacy decays over time, especially if replacement campaigns are delayed. Integrating these approaches can also dramatically improve the attainability of local elimination; endectocidal treatment schedules required to achieve this aim are provided for malaria vectors with different biting ecologies. Targeting blood-feeding mosquitoes by treating livestock with endectocides offers a potentially useful complement to existing malaria control programmes centred on LLIN distribution. This approach is likely to be effective against vectors with a wide range of host-preferences and biting behaviours, with the exception of species that are so strictly anthropophilic that most blood meals are taken on humans even when humans are much less available than non-human hosts. Identifying this functional relationship in wild mosquito populations and ascertaining the extent to which it differs, within as well as between species, is a critical next step before targets can be set for employing this novel approach and combination.

Quantum Social Science

NASA Astrophysics Data System (ADS)

Haven, Emmanuel; Khrennikov, Andrei

2013-01-01

Preface; Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one; 2. Econophysics: statistical physics and social science; 3. Quantum social science: a non-mathematical motivation; Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries; 5. Basic elements of quantum mechanics; 6. Basic elements of Bohmian mechanics; Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview; 8. Interference effects in psychology - an introduction; 9. A quantum-like model of decision making; Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis; 11. Bohmian mechanics in finance and economics; 12. The Bohm-Vigier Model and path simulation; 13. Other applications to economic/financial theory; 14. The neurophysiological sources of quantum-like processing in the brain; Conclusion; Glossary; Index.

Mathematical supply-chain modelling: Product analysis of cost and time

NASA Astrophysics Data System (ADS)

Easters, D. J.

2014-03-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

Modeling infectious disease dynamics in the complex landscape of global health

PubMed Central

Heesterbeek, Hans; Anderson, Roy; Andreasen, Viggo; Bansal, Shweta; De Angelis, Daniela; Dye, Chris; Eames, Ken; Edmunds, John; Frost, Simon; Funk, Sebastian; Hollingsworth, Deirdre; House, Thomas; Isham, Valerie; Klepac, Petra; Lessler, Justin; Lloyd-Smith, James; Metcalf, Jessica; Mollison, Denis; Pellis, Lorenzo; Pulliam, Juliet; Roberts, Mick; Viboud, Cecile

2015-01-01

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational and spatial scales, which even within a single pathogen often span hours to months, cellular to ecosystem levels, and local to pandemic spread. Some pathogens are directly transmitted between individuals of a single species, while others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity, and dynamic human behavior, raise prevention and control from formerly national to international issues. In the face of this complexity, mathematical models offer essential tools for synthesizing information to understand epidemiological patterns, and for developing the quantitative evidence base for decision-making in global health. PMID:25766240

Modeling Combinations of Pre-erythrocytic Plasmodium falciparum Malaria Vaccines.

PubMed

Walker, Andrew S; Lourenço, José; Hill, Adrian V S; Gupta, Sunetra

2015-12-01

Despite substantial progress in the control of Plasmodium falciparum infection due to the widespread deployment of insecticide-treated bed nets and artemisinin combination therapies, malaria remains a prolific killer, with over half a million deaths estimated to have occurred in 2013 alone. Recent evidence of the development of resistance to treatments in both parasites and their mosquito vectors has underscored the need for a vaccine. Here, we use a mathematical model of the within-host dynamics of P. falciparum infection, fit to data from controlled human malaria infection clinical trials, to predict the efficacy of co-administering the two most promising subunit vaccines, RTS,S/AS01 and ChAd63-MVA ME-TRAP. We conclude that currently available technologies could be combined to induce very high levels of sterile efficacy, even in immune-naive individuals. © The American Society of Tropical Medicine and Hygiene.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

PubMed

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

PubMed Central

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

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.

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

Fault Detection of Bearing Systems through EEMD and Optimization Algorithm

PubMed Central

Lee, Dong-Han; Ahn, Jong-Hyo; Koh, Bong-Hwan

2017-01-01

This study proposes a fault detection and diagnosis method for bearing systems using ensemble empirical mode decomposition (EEMD) based feature extraction, in conjunction with particle swarm optimization (PSO), principal component analysis (PCA), and Isomap. First, a mathematical model is assumed to generate vibration signals from damaged bearing components, such as the inner-race, outer-race, and rolling elements. The process of decomposing vibration signals into intrinsic mode functions (IMFs) and extracting statistical features is introduced to develop a damage-sensitive parameter vector. Finally, PCA and Isomap algorithm are used to classify and visualize this parameter vector, to separate damage characteristics from healthy bearing components. Moreover, the PSO-based optimization algorithm improves the classification performance by selecting proper weightings for the parameter vector, to maximize the visualization effect of separating and grouping of parameter vectors in three-dimensional space. PMID:29143772

A simple dynamic engine model for use in a real-time aircraft simulation with thrust vectoring

NASA Technical Reports Server (NTRS)

Johnson, Steven A.

1990-01-01

A simple dynamic engine model was developed at the NASA Ames Research Center, Dryden Flight Research Facility, for use in thrust vectoring control law development and real-time aircraft simulation. The simple dynamic engine model of the F404-GE-400 engine (General Electric, Lynn, Massachusetts) operates within the aircraft simulator. It was developed using tabular data generated from a complete nonlinear dynamic engine model supplied by the manufacturer. Engine dynamics were simulated using a throttle rate limiter and low-pass filter. Included is a description of a method to account for axial thrust loss resulting from thrust vectoring. In addition, the development of the simple dynamic engine model and its incorporation into the F-18 high alpha research vehicle (HARV) thrust vectoring simulation. The simple dynamic engine model was evaluated at Mach 0.2, 35,000 ft altitude and at Mach 0.7, 35,000 ft altitude. The simple dynamic engine model is within 3 percent of the steady state response, and within 25 percent of the transient response of the complete nonlinear dynamic engine model.

Efficacies of prevention and control measures applied during an outbreak in Southwest Madrid, Spain

PubMed Central

Martcheva, Maia; Tuncer, Necibe; Fontana, Isabella; Carrillo, Eugenia; Moreno, Javier; Keesling, James

2017-01-01

Leishmaniasis is a vector-borne disease of worldwide distribution, currently present in 98 countries. Since late 2010, an unusual increase of human visceral and cutaneous leishmaniasis cases has been observed in the south-western Madrid region, totaling more than 600 cases until 2015. Some hosts, such as human, domestic dog and cat, rabbit (Oryctolagus cuniculus), and hare (Lepus granatensis), were found infected by the parasite of this disease in the area. Hares were described as the most important reservoir due to their higher prevalence, capacity to infect the vector, and presence of the same strains as in humans. Various measures were adopted to prevent and control the disease, and since 2013 there was a slight decline in the human sickness. We used a mathematical model to evaluate the efficacy of each measure in reducing the number of infected hosts. We identified in the present model that culling both hares and rabbits, without immediate reposition of the animals, was the best measure adopted, decreasing the proportion of all infected hosts. Particularly, culling hares was more efficacious than culling rabbits to reduce the proportion of infected individuals of all hosts. Likewise, lowering vector contact with hares highly influenced the reduction of the proportion of infected hosts. The reduction of the vector density per host in the park decreased the leishmaniasis incidence of hosts in the park and the urban areas. On the other hand, the reduction of the vector density per host of the urban area (humans, dogs and cats) decreased only their affected population, albeit at a higher proportion. The use of insecticide-impregnated collar and vaccination in dogs affected only the infected dogs’ population. The parameters related to the vector contact with dog, cat or human do not present a high impact on the other hosts infected by Leishmania. In conclusion, the efficacy of each control strategy was determined, in order to direct future actions in this and in other similar outbreaks. The present mathematical model was able to reproduce the leishmaniasis dynamics in the Madrid outbreak, providing theoretical support based on successful experiences, such as the reduction of human cases in Southwest Madrid, Spain. PMID:29028841

Efficacies of prevention and control measures applied during an outbreak in Southwest Madrid, Spain.

PubMed

Sevá, Anaiá da Paixão; Martcheva, Maia; Tuncer, Necibe; Fontana, Isabella; Carrillo, Eugenia; Moreno, Javier; Keesling, James

2017-01-01

Leishmaniasis is a vector-borne disease of worldwide distribution, currently present in 98 countries. Since late 2010, an unusual increase of human visceral and cutaneous leishmaniasis cases has been observed in the south-western Madrid region, totaling more than 600 cases until 2015. Some hosts, such as human, domestic dog and cat, rabbit (Oryctolagus cuniculus), and hare (Lepus granatensis), were found infected by the parasite of this disease in the area. Hares were described as the most important reservoir due to their higher prevalence, capacity to infect the vector, and presence of the same strains as in humans. Various measures were adopted to prevent and control the disease, and since 2013 there was a slight decline in the human sickness. We used a mathematical model to evaluate the efficacy of each measure in reducing the number of infected hosts. We identified in the present model that culling both hares and rabbits, without immediate reposition of the animals, was the best measure adopted, decreasing the proportion of all infected hosts. Particularly, culling hares was more efficacious than culling rabbits to reduce the proportion of infected individuals of all hosts. Likewise, lowering vector contact with hares highly influenced the reduction of the proportion of infected hosts. The reduction of the vector density per host in the park decreased the leishmaniasis incidence of hosts in the park and the urban areas. On the other hand, the reduction of the vector density per host of the urban area (humans, dogs and cats) decreased only their affected population, albeit at a higher proportion. The use of insecticide-impregnated collar and vaccination in dogs affected only the infected dogs' population. The parameters related to the vector contact with dog, cat or human do not present a high impact on the other hosts infected by Leishmania. In conclusion, the efficacy of each control strategy was determined, in order to direct future actions in this and in other similar outbreaks. The present mathematical model was able to reproduce the leishmaniasis dynamics in the Madrid outbreak, providing theoretical support based on successful experiences, such as the reduction of human cases in Southwest Madrid, Spain.

An Inexpensive Mechanical Model for Projectile Motion

ERIC Educational Resources Information Center

Kagan, David

2011-01-01

As experienced physicists, we see the beauty and simplicity of projectile motion. It is merely the superposition of uniform linear motion along the direction of the initial velocity vector and the downward motion due to the constant acceleration of gravity. We see the kinematic equations as just the mathematical machinery to perform the…

An asymptotical machine

NASA Astrophysics Data System (ADS)

Cristallini, Achille

2016-07-01

A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System.

PubMed

Liu, Ying-Pei; Liang, Hai-Ping; Gao, Zhong-Ke

2015-01-01

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane.

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System

PubMed Central

Gao, Zhong-Ke

2015-01-01

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane. PMID:26098556

Pseudo-Linear Attitude Determination of Spinning Spacecraft

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Harman, Richard R.

2004-01-01

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler s equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate. The performance of the two filters is examined using simulated data.

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2016-01-01

This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

Information modeling system for blast furnace control

NASA Astrophysics Data System (ADS)

Spirin, N. A.; Gileva, L. Y.; Lavrov, V. V.

2016-09-01

Modern Iron & Steel Works as a rule are equipped with powerful distributed control systems (DCS) and databases. Implementation of DSC system solves the problem of storage, control, protection, entry, editing and retrieving of information as well as generation of required reporting data. The most advanced and promising approach is to use decision support information technologies based on a complex of mathematical models. The model decision support system for control of blast furnace smelting is designed and operated. The basis of the model system is a complex of mathematical models created using the principle of natural mathematical modeling. This principle provides for construction of mathematical models of two levels. The first level model is a basic state model which makes it possible to assess the vector of system parameters using field data and blast furnace operation results. It is also used to calculate the adjustment (adaptation) coefficients of the predictive block of the system. The second-level model is a predictive model designed to assess the design parameters of the blast furnace process when there are changes in melting conditions relative to its current state. Tasks for which software is developed are described. Characteristics of the main subsystems of the blast furnace process as an object of modeling and control - thermal state of the furnace, blast, gas dynamic and slag conditions of blast furnace smelting - are presented.

Analysis of the sensitivity properties of a model of vector-borne bubonic plague.

PubMed

Buzby, Megan; Neckels, David; Antolin, Michael F; Estep, Donald

2008-09-06

Model sensitivity is a key to evaluation of mathematical models in ecology and evolution, especially in complex models with numerous parameters. In this paper, we use some recently developed methods for sensitivity analysis to study the parameter sensitivity of a model of vector-borne bubonic plague in a rodent population proposed by Keeling & Gilligan. The new sensitivity tools are based on a variational analysis involving the adjoint equation. The new approach provides a relatively inexpensive way to obtain derivative information about model output with respect to parameters. We use this approach to determine the sensitivity of a quantity of interest (the force of infection from rats and their fleas to humans) to various model parameters, determine a region over which linearization at a specific parameter reference point is valid, develop a global picture of the output surface, and search for maxima and minima in a given region in the parameter space.

Network-level reproduction number and extinction threshold for vector-borne diseases.

PubMed

Xue, Ling; Scoglio, Caterina

2015-06-01

The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

NASA Astrophysics Data System (ADS)

Byun, Do-Seong; Hart, Deirdre E.

2017-04-01

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world's coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical "boundaries" between 359° and 0° degrees (or 179° and 0°). In nature, such "boundaries" are in fact smooth transitions, but if these mathematical "boundaries" are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman's (1978) "northern semi-major axis convention" since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based "vector embodiment" solutions are employed.

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Teleoperator and robotics system analysis

NASA Technical Reports Server (NTRS)

Teoh, William

1987-01-01

The Orbital Maneuvering Vehicle (OMV) was designed to operate as a remotely controlled space teleoperator. The design and implementation of OMM (a mathematical model of the OMV) are discussed. The State Vector Transformation Module (SVX), an interface between the OMV simulation model and the mobile base (TOM-B) of the flat floor simulation system is described. A summary of testing procedures and conclusions are presented together with the test data obtained.

A realistic host-vector transmission model for describing malaria prevalence pattern.

PubMed

Mandal, Sandip; Sinha, Somdatta; Sarkar, Ram Rup

2013-12-01

Malaria continues to be a major public health concern all over the world even after effective control policies have been employed, and considerable understanding of the disease biology have been attained, from both the experimental and modelling perspective. Interactions between different general and local processes, such as dependence on age and immunity of the human host, variations of temperature and rainfall in tropical and sub-tropical areas, and continued presence of asymptomatic infections, regulate the host-vector interactions, and are responsible for the continuing disease prevalence pattern.In this paper, a general mathematical model of malaria transmission is developed considering short and long-term age-dependent immunity of human host and its interaction with pathogen-infected mosquito vector. The model is studied analytically and numerically to understand the role of different parameters related to mosquitoes and humans. To validate the model with a disease prevalence pattern in a particular region, real epidemiological data from the north-eastern part of India was used, and the effect of seasonal variation in mosquito density was modelled based on local climactic data. The model developed based on general features of host-vector interactions, and modified simply incorporating local environmental factors with minimal changes, can successfully explain the disease transmission process in the region. This provides a general approach toward modelling malaria that can be adapted to control future outbreaks of malaria.

Conceptualizing Vectors in College Geometry: A New Framework for Analysis of Student Approaches and Difficulties

ERIC Educational Resources Information Center

Kwon, Oh Hoon

2012-01-01

This dissertation documents a new way of conceptualizing vectors in college mathematics, especially in geometry. First, I will introduce three problems to show the complexity and subtlety of the construct of vectors with the classical vector representations. These highlight the need for a new framework that: (1) differentiates abstraction from a…

Challenging assumptions of notational transparency: the case of vectors in engineering mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2017-11-01

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing the components of a vector are discussed in historical and current context. Popular mathematical texts use the two notations as if they are transparent and interchangeable. In this research project, engineering students' proficiency at vector analysis was assessed and the data were analyzed using the Rasch measurement method. Results indicate that the students found items expressed in unit vector notation more difficult than those expressed in parenthesis notation. The expert experience of notation as transparent and unproblematically symbolic of underlying processes independent of notation is shown to contrast with the student experience where the less familiar notation is experienced as harder to work with.

A Feature Mining Based Approach for the Classification of Text Documents into Disjoint Classes.

ERIC Educational Resources Information Center

Nieto Sanchez, Salvador; Triantaphyllou, Evangelos; Kraft, Donald

2002-01-01

Proposes a new approach for classifying text documents into two disjoint classes. Highlights include a brief overview of document clustering; a data mining approach called the One Clause at a Time (OCAT) algorithm which is based on mathematical logic; vector space model (VSM); and comparing the OCAT to the VSM. (Author/LRW)

Predators indirectly control vector-borne disease: linking predator-prey and host-pathogen models.

PubMed

Moore, Sean M; Borer, Elizabeth T; Hosseini, Parviez R

2010-01-06

Pathogens transmitted by arthropod vectors are common in human populations, agricultural systems and natural communities. Transmission of these vector-borne pathogens depends on the population dynamics of the vector species as well as its interactions with other species within the community. In particular, predation may be sufficient to control pathogen prevalence indirectly via the vector. To examine the indirect effect of predators on vectored-pathogen dynamics, we developed a theoretical model that integrates predator-prey and host-pathogen theory. We used this model to determine whether predation can prevent pathogen persistence or alter the stability of host-pathogen dynamics. We found that, in the absence of predation, pathogen prevalence in the host increases with vector fecundity, whereas predation on the vector causes pathogen prevalence to decline, or even become extinct, with increasing vector fecundity. We also found that predation on a vector may drastically slow the initial spread of a pathogen. The predator can increase host abundance indirectly by reducing or eliminating infection in the host population. These results highlight the importance of studying interactions that, within the greater community, may alter our predictions when studying disease dynamics. From an applied perspective, these results also suggest situations where an introduced predator or the natural enemies of a vector may slow the rate of spread of an emerging vector-borne pathogen.

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty.

PubMed

Zhao, Jing-Xin; Su, Xiu-Yun; Xiao, Ruo-Xiu; Zhao, Zhe; Zhang, Li-Hai; Zhang, Li-Cheng; Tang, Pei-Fu

2016-11-01

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior-posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

A Critical Protection Level Derived from Dengue Infection Mathematical Model Considering Asymptomatic and Symptomatic Classes

NASA Astrophysics Data System (ADS)

Anggriani, N.; Supriatna, A. K.; Soewono, E.

2013-04-01

In this paper we formulate a model of dengue fever transmission by considering the presence of asymptomatic and symptomatic compartments. The model takes the form as a system of differential equations representing a host-vector SIR (Susceptible - Infective -Recovered) disease transmission. It is assumed that both host and vector populations are constant. It is also assumed that reinfection of recovered hosts by the disease is possible due to a wanning immunity in human body. We analyze the model to determine the qualitative behavior of the model solution and use the concept of effective basic reproduction number (fraktur Rp) as a control criteria of the disease transmission. The effect of mosquito biting protection (e.g. by using insect repellent) is also considered. We compute the long-term ratio of the asymptomatic and symptomatic classes and show a condition for which the iceberg phenomenon could appear.

A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors.

PubMed

Sawamura, Jitsuki; Morishita, Shigeru; Ishigooka, Jun

2016-02-09

Previously, we applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). To gain a more concrete comprehension, we here apply the concept of matrix representation, which was not explicitly exploited in our previous work. Starting with a set of orthonormal vectors, called the basis, an operator Rj (an N-tuple patient disease state at the j-th session) was expressed as a set of stratified vectors representing plural operations on individual components, so as to satisfy the group matrix representation. The stratified vectors containing individual unit operations were combined into one-dimensional square matrices [Rj]s. The [Rj]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of [Rj]s. The method is demonstrated on simple examples. Despite the incompleteness of our model, the group matrix representation of stratified vectors offers a formal mathematical approach to clinical medicine, aligning it with other branches of natural science.

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

ERIC Educational Resources Information Center

Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

Climate-driven mathematical models to understand the spatio-temporal heterogeneity of a chikungunya outbreak in the presence of widespread asymptomatic infection

NASA Astrophysics Data System (ADS)

Dommar, Carlos J.; Robinson, Marguerite; Lowe, Rachel; Conan, Anne; Buchy, Philippe; Tarantola, Arnaud; Rodó, Xavier

2014-05-01

The emergence and persistence of human pathogens in the environment represents a constant threat to society, with global implications for human health, economies and ecosystems. Of particular concern are vector-borne diseases, such as dengue, malaria and chikungunya, which are increasing across their traditional ranges and continuing to infiltrate new regions. This unprecedented situation has been partly attributed to the increase in global temperatures in recent decades which has allowed non-native mosquito species to invade and successfully colonise previously inhospitable environments. The spatio-temporal evolution of these diseases is determined by the interaction of the host and vector, which is strongly dependent on social structures and mobility patterns. In turn, vector populations are thought to be driven by external environmental variables, such as precipitation and temperature. Furthermore, the ability of asymptomatic individuals to successfully transmit the infection and evade control measures can undermine public health interventions. We employed a stochastic model, which explicitly included asymptomatic and undocumented laboratory confirmed cases, and applied it to a documented outbreak in Cambodia in 2012 (Trapeang Roka village, Kampong Speu Province). The resulting estimate of the reproduction number was considerably higher than values obtained for previous outbreaks and highlights the importance of asymptomatic transmission. Subsequently, we develop an agent-based model (ABM), in which each individual is explicitly represented and vector populations are linked to precipitation estimates in a tropical setting. The model is implemented on both scale-free and regular networks. The spatio-temporal transmission of chikungunya is analysed and the presence of asymptomatic silent spreaders within the population is investigated in the context of implementing travel restrictions during an outbreak. Preventing the movement of symptomatic individuals alone is found to be an insufficient mechanism to halt the spread of the disease, which can be readily carried to neighbouring nodes via sub-clinical individuals. Furthermore, the impact of topology structure versus precipitation levels is assessed and precipitation is found to be the dominant factor driving spatio-temporal transmission. Our results highlight the urgent need to establish adequate monitoring and mosquito control programs in vulnerable countries. These models can help to inform public health officials on both the impact and potential spatial expansion of vector-borne diseases through both urban and rural regions under the influence of dynamic climatic conditions. Given the climate sensitivity of vector-borne diseases, such as chikungunya, it is important to link the monitoring of meteorological conditions to public health surveillance and control.

Hermann-Bernoulli-Laplace-Hamilton-Runge-Lenz Vector.

ERIC Educational Resources Information Center

Subramanian, P. R.; And Others

1991-01-01

A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector.

PubMed

Sardar, Tridip; Rana, Sourav; Bhattacharya, Sabyasachi; Al-Khaled, Kamel; Chattopadhyay, Joydev

2015-05-01

In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector. Copyright © 2015 Elsevier Inc. All rights reserved.

Fundamentals of continuum mechanics – classical approaches and new trends

NASA Astrophysics Data System (ADS)

Altenbach, H.

2018-04-01

Continuum mechanics is a branch of mechanics that deals with the analysis of the mechanical behavior of materials modeled as a continuous manifold. Continuum mechanics models begin mostly by introducing of three-dimensional Euclidean space. The points within this region are defined as material points with prescribed properties. Each material point is characterized by a position vector which is continuous in time. Thus, the body changes in a way which is realistic, globally invertible at all times and orientation-preserving, so that the body cannot intersect itself and as transformations which produce mirror reflections are not possible in nature. For the mathematical formulation of the model it is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated. Finally, the kinematical relations, the balance equations, the constitutive and evolution equations and the boundary and/or initial conditions should be defined. If the physical fields are non-smooth jump conditions must be taken into account. The basic equations of continuum mechanics are presented following a short introduction. Additionally, some examples of solid deformable continua will be discussed within the presentation. Finally, advanced models of continuum mechanics will be introduced. The paper is dedicated to Alexander Manzhirov’s 60th birthday.

A computational model for reference-frame synthesis with applications to motion perception.

PubMed

Clarke, Aaron M; Öğmen, Haluk; Herzog, Michael H

2016-09-01

As discovered by the Gestaltists, in particular by Duncker, we often perceive motion to be within a non-retinotopic reference frame. For example, the motion of a reflector on a bicycle appears to be circular, whereas, it traces out a cycloidal path with respect to external world coordinates. The reflector motion appears to be circular because the human brain subtracts the horizontal motion of the bicycle from the reflector motion. The bicycle serves as a reference frame for the reflector motion. Here, we present a general mathematical framework, based on vector fields, to explain non-retinotopic motion processing. Using four types of non-retinotopic motion paradigms, we show how the theory works in detail. For example, we show how non-retinotopic motion in the Ternus-Pikler display can be computed. Copyright © 2015 Elsevier Ltd. All rights reserved.

Spacecraft attitude determination using the earth's magnetic field

NASA Technical Reports Server (NTRS)

Simpson, David G.

1989-01-01

A method is presented by which the attitude of a low-Earth orbiting spacecraft may be determined using a vector magnetometer, a digital Sun sensor, and a mathematical model of the Earth's magnetic field. The method is currently being implemented for the Solar Maximum Mission spacecraft (as a backup for the failing star trackers) as a way to determine roll gyro drift.

Cross-Service Investigation of Geographical Information Systems

DTIC Science & Technology

2004-03-01

Figure 8 illustrates the combined layers. Information for the layers is stored in a database format. The two types of storage are vector and...raster models. In a vector model, the image and information are stored as geometric objects such as points, lines, or polygons. In a raster model...DNCs are a vector -based digital database with selected maritime significant physical features from hydrographic charts. Layers within the DNC are data

Preventing Superinfection in Malaria Spreads with Repellent and Medical Treatment Policy

NASA Astrophysics Data System (ADS)

Fitri, Fanny; Aldila, Dipo

2018-03-01

Malaria is a kind of a vector-borne disease. That means this disease needs a vector (in this case, the anopheles mosquito) to spread. In this article, a mathematical model for malaria disease spread will be discussed. The model is constructed as a seven-dimensional of a non-linear ordinary differential equation. The interventions of treatment for infected humans and use of repellent are included in the model to see how these interventions could be considered as alternative ways to control the spread of malaria. Analysis will be made of the disease-free equilibrium point along with its local stability criteria, construction of the next generation matrix which followed with the sensitivity analysis of basic reproduction number. We found that both medical treatment and repellent intervention succeeded in reducing the basic reproduction number as the endemic indicator of the model. Finally, some numerical simulations are given to give a better interpretation of the analytical results.

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

ERIC Educational Resources Information Center

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals.

PubMed

Soto-Quiros, Pablo

2015-01-01

This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

Combinatorial vector fields and the valley structure of fitness landscapes.

PubMed

Stadler, Bärbel M R; Stadler, Peter F

2010-12-01

Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.

Mathematical Modeling of Herpes Simplex Virus Distribution in Solid Tumors: Implications for Cancer Gene Therapy

PubMed Central

Mok, Wilson; Stylianopoulos, Triantafyllos; Boucher, Yves; Jain, Rakesh K.

2010-01-01

Purpose Although oncolytic viral vectors show promise for the treatment of various cancers, ineffective initial distribution and propagation throughout the tumor mass often limit the therapeutic response. A mathematical model is developed to describe the spread of herpes simplex virus from the initial injection site. Experimental Design The tumor is modeled as a sphere of radius R. The model incorporates reversible binding, interstitial diffusion, viral degradation, and internalization and physiologic parameters. Three species are considered as follows: free interstitial virus, virus bound to cell surfaces, and internalized virus. Results This analysis reveals that both rapid binding and internalization as well as hindered diffusion contain the virus to the initial injection volume, with negligible spread to the surrounding tissue. Unfortunately, increasing the dose to saturate receptors and promote diffusion throughout the tumor is not a viable option: the concentration necessary would likely compromise safety. However, targeted modifications to the virus that decrease the binding affinity have the potential to increase the number of infected cells by 1.5-fold or more. An increase in the effective diffusion coefficient can result in similar gains. Conclusions This analysis suggests criteria by which the potential response of a tumor to oncolytic herpes simplex virus therapy can be assessed. Furthermore, it reveals the potential of modifications to the vector delivery method, physicochemical properties of the virus, and tumor extracellular matrix composition to enhance efficacy. PMID:19318482

Vectors in Use in a 3D Juggling Game Simulation

ERIC Educational Resources Information Center

Kynigos, Chronis; Latsi, Maria

2006-01-01

The new representations enabled by the educational computer game the "Juggler" can place vectors in a central role both for controlling and measuring the behaviours of objects in a virtual environment simulating motion in three-dimensional spaces. The mathematical meanings constructed by 13 year-old students in relation to vectors as…

Universal Parameter Measurement and Sensorless Vector Control of Induction and Permanent Magnet Synchronous Motors

NASA Astrophysics Data System (ADS)

Yamamoto, Shu; Ara, Takahiro

Recently, induction motors (IMs) and permanent-magnet synchronous motors (PMSMs) have been used in various industrial drive systems. The features of the hardware device used for controlling the adjustable-speed drive in these motors are almost identical. Despite this, different techniques are generally used for parameter measurement and speed-sensorless control of these motors. If the same technique can be used for parameter measurement and sensorless control, a highly versatile adjustable-speed-drive system can be realized. In this paper, the authors describe a new universal sensorless control technique for both IMs and PMSMs (including salient pole and nonsalient pole machines). A mathematical model applicable for IMs and PMSMs is discussed. Using this model, the authors derive the proposed universal sensorless vector control algorithm on the basis of estimation of the stator flux linkage vector. All the electrical motor parameters are determined by a unified test procedure. The proposed method is implemented on three test machines. The actual driving test results demonstrate the validity of the proposed method.

Assessing semantic similarity of texts - Methods and algorithms

NASA Astrophysics Data System (ADS)

Rozeva, Anna; Zerkova, Silvia

2017-12-01

Assessing the semantic similarity of texts is an important part of different text-related applications like educational systems, information retrieval, text summarization, etc. This task is performed by sophisticated analysis, which implements text-mining techniques. Text mining involves several pre-processing steps, which provide for obtaining structured representative model of the documents in a corpus by means of extracting and selecting the features, characterizing their content. Generally the model is vector-based and enables further analysis with knowledge discovery approaches. Algorithms and measures are used for assessing texts at syntactical and semantic level. An important text-mining method and similarity measure is latent semantic analysis (LSA). It provides for reducing the dimensionality of the document vector space and better capturing the text semantics. The mathematical background of LSA for deriving the meaning of the words in a given text by exploring their co-occurrence is examined. The algorithm for obtaining the vector representation of words and their corresponding latent concepts in a reduced multidimensional space as well as similarity calculation are presented.

Distributed collaborative probabilistic design for turbine blade-tip radial running clearance using support vector machine of regression

NASA Astrophysics Data System (ADS)

Fei, Cheng-Wei; Bai, Guang-Chen

2014-12-01

To improve the computational precision and efficiency of probabilistic design for mechanical dynamic assembly like the blade-tip radial running clearance (BTRRC) of gas turbine, a distribution collaborative probabilistic design method-based support vector machine of regression (SR)(called as DCSRM) is proposed by integrating distribution collaborative response surface method and support vector machine regression model. The mathematical model of DCSRM is established and the probabilistic design idea of DCSRM is introduced. The dynamic assembly probabilistic design of aeroengine high-pressure turbine (HPT) BTRRC is accomplished to verify the proposed DCSRM. The analysis results reveal that the optimal static blade-tip clearance of HPT is gained for designing BTRRC, and improving the performance and reliability of aeroengine. The comparison of methods shows that the DCSRM has high computational accuracy and high computational efficiency in BTRRC probabilistic analysis. The present research offers an effective way for the reliability design of mechanical dynamic assembly and enriches mechanical reliability theory and method.

Virtual world reconstruction using the modeling and simulation extended vector product prototype

DOT National Transportation Integrated Search

1997-05-30

The MS Extended Vector Product (MSEVP) prototype being developed is an extended vector product format-based product containing a continuous surface representation and a consistent view of elevation across the thematic coverages contained within a dat...

Design of a universal two-layered neural network derived from the PLI theory

NASA Astrophysics Data System (ADS)

Hu, Chia-Lun J.

2004-05-01

The if-and-only-if (IFF) condition that a set of M analog-to-digital vector-mapping relations can be learned by a one-layered-feed-forward neural network (OLNN) is that all the input analog vectors dichotomized by the i-th output bit must be positively, linearly independent, or PLI. If they are not PLI, then the OLNN just cannot learn no matter what learning rules is employed because the solution of the connection matrix does not exist mathematically. However, in this case, one can still design a parallel-cascaded, two-layered, perceptron (PCTLP) to acheive this general mapping goal. The design principle of this "universal" neural network is derived from the major mathematical properties of the PLI theory - changing the output bits of the dependent relations existing among the dichotomized input vectors to make the PLD relations PLI. Then with a vector concatenation technique, the required mapping can still be learned by this PCTLP system with very high efficiency. This paper will report in detail the mathematical derivation of the general design principle and the design procedures of the PCTLP neural network system. It then will be verified in general by a practical numerical example.

Antipathogen genes and the replacement of disease-vectoring mosquito populations: a model-based evaluation

PubMed Central

Robert, Michael A; Okamoto, Kenichi W; Gould, Fred; Lloyd, Alun L

2014-01-01

Recently, genetic strategies aimed at controlling populations of disease-vectoring mosquitoes have received considerable attention as alternatives to traditional measures. Theoretical studies have shown that female-killing (FK), antipathogen (AP), and reduce and replace (R&R) strategies can each decrease the number competent vectors. In this study, we utilize a mathematical model to evaluate impacts on competent Aedes aegypti populations of FK, AP, and R&R releases as well as hybrid strategies that result from combinations of these three approaches. We show that while the ordering of efficacy of these strategies depends upon population life history parameters, sex ratio of releases, and switch time in combination strategies, AP-only and R&R/AP releases typically lead to the greatest long-term reduction in competent vectors. R&R-only releases are often less effective at long-term reduction of competent vectors than AP-only releases or R&R/AP releases. Furthermore, the reduction in competent vectors caused by AP-only releases is easier to maintain than that caused by FK-only or R&R-only releases even when the AP gene confers a fitness cost. We discuss the roles that density dependence and inclusion of females play in the order of efficacy of the strategies. We anticipate that our results will provide added impetus to continue developing AP strategies. PMID:25558284

Evaluating the promise of recombinant transmissible vaccines

PubMed Central

Basinski, Andrew J.; Varrelman, Tanner J.; Smithson, Mark W.; May, Ryan H.; Remien, Christopher H.; Nuismer, Scott L.

2018-01-01

Transmissible vaccines have the potential to revolutionize infectious disease control by reducing the vaccination effort required to protect a population against a disease. Recent efforts to develop transmissible vaccines focus on recombinant transmissible vaccine designs (RTVs) because they pose reduced risk if intra-host evolution causes the vaccine to revert to its vector form. However, the shared antigenicity of the vaccine and vector may confer vaccine-immunity to hosts infected with the vector, thwarting the ability of the vaccine to spread through the population. We build a mathematical model to test whether a RTV can facilitate disease management in instances where reversion is likely to introduce the vector into the population or when the vector organism is already established in the host population, and the vector and vaccine share perfect cross-immunity. Our results show that a RTV can autonomously eradicate a pathogen, or protect a population from pathogen invasion, when cross-immunity between vaccine and vector is absent. If cross-immunity between vaccine and vector exists, however, our results show that a RTV can substantially reduce the vaccination effort necessary to control or eradicate a pathogen only when continuously augmented with direct manual vaccination. These results demonstrate that estimating the extent of cross-immunity between vector and vaccine is a critical step in RTV design, and that herpesvirus vectors showing facile reinfection and weak cross-immunity are promising. PMID:29279283

Behaviour of mathematics and physics students in solving problem of Vector-Physics context

NASA Astrophysics Data System (ADS)

Sardi; Rizal, M.; Mansyur, J.

2018-04-01

This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.

Jupiter Environment Tool

NASA Technical Reports Server (NTRS)

Sturm, Erick J.; Monahue, Kenneth M.; Biehl, James P.; Kokorowski, Michael; Ngalande, Cedrick,; Boedeker, Jordan

2012-01-01

The Jupiter Environment Tool (JET) is a custom UI plug-in for STK that provides an interface to Jupiter environment models for visualization and analysis. Users can visualize the different magnetic field models of Jupiter through various rendering methods, which are fully integrated within STK s 3D Window. This allows users to take snapshots and make animations of their scenarios with magnetic field visualizations. Analytical data can be accessed in the form of custom vectors. Given these custom vectors, users have access to magnetic field data in custom reports, graphs, access constraints, coverage analysis, and anywhere else vectors are used within STK.

From Heuristic to Mathematical Modeling of Drugs Dissolution Profiles: Application of Artificial Neural Networks and Genetic Programming

PubMed Central

Mendyk, Aleksander; Güres, Sinan; Szlęk, Jakub; Wiśniowska, Barbara; Kleinebudde, Peter

2015-01-01

The purpose of this work was to develop a mathematical model of the drug dissolution (Q) from the solid lipid extrudates based on the empirical approach. Artificial neural networks (ANNs) and genetic programming (GP) tools were used. Sensitivity analysis of ANNs provided reduction of the original input vector. GP allowed creation of the mathematical equation in two major approaches: (1) direct modeling of Q versus extrudate diameter (d) and the time variable (t) and (2) indirect modeling through Weibull equation. ANNs provided also information about minimum achievable generalization error and the way to enhance the original dataset used for adjustment of the equations' parameters. Two inputs were found important for the drug dissolution: d and t. The extrudates length (L) was found not important. Both GP modeling approaches allowed creation of relatively simple equations with their predictive performance comparable to the ANNs (root mean squared error (RMSE) from 2.19 to 2.33). The direct mode of GP modeling of Q versus d and t resulted in the most robust model. The idea of how to combine ANNs and GP in order to escape ANNs' black-box drawback without losing their superior predictive performance was demonstrated. Open Source software was used to deliver the state-of-the-art models and modeling strategies. PMID:26101544

From Heuristic to Mathematical Modeling of Drugs Dissolution Profiles: Application of Artificial Neural Networks and Genetic Programming.

PubMed

Mendyk, Aleksander; Güres, Sinan; Jachowicz, Renata; Szlęk, Jakub; Polak, Sebastian; Wiśniowska, Barbara; Kleinebudde, Peter

2015-01-01

The purpose of this work was to develop a mathematical model of the drug dissolution (Q) from the solid lipid extrudates based on the empirical approach. Artificial neural networks (ANNs) and genetic programming (GP) tools were used. Sensitivity analysis of ANNs provided reduction of the original input vector. GP allowed creation of the mathematical equation in two major approaches: (1) direct modeling of Q versus extrudate diameter (d) and the time variable (t) and (2) indirect modeling through Weibull equation. ANNs provided also information about minimum achievable generalization error and the way to enhance the original dataset used for adjustment of the equations' parameters. Two inputs were found important for the drug dissolution: d and t. The extrudates length (L) was found not important. Both GP modeling approaches allowed creation of relatively simple equations with their predictive performance comparable to the ANNs (root mean squared error (RMSE) from 2.19 to 2.33). The direct mode of GP modeling of Q versus d and t resulted in the most robust model. The idea of how to combine ANNs and GP in order to escape ANNs' black-box drawback without losing their superior predictive performance was demonstrated. Open Source software was used to deliver the state-of-the-art models and modeling strategies.

Fundamental Principles of Classical Mechanics: a Geometrical Perspectives

NASA Astrophysics Data System (ADS)

Lam, Kai S.

2014-07-01

Classical mechanics is the quantitative study of the laws of motion for oscopic physical systems with mass. The fundamental laws of this subject, known as Newton's Laws of Motion, are expressed in terms of second-order differential equations governing the time evolution of vectors in a so-called configuration space of a system (see Chapter 12). In an elementary setting, these are usually vectors in 3-dimensional Euclidean space, such as position vectors of point particles; but typically they can be vectors in higher dimensional and more abstract spaces. A general knowledge of the mathematical properties of vectors, not only in their most intuitive incarnations as directed arrows in physical space but as elements of abstract linear vector spaces, and those of linear operators (transformations) on vector spaces as well, is then indispensable in laying the groundwork for both the physical and the more advanced mathematical - more precisely topological and geometrical - concepts that will prove to be vital in our subject. In this beginning chapter we will review these properties, and introduce the all-important related notions of dual spaces and tensor products of vector spaces. The notational convention for vectorial and tensorial indices used for the rest of this book (except when otherwise specified) will also be established...

An Institutional Approach to University Mathematics Education: From Dual Vector Spaces to Questioning the World

ERIC Educational Resources Information Center

Winsløw, Carl; Barquero, Berta; De Vleeschouwer, Martine; Hardy, Nadia

2014-01-01

University mathematics education (UME) is considered, in this paper, as a kind of "didactic practice"--characterised by institutional settings and by the purpose of inducting students into "mathematical practices." We present a research programme -- the anthropological theory of the didactic (ATD)--in which this rough…

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

PubMed

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

2016-03-31

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

A Hybrid Neuro-Fuzzy Model For Integrating Large Earth-Science Datasets

NASA Astrophysics Data System (ADS)

Porwal, A.; Carranza, J.; Hale, M.

2004-12-01

A GIS-based hybrid neuro-fuzzy approach to integration of large earth-science datasets for mineral prospectivity mapping is described. It implements a Takagi-Sugeno type fuzzy inference system in the framework of a four-layered feed-forward adaptive neural network. Each unique combination of the datasets is considered a feature vector whose components are derived by knowledge-based ordinal encoding of the constituent datasets. A subset of feature vectors with a known output target vector (i.e., unique conditions known to be associated with either a mineralized or a barren location) is used for the training of an adaptive neuro-fuzzy inference system. Training involves iterative adjustment of parameters of the adaptive neuro-fuzzy inference system using a hybrid learning procedure for mapping each training vector to its output target vector with minimum sum of squared error. The trained adaptive neuro-fuzzy inference system is used to process all feature vectors. The output for each feature vector is a value that indicates the extent to which a feature vector belongs to the mineralized class or the barren class. These values are used to generate a prospectivity map. The procedure is demonstrated by an application to regional-scale base metal prospectivity mapping in a study area located in the Aravalli metallogenic province (western India). A comparison of the hybrid neuro-fuzzy approach with pure knowledge-driven fuzzy and pure data-driven neural network approaches indicates that the former offers a superior method for integrating large earth-science datasets for predictive spatial mathematical modelling.

Finding exact constants in a Markov model of Zipfs law generation

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

2017-12-01

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

Mathematical model of the seismic electromagnetic signals (SEMS) in non crystalline substances

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

Dennis, L. C. C.; Yahya, N.; Daud, H.

The mathematical model of seismic electromagnetic waves in non crystalline substances is developed and the solutions are discussed to show the possibility of improving the electromagnetic waves especially the electric field. The shear stress of the medium in fourth order tensor gives the equation of motion. Analytic methods are selected for the solutions written in Hansen vector form. From the simulated SEMS, the frequency of seismic waves has significant effects to the SEMS propagating characteristics. EM waves transform into SEMS or energized seismic waves. Traveling distance increases once the frequency of the seismic waves increases from 100% to 1000%. SEMSmore » with greater seismic frequency will give seismic alike waves but greater energy is embedded by EM waves and hence further distance the waves travel.« less

Fourier transform inequalities for phylogenetic trees.

PubMed

Matsen, Frederick A

2009-01-01

Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.

Deorbit targeting

NASA Technical Reports Server (NTRS)

Tempelman, W. H.

1973-01-01

The navigation and control of the space shuttle during atmospheric entry are discussed. A functional flow diagram presenting the basic approach to the deorbit targeting problem is presented. The major inputs to be considered are: (1) vehicle state vector, (2) landing site location, (3) entry interface parameters, (4) earliest desired time of landing, and (5) maximum cross range. Mathematical models of the navigational procedures based on controlled thrust times are developed.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

The Curl of a Vector Field: Beyond the Formula

ERIC Educational Resources Information Center

Burch, Kimberly Jordan; Choi, Youngna

2006-01-01

It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical…

Equivalent Vectors

ERIC Educational Resources Information Center

Levine, Robert

2004-01-01

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…

A border-ownership model based on computational electromagnetism.

PubMed

Zainal, Zaem Arif; Satoh, Shunji

2018-03-01

The mathematical relation between a vector electric field and its corresponding scalar potential field is useful to formulate computational problems of lower/middle-order visual processing, specifically related to the assignment of borders to the side of the object: so-called border ownership (BO). BO coding is a key process for extracting the objects from the background, allowing one to organize a cluttered scene. We propose that the problem is solvable simultaneously by application of a theorem of electromagnetism, i.e., "conservative vector fields have zero rotation, or "curl." We hypothesize that (i) the BO signal is definable as a vector electric field with arrowheads pointing to the inner side of perceived objects, and (ii) its corresponding scalar field carries information related to perceived order in depth of occluding/occluded objects. A simple model was developed based on this computational theory. Model results qualitatively agree with object-side selectivity of BO-coding neurons, and with perceptions of object order. The model update rule can be reproduced as a plausible neural network that presents new interpretations of existing physiological results. Results of this study also suggest that T-junction detectors are unnecessary to calculate depth order. Copyright © 2017 Elsevier Ltd. All rights reserved.

Performance of a Bounce-Averaged Global Model of Super-Thermal Electron Transport in the Earth's Magnetic Field

NASA Technical Reports Server (NTRS)

McGuire, Tim

1998-01-01

In this paper, we report the results of our recent research on the application of a multiprocessor Cray T916 supercomputer in modeling super-thermal electron transport in the earth's magnetic field. In general, this mathematical model requires numerical solution of a system of partial differential equations. The code we use for this model is moderately vectorized. By using Amdahl's Law for vector processors, it can be verified that the code is about 60% vectorized on a Cray computer. Speedup factors on the order of 2.5 were obtained compared to the unvectorized code. In the following sections, we discuss the methodology of improving the code. In addition to our goal of optimizing the code for solution on the Cray computer, we had the goal of scalability in mind. Scalability combines the concepts of portabilty with near-linear speedup. Specifically, a scalable program is one whose performance is portable across many different architectures with differing numbers of processors for many different problem sizes. Though we have access to a Cray at this time, the goal was to also have code which would run well on a variety of architectures.

Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.

PubMed

Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark

2018-06-01

Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2018 Elsevier Ltd. All rights reserved.

Particle tracking velocimetry in three-dimensional flows

NASA Astrophysics Data System (ADS)

Maas, H. G.; Gruen, A.; Papantoniou, D.

1993-07-01

Particle Tracking Velocimetry (PTV) is a well-known technique for the determination of velocity vectors within an observation volume. However, for a long time it has rarely been applied because of the intensive effort necessary to measure coordinates of a large number of flow marker particles in many images. With today's imaging hardware in combination with the methods of digital image processing and digital photogrammetry, however, new possibilities have arisen for the design of completely automatic PTV systems. A powerful 3 D PTV has been developed in a cooperation of the Institute of Geodesy and Photogrammetry with the Institute of Hydromechanics and Water Resources Management at the Swiss Federal Institute of Technology. In this paper hardware components for 3 D PTV systems wil be discussed, and a strict mathematical model of photogrammetric 3 D coordinate determination, taking into account the different refractive indices in the optical path, will be presented. The system described is capable of determining coordinate sets of some 1000 particles in a flow field at a time resolution of 25 datasets per second and almost arbitrary sequence length completely automatically after an initialization by an operator. The strict mathematical modelling of the measurement geometry, together with a thorough calibration of the system provide for a coordinate accuracy of typically 0.06 mm in X, Y and 0.18 mm in Z (depth coordinate) in a volume of 200 × 160 × 50 mm3.

Mathematical model of biological order state or syndrome in traditional Chinese medicine: based on electromagnetic radiation within the human body.

PubMed

Han, Jinxiang; Huang, Jinzhao

2012-03-01

In this study, based on the resonator model and exciplex model of electromagnetic radiation within the human body, mathematical model of biological order state, also referred to as syndrome in traditional Chinese medicine, was established and expressed as: "Sy = v/ 1n(6I + 1)". This model provides the theoretical foundation for experimental research addressing the order state of living system, especially the quantitative research syndrome in traditional Chinese medicine.

A Novel Statistical Analysis and Interpretation of Flow Cytometry Data

DTIC Science & Technology

2013-03-31

the resulting residuals appear random. In the work that follows, I∗ = 200. The values of B and b̂j are known from the experiment. Notice that the...conjunction with the model parameter vector in a two- stage process. Unfortunately two- stage estimation may cause some parameters of the mathematical model to...information theoretic criteria such as Akaike’s Information Criterion (AIC). From (4.3), it follows that the scaled residuals rjk = λjI[n̂](tj , zk; ~q

Implementation of Gravity Model to Estimation of Transportation Market Shares

NASA Astrophysics Data System (ADS)

Krata, Przemysław

2010-03-01

The theoretical consideration presented in the paper is inspired by market gravity models, as an interesting attitude towards operations research on a market. The transportation market issues are emphasized. The mathematical model of relations, taking place between transportation companies and their customers on the market, which is applied in the course of the research is based on continuous functions characteristics. This attitude enables the use of the field theory notions. The resultant vector-type utility function facilitates obtaining of competitive advantage areas for all transportation companies located on the considered transportation market.

A Hierarchical Network Approach for Modeling Rift Valley Fever Epidemics with Applications in North America

PubMed Central

Xue, Ling; Cohnstaedt, Lee W.; Scott, H. Morgan; Scoglio, Caterina

2013-01-01

Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an important ranching area in the United States of America. The nodes of the networks represent livestock farms, livestock markets, and feedlots, and the links represent cattle movements and mosquito diffusion between different nodes. Cattle and mosquito (Aedes and Culex) populations are treated with different contact networks to assess virus propagation. Rift Valley fever virus spread is assessed under various initial infection conditions (infected mosquito eggs, adults or cattle). A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak. The delay is likely caused by a lack of herd immunity while the infection expands geographically before becoming an epidemic involving many dispersed farms and animals almost simultaneously. Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread. PMID:23667453

A hierarchical network approach for modeling Rift Valley fever epidemics with applications in North America.

PubMed

Xue, Ling; Cohnstaedt, Lee W; Scott, H Morgan; Scoglio, Caterina

2013-01-01

Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an important ranching area in the United States of America. The nodes of the networks represent livestock farms, livestock markets, and feedlots, and the links represent cattle movements and mosquito diffusion between different nodes. Cattle and mosquito (Aedes and Culex) populations are treated with different contact networks to assess virus propagation. Rift Valley fever virus spread is assessed under various initial infection conditions (infected mosquito eggs, adults or cattle). A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak. The delay is likely caused by a lack of herd immunity while the infection expands geographically before becoming an epidemic involving many dispersed farms and animals almost simultaneously. Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread.

Population biology of human onchocerciasis.

PubMed Central

Basáñez, M G; Boussinesq, M

1999-01-01

Human onchocerciasis (river blindness) is the filarial infection caused by Onchocerca volvulus and transmitted among people through the bites of the Simulium vector. Some 86 million people around the world are at risk of acquiring the nematode, with 18 million people infected and 600,000 visually impaired, half of them partially or totally blind. 99% of cases occur in tropical Africa; scattered foci exist in Latin America. Until recently control programmes, in operation since 1975, have consisted of antivectorial measures. With the introduction of ivermectin in 1988, safe and effective chemotherapy is now available. With the original Onchocerciasis Control Programme of West Africa coming to an end, both the new African Programme for Onchocerciasis Control and the Onchocerciasis Elimination Programme for the Americas, rely heavily on ivermectin self-sustained mass delivery. In consequence, the need for understanding the processes regulating parasite abundance in human and simuliid populations is of utmost importance. We present a simple mathematical framework built around recent analyses of exposure- and density-dependent processes operating, respectively, within the human and vector hosts. An expression for the basic reproductive ratio, R0, is derived and related to the minimum vector density required for parasite persistence in localities of West Africa in general and northern Cameroon in particular. Model outputs suggest that constraints acting against parasite establishment in both humans and vectors are necessary to reproduce field observations, but those in humans may not fully protect against reinfection. Analyses of host age-profiles of infection prevalence, intensity, and aggregation for increasing levels of endemicity and intensity of transmission in the Vina valley of northern Cameroon are in agreement with these results and discussed in light of novel work on onchocerciasis immunology. PMID:10365406

Research on the application of a decoupling algorithm for structure analysis

NASA Technical Reports Server (NTRS)

Denman, E. D.

1980-01-01

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent vectors as a subset. The spectral decomposition of a matrix and the application to differential equations is given.

Global differential geometry: An introduction for control engineers

NASA Technical Reports Server (NTRS)

Doolin, B. F.; Martin, C. F.

1982-01-01

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Biomedical Mathematics, Unit I: Measurement, Linear Functions and Dimensional Algebra. Student Text. Revised Version, 1975.

ERIC Educational Resources Information Center

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…

Quantum Bohmian model for financial market

NASA Astrophysics Data System (ADS)

Choustova, Olga Al.

2007-01-01

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

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

Fighting Cancer with Mathematics and Viruses.

PubMed

Santiago, Daniel N; Heidbuechel, Johannes P W; Kandell, Wendy M; Walker, Rachel; Djeu, Julie; Engeland, Christine E; Abate-Daga, Daniel; Enderling, Heiko

2017-08-23

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.

Fighting Cancer with Mathematics and Viruses

PubMed Central

Santiago, Daniel N.; Heidbuechel, Johannes P. W.; Kandell, Wendy M.; Walker, Rachel; Djeu, Julie; Abate-Daga, Daniel; Enderling, Heiko

2017-01-01

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments. PMID:28832539

Equivalent model of a dually-fed machine for electric drive control systems

NASA Astrophysics Data System (ADS)

Ostrovlyanchik, I. Yu; Popolzin, I. Yu

2018-05-01

The article shows that the mathematical model of a dually-fed machine is complicated because of the presence of a controlled voltage source in the rotor circuit. As a method of obtaining a mathematical model, the method of a generalized two-phase electric machine is applied and a rotating orthogonal coordinate system is chosen that is associated with the representing vector of a stator current. In the chosen coordinate system in the operator form the differential equations of electric equilibrium for the windings of the generalized machine (the Kirchhoff equation) are written together with the expression for the moment, which determines the electromechanical energy transformation in the machine. Equations are transformed so that they connect the currents of the windings, that determine the moment of the machine, and the voltages on these windings. The structural diagram of the machine is assigned to the written equations. Based on the written equations and accepted assumptions, expressions were obtained for the balancing the EMF of windings, and on the basis of these expressions an equivalent mathematical model of a dually-fed machine is proposed, convenient for use in electric drive control systems.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Analysis of the precision parameters of an optoelectronic vector-matrix processor of digital information

NASA Astrophysics Data System (ADS)

Odinokov, S. B.; Petrov, A. V.

1995-10-01

Mathematical models of components of a vector-matrix optoelectronic multiplier are considered. Perturbing factors influencing a real optoelectronic system — noise and errors of radiation sources and detectors, nonlinearity of an analogue—digital converter, nonideal optical systems — are taken into account. Analytic expressions are obtained for relating the precision of such a multiplier to the probability of an error amounting to one bit, to the parameters describing the quality of the multiplier components, and to the quality of the optical system of the processor. Various methods of increasing the dynamic range of a multiplier are considered at the technical systems level.

A vectorized algorithm for 3D dynamics of a tethered satellite

NASA Technical Reports Server (NTRS)

Wilson, Howard B.

1989-01-01

Equations of motion characterizing the three dimensional motion of a tethered satellite during the retrieval phase are studied. The mathematical model involves an arbitrary number of point masses connected by weightless cords. Motion occurs in a gravity gradient field. The formulation presented accounts for general functions describing support point motion, rate of tether retrieval, and arbitrary forces applied to the point masses. The matrix oriented program language MATLAB is used to produce an efficient vectorized formulation for computing natural frequencies and mode shapes for small oscillations about the static equilibrium configuration; and for integrating the nonlinear differential equations governing large amplitude motions. An example of time response pertaining to the skip rope effect is investigated.

Effective learning strategies for real-time image-guided adaptive control of multiple-source hyperthermia applicators.

PubMed

Cheng, Kung-Shan; Dewhirst, Mark W; Stauffer, Paul R; Das, Shiva

2010-03-01

This paper investigates overall theoretical requirements for reducing the times required for the iterative learning of a real-time image-guided adaptive control routine for multiple-source heat applicators, as used in hyperthermia and thermal ablative therapy for cancer. Methods for partial reconstruction of the physical system with and without model reduction to find solutions within a clinically practical timeframe were analyzed. A mathematical analysis based on the Fredholm alternative theorem (FAT) was used to compactly analyze the existence and uniqueness of the optimal heating vector under two fundamental situations: (1) noiseless partial reconstruction and (2) noisy partial reconstruction. These results were coupled with a method for further acceleration of the solution using virtual source (VS) model reduction. The matrix approximation theorem (MAT) was used to choose the optimal vectors spanning the reduced-order subspace to reduce the time for system reconstruction and to determine the associated approximation error. Numerical simulations of the adaptive control of hyperthermia using VS were also performed to test the predictions derived from the theoretical analysis. A thigh sarcoma patient model surrounded by a ten-antenna phased-array applicator was retained for this purpose. The impacts of the convective cooling from blood flow and the presence of sudden increase of perfusion in muscle and tumor were also simulated. By FAT, partial system reconstruction directly conducted in the full space of the physical variables such as phases and magnitudes of the heat sources cannot guarantee reconstructing the optimal system to determine the global optimal setting of the heat sources. A remedy for this limitation is to conduct the partial reconstruction within a reduced-order subspace spanned by the first few maximum eigenvectors of the true system matrix. By MAT, this VS subspace is the optimal one when the goal is to maximize the average tumor temperature. When more than 6 sources present, the steps required for a nonlinear learning scheme is theoretically fewer than that of a linear one, however, finite number of iterative corrections is necessary for a single learning step of a nonlinear algorithm. Thus, the actual computational workload for a nonlinear algorithm is not necessarily less than that required by a linear algorithm. Based on the analysis presented herein, obtaining a unique global optimal heating vector for a multiple-source applicator within the constraints of real-time clinical hyperthermia treatments and thermal ablative therapies appears attainable using partial reconstruction with minimum norm least-squares method with supplemental equations. One way to supplement equations is the inclusion of a method of model reduction.

Detection and Alert of muscle fatigue considering a Surface Electromyography Chaotic Model

NASA Astrophysics Data System (ADS)

Herrera, V.; Romero, J. F.; Amestegui, M.

2011-03-01

This work propose a detection and alert algorithm for muscle fatigue in paraplegic patients undergoing electro-therapy sessions. The procedure is based on a mathematical chaotic model emulating physiological signals and Continuous Wavelet Transform (CWT). The chaotic model developed is based on a logistic map that provides suitable data accomplishing some physiological signal class patterns. The CWT was applied to signals generated by the model and the resulting vector was obtained through Total Wavelet Entropy (TWE). In this sense, the presented work propose a viable and practical alert and detection algorithm for muscle fatigue.

Modelling and Prediction of Spark-ignition Engine Power Performance Using Incremental Least Squares Support Vector Machines

NASA Astrophysics Data System (ADS)

Wong, Pak-kin; Vong, Chi-man; Wong, Hang-cheong; Li, Ke

2010-05-01

Modern automotive spark-ignition (SI) power performance usually refers to output power and torque, and they are significantly affected by the setup of control parameters in the engine management system (EMS). EMS calibration is done empirically through tests on the dynamometer (dyno) because no exact mathematical engine model is yet available. With an emerging nonlinear function estimation technique of Least squares support vector machines (LS-SVM), the approximate power performance model of a SI engine can be determined by training the sample data acquired from the dyno. A novel incremental algorithm based on typical LS-SVM is also proposed in this paper, so the power performance models built from the incremental LS-SVM can be updated whenever new training data arrives. With updating the models, the model accuracies can be continuously increased. The predicted results using the estimated models from the incremental LS-SVM are good agreement with the actual test results and with the almost same average accuracy of retraining the models from scratch, but the incremental algorithm can significantly shorten the model construction time when new training data arrives.

Modeling Vehicle Collision Angle in Traffic Crashes Based on Three-Dimensional Laser Scanning Data

PubMed Central

Lyu, Nengchao; Huang, Gang; Wu, Chaozhong; Duan, Zhicheng; Li, Pingfan

2017-01-01

In road traffic accidents, the analysis of a vehicle’s collision angle plays a key role in identifying a traffic accident’s form and cause. However, because accurate estimation of vehicle collision angle involves many factors, it is difficult to accurately determine it in cases in which less physical evidence is available and there is a lack of monitoring. This paper establishes the mathematical relation model between collision angle, deformation, and normal vector in the collision region according to the equations of particle deformation and force in Hooke’s law of classical mechanics. At the same time, the surface reconstruction method suitable for a normal vector solution is studied. Finally, the estimation model of vehicle collision angle is presented. In order to verify the correctness of the model, verification of multi-angle collision experiments and sensitivity analysis of laser scanning precision for the angle have been carried out using three-dimensional (3D) data obtained by a 3D laser scanner in the collision deformation zone. Under the conditions with which the model has been defined, validation results show that the collision angle is a result of the weighted synthesis of the normal vector of the collision point and the weight value is the deformation of the collision point corresponding to normal vectors. These conclusions prove the applicability of the model. The collision angle model proposed in this paper can be used as the theoretical basis for traffic accident identification and cause analysis. It can also be used as a theoretical reference for the study of the impact deformation of elastic materials. PMID:28264517

Modeling Vehicle Collision Angle in Traffic Crashes Based on Three-Dimensional Laser Scanning Data.

PubMed

Lyu, Nengchao; Huang, Gang; Wu, Chaozhong; Duan, Zhicheng; Li, Pingfan

2017-02-28

In road traffic accidents, the analysis of a vehicle's collision angle plays a key role in identifying a traffic accident's form and cause. However, because accurate estimation of vehicle collision angle involves many factors, it is difficult to accurately determine it in cases in which less physical evidence is available and there is a lack of monitoring. This paper establishes the mathematical relation model between collision angle, deformation, and normal vector in the collision region according to the equations of particle deformation and force in Hooke's law of classical mechanics. At the same time, the surface reconstruction method suitable for a normal vector solution is studied. Finally, the estimation model of vehicle collision angle is presented. In order to verify the correctness of the model, verification of multi-angle collision experiments and sensitivity analysis of laser scanning precision for the angle have been carried out using three-dimensional (3D) data obtained by a 3D laser scanner in the collision deformation zone. Under the conditions with which the model has been defined, validation results show that the collision angle is a result of the weighted synthesis of the normal vector of the collision point and the weight value is the deformation of the collision point corresponding to normal vectors. These conclusions prove the applicability of the model. The collision angle model proposed in this paper can be used as the theoretical basis for traffic accident identification and cause analysis. It can also be used as a theoretical reference for the study of the impact deformation of elastic materials.

A natural way to do spatial linear geometry in MACSYMA

NASA Technical Reports Server (NTRS)

Bulnes, J.

1977-01-01

A set of routines appropriate for use as an interactive aid in 3-dimensional calculations with planes, lines and points is presented. The mathematical language used is vector calculus. The simplicity with which these routines can be written in MACSYMA is demonstrated. Because of the natural way in which geometric intuition is mapped into them, they can serve as a model for an interactive computational aid for architects.

The mathematical modeling of the experiment on the determination of correlation coefficients in neutron beta-decay

NASA Astrophysics Data System (ADS)

Serebrov, A. P.; Zherebtsov, O. M.; Klyushnikov, G. N.

2018-05-01

An experiment on the measurement of the ratio of the axial coupling constant to the vector one is under development. The main idea of the experiment is to measure the values of A and B in the same setup. An additional measurement of the polarization is not necessary. The accuracy achieved to date in measuring λ is 2 × 10-3. It is expected that in the experiment the accuracy will be of the order of 10-4. Some particular problems of mathematical modeling concerning the experiment on the measurement of the ratio of the axial coupling constant to the vector one are considered. The force lines for the given tabular field of a magnetic trap are studied. The dependences of the longitudinal and transverse field non-uniformity coefficients on the coordinates are regarded. A special computational algorithm based on the law of a charged particle motion along a local magnetic force line is performed for the calculation of the electrons and protons motion time as well as for the evaluation of the total number of electrons colliding with the detector surface. The average values of the cosines of the angles with the coefficients of a, A and B have been estimated.

Digital TV processing system

NASA Technical Reports Server (NTRS)

1975-01-01

Two digital video data compression systems directly applicable to the Space Shuttle TV Communication System were described: (1) For the uplink, a low rate monochrome data compressor is used. The compression is achieved by using a motion detection technique in the Hadamard domain. To transform the variable source rate into a fixed rate, an adaptive rate buffer is provided. (2) For the downlink, a color data compressor is considered. The compression is achieved first by intra-color transformation of the original signal vector, into a vector which has lower information entropy. Then two-dimensional data compression techniques are applied to the Hadamard transformed components of this last vector. Mathematical models and data reliability analyses were also provided for the above video data compression techniques transmitted over a channel encoded Gaussian channel. It was shown that substantial gains can be achieved by the combination of video source and channel coding.

Geographical traceability of Marsdenia tenacissima by Fourier transform infrared spectroscopy and chemometrics

NASA Astrophysics Data System (ADS)

Li, Chao; Yang, Sheng-Chao; Guo, Qiao-Sheng; Zheng, Kai-Yan; Wang, Ping-Li; Meng, Zhen-Gui

2016-01-01

A combination of Fourier transform infrared spectroscopy with chemometrics tools provided an approach for studying Marsdenia tenacissima according to its geographical origin. A total of 128 M. tenacissima samples from four provinces in China were analyzed with FTIR spectroscopy. Six pattern recognition methods were used to construct the discrimination models: support vector machine-genetic algorithms, support vector machine-particle swarm optimization, K-nearest neighbors, radial basis function neural network, random forest and support vector machine-grid search. Experimental results showed that K-nearest neighbors was superior to other mathematical algorithms after data were preprocessed with wavelet de-noising, with a discrimination rate of 100% in both the training and prediction sets. This study demonstrated that FTIR spectroscopy coupled with K-nearest neighbors could be successfully applied to determine the geographical origins of M. tenacissima samples, thereby providing reliable authentication in a rapid, cheap and noninvasive way.

Use of Interactive Whiteboard in the Mathematics Classroom: Students' Perceptions within the Framework of the Technology Acceptance Model

ERIC Educational Resources Information Center

Önal, Nezih

2017-01-01

The purpose of the present research was to reveal students' perceptions regarding the use of the interactive whiteboard in the mathematics classroom within the framework of the Technology Acceptance Model. Semi-structured interviews were performed with 58 secondary school students (5th, 6th, 7th, and 8th grades) to collect data. The data obtained…

Biodiversity can help prevent malaria outbreaks in tropical forests.

PubMed

Laporta, Gabriel Zorello; Lopez de Prado, Paulo Inácio Knegt; Kraenkel, Roberto André; Coutinho, Renato Mendes; Sallum, Maria Anice Mureb

2013-01-01

Plasmodium vivax is a widely distributed, neglected parasite that can cause malaria and death in tropical areas. It is associated with an estimated 80-300 million cases of malaria worldwide. Brazilian tropical rain forests encompass host- and vector-rich communities, in which two hypothetical mechanisms could play a role in the dynamics of malaria transmission. The first mechanism is the dilution effect caused by presence of wild warm-blooded animals, which can act as dead-end hosts to Plasmodium parasites. The second is diffuse mosquito vector competition, in which vector and non-vector mosquito species compete for blood feeding upon a defensive host. Considering that the World Health Organization Malaria Eradication Research Agenda calls for novel strategies to eliminate malaria transmission locally, we used mathematical modeling to assess those two mechanisms in a pristine tropical rain forest, where the primary vector is present but malaria is absent. The Ross-Macdonald model and a biodiversity-oriented model were parameterized using newly collected data and data from the literature. The basic reproduction number ([Formula: see text]) estimated employing Ross-Macdonald model indicated that malaria cases occur in the study location. However, no malaria cases have been reported since 1980. In contrast, the biodiversity-oriented model corroborated the absence of malaria transmission. In addition, the diffuse competition mechanism was negatively correlated with the risk of malaria transmission, which suggests a protective effect provided by the forest ecosystem. There is a non-linear, unimodal correlation between the mechanism of dead-end transmission of parasites and the risk of malaria transmission, suggesting a protective effect only under certain circumstances (e.g., a high abundance of wild warm-blooded animals). To achieve biological conservation and to eliminate Plasmodium parasites in human populations, the World Health Organization Malaria Eradication Research Agenda should take biodiversity issues into consideration.

The Vector Calculus Gap: Mathematics (Does Not Equal) Physics.

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corinne A.

1999-01-01

Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK)

Broad patterns in domestic vector-borne Trypanosoma cruzi transmission dynamics: synanthropic animals and vector control.

PubMed

Peterson, Jennifer K; Bartsch, Sarah M; Lee, Bruce Y; Dobson, Andrew P

2015-10-22

Chagas disease (caused by Trypanosoma cruzi) is the most important neglected tropical disease (NTD) in Latin America, infecting an estimated 5.7 million people in the 21 countries where it is endemic. It is one of the NTDs targeted for control and elimination by the 2020 London Declaration goals, with the first goal being to interrupt intra-domiciliary vector-borne T. cruzi transmission. A key question in domestic T. cruzi transmission is the role that synanthropic animals play in T. cruzi transmission to humans. Here, we ask, (1) do synanthropic animals need to be targeted in Chagas disease prevention policies?, and (2) how does the presence of animals affect the efficacy of vector control? We developed a simple mathematical model to simulate domestic vector-borne T. cruzi transmission and to specifically examine the interaction between the presence of synanthropic animals and effects of vector control. We used the model to explore how the interactions between triatomine bugs, humans and animals impact the number and proportion of T. cruzi-infected bugs and humans. We then examined how T. cruzi dynamics change when control measures targeting vector abundance are introduced into the system. We found that the presence of synanthropic animals slows the speed of T. cruzi transmission to humans, and increases the sensitivity of T. cruzi transmission dynamics to vector control measures at comparable triatomine carrying capacities. However, T. cruzi transmission is amplified when triatomine carrying capacity increases with the abundance of syntathoropic hosts. Our results suggest that in domestic T. cruzi transmission scenarios where no vector control measures are in place, a reduction in synanthropic animals may slow T. cruzi transmission to humans, but it would not completely eliminate transmission. To reach the 2020 goal of interrupting intra-domiciliary T. cruzi transmission, it is critical to target vector populations. Additionally, where vector control measures are in place, synanthropic animals may be beneficial.

The Importance of Mathematical Models to Scientific Discovery: A Case Study on the Feeding Mechanism of the Goliath Grouper "Epinephelus itajara"

ERIC Educational Resources Information Center

Huber, Daniel; Jones, Leslie; Helminski, Christine

2015-01-01

The use of collaborative problem solving within mathematics education is imperative in this day and age of integrative science. The formation of interdisciplinary teams of mathematicians and scientists to investigate crucial problems is on the rise, as greater insight can be gained from an interdisciplinary perspective. Mathematical modelling, in…

Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Ages 4 to 11

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

2017-01-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math…

Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Age 4 to 11

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

2016-01-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An Early Math Trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from age 4 to 11. This model includes a broad range of math…

A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

NASA Technical Reports Server (NTRS)

Maddalon, Jeffrey M.; Butler, Ricky W.; Munoz, Cesar A.; Dowek, Gilles

2009-01-01

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Vectors as Epidemiological Sentinels: Patterns of Within-Tick Borrelia burgdorferi Diversity

PubMed Central

Walter, Katharine S.; Carpi, Giovanna; Evans, Benjamin R.; Caccone, Adalgisa; Diuk-Wasser, Maria A.

2016-01-01

Hosts including humans, other vertebrates, and arthropods, are frequently infected with heterogeneous populations of pathogens. Within-host pathogen diversity has major implications for human health, epidemiology, and pathogen evolution. However, pathogen diversity within-hosts is difficult to characterize and little is known about the levels and sources of within-host diversity maintained in natural populations of disease vectors. Here, we examine genomic variation of the Lyme disease bacteria, Borrelia burgdorferi (Bb), in 98 individual field-collected tick vectors as a model for study of within-host processes. Deep population sequencing reveals extensive and previously undocumented levels of Bb variation: the majority (~70%) of ticks harbor mixed strain infections, which we define as levels Bb diversity pre-existing in a diverse inoculum. Within-tick diversity is thus a sample of the variation present within vertebrate hosts. Within individual ticks, we detect signatures of positive selection. Genes most commonly under positive selection across ticks include those involved in dissemination in vertebrate hosts and evasion of the vertebrate immune complement. By focusing on tick-borne Bb, we show that vectors can serve as epidemiological and evolutionary sentinels: within-vector pathogen diversity can be a useful and unbiased way to survey circulating pathogen diversity and identify evolutionary processes occurring in natural transmission cycles. PMID:27414806

Helminths as vectors of pathogens in vertebrate hosts: a theoretical approach.

PubMed

Perkins, Sarah E; Fenton, Andy

2006-07-01

Pathogens frequently use vectors to facilitate transmission between hosts and, for vertebrate hosts, the vectors are typically ectoparasitic arthropods. However, other parasites that are intimately associated with their hosts may also be ideal candidate vectors; namely the parasitic helminths. Here, we present empirical evidence that helminth vectoring of pathogens occurs in a range of vertebrate systems by a variety of helminth taxa. Using a novel theoretical framework we explore the dynamics of helminth vectoring and determine which host-helminth-pathogen characteristics may favour the evolution of helminth vectoring. We use two theoretical models: the first is a population dynamic model amalgamated from standard macro- and microparasite models, which serves as a framework for investigation of within-host interactions between co-infecting pathogens and helminths. The second is an evolutionary model, which we use to predict the ecological conditions under which we would expect helminth vectoring to evolve. We show that, like arthropod vectors, helminth vectors increase pathogen fitness. However, unlike arthropod vectors, helminth vectoring increases the pathogenic impact on the host and may allow the evolution of high pathogen virulence. We show that concomitant infection of a host with a helminth and pathogen are not necessarily independent of one another, due to helminth vectoring of microparasites, with profound consequences for pathogen persistence and the impact of disease on the host population.

Bridging the Vector Calculus Gap

NASA Astrophysics Data System (ADS)

Dray, Tevian; Manogue, Corinne

2003-05-01

As with Britain and America, mathematicians and physicists are separated from each other by a common language. In a nutshell, mathematics is about functions, but physics is about things. For the last several years, we have led an NSF-supported effort to "bridge the vector calculus gap" between mathematics and physics. The unifying theme we have discovered is to emphasize geometric reasoning, not (just) algebraic computation. In this talk, we will illustrate the language differences between mathematicians and physicists, and how we are trying reconcile them in the classroom. For further information about the project go to: http://www.physics.orst.edu/bridge

Generalizations of Tikhonov's regularized method of least squares to non-Euclidean vector norms

NASA Astrophysics Data System (ADS)

Volkov, V. V.; Erokhin, V. I.; Kakaev, V. V.; Onufrei, A. Yu.

2017-09-01

Tikhonov's regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by "instrumental" generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.

A link between torse-forming vector fields and rotational hypersurfaces

NASA Astrophysics Data System (ADS)

Chen, Bang-Yen; Verstraelen, Leopold

Torse-forming vector fields introduced by Yano [On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo 20 (1944) 340-346] are natural extension of concurrent and concircular vector fields. Such vector fields have many nice applications to geometry and mathematical physics. In this paper, we establish a link between rotational hypersurfaces and torse-forming vector fields. More precisely, our main result states that, for a hypersurface M of 𝔼n+1 with n ≥ 3, the tangential component xT of the position vector field of M is a proper torse-forming vector field on M if and only if M is contained in a rotational hypersurface whose axis of rotation contains the origin.

Definition of Contravariant Velocity Components

NASA Technical Reports Server (NTRS)

Hung, Ching-moa; Kwak, Dochan (Technical Monitor)

2002-01-01

In this paper we have reviewed the basics of tensor analysis in an attempt to clarify some misconceptions regarding contravariant and covariant vector components as used in fluid dynamics. We have indicated that contravariant components are components of a given vector expressed as a unique combination of the covariant base vector system and, vice versa, that the covariant components are components of a vector expressed with the contravariant base vector system. Mathematically, expressing a vector with a combination of base vector is a decomposition process for a specific base vector system. Hence, the contravariant velocity components are decomposed components of velocity vector along the directions of coordinate lines, with respect to the covariant base vector system. However, the contravariant (and covariant) components are not physical quantities. Their magnitudes and dimensions are controlled by their corresponding covariant (and contravariant) base vectors.

"Lollipop-shaped" high-sensitivity Microelectromechanical Systems vector hydrophone based on Parylene encapsulation

NASA Astrophysics Data System (ADS)

Liu, Yuan; Wang, Renxin; Zhang, Guojun; Du, Jin; Zhao, Long; Xue, Chenyang; Zhang, Wendong; Liu, Jun

2015-07-01

This paper presents methods of promoting the sensitivity of Microelectromechanical Systems (MEMS) vector hydrophone by increasing the sensing area of cilium and perfect insulative Parylene membrane. First, a low-density sphere is integrated with the cilium to compose a "lollipop shape," which can considerably increase the sensing area. A mathematic model on the sensitivity of the "lollipop-shaped" MEMS vector hydrophone is presented, and the influences of different structural parameters on the sensitivity are analyzed via simulation. Second, the MEMS vector hydrophone is encapsulated through the conformal deposition of insulative Parylene membrane, which enables underwater acoustic monitoring without any typed sound-transparent encapsulation. Finally, the characterization results demonstrate that the sensitivity reaches up to -183 dB (500 Hz 0dB at 1 V/ μPa ), which is increased by more than 10 dB, comparing with the previous cilium-shaped MEMS vector hydrophone. Besides, the frequency response takes on a sensitivity increment of 6 dB per octave. The working frequency band is 20-500 Hz and the concave point depth of 8-shaped directivity is beyond 30 dB, indicating that the hydrophone is promising in underwater acoustic application.

The Potential Effects of the Defense Business Board Military Compensation Task Group’s 2011 Recommendations on Active-Duty Service Member Retirement

DTIC Science & Technology

2012-12-01

system be implemented. In this study, we created a mathematical model to simulate accumulated savings under the proposed defined...retirement system be implemented. In this study, we created a mathematical model to simulate accumulated savings under the proposed defined...lumbering recovery, it has reemerged as a potential austerity measure within the U.S. government. B. METHODOLOGY We created a mathematical model of

A model for Huanglongbing spread between citrus plants including delay times and human intervention

NASA Astrophysics Data System (ADS)

Vilamiu, Raphael G. d'A.; Ternes, Sonia; Braga, Guilherme A.; Laranjeira, Francisco F.

2012-09-01

The objective of this work was to present a compartmental deterministic mathematical model for representing the dynamics of HLB disease in a citrus orchard, including delay in the disease's incubation phase in the plants, and a delay period on the nymphal stage of Diaphorina citri, the most important HLB insect vector in Brazil. Numerical simulations were performed to assess the possible impacts of human detection efficiency of symptomatic plants, as well as the influence of a long incubation period of HLB in the plant.

Cloud motion in relation to the ambient wind field

NASA Technical Reports Server (NTRS)

Fuelberg, H. E.; Scoggins, J. R.

1975-01-01

Trajectories of convective clouds were computed from a mathematical model and compared with trajectories observed by radar. The ambient wind field was determined from the AVE IIP data. The model includes gradient, coriolis, drag, lift, and lateral forces. The results show that rotational effects may account for large differences between the computed and observed trajectories and that convective clouds may move 10 to 20 degrees to the right or left of the average wind vector and at speeds 5 to 10 m/sec faster or slower than the average ambient wind speed.

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.

Characterizing Preservice Teachers' Mathematical Understanding of Algebraic Relationships

ERIC Educational Resources Information Center

Nillas, Leah A.

2010-01-01

Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…

Modeling the effects of palm-house proximity on the theoretical risk of Chagas disease transmission in a rural locality of the Orinoco basin, Colombia.

PubMed

Erazo, Diana; Cordovez, Juan

2016-11-18

Chagas disease is a major public health concern in Latin America and it is transmitted by insects of the subfamily Triatominae, including Rhodnius spp. Since palm trees are ubiquitous in Colombia and a habitat for Rhodnius spp., the presence of palms near villages could increase contact rates between vectors and humans. Therefore, knowing whether a relationship exists between the proximity of palms to villages and the abundance and distribution of vectors therein, may be critical for Chagas disease prevention programs. Adapting a mathematical model for R. prolixus population dynamics in a small village, we model the implications of changing distances between palms and dwellings, to the risk of Chagas disease infection. We implemented a mathematical model that reflects R. prolixus population dynamics in a small village located in the department of Casanare (Colombia) to study the role of palm-house proximity. We varied the distance between palms and houses by monitoring the network global efficiency metric. We constructed 1,000 hypothetical villages varying distances and each one was run 100 times. According to the model, as palm-house proximity increases, houses were more likely to be visited by triatomine bugs. The number of bugs per unit time increased progressively in a non-linear fashion with high variability. We stress the importance of village configuration on the model output. From a theoretical perspective, palm-house proximity may have a positive effect on the incidence of Chagas disease. The model predicts a 1% increase in new human cases per year when houses and palms are brought closer by 75%.

The Reciprocal Internal/External Frame of Reference Model: An Integration of Models of Relations between Academic Achievement and Self-Concept

ERIC Educational Resources Information Center

Moller, Jens; Retelsdorf, Jan; Koller, Olaf; Marsh, Herb W.

2011-01-01

The reciprocal internal/external frame of reference model (RI/EM) combines the internal/external frame of reference model and the reciprocal effects model. The RI/EM predicts positive effects of mathematics and verbal achievement and academic self-concepts (ASC) on subsequent mathematics and verbal achievements and ASCs within domains and negative…

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

How Can Onchocerciasis Elimination in Africa Be Accelerated? Modeling the Impact of Increased Ivermectin Treatment Frequency and Complementary Vector Control.

PubMed

Verver, Suzanne; Walker, Martin; Kim, Young Eun; Fobi, Grace; Tekle, Afework H; Zouré, Honorat G M; Wanji, Samuel; Boakye, Daniel A; Kuesel, Annette C; de Vlas, Sake J; Boussinesq, Michel; Basáñez, Maria-Gloria; Stolk, Wilma A

2018-06-01

Great strides have been made toward onchocerciasis elimination by mass drug administration (MDA) of ivermectin. Focusing on MDA-eligible areas, we investigated where the elimination goal can be achieved by 2025 by continuation of current practice (annual MDA with ivermectin) and where intensification or additional vector control is required. We did not consider areas hypoendemic for onchocerciasis with loiasis coendemicity where MDA is contraindicated. We used 2 previously published mathematical models, ONCHOSIM and EPIONCHO, to simulate future trends in microfilarial prevalence for 80 different settings (defined by precontrol endemicity and past MDA frequency and coverage) under different future treatment scenarios (annual, biannual, or quarterly MDA with different treatment coverage through 2025, with or without vector control strategies), assessing for each strategy whether it eventually leads to elimination. Areas with 40%-50% precontrol microfilarial prevalence and ≥10 years of annual MDA may achieve elimination with a further 7 years of annual MDA, if not achieved already, according to both models. For most areas with 70%-80% precontrol prevalence, ONCHOSIM predicts that either annual or biannual MDA is sufficient to achieve elimination by 2025, whereas EPIONCHO predicts that elimination will not be achieved even with complementary vector control. Whether elimination will be reached by 2025 depends on precontrol endemicity, control history, and strategies chosen from now until 2025. Biannual or quarterly MDA will accelerate progress toward elimination but cannot guarantee it by 2025 in high-endemicity areas. Long-term concomitant MDA and vector control for high-endemicity areas might be useful.

Feedback controlled optics with wavefront compensation

NASA Technical Reports Server (NTRS)

Breckenridge, William G. (Inventor); Redding, David C. (Inventor)

1993-01-01

The sensitivity model of a complex optical system obtained by linear ray tracing is used to compute a control gain matrix by imposing the mathematical condition for minimizing the total wavefront error at the optical system's exit pupil. The most recent deformations or error states of the controlled segments or optical surfaces of the system are then assembled as an error vector, and the error vector is transformed by the control gain matrix to produce the exact control variables which will minimize the total wavefront error at the exit pupil of the optical system. These exact control variables are then applied to the actuators controlling the various optical surfaces in the system causing the immediate reduction in total wavefront error observed at the exit pupil of the optical system.

An Improved Azimuth Angle Estimation Method with a Single Acoustic Vector Sensor Based on an Active Sonar Detection System.

PubMed

Zhao, Anbang; Ma, Lin; Ma, Xuefei; Hui, Juan

2017-02-20

In this paper, an improved azimuth angle estimation method with a single acoustic vector sensor (AVS) is proposed based on matched filtering theory. The proposed method is mainly applied in an active sonar detection system. According to the conventional passive method based on complex acoustic intensity measurement, the mathematical and physical model of this proposed method is described in detail. The computer simulation and lake experiments results indicate that this method can realize the azimuth angle estimation with high precision by using only a single AVS. Compared with the conventional method, the proposed method achieves better estimation performance. Moreover, the proposed method does not require complex operations in frequencydomain and achieves computational complexity reduction.

Eigenfunction Expansions and Lippmann-Schwinger Formulas

NASA Astrophysics Data System (ADS)

Gadella, M.; Kielanowski, P.

2011-12-01

In this paper we discuss in the mathematically precise way the definition of a resonance, that requires two Hamiltonians (free and perturbed), the notion of Gamow vectors, Lippmann-Schwinger equations and the analytic properties of their solutions in the context of the Gamow vectors. Next we discuss the eigenfunction expansions in the presence of resonances. In the case of the Friedrichs model, the precise form of these generalized eigenfunctions has been given in the literature. Although there are two families of eigenfunction expansions which are related through the time reversal operator, free and perturbed Hamiltonians are time invariant. On the other hand, PT symmetries play no role in this discussion. Our discussion clarifies the results of the paper [1], which contains imprecise or even wrong statements.

Chagas disease vector control and Taylor's law

PubMed Central

Rodríguez-Planes, Lucía I.; Gaspe, María S.; Cecere, María C.; Cardinal, Marta V.

2017-01-01

Background Large spatial and temporal fluctuations in the population density of living organisms have profound consequences for biodiversity conservation, food production, pest control and disease control, especially vector-borne disease control. Chagas disease vector control based on insecticide spraying could benefit from improved concepts and methods to deal with spatial variations in vector population density. Methodology/Principal findings We show that Taylor's law (TL) of fluctuation scaling describes accurately the mean and variance over space of relative abundance, by habitat, of four insect vectors of Chagas disease (Triatoma infestans, Triatoma guasayana, Triatoma garciabesi and Triatoma sordida) in 33,908 searches of people's dwellings and associated habitats in 79 field surveys in four districts in the Argentine Chaco region, before and after insecticide spraying. As TL predicts, the logarithm of the sample variance of bug relative abundance closely approximates a linear function of the logarithm of the sample mean of abundance in different habitats. Slopes of TL indicate spatial aggregation or variation in habitat suitability. Predictions of new mathematical models of the effect of vector control measures on TL agree overall with field data before and after community-wide spraying of insecticide. Conclusions/Significance A spatial Taylor's law identifies key habitats with high average infestation and spatially highly variable infestation, providing a new instrument for the control and elimination of the vectors of a major human disease. PMID:29190728

Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations

DTIC Science & Technology

1999-01-01

purpose of the second partitioning phase , on each SMP, is to minimize the communication within the SMP; even if a multi - threaded matrix vector product...8.7 Comparison of model with experimental data for send phase of matrix vector product on ne grid...140 8.4 Matrix vector product phase times : : : : : : : : : : : : : : : : : : : : : : : 145 9.1 Flat and

Analysis of structural response data using discrete modal filters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Freudinger, Lawrence C.

1991-01-01

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Mathematical modelling of Bit-Level Architecture using Reciprocal Quantum Logic

NASA Astrophysics Data System (ADS)

Narendran, S.; Selvakumar, J.

2018-04-01

Efficiency of high-performance computing is on high demand with both speed and energy efficiency. Reciprocal Quantum Logic (RQL) is one of the technology which will produce high speed and zero static power dissipation. RQL uses AC power supply as input rather than DC input. RQL has three set of basic gates. Series of reciprocal transmission lines are placed in between each gate to avoid loss of power and to achieve high speed. Analytical model of Bit-Level Architecture are done through RQL. Major drawback of reciprocal Quantum Logic is area, because of lack in proper power supply. To achieve proper power supply we need to use splitters which will occupy large area. Distributed arithmetic uses vector- vector multiplication one is constant and other is signed variable and each word performs as a binary number, they rearranged and mixed to form distributed system. Distributed arithmetic is widely used in convolution and high performance computational devices.

Search for the algorithm of genes distribution during the process of microbial evolution

NASA Astrophysics Data System (ADS)

Pikuta, Elena V.

2015-09-01

Previous two and three dimensional graph analysis of eco-physiological data of Archaea demonstrated specific geometry for distribution of major Prokaryotic groups in a hyperboloid function. The function of a two-sheet hyperboloid covered all known biological groups, and therefore, could be applied for the entire evolution of life on Earth. The vector of evolution was indicated from the point of hyper temperature, extreme acidity and low salinity to the point of low temperature and increased alkalinity and salinity. According to this vector, the following groups were chosen for the gene screening analysis. In the vector "High-Temperature → Low-Temperature" within extreme acidic pH (0-3), it is: 1) the hyperthermophilic Crenarchaeota - order Sulfolobales, 2) moderately thermophilic Euryarchaeota - Class Thermoplasmata, and 3) mesophilic acidophiles- genus Thiobacillus and others. In the vector "Low pH → High pH" the following groups were selected in three temperature ranges: a) Hyperthermophilic Archaea and Eubacteria, b) moderately thermophilic - representatives of the genera Anaerobacter and Anoxybacillus, and c) mesophilic haloalkaliphiles (Eubacteria and Archaea). The genes associated with acidophily (H+ pump), chemolitho-autotrophy (proteins of biochemichal cycles), polymerases, and histones were proposed for the first vector, and for the second vector the genes associated with halo-alkaliphily (Na+ pumps), enzymes of organotrophic metabolisms (sugar- and proteolytics), and others were indicated for the screening. Here, an introduction to the phylogenetic constant (ρη) is presented and discussed. This universal characteristic is calculated for two principally different life forms -Prokaryotes and Eukaryotes; Existence of the second type of living forms is impossible without the first one. The number of chromosomes in Prokaryotic organisms is limited to one (with very rare exceptions, to two), while in Eukaryotic organisms this number is larger. Currently, accumulation of data for genome sequences is in progress: about 3,500 draft sequences of genomes are available (of the total 12,000 species Bacteria and Archaea). The possibility of confirmation of the previously proposed mathematical model with an approach for genes screening in determined key groups of microorganisms in genomes databases is outlined and discussed in this article.

Optical modular arithmetic

NASA Astrophysics Data System (ADS)

Pavlichin, Dmitri S.; Mabuchi, Hideo

2014-06-01

Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.

Mathematics, Vol. 2.

ERIC Educational Resources Information Center

Bureau of Naval Personnel, Washington, DC.

The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…

Some Mathematics and Physics of Ball Games.

ERIC Educational Resources Information Center

Hughes, D. E.

1985-01-01

Gives examples on the applications of arithmetic, geometry, and some calculus, vector algebra, and mechanics to ball games. Suggestions for further interesting investigations are provided together with references to other articles and books on applications of mathematics and physics to ball games and sports in general. (JN)

The brian simulator.

PubMed

Goodman, Dan F M; Brette, Romain

2009-09-01

"Brian" is a simulator for spiking neural networks (http://www.briansimulator.org). The focus is on making the writing of simulation code as quick and easy as possible for the user, and on flexibility: new and non-standard models are no more difficult to define than standard ones. This allows scientists to spend more time on the details of their models, and less on their implementation. Neuron models are defined by writing differential equations in standard mathematical notation, facilitating scientific communication. Brian is written in the Python programming language, and uses vector-based computation to allow for efficient simulations. It is particularly useful for neuroscientific modelling at the systems level, and for teaching computational neuroscience.

A STEM Exploration with Gears

ERIC Educational Resources Information Center

Deis, Timothy; Julius, Julie

2017-01-01

Science, engineering, and mathematics are fields that many students see as separate entities. But if these fields are combined with technology, they become STEM. This investigation provides a context and allows students to explore mathematics, science, and engineering within that context. It requires students to model with mathematics and find…

Children thinking mathematically beyond authoritative identities

NASA Astrophysics Data System (ADS)

MacMillan, Agnes

1995-10-01

A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children's interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.

Forecasting Caspian Sea level changes using satellite altimetry data (June 1992-December 2013) based on evolutionary support vector regression algorithms and gene expression programming

NASA Astrophysics Data System (ADS)

Imani, Moslem; You, Rey-Jer; Kuo, Chung-Yen

2014-10-01

Sea level forecasting at various time intervals is of great importance in water supply management. Evolutionary artificial intelligence (AI) approaches have been accepted as an appropriate tool for modeling complex nonlinear phenomena in water bodies. In the study, we investigated the ability of two AI techniques: support vector machine (SVM), which is mathematically well-founded and provides new insights into function approximation, and gene expression programming (GEP), which is used to forecast Caspian Sea level anomalies using satellite altimetry observations from June 1992 to December 2013. SVM demonstrates the best performance in predicting Caspian Sea level anomalies, given the minimum root mean square error (RMSE = 0.035) and maximum coefficient of determination (R2 = 0.96) during the prediction periods. A comparison between the proposed AI approaches and the cascade correlation neural network (CCNN) model also shows the superiority of the GEP and SVM models over the CCNN.

Modelling malaria control by introduction of larvivorous fish.

PubMed

Lou, Yijun; Zhao, Xiao-Qiang

2011-10-01

Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host-vector interaction and the predator-prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.

OMV: A simplified mathematical model of the orbital maneuvering vehicle

NASA Technical Reports Server (NTRS)

Teoh, W.

1984-01-01

A model of the orbital maneuvering vehicle (OMV) is presented which contains several simplications. A set of hand controller signals may be used to control the motion of the OMV. Model verification is carried out using a sequence of tests. The dynamic variables generated by the model are compared, whenever possible, with the corresponding analytical variables. The results of the tests show conclusively that the present model is behaving correctly. Further, this model interfaces properly with the state vector transformation module (SVX) developed previously. Correct command sentence sequences are generated by the OMV and and SVX system, and these command sequences can be used to drive the flat floor simulation system at MSFC.

Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules

NASA Astrophysics Data System (ADS)

Dzuba, V. A.; Flambaum, V. V.; Stadnik, Y. V.

2017-12-01

In the presence of P -violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, Ba+ , Yb, Tl, Fr, and Ra+ using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector-boson exchange using a simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of 133Cs, we constrain the P -violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2014-03-01

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

Pyomo v5.0

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

Woodruff, David; Hackebeil, Gabe; Laird, Carl Damon

Pyomo supports the formulation and analysis of mathematical models for complex optimization applications. This capability is commonly associated with algebraic modeling languages (AMLs), which support the description and analysis of mathematical models with a high-level language. Although most AMLs are implemented in custom modeling languages, Pyomo's modeling objects are embedded within Python, a full- featured high-level programming language that contains a rich set of supporting libraries.

Modeling Virus Coinfection to Inform Management of Maize Lethal Necrosis in Kenya

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

Hilker, Frank M.; Allen, Linda J. S.; Bokil, Vrushali A.

Maize lethal necrosis (MLN) has emerged as a serious threat to food security in sub-Saharan Africa. MLN is caused by coinfection with two viruses, Maize chlorotic mottle virus and a potyvirus, often Sugarcane mosaic virus. To better understand the dynamics of MLN and to provide insight into disease management, we modeled the spread of the viruses causing MLN within and between growing seasons. The model allows for transmission via vectors, soil, and seed, as well as exogenous sources of infection. Following model parameterization, we predict how management affects disease prevalence and crop performance over multiple seasons. Resource-rich farmers with largemore » holdings can achieve good control by combining clean seed and insect control. However, crop rotation is often required to effect full control. Resource-poor farmers with smaller holdings must rely on rotation and roguing, and achieve more limited control. For both types of farmer, unless management is synchronized over large areas, exogenous sources of infection can thwart control. As well as providing practical guidance, our modeling framework is potentially informative for other cropping systems in which coinfection has devastating effects. Finally, our work also emphasizes how mathematical modeling can inform management of an emerging disease even when epidemiological information remains scanty.« less

Modeling Virus Coinfection to Inform Management of Maize Lethal Necrosis in Kenya

DOE PAGES

Hilker, Frank M.; Allen, Linda J. S.; Bokil, Vrushali A.; ...

2017-08-01

Maize lethal necrosis (MLN) has emerged as a serious threat to food security in sub-Saharan Africa. MLN is caused by coinfection with two viruses, Maize chlorotic mottle virus and a potyvirus, often Sugarcane mosaic virus. To better understand the dynamics of MLN and to provide insight into disease management, we modeled the spread of the viruses causing MLN within and between growing seasons. The model allows for transmission via vectors, soil, and seed, as well as exogenous sources of infection. Following model parameterization, we predict how management affects disease prevalence and crop performance over multiple seasons. Resource-rich farmers with largemore » holdings can achieve good control by combining clean seed and insect control. However, crop rotation is often required to effect full control. Resource-poor farmers with smaller holdings must rely on rotation and roguing, and achieve more limited control. For both types of farmer, unless management is synchronized over large areas, exogenous sources of infection can thwart control. As well as providing practical guidance, our modeling framework is potentially informative for other cropping systems in which coinfection has devastating effects. Finally, our work also emphasizes how mathematical modeling can inform management of an emerging disease even when epidemiological information remains scanty.« less

The Levi-Civita Tensor and Identities in Vector Analysis. Vector Field Identities. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 427.

ERIC Educational Resources Information Center

Yiu, Chang-li; Wilde, Carroll O.

Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…

Modelling strategies to break transmission of lymphatic filariasis--aggregation, adherence and vector competence greatly alter elimination.

PubMed

Irvine, M A; Reimer, L J; Njenga, S M; Gunawardena, S; Kelly-Hope, L; Bockarie, M; Hollingsworth, T D

2015-10-22

With ambitious targets to eliminate lymphatic filariasis over the coming years, there is a need to identify optimal strategies to achieve them in areas with different baseline prevalence and stages of control. Modelling can assist in identifying what data should be collected and what strategies are best for which scenarios. We develop a new individual-based, stochastic mathematical model of the transmission of lymphatic filariasis. We validate the model by fitting to a first time point and predicting future timepoints from surveillance data in Kenya and Sri Lanka, which have different vectors and different stages of the control programme. We then simulate different treatment scenarios in low, medium and high transmission settings, comparing once yearly mass drug administration (MDA) with more frequent MDA and higher coverage. We investigate the potential impact that vector control, systematic non-compliance and different levels of aggregation have on the dynamics of transmission and control. In all settings, increasing coverage from 65 to 80 % has a similar impact on control to treating twice a year at 65 % coverage, for fewer drug treatments being distributed. Vector control has a large impact, even at moderate levels. The extent of aggregation of parasite loads amongst a small portion of the population, which has been estimated to be highly variable in different settings, can undermine the success of a programme, particularly if high risk sub-communities are not accessing interventions. Even moderate levels of vector control have a large impact both on the reduction in prevalence and the maintenance of gains made during MDA, even when parasite loads are highly aggregated, and use of vector control is at moderate levels. For the same prevalence, differences in aggregation and adherence can result in very different dynamics. The novel analysis of a small amount of surveillance data and resulting simulations highlight the need for more individual level data to be analysed to effectively tailor programmes in the drive for elimination.

Discrete-Event Simulation Models of Plasmodium falciparum Malaria

PubMed Central

McKenzie, F. Ellis; Wong, Roger C.; Bossert, William H.

2008-01-01

We develop discrete-event simulation models using a single “timeline” variable to represent the Plasmodium falciparum lifecycle in individual hosts and vectors within interacting host and vector populations. Where they are comparable our conclusions regarding the relative importance of vector mortality and the durations of host immunity and parasite development are congruent with those of classic differential-equation models of malaria, epidemiology. However, our results also imply that in regions with intense perennial transmission, the influence of mosquito mortality on malaria prevalence in humans may be rivaled by that of the duration of host infectivity. PMID:18668185

Structural analysis of online handwritten mathematical symbols based on support vector machines

NASA Astrophysics Data System (ADS)

Simistira, Foteini; Papavassiliou, Vassilis; Katsouros, Vassilis; Carayannis, George

2013-01-01

Mathematical expression recognition is still a very challenging task for the research community mainly because of the two-dimensional (2d) structure of mathematical expressions (MEs). In this paper, we present a novel approach for the structural analysis between two on-line handwritten mathematical symbols of a ME, based on spatial features of the symbols. We introduce six features to represent the spatial affinity of the symbols and compare two multi-class classification methods that employ support vector machines (SVMs): one based on the "one-against-one" technique and one based on the "one-against-all", in identifying the relation between a pair of symbols (i.e. subscript, numerator, etc). A dataset containing 1906 spatial relations derived from the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2012 training dataset is constructed to evaluate the classifiers and compare them with the rule-based classifier of the ILSP-1 system participated in the contest. The experimental results give an overall mean error rate of 2.61% for the "one-against-one" SVM approach, 6.57% for the "one-against-all" SVM technique and 12.31% error rate for the ILSP-1 classifier.

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

Envisioning migration: Mathematics in both experimental analysis and modeling of cell behavior

PubMed Central

Zhang, Elizabeth R.; Wu, Lani F.; Altschuler, Steven J.

2013-01-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution—potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. PMID:23660413

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

PubMed

Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J

2013-10-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

A description of rotations for DEM models of particle systems

NASA Astrophysics Data System (ADS)

Campello, Eduardo M. B.

2015-06-01

In this work, we show how a vector parameterization of rotations can be adopted to describe the rotational motion of particles within the framework of the discrete element method (DEM). It is based on the use of a special rotation vector, called Rodrigues rotation vector, and accounts for finite rotations in a fully exact manner. The use of fictitious entities such as quaternions or complicated structures such as Euler angles is thereby circumvented. As an additional advantage, stick-slip friction models with inter-particle rolling motion are made possible in a consistent and elegant way. A few examples are provided to illustrate the applicability of the scheme. We believe that simple vector descriptions of rotations are very useful for DEM models of particle systems.

Climate Science Program at California State University, Northridge

NASA Astrophysics Data System (ADS)

Steele Cox, H.; Klein, D.; Cadavid, A. C.; Foley, B.

2012-12-01

Due to its interdisciplinary nature, climate science poses wide-ranging challenges for science and mathematics students seeking careers in this field. There is a compelling need for universities to provide coherent programs in climate science in order to train future climate scientists. With funding from NASA Innovations in Climate Education (NICE), California State University, Northridge (CSUN), is creating the CSUN Climate Science Program. An interdisciplinary team of faculty members is working in collaboration with UCLA, Santa Monica College and NASA/JPL partners to create a new curriculum in climate science. The resulting sequence of climate science courses, or Pathway for studying the Mathematics of Climate Change (PMCC), is integrated into a Bachelor of Science degree program in the Applied Mathematical Sciences offered by the Mathematics Department at CSUN. The PMCC consists of courses offered by the departments of Mathematics, Physics, and Geography and is designed to prepare students for Ph.D. programs in technical fields relevant to global climate change and related careers. The students who choose to follow this program will be guided to enroll in the following sequence of courses for their 12 units of upper division electives: 1) A newly created course junior level course, Math 396CL, in applied mathematics which will introduce students to applications of vector calculus and differential equations to the study of thermodynamics and atmospheric dynamics. 2) An already existing course, Math 483, with new content on mathematical modeling specialized for this program; 3) An improved version of Phys 595CL on the mathematics and physics of climate change with emphasis on Radiative Transfer; 4) A choice of Geog 407 on Remote Sensing or Geog 416 on Climate Change with updated content to train the students in the analysis of satellite data obtained with the NASA Earth Observing System and instruction in the analysis of data obtained within a Geographical Information System (GIS). In addition the Geography department will similarly update the corresponding graduate courses on Remote Sensing, Geog 690D, and Climate Change Geog 620F, and there will be a reciprocal curriculum and data sharing collaboration with the Earth and Environmental Sciences program at Santa Monica College. Throughout the academic year a seminar series offers the students the opportunity to learn about ongoing work on Atmospheric Sciences and Climate and during the summer they have access to research experiences at NASA's Jet Propulsion Laboratory.

Numeracy for the 21st Century: A Commentary

ERIC Educational Resources Information Center

Askew, Mike

2015-01-01

Many of the papers in this special issue draw on the fundamental model of numeracy developed by Goos et al. (Transforming mathematics instruction: multiple approaches and practices. 81-102, 2014). Four elements in that model--contexts, tools, dispositions, and mathematical knowledge--are embedded within a critical orientation, and being, or…

Faculty Sufficiency and AACSB Accreditation Compliance within a Global University: A Mathematical Modeling Approach

ERIC Educational Resources Information Center

Boronico, Jess; Murdy, Jim; Kong, Xinlu

2014-01-01

This manuscript proposes a mathematical model to address faculty sufficiency requirements towards assuring overall high quality management education at a global university. Constraining elements include full-time faculty coverage by discipline, location, and program, across multiple campus locations subject to stated service quality standards of…

Balancing aggregation and smoothing errors in inverse models

DOE PAGES

Turner, A. J.; Jacob, D. J.

2015-06-30

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function ofmore » state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.« less

Balancing aggregation and smoothing errors in inverse models

NASA Astrophysics Data System (ADS)

Turner, A. J.; Jacob, D. J.

2015-01-01

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Balancing aggregation and smoothing errors in inverse models

NASA Astrophysics Data System (ADS)

Turner, A. J.; Jacob, D. J.

2015-06-01

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Nonlinearity analysis of measurement model for vision-based optical navigation system

NASA Astrophysics Data System (ADS)

Li, Jianguo; Cui, Hutao; Tian, Yang

2015-02-01

In the autonomous optical navigation system based on line-of-sight vector observation, nonlinearity of measurement model is highly correlated with the navigation performance. By quantitatively calculating the degree of nonlinearity of the focal plane model and the unit vector model, this paper focuses on determining which optical measurement model performs better. Firstly, measurement equations and measurement noise statistics of these two line-of-sight measurement models are established based on perspective projection co-linearity equation. Then the nonlinear effects of measurement model on the filter performance are analyzed within the framework of the Extended Kalman filter, also the degrees of nonlinearity of two measurement models are compared using the curvature measure theory from differential geometry. Finally, a simulation of star-tracker-based attitude determination is presented to confirm the superiority of the unit vector measurement model. Simulation results show that the magnitude of curvature nonlinearity measurement is consistent with the filter performance, and the unit vector measurement model yields higher estimation precision and faster convergence properties.

Evaluating Middle School Students' Spatial-scientific Performance in Earth-space Science

NASA Astrophysics Data System (ADS)

Wilhelm, Jennifer; Jackson, C.; Toland, M. D.; Cole, M.; Wilhelm, R. J.

2013-06-01

Many astronomical concepts cannot be understood without a developed understanding of four spatial-mathematics domains defined as follows: a) Geometric Spatial Visualization (GSV) - Visualizing the geometric features of a system as it appears above, below, and within the system’s plane; b) Spatial Projection (SP) - Projecting to a different location and visualizing from that global perspective; c) Cardinal Directions (CD) - Distinguishing directions (N, S, E, W) in order to document an object’s vector position in space; and d) Periodic Patterns - (PP) Recognizing occurrences at regular intervals of time and/or space. For this study, differences were examined between groups of sixth grade students’ spatial-scientific development pre/post implementation of an Earth/Space unit. Treatment teachers employed a NASA-based curriculum (Realistic Explorations in Astronomical Learning), while control teachers implemented their regular Earth/Space units. A 2-level hierarchical linear model was used to evaluate student performance on the Lunar Phases Concept Inventory (LPCI) and four spatial-mathematics domains, while controlling for two variables (gender and ethnicity) at the student level and one variable (teaching experience) at the teacher level. Overall LPCI results show pre-test scores predicted post-test scores, boys performed better than girls, and Whites performed better than non-Whites. We also compared experimental and control groups’ by spatial-mathematics domain outcomes. For GSV, it was found that boys, in general, tended to have higher GSV post-scores. For domains CD and SP, no statistically significant differences were observed. PP results show Whites performed better than non-Whites. Also for PP, a significant cross-level interaction term (gender-treatment) was observed, which means differences in control and experimental groups are dependent on students’ gender. These findings can be interpreted as: (a) the experimental girls scored higher than the control girls and/or (b) the control group displayed a gender gap in favor of boys while no gender gap was displayed within the experimental group.

The Classical Version of Stokes' Theorem Revisited

ERIC Educational Resources Information Center

Markvorsen, Steen

2008-01-01

Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

A Lesson in Vectors "Plain" and Simple

ERIC Educational Resources Information Center

Bradshaw, David M.

2004-01-01

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

A Mathematical Motivation for Complex-Valued Convolutional Networks.

PubMed

Tygert, Mark; Bruna, Joan; Chintala, Soumith; LeCun, Yann; Piantino, Serkan; Szlam, Arthur

2016-05-01

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach.

PubMed

Xenidou-Dervou, Iro; Van Luit, Johannes E H; Kroesbergen, Evelyn H; Friso-van den Bos, Ilona; Jonkman, Lisa M; van der Schoot, Menno; van Lieshout, Ernest C D M

2018-04-24

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 children's domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children's starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children's initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children's individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one's mathematical success. We argue the need for more research focus on explaining children's individual growth rates in mathematics achievement. © 2018 John Wiley & Sons Ltd.

Assessing Attitudes toward Mathematics across Teacher Education Contexts

ERIC Educational Resources Information Center

Jong, Cindy; Hodges, Thomas E.

2015-01-01

This article reports on the development of attitudes toward mathematics among pre-service elementary teachers (n = 146) in relation to their experiences as K-12 learners of mathematics and experiences within a teacher education program. Using a combination of the Rasch Rating Scale Model and traditional parametric analyses, results indicate that…

A Framework for Authenticity in the Mathematics and Statistics Classroom

ERIC Educational Resources Information Center

Garrett, Lauretta; Huang, Li; Charleton, Maria Calhoun

2016-01-01

Authenticity is a term commonly used in reference to pedagogical and curricular qualities of mathematics teaching and learning, but its use lacks a coherent framework. The work of researchers in engineering education provides such a framework. Authentic qualities of mathematics teaching and learning are fit within a model described by Strobel,…

Angular motion estimation using dynamic models in a gyro-free inertial measurement unit.

PubMed

Edwan, Ezzaldeen; Knedlik, Stefan; Loffeld, Otmar

2012-01-01

In this paper, we summarize the results of using dynamic models borrowed from tracking theory in describing the time evolution of the state vector to have an estimate of the angular motion in a gyro-free inertial measurement unit (GF-IMU). The GF-IMU is a special type inertial measurement unit (IMU) that uses only a set of accelerometers in inferring the angular motion. Using distributed accelerometers, we get an angular information vector (AIV) composed of angular acceleration and quadratic angular velocity terms. We use a Kalman filter approach to estimate the angular velocity vector since it is not expressed explicitly within the AIV. The bias parameters inherent in the accelerometers measurements' produce a biased AIV and hence the AIV bias parameters are estimated within an augmented state vector. Using dynamic models, the appended bias parameters of the AIV become observable and hence we can have unbiased angular motion estimate. Moreover, a good model is required to extract the maximum amount of information from the observation. Observability analysis is done to determine the conditions for having an observable state space model. For higher grades of accelerometers and under relatively higher sampling frequency, the error of accelerometer measurements is dominated by the noise error. Consequently, simulations are conducted on two models, one has bias parameters appended in the state space model and the other is a reduced model without bias parameters.

Angular Motion Estimation Using Dynamic Models in a Gyro-Free Inertial Measurement Unit

PubMed Central

Edwan, Ezzaldeen; Knedlik, Stefan; Loffeld, Otmar

2012-01-01

In this paper, we summarize the results of using dynamic models borrowed from tracking theory in describing the time evolution of the state vector to have an estimate of the angular motion in a gyro-free inertial measurement unit (GF-IMU). The GF-IMU is a special type inertial measurement unit (IMU) that uses only a set of accelerometers in inferring the angular motion. Using distributed accelerometers, we get an angular information vector (AIV) composed of angular acceleration and quadratic angular velocity terms. We use a Kalman filter approach to estimate the angular velocity vector since it is not expressed explicitly within the AIV. The bias parameters inherent in the accelerometers measurements' produce a biased AIV and hence the AIV bias parameters are estimated within an augmented state vector. Using dynamic models, the appended bias parameters of the AIV become observable and hence we can have unbiased angular motion estimate. Moreover, a good model is required to extract the maximum amount of information from the observation. Observability analysis is done to determine the conditions for having an observable state space model. For higher grades of accelerometers and under relatively higher sampling frequency, the error of accelerometer measurements is dominated by the noise error. Consequently, simulations are conducted on two models, one has bias parameters appended in the state space model and the other is a reduced model without bias parameters. PMID:22778586

Research on bearing fault diagnosis of large machinery based on mathematical morphology

NASA Astrophysics Data System (ADS)

Wang, Yu

2018-04-01

To study the automatic diagnosis of large machinery fault based on support vector machine, combining the four common faults of the large machinery, the support vector machine is used to classify and identify the fault. The extracted feature vectors are entered. The feature vector is trained and identified by multi - classification method. The optimal parameters of the support vector machine are searched by trial and error method and cross validation method. Then, the support vector machine is compared with BP neural network. The results show that the support vector machines are short in time and high in classification accuracy. It is more suitable for the research of fault diagnosis in large machinery. Therefore, it can be concluded that the training speed of support vector machines (SVM) is fast and the performance is good.

The discursive production of classroom mathematics

NASA Astrophysics Data System (ADS)

Smith, Kim; Hodson, Elaine; Brown, Tony

2013-09-01

School mathematics is a function of its discursive environment where the language being used formats mathematical activity. The paper explores this theme through an extended example in which the conduct of mathematical teaching and learning is restricted by regulative educational policies. It considers how mathematics is discursively produced by student teachers within an employment-based model of teacher education in England where there is a low university input. It is argued that teacher reflections on mathematical learning and teaching within the course are patterned discursively in line with formal curriculum framings, assessment requirements and the local demands of their placement school. Both teachers and students are subject to regulative discourses that shape their actions and as a consequence this regulation influences the forms of mathematical activity that can take place. It is shown how university sessions can provide a limited critical platform from which to interrogate these restrictions and renegotiate them.

Industrial Prep, Volume Four, Junior Year--Contents: Mathematics and Guidance.

ERIC Educational Resources Information Center

Hackensack Public Schools, NJ.

As part of a 3-year comprehensive interdisciplinary program in industrial preparation for vocational students, this 11th Grade teaching guide consists of units on technical mathematics and guidance. Designed as supportive material for related physics and English curriculums, the first four sections of Volume 4 on algebra, vectors, simple machines,…

Mathematical models application for mapping soils spatial distribution on the example of the farm from the North of Udmurt Republic of Russia

NASA Astrophysics Data System (ADS)

Dokuchaev, P. M.; Meshalkina, J. L.; Yaroslavtsev, A. M.

2018-01-01

Comparative analysis of soils geospatial modeling using multinomial logistic regression, decision trees, random forest, regression trees and support vector machines algorithms was conducted. The visual interpretation of the digital maps obtained and their comparison with the existing map, as well as the quantitative assessment of the individual soil groups detection overall accuracy and of the models kappa showed that multiple logistic regression, support vector method, and random forest models application with spatial prediction of the conditional soil groups distribution can be reliably used for mapping of the study area. It has shown the most accurate detection for sod-podzolics soils (Phaeozems Albic) lightly eroded and moderately eroded soils. In second place, according to the mean overall accuracy of the prediction, there are sod-podzolics soils - non-eroded and warp one, as well as sod-gley soils (Umbrisols Gleyic) and alluvial soils (Fluvisols Dystric, Umbric). Heavy eroded sod-podzolics and gray forest soils (Phaeozems Albic) were detected by methods of automatic classification worst of all.

Bayesian data assimilation provides rapid decision support for vector-borne diseases

PubMed Central

Jewell, Chris P.; Brown, Richard G.

2015-01-01

Predicting the spread of vector-borne diseases in response to incursions requires knowledge of both host and vector demographics in advance of an outbreak. Although host population data are typically available, for novel disease introductions there is a high chance of the pathogen using a vector for which data are unavailable. This presents a barrier to estimating the parameters of dynamical models representing host–vector–pathogen interaction, and hence limits their ability to provide quantitative risk forecasts. The Theileria orientalis (Ikeda) outbreak in New Zealand cattle demonstrates this problem: even though the vector has received extensive laboratory study, a high degree of uncertainty persists over its national demographic distribution. Addressing this, we develop a Bayesian data assimilation approach whereby indirect observations of vector activity inform a seasonal spatio-temporal risk surface within a stochastic epidemic model. We provide quantitative predictions for the future spread of the epidemic, quantifying uncertainty in the model parameters, case infection times and the disease status of undetected infections. Importantly, we demonstrate how our model learns sequentially as the epidemic unfolds and provide evidence for changing epidemic dynamics through time. Our approach therefore provides a significant advance in rapid decision support for novel vector-borne disease outbreaks. PMID:26136225

An Improved Azimuth Angle Estimation Method with a Single Acoustic Vector Sensor Based on an Active Sonar Detection System

PubMed Central

Zhao, Anbang; Ma, Lin; Ma, Xuefei; Hui, Juan

2017-01-01

In this paper, an improved azimuth angle estimation method with a single acoustic vector sensor (AVS) is proposed based on matched filtering theory. The proposed method is mainly applied in an active sonar detection system. According to the conventional passive method based on complex acoustic intensity measurement, the mathematical and physical model of this proposed method is described in detail. The computer simulation and lake experiments results indicate that this method can realize the azimuth angle estimation with high precision by using only a single AVS. Compared with the conventional method, the proposed method achieves better estimation performance. Moreover, the proposed method does not require complex operations in frequency-domain and achieves computational complexity reduction. PMID:28230763

Assessing the Role of Climate Change in Malaria Transmission in Africa.

PubMed

Ngarakana-Gwasira, E T; Bhunu, C P; Masocha, M; Mashonjowa, E

2016-01-01

The sensitivity of vector borne diseases like malaria to climate continues to raise considerable concern over the implications of climate change on future disease dynamics. The problem of malaria vectors shifting from their traditional locations to invade new zones is of important concern. A mathematical model incorporating rainfall and temperature is constructed to study the transmission dynamics of malaria. The reproduction number obtained is applied to gridded temperature and rainfall datasets for baseline climate and future climate with aid of GIS. As a result of climate change, malaria burden is likely to increase in the tropics, the highland regions, and East Africa and along the northern limit of falciparum malaria. Falciparum malaria will spread into the African highlands; however it is likely to die out at the southern limit of the disease.

Simulations of a epidemic model with parameters variation analysis for the dengue fever

NASA Astrophysics Data System (ADS)

Jardim, C. L. T. F.; Prates, D. B.; Silva, J. M.; Ferreira, L. A. F.; Kritz, M. V.

2015-09-01

Mathematical models can be widely found in the literature for describing and analyzing epidemics. The models that use differential equations to represent mathematically such description are specially sensible to parameters involved in the modelling. In this work, an already developed model, called SIR, is analyzed when applied to a scenario of a dengue fever epidemic. Such choice is powered by the existence of useful tools presented by a variation of this original model, which allow an inclusion of different aspects of the dengue fever disease, as its seasonal characteristics, the presence of more than one strain of the vector and of the biological factor of cross-immunity. The analysis and results interpretation are performed through numerical solutions of the model in question, and a special attention is given to the different solutions generated by the use of different values for the parameters present in this model. Slight variations are performed either dynamically or statically in those parameters, mimicking hypothesized changes in the biological scenario of this simulation and providing a source of evaluation of how those changes would affect the outcomes of the epidemic in a population.

The Use of Mathematical Modelling for Improving the Tissue Engineering of Organs and Stem Cell Therapy.

PubMed

Lemon, Greg; Sjoqvist, Sebastian; Lim, Mei Ling; Feliu, Neus; Firsova, Alexandra B; Amin, Risul; Gustafsson, Ylva; Stuewer, Annika; Gubareva, Elena; Haag, Johannes; Jungebluth, Philipp; Macchiarini, Paolo

2016-01-01

Regenerative medicine is a multidisciplinary field where continued progress relies on the incorporation of a diverse set of technologies from a wide range of disciplines within medicine, science and engineering. This review describes how one such technique, mathematical modelling, can be utilised to improve the tissue engineering of organs and stem cell therapy. Several case studies, taken from research carried out by our group, ACTREM, demonstrate the utility of mechanistic mathematical models to help aid the design and optimisation of protocols in regenerative medicine.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Advanced computer techniques for inverse modeling of electric current in cardiac tissue

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

Hutchinson, S.A.; Romero, L.A.; Diegert, C.F.

1996-08-01

For many years, ECG`s and vector cardiograms have been the tools of choice for non-invasive diagnosis of cardiac conduction problems, such as found in reentrant tachycardia or Wolff-Parkinson-White (WPW) syndrome. Through skillful analysis of these skin-surface measurements of cardiac generated electric currents, a physician can deduce the general location of heart conduction irregularities. Using a combination of high-fidelity geometry modeling, advanced mathematical algorithms and massively parallel computing, Sandia`s approach would provide much more accurate information and thus allow the physician to pinpoint the source of an arrhythmia or abnormal conduction pathway.

The two-dimensional Monte Carlo: a new methodologic paradigm for dose reconstruction for epidemiological studies.

PubMed

Simon, Steven L; Hoffman, F Owen; Hofer, Eduard

2015-01-01

Retrospective dose estimation, particularly dose reconstruction that supports epidemiological investigations of health risk, relies on various strategies that include models of physical processes and exposure conditions with detail ranging from simple to complex. Quantification of dose uncertainty is an essential component of assessments for health risk studies since, as is well understood, it is impossible to retrospectively determine the true dose for each person. To address uncertainty in dose estimation, numerical simulation tools have become commonplace and there is now an increased understanding about the needs and what is required for models used to estimate cohort doses (in the absence of direct measurement) to evaluate dose response. It now appears that for dose-response algorithms to derive the best, unbiased estimate of health risk, we need to understand the type, magnitude and interrelationships of the uncertainties of model assumptions, parameters and input data used in the associated dose estimation models. Heretofore, uncertainty analysis of dose estimates did not always properly distinguish between categories of errors, e.g., uncertainty that is specific to each subject (i.e., unshared error), and uncertainty of doses from a lack of understanding and knowledge about parameter values that are shared to varying degrees by numbers of subsets of the cohort. While mathematical propagation of errors by Monte Carlo simulation methods has been used for years to estimate the uncertainty of an individual subject's dose, it was almost always conducted without consideration of dependencies between subjects. In retrospect, these types of simple analyses are not suitable for studies with complex dose models, particularly when important input data are missing or otherwise not available. The dose estimation strategy presented here is a simulation method that corrects the previous deficiencies of analytical or simple Monte Carlo error propagation methods and is termed, due to its capability to maintain separation between shared and unshared errors, the two-dimensional Monte Carlo (2DMC) procedure. Simply put, the 2DMC method simulates alternative, possibly true, sets (or vectors) of doses for an entire cohort rather than a single set that emerges when each individual's dose is estimated independently from other subjects. Moreover, estimated doses within each simulated vector maintain proper inter-relationships such that the estimated doses for members of a cohort subgroup that share common lifestyle attributes and sources of uncertainty are properly correlated. The 2DMC procedure simulates inter-individual variability of possibly true doses within each dose vector and captures the influence of uncertainty in the values of dosimetric parameters across multiple realizations of possibly true vectors of cohort doses. The primary characteristic of the 2DMC approach, as well as its strength, are defined by the proper separation between uncertainties shared by members of the entire cohort or members of defined cohort subsets, and uncertainties that are individual-specific and therefore unshared.

Bayesian data assimilation provides rapid decision support for vector-borne diseases.

PubMed

Jewell, Chris P; Brown, Richard G

2015-07-06

Predicting the spread of vector-borne diseases in response to incursions requires knowledge of both host and vector demographics in advance of an outbreak. Although host population data are typically available, for novel disease introductions there is a high chance of the pathogen using a vector for which data are unavailable. This presents a barrier to estimating the parameters of dynamical models representing host-vector-pathogen interaction, and hence limits their ability to provide quantitative risk forecasts. The Theileria orientalis (Ikeda) outbreak in New Zealand cattle demonstrates this problem: even though the vector has received extensive laboratory study, a high degree of uncertainty persists over its national demographic distribution. Addressing this, we develop a Bayesian data assimilation approach whereby indirect observations of vector activity inform a seasonal spatio-temporal risk surface within a stochastic epidemic model. We provide quantitative predictions for the future spread of the epidemic, quantifying uncertainty in the model parameters, case infection times and the disease status of undetected infections. Importantly, we demonstrate how our model learns sequentially as the epidemic unfolds and provide evidence for changing epidemic dynamics through time. Our approach therefore provides a significant advance in rapid decision support for novel vector-borne disease outbreaks. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Designing Online Learning for Developing Pre-Service Teachers' Capabilities in Mathematical Modelling and Applications

ERIC Educational Resources Information Center

Geiger, Vince; Date-Huxtable, Liz; Ahlip, Rehez; Herberstein, Marie; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian; Mulligan, Joanne

2016-01-01

The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project--"Modelling the present: Predicting the future." The module was realised through an interdisciplinary collaboration, among mathematicians, scientists and mathematics and science educators that…

Schoolwide Mathematics Achievement within the Gifted Cluster Grouping Model

ERIC Educational Resources Information Center

Brulles, Dina; Peters, Scott J.; Saunders, Rachel

2012-01-01

An increasing number of schools are implementing gifted cluster grouping models as a cost-effective way to provide gifted services. This study is an example of comparative action research in the form of a quantitative case study that focused on mathematic achievement for nongifted students in a district that incorporated a schoolwide cluster…

Scaling up complexity in host-pathogens interaction models. Comment on "Coupled disease-behavior dynamics on complex networks: A review" by Z. Wang et al.

NASA Astrophysics Data System (ADS)

Aguiar, Maíra

2015-12-01

Caused by micro-organisms that are pathogenic to the host, infectious diseases have caused debilitation and premature death to large portions of the human population, leading to serious social-economic concerns. The persistence and increase in the occurrence of infectious diseases as well the emergence or resurgence of vector-borne diseases are closely related with demographic factors such as the uncontrolled urbanization and remarkable population growth, political, social and economical changes, deforestation, development of resistance to insecticides and drugs and increased human travel. In recent years, mathematical modeling became an important tool for the understanding of infectious disease epidemiology and dynamics, addressing ideas about the components of host-pathogen interactions. Acting as a possible tool to understand, predict the spread of infectious diseases these models are also used to evaluate the introduction of intervention strategies like vector control and vaccination. Many scientific papers have been published recently on these topics, and most of the models developed try to incorporate factors focusing on several different aspects of the disease (and eventually biological aspects of the vector), which can imply rich dynamic behavior even in the most basic dynamical models. As one example to be cited, there is a minimalistic dengue model that has shown rich dynamic structures, with bifurcations (Hopf, pitchfork, torus and tangent bifurcations) up to chaotic attractors in unexpected parameter regions [1,2], which was able to describe the large fluctuations observed in empirical outbreak data [3,4].

Biodiversity Can Help Prevent Malaria Outbreaks in Tropical Forests

PubMed Central

Laporta, Gabriel Zorello; de Prado, Paulo Inácio Knegt Lopez; Kraenkel, Roberto André; Coutinho, Renato Mendes; Sallum, Maria Anice Mureb

2013-01-01

Background Plasmodium vivax is a widely distributed, neglected parasite that can cause malaria and death in tropical areas. It is associated with an estimated 80–300 million cases of malaria worldwide. Brazilian tropical rain forests encompass host- and vector-rich communities, in which two hypothetical mechanisms could play a role in the dynamics of malaria transmission. The first mechanism is the dilution effect caused by presence of wild warm-blooded animals, which can act as dead-end hosts to Plasmodium parasites. The second is diffuse mosquito vector competition, in which vector and non-vector mosquito species compete for blood feeding upon a defensive host. Considering that the World Health Organization Malaria Eradication Research Agenda calls for novel strategies to eliminate malaria transmission locally, we used mathematical modeling to assess those two mechanisms in a pristine tropical rain forest, where the primary vector is present but malaria is absent. Methodology/Principal Findings The Ross–Macdonald model and a biodiversity-oriented model were parameterized using newly collected data and data from the literature. The basic reproduction number () estimated employing Ross–Macdonald model indicated that malaria cases occur in the study location. However, no malaria cases have been reported since 1980. In contrast, the biodiversity-oriented model corroborated the absence of malaria transmission. In addition, the diffuse competition mechanism was negatively correlated with the risk of malaria transmission, which suggests a protective effect provided by the forest ecosystem. There is a non-linear, unimodal correlation between the mechanism of dead-end transmission of parasites and the risk of malaria transmission, suggesting a protective effect only under certain circumstances (e.g., a high abundance of wild warm-blooded animals). Conclusions/Significance To achieve biological conservation and to eliminate Plasmodium parasites in human populations, the World Health Organization Malaria Eradication Research Agenda should take biodiversity issues into consideration. PMID:23556023

System Dynamics based Dengue modeling environment to simulate evolution of Dengue infection under different climate scenarios

NASA Astrophysics Data System (ADS)

Anwar, R.; Khan, R.; Usmani, M.; Colwell, R. R.; Jutla, A.

2017-12-01

Vector borne infectious diseases such as Dengue, Zika and Chikungunya remain a public health threat. An estimate of the World Health Organization (WHO) suggests that about 2.5 billion people, representing ca. 40% of human population,are at increased risk of dengue; with more than 100 million infection cases every year. Vector-borne infections cannot be eradicated since disease causing pathogens survive in the environment. Over the last few decades dengue infection has been reported in more than 100 countries and is expanding geographically. Female Ae. Aegypti mosquito, the daytime active and a major vector for dengue virus, is associated with urban population density and regional climatic processes. However, mathematical quantification of relationships on abundance of vectors and climatic processes remain a challenge, particularly in regions where such data are not routinely collected. Here, using system dynamics based feedback mechanism, an algorithm integrating knowledge from entomological, meteorological and epidemiological processes is developed that has potential to provide ensemble simulations on risk of occurrence of dengue infection in human population. Using dataset from satellite remote sensing, the algorithm was calibrated and validated using actual dengue case data of Iquitos, Peru. We will show results on model capabilities in capturing initiation and peak in the observed time series. In addition, results from several simulation scenarios under different climatic conditions will be discussed.

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

NASA Astrophysics Data System (ADS)

Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

The Brian Simulator

PubMed Central

Goodman, Dan F. M.; Brette, Romain

2009-01-01

“Brian” is a simulator for spiking neural networks (http://www.briansimulator.org). The focus is on making the writing of simulation code as quick and easy as possible for the user, and on flexibility: new and non-standard models are no more difficult to define than standard ones. This allows scientists to spend more time on the details of their models, and less on their implementation. Neuron models are defined by writing differential equations in standard mathematical notation, facilitating scientific communication. Brian is written in the Python programming language, and uses vector-based computation to allow for efficient simulations. It is particularly useful for neuroscientific modelling at the systems level, and for teaching computational neuroscience. PMID:20011141

Early Math Trajectories: Low-Income Children's Mathematics Knowledge From Ages 4 to 11.

PubMed

Rittle-Johnson, Bethany; Fyfe, Emily R; Hofer, Kerry G; Farran, Dale C

2017-09-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math topics, as well as potential pathways from preschool to middle grades mathematics achievement. In preschool, nonsymbolic quantity, counting, and patterning knowledge predicted fifth-grade mathematics achievement. By the end of first grade, symbolic mapping, calculation, and patterning knowledge were the important predictors. Furthermore, the first-grade predictors mediated the relation between preschool math knowledge and fifth-grade mathematics achievement. Findings support the early math trajectories model among low-income children. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

Mathematical simulation of convective-radiative heat transfer in a ventilated rectangular cavity with consideration of internal mass transfer

NASA Astrophysics Data System (ADS)

Sheremet, M. A.; Shishkin, N. I.

2012-07-01

Mathematical simulation of the nonstationary regimes of heat-and-mass transfer in a ventilated rectangular cavity with heat-conducting walls of finite thickness in the presence of a heat-generating element of constant temperature has been carried out with account for the radiative heat transfer in the Rosseland approximation. As mechanisms of energy transfer in this cavity, the combined convection and the thermal radiation in the gas space of the cavity and the heat conduction in the elements of its fencing solid shell were considered. The mathematical model formulated in the dimensionless stream function-vorticity vector-temperature-concentration variables was realized numerically with the use of the finite-difference method. The streamline, temperature-field, and concentration distributions reflecting the influence of the Rayleigh number (Ra = 104, 105, 106), the nonstationarity (0 < τ ≤ 1000), and the optical thickness of the medium (τλ = 50, 100, 200) on the regimes of the gas flow and the heat-and-mass transfer in the cavity have been obtained.

Mathematical Modeling for Scrub Typhus and Its Implications for Disease Control.

PubMed

Min, Kyung Duk; Cho, Sung Il

2018-03-19

The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease. We developed mathematical models of ordinary differential equations including human, rodent and mite groups. Two models, including simple and complex models, were developed, and all parameters employed in the models were adopted from previous articles that represent epidemiological situations in the Republic of Korea. The simulation results showed that the force of infection at the equilibrium state under the simple model was 0.236 (per 100,000 person-months), and that in the complex model was 26.796 (per 100,000 person-months). Sensitivity analyses indicated that the most influential parameters were rodent and mite populations and contact rate between them for the simple model, and trans-ovarian transmission for the complex model. In both models, contact rate between humans and mites is more influential than morality rate of rodent and mite group. The results indicate that the effect of controlling either rodents or mites could be limited, and reducing the contact rate between humans and mites is more practical and effective strategy. However, the current level of control would be insufficient relative to the growing mite population. © 2018 The Korean Academy of Medical Sciences.

A Mathematical and Sociological Analysis of Google Search Algorithm

DTIC Science & Technology

2013-01-16

through the collective intelligence of the web to determine a page’s importance. Let v be a vector of RN with N ≥ 8 billion. Any unit vector in RN is...scrolled up by some artifical hits. Aknowledgment: The authors would like to thank Dr. John Lavery for his encouragement and support which enable them to

Usability Evaluation of an Augmented Reality System for Teaching Euclidean Vectors

ERIC Educational Resources Information Center

Martin-Gonzalez, Anabel; Chi-Poot, Angel; Uc-Cetina, Victor

2016-01-01

Augmented reality (AR) is one of the emerging technologies that has demonstrated to be an efficient technological tool to enhance learning techniques. In this paper, we describe the development and evaluation of an AR system for teaching Euclidean vectors in physics and mathematics. The goal of this pedagogical tool is to facilitate user's…

Data-driven identification of potential Zika virus vectors

PubMed Central

Evans, Michelle V; Dallas, Tad A; Han, Barbara A; Murdock, Courtney C; Drake, John M

2017-01-01

Zika is an emerging virus whose rapid spread is of great public health concern. Knowledge about transmission remains incomplete, especially concerning potential transmission in geographic areas in which it has not yet been introduced. To identify unknown vectors of Zika, we developed a data-driven model linking vector species and the Zika virus via vector-virus trait combinations that confer a propensity toward associations in an ecological network connecting flaviviruses and their mosquito vectors. Our model predicts that thirty-five species may be able to transmit the virus, seven of which are found in the continental United States, including Culex quinquefasciatus and Cx. pipiens. We suggest that empirical studies prioritize these species to confirm predictions of vector competence, enabling the correct identification of populations at risk for transmission within the United States. DOI: http://dx.doi.org/10.7554/eLife.22053.001 PMID:28244371

Data discretization for novel resource discovery in large medical data sets.

PubMed Central

Benoît, G.; Andrews, J. E.

2000-01-01

This paper is motivated by the problems of dealing with large data sets in information retrieval. The authors suggest an information retrieval framework based on mathematical principles to organize and permit end-user manipulation of a retrieval set. By adjusting through the interface the weights and types of relationships between query and set members, it is possible to expose unanticipated, novel relationships between the query/document pair. The retrieval set as a whole is parsed into discrete concept-oriented subsets (based on within-set similarity measures) and displayed on screen as interactive "graphic nodes" in an information space, distributed at first based on the vector model (similarity measure of set to query). The result is a visualized map wherein it is possible to identify main concept regions and multiple sub-regions as dimensions of the same data. Users may examine the membership within sub-regions. Based on this framework, a data visualization user interface was designed to encourage users to work with the data on multiple levels to find novel relationships between the query and retrieval set members. Space constraints prohibit addressing all aspects of this project. PMID:11079845

Predicting the Impact of Intervention Strategies for Sleeping Sickness in Two High-Endemicity Health Zones of the Democratic Republic of Congo.

PubMed

Rock, Kat S; Torr, Steve J; Lumbala, Crispin; Keeling, Matt J

2017-01-01

Two goals have been set for Gambian human African trypanosomiasis (HAT), the first is to achieve elimination as a public health problem in 90% of foci by 2020, and the second is to achieve zero transmission globally by 2030. It remains unclear if certain HAT hotspots could achieve elimination as a public health problem by 2020 and, of greater concern, it appears that current interventions to control HAT in these areas may not be sufficient to achieve zero transmission by 2030. A mathematical model of disease dynamics was used to assess the potential impact of changing the intervention strategy in two high-endemicity health zones of Kwilu province, Democratic Republic of Congo. Six key strategies and twelve variations were considered which covered a range of recruitment strategies for screening and vector control. It was found that effectiveness of HAT screening could be improved by increasing effort to recruit high-risk groups for screening. Furthermore, seven proposed strategies which included vector control were predicted to be sufficient to achieve an incidence of less than 1 reported case per 10,000 people by 2020 in the study region. All vector control strategies simulated reduced transmission enough to meet the 2030 goal, even if vector control was only moderately effective (60% tsetse population reduction). At this level of control the full elimination threshold was expected to be met within six years following the start of the change in strategy and over 6000 additional cases would be averted between 2017 and 2030 compared to current screening alone. It is recommended that a two-pronged strategy including both enhanced active screening and tsetse control is implemented in this region and in other persistent HAT foci to ensure the success of the control programme and meet the 2030 elimination goal for HAT.

Predicting the Impact of Intervention Strategies for Sleeping Sickness in Two High-Endemicity Health Zones of the Democratic Republic of Congo

PubMed Central

Torr, Steve J.; Lumbala, Crispin; Keeling, Matt J.

2017-01-01

Two goals have been set for Gambian human African trypanosomiasis (HAT), the first is to achieve elimination as a public health problem in 90% of foci by 2020, and the second is to achieve zero transmission globally by 2030. It remains unclear if certain HAT hotspots could achieve elimination as a public health problem by 2020 and, of greater concern, it appears that current interventions to control HAT in these areas may not be sufficient to achieve zero transmission by 2030. A mathematical model of disease dynamics was used to assess the potential impact of changing the intervention strategy in two high-endemicity health zones of Kwilu province, Democratic Republic of Congo. Six key strategies and twelve variations were considered which covered a range of recruitment strategies for screening and vector control. It was found that effectiveness of HAT screening could be improved by increasing effort to recruit high-risk groups for screening. Furthermore, seven proposed strategies which included vector control were predicted to be sufficient to achieve an incidence of less than 1 reported case per 10,000 people by 2020 in the study region. All vector control strategies simulated reduced transmission enough to meet the 2030 goal, even if vector control was only moderately effective (60% tsetse population reduction). At this level of control the full elimination threshold was expected to be met within six years following the start of the change in strategy and over 6000 additional cases would be averted between 2017 and 2030 compared to current screening alone. It is recommended that a two-pronged strategy including both enhanced active screening and tsetse control is implemented in this region and in other persistent HAT foci to ensure the success of the control programme and meet the 2030 elimination goal for HAT. PMID:28056016

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Hybrid NN/SVM Computational System for Optimizing Designs

NASA Technical Reports Server (NTRS)

Rai, Man Mohan

2009-01-01

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Students' difficulties with vector calculus in electrodynamics

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-12-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.

A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models

NASA Astrophysics Data System (ADS)

Burger, Martin; Dirks, Hendrik; Frerking, Lena; Hauptmann, Andreas; Helin, Tapio; Siltanen, Samuli

2017-12-01

In this paper we study the reconstruction of moving object densities from undersampled dynamic x-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications, i.e. we do not assume to have a full Radon transform in each time step, but only projections in few angular directions. This restriction enforces a space-time reconstruction, which we perform by incorporating physical motion models and regularization of motion vectors in a variational framework. The methodology of optical flow, which is one of the most common methods to estimate motion between two images, is utilized to formulate a joint variational model for reconstruction and motion estimation. We provide a basic mathematical analysis of the forward model and the variational model for the image reconstruction. Moreover, we discuss the efficient numerical minimization based on alternating minimizations between images and motion vectors. A variety of results are presented for simulated and real measurement data with different sampling strategy. A key observation is that random sampling combined with our model allows reconstructions of similar amount of measurements and quality as a single static reconstruction.

Mathematics in the Making: Mapping Verbal Discourse in Polya's "Let Us Teach Guessing" Lesson

ERIC Educational Resources Information Center

Truxaw, Mary P.; DeFranco, Thomas C.

2007-01-01

This paper describes a detailed analysis of verbal discourse within an exemplary mathematics lesson--that is, George Polya teaching in the Mathematics Association of America [MAA] video classic, "Let Us Teach Guessing" (1966). The results of the analysis reveal an inductive model of teaching that represents recursive cycles rather than linear…

Identifying Subtypes among Children with Developmental Coordination Disorder and Mathematical Learning Disabilities, Using Model-Based Clustering

ERIC Educational Resources Information Center

Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie

2015-01-01

A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…

Integrating STEM in Elementary Classrooms Using Model-Eliciting Activities: Responsive Professional Development for Mathematics Coaches and Teachers

ERIC Educational Resources Information Center

Baker, Courtney K.; Galanti, Terrie M.

2017-01-01

Background: This research highlights a school-university collaboration to pilot a professional development framework for integrating STEM in K-6 mathematics classrooms in a mid-Atlantic suburban school division. Because mathematics within STEM integration is often characterized as the calculations or the data representations in science classrooms,…

Parental Characteristics and the Achievement Gap in Mathematics: Hierarchical Linear Modeling Analysis of Longitudinal Study of American Youth (LSAY)

ERIC Educational Resources Information Center

Shoraka, Mohammad; Arnold, Robert; Kim, Eun Sook; Salinitri, Geri; Kromrey, Jeffrey

2015-01-01

One of the most salient problems in education is the achievement gap. The researchers investigated the effects of parental education and parental occupations in science, technology, engineering, mathematics, or medical professions (STEMM) on the achievement gap in mathematics. Because students were nested within schools, two-level Hierarchical…

Modeling the geographic distribution of Ixodes scapularis and Ixodes pacificus (Acari: Ixodidae) in the contiguous United States

USGS Publications Warehouse

Hahn, Micah; Jarnevich, Catherine S.; Monaghan, Andrew J.; Eisen, Rebecca J.

2016-01-01

In addition to serving as vectors of several other human pathogens, the black-legged tick, Ixodes scapularis Say, and western black-legged tick, Ixodes pacificus Cooley and Kohls, are the primary vectors of the spirochete (Borrelia burgdorferi ) that causes Lyme disease, the most common vector-borne disease in the United States. Over the past two decades, the geographic range of I. pacificus has changed modestly while, in contrast, the I. scapularis range has expanded substantially, which likely contributes to the concurrent expansion in the distribution of human Lyme disease cases in the Northeastern, North-Central and Mid-Atlantic states. Identifying counties that contain suitable habitat for these ticks that have not yet reported established vector populations can aid in targeting limited vector surveillance resources to areas where tick invasion and potential human risk are likely to occur. We used county-level vector distribution information and ensemble modeling to map the potential distribution of I. scapularis and I. pacificus in the contiguous United States as a function of climate, elevation, and forest cover. Results show that I. pacificus is currently present within much of the range classified by our model as suitable for establishment. In contrast, environmental conditions are suitable for I. scapularis to continue expanding its range into northwestern Minnesota, central and northern Michigan, within the Ohio River Valley, and inland from the southeastern and Gulf coasts. Overall, our ensemble models show suitable habitat for I. scapularis in 441 eastern counties and for I. pacificus in 11 western counties where surveillance records have not yet supported classification of the counties as established.

A tool for multi-scale modelling of the renal nephron

PubMed Central

Nickerson, David P.; Terkildsen, Jonna R.; Hamilton, Kirk L.; Hunter, Peter J.

2011-01-01

We present the development of a tool, which provides users with the ability to visualize and interact with a comprehensive description of a multi-scale model of the renal nephron. A one-dimensional anatomical model of the nephron has been created and is used for visualization and modelling of tubule transport in various nephron anatomical segments. Mathematical models of nephron segments are embedded in the one-dimensional model. At the cellular level, these segment models use models encoded in CellML to describe cellular and subcellular transport kinetics. A web-based presentation environment has been developed that allows the user to visualize and navigate through the multi-scale nephron model, including simulation results, at the different spatial scales encompassed by the model description. The Zinc extension to Firefox is used to provide an interactive three-dimensional view of the tubule model and the native Firefox rendering of scalable vector graphics is used to present schematic diagrams for cellular and subcellular scale models. The model viewer is embedded in a web page that dynamically presents content based on user input. For example, when viewing the whole nephron model, the user might be presented with information on the various embedded segment models as they select them in the three-dimensional model view. Alternatively, the user chooses to focus the model viewer on a cellular model located in a particular nephron segment in order to view the various membrane transport proteins. Selecting a specific protein may then present the user with a description of the mathematical model governing the behaviour of that protein—including the mathematical model itself and various simulation experiments used to validate the model against the literature. PMID:22670210

Progressive Classification Using Support Vector Machines

NASA Technical Reports Server (NTRS)

Wagstaff, Kiri; Kocurek, Michael

2009-01-01

An algorithm for progressive classification of data, analogous to progressive rendering of images, makes it possible to compromise between speed and accuracy. This algorithm uses support vector machines (SVMs) to classify data. An SVM is a machine learning algorithm that builds a mathematical model of the desired classification concept by identifying the critical data points, called support vectors. Coarse approximations to the concept require only a few support vectors, while precise, highly accurate models require far more support vectors. Once the model has been constructed, the SVM can be applied to new observations. The cost of classifying a new observation is proportional to the number of support vectors in the model. When computational resources are limited, an SVM of the appropriate complexity can be produced. However, if the constraints are not known when the model is constructed, or if they can change over time, a method for adaptively responding to the current resource constraints is required. This capability is particularly relevant for spacecraft (or any other real-time systems) that perform onboard data analysis. The new algorithm enables the fast, interactive application of an SVM classifier to a new set of data. The classification process achieved by this algorithm is characterized as progressive because a coarse approximation to the true classification is generated rapidly and thereafter iteratively refined. The algorithm uses two SVMs: (1) a fast, approximate one and (2) slow, highly accurate one. New data are initially classified by the fast SVM, producing a baseline approximate classification. For each classified data point, the algorithm calculates a confidence index that indicates the likelihood that it was classified correctly in the first pass. Next, the data points are sorted by their confidence indices and progressively reclassified by the slower, more accurate SVM, starting with the items most likely to be incorrectly classified. The user can halt this reclassification process at any point, thereby obtaining the best possible result for a given amount of computation time. Alternatively, the results can be displayed as they are generated, providing the user with real-time feedback about the current accuracy of classification.

Mathematical estimation of the level of microbial contamination on spacecraft surfaces by volumetric air sampling

NASA Technical Reports Server (NTRS)

Oxborrow, G. S.; Roark, A. L.; Fields, N. D.; Puleo, J. R.

1974-01-01

Microbiological sampling methods presently used for enumeration of microorganisms on spacecraft surfaces require contact with easily damaged components. Estimation of viable particles on surfaces using air sampling methods in conjunction with a mathematical model would be desirable. Parameters necessary for the mathematical model are the effect of angled surfaces on viable particle collection and the number of viable cells per viable particle. Deposition of viable particles on angled surfaces closely followed a cosine function, and the number of viable cells per viable particle was consistent with a Poisson distribution. Other parameters considered by the mathematical model included deposition rate and fractional removal per unit time. A close nonlinear correlation between volumetric air sampling and airborne fallout on surfaces was established with all fallout data points falling within the 95% confidence limits as determined by the mathematical model.

Data-driven models to predict the elimination of sleeping sickness in former Equateur province of DRC.

PubMed

Rock, K S; Pandey, A; Ndeffo-Mbah, M L; Atkins, K E; Lumbala, C; Galvani, A; Keeling, M J

2017-03-01

Approaching disease elimination, it is crucial to be able to assess progress towards key objectives using quantitative tools. For Gambian human African trypanosomiasis (HAT), the ultimate goal is to stop transmission by 2030, while intermediary targets include elimination as a public health problem - defined as <1 new case per 10,000 inhabitants in 90% of foci, and <2000 reported cases by 2020. Using two independent mathematical models, this study assessed the achievability of these goals in the former Equateur province of the Democratic Republic of Congo, which historically had endemic levels of disease. The two deterministic models used different assumptions on disease progression, risk of infection and non-participation in screening, reflecting biological uncertainty. To validate the models a censor-fit-uncensor procedure was used to fit to health-zone level data from 2000 to 2012; initially the last six years were censored, then three and the final step utilised all data. The different model projections were used to evaluate the expected transmission and reporting for each health zone within each province under six intervention strategies using currently available tools. In 2012 there were 197 reported HAT cases in former Equateur reduced from 6828 in 2000, however this reflects lower active testing for HAT (1.3% of the population compared to 7.2%). Modelling results indicate that there are likely to be <300 reported cases in former Equateur in 2020 if screening continues at the mean level for 2000-2012 (6.2%), and <120 cases if vector control is introduced. Some health zones may fail to achieve <1 new case per 10,000 by 2020 without vector control, although most appear on track for this target using medical interventions alone. The full elimination goal will be harder to reach; between 39 and 54% of health zones analysed may have to improve their current medical-only strategy to stop transmission completely by 2030. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Characterization of vector stimulated Brillouin scattering gain over wide power range

NASA Astrophysics Data System (ADS)

Li, Yongqian; An, Qi; Li, Xiaojuan; Zhang, Lixin

2017-07-01

The wide range power dependence of vector stimulated Brillouin scattering (SBS) gain is theoretically and experimentally characterized by a mathematical model and measurement system based on the heterodyne pump-Stokes technique. The results show that SBS phase shift is much more tolerant of pump depletion than SBS amplitude gain, hence the performance improvement of the SBS-based distributed sensing system can be achieved by measuring the SBS phase shift spectrum. The discussion about the measured Brillouin spectrum width versus pump power at different Stokes powers reveals that the occurrence of nonnegligible pump depletion imposes a restriction on the determination of pump and Stokes powers in an SBS amplitude gain-based application system. The amplitude gain and phase shift of vector SBS gain increase with the increase of pump power and decrease with the increase of Stokes power, which indicates that the design strategy with smaller Stokes power and higher pump power is reasonable. And the measured center-asymmetry of the SBS phase shift spectrum is mainly caused by the nonlinear refractive index, which puts a limitation on the maximum pump power. The obtained results can provide a useful basis for the optimal design of practical vector SBS gain-based application systems.

Observations on Student Difficulties with Mathematics in Upper-Division Electricity and Magnetism

ERIC Educational Resources Information Center

Pepper, Rachel E.; Chasteen, Stephanie V.; Pollock, Steven J.; Perkins, Katherine K.

2012-01-01

We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss's law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students…

Reservoir host competence and the role of domestic and commensal hosts in the transmission of Trypanosoma cruzi.

PubMed

Gürtler, Ricardo E; Cardinal, M V

2015-11-01

We review the epidemiological role of domestic and commensal hosts of Trypanosoma cruzi using a quantitative approach, and compiled >400 reports on their natural infection. We link the theory underlying simple mathematical models of vector-borne parasite transmission to the types of evidence used for reservoir host identification: mean duration of infectious life; host infection and infectiousness; and host-vector contact. The infectiousness of dogs or cats most frequently exceeded that of humans. The host-feeding patterns of major vectors showed wide variability among and within triatomine species related to their opportunistic behavior and variable ecological, biological and social contexts. The evidence shows that dogs, cats, commensal rodents and domesticated guinea pigs are able to maintain T. cruzi in the absence of any other host species. They play key roles as amplifying hosts and sources of T. cruzi in many (peri)domestic transmission cycles covering a broad diversity of ecoregions, ecotopes and triatomine species: no other domestic animal plays that role. Dogs comply with the desirable attributes of natural sentinels and sometimes were a point of entry of sylvatic parasite strains. The controversies on the role of cats and other hosts illustrate the issues that hamper assessing the relative importance of reservoir hosts on the basis of fragmentary evidence. We provide various study cases of how eco-epidemiological and genetic-marker evidence helped to unravel transmission cycles and identify the implicated hosts. Keeping dogs, cats and rodents out of human sleeping quarters and reducing their exposure to triatomine bugs are predicted to strongly reduce transmission risks. Copyright © 2015. Published by Elsevier B.V.

Accurate Descriptions of Hot Flow Behaviors Across β Transus of Ti-6Al-4V Alloy by Intelligence Algorithm GA-SVR

NASA Astrophysics Data System (ADS)

Wang, Li-yong; Li, Le; Zhang, Zhi-hua

2016-09-01

Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.

Quantifying the roles of host movement and vector dispersal in the transmission of vector-borne diseases of livestock.

PubMed

Sumner, Tom; Orton, Richard J; Green, Darren M; Kao, Rowland R; Gubbins, Simon

2017-04-01

The role of host movement in the spread of vector-borne diseases of livestock has been little studied. Here we develop a mathematical framework that allows us to disentangle and quantify the roles of vector dispersal and livestock movement in transmission between farms. We apply this framework to outbreaks of bluetongue virus (BTV) and Schmallenberg virus (SBV) in Great Britain, both of which are spread by Culicoides biting midges and have recently emerged in northern Europe. For BTV we estimate parameters by fitting the model to outbreak data using approximate Bayesian computation, while for SBV we use previously derived estimates. We find that around 90% of transmission of BTV between farms is a result of vector dispersal, while for SBV this proportion is 98%. This difference is a consequence of higher vector competence and shorter duration of viraemia for SBV compared with BTV. For both viruses we estimate that the mean number of secondary infections per infected farm is greater than one for vector dispersal, but below one for livestock movements. Although livestock movements account for a small proportion of transmission and cannot sustain an outbreak on their own, they play an important role in establishing new foci of infection. However, the impact of restricting livestock movements on the spread of both viruses depends critically on assumptions made about the distances over which vector dispersal occurs. If vector dispersal occurs primarily at a local scale (99% of transmission occurs <25 km), movement restrictions are predicted to be effective at reducing spread, but if dispersal occurs frequently over longer distances (99% of transmission occurs <50 km) they are not.

Quantifying the roles of host movement and vector dispersal in the transmission of vector-borne diseases of livestock

PubMed Central

Sumner, Tom; Orton, Richard J.; Green, Darren M.; Kao, Rowland R.

2017-01-01

The role of host movement in the spread of vector-borne diseases of livestock has been little studied. Here we develop a mathematical framework that allows us to disentangle and quantify the roles of vector dispersal and livestock movement in transmission between farms. We apply this framework to outbreaks of bluetongue virus (BTV) and Schmallenberg virus (SBV) in Great Britain, both of which are spread by Culicoides biting midges and have recently emerged in northern Europe. For BTV we estimate parameters by fitting the model to outbreak data using approximate Bayesian computation, while for SBV we use previously derived estimates. We find that around 90% of transmission of BTV between farms is a result of vector dispersal, while for SBV this proportion is 98%. This difference is a consequence of higher vector competence and shorter duration of viraemia for SBV compared with BTV. For both viruses we estimate that the mean number of secondary infections per infected farm is greater than one for vector dispersal, but below one for livestock movements. Although livestock movements account for a small proportion of transmission and cannot sustain an outbreak on their own, they play an important role in establishing new foci of infection. However, the impact of restricting livestock movements on the spread of both viruses depends critically on assumptions made about the distances over which vector dispersal occurs. If vector dispersal occurs primarily at a local scale (99% of transmission occurs <25 km), movement restrictions are predicted to be effective at reducing spread, but if dispersal occurs frequently over longer distances (99% of transmission occurs <50 km) they are not. PMID:28369082

Silver release from nanocomposite Ag/alginate hydrogels in the presence of chloride ions: experimental results and mathematical modeling

NASA Astrophysics Data System (ADS)

Kostic, Danijela; Vidovic, Srđan; Obradovic, Bojana

2016-03-01

A stepwise experimental and mathematical modeling approach was used to assess silver release from nanocomposite Ag/alginate microbeads in wet and dried forms into water and into normal saline solution chosen as a simplified model for certain biological fluids (e.g., blood plasma, wound exudates, sweat, etc). Three phenomena were connected and mathematically described: diffusion of silver nanoparticles (AgNPs) within the alginate hydrogel, AgNP oxidation/dissolution and reaction with chloride ions, and diffusion of the resultant silver-chloride species. Mathematical modeling results agreed well with the experimental data with the AgNP diffusion coefficient estimated as 1.3 × 10-18 m2 s-1, while the first-order kinetic rate constant of AgNP oxidation/dissolution and diffusivity of silver-chloride species were shown to be inversely related. In specific, rapid rehydration and swelling of dry Ag/alginate microbeads induced fast AgNP oxidation/dissolution reaction with Cl- and AgCl precipitation within the microbeads with the lowest diffusivity of silver-chloride species compared to wet microbeads in normal saline. The proposed mathematical model provided an insight into the phenomena related to silver release from nanocomposite Ca-alginate hydrogels relevant for use of antimicrobial devices and established, at the same time, a basis for further in-depth studies of AgNP interactions in hydrogels in the presence of chloride ions.

A new vector radiative transfer model as a part of SCIATRAN 3.0 software package.

NASA Astrophysics Data System (ADS)

Rozanov, Alexei; Rozanov, Vladimir; Burrows, John P.

The SCIATRAN 3.0 package is a result of further development of the SCIATRAN 2.x software family which, similar to previous versions, comprises a radiative transfer model and a retrieval block. A major improvement was achieved in comparison to previous software versions by adding the vector mode to the radiative transfer model. Thus, the well-established Discrete Ordinate solver can now be run in the vector mode to calculate the scattered solar radiation including polarization, i.e., to simulate all four components of the Stockes vector. Similar to the scalar version, the simulations can be performed for any viewing geometry typical for atmospheric observations in the UV-Vis-NIR spectral range (nadir, limb, off-axis, etc.) as well as for any observer position within or outside the Earth's atmosphere. Similar to the precursor version, the new model is freely available for non-commercial use via the web page of the University of Bremen. In this presentation a short description of the software package, especially of the new vector radiative transfer model will be given, including remarks on the availability for the scientific community. Furthermore, comparisons to other vector models will be shown and some example problems will be considered where the polarization of the observed radiation must be accounted for to obtain high quality results.

Assessing dengue vaccination impact: Model challenges and future directions.

PubMed

Recker, Mario; Vannice, Kirsten; Hombach, Joachim; Jit, Mark; Simmons, Cameron P

2016-08-31

In response to the sharp rise in the global burden caused by dengue virus (DENV) over the last few decades, the WHO has set out three specific key objectives in its disease control strategy: (i) to estimate the true burden of dengue by 2015; (ii) a reduction in dengue mortality by at least 50% by 2020 (used as a baseline); and (iii) a reduction in dengue morbidity by at least 25% by 2020. Although various elements will all play crucial parts in achieving this goal, from diagnosis and case management to integrated surveillance and outbreak response, sustainable vector control, vaccine implementation and finally operational and implementation research, it seems clear that new tools (e.g. a safe and effective vaccine and/or effective vector control) are key to success. The first dengue vaccine was licensed in December 2015, Dengvaxia® (CYD-TDV) developed by Sanofi Pasteur. The WHO has provided guidance on the use of CYD-TDV in endemic countries, for which there are a variety of considerations beyond the risk-benefit evaluation done by regulatory authorities, including public health impact and cost-effectiveness. Population-level vaccine impact and economic and financial aspects are two issues that can potentially be considered by means of mathematical modelling, especially for new products for which empirical data are still lacking. In December 2014 a meeting was convened by the WHO in order to revisit the current status of dengue transmission models and their utility for public health decision-making. Here, we report on the main points of discussion and the conclusions of this meeting, as well as next steps for maximising the use of mathematical models for vaccine decision-making. Copyright © 2016.

Discovering and understanding the vector field using simulation in android app

NASA Astrophysics Data System (ADS)

Budi, A.; Muliyati, D.

2018-05-01

An understanding of vector field’s concepts are fundamental parts of the electrodynamics course. In this paper, we use a simple simulation that can be used to show qualitative imaging results as a variation of the vector field. Android application packages the simulation with consideration of the efficiency of use during the lecture. In addition, this simulation also trying to cover the divergences and curl concepts from the same conditions that students have a complete understanding and can distinguish concepts that have been described only mathematically. This simulation is designed to show the relationship between the field magnitude and its potential. This application can show vector field simulations in various conditions that help to improve students’ understanding of vector field concepts and their relation to particle existence around the field vector.

Design of an ion thruster movable grid thrust vectoring system

NASA Astrophysics Data System (ADS)

Kural, Aleksander; Leveque, Nicolas; Welch, Chris; Wolanski, Piotr

2004-08-01

Several reasons justify the development of an ion propulsion system thrust vectoring system. Spacecraft launched to date have used ion thrusters mounted on gimbals to control the thrust vector within a range of about ±5°. Such devices have large mass and dimensions, hence the need exists for a more compact system, preferably mounted within the thruster itself. Since the 1970s several thrust vectoring systems have been developed, with the translatable accelerator grid electrode being considered the most promising. Laboratory models of this system have already been built and successfully tested, but there is still room for improvement in their mechanical design. This work aims to investigate possibilities of refining the design of such movable grid thrust vectoring systems. Two grid suspension designs and three types of actuators were evaluated. The actuators examined were a micro electromechanical system, a NanoMuscle shape memory alloy actuator and a piezoelectric driver. Criteria used for choosing the best system included mechanical simplicity (use of the fewest mechanical parts), accuracy, power consumption and behaviour in space conditions. Designs of systems using these actuators are proposed. In addition, a mission to Mercury using the system with piezoelectric drivers has been modelled and its performance presented.

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

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Controlling Malaria Using Livestock-Based Interventions: A One Health Approach

PubMed Central

Franco, Ana O.; Gomes, M. Gabriela M.; Rowland, Mark; Coleman, Paul G.

2014-01-01

Where malaria is transmitted by zoophilic vectors, two types of malaria control strategies have been proposed based on animals: using livestock to divert vector biting from people (zooprophylaxis) or as baits to attract vectors to insecticide sources (insecticide-treated livestock). Opposing findings have been obtained on malaria zooprophylaxis, and despite the success of an insecticide-treated livestock trial in Pakistan, where malaria vectors are highly zoophilic, its effectiveness is yet to be formally tested in Africa where vectors are more anthropophilic. This study aims to clarify the different effects of livestock on malaria and to understand under what circumstances livestock-based interventions could play a role in malaria control programmes. This was explored by developing a mathematical model and combining it with data from Pakistan and Ethiopia. Consistent with previous work, a zooprophylactic effect of untreated livestock is predicted in two situations: if vector population density does not increase with livestock introduction, or if livestock numbers and availability to vectors are sufficiently high such that the increase in vector density is counteracted by the diversion of bites from humans to animals. Although, as expected, insecticide-treatment of livestock is predicted to be more beneficial in settings with highly zoophilic vectors, like South Asia, we find that the intervention could also considerably decrease malaria transmission in regions with more anthropophilic vectors, like Anopheles arabiensis in Africa, under specific circumstances: high treatment coverage of the livestock population, using a product with stronger or longer lasting insecticidal effect than in the Pakistan trial, and with small (ideally null) repellency effect, or if increasing the attractiveness of treated livestock to malaria vectors. The results suggest these are the most appropriate conditions for field testing insecticide-treated livestock in an Africa region with moderately zoophilic vectors, where this intervention could contribute to the integrated control of malaria and livestock diseases. PMID:25050703

Vector-like quarks and leptons, SU(5) ⊗ SU(5) grand unification, and proton decay

NASA Astrophysics Data System (ADS)

Lee, Chang-Hun; Mohapatra, Rabindra N.

2017-02-01

SU(5) ⊗ SU(5) provides a minimal grand unification scheme for fermions and gauge forces if there are vector-like quarks and leptons in nature. We explore the gauge coupling unification in a non-supersymmetric model of this type, and study its implications for proton decay. The properties of vector-like quarks and intermediate scales that emerge from coupling unification play a central role in suppressing proton decay. We find that in this model, the familiar decay mode p → e +π0 may have a partial lifetime within the reach of currently planned experiments.

Rate of biological invasions is lower in coastal marine protected areas.

PubMed

Ardura, A; Juanes, F; Planes, S; Garcia-Vazquez, E

2016-09-09

Marine biological invasions threaten biodiversity worldwide. Here we explore how Marine Protected areas, by reducing human use of the coast, confer resilience against the introduction of non-indigenous species (NIS), using two very different Pacific islands as case studies for developing and testing mathematical models. We quantified NIS vectors and promoters on Vancouver (Canada) and Moorea (French Polynesia) islands, sampled and barcoded NIS, and tested models at different spatial scales with different types of interaction among vectors and between marine protection and NIS frequency. In our results NIS were negatively correlated with the dimension of the protected areas and the intensity of the protection. Small to medium geographical scale protection seemed to be efficient against NIS introductions. The likely benefit of MPAs was by exclusion of aquaculture, principally in Canada. These results emphasize the importance of marine protected areas for biodiversity conservation, and suggest that small or medium protected zones would confer efficient protection against NIS introduction.

Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex

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

Gover, A. R.; Hallowell, K.; Waldron, A.

2007-01-15

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar,more » and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.« less

Dynamical Causal Modeling from a Quantum Dynamical Perspective

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

Demiralp, Emre; Demiralp, Metin

Recent research suggests that any set of first order linear vector ODEs can be converted to a set of specific vector ODEs adhering to what we have called ''Quantum Harmonical Form (QHF)''. QHF has been developed using a virtual quantum multi harmonic oscillator system where mass and force constants are considered to be time variant and the Hamiltonian is defined as a conic structure over positions and momenta to conserve the Hermiticity. As described in previous works, the conversion to QHF requires the matrix coefficient of the first set of ODEs to be a normal matrix. In this paper, thismore » limitation is circumvented using a space extension approach expanding the potential applicability of this method. Overall, conversion to QHF allows the investigation of a set of ODEs using mathematical tools available to the investigation of the physical concepts underlying quantum harmonic oscillators. The utility of QHF in the context of dynamical systems and dynamical causal modeling in behavioral and cognitive neuroscience is briefly discussed.« less

Estimation of the chemical rank for the three-way data: a principal norm vector orthogonal projection approach.

PubMed

Hong-Ping, Xie; Jian-Hui, Jiang; Guo-Li, Shen; Ru-Qin, Yu

2002-01-01

A new approach for estimating the chemical rank of the three-way array called the principal norm vector orthogonal projection method has been proposed. The method is based on the fact that the chemical rank of the three-way data array is equal to one of the column space of the unfolded matrix along the spectral or chromatographic mode. A vector with maximum Frobenius norm is selected among all the column vectors of the unfolded matrix as the principal norm vector (PNV). A transformation is conducted for the column vectors with an orthogonal projection matrix formulated by PNV. The mathematical rank of the column space of the residual matrix thus obtained should decrease by one. Such orthogonal projection is carried out repeatedly till the contribution of chemical species to the signal data is all deleted. At this time the decrease of the mathematical rank would equal that of the chemical rank, and the remaining residual subspace would entirely be due to the noise contribution. The chemical rank can be estimated easily by using an F-test. The method has been used successfully to the simulated HPLC-DAD type three-way data array and two real excitation-emission fluorescence data sets of amino acid mixtures and dye mixtures. The simulation with added relatively high level noise shows that the method is robust in resisting the heteroscedastic noise. The proposed algorithm is simple and easy to program with quite light computational burden.

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Examining Teachers' Struggles as They Attempt to Implement Dialogical Interaction as Part of Promoting Mathematical Reasoning within Their Classrooms

ERIC Educational Resources Information Center

Akkus, Recai; Hand, Brian

2011-01-01

This study examines the changes in teaching practices during the implementation of a pedagogical model called the mathematics reasoning approach (MRA), which was founded on 2 critical areas in mathematics, problem solving, and writing to learn. Three algebra teachers implemented the approach with their classes, which were divided into control…

Partnership in Being a Specialist Mathematics and Computing College--Who Gains What, How and Why?

ERIC Educational Resources Information Center

Sinkinson, Anne J.

2007-01-01

The research took place in a mathematics and computing specialist school. The article reports on part of a case study of the mathematics department's experience of being a major contributor to the requirements of being a specialist school. This article aims to explore and describe one model of partnership within the "community" remit of…

Exploring the Impact of Written Reflections on Learning in the Elementary Mathematics Classroom

ERIC Educational Resources Information Center

Martin, Christie S.; Polly, Drew; Kissel, Brian

2017-01-01

The authors examined the implementation of written reflections in a Grade 4 mathematics classroom over the course of 8 weeks. Students in this case study engaged in a workshop modeled after Calkin's Writers' Workshop and within this workshop the use of writing as a reflective tool in mathematics was introduced. The authors explore how students…

Instruction-Based Clinical Eye-Tracking Study on the Visual Interpretation of Divergence: How Do Students Look at Vector Field Plots?

ERIC Educational Resources Information Center

Klein, P.; Viiri, J.; Mozaffari, S.; Dengel, A.; Kuhn, J.

2018-01-01

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux…

Estimation of Teacher Practices Based on Text Transcripts of Teacher Speech Using a Support Vector Machine Algorithm

ERIC Educational Resources Information Center

Araya, Roberto; Plana, Francisco; Dartnell, Pablo; Soto-Andrade, Jorge; Luci, Gina; Salinas, Elena; Araya, Marylen

2012-01-01

Teacher practice is normally assessed by observers who watch classes or videos of classes. Here, we analyse an alternative strategy that uses text transcripts and a support vector machine classifier. For each one of the 710 videos of mathematics classes from the 2005 Chilean National Teacher Assessment Programme, a single 4-minute slice was…

Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Tobak, M.; Malcolm, G. N.

1980-01-01

This paper is a review of the current state of aerodynamic mathematical modeling for aircraft motions at high angles of attack. The mathematical model serves to define a set of characteristic motions from whose known aerodynamic responses the aerodynamic response to an arbitrary high angle-of-attack flight maneuver can be predicted. Means are explored of obtaining stability parameter information in terms of the characteristic motions, whether by wind-tunnel experiments, computational methods, or by parameter-identification methods applied to flight-test data. A rationale is presented for selecting and verifying the aerodynamic mathematical model at the lowest necessary level of complexity. Experimental results describing the wing-rock phenomenon are shown to be accommodated within the most recent mathematical model by admitting the existence of aerodynamic hysteresis in the steady-state variation of the rolling moment with roll angle. Interpretation of the experimental results in terms of bifurcation theory reveals the general conditions under which aerodynamic hysteresis must exist.

Evaluating long-term effectiveness of sleeping sickness control measures in Guinea.

PubMed

Pandey, Abhishek; Atkins, Katherine E; Bucheton, Bruno; Camara, Mamadou; Aksoy, Serap; Galvani, Alison P; Ndeffo-Mbah, Martial L

2015-10-22

Human African Trypanosomiasis threatens human health across Africa. The subspecies T.b. gambiense is responsible for the vast majority of reported HAT cases. Over the past decade, expanded control efforts accomplished a substantial reduction in HAT transmission, spurring the WHO to include Gambian HAT on its roadmap for 2020 elimination. To inform the implementation of this elimination goal, we evaluated the likelihood that current control interventions will achieve the 2020 target in Boffa prefecture in Guinea, which has one of the highest prevalences for HAT in the country, and where vector control measures have been implemented in combination with the traditional screen and treat strategy. We developed a three-species mathematical model of HAT and used a Bayesian melding approach to calibrate the model to epidemiological and entomological data from Boffa. From the calibrated model, we generated the probabilistic predictions regarding the likelihood that the current HAT control programs could achieve elimination by 2020 in Boffa. Our model projections indicate that if annual vector control is implemented in combination with annual or biennial active case detection and treatment, the probability of eliminating HAT as public health problem in Boffa by 2020 is over 90%. Annual implementation of vector control alone has a significant impact but a decreased chance of reaching the objective (77%). However, if the ongoing control efforts are interrupted, HAT will continue to remain a public health problem. In the presence of a non-human animal transmission reservoir, intervention strategies must be maintained at high coverage, even after 2020 elimination, to prevent HAT reemerging as a public health problem. Complementing active screening and treatment with vector control has the potential to achieve the elimination target before 2020 in the Boffa focus. However, surveillance must continue after elimination to prevent reemergence.

Incorporating individual health-protective decisions into disease transmission models: a mathematical framework.

PubMed

Durham, David P; Casman, Elizabeth A

2012-03-07

It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak.

Incorporating individual health-protective decisions into disease transmission models: a mathematical framework

PubMed Central

Durham, David P.; Casman, Elizabeth A.

2012-01-01

It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak. PMID:21775324

Modeling mass drug treatment and resistant filaria disease transmission

NASA Astrophysics Data System (ADS)

Fuady, A. M.; Nuraini, N.; Soewono, E.; Tasman, H.; Supriatna, A. K.

2014-03-01

It has been indicated that a long term application of combined mass drug treatment may contribute to the development of drug resistance in lymphatic filariasis. This phenomenon is not well understood due to the complexity of filaria life cycle. In this paper we formulate a mathematical model for the spread of mass drug resistant in a filaria endemic region. The model is represented in a 13-dimensional Host-Vector system. The basic reproductive ratio of the system which is obtained from the next generation matrix, and analysis of stability of both the disease free equilibrium and the coexistence equilibria are shown. Numerical simulation for long term dynamics for possible field conditions is also shown.

Modeling Virus Coinfection to Inform Management of Maize Lethal Necrosis in Kenya.

PubMed

Hilker, Frank M; Allen, Linda J S; Bokil, Vrushali A; Briggs, Cheryl J; Feng, Zhilan; Garrett, Karen A; Gross, Louis J; Hamelin, Frédéric M; Jeger, Michael J; Manore, Carrie A; Power, Alison G; Redinbaugh, Margaret G; Rúa, Megan A; Cunniffe, Nik J

2017-10-01

Maize lethal necrosis (MLN) has emerged as a serious threat to food security in sub-Saharan Africa. MLN is caused by coinfection with two viruses, Maize chlorotic mottle virus and a potyvirus, often Sugarcane mosaic virus. To better understand the dynamics of MLN and to provide insight into disease management, we modeled the spread of the viruses causing MLN within and between growing seasons. The model allows for transmission via vectors, soil, and seed, as well as exogenous sources of infection. Following model parameterization, we predict how management affects disease prevalence and crop performance over multiple seasons. Resource-rich farmers with large holdings can achieve good control by combining clean seed and insect control. However, crop rotation is often required to effect full control. Resource-poor farmers with smaller holdings must rely on rotation and roguing, and achieve more limited control. For both types of farmer, unless management is synchronized over large areas, exogenous sources of infection can thwart control. As well as providing practical guidance, our modeling framework is potentially informative for other cropping systems in which coinfection has devastating effects. Our work also emphasizes how mathematical modeling can inform management of an emerging disease even when epidemiological information remains scanty. [Formula: see text] Copyright © 2017 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .

Modelling virus- and host-limitation in vectored plant disease epidemics.

PubMed

Jeger, M J; van den Bosch, F; Madden, L V

2011-08-01

Models of plant virus epidemics have received less attention than those caused by fungal pathogens. Intuitively, the fact that virus diseases are systemic means that the individual diseased plant can be considered as the population unit which simplifies modelling. However, the fact that a vector is required in the vast majority of cases for virus transmission, means that explicit consideration must be taken of the vector, or, the involvement of the vector in the transmission process must be considered implicitly. In the latter case it is also important that within-plant processes, such as virus multiplication and systemic movement, are taken into account. In this paper we propose an approach based on the linking of transmission at the population level with virus multiplication within plants. The resulting models are parameter-sparse and hence simplistic. However, the range of model outcomes is representative of field observations relating to the apparent limitation of epidemic development in populations of healthy susceptible plants. We propose that epidemic development can be constrained by virus limitation in the early stages of an epidemic when the availability of healthy susceptible hosts is not limiting. There is an inverse relationship between levels of transmission in the population and the mean virus titre/infected plant. In the case of competition between viruses, both virus and host limitation are likely to be important in determining whether one virus can displace another or whether both viruses can co-exist in a plant population. Lotka-Volterra type equations are derived to describe density-dependent competition between two viruses multiplying within plants, embedded within a population level epidemiological model. Explicit expressions determining displacement or co-existence of the viruses are obtained. Unlike the classical Lotka-Volterra competition equations, the co-existence requirement for the competition coefficients to be both less than 1 can be relaxed. Copyright © 2011 Elsevier B.V. All rights reserved.

The combined geodetic network adjusted on the reference ellipsoid - a comparison of three functional models for GNSS observations

NASA Astrophysics Data System (ADS)

Kadaj, Roman

2016-12-01

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

Direct model-based predictive control scheme without cost function for voltage source inverters with reduced common-mode voltage

NASA Astrophysics Data System (ADS)

Kim, Jae-Chang; Moon, Sung-Ki; Kwak, Sangshin

2018-04-01

This paper presents a direct model-based predictive control scheme for voltage source inverters (VSIs) with reduced common-mode voltages (CMVs). The developed method directly finds optimal vectors without using repetitive calculation of a cost function. To adjust output currents with the CMVs in the range of -Vdc/6 to +Vdc/6, the developed method uses voltage vectors, as finite control resources, excluding zero voltage vectors which produce the CMVs in the VSI within ±Vdc/2. In a model-based predictive control (MPC), not using zero voltage vectors increases the output current ripples and the current errors. To alleviate these problems, the developed method uses two non-zero voltage vectors in one sampling step. In addition, the voltage vectors scheduled to be used are directly selected at every sampling step once the developed method calculates the future reference voltage vector, saving the efforts of repeatedly calculating the cost function. And the two non-zero voltage vectors are optimally allocated to make the output current approach the reference current as close as possible. Thus, low CMV, rapid current-following capability and sufficient output current ripple performance are attained by the developed method. The results of a simulation and an experiment verify the effectiveness of the developed method.

Transmission dynamics of two dengue serotypes with vaccination scenarios.

PubMed

González Morales, N L; Núñez-López, M; Ramos-Castañeda, J; Velasco-Hernández, J X

2017-05-01

In this work we present a mathematical model that incorporates two Dengue serotypes. The model has been constructed to study both the epidemiological trends of the disease and conditions that allow coexistence in competing strains under vaccination. We consider two viral strains and temporary cross-immunity with one vector mosquito population. Results suggest that vaccination scenarios will not only reduce disease incidence but will also modify the transmission dynamics. Indeed, vaccination and cross immunity period are seen to decrease the frequency and magnitude of outbreaks but in a differentiated manner with specific effects depending upon the interaction vaccine and strain type. Copyright © 2016 Elsevier Inc. All rights reserved.

On a model of the processes of maintaining a technological area by a manipulator

NASA Astrophysics Data System (ADS)

Ghukasyan, A. A.; Ordyan, A. Ya

2018-04-01

The research refers to the results of mathematical modeling of the process of maintaining a technological area which consists of unstable or fixed objects (targets) and a controlled multi-link manipulator [1–9]. It is assumed that, in the maintenance process, the dynamic characteristics and the phase vector of the manipulator state can change at certain finite times depending on the mass of the cargo or instrument [10, 11]. Some controllability problems are investigated in the case where the manipulator motion on each maintenance interval is described by linear differential equations with constant coefficients and the motions of the objects are given.

Mathematical modelling of contact of ruled surfaces: theory and practical application

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Niteyskiy, A. S.

2016-04-01

In the theory of ruled surfaces there are well known researches of contact of ruled surfaces along their common generator line (Klein image is often used [1]). In this paper we propose a study of contact of non developable ruled surfaces via the dual vector calculus. The advantages of this method have been demonstrated by E. Study, W. Blaschke and D. N. Zeiliger in differential geometry studies of ruled surfaces in space R3 over the algebra of dual numbers. A practical use of contact is demonstrated by the example modeling of the working surface of the progressive tool for tillage.

The increase in the starting torque of PMSM motor by applying of FOC method

NASA Astrophysics Data System (ADS)

Plachta, Kamil

2017-05-01

The article presents field oriented control method of synchronous permanent magnet motor equipped in optical sensors. This method allows for a wide range regulation of torque and rotational speed of the electric motor. The paper presents mathematical model of electric motor and vector control method. Optical sensors have shorter time response as compared to the inductive sensors, which allow for faster response of the electronic control system to changes of motor loads. The motor driver is based on the digital signal processor which performs advanced mathematical operations in real time. The appliance of Clark and Park transformation in the software defines the angle of rotor position. The presented solution provides smooth adjustment of the rotational speed in the first operating zone and reduces the dead zone of the torque in the second and third operating zones.

Surface growth kinematics via local curve evolution.

PubMed

Moulton, Derek E; Goriely, Alain

2014-01-01

A mathematical framework is developed to model the kinematics of surface growth for objects that can be generated by evolving a curve in space, such as seashells and horns. Growth is dictated by a growth velocity vector field defined at every point on a generating curve. A local orthonormal basis is attached to each point of the generating curve and the velocity field is given in terms of the local coordinate directions, leading to a fully local and elegant mathematical structure. Several examples of increasing complexity are provided, and we demonstrate how biologically relevant structures such as logarithmic shells and horns emerge as analytical solutions of the kinematics equations with a small number of parameters that can be linked to the underlying growth process. Direct access to cell tracks and local orientation enables for connections to be made to the underlying growth process.

Visualization of the collective vortex-like motions in liquid argon and water: Molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Anikeenko, A. V.; Malenkov, G. G.; Naberukhin, Yu. I.

2018-03-01

We propose a new measure of collectivity of molecular motion in the liquid: the average vector of displacement of the particles, ⟨ΔR⟩, which initially have been localized within a sphere of radius Rsph and then have executed the diffusive motion during a time interval Δt. The more correlated the motion of the particles is, the longer will be the vector ⟨ΔR⟩. We visualize the picture of collective motions in molecular dynamics (MD) models of liquids by constructing the ⟨ΔR⟩ vectors and pinning them to the sites of the uniform grid which divides each of the edges of the model box into equal parts. MD models of liquid argon and water have been studied by this method. Qualitatively, the patterns of ⟨ΔR⟩ vectors are similar for these two liquids but differ in minor details. The most important result of our research is the revealing of the aggregates of ⟨ΔR⟩ vectors which have the form of extended flows which sometimes look like the parts of vortices. These vortex-like clusters of ⟨ΔR⟩ vectors have the mesoscopic size (of the order of 10 nm) and persist for tens of picoseconds. Dependence of the ⟨ΔR⟩ vector field on parameters Rsph, Δt, and on the model size has been investigated. This field in the models of liquids differs essentially from that in a random-walk model.

Characterization of the Dispersal of Non-Domiciliated Triatoma dimidiata through the Selection of Spatially Explicit Models

PubMed Central

Barbu, Corentin; Dumonteil, Eric; Gourbière, Sébastien

2010-01-01

Background Chagas disease is a major parasitic disease in Latin America, prevented in part by vector control programs that reduce domestic populations of triatomines. However, the design of control strategies adapted to non-domiciliated vectors, such as Triatoma dimidiata, remains a challenge because it requires an accurate description of their spatio-temporal distributions, and a proper understanding of the underlying dispersal processes. Methodology/Principal Findings We combined extensive spatio-temporal data sets describing house infestation dynamics by T. dimidiata within a village, and spatially explicit population dynamics models in a selection model approach. Several models were implemented to provide theoretical predictions under different hypotheses on the origin of the dispersers and their dispersal characteristics, which we compared with the spatio-temporal pattern of infestation observed in the field. The best models fitted the dynamic of infestation described by a one year time-series, and also predicted with a very good accuracy the infestation process observed during a second replicate one year time-series. The parameterized models gave key insights into the dispersal of these vectors. i) About 55% of the triatomines infesting houses came from the peridomestic habitat, the rest corresponding to immigration from the sylvatic habitat, ii) dispersing triatomines were 5–15 times more attracted by houses than by peridomestic area, and iii) the moving individuals spread on average over rather small distances, typically 40–60 m/15 days. Conclusion/Significance Since these dispersal characteristics are associated with much higher abundance of insects in the periphery of the village, we discuss the possibility that spatially targeted interventions allow for optimizing the efficacy of vector control activities within villages. Such optimization could prove very useful in the context of limited resources devoted to vector control. PMID:20689823

Assessing Principal Component Regression Prediction of Neurochemicals Detected with Fast-Scan Cyclic Voltammetry

PubMed Central

2011-01-01

Principal component regression is a multivariate data analysis approach routinely used to predict neurochemical concentrations from in vivo fast-scan cyclic voltammetry measurements. This mathematical procedure can rapidly be employed with present day computer programming languages. Here, we evaluate several methods that can be used to evaluate and improve multivariate concentration determination. The cyclic voltammetric representation of the calculated regression vector is shown to be a valuable tool in determining whether the calculated multivariate model is chemically appropriate. The use of Cook’s distance successfully identified outliers contained within in vivo fast-scan cyclic voltammetry training sets. This work also presents the first direct interpretation of a residual color plot and demonstrated the effect of peak shifts on predicted dopamine concentrations. Finally, separate analyses of smaller increments of a single continuous measurement could not be concatenated without substantial error in the predicted neurochemical concentrations due to electrode drift. Taken together, these tools allow for the construction of more robust multivariate calibration models and provide the first approach to assess the predictive ability of a procedure that is inherently impossible to validate because of the lack of in vivo standards. PMID:21966586

Assessing principal component regression prediction of neurochemicals detected with fast-scan cyclic voltammetry.

PubMed

Keithley, Richard B; Wightman, R Mark

2011-06-07

Principal component regression is a multivariate data analysis approach routinely used to predict neurochemical concentrations from in vivo fast-scan cyclic voltammetry measurements. This mathematical procedure can rapidly be employed with present day computer programming languages. Here, we evaluate several methods that can be used to evaluate and improve multivariate concentration determination. The cyclic voltammetric representation of the calculated regression vector is shown to be a valuable tool in determining whether the calculated multivariate model is chemically appropriate. The use of Cook's distance successfully identified outliers contained within in vivo fast-scan cyclic voltammetry training sets. This work also presents the first direct interpretation of a residual color plot and demonstrated the effect of peak shifts on predicted dopamine concentrations. Finally, separate analyses of smaller increments of a single continuous measurement could not be concatenated without substantial error in the predicted neurochemical concentrations due to electrode drift. Taken together, these tools allow for the construction of more robust multivariate calibration models and provide the first approach to assess the predictive ability of a procedure that is inherently impossible to validate because of the lack of in vivo standards.

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Propagation and scattering of vector light beam in turbid scattering medium

NASA Astrophysics Data System (ADS)

Doronin, Alexander; Milione, Giovanni; Meglinski, Igor; Alfano, Robert R.

2014-03-01

Due to its high sensitivity to subtle alterations in medium morphology the vector light beams have recently gained much attention in the area of photonics. This leads to development of a new non-invasive optical technique for tissue diagnostics. Conceptual design of the particular experimental systems requires careful selection of various technical parameters, including beam structure, polarization, coherence, wavelength of incident optical radiation, as well as an estimation of how the spatial and temporal structural alterations in biological tissues can be distinguished by variations of these parameters. Therefore, an accurate realistic description of vector light beams propagation within tissue-like media is required. To simulate and mimic the propagation of vector light beams within the turbid scattering media the stochastic Monte Carlo (MC) technique has been used. In current report we present the developed MC model and the results of simulation of different vector light beams propagation in turbid tissue-like scattering media. The developed MC model takes into account the coherent properties of light, the influence of reflection and refraction at the medium boundary, helicity flip of vortexes and their mutual interference. Finally, similar to the concept of higher order Poincaŕe sphere (HOPS), to link the spatial distribution of the intensity of the backscattered vector light beam and its state of polarization on the medium surface we introduced the color-coded HOPS.

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

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

A surface hydrology model for regional vector borne disease models

NASA Astrophysics Data System (ADS)

Tompkins, Adrian; Asare, Ernest; Bomblies, Arne; Amekudzi, Leonard

2016-04-01

Small, sun-lit temporary pools that form during the rainy season are important breeding sites for many key mosquito vectors responsible for the transmission of malaria and other diseases. The representation of this surface hydrology in mathematical disease models is challenging, due to their small-scale, dependence on the terrain and the difficulty of setting soil parameters. Here we introduce a model that represents the temporal evolution of the aggregate statistics of breeding sites in a single pond fractional coverage parameter. The model is based on a simple, geometrical assumption concerning the terrain, and accounts for the processes of surface runoff, pond overflow, infiltration and evaporation. Soil moisture, soil properties and large-scale terrain slope are accounted for using a calibration parameter that sets the equivalent catchment fraction. The model is calibrated and then evaluated using in situ pond measurements in Ghana and ultra-high (10m) resolution explicit simulations for a village in Niger. Despite the model's simplicity, it is shown to reproduce the variability and mean of the pond aggregate water coverage well for both locations and validation techniques. Example malaria simulations for Uganda will be shown using this new scheme with a generic calibration setting, evaluated using district malaria case data. Possible methods for implementing regional calibration will be briefly discussed.

Computing the modal mass from the state space model in combined experimental-operational modal analysis

NASA Astrophysics Data System (ADS)

Cara, Javier

2016-05-01

Modal parameters comprise natural frequencies, damping ratios, modal vectors and modal masses. In a theoretic framework, these parameters are the basis for the solution of vibration problems using the theory of modal superposition. In practice, they can be computed from input-output vibration data: the usual procedure is to estimate a mathematical model from the data and then to compute the modal parameters from the estimated model. The most popular models for input-output data are based on the frequency response function, but in recent years the state space model in the time domain has become popular among researchers and practitioners of modal analysis with experimental data. In this work, the equations to compute the modal parameters from the state space model when input and output data are available (like in combined experimental-operational modal analysis) are derived in detail using invariants of the state space model: the equations needed to compute natural frequencies, damping ratios and modal vectors are well known in the operational modal analysis framework, but the equation needed to compute the modal masses has not generated much interest in technical literature. These equations are applied to both a numerical simulation and an experimental study in the last part of the work.

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.

The boundary vector cell model of place cell firing and spatial memory

PubMed Central

Barry, Caswell; Lever, Colin; Hayman, Robin; Hartley, Tom; Burton, Stephen; O'Keefe, John; Jeffery, Kate; Burgess, Neil

2009-01-01

We review evidence for the boundary vector cell model of the environmental determinants of the firing of hippocampal place cells. Preliminary experimental results are presented concerning the effects of addition or removal of environmental boundaries on place cell firing and evidence that boundary vector cells may exist in the subiculum. We review and update computational simulations predicting the location of human search within a virtual environment of variable geometry, assuming that boundary vector cells provide one of the input representations of location used in mammalian spatial memory. Finally, we extend the model to include experience-dependent modification of connection strengths through a BCM-like learning rule, and compare the effects to experimental data on the firing of place cells under geometrical manipulations to their environment. The relationship between neurophysiological results in rats and spatial behaviour in humans is discussed. PMID:16703944

An approach of the exact linearization techniques to analysis of population dynamics of the mosquito Aedes aegypti.

PubMed

Dos Reis, Célia A; Florentino, Helenice de O; Cólon, Diego; Rosa, Suélia R Fleury; Cantane, Daniela R

2018-05-01

Dengue fever, chikungunya and zika are caused by different viruses and mainly transmitted by Aedes aegypti mosquitoes. These diseases have received special attention of public health officials due to the large number of infected people in tropical and subtropical countries and the possible sequels that those diseases can cause. In severe cases, the infection can have devastating effects, affecting the central nervous system, muscles, brain and respiratory system, often resulting in death. Vaccines against these diseases are still under development and, therefore, current studies are focused on the treatment of diseases and vector (mosquito) control. This work focuses on this last topic, and presents the analysis of a mathematical model describing the population dynamics of Aedes aegypti, as well as present the design of a control law for the mosquito population (vector control) via exact linearization techniques and optimal control. This control strategy optimizes the use of resources for vector control, and focuses on the aquatic stage of the mosquito life. Theoretical and computational results are also presented. Copyright © 2017 Elsevier Inc. All rights reserved.

Flow noise of an underwater vector sensor embedded in a flexible towed array.

PubMed

Korenbaum, Vladimir I; Tagiltsev, Alexander A

2012-05-01

The objective of this work is to simulate the flow noise of a vector sensor embedded in a flexible towed array. The mathematical model developed, based on long-wavelength analysis of the inner space of a cylindrical multipole source, predicts the reduction of the flow noise of a vector sensor embedded in an underwater flexible towed array by means of intensimetric processing (cross-spectral density calculation of oscillatory velocity and sound-pressure-sensor responses). It is found experimentally that intensimetric processing results in flow noise reduction by 12-25 dB at mean levels and by 10-30 dB in fluctuations compared to a squared oscillatory velocity channel. The effect of flow noise suppression in the intensimetry channel relative to a squared sound pressure channel is observed, but only for frequencies above the threshold. These suppression values are 10-15 dB at mean noise levels and 3-6 dB in fluctuations. At towing velocities of 1.5-3 ms(-1) and an accumulation time of 98.3 s, the threshold frequency in fluctuations is between 30 and 45 Hz.

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2016-12-01

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

Mathematical model of compact type evaporator

NASA Astrophysics Data System (ADS)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

L'espace articulaire de la Robotique Industrielle est un espace vectorielIndustrial Robotics joint space is a vector space

NASA Astrophysics Data System (ADS)

Tondu, Bertrand

2003-05-01

The mathematical modelling of industrial robots is based on the vectorial nature of the n-dimensional joint space of the robot, defined as a kinematic chain with n degrees of freedom. However, in our opinion, the vectorial nature of the joint space has been insufficiently discussed in the literature. We establish the vectorial nature of the joint space of an industrial robot from the fundamental studies of B. Roth on screws. To cite this article: B. Tondu, C. R. Mecanique 331 (2003).

Examining the Mathematical Modeling Processes of Primary School 4th-Grade Students: Shopping Problem

ERIC Educational Resources Information Center

Ulu, Mustafa

2017-01-01

The purpose of this study is to identify primary school students' thinking processes within the mathematical modeling process and the challenges they encounter, if any. This is a basic qualitative research study conducted in a primary school in the city of Kütahya in the academic year of 2015-2016. The study group of the research was composed of…

Why Johnny Struggles When Familiar Concepts Are Taken to a New Mathematical Domain: Towards a Polysemous Approach

ERIC Educational Resources Information Center

Kontorovich, Igor'

2018-01-01

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

Caring teaching practices in multiethnic mathematics classrooms: attending to health and well-being

NASA Astrophysics Data System (ADS)

Averill, Robin

2012-06-01

Factors that contribute to strong teacher-student relationships are vital to understand because of the influence these relationships have on achievement and motivation, particularly for minority group students. This article draws from a substantial quantity of empirical data, grounded in a wide theoretical and cultural base, regarding aspects of caring teacher practice to discuss mathematics teacher behaviours in relation to an existing model of health and well-being that encompasses cognitive, social, spiritual, and physical dimensions. Drawing from 100 Year 10 mathematics lesson observations involving six teachers and their classes across three urban schools, evidence emerged that for many indigenous (Māori), New Zealand Pacific, and New Zealand European students, caring teacher behaviours important for student engagement and achievement both include, and range beyond, traditional teaching practices. Examples include capitalising on student reactions and shared endeavours within the context of mathematics learning, expecting mathematical progress, showing respect for students and for their mathematics learning, being explicit about practice and expectations, incorporating one-to-one interactions, making opportunities within mathematics learning for sharing personal identities, and incorporating movement. This research illustrates how mathematics educators can attend to the specific and holistic mathematical learning needs of their students, including those often marginalised.

AAV vector encoding human VEGF165-transduced pectineus muscular flaps increase the formation of new tissue through induction of angiogenesis in an in vivo chamber for tissue engineering: A technique to enhance tissue and vessels in microsurgically engineered tissue.

PubMed

Moimas, Silvia; Manasseri, Benedetto; Cuccia, Giuseppe; Stagno d'Alcontres, Francesco; Geuna, Stefano; Pattarini, Lucia; Zentilin, Lorena; Giacca, Mauro; Colonna, Michele R

2015-01-01

In regenerative medicine, new approaches are required for the creation of tissue substitutes, and the interplay between different research areas, such as tissue engineering, microsurgery and gene therapy, is mandatory. In this article, we report a modification of a published model of tissue engineering, based on an arterio-venous loop enveloped in a cross-linked collagen-glycosaminoglycan template, which acts as an isolated chamber for angiogenesis and new tissue formation. In order to foster tissue formation within the chamber, which entails on the development of new vessels, we wondered whether we might combine tissue engineering with a gene therapy approach. Based on the well-described tropism of adeno-associated viral vectors for post-mitotic tissues, a muscular flap was harvested from the pectineus muscle, inserted into the chamber and transduced by either AAV vector encoding human VEGF165 or AAV vector expressing the reporter gene β-galactosidase, as a control. Histological analysis of the specimens showed that muscle transduction by AAV vector encoding human VEGF165 resulted in enhanced tissue formation, with a significant increase in the number of arterioles within the chamber in comparison with the previously published model. Pectineus muscular flap, transduced by adeno-associated viral vectors, acted as a source of the proangiogenic factor vascular endothelial growth factor, thus inducing a consistent enhancement of vessel growth into the newly formed tissue within the chamber. In conclusion, our present findings combine three different research fields such as microsurgery, tissue engineering and gene therapy, suggesting and showing the feasibility of a mixed approach for regenerative medicine.

Predicting the host of influenza viruses based on the word vector.

PubMed

Xu, Beibei; Tan, Zhiying; Li, Kenli; Jiang, Taijiao; Peng, Yousong

2017-01-01

Newly emerging influenza viruses continue to threaten public health. A rapid determination of the host range of newly discovered influenza viruses would assist in early assessment of their risk. Here, we attempted to predict the host of influenza viruses using the Support Vector Machine (SVM) classifier based on the word vector, a new representation and feature extraction method for biological sequences. The results show that the length of the word within the word vector, the sequence type (DNA or protein) and the species from which the sequences were derived for generating the word vector all influence the performance of models in predicting the host of influenza viruses. In nearly all cases, the models built on the surface proteins hemagglutinin (HA) and neuraminidase (NA) (or their genes) produced better results than internal influenza proteins (or their genes). The best performance was achieved when the model was built on the HA gene based on word vectors (words of three-letters long) generated from DNA sequences of the influenza virus. This results in accuracies of 99.7% for avian, 96.9% for human and 90.6% for swine influenza viruses. Compared to the method of sequence homology best-hit searches using the Basic Local Alignment Search Tool (BLAST), the word vector-based models still need further improvements in predicting the host of influenza A viruses.

Recent Advances in the Edge-Function Method 1979-1980

DTIC Science & Technology

1980-07-30

the residuals are within the limits within which an engineer can specify the boundary conditions of the problem, then the corresponding Mathematical ...truncation lvel . The consistent preference shown by the solver routine for verteA functions as opposed to polar functions reinforces the expectations of...Accordingly,each solution zr_.-4_des a Mathematical Model for the given physical problem- R.M.S. values provide a practical criterion for the enai--er to

Margin based ontology sparse vector learning algorithm and applied in biology science.

PubMed

Gao, Wei; Qudair Baig, Abdul; Ali, Haidar; Sajjad, Wasim; Reza Farahani, Mohammad

2017-01-01

In biology field, the ontology application relates to a large amount of genetic information and chemical information of molecular structure, which makes knowledge of ontology concepts convey much information. Therefore, in mathematical notation, the dimension of vector which corresponds to the ontology concept is often very large, and thus improves the higher requirements of ontology algorithm. Under this background, we consider the designing of ontology sparse vector algorithm and application in biology. In this paper, using knowledge of marginal likelihood and marginal distribution, the optimized strategy of marginal based ontology sparse vector learning algorithm is presented. Finally, the new algorithm is applied to gene ontology and plant ontology to verify its efficiency.

Potential for Zika Virus to Establish a Sylvatic Transmission Cycle in the Americas

PubMed Central

Althouse, Benjamin M.; Vasilakis, Nikos; Sall, Amadou A.; Diallo, Mawlouth; Weaver, Scott C.; Hanley, Kathryn A.

2016-01-01

Zika virus (ZIKV) originated and continues to circulate in a sylvatic transmission cycle between non-human primate hosts and arboreal mosquitoes in tropical Africa. Recently ZIKV invaded the Americas, where it poses a threat to human health, especially to pregnant women and their infants. Here we examine the risk that ZIKV will establish a sylvatic cycle in the Americas, focusing on Brazil. We review the natural history of sylvatic ZIKV and present a mathematical dynamic transmission model to assess the probability of establishment of a sylvatic ZIKV transmission cycle in non-human primates and/or other mammals and arboreal mosquito vectors in Brazil. Brazil is home to multiple species of primates and mosquitoes potentially capable of ZIKV transmission, though direct assessment of host competence (ability to mount viremia sufficient to infect a feeding mosquito) and vector competence (ability to become infected with ZIKV and disseminate and transmit upon subsequent feedings) of New World species is lacking. Modeling reveals a high probability of establishment of sylvatic ZIKV across a large range of biologically plausible parameters. Probability of establishment is dependent on host and vector population sizes, host birthrates, and ZIKV force of infection. Research on the host competence of New World monkeys or other small mammals to ZIKV, on vector competence of New World Aedes, Sabethes, and Haemagogus mosquitoes for ZIKV, and on the geographic range of potential New World hosts and vectors is urgently needed. A sylvatic cycle of ZIKV would make future elimination efforts in the Americas practically impossible, and paints a dire picture for the epidemiology of ZIKV and our ability to end the ongoing outbreak of congenital Zika syndrome. PMID:27977671

Potential for Zika Virus to Establish a Sylvatic Transmission Cycle in the Americas.

PubMed

Althouse, Benjamin M; Vasilakis, Nikos; Sall, Amadou A; Diallo, Mawlouth; Weaver, Scott C; Hanley, Kathryn A

2016-12-01

Zika virus (ZIKV) originated and continues to circulate in a sylvatic transmission cycle between non-human primate hosts and arboreal mosquitoes in tropical Africa. Recently ZIKV invaded the Americas, where it poses a threat to human health, especially to pregnant women and their infants. Here we examine the risk that ZIKV will establish a sylvatic cycle in the Americas, focusing on Brazil. We review the natural history of sylvatic ZIKV and present a mathematical dynamic transmission model to assess the probability of establishment of a sylvatic ZIKV transmission cycle in non-human primates and/or other mammals and arboreal mosquito vectors in Brazil. Brazil is home to multiple species of primates and mosquitoes potentially capable of ZIKV transmission, though direct assessment of host competence (ability to mount viremia sufficient to infect a feeding mosquito) and vector competence (ability to become infected with ZIKV and disseminate and transmit upon subsequent feedings) of New World species is lacking. Modeling reveals a high probability of establishment of sylvatic ZIKV across a large range of biologically plausible parameters. Probability of establishment is dependent on host and vector population sizes, host birthrates, and ZIKV force of infection. Research on the host competence of New World monkeys or other small mammals to ZIKV, on vector competence of New World Aedes, Sabethes, and Haemagogus mosquitoes for ZIKV, and on the geographic range of potential New World hosts and vectors is urgently needed. A sylvatic cycle of ZIKV would make future elimination efforts in the Americas practically impossible, and paints a dire picture for the epidemiology of ZIKV and our ability to end the ongoing outbreak of congenital Zika syndrome.

Reading-Enhanced Word Problem Solving: A Theoretical Model

ERIC Educational Resources Information Center

Capraro, Robert M.; Capraro, Mary Margaret; Rupley, William H.

2012-01-01

There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…

Mathematical model for Dengue with three states of infection

NASA Astrophysics Data System (ADS)

Hincapie, Doracelly; Ospina, Juan

2012-06-01

A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases.

Wess-Zumino current and the structure of the decay tau- -->K- pi- K+ nu tau.

PubMed

Coan, T E; Gao, Y S; Liu, F; Stroynowski, R; Artuso, M; Boulahouache, C; Blusk, S; Butt, J; Dambasuren, E; Dorjkhaidav, O; Haynes, J; Menaa, N; Mountain, R; Muramatsu, H; Nandakumar, R; Redjimi, R; Sia, R; Skwarnicki, T; Stone, S; Wang, J C; Zhang, Kevin; Mahmood, A H; Csorna, S E; Bonvicini, G; Cinabro, D; Dubrovin, M; Bornheim, A; Lipeles, E; Pappas, S P; Shapiro, A; Weinstein, A J; Briere, R A; Chen, G P; Ferguson, T; Tatishvili, G; Vogel, H; Watkins, M E; Adam, N E; Alexander, J P; Berkelman, K; Boisvert, V; Cassel, D G; Duboscq, J E; Ecklund, K M; Ehrlich, R; Galik, R S; Gibbons, L; Gittelman, B; Gray, S W; Hartill, D L; Heltsley, B K; Hsu, L; Jones, C D; Kandaswamy, J; Kreinick, D L; Kuznetsov, V E; Magerkurth, A; Mahlke-Krüger, H; Meyer, T O; Patterson, J R; Pedlar, T K; Peterson, D; Pivarski, J; Riley, D; Sadoff, A J; Schwarthoff, H; Shepherd, M R; Sun, W M; Thayer, J G; Urner, D; Wilksen, T; Weinberger, M; Athar, S B; Avery, P; Breva-Newell, L; Potlia, V; Stoeck, H; Yelton, J; Eisenstein, B I; Gollin, G D; Karliner, I; Lowrey, N; Naik, P; Sedlack, C; Selen, M; Thaler, J J; Williams, J; Edwards, K W; Besson, D; Gao, K Y; Gong, D T; Kubota, Y; Li, S Z; Poling, R; Scott, A W; Smith, A; Stepaniak, C J; Urheim, J; Metreveli, Z; Seth, K K; Tomaradze, A; Zweber, P; Arms, K; Eckhart, E; Gan, K K; Gwon, C; Severini, H; Skubic, P; Asner, D M; Dytman, S A; Mehrabyan, S; Mueller, J A; Nam, S; Savinov, V; Huang, G S; Miller, D H; Pavlunin, V; Sanghi, B; Shibata, E I; Shipsey, I P J; Adams, G S; Chasse, M; Cummings, J P; Danko, I; Napolitano, J; Cronin-Hennessy, D; Park, C S; Park, W; Thayer, J B; Thorndike, E H

2004-06-11

We present the first study of the vector (Wess-Zumino) current in tau(-)-->K-pi-K+nu(tau) decay using data collected with the CLEO III detector at the Cornell Electron Storage Ring. We determine the quantitative contributions to the decay width from the vector and axial vector currents. Within the framework of a model by Kühn and Mirkes, we identify the quantitative contributions to the total decay rate from the intermediate states omegapi, rho(')pi, and K*K.

Mathematical Modeling of Loop Heat Pipes

NASA Technical Reports Server (NTRS)

Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

1998-01-01

The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

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.

Modeling Dynamics of Culex pipiens Complex Populations and Assessing Abatement Strategies for West Nile Virus

PubMed Central

Pawelek, Kasia A.; Hager, Elizabeth J.; Hunt, Gregg J.

2014-01-01

The primary mosquito species associated with underground stormwater systems in the United States are the Culex pipiens complex species. This group represents important vectors of West Nile virus (WNV) throughout regions of the continental U.S. In this study, we designed a mathematical model and compared it with surveillance data for the Cx. pipiens complex collected in Beaufort County, South Carolina. Based on the best fit of the model to the data, we estimated parameters associated with the effectiveness of public health insecticide (adulticide) treatments (primarily pyrethrin products) as well as the birth, maturation, and death rates of immature and adult Cx. pipiens complex mosquitoes. We used these estimates for modeling the spread of WNV to obtain more reliable disease outbreak predictions and performed numerical simulations to test various mosquito abatement strategies. We demonstrated that insecticide treatments produced significant reductions in the Cx. pipiens complex populations. However, abatement efforts were effective for approximately one day and the vector mosquitoes rebounded until the next treatment. These results suggest that frequent insecticide applications are necessary to control these mosquitoes. We derived the basic reproductive number (ℜ0) to predict the conditions under which disease outbreaks are likely to occur and to evaluate mosquito abatement strategies. We concluded that enhancing the mosquito death rate results in lower values of ℜ0, and if ℜ0<1, then an epidemic will not occur. Our modeling results provide insights about control strategies of the vector populations and, consequently, a potential decrease in the risk of a WNV outbreak. PMID:25268229

Effect of Internet-Based Cognitive Apprenticeship Model (i-CAM) on Statistics Learning among Postgraduate Students.

PubMed

Saadati, Farzaneh; Ahmad Tarmizi, Rohani; Mohd Ayub, Ahmad Fauzi; Abu Bakar, Kamariah

2015-01-01

Because students' ability to use statistics, which is mathematical in nature, is one of the concerns of educators, embedding within an e-learning system the pedagogical characteristics of learning is 'value added' because it facilitates the conventional method of learning mathematics. Many researchers emphasize the effectiveness of cognitive apprenticeship in learning and problem solving in the workplace. In a cognitive apprenticeship learning model, skills are learned within a community of practitioners through observation of modelling and then practice plus coaching. This study utilized an internet-based Cognitive Apprenticeship Model (i-CAM) in three phases and evaluated its effectiveness for improving statistics problem-solving performance among postgraduate students. The results showed that, when compared to the conventional mathematics learning model, the i-CAM could significantly promote students' problem-solving performance at the end of each phase. In addition, the combination of the differences in students' test scores were considered to be statistically significant after controlling for the pre-test scores. The findings conveyed in this paper confirmed the considerable value of i-CAM in the improvement of statistics learning for non-specialized postgraduate students.

Focusing properties of arbitrary optical fields combining spiral phase and cylindrically symmetric state of polarization.

PubMed

Man, Zhongsheng; Bai, Zhidong; Zhang, Shuoshuo; Li, Jinjian; Li, Xiaoyu; Ge, Xiaolu; Zhang, Yuquan; Fu, Shenggui

2018-06-01

The tight focusing properties of optical fields combining a spiral phase and cylindrically symmetric state of polarization are presented. First, we theoretically analyze the mathematical characterization, Stokes parameters, and Poincaré sphere representations of arbitrary cylindrical vector (CV) vortex beams. Then, based on the vector diffraction theory, we derive and build an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input CV vortex beams. The calculations reveal that a generalized CV vortex beam can generate a sharper focal spot than that of a radially polarized (RP) plane beam in the focal plane. Besides, the focal size decrease accompanies its elongation along the optical axis. Hence, it seems that there is a trade-off between the transverse and axial resolutions. In addition, under the precondition that the absolute values between polarization order and topological charge are equal, a higher-order CV vortex can also achieve a smaller focal size than an RP plane beam. Further, the intensity for the sidelobe admits a significant suppression. To give a deep understanding of the peculiar focusing properties, the magnetic field and Poynting vector distributions are also demonstrated in detail. These properties may be helpful in applications such as optical trapping and manipulation of particles and superresolution microscopy imaging.

Image size invariant visual cryptography for general access structures subject to display quality constraints.

PubMed

Lee, Kai-Hui; Chiu, Pei-Ling

2013-10-01

Conventional visual cryptography (VC) suffers from a pixel-expansion problem, or an uncontrollable display quality problem for recovered images, and lacks a general approach to construct visual secret sharing schemes for general access structures. We propose a general and systematic approach to address these issues without sophisticated codebook design. This approach can be used for binary secret images in non-computer-aided decryption environments. To avoid pixel expansion, we design a set of column vectors to encrypt secret pixels rather than using the conventional VC-based approach. We begin by formulating a mathematic model for the VC construction problem to find the column vectors for the optimal VC construction, after which we develop a simulated-annealing-based algorithm to solve the problem. The experimental results show that the display quality of the recovered image is superior to that of previous papers.

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

NASA Technical Reports Server (NTRS)

Strelkov, S. A.; Sushkevich, T. A.

1983-01-01

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

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

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana

2017-12-01

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

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Vector processing efficiency of plasma MHD codes by use of the FACOM 230-75 APU

NASA Astrophysics Data System (ADS)

Matsuura, T.; Tanaka, Y.; Naraoka, K.; Takizuka, T.; Tsunematsu, T.; Tokuda, S.; Azumi, M.; Kurita, G.; Takeda, T.

1982-06-01

In the framework of pipelined vector architecture, the efficiency of vector processing is assessed with respect to plasma MHD codes in nuclear fusion research. By using a vector processor, the FACOM 230-75 APU, the limit of the enhancement factor due to parallelism of current vector machines is examined for three numerical codes based on a fluid model. Reasonable speed-up factors of approximately 6,6 and 4 times faster than the highly optimized scalar version are obtained for ERATO (linear stability code), AEOLUS-R1 (nonlinear stability code) and APOLLO (1-1/2D transport code), respectively. Problems of the pipelined vector processors are discussed from the viewpoint of restructuring, optimization and choice of algorithms. In conclusion, the important concept of "concurrency within pipelined parallelism" is emphasized.

The Menu for Every Young Mathematician's Appetite

ERIC Educational Resources Information Center

Legnard, Danielle S.; Austin, Susan L.

2012-01-01

Math Workshop offers differentiated instruction to foster a deep understanding of rich, rigorous mathematics that is attainable by all learners. The inquiry-based model provides a menu of multilevel math tasks, within the daily math block, that focus on similar mathematical content. Math Workshop promotes a culture of engagement and…

Characteristics pertaining to a stiffness cross-coupled Jeffcott model

NASA Technical Reports Server (NTRS)

Spanyer, K. L.

1985-01-01

Rotordynamic studies of complex systems utilizing multiple degree-of-freedom analysis have been performed to understand response, loads, and stability. In order to understand the fundamental nature of rotordynamic response, the Jeffcott rotor model has received wide attention. The purpose of this paper is to provide a generic rotordynamic analysis of a stiffness cross-coupled Jeffcott rotor model to illustrate characteristics of a second order stiffness-coupled linear system. The particular characteristics investigated were forced response, force vector diagrams, response orbits, and stability. Numerical results were achieved through a fourth order Runge-Kutta method for solving differential equations and the Routh Hurwitz stability criterion. The numerical results were verified to an exact mathematical solution for the steady state response.

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

Vector Data Model: A New Model of HDF-EOS to Support GIS Applications in EOS

NASA Astrophysics Data System (ADS)

Chi, E.; Edmonds, R d

2001-05-01

NASA's Earth Science Data Information System (ESDIS) project has an active program of research and development of systems for the storage and management of Earth science data for Earth Observation System (EOS) mission, a key program of NASA Earth Science Enterprise. EOS has adopted an extension of the Hierarchical Data Format (HDF) as the format of choice for standard product distribution. Three new EOS specific datatypes - point, swath and grid - have been defined within the HDF framework. The enhanced data format is named HDF-EOS. Geographic Information Systems (GIS) are used by Earth scientists in EOS data product generation, visualization, and analysis. There are two major data types in GIS applications, raster and vector. The current HDF-EOS handles only raster type in the swath data model. The vector data model is identified and developed as a new HDFEOS format to meet the requirements of scientists working with EOS data products in vector format. The vector model is designed using a topological data structure, which defines the spatial relationships among points, lines, and polygons. The three major topological concepts that the vector model adopts are: a) lines connect to each other at nodes (connectivity), b) lines that connect to surround an area define a polygon (area definition), and c) lines have direction and left and right sides (contiguity). The vector model is implemented in HDF by mapping the conceptual model to HDF internal data models and structures, viz. Vdata, Vgroup, and their associated attribute structures. The point, line, and polygon geometry and attribute data are stored in similar tables. Further, the vector model utilizes the structure and product metadata, which characterize the HDF-EOS. Both types of metadata are stored as attributes in HDF-EOS files, and are encoded in text format by using Object Description Language (ODL) and stored as global attributes in HDF-EOS files. EOS has developed a series of routines for storing, retrieving, and manipulating vector data in category of access, definition, basic I/O, inquiry, and subsetting. The routines are tested and form a package, HDF-EOS/Vector. The alpha version of HDFEOS/Vector has been distributed through the HDF-EOS project web site at http://hdfeos.gsfc.nasa.gov. We are also developing translators between HDF-EOS vector format and variety of GIS formats, such as Shapefile. The HDF-EOS vector model enables EOS scientists to deliver EOS data in a way ready for Earth scientists to analyze using GIS software, and also provides EOS project a mechanism to store GIS data product in meaningful vector format with significant economy in storage.

Interaction of mathematical modeling and social and behavioral HIV/AIDS research.

PubMed

Cassels, Susan; Goodreau, Steven M

2011-03-01

HIV is transmitted within complex biobehavioral systems. Mathematical modeling can provide insight to complex population-level outcomes of various behaviors measured at an individual level. HIV models in the social and behavioral sciences can be categorized in a number of ways; here, we consider two classes of applications common in the field generally, and in the past year in particular: those models that explore significant behavioral determinants of HIV disparities within and between populations; and those models that seek to evaluate the potential impact of specific social and behavioral interventions. We discuss two overarching issues we see in the field: the need to further systematize effectiveness models of behavioral interventions, and the need for increasing investigation of the use of behavioral data in epidemic models. We believe that a recent initiative by the National Institutes of Health will qualitatively change the relationships between epidemic modeling and sociobehavioral prevention research in the coming years.

On the analysis of competitive displacement in dengue disease transmission

NASA Astrophysics Data System (ADS)

Wijaya, Karunia P.; Nuraini, Nuning; Soewono, Edy; Handayani, Dewi

2014-03-01

We study a host-vector model involving the interplay of competitive displacement mechanism in a specific DENV serotype, both in human blood and mosquito blood. Using phylogenetic analysis, world virologists investigate the severe manifestations of dengue fever caused by the displacements within weakly virulent pathogens (native strains) by more virulent pathogens (invasive strains) in one serotype. We construct SIR model for human and SI model for mosquito to explore the key determinants of those displacements. Analysis of nonnegativity and boundedness of the solution as well as the basic reproduction number (R0) are taken into account for verifying the model into biological meaningfulness. To generate predictions of the outcomes of control strategies, we derive an optimal control model which involves two control apparatus: fluid infusion (for human) and fumigation (for vector). Numerical results show the dynamics of host-vector in an observation period, both under control and without control.

Climate-based models for West Nile Culex mosquito vectors in the Northeastern US

NASA Astrophysics Data System (ADS)

Gong, Hongfei; Degaetano, Arthur T.; Harrington, Laura C.

2011-05-01

Climate-based models simulating Culex mosquito population abundance in the Northeastern US were developed. Two West Nile vector species, Culex pipiens and Culex restuans, were included in model simulations. The model was optimized by a parameter-space search within biological bounds. Mosquito population dynamics were driven by major environmental factors including temperature, rainfall, evaporation rate and photoperiod. The results show a strong correlation between the timing of early population increases (as early warning of West Nile virus risk) and decreases in late summer. Simulated abundance was highly correlated with actual mosquito capture in New Jersey light traps and validated with field data. This climate-based model simulates the population dynamics of both the adult and immature mosquito life stage of Culex arbovirus vectors in the Northeastern US. It is expected to have direct and practical application for mosquito control and West Nile prevention programs.

Classification of customer lifetime value models using Markov chain

NASA Astrophysics Data System (ADS)

Permana, Dony; Pasaribu, Udjianna S.; Indratno, Sapto W.; Suprayogi

2017-10-01

A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm.

Mathematical modeling analysis of intratumoral disposition of anticancer agents and drug delivery systems.

PubMed

Popilski, Hen; Stepensky, David

2015-05-01

Solid tumors are characterized by complex morphology. Numerous factors relating to the composition of the cells and tumor stroma, vascularization and drainage of fluids affect the local microenvironment within a specific location inside the tumor. As a result, the intratumoral drug/drug delivery system (DDS) disposition following systemic or local administration is non-homogeneous and its complexity reflects the differences in the local microenvironment. Mathematical models can be used to analyze the intratumoral drug/DDS disposition and pharmacological effects and to assist in choice of optimal anticancer treatment strategies. The mathematical models that have been applied by different research groups to describe the intratumoral disposition of anticancer drugs/DDSs are summarized in this article. The properties of these models and of their suitability for prediction of the drug/DDS intratumoral disposition and pharmacological effects are reviewed. Currently available mathematical models appear to neglect some of the major factors that govern the drug/DDS intratumoral disposition, and apparently possess limited prediction capabilities. More sophisticated and detailed mathematical models and their extensive validation are needed for reliable prediction of different treatment scenarios and for optimization of drug treatment in the individual cancer patients.

Temperature Coefficient for Modeling Denitrification in Surface Water Sediments Using the Mass Transfer Coefficient

Treesearch

T. W. Appelboom; G. M. Chescheir; R. W. Skaggs; J. W. Gilliam; Devendra M. Amatya

2006-01-01

Watershed modeling has become an important tool for researchers with the high costs of water quality monitoring. When modeling nitrate transport within drainage networks, denitrification within the sediments needs to be accounted for. Birgand et. al. developed an equation using a term called a mass transfer coefficient to mathematically describe sediment...

Temperature coefficient for modeling denitrification in surface water sediments using the mass transfer coefficient

Treesearch

T.W. Appelboom; G.M. Chescheir; F. Birgand; R.W. Skaggs; J.W. Gilliam; D. Amatya

2010-01-01

Watershed modeling has become an important tool for researchers. Modeling nitrate transport within drainage networks requires quantifying the denitrification within the sediments in canals and streams. In a previous study, several of the authors developed an equation using a term called a mass transfer coefficient to mathematically describe sediment denitrification....

Temperature coefficient for modeling denitrification in surface water sediments using the mass transfer coefficient.

Treesearch

T.W. Appelboom; G.M. Chescheir; F. Birgand; R.W. Skaggs; J.W. Gilliam; D. Amatya

2010-01-01

Watershed modeling has become an important tool for researchers. Modeling nitrate transport within drainage networks requires quantifying the denitrification within the sediments in canals and streams. In a previous study, several of the authors developed an equation using a term called a mass transfer coefficient to mathematically describe sediment denitrification....

D GIS for Flood Modelling in River Valleys

NASA Astrophysics Data System (ADS)

Tymkow, P.; Karpina, M.; Borkowski, A.

2016-06-01

The objective of this study is implementation of system architecture for collecting and analysing data as well as visualizing results for hydrodynamic modelling of flood flows in river valleys using remote sensing methods, tree-dimensional geometry of spatial objects and GPU multithread processing. The proposed solution includes: spatial data acquisition segment, data processing and transformation, mathematical modelling of flow phenomena and results visualization. Data acquisition segment was based on aerial laser scanning supplemented by images in visible range. Vector data creation was based on automatic and semiautomatic algorithms of DTM and 3D spatial features modelling. Algorithms for buildings and vegetation geometry modelling were proposed or adopted from literature. The implementation of the framework was designed as modular software using open specifications and partially reusing open source projects. The database structure for gathering and sharing vector data, including flood modelling results, was created using PostgreSQL. For the internal structure of feature classes of spatial objects in a database, the CityGML standard was used. For the hydrodynamic modelling the solutions of Navier-Stokes equations in two-dimensional version was implemented. Visualization of geospatial data and flow model results was transferred to the client side application. This gave the independence from server hardware platform. A real-world case in Poland, which is a part of Widawa River valley near Wroclaw city, was selected to demonstrate the applicability of proposed system.

A manufacturing error measurement methodology for a rotary vector reducer cycloidal gear based on a gear measuring center

NASA Astrophysics Data System (ADS)

Li, Tianxing; Zhou, Junxiang; Deng, Xiaozhong; Li, Jubo; Xing, Chunrong; Su, Jianxin; Wang, Huiliang

2018-07-01

A manufacturing error of a cycloidal gear is the key factor affecting the transmission accuracy of a robot rotary vector (RV) reducer. A methodology is proposed to realize the digitized measurement and data processing of the cycloidal gear manufacturing error based on the gear measuring center, which can quickly and accurately measure and evaluate the manufacturing error of the cycloidal gear by using both the whole tooth profile measurement and a single tooth profile measurement. By analyzing the particularity of the cycloidal profile and its effect on the actual meshing characteristics of the RV transmission, the cycloid profile measurement strategy is planned, and the theoretical profile model and error measurement model of cycloid-pin gear transmission are established. Through the digital processing technology, the theoretical trajectory of the probe and the normal vector of the measured point are calculated. By means of precision measurement principle and error compensation theory, a mathematical model for the accurate calculation and data processing of manufacturing error is constructed, and the actual manufacturing error of the cycloidal gear is obtained by the optimization iterative solution. Finally, the measurement experiment of the cycloidal gear tooth profile is carried out on the gear measuring center and the HEXAGON coordinate measuring machine, respectively. The measurement results verify the correctness and validity of the measurement theory and method. This methodology will provide the basis for the accurate evaluation and the effective control of manufacturing precision of the cycloidal gear in a robot RV reducer.

A mathematical model for predicting cyclic voltammograms of electronically conductive polypyrrole

NASA Technical Reports Server (NTRS)

Yeu, Taewhan; Nguyen, Trung V.; White, Ralph E.

1988-01-01

Polypyrrole is an attractive polymer for use as a high-energy-density secondary battery because of its potential as an inexpensive, lightweight, and noncorrosive electrode material. A mathematical model to simulate cyclic voltammograms for polypyrrole is presented. The model is for a conductive porous electrode film on a rotating disk electrode (RDE) and is used to predict the spatial and time dependence of concentration, overpotential, and stored charge profiles within a polypyrrole film. The model includes both faradic and capacitance charge components in the total current density expression.

A mathematical model for predicting cyclic voltammograms of electronically conductive polypyrrole

NASA Technical Reports Server (NTRS)

Yeu, Taewhan; Nguyen, Trung V.; White, Ralph E.

1987-01-01

Polypyrrole is an attractive polymer for use as a high-energy-density secondary battery because of its potential as an inexpensive, lightweight, and noncorrosive electrode material. A mathematical model to simulate cyclic voltammograms for polypyrrole is presented. The model is for a conductive porous electrode film on a rotating disk electrode (RDE) and is used to predict the spatial and time dependence of concentration, overpotential, and stored charge profiles within a polypyrrole film. The model includes both faradic and capacitance charge components in the total current density expression.

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

PubMed

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

2016-06-01

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

The Prediction of Scattered Broadband Shock-Associated Noise

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

PubMed Central

Bucksch, Alexander; Atta-Boateng, Acheampong; Azihou, Akomian F.; Battogtokh, Dorjsuren; Baumgartner, Aly; Binder, Brad M.; Braybrook, Siobhan A.; Chang, Cynthia; Coneva, Viktoirya; DeWitt, Thomas J.; Fletcher, Alexander G.; Gehan, Malia A.; Diaz-Martinez, Diego Hernan; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Klein, Laura L.; Leiboff, Samuel; Li, Mao; Lynch, Jonathan P.; Maizel, Alexis; Maloof, Julin N.; Markelz, R. J. Cody; Martinez, Ciera C.; Miller, Laura A.; Mio, Washington; Palubicki, Wojtek; Poorter, Hendrik; Pradal, Christophe; Price, Charles A.; Puttonen, Eetu; Reese, John B.; Rellán-Álvarez, Rubén; Spalding, Edgar P.; Sparks, Erin E.; Topp, Christopher N.; Williams, Joseph H.; Chitwood, Daniel H.

2017-01-01

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics. PMID:28659934

Software and mathematical support of Kazakhstani star tracker

NASA Astrophysics Data System (ADS)

Akhmedov, D.; Yelubayev, S.; Ten, V.; Bopeyev, T.; Alipbayev, K.; Sukhenko, A.

2016-10-01

Currently the specialists of Kazakhstan have been developing the star tracker that is further planned to use on Kazakhstani satellites of various purposes. At the first stage it has been developed the experimental model of star tracker that has following characteristics: field of view 20°, update frequency 2 Hz, exclusion angle 40°, accuracy of attitude determination of optical axis/around optical axis 15/50 arcsec. Software and mathematical support are the most high technology parts of star tracker. The results of software and mathematical support development of experimental model of Kazakhstani star tracker are represented in this article. In particular, there are described the main mathematical models and algorithms that have been used as a basis for program units of preliminary image processing of starry sky, stars identification and star tracker attitude determination. The results of software and mathematical support testing with the help of program simulation complex using various configurations of defects including image sensor noises, point spread function modeling, optical system distortion up to 2% are presented. Analysis of testing results has shown that accuracy of attitude determination of star tracker is within the permissible range

Mathematical (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters

PubMed Central

Baten, Elke; Desoete, Annemie

2018-01-01

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. PMID:29867645

Mathematical (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters.

PubMed

Baten, Elke; Desoete, Annemie

2018-01-01

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers' experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided.

Reduced modeling of signal transduction – a modular approach

PubMed Central

Koschorreck, Markus; Conzelmann, Holger; Ebert, Sybille; Ederer, Michael; Gilles, Ernst Dieter

2007-01-01

Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties. PMID:17854494

Flipping the Electromagnetic Theory classroom

NASA Astrophysics Data System (ADS)

Berger, Andrew J.

2017-08-01

Electromagnetic Theory is a required junior-year course for Optics majors at the University of Rochester. This foundational course gives students their first rigorous exposure to electromagnetic vector fields, dipole radiation patterns, Fresnel reflection/transmission coefficients, waveguided modes, Jones vectors, waveplates, birefringence, and the Lorentz model of refractive index. To increase the percentage of class time devoted to student-centered conceptual reasoning and instructor feedback, this course was recently "flipped". Nearly all of the mathematically-intensive derivations were converted to narrated screencasts ("Khan Academy" style) and made available to students through the course's learning management system. On average, the students were assigned two 10-15 minute videos to watch in advance of each lecture. An electronic survey after each tutorial encouraged reflection and counted towards the student's participation grade. Over the past three years, students have consistently rated the videos as being highly valuable. This presentation will discuss the technical aspects of creating tutorial videos and the educational tradeoffs of flipping a mathematically-intensive upper-level course. The most important advantage is the instructor's increased ability to identify and respond to student confusion, via activities that would consume too much time in a lecture-centered course. Several examples of such activities will be given. Two pitfalls to avoid are the temptation for the instructor not to update the videos from year to year and the tendency of students not to take lecture notes while watching the videos.

Towards a Methodology for the Characterization of Teachers' Didactic-Mathematical Knowledge

ERIC Educational Resources Information Center

Pino-Fan, Luis R.; Assis, Adriana; Castro, Walter F.

2015-01-01

This research study aims at exploring the use of some dimensions and theoretical-methodological tools suggested by the model of Didactic-Mathematical Knowledge (DMK) for the analysis, characterization and development of knowledge that teachers should have in order to efficiently develop within their practice. For this purpose, we analyzed the…

Viability of strongly coupled scenarios with a light Higgs-like boson.

PubMed

Pich, Antonio; Rosell, Ignasi; Sanz-Cillero, Juan José

2013-05-03

We present a one-loop calculation of the oblique S and T parameters within strongly coupled models of electroweak symmetry breaking with a light Higgs-like boson. We use a general effective Lagrangian, implementing the chiral symmetry breaking SU(2)(L) [Symbol: see text]SU(2)(R) → SU(2)(L+R) with Goldstone bosons, gauge bosons, the Higgs-like scalar, and one multiplet of vector and axial-vector massive resonance states. Using a dispersive representation and imposing a proper ultraviolet behavior, we obtain S and T at the next-to-leading order in terms of a few resonance parameters. The experimentally allowed range forces the vector and axial-vector states to be heavy, with masses above the TeV scale, and suggests that the Higgs-like scalar should have a WW coupling close to the standard model one. Our conclusions are generic and apply to more specific scenarios such as the minimal SO(5)/SO(4) composite Higgs model.

An Introduction to Tensors for Students of Physics and Engineering

NASA Technical Reports Server (NTRS)

Kolecki, Joseph C.

2002-01-01

Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.

On-line object feature extraction for multispectral scene representation

NASA Technical Reports Server (NTRS)

Ghassemian, Hassan; Landgrebe, David

1988-01-01

A new on-line unsupervised object-feature extraction method is presented that reduces the complexity and costs associated with the analysis of the multispectral image data and data transmission, storage, archival and distribution. The ambiguity in the object detection process can be reduced if the spatial dependencies, which exist among the adjacent pixels, are intelligently incorporated into the decision making process. The unity relation was defined that must exist among the pixels of an object. Automatic Multispectral Image Compaction Algorithm (AMICA) uses the within object pixel-feature gradient vector as a valuable contextual information to construct the object's features, which preserve the class separability information within the data. For on-line object extraction the path-hypothesis and the basic mathematical tools for its realization are introduced in terms of a specific similarity measure and adjacency relation. AMICA is applied to several sets of real image data, and the performance and reliability of features is evaluated.

Toward Brain Tumor Gene Therapy Using Multipotent Mesenchymal Stromal Cell Vectors

PubMed Central

Bexell, Daniel; Scheding, Stefan; Bengzon, Johan

2010-01-01

Gene therapy of solid cancers has been severely restricted by the limited distribution of vectors within tumors. However, cellular vectors have emerged as an effective migratory system for gene delivery to invasive cancers. Implanted and injected multipotent mesenchymal stromal cells (MSCs) have shown tropism for several types of primary tumors and metastases. This capacity of MSCs forms the basis for their use as a gene vector system in neoplasms. Here, we review the tumor-directed migratory potential of MSCs, mechanisms of the migration, and the choice of therapeutic transgenes, with a focus on malignant gliomas as a model system for invasive and highly vascularized tumors. We examine recent findings demonstrating that MSCs share many characteristics with pericytes and that implanted MSCs localize primarily to perivascular niches within tumors, which might have therapeutic implications. The use of MSC vectors in cancer gene therapy raises concerns, however, including a possible MSC contribution to tumor stroma and vasculature, MSC-mediated antitumor immune suppression, and the potential malignant transformation of cultured MSCs. Nonetheless, we highlight the novel prospects of MSC-based tumor therapy, which appears to be a promising approach. PMID:20407426

Can Horton hear the whos? The importance of scale in mosquito-borne disease.

PubMed

Lord, C C; Alto, B W; Anderson, S L; Connelly, C R; Day, J F; Richards, S L; Smartt, C T; Tabachnick, W J

2014-03-01

The epidemiology of vector-borne pathogens is determined by mechanisms and interactions at different scales of biological organization, from individual-level cellular processes to community interactions between species and with the environment. Most research, however, focuses on one scale or level with little integration between scales or levels within scales. Understanding the interactions between levels and how they influence our perception of vector-borne pathogens is critical. Here two examples of biological scales (pathogen transmission and mosquito mortality) are presented to illustrate some of the issues of scale and to explore how processes on different levels may interact to influence mosquito-borne pathogen transmission cycles. Individual variation in survival, vector competence, and other traits affect population abundance, transmission potential, and community structure. Community structure affects interactions between individuals such as competition and predation, and thus influences the individual-level dynamics and transmission potential. Modeling is a valuable tool to assess interactions between scales and how processes at different levels can affect transmission dynamics. We expand an existing model to illustrate the types of studies needed, showing that individual-level variation in viral dose acquired or needed for infection can influence the number of infectious vectors. It is critical that interactions within and among biological scales and levels of biological organization are understood for greater understanding of pathogen transmission with the ultimate goal of improving control of vector-borne pathogens.

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

NASA Technical Reports Server (NTRS)

Fischbach, S. R.

2015-01-01

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and ? as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

QR-STEM: Energy and Environment as a Context for Improving QR and STEM Understandings of 6-12 Grade Teachers II. The Quantitative Reasoning

NASA Astrophysics Data System (ADS)

Mayes, R.; Lyford, M. E.; Myers, J. D.

2009-12-01

The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.

Evaluation of a Pair-Wise Conflict Detection and Resolution Algorithm in a Multiple Aircraft Scenario

NASA Technical Reports Server (NTRS)

Carreno, Victor A.

2002-01-01

The KB3D algorithm is a pairwise conflict detection and resolution (CD&R) algorithm. It detects and generates trajectory vectoring for an aircraft which has been predicted to be in an airspace minima violation within a given look-ahead time. It has been proven, using mechanized theorem proving techniques, that for a pair of aircraft, KB3D produces at least one vectoring solution and that all solutions produced are correct. Although solutions produced by the algorithm are mathematically correct, they might not be physically executable by an aircraft or might not solve multiple aircraft conflicts. This paper describes a simple solution selection method which assesses all solutions generated by KB3D and determines the solution to be executed. The solution selection method and KB3D are evaluated using a simulation in which N aircraft fly in a free-flight environment and each aircraft in the simulation uses KB3D to maintain separation. Specifically, the solution selection method filters KB3D solutions which are procedurally undesirable or physically not executable and uses a predetermined criteria for selection.

Balancing Chemical Reactions With Matrix Methods and Computer Assistance. Applications of Linear Algebra to Chemistry. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 339.

ERIC Educational Resources Information Center

Grimaldi, Ralph P.

This material was developed to provide an application of matrix mathematics in chemistry, and to show the concepts of linear independence and dependence in vector spaces of dimensions greater than three in a concrete setting. The techniques presented are not intended to be considered as replacements for such chemical methods as oxidation-reduction…

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part I: Fundamentals

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2016-12-01

Recent advances in signal processing and structural dynamics have spurred the adoption of transmissibility functions in academia and industry alike. Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty impacts its applications. This study is focused on statistical inference for raw scalar transmissibility functions modeled as complex ratio random variables. The goal is achieved through companion papers. This paper (Part I) is dedicated to dealing with a formal mathematical proof. New theorems on multivariate circularly-symmetric complex normal ratio distribution are proved on the basis of principle of probabilistic transformation of continuous random vectors. The closed-form distributional formulas for multivariate ratios of correlated circularly-symmetric complex normal random variables are analytically derived. Afterwards, several properties are deduced as corollaries and lemmas to the new theorems. Monte Carlo simulation (MCS) is utilized to verify the accuracy of some representative cases. This work lays the mathematical groundwork to find probabilistic models for raw scalar transmissibility functions, which are to be expounded in detail in Part II of this study.

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

MODELING DEPOSITION OF INHALED PARTICLES

EPA Science Inventory

Modeling Deposition of Inhaled Particles: ABSTRACT

The mathematical modeling of the deposition and distribution of inhaled aerosols within human lungs is an invaluable tool in predicting both the health risks associated with inhaled environmental aerosols and the therapeut...

The evolution of parasitic and mutualistic plant-virus symbioses through transmission-virulence trade-offs.

PubMed

Hamelin, Frédéric M; Hilker, Frank M; Sun, T Anthony; Jeger, Michael J; Hajimorad, M Reza; Allen, Linda J S; Prendeville, Holly R

2017-09-15

Virus-plant interactions range from parasitism to mutualism. Viruses have been shown to increase fecundity of infected plants in comparison with uninfected plants under certain environmental conditions. Increased fecundity of infected plants may benefit both the plant and the virus as seed transmission is one of the main virus transmission pathways, in addition to vector transmission. Trade-offs between vertical (seed) and horizontal (vector) transmission pathways may involve virulence, defined here as decreased fecundity in infected plants. To better understand plant-virus symbiosis evolution, we explore the ecological and evolutionary interplay of virus transmission modes when infection can lead to an increase in plant fecundity. We consider two possible trade-offs: vertical seed transmission vs infected plant fecundity, and horizontal vector transmission vs infected plant fecundity (virulence). Through mathematical models and numerical simulations, we show (1) that a trade-off between virulence and vertical transmission can lead to virus extinction during the course of evolution, (2) that evolutionary branching can occur with subsequent coexistence of mutualistic and parasitic virus strains, and (3) that mutualism can out-compete parasitism in the long-run. In passing, we show that ecological bi-stability is possible in a very simple discrete-time epidemic model. Possible extensions of this study include the evolution of conditional (environment-dependent) mutualism in plant viruses. Copyright © 2017 Elsevier B.V. All rights reserved.

Thermodynamic view on decision-making process: emotions as a potential power vector of realization of the choice.

PubMed

Pakhomov, Anton; Sudin, Natalya

2013-12-01

This research is devoted to possible mechanisms of decision-making in frames of thermodynamic principles. It is also shown that the decision-making system in reply to emotion includes vector component which seems to be often a necessary condition to transfer system from one state to another. The phases of decision-making system can be described as supposed to be nonequilibrium and irreversible to which thermodynamics laws are applied. The mathematical model of a decision choice, proceeding from principles of the nonlinear dynamics considering instability of movement and bifurcation is offered. The thermodynamic component of decision-making process on the basis of vector transfer of energy induced by emotion at the given time is surveyed. It is proposed a three-modular model of decision making based on principles of thermodynamics. Here it is suggested that at entropy impact due to effect of emotion, on the closed system-the human brain,-initially arises chaos, then after fluctuations of possible alternatives which were going on-reactions of brain zones in reply to external influence, an order is forming and there is choice of alternatives, according to primary entrance conditions and a state of the closed system. Entropy calculation of a choice expectation of negative and positive emotion shows judgment possibility of existence of "the law of emotion conservation" in accordance with several experimental data.

Neural-Network Simulator

NASA Technical Reports Server (NTRS)

Mitchell, Paul H.

1991-01-01

F77NNS (FORTRAN 77 Neural Network Simulator) computer program simulates popular back-error-propagation neural network. Designed to take advantage of vectorization when used on computers having this capability, also used on any computer equipped with ANSI-77 FORTRAN Compiler. Problems involving matching of patterns or mathematical modeling of systems fit class of problems F77NNS designed to solve. Program has restart capability so neural network solved in stages suitable to user's resources and desires. Enables user to customize patterns of connections between layers of network. Size of neural network F77NNS applied to limited only by amount of random-access memory available to user.

Response Mixture Modeling: Accounting for Heterogeneity in Item Characteristics across Response Times.

PubMed

Molenaar, Dylan; de Boeck, Paul

2018-06-01

In item response theory modeling of responses and response times, it is commonly assumed that the item responses have the same characteristics across the response times. However, heterogeneity might arise in the data if subjects resort to different response processes when solving the test items. These differences may be within-subject effects, that is, a subject might use a certain process on some of the items and a different process with different item characteristics on the other items. If the probability of using one process over the other process depends on the subject's response time, within-subject heterogeneity of the item characteristics across the response times arises. In this paper, the method of response mixture modeling is presented to account for such heterogeneity. Contrary to traditional mixture modeling where the full response vectors are classified, response mixture modeling involves classification of the individual elements in the response vector. In a simulation study, the response mixture model is shown to be viable in terms of parameter recovery. In addition, the response mixture model is applied to a real dataset to illustrate its use in investigating within-subject heterogeneity in the item characteristics across response times.

Targeted Screening Strategies to Detect Trypanosoma cruzi Infection in Children

PubMed Central

Levy, Michael Z.; Kawai, Vivian; Bowman, Natalie M.; Waller, Lance A.; Cabrera, Lilia; Pinedo-Cancino, Viviana V.; Seitz, Amy E.; Steurer, Frank J.; Cornejo del Carpio, Juan G.; Cordova-Benzaquen, Eleazar; Maguire, James H.; Gilman, Robert H.; Bern, Caryn

2007-01-01

Background Millions of people are infected with Trypanosoma cruzi, the causative agent of Chagas disease in Latin America. Anti-trypanosomal drug therapy can cure infected individuals, but treatment efficacy is highest early in infection. Vector control campaigns disrupt transmission of T. cruzi, but without timely diagnosis, children infected prior to vector control often miss the window of opportunity for effective chemotherapy. Methods and Findings We performed a serological survey in children 2–18 years old living in a peri-urban community of Arequipa, Peru, and linked the results to entomologic, spatial and census data gathered during a vector control campaign. 23 of 433 (5.3% [95% CI 3.4–7.9]) children were confirmed seropositive for T. cruzi infection by two methods. Spatial analysis revealed that households with infected children were very tightly clustered within looser clusters of households with parasite-infected vectors. Bayesian hierarchical mixed models, which controlled for clustering of infection, showed that a child's risk of being seropositive increased by 20% per year of age and 4% per vector captured within the child's house. Receiver operator characteristic (ROC) plots of best-fit models suggest that more than 83% of infected children could be identified while testing only 22% of eligible children. Conclusions We found evidence of spatially-focal vector-borne T. cruzi transmission in peri-urban Arequipa. Ongoing vector control campaigns, in addition to preventing further parasite transmission, facilitate the collection of data essential to identifying children at high risk of T. cruzi infection. Targeted screening strategies could make integration of diagnosis and treatment of children into Chagas disease control programs feasible in lower-resource settings. PMID:18160979

Heterotic line bundle models on elliptically fibered Calabi-Yau three-folds

NASA Astrophysics Data System (ADS)

Braun, Andreas P.; Brodie, Callum R.; Lukas, Andre

2018-04-01

We analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus on elliptically fibered three-folds with a second section and a freely-acting involution. Specifically, we consider toric weak Fano surfaces as base manifolds and identify six such manifolds with the required properties. The requisite mathematical tools for the construction of line bundle models on these spaces, including the calculation of line bundle cohomology, are developed. A computer scan leads to more than 400 line bundle models with the right number of families and an SU(5) GUT group which could descend to standard-like models after taking the ℤ2 quotient. A common and surprising feature of these models is the presence of a large number of vector-like states.

Early Mathematics Achievement Trajectories: English-Language Learner and Native English-Speaker Estimates, Using the Early Childhood Longitudinal Survey

PubMed Central

Roberts, Greg; Bryant, Diane

2012-01-01

This study used data from the Early Childhood Longitudinal Survey, Kindergarten Class of 1998 –1999, to (a) estimate mathematics achievement trends through 5th grade in the population of students who are English-language proficient by the end of kindergarten, (b) compare trends across primary language groups within this English-language proficient group, (c) evaluate the effect of low socioeconomic status (SES) for English-language proficient students and within different primary language groups, and (d) estimate language-group trends in specific mathematics skill areas. The group of English-language proficient English-language learners (ELLs) was disaggregated into native Spanish speakers and native speakers of Asian languages, the 2 most prevalent groups of ELLs in the United States. Results of multilevel latent variable growth modeling suggest that primary language may be less salient than SES in explaining the mathematics achievement of English-language proficient ELLs. The study also found that mathematics-related school readiness is a key factor in explaining subsequent achievement differences and that the readiness gap is prevalent across the range of mathematics-related skills. PMID:21574702

Effect of Internet-Based Cognitive Apprenticeship Model (i-CAM) on Statistics Learning among Postgraduate Students

PubMed Central

Saadati, Farzaneh; Ahmad Tarmizi, Rohani

2015-01-01

Because students’ ability to use statistics, which is mathematical in nature, is one of the concerns of educators, embedding within an e-learning system the pedagogical characteristics of learning is ‘value added’ because it facilitates the conventional method of learning mathematics. Many researchers emphasize the effectiveness of cognitive apprenticeship in learning and problem solving in the workplace. In a cognitive apprenticeship learning model, skills are learned within a community of practitioners through observation of modelling and then practice plus coaching. This study utilized an internet-based Cognitive Apprenticeship Model (i-CAM) in three phases and evaluated its effectiveness for improving statistics problem-solving performance among postgraduate students. The results showed that, when compared to the conventional mathematics learning model, the i-CAM could significantly promote students’ problem-solving performance at the end of each phase. In addition, the combination of the differences in students' test scores were considered to be statistically significant after controlling for the pre-test scores. The findings conveyed in this paper confirmed the considerable value of i-CAM in the improvement of statistics learning for non-specialized postgraduate students. PMID:26132553

TVC actuator model. [for the space shuttle main engine

NASA Technical Reports Server (NTRS)

Baslock, R. W.

1977-01-01

A prototype Space Shuttle Main Engine (SSME) Thrust Vector Control (TVC) Actuator analog model was successfully completed. The prototype, mounted on five printed circuit (PC) boards, was delivered to NASA, checked out and tested using a modular replacement technique on an analog computer. In all cases, the prototype model performed within the recording techniques of the analog computer which is well within the tolerances of the specifications.

Conformal mapping in optical biosensor applications.

PubMed

Zumbrum, Matthew E; Edwards, David A

2015-09-01

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

Dynamics of Vector-Host Interactions in Avian Communities in Four Eastern Equine Encephalitis Virus Foci in the Northeastern U.S.

PubMed Central

Molaei, Goudarz; Thomas, Michael C.; Muller, Tim; Medlock, Jan; Shepard, John J.; Armstrong, Philip M.; Andreadis, Theodore G.

2016-01-01

Background Eastern equine encephalitis (EEE) virus (Togaviridae, Alphavirus) is a highly pathogenic mosquito-borne zoonosis that is responsible for occasional outbreaks of severe disease in humans and equines, resulting in high mortality and neurological impairment in most survivors. In the past, human disease outbreaks in the northeastern U.S. have occurred intermittently with no apparent pattern; however, during the last decade we have witnessed recurring annual emergence where EEE virus activity had been historically rare, and expansion into northern New England where the virus had been previously unknown. In the northeastern U.S., EEE virus is maintained in an enzootic cycle involving the ornithophagic mosquito, Culiseta melanura, and wild passerine (perching) birds in freshwater hardwood swamps. However, the identity of key avian species that serve as principal virus reservoir and amplification hosts has not been established. The efficiency with which pathogen transmission occurs within an avian community is largely determined by the relative reservoir competence of each species and by ecological factors that influence contact rates between these avian hosts and mosquito vectors. Methodology and principle findings Contacts between vector mosquitoes and potential avian hosts may be directly quantified by analyzing the blood meal contents of field-collected specimens. We used PCR-based molecular methods and direct sequencing of the mitochondrial cytochrome b gene for profiling of blood meals in Cs. melanura, in an effort to quantify its feeding behavior on specific vertebrate hosts, and to infer epidemiologic implications in four historic EEE virus foci in the northeastern U.S. Avian point count surveys were conducted to determine spatiotemporal host community composition. Of 1,127 blood meals successfully identified to species level, >99% of blood meals were from 65 avian hosts in 27 families and 11 orders, and only seven were from mammalian hosts representing three species. We developed an empirically informed mathematical model for EEE virus transmission using Cs. melanura abundance and preferred and non-preferred avian hosts. To our knowledge this is the first mathematical model for EEE virus, a pathogen with many potential hosts, in the northeastern U.S. We measured strong feeding preferences for a number of avian species based on the proportion of mosquito blood meals identified from these bird species in relation to their observed frequencies. These included: American Robin, Tufted Titmouse, Common Grackle, Wood Thrush, Chipping Sparrow, Black-capped Chickadee, Northern Cardinal, and Warbling Vireo. We found that these bird species, most notably Wood Thrush, play a dominant role in supporting EEE virus amplification. It is also noteworthy that the competence of some of the aforementioned avian species for EEE virus has not been established. Our findings indicate that heterogeneity induced by mosquito host preference, is a key mediator of the epizootic transmission of vector-borne pathogens. Conclusion and significance Detailed knowledge of the vector-host interactions of mosquito populations in nature is essential for evaluating their vectorial capacity and for assessing the role of individual vertebrates as reservoir hosts involved in the maintenance and amplification of zoonotic agents of human diseases. Our study clarifies the host associations of Cs. melanura in four EEE virus foci in the northeastern U.S., identifies vector host preferences as the most important transmission parameter, and quantifies the contribution of preference-induced contact heterogeneity to enzootic transmission. Our study identifies Wood Thrush, American Robin and a few avian species that may serve as superspreaders of EEE virus. Our study elucidates spatiotemporal host species utilization by Cs. melanura in relation to avian host community. This research provides a basis to better understand the involvement of Cs. melanura and avian hosts in the transmission and ecology of EEE virus and the risk of human infection in virus foci. PMID:26751704

Dynamics of Vector-Host Interactions in Avian Communities in Four Eastern Equine Encephalitis Virus Foci in the Northeastern U.S.

PubMed

Molaei, Goudarz; Thomas, Michael C; Muller, Tim; Medlock, Jan; Shepard, John J; Armstrong, Philip M; Andreadis, Theodore G

2016-01-01

Eastern equine encephalitis (EEE) virus (Togaviridae, Alphavirus) is a highly pathogenic mosquito-borne zoonosis that is responsible for occasional outbreaks of severe disease in humans and equines, resulting in high mortality and neurological impairment in most survivors. In the past, human disease outbreaks in the northeastern U.S. have occurred intermittently with no apparent pattern; however, during the last decade we have witnessed recurring annual emergence where EEE virus activity had been historically rare, and expansion into northern New England where the virus had been previously unknown. In the northeastern U.S., EEE virus is maintained in an enzootic cycle involving the ornithophagic mosquito, Culiseta melanura, and wild passerine (perching) birds in freshwater hardwood swamps. However, the identity of key avian species that serve as principal virus reservoir and amplification hosts has not been established. The efficiency with which pathogen transmission occurs within an avian community is largely determined by the relative reservoir competence of each species and by ecological factors that influence contact rates between these avian hosts and mosquito vectors. Contacts between vector mosquitoes and potential avian hosts may be directly quantified by analyzing the blood meal contents of field-collected specimens. We used PCR-based molecular methods and direct sequencing of the mitochondrial cytochrome b gene for profiling of blood meals in Cs. melanura, in an effort to quantify its feeding behavior on specific vertebrate hosts, and to infer epidemiologic implications in four historic EEE virus foci in the northeastern U.S. Avian point count surveys were conducted to determine spatiotemporal host community composition. Of 1,127 blood meals successfully identified to species level, >99% of blood meals were from 65 avian hosts in 27 families and 11 orders, and only seven were from mammalian hosts representing three species. We developed an empirically informed mathematical model for EEE virus transmission using Cs. melanura abundance and preferred and non-preferred avian hosts. To our knowledge this is the first mathematical model for EEE virus, a pathogen with many potential hosts, in the northeastern U.S. We measured strong feeding preferences for a number of avian species based on the proportion of mosquito blood meals identified from these bird species in relation to their observed frequencies. These included: American Robin, Tufted Titmouse, Common Grackle, Wood Thrush, Chipping Sparrow, Black-capped Chickadee, Northern Cardinal, and Warbling Vireo. We found that these bird species, most notably Wood Thrush, play a dominant role in supporting EEE virus amplification. It is also noteworthy that the competence of some of the aforementioned avian species for EEE virus has not been established. Our findings indicate that heterogeneity induced by mosquito host preference, is a key mediator of the epizootic transmission of vector-borne pathogens. Detailed knowledge of the vector-host interactions of mosquito populations in nature is essential for evaluating their vectorial capacity and for assessing the role of individual vertebrates as reservoir hosts involved in the maintenance and amplification of zoonotic agents of human diseases. Our study clarifies the host associations of Cs. melanura in four EEE virus foci in the northeastern U.S., identifies vector host preferences as the most important transmission parameter, and quantifies the contribution of preference-induced contact heterogeneity to enzootic transmission. Our study identifies Wood Thrush, American Robin and a few avian species that may serve as superspreaders of EEE virus. Our study elucidates spatiotemporal host species utilization by Cs. melanura in relation to avian host community. This research provides a basis to better understand the involvement of Cs. melanura and avian hosts in the transmission and ecology of EEE virus and the risk of human infection in virus foci.

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

PubMed

Clément, Frédérique

2016-07-01

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

Stochastic nature of Landsat MSS data

NASA Technical Reports Server (NTRS)

Labovitz, M. L.; Masuoka, E. J.

1987-01-01

A multiple series generalization of the ARIMA models is used to model Landsat MSS scan lines as sequences of vectors, each vector having four elements (bands). The purpose of this work is to investigate if Landsat scan lines can be described by a general multiple series linear stochastic model and if the coefficients of such a model vary as a function of satellite system and target attributes. To accomplish this objective, an exploratory experimental design was set up incorporating six factors, four representing target attributes - location, cloud cover, row (within location), and column (within location) - and two factors representing system attributes - satellite number and detector bank. Each factor was included in the design at two levels and, with two replicates per treatment, 128 scan lines were analyzed. The results of the analysis suggests that a multiple AR(4) model is an adequate representation across all scan lines. Furthermore, the coefficients of the AR(4) model vary with location, particularly changes in physiography (slope regimes), and with percent cloud cover, but are insensitive to changes in system attributes.

Characterization of a 300-GHz Transmission System for Digital Communications

NASA Astrophysics Data System (ADS)

Hudlička, Martin; Salhi, Mohammed; Kleine-Ostmann, Thomas; Schrader, Thorsten

2017-08-01

The paper presents the characterization of a 300-GHz transmission system for modern digital communications. The quality of the modulated signal at the output of the system (error vector magnitude, EVM) is measured using a vector signal analyzer. A method using a digital real-time oscilloscope and consecutive mathematical processing in a computer is shown for analysis of signals with bandwidths exceeding that of state-of-the-art vector signal analyzers. The uncertainty of EVM measured using the real-time oscilloscope is open to analysis. Behaviour of the 300-GHz transmission system is studied with respect to various modulation schemes and different signal symbol rates.

Preliminary design study of a lateral-directional control system using thrust vectoring

NASA Technical Reports Server (NTRS)

Lallman, F. J.

1985-01-01

A preliminary design of a lateral-directional control system for a fighter airplane capable of controlled operation at extreme angles of attack is developed. The subject airplane is representative of a modern twin-engine high-performance jet fighter, is equipped with ailerons, rudder, and independent horizontal-tail surfaces. Idealized bidirectional thrust-vectoring engine nozzles are appended to the mathematic model of the airplane to provide additional control moments. Optimal schedules for lateral and directional pseudo control variables are calculated. Use of pseudo controls results in coordinated operation of the aerodynamic and thrust-vectoring controls with minimum coupling between the lateral and directional airplane dynamics. Linear quadratic regulator designs are used to specify a preliminary flight control system to improve the stability and response characteristics of the airplane. Simulated responses to step pilot control inputs are stable and well behaved. For lateral stick deflections, peak stability axis roll rates are between 1.25 and 1.60 rad/sec over an angle-of-attack range of 10 deg to 70 deg. For rudder pedal deflections, the roll rates accompanying the sideslip responses can be arrested by small lateral stick motions.

Can different quantum state vectors correspond to the same physical state? An experimental test

NASA Astrophysics Data System (ADS)

Nigg, Daniel; Monz, Thomas; Schindler, Philipp; Martinez, Esteban A.; Hennrich, Markus; Blatt, Rainer; Pusey, Matthew F.; Rudolph, Terry; Barrett, Jonathan

2016-01-01

A century after the development of quantum theory, the interpretation of a quantum state is still discussed. If a physicist claims to have produced a system with a particular quantum state vector, does this represent directly a physical property of the system, or is the state vector merely a summary of the physicist’s information about the system? Assume that a state vector corresponds to a probability distribution over possible values of an unknown physical or ‘ontic’ state. Then, a recent no-go theorem shows that distinct state vectors with overlapping distributions lead to predictions different from quantum theory. We report an experimental test of these predictions using trapped ions. Within experimental error, the results confirm quantum theory. We analyse which kinds of models are ruled out.

Representation and display of vector field topology in fluid flow data sets

NASA Technical Reports Server (NTRS)

Helman, James; Hesselink, Lambertus

1989-01-01

The visualization of physical processes in general and of vector fields in particular is discussed. An approach to visualizing flow topology that is based on the physics and mathematics underlying the physical phenomenon is presented. It involves determining critical points in the flow where the velocity vector vanishes. The critical points, connected by principal lines or planes, determine the topology of the flow. The complexity of the data is reduced without sacrificing the quantitative nature of the data set. By reducing the original vector field to a set of critical points and their connections, a representation of the topology of a two-dimensional vector field that is much smaller than the original data set but retains with full precision the information pertinent to the flow topology is obtained. This representation can be displayed as a set of points and tangent curves or as a graph. Analysis (including algorithms), display, interaction, and implementation aspects are discussed.

Kny Coupling Constants and Form Factors from the Chiral Bag Model

NASA Astrophysics Data System (ADS)

Jeong, M. T.; Cheon, Il-T.

2000-09-01

The form factors and coupling constants for KNΛ and KNΣ interactions have been calculated in the framework of the Chiral Bag Model with vector mesons. Taking into account vector meson (ρ, ω, K*) field effects, we find -3.88 ≤ gKNΛ ≤ -3.67 and 1.15 ≤ gKNΣ ≤ 1.24, where the quark-meson coupling constants are determined by fitting the renormalized, πNN coupling constant, [gπNN(0)]2/4π = 14.3. It is shown that vector mesons make significant contributions to the coupling constants gKNΛ and gKNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photo production experiments.

Grip Forces During Object Manipulation: Experiment, Mathematical Model & Validation

PubMed Central

Slota, Gregory P.; Latash, Mark L.; Zatsiorsky, Vladimir M.

2011-01-01

When people transport handheld objects, they change the grip force with the object movement. Circular movement patterns were tested within three planes at two different rates (1.0, 1.5 Hz), and two diameters (20, 40 cm). Subjects performed the task reasonably well, matching frequencies and dynamic ranges of accelerations within expectations. A mathematical model was designed to predict the applied normal forces from kinematic data. The model is based on two hypotheses: (a) the grip force changes during movements along complex trajectories can be represented as the sum of effects of two basic commands associated with the parallel and orthogonal manipulation, respectively; (b) different central commands are sent to the thumb and virtual finger (Vf- four fingers combined). The model predicted the actual normal forces with a total variance accounted for of better than 98%. The effects of the two components of acceleration—along the normal axis and the resultant acceleration within the shear plane—on the digit normal forces are additive. PMID:21735245

Engineering tradeoff problems viewed as multiple objective optimizations and the VODCA methodology

NASA Astrophysics Data System (ADS)

Morgan, T. W.; Thurgood, R. L.

1984-05-01

This paper summarizes a rational model for making engineering tradeoff decisions. The model is a hybrid from the fields of social welfare economics, communications, and operations research. A solution methodology (Vector Optimization Decision Convergence Algorithm - VODCA) firmly grounded in the economic model is developed both conceptually and mathematically. The primary objective for developing the VODCA methodology was to improve the process for extracting relative value information about the objectives from the appropriate decision makers. This objective was accomplished by employing data filtering techniques to increase the consistency of the relative value information and decrease the amount of information required. VODCA is applied to a simplified hypothetical tradeoff decision problem. Possible use of multiple objective analysis concepts and the VODCA methodology in product-line development and market research are discussed.

Modelling the effect of an alternative host population on the spread of citrus Huanglongbing

NASA Astrophysics Data System (ADS)

d'A. Vilamiu, Raphael G.; Ternes, Sonia; Laranjeira, Francisco F.; de C. Santos, Tâmara T.

2013-10-01

The objective of this work was to model the spread of citrus Huanglongbing (HLB) considering the presence of a population of alternative hosts (Murraya paniculata). We developed a compartmental deterministic mathematical model for representing the dynamics of HLB disease in a citrus orchard, including delays in the latency and incubation phases of the disease in the plants and a delay period on the nymphal stage of Diaphorina citri, the insect vector of HLB in Brazil. The results of numerical simulations indicate that alternative hosts should not play a crucial role on HLB dynamics considering a typical scenario for the Recôncavo Baiano region in Brazil . Also, the current policy of removing symptomatic plants every three months should not be expected to significantly hinder HLB spread.

A mathematical model of transmission of rice tungro disease by Nephotettix Virescens

NASA Astrophysics Data System (ADS)

Blas, Nikki T.; Addawe, Joel M.; David, Guido

2016-11-01

One of the major threats in rice agriculture is the Tungro virus, which is transmitted semi-persistently to rice plants via green rice leafhoppers called Nephotettix Virescens. Tungro is polycyclic and complex disease of rice associated by dual infection with Rice Tungro Bacilliform Virus (RTBV) and Rice Tungro Spherical Virus (RTSV). Interaction of the two viruses results in the degeneration of the host. In this paper, we used a plant-vector system of ordinary differential equations to model the spread of the disease in a model rice field. Parameter values were obtained from studies on the entomology of Nephotettix Virescens and infection rates of RTSV and RTBV. The system was analyzed for equilibrium solutions, and solved numerically for susceptible rice varieties (Taichung Native 1).

An epidemiological model for externally sourced vector-borne viruses applied to Bean yellow mosaic virus in lupin crops in a Mediterranean-type environment.

PubMed

Maling, T; Diggle, A J; Thackray, D J; Siddique, K H M; Jones, R A C

2008-12-01

A hybrid mechanistic/statistical model was developed to predict vector activity and epidemics of vector-borne viruses spreading from external virus sources to an adjacent crop. The pathosystem tested was Bean yellow mosaic virus (BYMV) spreading from annually self-regenerating, legume-based pastures to adjacent crops of narrow-leafed lupin (Lupinus angustifolius) in the winter-spring growing season in a region with a Mediterranean-type environment where the virus persists over summer within dormant seed of annual clovers. The model uses a combination of daily rainfall and mean temperature during late summer and early fall to drive aphid population increase, migration of aphids from pasture to lupin crops, and the spread of BYMV. The model predicted time of arrival of aphid vectors and resulting BYMV spread successfully for seven of eight datasets from 2 years of field observations at four sites representing different rainfall and geographic zones of the southwestern Australian grainbelt. Sensitivity analysis was performed to determine the relative importance of the main parameters that describe the pathosystem. The hybrid mechanistic/statistical approach used created a flexible analytical tool for vector-mediated plant pathosystems that made useful predictions even when field data were not available for some components of the system.

O Antigen Modulates Insect Vector Acquisition of the Bacterial Plant Pathogen Xylella fastidiosa

PubMed Central

Rapicavoli, Jeannette N.; Kinsinger, Nichola; Perring, Thomas M.; Backus, Elaine A.; Shugart, Holly J.; Walker, Sharon

2015-01-01

Hemipteran insect vectors transmit the majority of plant pathogens. Acquisition of pathogenic bacteria by these piercing/sucking insects requires intimate associations between the bacterial cells and insect surfaces. Lipopolysaccharide (LPS) is the predominant macromolecule displayed on the cell surface of Gram-negative bacteria and thus mediates bacterial interactions with the environment and potential hosts. We hypothesized that bacterial cell surface properties mediated by LPS would be important in modulating vector-pathogen interactions required for acquisition of the bacterial plant pathogen Xylella fastidiosa, the causative agent of Pierce's disease of grapevines. Utilizing a mutant that produces truncated O antigen (the terminal portion of the LPS molecule), we present results that link this LPS structural alteration to a significant decrease in the attachment of X. fastidiosa to blue-green sharpshooter foreguts. Scanning electron microscopy confirmed that this defect in initial attachment compromised subsequent biofilm formation within vector foreguts, thus impairing pathogen acquisition. We also establish a relationship between O antigen truncation and significant changes in the physiochemical properties of the cell, which in turn affect the dynamics of X. fastidiosa adhesion to the vector foregut. Lastly, we couple measurements of the physiochemical properties of the cell with hydrodynamic fluid shear rates to produce a Comsol model that predicts primary areas of bacterial colonization within blue-green sharpshooter foreguts, and we present experimental data that support the model. These results demonstrate that, in addition to reported protein adhesin-ligand interactions, O antigen is crucial for vector-pathogen interactions, specifically in the acquisition of this destructive agricultural pathogen. PMID:26386068

O antigen modulates insect vector acquisition of the bacterial plant pathogen Xylella fastidiosa.

PubMed

Rapicavoli, Jeannette N; Kinsinger, Nichola; Perring, Thomas M; Backus, Elaine A; Shugart, Holly J; Walker, Sharon; Roper, M Caroline

2015-12-01

Hemipteran insect vectors transmit the majority of plant pathogens. Acquisition of pathogenic bacteria by these piercing/sucking insects requires intimate associations between the bacterial cells and insect surfaces. Lipopolysaccharide (LPS) is the predominant macromolecule displayed on the cell surface of Gram-negative bacteria and thus mediates bacterial interactions with the environment and potential hosts. We hypothesized that bacterial cell surface properties mediated by LPS would be important in modulating vector-pathogen interactions required for acquisition of the bacterial plant pathogen Xylella fastidiosa, the causative agent of Pierce's disease of grapevines. Utilizing a mutant that produces truncated O antigen (the terminal portion of the LPS molecule), we present results that link this LPS structural alteration to a significant decrease in the attachment of X. fastidiosa to blue-green sharpshooter foreguts. Scanning electron microscopy confirmed that this defect in initial attachment compromised subsequent biofilm formation within vector foreguts, thus impairing pathogen acquisition. We also establish a relationship between O antigen truncation and significant changes in the physiochemical properties of the cell, which in turn affect the dynamics of X. fastidiosa adhesion to the vector foregut. Lastly, we couple measurements of the physiochemical properties of the cell with hydrodynamic fluid shear rates to produce a Comsol model that predicts primary areas of bacterial colonization within blue-green sharpshooter foreguts, and we present experimental data that support the model. These results demonstrate that, in addition to reported protein adhesin-ligand interactions, O antigen is crucial for vector-pathogen interactions, specifically in the acquisition of this destructive agricultural pathogen. Copyright © 2015, American Society for Microbiology. All Rights Reserved.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

PubMed

Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen

2018-05-01

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli. We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

An Application of Mathematical Groups to Structures of Human Groups. Applications of Finite Mathematics to Anthropology and Sociology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 476.

ERIC Educational Resources Information Center

Carlson, Roger

This module is designed for students with a high school algebra background. The goal is to present the elements of the group idea, primarily by way of a geometric model, and to see its application to the study of kinship relations within certain human groups. The material opens with a presentation of clans in a hypothetical society in an early…

Aquarius - A Modelling Package for Groundwater Flow and Coupled Heat Transport in the Range 0.1 to 100 MPa and 0.1 to 1000 C

NASA Astrophysics Data System (ADS)

Cook, S. J.

2009-05-01

Aquarius is a Windows application that models fluid flow and heat transport under conditions in which fluid buoyancy can significantly impact patterns and magnitudes of fluid flow. The package is designed as a visualization tool through which users can examine flow systems in environments, both low temperature aquifers and regions with elevated PT regimes such as deep sedimentary basins, hydrothermal systems, and contact thermal aureoles. The package includes 4 components: (1) A finite-element mesh generator/assembler capable of representing complex geologic structures. Left-hand, right-hand and alternating linear triangles can be mixed within the mesh. Planer horizontal, planer vertical and cylindrical vertical coordinate sections are supported. (2) A menu-selectable system for setting properties and boundary/initial conditions. The design retains mathematical terminology for all input parameters such as scalars (e.g., porosity), tensors (e.g., permeability), and boundary/initial conditions (e.g., fixed potential). This makes the package an effective instructional aide by linking model requirements with the underlying mathematical concepts of partial differential equations and the solution logic of boundary/initial value problems. (3) Solution algorithms for steady-state and time-transient fluid flow/heat transport problems. For all models, the nonlinear global matrix equations are solved sequentially using over-relaxation techniques. Matrix storage design allows for large (e.g., 20000) element models to run efficiently on a typical PC. (4) A plotting system that supports contouring nodal data (e.g., head), vector plots for flux data (e.g., specific discharge), and colour gradient plots for elemental data (e.g., porosity), water properties (e.g., density), and performance measures (e.g., Peclet numbers). Display graphics can be printed or saved in standard graphic formats (e.g., jpeg). This package was developed from procedural codes in C written originally to model the hydrothermal flow system responsible for contact metamorphism of Utah's Alta Stock (Cook et al., AJS 1997). These codes were reprogrammed in Microsoft C# to take advantage of object oriented design and the capabilities of Microsoft's .NET framework. The package is available at no cost by e-mail request from the author.

Modeling the indirect effect of Wolbachia on the infection dynamics of horizontally transmitted viruses

PubMed Central

Strauß, Jakob F.; Telschow, Arndt

2015-01-01

Intracellular bacteria of the genus Wolbachia are widely distributed in arthropods. There is growing empirical evidence that Wolbachia directly interacts with viruses and other parasites inside the arthropod host, sometimes resulting in low or no pathogen replication. Previous theoretical studies showed that this direct effect of Wolbachia can result in a reduced virus prevalence (within the population), suggesting that Wolbachia could be used in the biological control of vector-borne diseases (e.g., dengue fever). However, Wolbachia might also indirectly affect virus dynamics because Wolbachia-induced reproductive phenotypes (cytoplasmic incompatibility or male killing) increase the larval mortality of hosts and thus alter the age structure of populations. We investigated this indirect effect using mathematical models with overlapping generations, and found the results to depend strongly on the host's life history. In general, the indirect effect can result in two different outcomes: (1) reduced virus prevalence and virus invasion ability, and (2) increased virus prevalence and virus invasion ability. The former occurs for host species with larval competition and undercompensation, the latter for hosts with either adult competition or larval competition and overcompensation. These findings suggest that the effect of Wolbachia on a specific virus is sensitive to the host's life history. We discuss the results with respect to biocontrol programs using Wolbachia. PMID:25972858

Microclimatic temperatures at Danish cattle farms, 2000-2016: quantifying the temporal and spatial variation in the transmission potential of Schmallenberg virus.

PubMed

Haider, Najmul; Cuellar, Ana Carolina; Kjær, Lene Jung; Sørensen, Jens Havskov; Bødker, Rene

2018-03-05

Microclimatic temperatures provide better estimates of vector-borne disease transmission parameters than standard meteorological temperatures, as the microclimate represent the actual temperatures to which the vectors are exposed. The objectives of this study were to quantify farm-level geographic variations and temporal patterns in the extrinsic incubation period (EIP) of Schmallenberg virus transmitted by Culicoides in Denmark through generation of microclimatic temperatures surrounding all Danish cattle farms. We calculated the hourly microclimatic temperatures at potential vector-resting sites within a 500 m radius of 22,004 Danish cattle farms for the months April to November from 2000 to 2016. We then modeled the daily EIP of Schmallenberg virus at each farm, assuming vectors choose resting sites either randomly or based on temperatures (warmest or coolest available) every hour. The results of the model output are presented as 17-year averages. The difference between the warmest and coolest microhabitats at the same farm was on average 3.7 °C (5th and 95th percentiles: 1.0 °C to 7.8 °C). The mean EIP of Schmallenberg virus (5th and 95th percentiles) for all cattle farms during spring, summer, and autumn was: 23 (18-33), 14 (12-18) and 51 (48-55) days, respectively, assuming Culicoides select resting sites randomly. These estimated EIP values were considerably shorter than those estimated using standard meteorological temperatures obtained from a numerical weather prediction model for the same periods: 43 (39-52), 21 (17-24) and 57 (55-58) days, respectively. When assuming that vectors actively select the coolest resting sites at a farm, the EIP was 2.3 (range: 1.1 to 4.1) times longer compared to that of the warmest sites at the same farm. We estimated a wide range of EIP in different microclimatic habitats surrounding Danish cattle farms, stressing the importance of identifying the specific resting sites of vectors when modeling vector-borne disease transmission. We found a large variation in the EIP among different farms, suggesting disease transmission may vary substantially between regions, even within a small country. Our findings could be useful for designing risk-based surveillance, and in the control and prevention of emerging and re-emerging vector-borne diseases.

Hybrid Model Based on Genetic Algorithms and SVM Applied to Variable Selection within Fruit Juice Classification

PubMed Central

Fernandez-Lozano, C.; Canto, C.; Gestal, M.; Andrade-Garda, J. M.; Rabuñal, J. R.; Dorado, J.; Pazos, A.

2013-01-01

Given the background of the use of Neural Networks in problems of apple juice classification, this paper aim at implementing a newly developed method in the field of machine learning: the Support Vector Machines (SVM). Therefore, a hybrid model that combines genetic algorithms and support vector machines is suggested in such a way that, when using SVM as a fitness function of the Genetic Algorithm (GA), the most representative variables for a specific classification problem can be selected. PMID:24453933

Vector- and tensor-meson production and the Pomeron-f identity hypothesis

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

Jones, S.T.

Within the context of a model introduced some time ago, the differential and total production cross sections for vector and tensor mesons are shown to be compatible with the hypothesis that the Pomeron and f are a single Regge trajectory. The model incorporates both cylinder and flavoring renormalizations of the Pomeron-f trajectory. The processes K/sup +- /p..-->..K/sup */(892)/sup +- /p, K/sup +- /p ..-->..K/sub 2//sup */(1430)/sup +- /p, and ..pi../sup +- /p..-->..A/sub 2/(1320)/sup +- /p are analyzed in some detail.

Functional mathematical model of a hydrogen-driven combustion chamber for a scramjet

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2015-09-01

A functional mathematical model of a hydrogen-driven combustion chamber for a scramjet is described. The model is constructed with the use of one-dimensional steady gas-dynamic equations and parametrization of the channel configuration and the governing parameters (fuel injection into the flow, fuel burnout along the channel, dissipation of kinetic energy, removal of some part of energy generated by gases for modeling cooling of channel walls by the fuel) with allowance for real thermophysical properties of the gases. Through parametric calculations, it is found that fuel injection in three cross sections of the channel consisting of segments with weak and strong expansion ensures a supersonic velocity of combustion products in the range of free-stream Mach numbers M∞ = 6-12. It is demonstrated that the angle between the velocity vectors of the gaseous hydrogen flow and the main gas flow can be fairly large in the case of distributed injection of the fuel. This allows effective control of the mixing process. It is proposed to use the exergy of combustion products as a criterion of the efficiency of heat supply in the combustion chamber. Based on the calculated values of exergy, the critical free-stream Mach number that still allows scramjet operation is estimated.

Thermal and Pressure Characterization of a Wind Tunnel Force Balance Using the Single Vector System. Experimental Design and Analysis Approach to Model Pressure and Temperature Effects in Hypersonic Wind Tunnel Research

NASA Technical Reports Server (NTRS)

Lynn, Keith C.; Commo, Sean A.; Johnson, Thomas H.; Parker, Peter A,

2011-01-01

Wind tunnel research at NASA Langley Research Center s 31-inch Mach 10 hypersonic facility utilized a 5-component force balance, which provided a pressurized flow-thru capability to the test article. The goal of the research was to determine the interaction effects between the free-stream flow and the exit flow from the reaction control system on the Mars Science Laboratory aeroshell during planetary entry. In the wind tunnel, the balance was exposed to aerodynamic forces and moments, steady-state and transient thermal gradients, and various internal balance cavity pressures. Historically, these effects on force measurement accuracy have not been fully characterized due to limitations in the calibration apparatus. A statistically designed experiment was developed to adequately characterize the behavior of the balance over the expected wind tunnel operating ranges (forces/moments, temperatures, and pressures). The experimental design was based on a Taylor-series expansion in the seven factors for the mathematical models. Model inversion was required to calculate the aerodynamic forces and moments as a function of the strain-gage readings. Details regarding transducer on-board compensation techniques, experimental design development, mathematical modeling, and wind tunnel data reduction are included in this paper.

Estimation of mechanical properties of nanomaterials using artificial intelligence methods

NASA Astrophysics Data System (ADS)

Vijayaraghavan, V.; Garg, A.; Wong, C. H.; Tai, K.

2014-09-01

Computational modeling tools such as molecular dynamics (MD), ab initio, finite element modeling or continuum mechanics models have been extensively applied to study the properties of carbon nanotubes (CNTs) based on given input variables such as temperature, geometry and defects. Artificial intelligence techniques can be used to further complement the application of numerical methods in characterizing the properties of CNTs. In this paper, we have introduced the application of multi-gene genetic programming (MGGP) and support vector regression to formulate the mathematical relationship between the compressive strength of CNTs and input variables such as temperature and diameter. The predictions of compressive strength of CNTs made by these models are compared to those generated using MD simulations. The results indicate that MGGP method can be deployed as a powerful method for predicting the compressive strength of the carbon nanotubes.

Microsatellites Reveal a High Population Structure in Triatoma infestans from Chuquisaca, Bolivia

PubMed Central

Pizarro, Juan Carlos; Gilligan, Lauren M.; Stevens, Lori

2008-01-01

Background For Chagas disease, the most serious infectious disease in the Americas, effective disease control depends on elimination of vectors through spraying with insecticides. Molecular genetic research can help vector control programs by identifying and characterizing vector populations and then developing effective intervention strategies. Methods and Findings The population genetic structure of Triatoma infestans (Hemiptera: Reduviidae), the main vector of Chagas disease in Bolivia, was investigated using a hierarchical sampling strategy. A total of 230 adults and nymphs from 23 localities throughout the department of Chuquisaca in Southern Bolivia were analyzed at ten microsatellite loci. Population structure, estimated using analysis of molecular variance (AMOVA) to estimate FST (infinite alleles model) and RST (stepwise mutation model), was significant between western and eastern regions within Chuquisaca and between insects collected in domestic and peri-domestic habitats. Genetic differentiation at three different hierarchical geographic levels was significant, even in the case of adjacent households within a single locality (R ST = 0.14, F ST = 0.07). On the largest geographic scale, among five communities up to 100 km apart, R ST = 0.12 and F ST = 0.06. Cluster analysis combined with assignment tests identified five clusters within the five communities. Conclusions Some houses are colonized by insects from several genetic clusters after spraying, whereas other households are colonized predominately by insects from a single cluster. Significant population structure, measured by both R ST and F ST, supports the hypothesis of poor dispersal ability and/or reduced migration of T. infestans. The high degree of genetic structure at small geographic scales, inferences from cluster analysis and assignment tests, and demographic data suggest reinfesting vectors are coming from nearby and from recrudescence (hatching of eggs that were laid before insecticide spraying). Suggestions for using these results in vector control strategies are made. PMID:18365033

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

Zhu, Li; Fuhrer, Tobias; Schaefer, Bastian

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures.more » The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.« less

Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains

NASA Astrophysics Data System (ADS)

Koulouri, Alexandra; Brookes, Mike; Rimpiläinen, Ville

2017-01-01

In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field.

Adolescents' perceptions of socializers' beliefs, career-related conversations, and motivation in mathematics.

PubMed

Lazarides, Rebecca; Rubach, Charlott; Ittel, Angela

2017-03-01

Research based on the Eccles model of parent socialization demonstrated that parents are an important source of value and ability information for their children. Little is known, however, about the bidirectional effects between students' perceptions of their parents' beliefs and behaviors and the students' own domain-specific values. This study analyzed how students' perceptions of parents' beliefs and behaviors and students' mathematics values and mathematics-related career plans affect each other bidirectionally, and analyzed the role of students' gender as a moderator of these relations. Data from 475 students in 11th and 12th grade (girls: 50.3%; 31 classrooms; 12 schools), who participated in 2 waves of the study, were analyzed. Results of longitudinal structural equation models demonstrated that students' perceptions of their parents' mathematics value beliefs at Time 1 affected the students' own mathematics utility value at Time 2. Bidirectional effects were not shown in the full sample but were identified for boys. The paths within the tested model varied for boys and girls. For example, boys', not girls', mathematics intrinsic value predicted their reported conversations with their fathers about future occupational plans. Boys', not girls', perceived parents' mathematics value predicted the mathematics utility value. Findings are discussed in relation to their implications for parents and teachers, as well as in relation to gendered motivational processes. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Diderot: a Domain-Specific Language for Portable Parallel Scientific Visualization and Image Analysis.

PubMed

Kindlmann, Gordon; Chiw, Charisee; Seltzer, Nicholas; Samuels, Lamont; Reppy, John

2016-01-01

Many algorithms for scientific visualization and image analysis are rooted in the world of continuous scalar, vector, and tensor fields, but are programmed in low-level languages and libraries that obscure their mathematical foundations. Diderot is a parallel domain-specific language that is designed to bridge this semantic gap by providing the programmer with a high-level, mathematical programming notation that allows direct expression of mathematical concepts in code. Furthermore, Diderot provides parallel performance that takes advantage of modern multicore processors and GPUs. The high-level notation allows a concise and natural expression of the algorithms and the parallelism allows efficient execution on real-world datasets.

Mechanistic, Mathematical Model to Predict the Dynamics of Tissue Genesis in Bone Defects via Mechanical Feedback and Mediation of Biochemical Factors

PubMed Central

Moore, Shannon R.; Saidel, Gerald M.; Knothe, Ulf; Knothe Tate, Melissa L.

2014-01-01

The link between mechanics and biology in the generation and the adaptation of bone has been well studied in context of skeletal development and fracture healing. Yet, the prediction of tissue genesis within - and the spatiotemporal healing of - postnatal defects, necessitates a quantitative evaluation of mechano-biological interactions using experimental and clinical parameters. To address this current gap in knowledge, this study aims to develop a mechanistic mathematical model of tissue genesis using bone morphogenetic protein (BMP) to represent of a class of factors that may coordinate bone healing. Specifically, we developed a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteal progenitor cells within a long bone defect surrounded by periosteum and stabilized via an intramedullary nail. The emergent material properties and mechanical environment associated with nascent tissue genesis influence the strain stimulus sensed by progenitor cells within the periosteum. Using a mechanical finite element model, periosteal surface strains are predicted as a function of emergent, nascent tissue properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and tissue production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of endochondral tissue regeneration, assessed as areas of cartilage and mineralized bone, as functions of radial distance from the periosteum and time. Comparing model results to histological outcomes from two previous studies of periosteum-mediated bone regeneration in a common ovine model, it was shown that mechanistic models incorporating mechanical feedback successfully predict patterns (spatial) and trends (temporal) of bone tissue regeneration. The novel model framework presented here integrates a mechanistic feedback system based on the mechanosensitivity of periosteal progenitor cells, which allows for modeling and prediction of tissue regeneration on multiple length and time scales. Through combination of computational, physical and engineering science approaches, the model platform provides a means to test new hypotheses in silico and to elucidate conditions conducive to endogenous tissue genesis. Next generation models will serve to unravel intrinsic differences in bone genesis by endochondral and intramembranous mechanisms. PMID:24967742

In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400

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

Oginni, B.M.; Bronson, F.L.; Field, M.B.

2012-07-01

Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extensionmore » to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can now be used for quickly and accurately evaluating efficiencies for wider range of gamma-ray spectroscopy applications. (authors)« less

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

EPA Science Inventory

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

Examples of Mathematical Modeling

PubMed Central

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

2008-01-01

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

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Mathematical modeling and numerical simulation of the mitotic spindle orientation system.

PubMed

Ibrahim, Bashar

2018-05-21

The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division. Copyright © 2018. Published by Elsevier Inc.

Representation of magnetic fields in space. [special attention to Geomagnetic fields and Magnetospheric models

NASA Technical Reports Server (NTRS)

Stern, D. P.

1976-01-01

Several mathematical methods which are available for the description of magnetic fields in space are reviewed. Examples of the application of such methods are given, with particular emphasis on work related to the geomagnetic field, and their individual properties and associated problems are described. The methods are grouped in five main classes: (1) methods based on the current density, (2) methods using the scalar magnetic potential, (3) toroidal and poloidal components of the field and spherical vector harmonics, (4) Euler potentials, and (5) local expansions of the field near a given reference point. Special attention is devoted to models of the magnetosphere, to the uniqueness of the scalar potential as derived from observed data, and to the L parameter.

Current algebra, statistical mechanics and quantum models

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2017-11-01

Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

Numerical implementation of the S-matrix algorithm for modeling of relief diffraction gratings

NASA Astrophysics Data System (ADS)

Yaremchuk, Iryna; Tamulevičius, Tomas; Fitio, Volodymyr; Gražulevičiūte, Ieva; Bobitski, Yaroslav; Tamulevičius, Sigitas

2013-11-01

A new numerical implementation is developed to calculate the diffraction efficiency of relief diffraction gratings. In the new formulation, vectors containing the expansion coefficients of electric and magnetic fields on boundaries of the grating layer are expressed by additional constants. An S-matrix algorithm has been systematically described in detail and adapted to a simple matrix form. This implementation is suitable for the study of optical characteristics of periodic structures by using modern object-oriented programming languages and different standard mathematical software. The modeling program has been developed on the basis of this numerical implementation and tested by comparison with other commercially available programs and experimental data. Numerical examples are given to show the usefulness of the new implementation.

Shaded computer graphic techniques for visualizing and interpreting analytic fluid flow models

NASA Technical Reports Server (NTRS)

Parke, F. I.

1981-01-01

Mathematical models which predict the behavior of fluid flow in different experiments are simulated using digital computers. The simulations predict values of parameters of the fluid flow (pressure, temperature and velocity vector) at many points in the fluid. Visualization of the spatial variation in the value of these parameters is important to comprehend and check the data generated, to identify the regions of interest in the flow, and for effectively communicating information about the flow to others. The state of the art imaging techniques developed in the field of three dimensional shaded computer graphics is applied to visualization of fluid flow. Use of an imaging technique known as 'SCAN' for visualizing fluid flow, is studied and the results are presented.

Implementation details of the coupled QMR algorithm

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1992-01-01

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

Solving the multi-frequency electromagnetic inverse source problem by the Fourier method

NASA Astrophysics Data System (ADS)

Wang, Guan; Ma, Fuming; Guo, Yukun; Li, Jingzhi

2018-07-01

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.

The Forecasting of Future Inventory and the Optimization of Training Requirements within the Airborne Community.

DTIC Science & Technology

1983-12-01

grade levels. Chapter 2 discusses the formulation of the model. It highlights the theoretical and mathematical concepts perti- nant to the model...assignments. This is to insure the professional development of the soldier and is in accordance with the "whole man" concept. 11. IALUI2U Lvels !Wii...objective function can be mathematically expressed as: (aijk (bk ijk This objective function assesses the same penalty to each vacancy of each type of

Development of a nonlinear switching function and its application to static lift characteristics of straight wings

NASA Technical Reports Server (NTRS)

Hewes, D. E.

1978-01-01

A mathematical modeling technique was developed for the lift characteristics of straight wings throughout a very wide angle of attack range. The technique employs a mathematical switching function that facilitates the representation of the nonlinear aerodynamic characteristics in the partially and fully stalled regions and permits matching empirical data within + or - 4 percent of maximum values. Although specifically developed for use in modeling the lift characteristics, the technique appears to have other applications in both aerodynamic and nonaerodynamic fields.

Finding a Hadamard matrix by simulated annealing of spin vectors

NASA Astrophysics Data System (ADS)

Bayu Suksmono, Andriyan

2017-05-01

Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.

Blurring Boundaries within Mathematics Education: Prospective K-8 Teachers Interrogating Intersectional Identities, Narratives, and Positionings in Out-of-School Contexts

ERIC Educational Resources Information Center

Guzman, Lynette DeAun

2017-01-01

Mathematics teacher noticing as a pedagogical practice--attending to, interpreting, and responding to children's mathematical thinking--is growing within mathematics education communities. Much of the research literature primarily focuses on supporting teacher noticing of children's mathematical thinking within classroom contexts, such as…

Linear models to perform treaty verification tasks for enhanced information security

DOE PAGES

MacGahan, Christopher J.; Kupinski, Matthew A.; Brubaker, Erik M.; ...

2016-11-12

Linear mathematical models were applied to binary-discrimination tasks relevant to arms control verification measurements in which a host party wishes to convince a monitoring party that an item is or is not treaty accountable. These models process data in list-mode format and can compensate for the presence of variability in the source, such as uncertain object orientation and location. The Hotelling observer applies an optimal set of weights to binned detector data, yielding a test statistic that is thresholded to make a decision. The channelized Hotelling observer applies a channelizing matrix to the vectorized data, resulting in a lower dimensionalmore » vector available to the monitor to make decisions. We demonstrate how incorporating additional terms in this channelizing-matrix optimization offers benefits for treaty verification. We present two methods to increase shared information and trust between the host and monitor. The first method penalizes individual channel performance in order to maximize the information available to the monitor while maintaining optimal performance. Second, we present a method that penalizes predefined sensitive information while maintaining the capability to discriminate between binary choices. Data used in this study was generated using Monte Carlo simulations for fission neutrons, accomplished with the GEANT4 toolkit. Custom models for plutonium inspection objects were measured in simulation by a radiation imaging system. Model performance was evaluated and presented using the area under the receiver operating characteristic curve.« less

Linear models to perform treaty verification tasks for enhanced information security

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

MacGahan, Christopher J.; Kupinski, Matthew A.; Brubaker, Erik M.

Linear mathematical models were applied to binary-discrimination tasks relevant to arms control verification measurements in which a host party wishes to convince a monitoring party that an item is or is not treaty accountable. These models process data in list-mode format and can compensate for the presence of variability in the source, such as uncertain object orientation and location. The Hotelling observer applies an optimal set of weights to binned detector data, yielding a test statistic that is thresholded to make a decision. The channelized Hotelling observer applies a channelizing matrix to the vectorized data, resulting in a lower dimensionalmore » vector available to the monitor to make decisions. We demonstrate how incorporating additional terms in this channelizing-matrix optimization offers benefits for treaty verification. We present two methods to increase shared information and trust between the host and monitor. The first method penalizes individual channel performance in order to maximize the information available to the monitor while maintaining optimal performance. Second, we present a method that penalizes predefined sensitive information while maintaining the capability to discriminate between binary choices. Data used in this study was generated using Monte Carlo simulations for fission neutrons, accomplished with the GEANT4 toolkit. Custom models for plutonium inspection objects were measured in simulation by a radiation imaging system. Model performance was evaluated and presented using the area under the receiver operating characteristic curve.« less

Linear models to perform treaty verification tasks for enhanced information security

NASA Astrophysics Data System (ADS)

MacGahan, Christopher J.; Kupinski, Matthew A.; Brubaker, Erik M.; Hilton, Nathan R.; Marleau, Peter A.

2017-02-01

Linear mathematical models were applied to binary-discrimination tasks relevant to arms control verification measurements in which a host party wishes to convince a monitoring party that an item is or is not treaty accountable. These models process data in list-mode format and can compensate for the presence of variability in the source, such as uncertain object orientation and location. The Hotelling observer applies an optimal set of weights to binned detector data, yielding a test statistic that is thresholded to make a decision. The channelized Hotelling observer applies a channelizing matrix to the vectorized data, resulting in a lower dimensional vector available to the monitor to make decisions. We demonstrate how incorporating additional terms in this channelizing-matrix optimization offers benefits for treaty verification. We present two methods to increase shared information and trust between the host and monitor. The first method penalizes individual channel performance in order to maximize the information available to the monitor while maintaining optimal performance. Second, we present a method that penalizes predefined sensitive information while maintaining the capability to discriminate between binary choices. Data used in this study was generated using Monte Carlo simulations for fission neutrons, accomplished with the GEANT4 toolkit. Custom models for plutonium inspection objects were measured in simulation by a radiation imaging system. Model performance was evaluated and presented using the area under the receiver operating characteristic curve.

Using mathematics to solve real world problems: the role of enablers

NASA Astrophysics Data System (ADS)

Geiger, Vincent; Stillman, Gloria; Brown, Jill; Galbriath, Peter; Niss, Mogens

2018-03-01

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of "enablers" within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students' development as modellers.

Predicting potential ranges of primary malaria vectors and malaria in northern South America based on projected changes in climate, land cover and human population.

PubMed

Alimi, Temitope O; Fuller, Douglas O; Qualls, Whitney A; Herrera, Socrates V; Arevalo-Herrera, Myriam; Quinones, Martha L; Lacerda, Marcus V G; Beier, John C

2015-08-20

Changes in land use and land cover (LULC) as well as climate are likely to affect the geographic distribution of malaria vectors and parasites in the coming decades. At present, malaria transmission is concentrated mainly in the Amazon basin where extensive agriculture, mining, and logging activities have resulted in changes to local and regional hydrology, massive loss of forest cover, and increased contact between malaria vectors and hosts. Employing presence-only records, bioclimatic, topographic, hydrologic, LULC and human population data, we modeled the distribution of malaria and two of its dominant vectors, Anopheles darlingi, and Anopheles nuneztovari s.l. in northern South America using the species distribution modeling platform Maxent. Results from our land change modeling indicate that about 70,000 km(2) of forest land would be lost by 2050 and 78,000 km(2) by 2070 compared to 2010. The Maxent model predicted zones of relatively high habitat suitability for malaria and the vectors mainly within the Amazon and along coastlines. While areas with malaria are expected to decrease in line with current downward trends, both vectors are predicted to experience range expansions in the future. Elevation, annual precipitation and temperature were influential in all models both current and future. Human population mostly affected An. darlingi distribution while LULC changes influenced An. nuneztovari s.l. distribution. As the region tackles the challenge of malaria elimination, investigations such as this could be useful for planning and management purposes and aid in predicting and addressing potential impediments to elimination.

Data-driven probability concentration and sampling on manifold

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

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2016-09-15

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation methodmore » for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.« less

A stochastic evolution model for residue Insertion-Deletion Independent from Substitution.

PubMed

Lèbre, Sophie; Michel, Christian J

2010-12-01

We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field. Copyright © 2010 Elsevier Ltd. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David

2000-01-01

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