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

PubMed

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

2002-01-01

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

A log-linear model approach to estimation of population size using the line-transect sampling method

USGS Publications Warehouse

Anderson, D.R.; Burnham, K.P.; Crain, B.R.

1978-01-01

The technique of estimating wildlife population size and density using the belt or line-transect sampling method has been used in many past projects, such as the estimation of density of waterfowl nestling sites in marshes, and is being used currently in such areas as the assessment of Pacific porpoise stocks in regions of tuna fishing activity. A mathematical framework for line-transect methodology has only emerged in the last 5 yr. In the present article, we extend this mathematical framework to a line-transect estimator based upon a log-linear model approach.

What Is the Long-Run Impact of Learning Mathematics During Preschool?

PubMed

Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie

2018-03-01

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change at age 4 is associated with a 0.24-SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., ) using national data sets. Implications for developmental theory and practice are discussed. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

Irrigation water demand: A meta-analysis of price elasticities

NASA Astrophysics Data System (ADS)

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

2006-01-01

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

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

PubMed

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

2014-06-01

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

The College Mathematics Experience and Changes in Majors: A Structural Model Analysis.

ERIC Educational Resources Information Center

Whiteley, Meredith A.; Fenske, Robert H.

1990-01-01

Testing of a structural equation model with college mathematics experience as the focal variable in 745 students' final decisions concerning major or dropping out over 4 years of college yielded separate model estimates for 3 fields: scientific/technical, quantitative business, and business management majors. (Author/MSE)

[Stature estimation for Sichuan Han nationality female based on X-ray technology with measurement of lumbar vertebrae].

PubMed

Qing, Si-han; Chang, Yun-feng; Dong, Xiao-ai; Li, Yuan; Chen, Xiao-gang; Shu, Yong-kang; Deng, Zhen-hua

2013-10-01

To establish the mathematical models of stature estimation for Sichuan Han female with measurement of lumbar vertebrae by X-ray to provide essential data for forensic anthropology research. The samples, 206 Sichuan Han females, were divided into three groups including group A, B and C according to the ages. Group A (206 samples) consisted of all ages, group B (116 samples) were 20-45 years old and 90 samples over 45 years old were group C. All the samples were examined lumbar vertebrae through CR technology, including the parameters of five centrums (L1-L5) as anterior border, posterior border and central heights (x1-x15), total central height of lumbar spine (x16), and the real height of every sample. The linear regression analysis was produced using the parameters to establish the mathematical models of stature estimation. Sixty-two trained subjects were tested to verify the accuracy of the mathematical models. The established mathematical models by hypothesis test of linear regression equation model were statistically significant (P<0.05). The standard errors of the equation were 2.982-5.004 cm, while correlation coefficients were 0.370-0.779 and multiple correlation coefficients were 0.533-0.834. The return tests of the highest correlation coefficient and multiple correlation coefficient of each group showed that the highest accuracy of the multiple regression equation, y = 100.33 + 1.489 x3 - 0.548 x6 + 0.772 x9 + 0.058 x12 + 0.645 x15, in group A were 80.6% (+/- lSE) and 100% (+/- 2SE). The established mathematical models in this study could be applied for the stature estimation for Sichuan Han females.

Estimating tuberculosis incidence from primary survey data: a mathematical modeling approach.

PubMed

Pandey, S; Chadha, V K; Laxminarayan, R; Arinaminpathy, N

2017-04-01

There is an urgent need for improved estimations of the burden of tuberculosis (TB). To develop a new quantitative method based on mathematical modelling, and to demonstrate its application to TB in India. We developed a simple model of TB transmission dynamics to estimate the annual incidence of TB disease from the annual risk of tuberculous infection and prevalence of smear-positive TB. We first compared model estimates for annual infections per smear-positive TB case using previous empirical estimates from China, Korea and the Philippines. We then applied the model to estimate TB incidence in India, stratified by urban and rural settings. Study model estimates show agreement with previous empirical estimates. Applied to India, the model suggests an annual incidence of smear-positive TB of 89.8 per 100 000 population (95%CI 56.8-156.3). Results show differences in urban and rural TB: while an urban TB case infects more individuals per year, a rural TB case remains infectious for appreciably longer, suggesting the need for interventions tailored to these different settings. Simple models of TB transmission, in conjunction with necessary data, can offer approaches to burden estimation that complement those currently being used.

A mathematical programming method for formulating a fuzzy regression model based on distance criterion.

PubMed

Chen, Liang-Hsuan; Hsueh, Chan-Ching

2007-06-01

Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several alpha-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.

Assessing adult mortality in HIV-1-afflicted Zimbabwe (1998 -2003).

PubMed Central

Lopman, Ben A.; Barnabas, Ruanne; Hallett, Timothy B.; Nyamukapa, Constance; Mundandi, Costa; Mushati, Phyllis; Garnett, Geoff P.; Gregson, Simon

2006-01-01

OBJECTIVE: To compare alternative methods to vital registration systems for estimating adult mortality, and describe patterns of mortality in Manicaland, Zimbabwe, which has been severely affected by HIV. METHODS: We compared estimates of adult mortality from (1) a single question on household mortality, (2) repeated household censuses, and (3) an adult cohort study with linked HIV testing from Manicaland, with a mathematical model fitted to local age-specific HIV prevalence (1998 -2000). FINDINGS: The crude death rate from the single question (29 per 1000 person-years) was roughly consistent with that from the mathematical model (22 -25 per 1000 person-years), but much higher than that from the household censuses (12 per 1000 person-years). Adult mortality in the household censuses (males 0.65; females 0.51) was lower than in the cohort study (males 0.77; females 0.57), while mathematical models gave a much higher estimate, especially for females (males 0.80 -0.83; females 0.75 -0.80). The population attributable fraction of adult deaths due to HIV was 0.61 for men and 0.70 for women, with life expectancy estimated to be 34.3 years for males and 38.2 years for females. CONCLUSION: Each method for estimating adult mortality had limitations in terms of loss to follow-up (cohort study), under-ascertainment (household censuses), transparency of underlying processes (single question), and sensitivity to parameterization (mathematical model). However, these analyses make clear the advantages of longitudinal cohort data, which provide more complete ascertainment than household censuses, highlight possible inaccuracies in model assumptions, and allow direct quantification of the impact of HIV. PMID:16583077

Inverse modeling approach for evaluation of kinetic parameters of a biofilm reactor using tabu search.

PubMed

Kumar, B Shiva; Venkateswarlu, Ch

2014-08-01

The complex nature of biological reactions in biofilm reactors often poses difficulties in analyzing such reactors experimentally. Mathematical models could be very useful for their design and analysis. However, application of biofilm reactor models to practical problems proves somewhat ineffective due to the lack of knowledge of accurate kinetic models and uncertainty in model parameters. In this work, we propose an inverse modeling approach based on tabu search (TS) to estimate the parameters of kinetic and film thickness models. TS is used to estimate these parameters as a consequence of the validation of the mathematical models of the process with the aid of measured data obtained from an experimental fixed-bed anaerobic biofilm reactor involving the treatment of pharmaceutical industry wastewater. The results evaluated for different modeling configurations of varying degrees of complexity illustrate the effectiveness of TS for accurate estimation of kinetic and film thickness model parameters of the biofilm process. The results show that the two-dimensional mathematical model with Edward kinetics (with its optimum parameters as mu(max)rho(s)/Y = 24.57, Ks = 1.352 and Ki = 102.36) and three-parameter film thickness expression (with its estimated parameters as a = 0.289 x 10(-5), b = 1.55 x 10(-4) and c = 15.2 x 10(-6)) better describes the biofilm reactor treating the industry wastewater.

Milestones of mathematical model for business process management related to cost estimate documentation in petroleum industry

NASA Astrophysics Data System (ADS)

Khamidullin, R. I.

2018-05-01

The paper is devoted to milestones of the optimal mathematical model for a business process related to cost estimate documentation compiled during construction and reconstruction of oil and gas facilities. It describes the study and analysis of fundamental issues in petroleum industry, which are caused by economic instability and deterioration of a business strategy. Business process management is presented as business process modeling aimed at the improvement of the studied business process, namely main criteria of optimization and recommendations for the improvement of the above-mentioned business model.

Software For Computing Reliability Of Other Software

NASA Technical Reports Server (NTRS)

Nikora, Allen; Antczak, Thomas M.; Lyu, Michael

1995-01-01

Computer Aided Software Reliability Estimation (CASRE) computer program developed for use in measuring reliability of other software. Easier for non-specialists in reliability to use than many other currently available programs developed for same purpose. CASRE incorporates mathematical modeling capabilities of public-domain Statistical Modeling and Estimation of Reliability Functions for Software (SMERFS) computer program and runs in Windows software environment. Provides menu-driven command interface; enabling and disabling of menu options guides user through (1) selection of set of failure data, (2) execution of mathematical model, and (3) analysis of results from model. Written in C language.

Assessing Uncertainty of Interspecies Correlation Estimation Models for Aromatic Compounds

EPA Science Inventory

We developed Interspecies Correlation Estimation (ICE) models for aromatic compounds containing 1 to 4 benzene rings to assess uncertainty in toxicity extrapolation in two data compilation approaches. ICE models are mathematical relationships between surrogate and predicted test ...

Decision Support Tool for Deep Energy Efficiency Retrofits in DoD Installations

DTIC Science & Technology

2014-01-01

representations (HDMR). Chemical Engineering Science, 57, 4445–4460. 2. Sobol ’, I., 2001. Global sensitivity indices for nonlinear mathematical...models and their Monte Carlo estimates. Mathematics and computers in simulation, 55, 271–280. 3. Sobol , I. and Kucherenko, S., 2009. Derivative based...representations (HDMR). Chemical Engineering Science, 57, 4445–4460. 16. Sobol ’, I., 2001. Global sensitivity indices for nonlinear mathematical models and

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

USGS Publications Warehouse

Donato, David I.

2012-01-01

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

Brain temperature changes during selective cooling with endovascular intracarotid cold saline infusion: simulation using human data fitted with an integrated mathematical model.

PubMed

Neimark, Matthew Aaron Harold; Konstas, Angelos Aristeidis; Lee, Leslie; Laine, Andrew Francis; Pile-Spellman, John; Choi, Jae

2013-03-01

The feasibility of rapid cerebral hypothermia induction in humans with intracarotid cold saline infusion (ICSI) was investigated using a hybrid approach of jugular venous bulb temperature (JVBT) sampling and mathematical modeling of transient and steady state brain temperature distribution. This study utilized both forward mathematical modeling, in which brain temperatures were predicted based on input saline temperatures, and inverse modeling, where brain temperatures were inferred based on JVBT. Changes in ipsilateral anterior circulation territory temperature (IACT) were estimated in eight patients as a result of 10 min of a cold saline infusion of 33 ml/min. During ICSI, the measured JVBT dropped by 0.76±0.18°C while the modeled JVBT decreased by 0.86±0.18°C. The modeled IACT decreased by 2.1±0.23°C. In the inverse model, IACT decreased by 1.9±0.23°C. The results of this study suggest that mild cerebral hypothermia can be induced rapidly and safely with ICSI in the neuroangiographical setting. The JVBT corrected mathematical model can be used as a non-invasive estimate of transient and steady state cerebral temperature changes.

Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

NASA Astrophysics Data System (ADS)

Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

2013-07-01

Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

Estimating tuberculosis incidence from primary survey data: a mathematical modeling approach

PubMed Central

Chadha, V. K.; Laxminarayan, R.; Arinaminpathy, N.

2017-01-01

SUMMARY BACKGROUND: There is an urgent need for improved estimations of the burden of tuberculosis (TB). OBJECTIVE: To develop a new quantitative method based on mathematical modelling, and to demonstrate its application to TB in India. DESIGN: We developed a simple model of TB transmission dynamics to estimate the annual incidence of TB disease from the annual risk of tuberculous infection and prevalence of smear-positive TB. We first compared model estimates for annual infections per smear-positive TB case using previous empirical estimates from China, Korea and the Philippines. We then applied the model to estimate TB incidence in India, stratified by urban and rural settings. RESULTS: Study model estimates show agreement with previous empirical estimates. Applied to India, the model suggests an annual incidence of smear-positive TB of 89.8 per 100 000 population (95%CI 56.8–156.3). Results show differences in urban and rural TB: while an urban TB case infects more individuals per year, a rural TB case remains infectious for appreciably longer, suggesting the need for interventions tailored to these different settings. CONCLUSIONS: Simple models of TB transmission, in conjunction with necessary data, can offer approaches to burden estimation that complement those currently being used. PMID:28284250

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

PubMed

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

2016-02-01

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

Role of mathematical models in assessment of risk and in attempts to define management strategy.

PubMed

Flamm, W G; Winbush, J S

1984-06-01

Risk assessment of food-borne carcinogens is becoming a common practice at FDA. Actual risk is not being estimated, only the upper limit of risk. The risk assessment process involves a large number of steps and assumptions, many of which affect the numerical value estimated. The mathematical model which is to be applied is only one of the factors which affect these numerical values. To fulfill the policy objective of using the "worst plausible case" in estimating the upper limit of risk, recognition needs to be given to a proper balancing of assumptions and decisions. Interaction between risk assessors and risk managers should avoid making or giving the appearance of making specific technical decisions such as the choice of the mathematical model. The importance of this emerging field is too great to jeopardize it by inappropriately mixing scientific judgments with policy judgments. The risk manager should understand fully the points and range of uncertainty involved in arriving at the estimates of risk which must necessarily affect the choice of the policy or regulatory options available.

A mathematical model for computer image tracking.

PubMed

Legters, G R; Young, T Y

1982-06-01

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

Mathematical Modeling Groundwater Mercury Pollution, Post Demercuriztion Monitoring And Evaulation of Clean-up Efficiency

EPA Science Inventory

The aim of the model was to forecast the groundwater mercury pollution distribution aureole and to discuss the mathematical simulations of the estimated quantity of mercury entering the river Irtysh and the aquifer wells in the village of Pavlodarskoe. During the years of 1975-1...

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

USGS Publications Warehouse

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

2012-01-01

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

A study on nonlinear estimation of submaximal effort tolerance based on the generalized MET concept and the 6MWT in pulmonary rehabilitation

PubMed Central

Szczegielniak, Jan; Łuniewski, Jacek; Stanisławski, Rafał; Bogacz, Katarzyna; Krajczy, Marcin; Rydel, Marek

2018-01-01

Background The six-minute walk test (6MWT) is considered to be a simple and inexpensive tool for the assessment of functional tolerance of submaximal effort. The aim of this work was 1) to background the nonlinear nature of the energy expenditure process due to physical activity, 2) to compare the results/scores of the submaximal treadmill exercise test and those of 6MWT in pulmonary patients and 3) to develop nonlinear mathematical models relating the two. Methods The study group included patients with the COPD. All patients were subjected to a submaximal exercise test and a 6MWT. To develop an optimal mathematical solution and compare the results of the exercise test and the 6MWT, the least squares and genetic algorithms were employed to estimate parameters of polynomial expansion and piecewise linear models. Results Mathematical analysis enabled to construct nonlinear models for estimating the MET result of submaximal exercise test based on average walk velocity (or distance) in the 6MWT. Conclusions Submaximal effort tolerance in COPD patients can be effectively estimated from new, rehabilitation-oriented, nonlinear models based on the generalized MET concept and the 6MWT. PMID:29425213

A Time Hazard Analysis of Student Persistence: A US University Undergraduate Mathematics Major Experience

ERIC Educational Resources Information Center

Bahi, Saïd; Higgins, Devin; Staley, Patrick

2015-01-01

Individual level data for the entire cohort of undergraduate mathematics students of a relatively small US public university was used to estimate the risk that a student will switch major to another one before degree completion. The data set covers the period from 1999 to 2006. Survival tables and logistic models were estimated and used to discuss…

EXPOSURE RELATED DOSE ESTIMATING MODEL (ERDEM)

EPA Science Inventory

ERDEM is a physiologically-based pharmacokinetic (PBPK) model with a graphical user interface (GUI) front end. Such a mathematical model was needed to make reliable estimates of the chemical dose to organs of animals or humans because of uncertainties of making route-to route, lo...

Longitudinal associations between reading and mathematics achievement.

PubMed

Grimm, Kevin J

2008-01-01

The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.

Malaria transmission rates estimated from serological data.

PubMed Central

Burattini, M. N.; Massad, E.; Coutinho, F. A.

1993-01-01

A mathematical model was used to estimate malaria transmission rates based on serological data. The model is minimally stochastic and assumes an age-dependent force of infection for malaria. The transmission rates estimated were applied to a simple compartmental model in order to mimic the malaria transmission. The model has shown a good retrieving capacity for serological and parasite prevalence data. PMID:8270011

Wall Paint Exposure Assessment Model (WPEM)

EPA Pesticide Factsheets

WPEM uses mathematical models developed from small chamber data to estimate the emissions of chemicals from oil-based (alkyd) and latex wall paint which is then combined with detailed use, workload and occupancy data to estimate user exposure.

Software For Least-Squares And Robust Estimation

NASA Technical Reports Server (NTRS)

Jeffreys, William H.; Fitzpatrick, Michael J.; Mcarthur, Barbara E.; Mccartney, James

1990-01-01

GAUSSFIT computer program includes full-featured programming language facilitating creation of mathematical models solving least-squares and robust-estimation problems. Programming language designed to make it easy to specify complex reduction models. Written in 100 percent C language.

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.

Physiological responses at five estimates of critical velocity.

PubMed

Bull, Anthony J; Housh, Terry J; Johnson, Glen O; Rana, Sharon R

2008-04-01

The purpose of this study was to compare critical velocity (CV) estimates from five mathematical models, and to examine the oxygen uptake (VO(2)) and heart rate (HR) responses during treadmill runs at the five estimates of CV. Ten subjects (six males and four females) performed one incremental test to determine maximal oxygen consumption (VO(2max)) and four or five randomly ordered constant-velocity trials on a treadmill for the estimation of CV. Five mathematical models were used to estimate CV for each subject including two linear, two nonlinear, and an exponential model. Up to five randomly ordered runs to exhaustion were performed by each subject at treadmill velocities that corresponded to the five CV estimates, and VO(2) and HR responses were monitored throughout each trial. The 3-parameter, nonlinear (Non-3) model produced CV estimates that were significantly (P < 0.05) less than the other four models. During runs at CV estimates, five subjects did not complete 60 min at the their estimate from the Non-3 model, nine did not complete 60 min at their estimate from the Non-2 model, and no subjects completed 60 min at any estimate from the other three models. The mean HR value (179 +/- 18 beats min(-1), HR(peak)) at the end of runs at CV using the Non-3 model was significantly less than the maximal HR (195 +/- 7 beats min(-1), HR(max)) achieved during the incremental trial to exhaustion. However, mean HR(peak) values from runs at all other CV estimates were not significantly different from HR(max). Furthermore, data indicated that mean HR(peak) values increased during runs at CV estimates from the third minute to the end of exercise for all models, and that these increases in VO(2) (range = 367-458 ml min(-1)) were significantly greater than that typically associated with O(2) drift ( approximately 200 ml min(-1)) for all but the exponential model, indicating a VO(2) slow component associated with CV estimates from four of the five models. However, the mean VO(2) values at the end of exercise during the runs at CV estimates for all five mathematical models were significantly less than the mean VO(2max) value. These results suggest that, in most cases, CV estimated from the five models does not represent a fatigueless task. In addition, the mean CV estimates from the five models varied by 18%, and four of the five mean CV estimates were within the heavy exercise domain. Therefore, CV would not represent the demarcation point between heavy and severe exercise domains.

A Panel Analysis of Student Mathematics Achievement in the US in the 1990s: Does Increasing the Amount of Time in Learning Activities Affect Math Achievement?

ERIC Educational Resources Information Center

Aksoy, Tevfik; Link, Charles R.

2000-01-01

Uses panel estimation techniques to estimate econometric models of mathematics achievement determinants for a nationally representative sample of high-school students. Extra time spent on math homework increases test scores; an extra hour of TV viewing negatively affects scores. Longer math periods also help. (Contains 56 references.) (MLH)

Two Mathematical Models of Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William

2007-01-01

Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

Applying a mathematical model to estimate the fractional accessibility to quenching of serum albumin by risperidone

NASA Astrophysics Data System (ADS)

Carqueja, Marilena; Cortez, Celia Martins

2014-10-01

In this work we report the results from application of a mathematical model to estimate the fractional accessibility to fluorescence quenching by risperidone in human and bovine sera albumins. Risperidone is an atypical antipsychotic drug used to treat many kinds of psychiatric disorders. Results showed that but the fractional accessibility for trypyophan 134, sub domain 1B, is about 3 times higher than that to tryptophan 212, showing that the primary binding site for risperidone is close to tryptophan 134, in domain IB of BSA.

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

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

NASA Astrophysics Data System (ADS)

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

2008-12-01

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

TU-FG-209-09: Mathematical Estimation and Experimental Measurement of Patient Free-In-Air Skin Entrance Exposure During a Panoramic Dental X-Ray Procedure

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

Errico, A; Behrman, R; Li, B

Purpose: To develop a simple mathematical model for estimating the patient free-in-air skin entrance exposure (SEE) during a panoramic dental x-ray that does not require the use of a head phantom. This eliminates issues associated with phantom centering and the mounting of a detector on the phantom for routine QC testing. Methods: We used a Sirona Orthophos XG panoramic radiographic unit and a Radcal Accu-Gold system for this study. A solid state detector was attached over the slit of the Orthophos’ sensor with the help of a custom-built jig. A single measurement of the free-in-air exposure at this position wasmore » taken over a full panoramic scan. A mathematical model for estimating the SEE was developed based upon this measurement, the system geometry, x-ray field beam width, and x-ray sweep angle. To validate the model, patient geometry was simulated by a 16 cm diameter PMMA CTDI phantom centered at the machine’s isocenter. Measurements taken on the phantom’s surface were made using a solid state detector with lead backing, an ion chamber, and the ion chamber with the phantom wrapped in lead to mitigate backscatter. Measurements were taken near the start position of the tube and at 90 degrees from the start position. Results: Using the solid state detector, the average SEE was 23.5+/−0.02 mR and 55.5+/−0.08 mR at 64 kVp and 73 kVp, respectively. With the lead-wrapping, the measurements from the ion chamber matched those of the solid state detector to within 0.1%. Preliminary results gave the difference between the mathematical model and the phantom measurements to be approximately 5% at both kVps. Conclusion: Reasonable estimates of patient SEE for panoramic dental radiography can be made using a simple mathematical model without the need for a head phantom.« less

Mathematical methods in biological dosimetry: the 1996 Iranian accident.

PubMed

Voisin, P; Assaei, R G; Heidary, A; Varzegar, R; Zakeri, F; Durand, V; Sorokine-Durm, I

2000-11-01

To report 18 months of cytogenetic follow-up for an Iranian worker accidentally overexposed to 192Ir, the mathematical extrapolation and comparison with clinical data. Unstable chromosome aberrations were measured using conventional cytogenetic tests by French and Iranian biological dosimetry laboratories on five occasions after the exposure. The decrease in dicentrics over time was analysed mathematically. In addition, Dolphin and Qdr extrapolations were applied to the data to check the exposure estimates. FISH determination of translocation yields was performed twice by the French laboratory and the results compared with the Dolphin and Qdr corrected values. Dose estimates based on dicentrics decreased from 3.1 +/- 0.4 Gy at 5 days after the accident to 0.8 +/- 0.2 Gy at 529 days. This could be fitted by double-exponential regression with an inflexion point between rapid and slow decrease of dicentrics after about 40 days. Dose estimates of 3.4 +/- 0.4 Gy for the Qdr model and 3.6 +/- 0.5 Gy for the Dolphin model were calculated during the post-exposure period and were remarkably stable. FISH translocation data at 26 and 61 days appeared consistent with the Dolphin and Qdr estimates. Dose correction by the Qdr and Dolphin models and translocation scoring appeared consistent with the clinical data and provided better information about the radiation injury than did crude estimates from dicentric scoring alone. Estimation by the Dolphin model of the irradiated fraction of the body seemed unreliable: it correlated better with the fraction of originally irradiated lymphocytes.

An animated depiction of major depression epidemiology.

PubMed

Patten, Scott B

2007-06-08

Epidemiologic estimates are now available for a variety of parameters related to major depression epidemiology (incidence, prevalence, etc.). These estimates are potentially useful for policy and planning purposes, but it is first necessary that they be synthesized into a coherent picture of the epidemiology of the condition. Several attempts to do so have been made using mathematical modeling procedures. However, this information is not easy to communicate to users of epidemiological data (clinicians, administrators, policy makers). In this study, up-to-date data on major depression epidemiology were integrated using a discrete event simulation model. The mathematical model was animated in Virtual Reality Modeling Language (VRML) to create a visual, rather than mathematical, depiction of the epidemiology. Consistent with existing literature, the model highlights potential advantages of population health strategies that emphasize access to effective long-term treatment. The paper contains a web-link to the animation. Visual animation of epidemiological results may be an effective knowledge translation tool. In clinical practice, such animations could potentially assist with patient education and enhanced long-term compliance.

Establishment of a center of excellence for applied mathematical and statistical research

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Gray, H. L.

1983-01-01

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

Toxicity Estimation Software Tool (TEST)

EPA Science Inventory

The Toxicity Estimation Software Tool (TEST) was developed to allow users to easily estimate the toxicity of chemicals using Quantitative Structure Activity Relationships (QSARs) methodologies. QSARs are mathematical models used to predict measures of toxicity from the physical c...

Mathematical models for nonparametric inferences from line transect data

USGS Publications Warehouse

Burnham, K.P.; Anderson, D.R.

1976-01-01

A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).

Metamodels for Ozone: Comparison of Three Estimation Techniques

EPA Science Inventory

A metamodel for ozone is a mathematical relationship between the inputs and outputs of an air quality modeling experiment, permitting calculation of outputs for scenarios of interest without having to run the model again. In this study we compare three metamodel estimation techn...

Approaches to highly parameterized inversion: Pilot-point theory, guidelines, and research directions

USGS Publications Warehouse

Doherty, John E.; Fienen, Michael N.; Hunt, Randall J.

2011-01-01

Pilot points have been used in geophysics and hydrogeology for at least 30 years as a means to bridge the gap between estimating a parameter value in every cell of a model and subdividing models into a small number of homogeneous zones. Pilot points serve as surrogate parameters at which values are estimated in the inverse-modeling process, and their values are interpolated onto the modeling domain in such a way that heterogeneity can be represented at a much lower computational cost than trying to estimate parameters in every cell of a model. Although the use of pilot points is increasingly common, there are few works documenting the mathematical implications of their use and even fewer sources of guidelines for their implementation in hydrogeologic modeling studies. This report describes the mathematics of pilot-point use, provides guidelines for their use in the parameter-estimation software suite (PEST), and outlines several research directions. Two key attributes for pilot-point definitions are highlighted. First, the difference between the information contained in the every-cell parameter field and the surrogate parameter field created using pilot points should be in the realm of parameters which are not informed by the observed data (the null space). Second, the interpolation scheme for projecting pilot-point values onto model cells ideally should be orthogonal. These attributes are informed by the mathematics and have important ramifications for both the guidelines and suggestions for future research.

Gompertzian stochastic model with delay effect to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Models of Pilot Behavior and Their Use to Evaluate the State of Pilot Training

NASA Astrophysics Data System (ADS)

Jirgl, Miroslav; Jalovecky, Rudolf; Bradac, Zdenek

2016-07-01

This article discusses the possibilities of obtaining new information related to human behavior, namely the changes or progressive development of pilots' abilities during training. The main assumption is that a pilot's ability can be evaluated based on a corresponding behavioral model whose parameters are estimated using mathematical identification procedures. The mean values of the identified parameters are obtained via statistical methods. These parameters are then monitored and their changes evaluated. In this context, the paper introduces and examines relevant mathematical models of human (pilot) behavior, the pilot-aircraft interaction, and an example of the mathematical analysis.

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.

Mathematical Modeling of Hepatitis C Prevalence Reduction with Antiviral Treatment Scale-Up in Persons Who Inject Drugs in Metropolitan Chicago

DOE PAGES

Echevarria, Desarae; Gutfraind, Alexander; Boodram, Basmattee; ...

2015-08-21

New direct-acting antivirals (DAAs) provide an opportunity to combat hepatitis C virus (HCV) infection in persons who inject drugs (PWID). In our paper, we use a mathematical model to predict the impact of a DAA-treatment scale-up on HCV prevalence among PWID and the estimated cost in metropolitan Chicago.

Mathematical Modeling of Hepatitis C Prevalence Reduction with Antiviral Treatment Scale-Up in Persons Who Inject Drugs in Metropolitan Chicago

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

Echevarria, Desarae; Gutfraind, Alexander; Boodram, Basmattee

New direct-acting antivirals (DAAs) provide an opportunity to combat hepatitis C virus (HCV) infection in persons who inject drugs (PWID). In our paper, we use a mathematical model to predict the impact of a DAA-treatment scale-up on HCV prevalence among PWID and the estimated cost in metropolitan Chicago.

Discussion and revision of the mathematical modeling tool described in the previously published article "Modeling HIV Transmission risk among Mozambicans prior to their initiating highly active antiretroviral therapy".

PubMed

Cassels, Susan; Pearson, Cynthia R; Kurth, Ann E; Martin, Diane P; Simoni, Jane M; Matediana, Eduardo; Gloyd, Stephen

2009-07-01

Mathematical models are increasingly used in social and behavioral studies of HIV transmission; however, model structures must be chosen carefully to best answer the question at hand and conclusions must be interpreted cautiously. In Pearson et al. (2007), we presented a simple analytically tractable deterministic model to estimate the number of secondary HIV infections stemming from a population of HIV-positive Mozambicans and to evaluate how the estimate would change under different treatment and behavioral scenarios. In a subsequent application of the model with a different data set, we observed that the model produced an unduly conservative estimate of the number of new HIV-1 infections. In this brief report, our first aim is to describe a revision of the model to correct for this underestimation. Specifically, we recommend adjusting the population-level sexually transmitted infection (STI) parameters to be applicable to the individual-level model specification by accounting for the proportion of individuals uninfected with an STI. In applying the revised model to the original data, we noted an estimated 40 infections/1000 HIV-positive persons per year (versus the original 23 infections/1000 HIV-positive persons per year). In addition, the revised model estimated that highly active antiretroviral therapy (HAART) along with syphilis and herpes simplex virus type 2 (HSV-2) treatments combined could reduce HIV-1 transmission by 72% (versus 86% according to the original model). The second aim of this report is to discuss the advantages and disadvantages of mathematical models in the field and the implications of model interpretation. We caution that simple models should be used for heuristic purposes only. Since these models do not account for heterogeneity in the population and significantly simplify HIV transmission dynamics, they should be used to describe general characteristics of the epidemic and demonstrate the importance or sensitivity of parameters in the model.

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model.

PubMed

Iwata, Michio; Miyawaki-Kuwakado, Atsuko; Yoshida, Erika; Komori, Soichiro; Shiraishi, Fumihide

2018-02-02

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton-Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks. Copyright © 2018 Elsevier Inc. All rights reserved.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

A mathematical model of microalgae growth in cylindrical photobioreactor

NASA Astrophysics Data System (ADS)

Bakeri, Noorhadila Mohd; Jamaian, Siti Suhana

2017-08-01

Microalgae are unicellular organisms, which exist individually or in chains or groups but can be utilized in many applications. Researchers have done various efforts in order to increase the growth rate of microalgae. Microalgae have a potential as an effective tool for wastewater treatment, besides as a replacement for natural fuel such as coal and biodiesel. The growth of microalgae can be estimated by using Geider model, which this model is based on photosynthesis irradiance curve (PI-curve) and focused on flat panel photobioreactor. Therefore, in this study a mathematical model for microalgae growth in cylindrical photobioreactor is proposed based on the Geider model. The light irradiance is the crucial part that affects the growth rate of microalgae. The absorbed photon flux will be determined by calculating the average light irradiance in a cylindrical system illuminated by unidirectional parallel flux and considering the cylinder as a collection of differential parallelepipeds. Results from this study showed that the specific growth rate of microalgae increases until the constant level is achieved. Therefore, the proposed mathematical model can be used to estimate the rate of microalgae growth in cylindrical photobioreactor.

Dynamic Modeling of Cell-Free Biochemical Networks Using Effective Kinetic Models

DTIC Science & Technology

2015-03-16

sensitivity value was the maximum uncertainty in that value estimated by the Sobol method. 2.4. Global Sensitivity Analysis of the Reduced Order Coagulation...sensitivity analysis, using the variance-based method of Sobol , to estimate which parameters controlled the performance of the reduced order model [69]. We...Environment. Comput. Sci. Eng. 2007, 9, 90–95. 69. Sobol , I. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

Vaccine approaches to malaria control and elimination: Insights from mathematical models.

PubMed

White, Michael T; Verity, Robert; Churcher, Thomas S; Ghani, Azra C

2015-12-22

A licensed malaria vaccine would provide a valuable new tool for malaria control and elimination efforts. Several candidate vaccines targeting different stages of the malaria parasite's lifecycle are currently under development, with one candidate, RTS,S/AS01 for the prevention of Plasmodium falciparum infection, having recently completed Phase III trials. Predicting the public health impact of a candidate malaria vaccine requires using clinical trial data to estimate the vaccine's efficacy profile--the initial efficacy following vaccination and the pattern of waning of efficacy over time. With an estimated vaccine efficacy profile, the effects of vaccination on malaria transmission can be simulated with the aid of mathematical models. Here, we provide an overview of methods for estimating the vaccine efficacy profiles of pre-erythrocytic vaccines and transmission-blocking vaccines from clinical trial data. In the case of RTS,S/AS01, model estimates from Phase II clinical trial data indicate a bi-phasic exponential profile of efficacy against infection, with efficacy waning rapidly in the first 6 months after vaccination followed by a slower rate of waning over the next 4 years. Transmission-blocking vaccines have yet to be tested in large-scale Phase II or Phase III clinical trials so we review ongoing work investigating how a clinical trial might be designed to ensure that vaccine efficacy can be estimated with sufficient statistical power. Finally, we demonstrate how parameters estimated from clinical trials can be used to predict the impact of vaccination campaigns on malaria using a mathematical model of malaria transmission. Copyright © 2015 Elsevier Ltd. All rights reserved.

Detecting isotopic ratio outliers

NASA Astrophysics Data System (ADS)

Bayne, C. K.; Smith, D. H.

An alternative method is proposed for improving isotopic ratio estimates. This method mathematically models pulse-count data and uses iterative reweighted Poisson regression to estimate model parameters to calculate the isotopic ratios. This computer-oriented approach provides theoretically better methods than conventional techniques to establish error limits and to identify outliers.

Mathematical models for non-parametric inferences from line transect data

USGS Publications Warehouse

Burnham, K.P.; Anderson, D.R.

1976-01-01

A general mathematical theory of line transects is developed which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(0) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y I r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(0 I r).

Time estimation predicts mathematical intelligence.

PubMed

Kramer, Peter; Bressan, Paola; Grassi, Massimo

2011-01-01

Performing mental subtractions affects time (duration) estimates, and making time estimates disrupts mental subtractions. This interaction has been attributed to the concurrent involvement of time estimation and arithmetic with general intelligence and working memory. Given the extant evidence of a relationship between time and number, here we test the stronger hypothesis that time estimation correlates specifically with mathematical intelligence, and not with general intelligence or working-memory capacity. Participants performed a (prospective) time estimation experiment, completed several subtests of the WAIS intelligence test, and self-rated their mathematical skill. For five different durations, we found that time estimation correlated with both arithmetic ability and self-rated mathematical skill. Controlling for non-mathematical intelligence (including working memory capacity) did not change the results. Conversely, correlations between time estimation and non-mathematical intelligence either were nonsignificant, or disappeared after controlling for mathematical intelligence. We conclude that time estimation specifically predicts mathematical intelligence. On the basis of the relevant literature, we furthermore conclude that the relationship between time estimation and mathematical intelligence is likely due to a common reliance on spatial ability.

Using Mathematical Transmission Modelling to Investigate Drivers of Respiratory Syncytial Virus Seasonality in Children in the Philippines

PubMed Central

Paynter, Stuart; Yakob, Laith; Simões, Eric A. F.; Lucero, Marilla G.; Tallo, Veronica; Nohynek, Hanna; Ware, Robert S.; Weinstein, Philip; Williams, Gail; Sly, Peter D.

2014-01-01

We used a mathematical transmission model to estimate when ecological drivers of respiratory syncytial virus (RSV) transmissibility would need to act in order to produce the observed seasonality of RSV in the Philippines. We estimated that a seasonal peak in transmissibility would need to occur approximately 51 days prior to the observed peak in RSV cases (range 49 to 67 days). We then compared this estimated seasonal pattern of transmissibility to the seasonal patterns of possible ecological drivers of transmissibility: rainfall, humidity and temperature patterns, nutritional status, and school holidays. The timing of the seasonal patterns of nutritional status and rainfall were both consistent with the estimated seasonal pattern of transmissibility and these are both plausible drivers of the seasonality of RSV in this setting. PMID:24587222

A simple mathematical method to estimate ammonia emission from in-house windrowing of poultry litter.

PubMed

Ro, Kyoung S; Szogi, Ariel A; Moore, Philip A

2018-05-12

In-house windrowing between flocks is an emerging sanitary management practice to partially disinfect the built-up litter in broiler houses. However, this practice may also increase ammonia (NH 3 ) emission from the litter due to the increase in litter temperature. The objectives of this study were to develop mathematical models to estimate NH 3 emission rates from broiler houses practicing in-house windrowing between flocks. Equations to estimate mass-transfer areas form different shapes windrowed litter (triangular, rectangular, and semi-cylindrical prisms) were developed. Using these equations, the heights of windrows yielding the smallest mass-transfer area were estimated. Smaller mass-transfer area is preferred as it reduces both emission rates and heat loss. The heights yielding the minimum mass-transfer area were 0.8 and 0.5 m for triangular and rectangular windrows, respectively. Only one height (0.6 m) was theoretically possible for semi-cylindrical windrows because the base and the height were not independent. Mass-transfer areas were integrated with published process-based mathematical models to estimate the total house NH 3 emission rates during in-house windrowing of poultry litter. The NH 3 emission rate change calculated from the integrated model compared well with the observed values except for the very high NH 3 initial emission rate from mechanically disturbing the litter to form the windrows. This approach can be used to conveniently estimate broiler house NH 3 emission rates during in-house windrowing between flocks by simply measuring litter temperatures.

40 CFR 227.29 - Initial mixing.

Code of Federal Regulations, 2010 CFR

2010-07-01

... estimated by one of these methods, in order of preference: (1) When field data on the proposed dumping are... conjunction with an appropriate mathematical model acceptable to EPA or the District Engineer, as appropriate... proposed for discharge are available, these shall be used in conjunction with an appropriate mathematical...

Age estimation based on pulp chamber volume of first molars from cone-beam computed tomography images.

PubMed

Ge, Zhi-pu; Ma, Ruo-han; Li, Gang; Zhang, Ji-zong; Ma, Xu-chen

2015-08-01

To establish a method that can be used for human age estimation on the basis of pulp chamber volume of first molars and to identify whether the method is good enough for age estimation in real human cases. CBCT images of 373 maxillary first molars and 372 mandibular first molars were collected to establish the mathematical model from 190 female and 213 male patients whose age between 12 and 69 years old. The inclusion criteria of the first molars were: no caries, no excessive tooth wear, no dental restorations, no artifacts due to metal restorative materials present in adjacent teeth, and no pulpal calcification. All the CBCT images were acquired with a CBCT unit NewTom VG (Quantitative Radiology, Verona, Italy) and reconstructed with a voxel-size of 0.15mm. The images were subsequently exported as DICOM data sets and imported into an open source 3D image semi-automatic segmenting and voxel-counting software ITK-SNAP 2.4 for the calculation of pulp chamber volumes. A logarithmic regression analysis was conducted with age as dependent variable and pulp chamber volume as independent variables to establish a mathematical model for the human age estimation. To identify the precision and accuracy of the model for human age estimation, another 104 maxillary first molars and 103 mandibular first molars from 55 female and 57 male patients whose age between 12 and 67 years old were collected, too. Mean absolute error and root mean square error between the actual age and estimated age were used to determine the precision and accuracy of the mathematical model. The study was approved by the Institutional Review Board of Peking University School and Hospital of Stomatology. A mathematical model was suggested for: AGE=117.691-26.442×ln (pulp chamber volume). The regression was statistically significant (p=0.000<0.01). The coefficient of determination (R(2)) was 0.564. There is a mean absolute error of 8.122 and root mean square error of 5.603 between the actual age and estimated age for all the tested teeth. The pulp chamber volume of first molar is a useful index for the estimation of human age with reasonable precision and accuracy. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

[Application of GIS and integrated mathematic models on estimating forest land wood productiveness and solar energy use efficiency].

PubMed

Xing, Shihe; Lin, Dexi; Shen, Jinquan; Cao, Rongbin

2005-10-01

Based on the meteorological elements observation and mountain soil survey in Fujian Province, this paper approached the application of geographic information system (GIS) and integrated mathematic models on estimating the grid wood productiveness and solar energy use efficiency (SEUE) of regional forest land. The results showed that there was a significant quadratic correlation of annual mean temperature, precipitation and total solar radiation energy(TSRE) with longitude, latitude and altitude, and their multiple correlation coefficients ranged from 0.692 to 0.981. The regional annual mean TSRE, temperature and precipitation could be well estimated by GIS and integrated models of quadratic tendency curve, and linear, quadratic and quartic inverse distance weighted interpolation. These annual means estimated by the models did not differ greatly from observed data, and the t test values were 1.29, 0.12 and 0.06, respectively. The grid wood productiveness and SEUE of regional forest land in Fujian could also be well estimated with the aid of GIS and integrated models, which ranged from 2.32 m3 x hm(-2) yr(-1) to 18.61 m3 x hm(-2) yr(-1) and from 0.11% to 0.91%, respectively.

Mathematical models for Isoptera (Insecta) mound growth.

PubMed

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

2008-08-01

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

Space Station racks weight and CG measurement using the rack insertion end-effector

NASA Technical Reports Server (NTRS)

Brewer, William V.

1994-01-01

The objective was to design a method to measure weight and center of gravity (C.G.) location for Space Station Modules by adding sensors to the existing Rack Insertion End Effector (RIEE). Accomplishments included alternative sensor placement schemes organized into categories. Vendors were queried for suitable sensor equipment recommendations. Inverse mathematical models for each category determine expected maximum sensor loads. Sensors are selected using these computations, yielding cost and accuracy data. Accuracy data for individual sensors are inserted into forward mathematical models to estimate the accuracy of an overall sensor scheme. Cost of the schemes can be estimated. Ease of implementation and operation are discussed.

Study of ecological compensation in complex river networks based on a mathematical model.

PubMed

Wang, Xiao; Shen, Chunqi; Wei, Jun; Niu, Yong

2018-05-31

Transboundary water pollution has resulted in increasing conflicts between upstream and downstream administrative districts. Ecological compensation is an efficient means of restricting pollutant discharge and achieving sustainable utilization of water resources. The tri-provincial region of Taihu Basin is a typical river networks area. Pollutant flux across provincial boundaries in the Taihu Basin is hard to determine due to complex hydrologic and hydrodynamic conditions. In this study, ecological compensation estimation for the tri-provincial area based on a mathematical model is investigated for better environmental management. River discharge and water quality are predicted with the one-dimensional mathematical model and validated with field measurements. Different ecological compensation criteria are identified considering the notable regional discrepancy in sewage treatment costs. Finally, the total compensation payment is estimated. Our study indicates that Shanghai should be the receiver of payment from both Jiangsu and Zhenjiang in 2013, with 305 million and 300 million CNY, respectively. Zhejiang also contributes more pollutants to Jiangsu, and the compensation to Jiangsu is estimated as 9.3 million CNY. The proposed ecological compensation method provides an efficient way for solving the transboundary conflicts in a complex river networks area and is instructive for future policy-making.

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate

PubMed Central

Pradines, Joël R.; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-01-01

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements. PMID:27112127

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate.

PubMed

Pradines, Joël R; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-04-26

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements.

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate

NASA Astrophysics Data System (ADS)

Pradines, Joël R.; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-04-01

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements.

Data-driven outbreak forecasting with a simple nonlinear growth model

PubMed Central

Lega, Joceline; Brown, Heidi E.

2016-01-01

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. PMID:27770752

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

PubMed

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

2012-04-01

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

Estimating and Testing the Sources of Evoked Potentials in the Brain.

ERIC Educational Resources Information Center

Huizenga, Hilde M.; Molenaar, Peter C. M.

1994-01-01

The source of an event-related brain potential (ERP) is estimated from multivariate measures of ERP on the head under several mathematical and physical constraints on the parameters of the source model. Statistical aspects of estimation are discussed, and new tests are proposed. (SLD)

Parameter identification of material constants in a composite shell structure

NASA Technical Reports Server (NTRS)

Martinez, David R.; Carne, Thomas G.

1988-01-01

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Estimating the Stoichiometry of HIV Neutralization

PubMed Central

Magnus, Carsten; Regoes, Roland R.

2010-01-01

HIV-1 virions infect target cells by first establishing contact between envelope glycoprotein trimers on the virion's surface and CD4 receptors on a target cell, recruiting co-receptors, fusing with the cell membrane and finally releasing the genetic material into the target cell. Specific experimental setups allow the study of the number of trimer-receptor-interactions needed for infection, i.e., the stoichiometry of entry and also the number of antibodies needed to prevent one trimer from engaging successfully in the entry process, i.e., the stoichiometry of (trimer) neutralization. Mathematical models are required to infer the stoichiometric parameters from these experimental data. Recently, we developed mathematical models for the estimations of the stoichiometry of entry [1]. In this article, we show how our models can be extended to investigate the stoichiometry of trimer neutralization. We study how various biological parameters affect the estimate of the stoichiometry of neutralization. We find that the distribution of trimer numbers—which is also an important determinant of the stoichiometry of entry—influences the estimated value of the stoichiometry of neutralization. In contrast, other parameters, which characterize the experimental system, diminish the information we can extract from the data about the stoichiometry of neutralization, and thus reduce our confidence in the estimate. We illustrate the use of our models by re-analyzing previously published data on the neutralization sensitivity [2], which contains measurements of neutralization sensitivity of viruses with different envelope proteins to antibodies with various specificities. Our mathematical framework represents the formal basis for the estimation of the stoichiometry of neutralization. Together with the stoichiometry of entry, the stoichiometry of trimer neutralization will allow one to calculate how many antibodies are required to neutralize a virion or even an entire population of virions. PMID:20333245

Novel mathematical model to estimate ball impact force in soccer.

PubMed

Iga, Takahito; Nunome, Hiroyuki; Sano, Shinya; Sato, Nahoko; Ikegami, Yasuo

2017-11-22

To assess ball impact force during soccer kicking is important to quantify from both performance and chronic injury prevention perspectives. We aimed to verify the appropriateness of previous models used to estimate ball impact force and to propose an improved model to better capture the time history of ball impact force. A soccer ball was fired directly onto a force platform (10 kHz) at five realistic kicking ball velocities and ball behaviour was captured by a high-speed camera (5,000 Hz). The time history of ball impact force was estimated using three existing models and two new models. A new mathematical model that took into account a rapid change in ball surface area and heterogeneous ball deformation showed a distinctive advantage to estimate the peak forces and its occurrence times and to reproduce time history of ball impact forces more precisely, thereby reinforcing the possible mechanics of 'footballer's ankle'. Ball impact time was also systematically shortened when ball velocity increases in contrast to practical understanding for producing faster ball velocity, however, the aspect of ball contact time must be considered carefully from practical point of view.

In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue.

PubMed

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

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

Gravitational orientation of the orbital complex, Salyut-6--Soyuz

NASA Technical Reports Server (NTRS)

Grecho, G. M.; Sarychev, V. A.; Legostayev, V. P.; Sazonov, V. V.; Gansvind, I. N.

1983-01-01

A simple mathematical model is proposed for the Salyut-6-Soyuz orbital complex motion with respect to the center of mass under the one-axis gravity-gradient orientation regime. This model was used for processing the measurements of the orbital complex motion parameters when the above orientation region was implemented. Some actual satellite motions are simulated and the satellite's aerodynamic parameters are determined. Estimates are obtained for the accuracy of measurements as well as that of the mathematical model.

Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

PubMed

Yates, James W T

2008-07-03

One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.

The Mathematics of Navigating the Solar System

NASA Technical Reports Server (NTRS)

Hintz, Gerald

2000-01-01

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Teacher Support, Instructional Practices, Student Motivation, and Mathematics Achievement in High School

ERIC Educational Resources Information Center

Yu, Rongrong; Singh, Kusum

2018-01-01

The authors examined the relationships among teacher classroom practices, student motivation, and mathematics achievement in high school. The data for this study was drawn from the base-year data of High School Longitudinal Study of 2009. Structural equation modeling method was used to estimate the relationships among variables. The results…

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Mathematical modelling of respiratory syncytial virus (RSV): vaccination strategies and budget applications.

PubMed

Acedo, L; Díez-Domingo, J; Moraño, J-A; Villanueva, R-J

2010-06-01

We propose an age-structured mathematical model for respiratory syncytial virus in which children aged <1 year are especially considered. Real data on hospitalized children in the Spanish region of Valencia were used in order to determine some seasonal parameters of the model. Weekly predictions of the number of children aged <1 year that will be hospitalized in the following years in Valencia are presented using this model. Results are applied to estimate the regional cost of paediatric hospitalizations and to perform a cost-effectiveness analysis of possible vaccination strategies.

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

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

Jablonská, Jana, E-mail: jana.jablonska@vsb.cz; Kozubková, Milada, E-mail: milada.kozubkova@vsb.cz

Cavitation today is a very important problem that is solved by means of experimental and mathematical methods. The article deals with the generation of cavitation in convergent divergent nozzle of rectangular cross section. Measurement of pressure, flow rate, temperature, amount of dissolved air in the liquid and visualization of cavitation area using high-speed camera was performed for different flow rates. The measurement results were generalized by dimensionless analysis, which allows easy detection of cavitation in the nozzle. For numerical simulation the multiphase mathematical model of cavitation consisting of water and vapor was created. During verification the disagreement with the measurementsmore » for higher flow rates was proved, therefore the model was extended to multiphase mathematical model (water, vapor and air), due to release of dissolved air. For the mathematical modeling the multiphase turbulence RNG k-ε model for low Reynolds number flow with vapor and air cavitation was used. Subsequently the sizes of the cavitation area were verified. In article the inlet pressure and loss coefficient depending on the amount of air added to the mathematical model are evaluated. On the basis of the approach it may be create a methodology to estimate the amount of released air added at the inlet to the modeled area.« less

Lateral-Directional Parameter Estimation on the X-48B Aircraft Using an Abstracted, Multi-Objective Effector Model

NASA Technical Reports Server (NTRS)

Ratnayake, Nalin A.; Waggoner, Erin R.; Taylor, Brian R.

2011-01-01

The problem of parameter estimation on hybrid-wing-body aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aerodynamic control effectors that act in coplanar motion. This adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of flight and simulation data must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, time-decorrelation techniques are applied to a model structure selected through stepwise regression for simulated and flight-generated lateral-directional parameter estimation data. A virtual effector model that uses mathematical abstractions to describe the multi-axis effects of clamshell surfaces is developed and applied. Comparisons are made between time history reconstructions and observed data in order to assess the accuracy of the regression model. The Cram r-Rao lower bounds of the estimated parameters are used to assess the uncertainty of the regression model relative to alternative models. Stepwise regression was found to be a useful technique for lateral-directional model design for hybrid-wing-body aircraft, as suggested by available flight data. Based on the results of this study, linear regression parameter estimation methods using abstracted effectors are expected to perform well for hybrid-wing-body aircraft properly equipped for the task.

Reconstruction of neuronal input through modeling single-neuron dynamics and computations

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

Qin, Qing; Wang, Jiang; Yu, Haitao

Mathematical models provide a mathematical description of neuron activity, which can better understand and quantify neural computations and corresponding biophysical mechanisms evoked by stimulus. In this paper, based on the output spike train evoked by the acupuncture mechanical stimulus, we present two different levels of models to describe the input-output system to achieve the reconstruction of neuronal input. The reconstruction process is divided into two steps: First, considering the neuronal spiking event as a Gamma stochastic process. The scale parameter and the shape parameter of Gamma process are, respectively, defined as two spiking characteristics, which are estimated by a state-spacemore » method. Then, leaky integrate-and-fire (LIF) model is used to mimic the response system and the estimated spiking characteristics are transformed into two temporal input parameters of LIF model, through two conversion formulas. We test this reconstruction method by three different groups of simulation data. All three groups of estimates reconstruct input parameters with fairly high accuracy. We then use this reconstruction method to estimate the non-measurable acupuncture input parameters. Results show that under three different frequencies of acupuncture stimulus conditions, estimated input parameters have an obvious difference. The higher the frequency of the acupuncture stimulus is, the higher the accuracy of reconstruction is.« less

Reconstruction of neuronal input through modeling single-neuron dynamics and computations

NASA Astrophysics Data System (ADS)

Qin, Qing; Wang, Jiang; Yu, Haitao; Deng, Bin; Chan, Wai-lok

2016-06-01

Mathematical models provide a mathematical description of neuron activity, which can better understand and quantify neural computations and corresponding biophysical mechanisms evoked by stimulus. In this paper, based on the output spike train evoked by the acupuncture mechanical stimulus, we present two different levels of models to describe the input-output system to achieve the reconstruction of neuronal input. The reconstruction process is divided into two steps: First, considering the neuronal spiking event as a Gamma stochastic process. The scale parameter and the shape parameter of Gamma process are, respectively, defined as two spiking characteristics, which are estimated by a state-space method. Then, leaky integrate-and-fire (LIF) model is used to mimic the response system and the estimated spiking characteristics are transformed into two temporal input parameters of LIF model, through two conversion formulas. We test this reconstruction method by three different groups of simulation data. All three groups of estimates reconstruct input parameters with fairly high accuracy. We then use this reconstruction method to estimate the non-measurable acupuncture input parameters. Results show that under three different frequencies of acupuncture stimulus conditions, estimated input parameters have an obvious difference. The higher the frequency of the acupuncture stimulus is, the higher the accuracy of reconstruction is.

A one-model approach based on relaxed combinations of inputs for evaluating input congestion in DEA

NASA Astrophysics Data System (ADS)

Khodabakhshi, Mohammad

2009-08-01

This paper provides a one-model approach of input congestion based on input relaxation model developed in data envelopment analysis (e.g. [G.R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion -- Considering textile industry of China, Applied Mathematics and Computation (1) (2004) 263-273; G.R. Jahanshahloo, M. Khodabakhshi, Determining assurance interval for non-Archimedean ele improving outputs model in DEA, Applied Mathematics and Computation 151 (2) (2004) 501-506; M. Khodabakhshi, A super-efficiency model based on improved outputs in data envelopment analysis, Applied Mathematics and Computation 184 (2) (2007) 695-703; M. Khodabakhshi, M. Asgharian, An input relaxation measure of efficiency in stochastic data analysis, Applied Mathematical Modelling 33 (2009) 2010-2023]. This approach reduces solving three problems with the two-model approach introduced in the first of the above-mentioned reference to two problems which is certainly important from computational point of view. The model is applied to a set of data extracted from ISI database to estimate input congestion of 12 Canadian business schools.

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

DOE PAGES

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh; ...

2013-10-15

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

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

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

On the development of nugget growth model for resistance spot welding

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

Zhou, Kang, E-mail: zhoukang326@126.com, E-mail: melcai@ust.hk; Cai, Lilong, E-mail: zhoukang326@126.com, E-mail: melcai@ust.hk

2014-04-28

In this paper, we developed a general mathematical model to estimate the nugget growth process based on the heat energy delivered into the welds by the resistance spot welding. According to the principles of thermodynamics and heat transfer, and the effect of electrode force during the welding process, the shape of the nugget can be estimated. Then, a mathematical model between heat energy absorbed and nugget diameter can be obtained theoretically. It is shown in this paper that the nugget diameter can be precisely described by piecewise fractal polynomial functions. Experiments were conducted with different welding operation conditions, such asmore » welding currents, workpiece thickness, and widths, to validate the model and the theoretical analysis. All the experiments confirmed that the proposed model can predict the nugget diameters with high accuracy based on the input heat energy to the welds.« less

WNDCOM: estimating surface winds in mountainous terrain

Treesearch

Bill C. Ryan

1983-01-01

WNDCOM is a mathematical model for estimating surface winds in mountainous terrain. By following the procedures described, the sheltering and diverting effect of terrain, the individual components of the windflow, and the surface wind in remote mountainous areas can be estimated. Components include the contribution from the synoptic scale pressure gradient, the sea...

A Meta-Analysis of the Relation between RAN and Mathematics

ERIC Educational Resources Information Center

Koponen, Tuire; Georgiou, George; Salmi, Paula; Leskinen, Markku; Aro, Mikko

2017-01-01

Several studies have shown that rapid automatized naming (RAN) is a significant predictor of mathematics, but the nature of their relationship remains elusive. Thus, the purpose of this meta-analysis was to estimate the size of their relationship and determine the conditions under which they correlate. We used a random-effects model analysis of…

Examination of the Assumptions and Properties of the Graded Item Response Model: An Example Using a Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

1995-01-01

Over 5,000 students participated in a study of the dimensionality and stability of the item parameter estimates of a mathematics performance assessment developed for the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Project. Results demonstrate the test's dimensionality and illustrate ways to examine use of the…

Historical Analysis of the Battle of Little Bighorn Utilizing the Joint Conflict and Tactical Simulation (JCATS)

DTIC Science & Technology

2004-06-01

Frank Giordano , whose enlightening instruction and contagious enthusiasm in mathematical modeling provided us with the tools and concepts needed to...for each weapon, as taught by Brigadier General (Retired) Frank Giordano and Dr. Maurice Weir, authors of Mathematical Modeling and professors at...decision was to use the estimate given by Scott in a separate article he authored with Melissa A. Connor titled “Post-mortem at the Little Bighorn

Comparison of Mathematical Equation and Neural Network Modeling for Drying Kinetic of Mendong in Microwave Oven

NASA Astrophysics Data System (ADS)

Maulidah, Rifa'atul; Purqon, Acep

2016-08-01

Mendong (Fimbristylis globulosa) has a potentially industrial application. We investigate a predictive model for heat and mass transfer in drying kinetics during drying a Mendong. We experimentally dry the Mendong by using a microwave oven. In this study, we analyze three mathematical equations and feed forward neural network (FNN) with back propagation to describe the drying behavior of Mendong. Our results show that the experimental data and the artificial neural network model has a good agreement and better than a mathematical equation approach. The best FNN for the prediction is 3-20-1-1 structure with Levenberg- Marquardt training function. This drying kinetics modeling is potentially applied to determine the optimal parameters during mendong drying and to estimate and control of drying process.

Modeling stability of growth between mathematics and science achievement during middle and high school.

PubMed

Ma, Xin; Ma, Lingling

2004-04-01

In this study, the authors introduced a multivariate multilevel model to estimate the consistency among students and schools in the rates of growth between mathematics and science achievement during the entire middle and high school years with data from the Longitudinal Study of American Youth (LSAY). There was no evident consistency in the rates of growth between mathematics and science achievement among students, and this inconsistency was not much influenced by student characteristics and school characteristics. However, there was evident consistency in the average rates of growth between mathematics and science achievement among schools, and this consistency was influenced by student characteristics and school characteristics. Major school-level variables associated with parental involvement did not show any significant impacts on consistency among either students or schools. Results call for educational policies that promote collaboration between mathematics and science departments or teachers.

Estimating Setup of Driven Piles into Louisiana Clayey Soils

DOT National Transportation Integrated Search

2009-11-15

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

Estimating setup of driven piles into Louisiana clayey soils.

DOT National Transportation Integrated Search

2010-11-15

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

Combining Empirical and Stochastic Models for Extreme Floods Estimation

NASA Astrophysics Data System (ADS)

Zemzami, M.; Benaabidate, L.

2013-12-01

Hydrological models can be defined as physical, mathematical or empirical. The latter class uses mathematical equations independent of the physical processes involved in the hydrological system. The linear regression and Gradex (Gradient of Extreme values) are classic examples of empirical models. However, conventional empirical models are still used as a tool for hydrological analysis by probabilistic approaches. In many regions in the world, watersheds are not gauged. This is true even in developed countries where the gauging network has continued to decline as a result of the lack of human and financial resources. Indeed, the obvious lack of data in these watersheds makes it impossible to apply some basic empirical models for daily forecast. So we had to find a combination of rainfall-runoff models in which it would be possible to create our own data and use them to estimate the flow. The estimated design floods would be a good choice to illustrate the difficulties facing the hydrologist for the construction of a standard empirical model in basins where hydrological information is rare. The construction of the climate-hydrological model, which is based on frequency analysis, was established to estimate the design flood in the Anseghmir catchments, Morocco. The choice of using this complex model returns to its ability to be applied in watersheds where hydrological information is not sufficient. It was found that this method is a powerful tool for estimating the design flood of the watershed and also other hydrological elements (runoff, volumes of water...).The hydrographic characteristics and climatic parameters were used to estimate the runoff, water volumes and design flood for different return periods.

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.

Bayesian Estimation in the One-Parameter Latent Trait Model.

DTIC Science & Technology

1980-03-01

Journal of Mathematical and Statistical Psychology , 1973, 26, 31-44. (a) Andersen, E. B. A goodness of fit test for the Rasch model. Psychometrika, 1973, 28...technique for estimating latent trait mental test parameters. Educational and Psychological Measurement, 1976, 36, 705-715. Lindley, D. V. The...Lord, F. M. An analysis of verbal Scholastic Aptitude Test using Birnbaum’s three-parameter logistic model. Educational and Psychological

Identifiability of PBPK Models with Applications to ...

EPA Pesticide Factsheets

Any statistical model should be identifiable in order for estimates and tests using it to be meaningful. We consider statistical analysis of physiologically-based pharmacokinetic (PBPK) models in which parameters cannot be estimated precisely from available data, and discuss different types of identifiability that occur in PBPK models and give reasons why they occur. We particularly focus on how the mathematical structure of a PBPK model and lack of appropriate data can lead to statistical models in which it is impossible to estimate at least some parameters precisely. Methods are reviewed which can determine whether a purely linear PBPK model is globally identifiable. We propose a theorem which determines when identifiability at a set of finite and specific values of the mathematical PBPK model (global discrete identifiability) implies identifiability of the statistical model. However, we are unable to establish conditions that imply global discrete identifiability, and conclude that the only safe approach to analysis of PBPK models involves Bayesian analysis with truncated priors. Finally, computational issues regarding posterior simulations of PBPK models are discussed. The methodology is very general and can be applied to numerous PBPK models which can be expressed as linear time-invariant systems. A real data set of a PBPK model for exposure to dimethyl arsinic acid (DMA(V)) is presented to illustrate the proposed methodology. We consider statistical analy

The Value of 18F-FDG PET/CT Mathematical Prediction Model in Diagnosis of Solitary Pulmonary Nodules

PubMed Central

Chen, Yao; Tang, Kun; Lin, Jie

2018-01-01

Purpose To establish an 18F-fluorodeoxyglucose (18F-FDG) positron emission tomography/computed tomography (PET/CT) mathematical prediction model to improve the diagnosis of solitary pulmonary nodules (SPNs). Materials and Methods We retrospectively reviewed 177 consecutive patients who underwent 18F-FDG PET/CT for evaluation of SPNs. The mathematical model was established by logistic regression analysis. The diagnostic capabilities of the model were calculated, and the areas under the receiver operating characteristic curve (AUC) were compared with Mayo and VA model. Results The mathematical model was y = exp⁡(x)/[1 + exp⁡(x)], x = −7.363 + 0.079 × age + 1.900 × lobulation + 1.024 × vascular convergence + 1.530 × pleural retraction + 0.359 × the maximum of standardized uptake value (SUVmax). When the cut-off value was set at 0.56, the sensitivity, specificity, and accuracy of our model were 86.55%, 74.14%, and 81.4%, respectively. The area under the receiver operating characteristic curve (AUC) of our model was 0.903 (95% confidence interval (CI): 0.860 to 0.946). The AUC of our model was greater than that of the Mayo model, the VA model, and PET (P < 0.05) and has no difference with that of PET/CT (P > 0.05). Conclusion The mathematical predictive model has high accuracy in estimating the malignant probability of patients with SPNs. PMID:29789808

Contrasting two models of academic self-efficacy--domain-specific versus cross-domain--in children receiving and not receiving special instruction in mathematics.

PubMed

Jungert, Tomas; Hesser, Hugo; Träff, Ulf

2014-10-01

In social cognitive theory, self-efficacy is domain-specific. An alternative model, the cross-domain influence model, would predict that self-efficacy beliefs in one domain might influence performance in other domains. Research has also found that children who receive special instruction are not good at estimating their performance. The aim was to test two models of how self-efficacy beliefs influence achievement, and to contrast children receiving special instruction in mathematics with normally-achieving children. The participants were 73 fifth-grade children who receive special instruction and 70 children who do not receive any special instruction. In year four and five, the children's skills in mathematics and reading were assessed by national curriculum tests, and in their fifth year, self-efficacy in mathematics and reading were measured. Structural equation modeling showed that in domains where children do not receive special instruction in mathematics, self-efficacy is a mediating variable between earlier and later achievement in the same domain. Achievement in mathematics was not mediated by self-efficacy in mathematics for children who receive special instruction. For normal achieving children, earlier achievement in the language domain had an influence on later self-efficacy in the mathematics domain, and self-efficacy beliefs in different domains were correlated. Self-efficacy is mostly domain specific, but may play a different role in academic performance depending on whether children receive special instruction. The results of the present study provided some support of the Cross-Domain Influence Model for normal achieving children. © 2014 Scandinavian Psychological Associations and John Wiley & Sons Ltd.

Stochastic growth logistic model with aftereffect for batch fermentation process

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

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part 1. Mathematical models

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2008-12-01

Fuel economy at boost trajectory of the aerospace plane was estimated during energy supply to the free stream. Initial and final flight velocities were specified. The model of a gliding flight above cold air in an infinite isobaric thermal wake was used. The fuel consumption rates were compared at optimal trajectory. The calculations were carried out using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was built in the first part of the paper to estimate the ramjet thrust and specific impulse. A quadratic dependence on aerodynamic lift was used to estimate the aerodynamic drag of aircraft. The energy for flow heating was obtained at the expense of an equivalent reduction of the exergy of combustion products. The dependencies were obtained for increasing the range coefficient of cruise flight for different Mach numbers. The second part of the paper presents a mathematical model for the boost interval of the aircraft flight trajectory and the computational results for the reduction of fuel consumption at the boost trajectory for a given value of the energy supplied in front of the aircraft.

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part II. Mathematical model of the trajectory boost part and computational results

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2009-03-01

The fuel economy was estimated at boost trajectory of aerospace plane during energy supply to the free stream. Initial and final velocities of the flight were given. A model of planning flight above cold air in infinite isobaric thermal wake was used. The comparison of fuel consumption was done at optimal trajectories. The calculations were done using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was constructed in the first part of the paper for estimating the ramjet thrust and specific impulse. To estimate the aerodynamic drag of aircraft a quadratic dependence on aerodynamic lift is used. The energy for flow heating is obtained at the sacrifice of an equivalent decrease of exergy of combustion products. The dependencies are obtained for increasing the range coefficient of cruise flight at different Mach numbers. In the second part of the paper, a mathematical model is presented for the boost part of the flight trajectory of the flying vehicle and computational results for reducing the fuel expenses at the boost trajectory at a given value of the energy supplied in front of the aircraft.

Mathematical model of cycad cones' thermogenic temperature responses: inverse calorimetry to estimate metabolic heating rates.

PubMed

Roemer, R B; Booth, D; Bhavsar, A A; Walter, G H; Terry, L I

2012-12-21

A mathematical model based on conservation of energy has been developed and used to simulate the temperature responses of cones of the Australian cycads Macrozamia lucida and Macrozamia. macleayi during their daily thermogenic cycle. These cones generate diel midday thermogenic temperature increases as large as 12 °C above ambient during their approximately two week pollination period. The cone temperature response model is shown to accurately predict the cones' temperatures over multiple days as based on simulations of experimental results from 28 thermogenic events from 3 different cones, each simulated for either 9 or 10 sequential days. The verified model is then used as the foundation of a new, parameter estimation based technique (termed inverse calorimetry) that estimates the cones' daily metabolic heating rates from temperature measurements alone. The inverse calorimetry technique's predictions of the major features of the cones' thermogenic metabolism compare favorably with the estimates from conventional respirometry (indirect calorimetry). Because the new technique uses only temperature measurements, and does not require measurements of oxygen consumption, it provides a simple, inexpensive and portable complement to conventional respirometry for estimating metabolic heating rates. It thus provides an additional tool to facilitate field and laboratory investigations of the bio-physics of thermogenic plants. Copyright © 2012 Elsevier Ltd. All rights reserved.

Obtaining mathematical models for assessing efficiency of dust collectors using integrated system of analysis and data management STATISTICA Design of Experiments

NASA Astrophysics Data System (ADS)

Azarov, A. V.; Zhukova, N. S.; Kozlovtseva, E. Yu; Dobrinsky, D. R.

2018-05-01

The article considers obtaining mathematical models to assess the efficiency of the dust collectors using an integrated system of analysis and data management STATISTICA Design of Experiments. The procedure for obtaining mathematical models and data processing is considered by the example of laboratory studies on a mounted installation containing a dust collector in counter-swirling flows (CSF) using gypsum dust of various fractions. Planning of experimental studies has been carried out in order to reduce the number of experiments and reduce the cost of experimental research. A second-order non-position plan (Box-Bencken plan) was used, which reduced the number of trials from 81 to 27. The order of statistical data research of Box-Benken plan using standard tools of integrated system for analysis and data management STATISTICA Design of Experiments is considered. Results of statistical data processing with significance estimation of coefficients and adequacy of mathematical models are presented.

Voluntary Medical Male Circumcision for HIV Prevention: New Mathematical Models for Strategic Demand Creation Prioritizing Subpopulations by Age and Geography.

PubMed

Hankins, Catherine; Warren, Mitchell; Njeuhmeli, Emmanuel

2016-01-01

Over 11 million voluntary medical male circumcisions (VMMC) have been performed of the projected 20.3 million needed to reach 80% adult male circumcision prevalence in priority sub-Saharan African countries. Striking numbers of adolescent males, outside the 15-49-year-old age target, have been accessing VMMC services. What are the implications of overall progress in scale-up to date? Can mathematical modeling provide further insights on how to efficiently reach the male circumcision coverage levels needed to create and sustain further reductions in HIV incidence to make AIDS no longer a public health threat by 2030? Considering ease of implementation and cultural acceptability, decision makers may also value the estimates that mathematical models can generate of immediacy of impact, cost-effectiveness, and magnitude of impact resulting from different policy choices. This supplement presents the results of mathematical modeling using the Decision Makers' Program Planning Tool Version 2.0 (DMPPT 2.0), the Actuarial Society of South Africa (ASSA2008) model, and the age structured mathematical (ASM) model. These models are helping countries examine the potential effects on program impact and cost-effectiveness of prioritizing specific subpopulations for VMMC services, for example, by client age, HIV-positive status, risk group, and geographical location. The modeling also examines long-term sustainability strategies, such as adolescent and/or early infant male circumcision, to preserve VMMC coverage gains achieved during rapid scale-up. The 2016-2021 UNAIDS strategy target for VMMC is an additional 27 million VMMC in high HIV-prevalence settings by 2020, as part of access to integrated sexual and reproductive health services for men. To achieve further scale-up, a combination of evidence, analysis, and impact estimates can usefully guide strategic planning and funding of VMMC services and related demand-creation strategies in priority countries. Mid-course corrections now can improve cost-effectiveness and scale to achieve the impact needed to help turn the HIV pandemic on its head within 15 years.

An Empirical Investigation of Variance Design Parameters for Planning Cluster-Randomized Trials of Science Achievement.

PubMed

Westine, Carl D; Spybrook, Jessaca; Taylor, Joseph A

2013-12-01

Prior research has focused primarily on empirically estimating design parameters for cluster-randomized trials (CRTs) of mathematics and reading achievement. Little is known about how design parameters compare across other educational outcomes. This article presents empirical estimates of design parameters that can be used to appropriately power CRTs in science education and compares them to estimates using mathematics and reading. Estimates of intraclass correlations (ICCs) are computed for unconditional two-level (students in schools) and three-level (students in schools in districts) hierarchical linear models of science achievement. Relevant student- and school-level pretest and demographic covariates are then considered, and estimates of variance explained are computed. Subjects: Five consecutive years of Texas student-level data for Grades 5, 8, 10, and 11. Science, mathematics, and reading achievement raw scores as measured by the Texas Assessment of Knowledge and Skills. Results: Findings show that ICCs in science range from .172 to .196 across grades and are generally higher than comparable statistics in mathematics, .163-.172, and reading, .099-.156. When available, a 1-year lagged student-level science pretest explains the most variability in the outcome. The 1-year lagged school-level science pretest is the best alternative in the absence of a 1-year lagged student-level science pretest. Science educational researchers should utilize design parameters derived from science achievement outcomes. © The Author(s) 2014.

Informing Estimates of Program Effects for Studies of Mathematics Professional Development Using Teacher Content Knowledge Outcomes.

PubMed

Phelps, Geoffrey; Kelcey, Benjamin; Jones, Nathan; Liu, Shuangshuang

2016-10-03

Mathematics professional development is widely offered, typically with the goal of improving teachers' content knowledge, the quality of teaching, and ultimately students' achievement. Recently, new assessments focused on mathematical knowledge for teaching (MKT) have been developed to assist in the evaluation and improvement of mathematics professional development. This study presents empirical estimates of average program change in MKT and its variation with the goal of supporting the design of experimental trials that are adequately powered to detect a specified program effect. The study drew on a large database representing five different assessments of MKT and collectively 326 professional development programs and 9,365 teachers. Results from cross-classified hierarchical growth models found that standardized average change estimates across the five assessments ranged from a low of 0.16 standard deviations (SDs) to a high of 0.26 SDs. Power analyses using the estimated pre- and posttest change estimates indicated that hundreds of teachers are needed to detect changes in knowledge at the lower end of the distribution. Even studies powered to detect effects at the higher end of the distribution will require substantial resources to conduct rigorous experimental trials. Empirical benchmarks that describe average program change and its variation provide a useful preliminary resource for interpreting the relative magnitude of effect sizes associated with professional development programs and for designing adequately powered trials. © The Author(s) 2016.

Risk Assessment for Toxic Air Pollutants: A Citizen's Guide

MedlinePlus

... from the source(s). Engineers use either monitors or computer models to estimate the amount of pollutant released ... measure how much of the pollutant is present. Computer models use mathematical equations that represent the processes ...

VERIFICATION AND VALIDATION OF THE SPARC MODEL

EPA Science Inventory

Mathematical models for predicting the transport and fate of pollutants in the environment require reactivity parameter values--that is, the physical and chemical constants that govern reactivity. Although empirical structure-activity relationships that allow estimation of some ...

A user-friendly mathematical modelling web interface to assist local decision making in the fight against drug-resistant tuberculosis.

PubMed

Ragonnet, Romain; Trauer, James M; Denholm, Justin T; Marais, Ben J; McBryde, Emma S

2017-05-30

Multidrug-resistant and rifampicin-resistant tuberculosis (MDR/RR-TB) represent an important challenge for global tuberculosis (TB) control. The high rates of MDR/RR-TB observed among re-treatment cases can arise from diverse pathways: de novo amplification during initial treatment, inappropriate treatment of undiagnosed MDR/RR-TB, relapse despite appropriate treatment, or reinfection with MDR/RR-TB. Mathematical modelling allows quantification of the contribution made by these pathways in different settings. This information provides valuable insights for TB policy-makers, allowing better contextualised solutions. However, mathematical modelling outputs need to consider local data and be easily accessible to decision makers in order to improve their usefulness. We present a user-friendly web-based modelling interface, which can be used by people without technical knowledge. Users can input their own parameter values and produce estimates for their specific setting. This innovative tool provides easy access to mathematical modelling outputs that are highly relevant to national TB control programs. In future, the same approach could be applied to a variety of modelling applications, enhancing local decision making.

Monitoring and modeling for investigating driver/pressure-state/impact relationships in coastal ecosystems: Examples from the Lagoon of Venice

NASA Astrophysics Data System (ADS)

Pastres, Roberto; Solidoro, Cosimo

2012-01-01

In this paper, we show how the integration of monitoring data and mathematical model can generate valuable information by using a few examples taken from a well studied but complex ecosystem, namely the Lagoon of Venice. We will focus on three key issues, which are of concern also for many other coastal ecosystems, namely: (1) Nitrogen and Phosphorus annual budgets; (2) estimation of Net Ecosystem Metabolism and early warnings for anoxic events; (3) assessment of ecosystem status. The results highlight the importance of framing monitoring activities within the "DPSIR" conceptual model, thus going far beyond the monitoring of major biogeochemical variables and including: (1) the estimation of the fluxes of the main constituents at the boundaries; (2) the use of appropriate mathematical models. These tools can provide quantitative links among Pressures and State/Impacts, thus enabling decision makers and stakeholders to evaluate the effects of alternative management scenarios.

Data-driven outbreak forecasting with a simple nonlinear growth model.

PubMed

Lega, Joceline; Brown, Heidi E

2016-12-01

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Mathematical modeling of the gas extraction from the gas hydrate deposit taking into account the replacement technology

NASA Astrophysics Data System (ADS)

Musakaev, N. G.; Khasanov, M. K.; Borodin, S. L.

2018-03-01

In the work on the basis of methods and equations of mechanics of multiphase systems the mathematical model of the process of carbon dioxide burial in the reservoir saturated with methane hydrate is proposed. Estimates are obtained that allow for this problem to neglect diffusion mixing of carbon dioxide and methane. The features of the process of methane displacement from CH4 hydrate by filling them with carbon dioxide are studied.

F-111C Flight Data Reduction and Analysis Procedures

DTIC Science & Technology

1990-12-01

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

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

PubMed

Molina, Manuel; Mota, Manuel; Ramos, Alfonso

2015-01-01

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

Mathematical Simulation of Perturbations of Attack Angle of Asymmetric Nanosatellite Passing through Resonance

NASA Astrophysics Data System (ADS)

Lyubimov, V. V.; Kurkina, E. V.

2018-05-01

The authors consider the problem of a dynamic system passing through a low-order resonance, describing an uncontrolled atmospheric descent of an asymmetric nanosatellite in the Earth's atmosphere. The authors perform mathematical and numerical modeling of the motion of the nanosatellite with a small mass-aerodynamic asymmetry relative to the center of mass. The aim of the study is to obtain new reliable approximate analytical estimates of perturbations of the angle of attack of a nanosatellite passing through resonance at angles of attack of not more than 0.5π. By using the stationary phase method, the authors were able to investigate a discontinuous perturbation in the angle of attack of a nanosatellite passing through a resonance with two different nanosatellite designs. Comparison of the results of the numerical modeling and new approximate analytical estimates of the perturbation of the angle of attack confirms the reliability of the said estimates.

International Energy Module - NEMS Documentation

EIA Publications

2014-01-01

Summarizes the overall structure of the International Energy Model and its interface with other NEMS modules, mathematical specifications of behavioral relationships, and data sources and estimation methods.

Validation of a mathematical model of the bovine estrous cycle for cows with different estrous cycle characteristics.

PubMed

Boer, H M T; Butler, S T; Stötzel, C; Te Pas, M F W; Veerkamp, R F; Woelders, H

2017-11-01

A recently developed mechanistic mathematical model of the bovine estrous cycle was parameterized to fit empirical data sets collected during one estrous cycle of 31 individual cows, with the main objective to further validate the model. The a priori criteria for validation were (1) the resulting model can simulate the measured data correctly (i.e. goodness of fit), and (2) this is achieved without needing extreme, probably non-physiological parameter values. We used a least squares optimization procedure to identify parameter configurations for the mathematical model to fit the empirical in vivo measurements of follicle and corpus luteum sizes, and the plasma concentrations of progesterone, estradiol, FSH and LH for each cow. The model was capable of accommodating normal variation in estrous cycle characteristics of individual cows. With the parameter sets estimated for the individual cows, the model behavior changed for 21 cows, with improved fit of the simulated output curves for 18 of these 21 cows. Moreover, the number of follicular waves was predicted correctly for 18 of the 25 two-wave and three-wave cows, without extreme parameter value changes. Estimation of specific parameters confirmed results of previous model simulations indicating that parameters involved in luteolytic signaling are very important for regulation of general estrous cycle characteristics, and are likely responsible for differences in estrous cycle characteristics between cows.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Selected Tether Applications Cost Model

NASA Technical Reports Server (NTRS)

Keeley, Michael G.

1988-01-01

Diverse cost-estimating techniques and data combined into single program. Selected Tether Applications Cost Model (STACOM 1.0) is interactive accounting software tool providing means for combining several independent cost-estimating programs into fully-integrated mathematical model capable of assessing costs, analyzing benefits, providing file-handling utilities, and putting out information in text and graphical forms to screen, printer, or plotter. Program based on Lotus 1-2-3, version 2.0. Developed to provide clear, concise traceability and visibility into methodology and rationale for estimating costs and benefits of operations of Space Station tether deployer system.

Mathematical modelling of methanogenic reactor start-up: Importance of volatile fatty acids degrading population.

PubMed

Jabłoński, Sławomir J; Łukaszewicz, Marcin

2014-12-01

Development of balanced community of microorganisms is one of the obligatory for stable anaerobic digestion. Application of mathematical models might be helpful in development of reliable procedures during the process start-up period. Yet, the accuracy of forecast depends on the quality of input and parameters. In this study, the specific anaerobic activity (SAA) tests were applied in order to estimate microbial community structure. Obtained data was applied as input conditions for mathematical model of anaerobic digestion. The initial values of variables describing the amount of acetate and propionate utilizing microorganisms could be calculated on the basis of SAA results. The modelling based on those optimized variables could successfully reproduce the behavior of a real system during the continuous fermentation. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Design of a Field Test for Probability of Hit by Antiaircraft Guns

DTIC Science & Technology

1973-02-01

not available. • The cost of conducting the numerous field test trials that would be needed to establish the loss rates of aircraft to antiaircraft...mathematical models provide a readily available and relatively inexpensive way to obtain estimates of aircraft losses to antiaircraft guns. Because these...aircraft losses to antiaircraft guns, the use of the models can contribute greatly to better decisions. But if the models produce invalid estimates

Mathematical modeling of diphtheria transmission in Thailand.

PubMed

Sornbundit, Kan; Triampo, Wannapong; Modchang, Charin

2017-08-01

In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

USDA-ARS?s Scientific Manuscript database

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

Estimating Sobol Sensitivity Indices Using Correlations

EPA Science Inventory

Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol's method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on...

Mathematical model of glucose-insulin homeostasis in healthy rats.

PubMed

Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo

2013-10-01

According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.

The analysis of isotherms of radionuclides sorption by inorganic sorbents

NASA Astrophysics Data System (ADS)

Bykova, E. P.; Nedobukh, T. A.

2017-09-01

The isotherm of cesium sorption by an inorganic sorbent based on granulated glauconite obtained in a wide cesium concentrations range was mathematically treated using Langmuir, Freundlich and Redlich-Peterson sorption models. The algorithms of mathematical treatment of experimental data using these models were described; parameters of all isotherms were determined. It was shown that estimating the correctness of various sorption models relies not only on the correlation coefficient values but also on the closeness of the calculated and experimental data. Various types of sorption sites were found as a result of mathematical treatment of the isotherm of cesium sorption. The algorithm was described and calculation of parameters of the isotherm was performed under the assumption that simultaneous sorption on all three types of sorption sites occurs in accordance with Langmuir isotherm.

Development of a predictive model to estimate the effect of soil solarization on survival of soilborne inoculum of Phytophthora ramorum and Phytophthora pini

Treesearch

Fumiaki Funahashi; Jennifer L. Parke

2017-01-01

Soil solarization has been shown to be an effective tool to manage Phytophthora spp. within surface soils, but estimating the minimum time required to complete local eradication under variable weather conditions remains unknown. A mathematical model could help predict the effectiveness of solarization at different sites and soil depths....

A Practitioner's Instrument for Measuring Secondary Mathematics Teachers' Beliefs Surrounding Learner-Centered Classroom Practice.

PubMed

Lischka, Alyson E; Garner, Mary

In this paper we present the development and validation of a Mathematics Teaching Pedagogical and Discourse Beliefs Instrument (MTPDBI), a 20 item partial-credit survey designed and analyzed using Rasch measurement theory. Items on the MTPDBI address beliefs about the nature of mathematics, teaching and learning mathematics, and classroom discourse practices. A Rasch partial credit model (Masters, 1982) was estimated from the pilot study data. Results show that item separation reliability is .96 and person separation reliability is .71. Other analyses indicate the instrument is a viable measure of secondary teachers' beliefs about reform-oriented mathematics teaching and learning. This instrument is proposed as a useful measure of teacher beliefs for those working with pre-service and in-service teacher development.

What Is the Long-Run Impact of Learning Mathematics during Preschool?

ERIC Educational Resources Information Center

Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie

2018-01-01

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change…

The design, analysis and experimental evaluation of an elastic model wing

NASA Technical Reports Server (NTRS)

Cavin, R. K., III; Thisayakorn, C.

1974-01-01

An elastic orbiter model was developed to evaluate the effectiveness of aeroelasticity computer programs. The elasticity properties were introduced by constructing beam-like straight wings for the wind tunnel model. A standard influence coefficient mathematical model was used to estimate aeroelastic effects analytically. In general good agreement was obtained between the empirical and analytical estimates of the deformed shape. However, in the static aeroelasticity case, it was found that the physical wing exhibited less bending and more twist than was predicted by theory.

Estimating wildfire behavior and effects

Treesearch

Frank A. Albini

1976-01-01

This paper presents a brief survey of the research literature on wildfire behavior and effects and assembles formulae and graphical computation aids based on selected theoretical and empirical models. The uses of mathematical fire behavior models are discussed, and the general capabilities and limitations of currently available models are outlined.

The estimation of the thyroid volume before surgery--an important prerequisite for minimally invasive thyroidectomy.

PubMed

Ruggieri, M; Fumarola, A; Straniero, A; Maiuolo, A; Coletta, I; Veltri, A; Di Fiore, A; Trimboli, P; Gargiulo, P; Genderini, M; D'Armiento, M

2008-09-01

Actually, thyroid volume >25 ml, obtained by preoperative ultrasound evaluation, is a very important exclusion criteria for minimally invasive thyroidectomy. So far, among different imaging techniques, two-dimensional ultrasonography has become the more accepted method for the assessment of thyroid volume (US-TV). The aims of this study were: (1) to estimate the preoperative thyroid volume in patients undergoing minimally invasive total thyroidectomy using a mathematical formula and (2) to verify its validity by comparing it with the postsurgical TV (PS-TV). In 53 patients who underwent minimally invasive total thyroidectomy (from January 2003 to December 2007), US-TV, obtained by ellipsoid volume formula, was compared to PS-TV determined by the Archimedes' principle. A mathematical formula able to predict the TV from the US-TV was applied in 34 cases in the last 2 years. Mean US-TV (14.4 +/- 5.9 ml) was significantly lower than mean PS-TV (21.7 +/- 10.3 ml). This underestimation was related to gland multinodularity and/or nodular involvement of the isthmus. A mathematical formula to reduce US-TV underestimation and predict the real TV was developed using a linear model. Mean predicted TV (16.8 +/- 3.7 ml) perfectly matched mean PS-TV, underestimating PS-TV in 19% of cases. We verified the accuracy of this mathematical model in patients' eligibility for minimally invasive total thyroidectomy, and we demonstrated that a predicted TV <25 ml was confirmed post-surgery in 94% of cases. We demonstrated that using a linear model, it is possible to predict from US the PS-TV with high accuracy. In fact, the mean predicted TV perfectly matched the mean PS-TV in all cases. In particular, the percentage of cases in which the predicted TV perfectly matched the PS-TV increases from 23%, estimated by US, to 43%. Moreover, the percentage of TV underestimation was reduced from 77% to 19%, as well as the range of the disagreement from up to 200% to 80%. This study shows that two-dimensional US can provide the accurate estimation of thyroid volume but that it can be improved by a mathematical model. This may contribute to a more appropriate surgical management of thyroid diseases.

Quantification of tumor perfusion using dynamic contrast-enhanced ultrasound: impact of mathematical modeling

NASA Astrophysics Data System (ADS)

Doury, Maxime; Dizeux, Alexandre; de Cesare, Alain; Lucidarme, Olivier; Pellot-Barakat, Claire; Bridal, S. Lori; Frouin, Frédérique

2017-02-01

Dynamic contrast-enhanced ultrasound has been proposed to monitor tumor therapy, as a complement to volume measurements. To assess the variability of perfusion parameters in ideal conditions, four consecutive test-retest studies were acquired in a mouse tumor model, using controlled injections. The impact of mathematical modeling on parameter variability was then investigated. Coefficients of variation (CV) of tissue blood volume (BV) and tissue blood flow (BF) based-parameters were estimated inside 32 sub-regions of the tumors, comparing the log-normal (LN) model with a one-compartment model fed by an arterial input function (AIF) and improved by the introduction of a time delay parameter. Relative perfusion parameters were also estimated by normalization of the LN parameters and normalization of the one-compartment parameters estimated with the AIF, using a reference tissue (RT) region. A direct estimation (rRTd) of relative parameters, based on the one-compartment model without using the AIF, was also obtained by using the kinetics inside the RT region. Results of test-retest studies show that absolute regional parameters have high CV, whatever the approach, with median values of about 30% for BV, and 40% for BF. The positive impact of normalization was established, showing a coherent estimation of relative parameters, with reduced CV (about 20% for BV and 30% for BF using the rRTd approach). These values were significantly lower (p  <  0.05) than the CV of absolute parameters. The rRTd approach provided the smallest CV and should be preferred for estimating relative perfusion parameters.

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

ERIC Educational Resources Information Center

Casstevens, Thomas W.; And Others

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

Development of advanced techniques for rotorcraft state estimation and parameter identification

NASA Technical Reports Server (NTRS)

Hall, W. E., Jr.; Bohn, J. G.; Vincent, J. H.

1980-01-01

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.

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

NASA Technical Reports Server (NTRS)

Duval, R. W.; Bahrami, M.

1985-01-01

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

Spacecraft Dynamics Should be Considered in Kalman Filter Attitude Estimation

NASA Technical Reports Server (NTRS)

Yang, Yaguang; Zhou, Zhiqiang

2016-01-01

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

Effectiveness and cost-effectiveness of an awareness campaign for colorectal cancer: a mathematical modeling study.

PubMed

Whyte, Sophie; Harnan, Susan

2014-06-01

A campaign to increase the awareness of the signs and symptoms of colorectal cancer (CRC) and encourage self-presentation to a GP was piloted in two regions of England in 2011. Short-term data from the pilot evaluation on campaign cost and changes in GP attendances/referrals, CRC incidence, and CRC screening uptake were available. The objective was to estimate the effectiveness and cost-effectiveness of a CRC awareness campaign by using a mathematical model which extrapolates short-term outcomes to predict long-term impacts on cancer mortality, quality-adjusted life-years (QALYs), and costs. A mathematical model representing England (aged 30+) for a lifetime horizon was developed. Long-term changes to cancer incidence, cancer stage distribution, cancer mortality, and QALYs were estimated. Costs were estimated incorporating costs associated with delivering the campaign, additional GP attendances, and changes in CRC treatment. Data from the pilot campaign suggested that the awareness campaign caused a 1-month 10 % increase in presentation rates. Based on this, the model predicted the campaign to cost £5.5 million, prevent 66 CRC deaths and gain 404 QALYs. The incremental cost-effectiveness ratio compared to "no campaign" was £13,496 per QALY. Results were sensitive to the magnitude and duration of the increase in presentation rates and to disease stage. The effectiveness and cost-effectiveness of a cancer awareness campaign can be estimated based on short-term data. Such predictions will aid policy makers in prioritizing between cancer control strategies. Future cost-effectiveness studies would benefit from campaign evaluations reporting as follows: data completeness, duration of impact, impact on emergency presentations, and comparison with non-intervention regions.

Methods for cost estimation in software project management

NASA Astrophysics Data System (ADS)

Briciu, C. V.; Filip, I.; Indries, I. I.

2016-02-01

The speed in which the processes used in software development field have changed makes it very difficult the task of forecasting the overall costs for a software project. By many researchers, this task has been considered unachievable, but there is a group of scientist for which this task can be solved using the already known mathematical methods (e.g. multiple linear regressions) and the new techniques as genetic programming and neural networks. The paper presents a solution for building a model for the cost estimation models in the software project management using genetic algorithms starting from the PROMISE datasets related COCOMO 81 model. In the first part of the paper, a summary of the major achievements in the research area of finding a model for estimating the overall project costs is presented together with the description of the existing software development process models. In the last part, a basic proposal of a mathematical model of a genetic programming is proposed including here the description of the chosen fitness function and chromosome representation. The perspective of model described it linked with the current reality of the software development considering as basis the software product life cycle and the current challenges and innovations in the software development area. Based on the author's experiences and the analysis of the existing models and product lifecycle it was concluded that estimation models should be adapted with the new technologies and emerging systems and they depend largely by the chosen software development method.

Aids to determining fuel models for estimating fire behavior

Treesearch

Hal E. Anderson

1982-01-01

Presents photographs of wildland vegetation appropriate for the 13 fuel models used in mathematical models of fire behavior. Fuel model descriptions include fire behavior associated with each fuel and its physical characteristics. A similarity chart cross-references the 13 fire behavior fuel models to the 20 fuel models used in the National Fire Danger Rating System....

Tidal frequency estimation for closed basins

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.

1978-01-01

A method was developed for determining the fundamental tidal frequencies for closed basins of water, by means of an eigenvalue analysis. The mathematical model employed, was the Laplace tidal equations.

A mathematical model describing the glycemic response of diabetic patients to meal and i.v. infusion of insulin.

PubMed

Fabietti, P G; Calabrese, G; Iorio, M; Bistoni, S; Brunetti, P; Sarti, E; Benedetti, M M

2001-10-01

Nine type 1 diabetic patients were studied for 24 hours. During this period they were given three calibrated meals. The glycemia was feedback-controlled by means of an artificial pancreas. The blood concentration of glucose and the infusion speed of the insulin were measured every minute. The experimental data referring to each of the three meals were used to estimate the parameters of a mathematical model suitable for describing the glycemic response of diabetic patients at meals and at the i.v. infusion of exogenous insulin. From the estimate a marked dispersion of the parameters was found, both interindividual and intraindividual. Nevertheless the models thus obtained seem to be usable for the synthesis of a feedback controller, especially in view of creating a portable artificial pancreas that now seems possible owing to the realization (so far experimental) of sufficiently reliable glucose concentration sensors.

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method.

PubMed

Polidori, David; Rowley, Clarence

2014-07-22

The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method.

A Riparian Vegetation Ecophysiological Response Model

Treesearch

Jeffrey P. Leighton; Roland J. Risser

1989-01-01

A mathematical model is described that relates mature riparian vegetation ecophysiological response to changes in stream level. This model was developed to estimate the physiological response of riparian vegetation to reductions in streamflow. Field data from two sites on the North Fork of the Kings River were used in the model development. The physiological response...

A Reduced Form Model for Ozone Based on Two Decades of CMAQ Simulations for the Continental United States

EPA Science Inventory

A Reduced Form Model (RFM) is a mathematical relationship between the inputs and outputs of an air quality model, permitting estimation of additional modeling without costly new regional-scale simulations. A 21-year Community Multiscale Air Quality (CMAQ) simulation for the con...

Application of positive-real functions in hyperstable discrete model-reference adaptive system design.

NASA Technical Reports Server (NTRS)

Karmarkar, J. S.

1972-01-01

Proposal of an algorithmic procedure, based on mathematical programming methods, to design compensators for hyperstable discrete model-reference adaptive systems (MRAS). The objective of the compensator is to render the MRAS insensitive to initial parameter estimates within a maximized hypercube in the model parameter space.

ESTIMATION OF INFILTRATION RATE IN THE VADOSE ZONE: COMPILATION OF SIMPLE MATHEMATICAL MODELS - VOLUME I

EPA Science Inventory

The unsaturated or vadose zone provides a complex system for the simulation of water movement and contaminant transport and fate. Numerous models are available for performing simulations related to the movement of water. There exists extensive documentation of these models. Ho...

An exploration of the utility of mathematical modeling predicting fatigue from sleep/wake history and circadian phase applied in accident analysis and prevention: the crash of Comair Flight 5191.

PubMed

Pruchnicki, Shawn A; Wu, Lora J; Belenky, Gregory

2011-05-01

On 27 August 2006 at 0606 eastern daylight time (EDT) at Bluegrass Airport in Lexington, KY (LEX), the flight crew of Comair Flight 5191 inadvertently attempted to take off from a general aviation runway too short for their aircraft. The aircraft crashed killing 49 of the 50 people on board. To better understand this accident and to aid in preventing similar accidents, we applied mathematical modeling predicting fatigue-related degradation in performance for the Air Traffic Controller on-duty at the time of the crash. To provide the necessary input to the model, we attempted to estimate circadian phase and sleep/wake histories for the Captain, First Officer, and Air Traffic Controller. We were able to estimate with confidence the circadian phase for each. We were able to estimate with confidence the sleep/wake history for the Air Traffic Controller, but unable to do this for the Captain and First Officer. Using the sleep/wake history estimates for the Air Traffic Controller as input, the mathematical modeling predicted moderate fatigue-related performance degradation at the time of the crash. This prediction was supported by the presence of what appeared to be fatigue-related behaviors in the Air Traffic Controller during the 30 min prior to and in the minutes after the crash. Our modeling results do not definitively establish fatigue in the Air Traffic Controller as a cause of the accident, rather they suggest that had he been less fatigued he might have detected Comair Flight 5191's lining up on the wrong runway. We were not able to perform a similar analysis for the Captain and First Officer because we were not able to estimate with confidence their sleep/wake histories. Our estimates of sleep/wake history and circadian rhythm phase for the Air Traffic Controller might generalize to other air traffic controllers and to flight crew operating in the early morning hours at LEX. Relative to other times of day, the modeling results suggest an elevated risk of fatigue-related error, incident, or accident in the early morning due to truncated sleep from the early start and adverse circadian phase from the time of day. This in turn suggests that fatigue mitigation targeted to early morning starts might reduce fatigue risk. In summary, this study suggests that mathematical models predicting performance from sleep/wake history and circadian phase are (1) useful in retrospective accident analysis provided reliable sleep/wake histories are available for the accident personnel and, (2) useful in prospective fatigue-risk identification, mitigation, and accident prevention. Copyright © 2010 Elsevier Ltd. All rights reserved.

Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Reddy, C. J.

2011-01-01

This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

Numerical simulation of the coaxial magneto-plasma accelerator and non-axisymmetric radio frequency discharge

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.; Frolko, P. A.

2017-05-01

The paper presents the results of mathematical modeling of physical processes in electronic devices such as helicon discharge and coaxial pulsed plasma thruster. A mathematical model of coaxial magneto-plasma accelerator (with a preionization helicon discharge), which allows estimating the transformation of one form of energy to another, as well as to evaluate the level of the contribution of different types of energy, the increase in mass of the accelerated plasmoid in the process of changing the speed. Main plasma parameters with experimental data were compared.

Estimating formation properties from early-time oscillatory water levels in a pumped well

USGS Publications Warehouse

Shapiro, A.M.; Oki, D.S.

2000-01-01

Hydrologists often attempt to estimate formation properties from aquifer tests for which only the hydraulic responses in a pumped well are available. Borehole storage, turbulent head losses, and borehole skin, however, can mask the hydraulic behavior of the formation inferred from the water level in the pumped well. Also, in highly permeable formations or in formations at significant depth below land surface, where there is a long column of water in the well casing, oscillatory water levels may arise during the onset of pumping to further mask formation responses in the pumped well. Usually borehole phenomena are confined to the early stages of pumping or recovery, and late-time hydraulic data can be used to estimate formation properties. In many instances, however, early-time hydraulic data provide valuable information about the formation, especially if there are interferences in the late-time data. A mathematical model and its Laplace transform solution that account for inertial influences and turbulent head losses during pumping is developed for the coupled response between the pumped borehole and the formation. The formation is assumed to be homogeneous, isotropic, of infinite areal extent, and uniform thickness, with leakage from an overlying aquifer, and the screened or open interval of the pumped well is assumed to fully penetrate the pumped aquifer. Other mathematical models of aquifer flow can also be coupled with the equations describing turbulent head losses and the inertial effects on the water column in the pumped well. The mathematical model developed in this paper is sufficiently general to consider both underdamped conditions for which oscillations arise, and overdamped conditions for which there are no oscillations. Through numerical inversion of the Laplace transform solution, type curves from the mathematical model are developed to estimate formation properties through comparison with the measured hydraulic response in the pumped well. The mathematical model is applied to estimate formation properties from a singlewell test conducted near Waialua, Oahu, Hawaii. At this site, both the drawdown and recovery showed oscillatory water levels in the pumped well, and a step-drawdown test showed that approximately 86% of the drawdown is attributed to turbulent head losses. Analyses at this site using late-time drawdown data were confounded by the noise present in the measured water levels due primarily to nearby irrigation wells and ocean tides. By analyzing the early-time oscillatory recovery data at the Waialua site, upper and lower bounds were placed on the transmissivity, T, storage coefficient, S, and the leakance of the confining unit, K′/B′. The upper and lower bounds on T differ by a factor of 2. Upper and lower bounds on S and K′/B′ are much larger, because drawdown stabilized relatively quickly after the onset of pumping.

Taking the Guesswork out of Computational Estimation

ERIC Educational Resources Information Center

Cochran, Jill; Dugger, Megan Hartmann

2013-01-01

Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn, good…

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

PubMed

Schmid, Thomas; Bogdan, Martin; Günzel, Dorothee

2013-01-01

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

Predicting disease progression from short biomarker series using expert advice algorithm

NASA Astrophysics Data System (ADS)

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-01

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of ``prediction with expert advice'' to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

Predicting disease progression from short biomarker series using expert advice algorithm.

PubMed

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-20

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of "prediction with expert advice" to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition.

PubMed

Falgreen, Steffen; Laursen, Maria Bach; Bødker, Julie Støve; Kjeldsen, Malene Krag; Schmitz, Alexander; Nyegaard, Mette; Johnsen, Hans Erik; Dybkær, Karen; Bøgsted, Martin

2014-06-05

In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves' dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency. First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations. Time independent summary statistics may aid the understanding of drugs' action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies.

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition

PubMed Central

2014-01-01

Background In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves’ dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency. Results First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations. Conclusion Time independent summary statistics may aid the understanding of drugs’ action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies. PMID:24902483

Estimation Of Rheological Law By Inverse Method From Flow And Temperature Measurements With An Extrusion Die

NASA Astrophysics Data System (ADS)

Pujos, Cyril; Regnier, Nicolas; Mousseau, Pierre; Defaye, Guy; Jarny, Yvon

2007-05-01

Simulation quality is determined by the knowledge of the parameters of the model. Yet the rheological models for polymer are often not very accurate, since the viscosity measurements are made under approximations as homogeneous temperature and empirical corrections as Bagley one. Furthermore rheological behaviors are often traduced by mathematical laws as the Cross or the Carreau-Yasuda ones, whose parameters are fitted from viscosity values, obtained with corrected experimental data, and not appropriate for each polymer. To correct these defaults, a table-like rheological model is proposed. This choice makes easier the estimation of model parameters, since each parameter has the same order of magnitude. As the mathematical shape of the model is not imposed, the estimation process is appropriate for each polymer. The proposed method consists in minimizing the quadratic norm of the difference between calculated variables and measured data. In this study an extrusion die is simulated, in order to provide us temperature along the extrusion channel, pressure and flow references. These data allow to characterize thermal transfers and flow phenomena, in which the viscosity is implied. Furthermore the different natures of data allow to estimate viscosity for a large range of shear rates. The estimated rheological model improves the agreement between measurements and simulation: for numerical cases, the error on the flow becomes less than 0.1% for non-Newtonian rheology. This method couples measurements and simulation, constitutes a very accurate mean of rheology determination, and allows to improve the prediction abilities of the model.

Bottom-up modeling approach for the quantitative estimation of parameters in pathogen-host interactions

PubMed Central

Lehnert, Teresa; Timme, Sandra; Pollmächer, Johannes; Hünniger, Kerstin; Kurzai, Oliver; Figge, Marc Thilo

2015-01-01

Opportunistic fungal pathogens can cause bloodstream infection and severe sepsis upon entering the blood stream of the host. The early immune response in human blood comprises the elimination of pathogens by antimicrobial peptides and innate immune cells, such as neutrophils or monocytes. Mathematical modeling is a predictive method to examine these complex processes and to quantify the dynamics of pathogen-host interactions. Since model parameters are often not directly accessible from experiment, their estimation is required by calibrating model predictions with experimental data. Depending on the complexity of the mathematical model, parameter estimation can be associated with excessively high computational costs in terms of run time and memory. We apply a strategy for reliable parameter estimation where different modeling approaches with increasing complexity are used that build on one another. This bottom-up modeling approach is applied to an experimental human whole-blood infection assay for Candida albicans. Aiming for the quantification of the relative impact of different routes of the immune response against this human-pathogenic fungus, we start from a non-spatial state-based model (SBM), because this level of model complexity allows estimating a priori unknown transition rates between various system states by the global optimization method simulated annealing. Building on the non-spatial SBM, an agent-based model (ABM) is implemented that incorporates the migration of interacting cells in three-dimensional space. The ABM takes advantage of estimated parameters from the non-spatial SBM, leading to a decreased dimensionality of the parameter space. This space can be scanned using a local optimization approach, i.e., least-squares error estimation based on an adaptive regular grid search, to predict cell migration parameters that are not accessible in experiment. In the future, spatio-temporal simulations of whole-blood samples may enable timely stratification of sepsis patients by distinguishing hyper-inflammatory from paralytic phases in immune dysregulation. PMID:26150807

Bottom-up modeling approach for the quantitative estimation of parameters in pathogen-host interactions.

PubMed

Lehnert, Teresa; Timme, Sandra; Pollmächer, Johannes; Hünniger, Kerstin; Kurzai, Oliver; Figge, Marc Thilo

2015-01-01

Opportunistic fungal pathogens can cause bloodstream infection and severe sepsis upon entering the blood stream of the host. The early immune response in human blood comprises the elimination of pathogens by antimicrobial peptides and innate immune cells, such as neutrophils or monocytes. Mathematical modeling is a predictive method to examine these complex processes and to quantify the dynamics of pathogen-host interactions. Since model parameters are often not directly accessible from experiment, their estimation is required by calibrating model predictions with experimental data. Depending on the complexity of the mathematical model, parameter estimation can be associated with excessively high computational costs in terms of run time and memory. We apply a strategy for reliable parameter estimation where different modeling approaches with increasing complexity are used that build on one another. This bottom-up modeling approach is applied to an experimental human whole-blood infection assay for Candida albicans. Aiming for the quantification of the relative impact of different routes of the immune response against this human-pathogenic fungus, we start from a non-spatial state-based model (SBM), because this level of model complexity allows estimating a priori unknown transition rates between various system states by the global optimization method simulated annealing. Building on the non-spatial SBM, an agent-based model (ABM) is implemented that incorporates the migration of interacting cells in three-dimensional space. The ABM takes advantage of estimated parameters from the non-spatial SBM, leading to a decreased dimensionality of the parameter space. This space can be scanned using a local optimization approach, i.e., least-squares error estimation based on an adaptive regular grid search, to predict cell migration parameters that are not accessible in experiment. In the future, spatio-temporal simulations of whole-blood samples may enable timely stratification of sepsis patients by distinguishing hyper-inflammatory from paralytic phases in immune dysregulation.

A mathematical approach to molecular organization and proteolytic disintegration of bacterial inclusion bodies.

PubMed

Cubarsi, R; Carrió, M M; Villaverde, A

2005-09-01

The in vivo proteolytic digestion of bacterial inclusion bodies (IBs) and the kinetic analysis of the resulting protein fragments is an interesting approach to investigate the molecular organization of these unconventional protein aggregates. In this work, we describe a set of mathematical instruments useful for such analysis and interpretation of observed data. These methods combine numerical estimation of digestion rate and approximation of its high-order derivatives, modelling of fragmentation events from a mixture of Poisson processes associated with differentiated protein species, differential equations techniques in order to estimate the mixture parameters, an iterative predictor-corrector algorithm for describing the flow diagram along the cascade process, as well as least squares procedures with minimum variance estimates. The models are formulated and compared with data, and successively refined to better match experimental observations. By applying such procedures as well as newer improved algorithms of formerly developed equations, it has been possible to model, for two kinds of bacterially produced aggregation prone recombinant proteins, their cascade digestion process that has revealed intriguing features of the IB-forming polypeptides.

A Primary Care Workload Production Model for Estimating Relative Value Unit Output

DTIC Science & Technology

2011-03-01

for Medicare and Medicaid Services, Office of the Actuary , National Health Statistics Group; and U.S. Department of Commerce, Bureau of Economic...The systematic variation in a relationship can be represented by a mathematical expression, whereas stochastic variation cannot. Further, stochastic...expressed mathematically as an equation, whereby a response variable Y is fitted to a function of “regressor variables and parameters” (SAS©, 2010). A

Analysis of Student and School Level Variables Related to Mathematics Self-Efficacy Level Based on PISA 2012 Results for China-Shanghai, Turkey, and Greece

ERIC Educational Resources Information Center

Usta, H. Gonca

2016-01-01

This study aims to analyze the student and school level variables that affect students' self-efficacy levels in mathematics in China-Shanghai, Turkey, and Greece based on PISA 2012 results. In line with this purpose, the hierarchical linear regression model (HLM) was employed. The interschool variability is estimated at approximately 17% in…

Orthogonal Projection in Teaching Regression and Financial Mathematics

ERIC Educational Resources Information Center

Kachapova, Farida; Kachapov, Ilias

2010-01-01

Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear…

A Survey of Methods for Computing Best Estimates of Endoatmospheric and Exoatmospheric Trajectories

NASA Technical Reports Server (NTRS)

Bernard, William P.

2018-01-01

Beginning with the mathematical prediction of planetary orbits in the early seventeenth century up through the most recent developments in sensor fusion methods, many techniques have emerged that can be employed on the problem of endo and exoatmospheric trajectory estimation. Although early methods were ad hoc, the twentieth century saw the emergence of many systematic approaches to estimation theory that produced a wealth of useful techniques. The broad genesis of estimation theory has resulted in an equally broad array of mathematical principles, methods and vocabulary. Among the fundamental ideas and methods that are briefly touched on are batch and sequential processing, smoothing, estimation, and prediction, sensor fusion, sensor fusion architectures, data association, Bayesian and non Bayesian filtering, the family of Kalman filters, models of the dynamics of the phases of a rocket's flight, and asynchronous, delayed, and asequent data. Along the way, a few trajectory estimation issues are addressed and much of the vocabulary is defined.

Evaluating AIDS Prevention: Contributions of Multiple Disciplines.

ERIC Educational Resources Information Center

Leviton, Laura C., Ed.; And Others

1990-01-01

Seven essays on efforts of evaluate prevention programs aimed at the acquired immune deficiency syndrome (AIDS) are presented. Topics include public health psychology, mathematical models of epidemiology, estimates of incubation periods, ethnographic evaluations of AIDS prevention programs, an AIDS education model, theory-based evaluation, and…

Which preparatory curriculum for the International Baccalaureate Diploma Programme is best? The challenge for international schools with regard to mathematics and science

NASA Astrophysics Data System (ADS)

Corlu, M. Sencer

2014-12-01

There are two mainstream curricula for international school students at the junior high level: the International Baccalaureate (IB) Middle Years Programme (MYP) and the Cambridge International General Certificate of Secondary Education (IGCSE). The former was developed in the mid-1990s and is currently being relaunched in a 21st-century approach. The latter programme of study was developed by University of Cambridge International Examinations in 1985 and has become popular in recent years among British domestic and international schools worldwide due to the clarity of its learning content. The prevailing uncertainty about which curriculum is best to prepare students for the IB Diploma Programme represents a challenge for international schools. The purpose of the current study is to develop a methodology through causal models which can explain the relationship between student performance in the IGCSE and the Diploma Programme with regard to mathematics and science. The data evaluated here consisted of external examination scores of students who attended a private international high school between the years 2005 and 2012. Two structural equation models were developed. The first model employed a maximum likelihood estimation, while the second model used a Bayesian estimation with a Markov Chain Monte Carlo method. Both models fit the data well. The evidence suggests that the IGCSE provides a good foundational preparation for the Diploma Programme in mathematics and science.

Mathematical Modeling to Reduce Waste of Compounded Sterile Products in Hospital Pharmacies

PubMed Central

Dobson, Gregory; Haas, Curtis E.; Tilson, David

2014-01-01

Abstract In recent years, many US hospitals embarked on “lean” projects to reduce waste. One advantage of the lean operational improvement methodology is that it relies on process observation by those engaged in the work and requires relatively little data. However, the thoughtful analysis of the data captured by operational systems allows the modeling of many potential process options. Such models permit the evaluation of likely waste reductions and financial savings before actual process changes are made. Thus the most promising options can be identified prospectively, change efforts targeted accordingly, and realistic targets set. This article provides one example of such a datadriven process redesign project focusing on waste reduction in an in-hospital pharmacy. A mathematical model of the medication prepared and delivered by the pharmacy is used to estimate the savings from several potential redesign options (rescheduling the start of production, scheduling multiple batches, or reordering production within a batch) as well as the impact of information system enhancements. The key finding is that mathematical modeling can indeed be a useful tool. In one hospital setting, it estimated that waste could be realistically reduced by around 50% by using several process changes and that the greatest benefit would be gained by rescheduling the start of production (for a single batch) away from the period when most order cancellations are made. PMID:25477580

Table look-up estimation of signal and noise parameters from quantized observables

NASA Technical Reports Server (NTRS)

Vilnrotter, V. A.; Rodemich, E. R.

1986-01-01

A table look-up algorithm for estimating underlying signal and noise parameters from quantized observables is examined. A general mathematical model is developed, and a look-up table designed specifically for estimating parameters from four-bit quantized data is described. Estimator performance is evaluated both analytically and by means of numerical simulation, and an example is provided to illustrate the use of the look-up table for estimating signal-to-noise ratios commonly encountered in Voyager-type data.

Voluntary Medical Male Circumcision for HIV Prevention: New Mathematical Models for Strategic Demand Creation Prioritizing Subpopulations by Age and Geography

PubMed Central

Hankins, Catherine; Warren, Mitchell

2016-01-01

Over 11 million voluntary medical male circumcisions (VMMC) have been performed of the projected 20.3 million needed to reach 80% adult male circumcision prevalence in priority sub-Saharan African countries. Striking numbers of adolescent males, outside the 15-49-year-old age target, have been accessing VMMC services. What are the implications of overall progress in scale-up to date? Can mathematical modeling provide further insights on how to efficiently reach the male circumcision coverage levels needed to create and sustain further reductions in HIV incidence to make AIDS no longer a public health threat by 2030? Considering ease of implementation and cultural acceptability, decision makers may also value the estimates that mathematical models can generate of immediacy of impact, cost-effectiveness, and magnitude of impact resulting from different policy choices. This supplement presents the results of mathematical modeling using the Decision Makers’ Program Planning Tool Version 2.0 (DMPPT 2.0), the Actuarial Society of South Africa (ASSA2008) model, and the age structured mathematical (ASM) model. These models are helping countries examine the potential effects on program impact and cost-effectiveness of prioritizing specific subpopulations for VMMC services, for example, by client age, HIV-positive status, risk group, and geographical location. The modeling also examines long-term sustainability strategies, such as adolescent and/or early infant male circumcision, to preserve VMMC coverage gains achieved during rapid scale-up. The 2016–2021 UNAIDS strategy target for VMMC is an additional 27 million VMMC in high HIV-prevalence settings by 2020, as part of access to integrated sexual and reproductive health services for men. To achieve further scale-up, a combination of evidence, analysis, and impact estimates can usefully guide strategic planning and funding of VMMC services and related demand-creation strategies in priority countries. Mid-course corrections now can improve cost-effectiveness and scale to achieve the impact needed to help turn the HIV pandemic on its head within 15 years. PMID:27783613

Regression Analysis as a Cost Estimation Model for Unexploded Ordnance Cleanup at Former Military Installations

DTIC Science & Technology

2002-06-01

fits our actual data . To determine the goodness of fit, statisticians typically use the following four measures: R2 Statistic. The R2 statistic...reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of...mathematical model is developed to better estimate cleanup costs using historical cost data that could be used by the Defense Department prior to placing

Estimating the number of terrestrial organisms on the moon.

NASA Technical Reports Server (NTRS)

Dillon, R. T.; Gavin, W. R.; Roark, A. L.; Trauth, C. A., Jr.

1973-01-01

Methods used to obtain estimates for the biological loadings on moon bound spacecraft prior to launch are reviewed, along with the mathematical models used to calculate the microorganism density on the lunar surface (such as it results from contamination deposited by manned and unmanned flights) and the probability of lunar soil sample contamination. Some of the results obtained by the use of a lunar inventory system based on these models are presented.

A model to estimate the relative position of sites for ligands in serum albumins

NASA Astrophysics Data System (ADS)

Motta, Art Adriel Emidio de Araújo; Grassini, Maria Carolina Vilela; Cortez, Célia Martins; Silva, Dilson

2017-11-01

In this work, we present a mathematical-computational model developed to estimate the relative position of ligand binding sites in HSA and BSA, based on the theory of fluorescence quenching, considering the molecular and spectrofluorimetric differences and similarities between these two albumins. Albumin is the largest and the most abundant serum protein in vertebrates. The ability to bind xenobiotics makes albumin important to the bioavailability and effectiveness of drugs.

A mathematical model of salmonid spawning habitat

Treesearch

Robert N. Havis; Carlos V. Alonzo; Keith E Woeste; Russell F. Thurow

1993-01-01

A simulation model [Salmonid Spawning Analysis Model (SSAM)I was developed as a management tool to evaluate the relative impacts of stream sediment load and water temperature on salmonid egg survival. The model is usefi.il for estimating acceptable sediment loads to spawning habitat that may result from upland development, such as logging and agriculture. Software in...

Mathematical model of depolarization mechanism of conducted vasoreactivity

NASA Astrophysics Data System (ADS)

Neganova, Anastasiia Y.; Stiukhina, Elena S.; Postnov, Dmitry E.

2015-03-01

We address the problem of conducted vasodilation, the phenomenon which is also known as functional hyperemia. Specifically, we test the mechanism of nondecremental propagation of electric signals along endothelial cell layer recently hypothesized by Figueroa et al. By means of functional modeling we focus on possible nonlinear mechanisms that can underlie such regenerative pulse transmission (RPT). Since endothelial cells (EC) are generally known as electrically inexcitable, the possible role of ECs in RPT mechanisms is not evident. By means of mathematical modeling we check the dynamical self-consistency of Figueroa's hypothesis, as well as estimate the possible contribution of specific ionic currents to the suggested RPT mechanism.

Troy: A simple nonlinear mathematical perspective

NASA Astrophysics Data System (ADS)

Flores, J. C.; Bologna, Mauro

2013-10-01

In this paper, we propose a mathematical model for the Trojan war that, supposedly, took place around 1180 BC. Supported by archaeological findings and by Homer’s Iliad, we estimate the numbers of warriors, the struggle rate parameters, the number of individuals per hectare, and other related quantities. We show that the long siege of the city, described in the Iliad, is compatible with a power-law behaviour for the time evolution of the number of individuals. We are able to evaluate the parameters of our model during the phase of the siege and the fall. The proposed model is general, and it can be applied to other historical conflicts.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Towards new-generation soil erosion modeling: Building a unified omnivorous model

USDA-ARS?s Scientific Manuscript database

Soil erosion is a global threat to agricultural production, and results in off-site sediment and nutrient losses that negatively impact water and air quality. Models are mathematical equations used to estimate the amount of soil lost from a land air, due to the erosive forces of water or wind. Early...

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

PubMed Central

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

2015-01-01

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

Modeling Influenza Virus Infection: A Roadmap for Influenza Research.

PubMed

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

2015-10-12

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

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Characteristic Energy Scales of Quantum Systems.

ERIC Educational Resources Information Center

Morgan, Michael J.; Jakovidis, Greg

1994-01-01

Provides a particle-in-a-box model to help students understand and estimate the magnitude of the characteristic energy scales of a number of quantum systems. Also discusses the mathematics involved with general computations. (MVL)

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Physiological pharmacokinetic modeling

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

Menzel, D.B.

1987-10-01

Risk assessment often defines the approach and the degree of regulation, decisions in risk assessment often have major regulatory impacts. Chemicals that have economic value or that were byproducts of the chemical industry are common subjects of such decisions. Regrettably, decisions related to risk assessment, science, or regulatory matters will frequently be made with incomplete information and on the basis of intuitive reasoning. Statistical fits to experimental data have been used to estimate risks in humans from experimental data in animals. These treatments have not taken into account the obvious differences in physiology, biochemistry, and size between aniamals and humans.more » In this article the use of mathematical models based on continuous relationships, rather than quantal events, are discussed. The mathematical models can be used to adjust the dose in the quantal response model, but the emphasis will be on how these mathematical models are conceived and what implications their use holds for risk assessment. Experiments with humans that produce toxic effects cannot be done. Data for human toxicity will always be lacking.« less

Nonparametric Estimation of the Probability of Ruin.

DTIC Science & Technology

1985-02-01

MATHEMATICS RESEARCH CENTER I E N FREES FEB 85 MRC/TSR...in NONPARAMETRIC ESTIMATION OF THE PROBABILITY OF RUIN Lf Edward W. Frees * Mathematics Research Center University of Wisconsin-Madison 610 Walnut...34 - .. --- - • ’. - -:- - - ..- . . .- -- .-.-. . -. . .- •. . - . . - . . .’ . ’- - .. -’vi . .-" "-- -" ,’- UNIVERSITY OF WISCONSIN-MADISON MATHEMATICS RESEARCH CENTER NONPARAMETRIC ESTIMATION OF THE PROBABILITY

Predicting plot soil loss by empirical and process-oriented approaches: A review

USDA-ARS?s Scientific Manuscript database

Soil erosion directly affects the quality of the soil, its agricultural productivity and its biological diversity. Many mathematical models have been developed to estimate plot soil erosion at different temporal scales. At present, empirical soil loss equations and process-oriented models are consid...

Selection Criteria for Mathematical Models Used in Exposure Assessments: Atmospheric Dispersion Models

EPA Science Inventory

Before the U.S. Environmental Protection Agency issued the 1988 Guidelines for Estimating Exposures, it published proposed guidelines in the Federal Register for public review and comment. he guidelines are intended to give risk analysis a basic framework and the tools they need ...

Estimation of Physical Properties and Chemical Reactivity Parameters of Organic Compounds for Environmental Modeling by SPARC

EPA Science Inventory

Mathematical models for predicting the transport and fate of pollutants in the environment require reactivity parameter values that is value of the physical and chemical constants that govern reactivity. Although empirical structure activity relationships have been developed th...

Parallel particle filters for online identification of mechanistic mathematical models of physiology from monitoring data: performance and real-time scalability in simulation scenarios.

PubMed

Zenker, Sven

2010-08-01

Combining mechanistic mathematical models of physiology with quantitative observations using probabilistic inference may offer advantages over established approaches to computerized decision support in acute care medicine. Particle filters (PF) can perform such inference successively as data becomes available. The potential of PF for real-time state estimation (SE) for a model of cardiovascular physiology is explored using parallel computers and the ability to achieve joint state and parameter estimation (JSPE) given minimal prior knowledge tested. A parallelized sequential importance sampling/resampling algorithm was implemented and its scalability for the pure SE problem for a non-linear five-dimensional ODE model of the cardiovascular system evaluated on a Cray XT3 using up to 1,024 cores. JSPE was implemented using a state augmentation approach with artificial stochastic evolution of the parameters. Its performance when simultaneously estimating the 5 states and 18 unknown parameters when given observations only of arterial pressure, central venous pressure, heart rate, and, optionally, cardiac output, was evaluated in a simulated bleeding/resuscitation scenario. SE was successful and scaled up to 1,024 cores with appropriate algorithm parametrization, with real-time equivalent performance for up to 10 million particles. JSPE in the described underdetermined scenario achieved excellent reproduction of observables and qualitative tracking of enddiastolic ventricular volumes and sympathetic nervous activity. However, only a subset of the posterior distributions of parameters concentrated around the true values for parts of the estimated trajectories. Parallelized PF's performance makes their application to complex mathematical models of physiology for the purpose of clinical data interpretation, prediction, and therapy optimization appear promising. JSPE in the described extremely underdetermined scenario nevertheless extracted information of potential clinical relevance from the data in this simulation setting. However, fully satisfactory resolution of this problem when minimal prior knowledge about parameter values is available will require further methodological improvements, which are discussed.

Recent advances in mathematical modeling of nitrous oxides emissions from wastewater treatment processes.

PubMed

Ni, Bing-Jie; Yuan, Zhiguo

2015-12-15

Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. Copyright © 2015 Elsevier Ltd. All rights reserved.

Directional Canopy Emissivity Estimation Based on Spectral Invariants

NASA Astrophysics Data System (ADS)

Guo, M.; Cao, B.; Ren, H.; Yongming, D.; Peng, J.; Fan, W.

2017-12-01

Land surface emissivity is a crucial parameter for estimating land surface temperature from remote sensing data and also plays an important role in the physical process of surface energy and water balance from local to global scales. To our knowledge, the emissivity varies with surface type and cover. As for the vegetation, its canopy emissivity is dependent on vegetation types, viewing zenith angle and structure that changes in different growing stages. Lots of previous studies have focused on the emissivity model, but few of them are analytic and suited to different canopy structures. In this paper, a new physical analytic model is proposed to estimate the directional emissivity of homogenous vegetation canopy based on spectral invariants. The initial model counts the directional absorption in six parts: the direct absorption of the canopy and the soil, the absorption of the canopy and soil after a single scattering and after multiple scattering within the canopy-soil system. In order to analytically estimate the emissivity, the pathways of photons absorbed in the canopy-soil system are traced using the re-collision probability in Fig.1. After sensitive analysis on the above six absorptions, the initial complicated model was further simplified as a fixed mathematic expression to estimate the directional emissivity for vegetation canopy. The model was compared with the 4SAIL model, FRA97 model, FRA02 model and DART model in Fig.2, and the results showed that the FRA02 model is significantly underestimated while the FRA97 model is a little underestimated, on basis of the new model. On the contrary, the emissivity difference between the new model with the 4SAIL model and DART model was found to be less than 0.002. In general, since the new model has the advantages of mathematic expression with accurate results and clear physical meaning, the model is promising to be extended to simulate the directional emissivity for the discrete canopy in further study.

Mathematical models in simulation process in rehabilitation of persons with disabilities

NASA Astrophysics Data System (ADS)

Gorie, Nina; Dolga, Valer; Mondoc, Alina

2012-11-01

The problems of people with disability are varied. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these. The major disabilities which can appear in people's lives are: the blindness, the deafness, the limb-girdle muscular dystrophy, the orthopedic impairment, the visual impairment. A disability is an umbrella term, covering impairments, activity limitations and participation restrictions. A disability may occur during a person's lifetime or may be present from birth. The authors conclude that some of these disabilities like physical, cognitive, mental, sensory, emotional, developmental can be rehabilitated. Starting from this state of affairs the authors present briefly the possibility of using certain mechatronic systems for rehabilitation of persons with different disabilities. The authors focus their presentation on alternative calling the Stewart platform in order to achieve the proposed goal. The authors present a mathematical model of systems theory approach under the parallel system and described its contents can. The authors analyze in a meaningful mathematical model describing the procedure of rehabilitation process. From the affected function biomechanics and taking into account medical recommendations the authors illustrate the mathematical models of rehabilitation work. The authors assemble a whole mathematical model of parallel structure and the rehabilitation process and making simulation and highlighting the results estimated. The authors present in the end work the results envisaged in the end analysis work, conclusions and steps for future work program..

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.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

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

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

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

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

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1978-01-01

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

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method

PubMed Central

2014-01-01

Background The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. Methods We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Conclusions Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method. PMID:25052018

Some thoughts on estimating the cost of common equity for a regulated business

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

Malko, J. Robert; Swensen, Philip R.; Monteleone, Joseph A.

2007-06-15

While mathematical models are useful in establishing a zone of reasonableness for a determination of allowed return on equity, it is important to consider the results of several models. Also key is to consider whether the analysis appropriately reflects longer-term market conditions. (author)

Discerning Apical and Basolateral Properties of HT-29/B6 and IPEC-J2 Cell Layers by Impedance Spectroscopy, Mathematical Modeling and Machine Learning

PubMed Central

Schmid, Thomas; Bogdan, Martin; Günzel, Dorothee

2013-01-01

Quantifying changes in partial resistances of epithelial barriers in vitro is a challenging and time-consuming task in physiology and pathophysiology. Here, we demonstrate that electrical properties of epithelial barriers can be estimated reliably by combining impedance spectroscopy measurements, mathematical modeling and machine learning algorithms. Conventional impedance spectroscopy is often used to estimate epithelial capacitance as well as epithelial and subepithelial resistance. Based on this, the more refined two-path impedance spectroscopy makes it possible to further distinguish transcellular and paracellular resistances. In a next step, transcellular properties may be further divided into their apical and basolateral components. The accuracy of these derived values, however, strongly depends on the accuracy of the initial estimates. To obtain adequate accuracy in estimating subepithelial and epithelial resistance, artificial neural networks were trained to estimate these parameters from model impedance spectra. Spectra that reflect behavior of either HT-29/B6 or IPEC-J2 cells as well as the data scatter intrinsic to the used experimental setup were created computationally. To prove the proposed approach, reliability of the estimations was assessed with both modeled and measured impedance spectra. Transcellular and paracellular resistances obtained by such neural network-enhanced two-path impedance spectroscopy are shown to be sufficiently reliable to derive the underlying apical and basolateral resistances and capacitances. As an exemplary perturbation of pathophysiological importance, the effect of forskolin on the apical resistance of HT-29/B6 cells was quantified. PMID:23840862

Feasibility study for automatic reduction of phase change imagery

NASA Technical Reports Server (NTRS)

Nossaman, G. O.

1971-01-01

The feasibility of automatically reducing a form of pictorial aerodynamic heating data is discussed. The imagery, depicting the melting history of a thin coat of fusible temperature indicator painted on an aerodynamically heated model, was previously reduced by manual methods. Careful examination of various lighting theories and approaches led to an experimentally verified illumination concept capable of yielding high-quality imagery. Both digital and video image processing techniques were applied to reduction of the data, and it was demonstrated that either method can be used to develop superimposed contours. Mathematical techniques were developed to find the model-to-image and the inverse image-to-model transformation using six conjugate points, and methods were developed using these transformations to determine heating rates on the model surface. A video system was designed which is able to reduce the imagery rapidly, economically and accurately. Costs for this system were estimated. A study plan was outlined whereby the mathematical transformation techniques developed to produce model coordinate heating data could be applied to operational software, and methods were discussed and costs estimated for obtaining the digital information necessary for this software.

Effects of low-level chronic irradiation on the radiosensitivity of mammals: Modeling studies

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

Mathematical models of the major hematopoietic lines are used to study the modifying effects of low-level chronic preirradiation on radiosensitivity of mammals which resulted in their reduced radiosensitivity (acquired radioresistance) and elevated radiosensitivity (hypersensitivity) to the subsequent radiation exposure. These effects of preirradiation manifest themselves, respectively, in decreased and increased mortality of preirradiated experimental animals (mice) after challenge acute exposure in comparison with that for previously nonirradiated ones. Analysis of the modeling results reveals the biological mechanisms of these radioprotection and radiosensitization effects, and enables one to estimate the ranges of dose rate and duration of chronic preirradiation where these effects are realized. Juxtapositions of the modeling predictions with the relevant experimental data show their qualitative agreement. All this testifies to the importance of accounting the nonlinear effect of low-level chronic irradiation on radiosensitivity of the hematopoiesis system and organism as a whole, when the radiation risk for astronauts on long-term space missions is estimated. The developed models of hematopoiesis can be used, after appropriate identification, as a component of the mathematical tools for radiation risk assessment.

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

Some problems of control of dynamical conditions of technological vibrating machines

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Control by model error estimation

NASA Technical Reports Server (NTRS)

Likins, P. W.; Skelton, R. E.

1976-01-01

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).

A mathematical model for simulating spring discharge and estimating sinkhole porosity in a karst watershed

NASA Astrophysics Data System (ADS)

Li, Guangquan; Field, Malcolm S.

2014-03-01

Documenting and understanding water balances in a karst watershed in which groundwater and surface water resources are strongly interconnected are important aspects for managing regional water resources. Assessing water balances in karst watersheds can be difficult, however, because karst watersheds are so very strongly affected by groundwater flows through solution conduits that are often connected to one or more sinkholes. In this paper we develop a mathematical model to approximate sinkhole porosity from discharge at a downstream spring. The model represents a combination of a traditional linear reservoir model with turbulent hydrodynamics in the solution conduit connecting the downstream spring with the upstream sinkhole, which allows for the simulation of spring discharges and estimation of sinkhole porosity. Noting that spring discharge is an integral of all aspects of water storage and flow, it is mainly dependent on the behavior of the karst aquifer as a whole and can be adequately simulated using the analytical model described in this paper. The model is advantageous in that it obviates the need for a sophisticated numerical model that is much more costly to calibrate and operate. The model is demonstrated using the St. Marks River Watershed in northwestern Florida.

On-line Model Structure Selection for Estimation of Plasma Boundary in a Tokamak

NASA Astrophysics Data System (ADS)

Škvára, Vít; Šmídl, Václav; Urban, Jakub

2015-11-01

Control of the plasma field in the tokamak requires reliable estimation of the plasma boundary. The plasma boundary is given by a complex mathematical model and the only available measurements are responses of induction coils around the plasma. For the purpose of boundary estimation the model can be reduced to simple linear regression with potentially infinitely many elements. The number of elements must be selected manually and this choice significantly influences the resulting shape. In this paper, we investigate the use of formal model structure estimation techniques for the problem. Specifically, we formulate a sparse least squares estimator using the automatic relevance principle. The resulting algorithm is a repetitive evaluation of the least squares problem which could be computed in real time. Performance of the resulting algorithm is illustrated on simulated data and evaluated with respect to a more detailed and computationally costly model FREEBIE.

Adequacy assessment of mathematical models in the dynamics of litter decomposition in a tropical forest Mosaic Atlantic, in southeastern Brazil.

PubMed

Nunes, F P; Garcia, Q S

2015-05-01

The study of litter decomposition and nutrient cycling is essential to know native forests structure and functioning. Mathematical models can help to understand the local and temporal litter fall variations and their environmental variables relationships. The objective of this study was test the adequacy of mathematical models for leaf litter decomposition in the Atlantic Forest in southeastern Brazil. We study four native forest sites in Parque Estadual do Rio Doce, a Biosphere Reserve of the Atlantic, which were installed 200 bags of litter decomposing with 20 × 20 cm nylon screen of 2 mm, with 10 grams of litter. Monthly from 09/2007 to 04/2009, 10 litterbags were removed for determination of the mass loss. We compared 3 nonlinear models: 1 - Olson Exponential Model (1963), which considers the constant K, 2 - Model proposed by Fountain and Schowalter (2004), 3 - Model proposed by Coelho and Borges (2005), which considers the variable K through QMR, SQR, SQTC, DMA and Test F. The Fountain and Schowalter (2004) model was inappropriate for this study by overestimating decomposition rate. The decay curve analysis showed that the model with the variable K was more appropriate, although the values of QMR and DMA revealed no significant difference (p > 0.05) between the models. The analysis showed a better adjustment of DMA using K variable, reinforced by the values of the adjustment coefficient (R2). However, convergence problems were observed in this model for estimate study areas outliers, which did not occur with K constant model. This problem can be related to the non-linear fit of mass/time values to K variable generated. The model with K constant shown to be adequate to describe curve decomposition for separately areas and best adjustability without convergence problems. The results demonstrated the adequacy of Olson model to estimate tropical forest litter decomposition. Although use of reduced number of parameters equaling the steps of the decomposition process, no difficulties of convergence were observed in Olson model. So, this model can be used to describe decomposition curves in different types of environments, estimating K appropriately.

Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

PubMed

Agur, Zvia; Elishmereni, Moran; Kheifetz, Yuri

2014-01-01

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. © 2014 Wiley Periodicals, Inc.

Variations of anthropogenic CO2 in urban area deduced by radiocarbon concentration in modern tree rings.

PubMed

Rakowski, Andrzej Z; Nakamura, Toshio; Pazdur, Anna

2008-10-01

Radiocarbon concentration in the atmosphere is significantly lower in areas where man-made emissions of carbon dioxide occur. This phenomenon is known as Suess effect, and is caused by the contamination of clean air with non-radioactive carbon from fossil fuel combustion. The effect is more strongly observed in industrial and densely populated urban areas. Measurements of carbon isotope concentrations in a study area can be compared to those from areas of clear air in order to estimate the amount of carbon dioxide emission from fossil fuel combustion by using a simple mathematical model. This can be calculated using the simple mathematical model. The result of the mathematical model followed in this study suggests that the use of annual rings of trees to obtain the secular variations of 14C concentration of atmospheric CO2 can be useful and efficient for environmental monitoring and modeling of the carbon distribution in local scale.

Annette Bunge: developing the principles in percutaneous absorption using chemical engineering principles.

PubMed

Stinchcomb, A L

2013-01-01

Annette Bunge and her research group have had the central theme of mathematically modeling the dermal absorption process. Most of the research focus has been on estimating dermal absorption for the purpose of risk assessment, for exposure scenarios in the environment and in the occupational setting. Her work is the basis for the United States Environmental Protection Agency's estimations for dermal absorption from contaminated water. It is also the basis of the dermal absorption estimates used in determining if chemicals should be assigned a 'skin notation' for potential systemic toxicity following occupational skin exposure. The work is truly translational in that it started with mathematical theory, is validated with preclinical and human experiments, and then is used in guidelines to protect human health. Her valued research has also extended into the topical drug bioavailability and bioequivalence assessment field.

Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model

NASA Astrophysics Data System (ADS)

Feng, Jinchao; Lansford, Joshua; Mironenko, Alexander; Pourkargar, Davood Babaei; Vlachos, Dionisios G.; Katsoulakis, Markos A.

2018-03-01

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated.

An MDI Model and an Algorithm for Composite Hypotheses Testing and Estimation in Marketing

DTIC Science & Technology

1981-09-01

Other, more general, developments in statistics and mathematical programming (duality) theories and methods are also briefly discussed for their possible bearing on further uses in marketing research and management. (Author)

Nonlinear model predictive control for chemical looping process

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

Joshi, Abhinaya; Lei, Hao; Lou, Xinsheng

A control system for optimizing a chemical looping ("CL") plant includes a reduced order mathematical model ("ROM") that is designed by eliminating mathematical terms that have minimal effect on the outcome. A non-linear optimizer provides various inputs to the ROM and monitors the outputs to determine the optimum inputs that are then provided to the CL plant. An estimator estimates the values of various internal state variables of the CL plant. The system has one structure adapted to control a CL plant that only provides pressure measurements in the CL loops A and B, a second structure adapted to amore » CL plant that provides pressure measurements and solid levels in both loops A, and B, and a third structure adapted to control a CL plant that provides full information on internal state variables. A final structure provides a neural network NMPC controller to control operation of loops A and B.« less

A phase space model of Fourier ptychographic microscopy

PubMed Central

Horstmeyer, Roarke; Yang, Changhuei

2014-01-01

A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution complex sample estimate. Here, we propose a mathematical model of FPM that explicitly connects its operation to conventional ptychography, a common procedure applied to electron and X-ray diffractive imaging. Our mathematical framework demonstrates that under ideal illumination conditions, conventional ptychography and FPM both produce datasets that are mathematically linked by a linear transformation. We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures. In addition, the coherence state of the illumination source used by each imaging platform is critical to successful operation, yet currently not well understood. We apply our mathematical framework to demonstrate that partial coherence uniquely alters both conventional ptychography’s and FPM’s captured data, but up to a certain threshold can still lead to accurate resolution-enhanced imaging through appropriate computational post-processing. We verify this theoretical finding through simulation and experiment. PMID:24514995

Estimating snowpack density from Albedo measurement

Treesearch

James L. Smith; Howard G. Halverson

1979-01-01

Snow is a major source of water in Western United States. Data on snow depth and average snowpack density are used in mathematical models to predict water supply. In California, about 75 percent of the snow survey sites above 2750-meter elevation now used to collect data are in statutory wilderness areas. There is need for a method of estimating the water content of a...

A Computational Model of the Rainbow Trout Hypothalamus-Pituitary-Ovary-Liver Axis

PubMed Central

Gillies, Kendall; Krone, Stephen M.; Nagler, James J.; Schultz, Irvin R.

2016-01-01

Reproduction in fishes and other vertebrates represents the timely coordination of many endocrine factors that culminate in the production of mature, viable gametes. In recent years there has been rapid growth in understanding fish reproductive biology, which has been motivated in part by recognition of the potential effects that climate change, habitat destruction and contaminant exposure can have on natural and cultured fish populations. New approaches to understanding the impacts of these stressors are being developed that require a systems biology approach with more biologically accurate and detailed mathematical models. We have developed a multi-scale mathematical model of the female rainbow trout hypothalamus-pituitary-ovary-liver axis to use as a tool to help understand the functioning of the system and for extrapolation of laboratory findings of stressor impacts on specific components of the axis. The model describes the essential endocrine components of the female rainbow trout reproductive axis. The model also describes the stage specific growth of maturing oocytes within the ovary and permits the presence of sub-populations of oocytes at different stages of development. Model formulation and parametrization was largely based on previously published in vivo and in vitro data in rainbow trout and new data on the synthesis of gonadotropins in the pituitary. Model predictions were validated against several previously published data sets for annual changes in gonadotropins and estradiol in rainbow trout. Estimates of select model parameters can be obtained from in vitro assays using either quantitative (direct estimation of rate constants) or qualitative (relative change from control values) approaches. This is an important aspect of mathematical models as in vitro, cell-based assays are expected to provide the bulk of experimental data for future risk assessments and will require quantitative physiological models to extrapolate across biological scales. PMID:27096735

A Computational Model of the Rainbow Trout Hypothalamus-Pituitary-Ovary-Liver Axis.

PubMed

Gillies, Kendall; Krone, Stephen M; Nagler, James J; Schultz, Irvin R

2016-04-01

Reproduction in fishes and other vertebrates represents the timely coordination of many endocrine factors that culminate in the production of mature, viable gametes. In recent years there has been rapid growth in understanding fish reproductive biology, which has been motivated in part by recognition of the potential effects that climate change, habitat destruction and contaminant exposure can have on natural and cultured fish populations. New approaches to understanding the impacts of these stressors are being developed that require a systems biology approach with more biologically accurate and detailed mathematical models. We have developed a multi-scale mathematical model of the female rainbow trout hypothalamus-pituitary-ovary-liver axis to use as a tool to help understand the functioning of the system and for extrapolation of laboratory findings of stressor impacts on specific components of the axis. The model describes the essential endocrine components of the female rainbow trout reproductive axis. The model also describes the stage specific growth of maturing oocytes within the ovary and permits the presence of sub-populations of oocytes at different stages of development. Model formulation and parametrization was largely based on previously published in vivo and in vitro data in rainbow trout and new data on the synthesis of gonadotropins in the pituitary. Model predictions were validated against several previously published data sets for annual changes in gonadotropins and estradiol in rainbow trout. Estimates of select model parameters can be obtained from in vitro assays using either quantitative (direct estimation of rate constants) or qualitative (relative change from control values) approaches. This is an important aspect of mathematical models as in vitro, cell-based assays are expected to provide the bulk of experimental data for future risk assessments and will require quantitative physiological models to extrapolate across biological scales.

A method to improve the accuracy of pair-wise combinations of anthropometric elements when only limited data are available.

PubMed

Albin, Thomas J

2013-01-01

Designers and ergonomists occasionally must produce anthropometric models of workstations with only summary percentile data available regarding the intended users. Until now the only option available was adding or subtracting percentiles of the anthropometric elements, e.g. heights and widths, used in the model, despite the known resultant errors in the estimate of the percent of users accommodated. This paper introduces a new method, the Median Correlation Method (MCM) that reduces the error. Compare the relative accuracy of MCM to combining percentiles for anthropometric models comprised of all possible pairs of five anthropometric elements. Describe the mathematical basis of the greater accuracy of MCM. MCM is described. 95th percentile accommodation percentiles are calculated for the sums and differences of all combinations of five anthropometric elements by combining percentiles and using MCM. The resulting estimates are compared with empirical values of the 95th percentiles, and the relative errors are reported. The MCM method is shown to be significantly more accurate than adding percentiles. MCM is demonstrated to have a mathematical advantage estimating accommodation relative to adding or subtracting percentiles. The MCM method should be used in preference to adding or subtracting percentiles when limited data prevent more sophisticated anthropometric models.

Unsteady Aerodynamic Modeling in Roll for the NASA Generic Transport Model

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.

2012-01-01

Reducing the impact of loss-of-control conditions on commercial transport aircraft is a primary goal of the NASA Aviation Safety Program. One aspect in developing the supporting technologies is to improve the aerodynamic models that represent these adverse conditions. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. In this paper, a more general mathematical model is proposed for the subscale NASA Generic Transport Model (GTM) that covers both low and high angles of attack. Particular attention is devoted to the stall region where full-scale transports have demonstrated a tendency for roll instability. The complete aerodynamic model was estimated from dynamic wind-tunnel data. Advanced computational methods are used to improve understanding and visualize the flow physics within the region where roll instability is a factor.

HIV Treatment as Prevention: Systematic Comparison of Mathematical Models of the Potential Impact of Antiretroviral Therapy on HIV Incidence in South Africa

PubMed Central

Eaton, Jeffrey W.; Johnson, Leigh F.; Salomon, Joshua A.; Bärnighausen, Till; Bendavid, Eran; Bershteyn, Anna; Bloom, David E.; Cambiano, Valentina; Fraser, Christophe; Hontelez, Jan A. C.; Humair, Salal; Klein, Daniel J.; Long, Elisa F.; Phillips, Andrew N.; Pretorius, Carel; Stover, John; Wenger, Edward A.; Williams, Brian G.; Hallett, Timothy B.

2012-01-01

Background Many mathematical models have investigated the impact of expanding access to antiretroviral therapy (ART) on new HIV infections. Comparing results and conclusions across models is challenging because models have addressed slightly different questions and have reported different outcome metrics. This study compares the predictions of several mathematical models simulating the same ART intervention programmes to determine the extent to which models agree about the epidemiological impact of expanded ART. Methods and Findings Twelve independent mathematical models evaluated a set of standardised ART intervention scenarios in South Africa and reported a common set of outputs. Intervention scenarios systematically varied the CD4 count threshold for treatment eligibility, access to treatment, and programme retention. For a scenario in which 80% of HIV-infected individuals start treatment on average 1 y after their CD4 count drops below 350 cells/µl and 85% remain on treatment after 3 y, the models projected that HIV incidence would be 35% to 54% lower 8 y after the introduction of ART, compared to a counterfactual scenario in which there is no ART. More variation existed in the estimated long-term (38 y) reductions in incidence. The impact of optimistic interventions including immediate ART initiation varied widely across models, maintaining substantial uncertainty about the theoretical prospect for elimination of HIV from the population using ART alone over the next four decades. The number of person-years of ART per infection averted over 8 y ranged between 5.8 and 18.7. Considering the actual scale-up of ART in South Africa, seven models estimated that current HIV incidence is 17% to 32% lower than it would have been in the absence of ART. Differences between model assumptions about CD4 decline and HIV transmissibility over the course of infection explained only a modest amount of the variation in model results. Conclusions Mathematical models evaluating the impact of ART vary substantially in structure, complexity, and parameter choices, but all suggest that ART, at high levels of access and with high adherence, has the potential to substantially reduce new HIV infections. There was broad agreement regarding the short-term epidemiologic impact of ambitious treatment scale-up, but more variation in longer term projections and in the efficiency with which treatment can reduce new infections. Differences between model predictions could not be explained by differences in model structure or parameterization that were hypothesized to affect intervention impact. Please see later in the article for the Editors' Summary PMID:22802730

Personality, Motivation, and Math Achievement Among Turkish Students.

PubMed

Akben-Selcuk, Elif

2017-04-01

Using the Turkish portion of the Programme for International Student Assessment dataset ( N = 4,848; 51% boys, 49% girls; age, M = 15.81 years, SD = 0.28), this study investigated factors associated with mathematics achievement among Turkish students. Three different models were estimated using the method of balanced repeated replication with Fay's method and taking into account the presence of five plausible values of the dependent variable. Results showed that male students and older students had better mathematics proficiency. Socio-economic status and school resources also played a significant role in explaining student achievement in mathematics. Finally, students who were more open to problem solving, who attributed their failure to external factors, and who were intrinsically motivated to learn mathematics achieved higher scores. Policy implications are provided.

Maneuverability Estimation of High-Speed Craft

DTIC Science & Technology

2015-06-01

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

What If We Took Our Models Seriously? Estimating Latent Scores in Individuals

ERIC Educational Resources Information Center

Schneider, W. Joel

2013-01-01

Researchers often argue that the structural models of the constructs they study are relevant to clinicians. Unfortunately, few clinicians are able to translate the mathematically precise relationships between latent constructs and observed scores into information that can be usefully applied to individuals. Typically this means that when a new…

Model verification of large structural systems

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Mathematical model for Trametes versicolor growth in submerged cultivation.

PubMed

Tisma, Marina; Sudar, Martina; Vasić-Racki, Durda; Zelić, Bruno

2010-08-01

Trametes versicolor is a white-rot fungus known as a producer of extracellular enzymes such as laccase, manganese-peroxidase, and lignin-peroxidase. The production of these enzymes requires detailed knowledge of the growth characteristics and physiology of the fungus. Submerged cultivations of T. versicolor on glucose, fructose, and sucrose as sole carbon sources were performed in shake flasks. Sucrose hydrolysis catalyzed by the whole cells of T. versicolor was considered as one-step enzymatic reaction described with Michaelis-Menten kinetics. Kinetic parameters of invertase-catalyzed sucrose hydrolysis were estimated (K (m) = 7.99 g dm(-3) and V (m) = 0.304 h(-1)). Monod model was used for description of kinetics of T. versicolor growth on glucose and fructose as sole carbon sources. Growth associated model parameters were estimated from the experimental results obtained by independent experiments (mu(G)(max) = 0.14 h(-1), K(G)(S) = 8.06 g dm(-3), mu(F)(max) = 0.37 h(-1) and K(F)(S) = 54.8 g dm(-3)). Developed mathematical model is in good agreement with the experimental results.

Determining the accuracy of maximum likelihood parameter estimates with colored residuals

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; Klein, Vladislav

1994-01-01

An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.

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

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

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

Assessing evidence for behaviour change affecting the course of HIV epidemics: a new mathematical modelling approach and application to data from Zimbabwe.

PubMed

Hallett, Timothy B; Gregson, Simon; Mugurungi, Owen; Gonese, Elizabeth; Garnett, Geoff P

2009-06-01

Determining whether interventions to reduce HIV transmission have worked is essential, but complicated by the potential for generalised epidemics to evolve over time without individuals changing risk behaviour. We aimed to develop a method to evaluate evidence for changes in risk behaviour altering the course of an HIV epidemic. We developed a mathematical model of HIV transmission, incorporating the potential for natural changes in the epidemic as it matures and the introduction of antiretroviral treatment, and applied a Bayesian Melding framework, in which the model and observed trends in prevalence can be compared. We applied the model to Zimbabwe, using HIV prevalence estimates from antenatal clinic surveillance and house-hold based surveys, and basing model parameters on data from sexual behaviour surveys. There was strong evidence for reductions in risk behaviour stemming HIV transmission. We estimate these changes occurred between 1999 and 2004 and averted 660,000 (95% credible interval: 460,000-860,000) infections by 2008. The model and associated analysis framework provide a robust way to evaluate the evidence for changes in risk behaviour affecting the course of HIV epidemics, avoiding confounding by the natural evolution of HIV epidemics.

A mathematical model relating response durations to amount of subclinical resistant disease.

PubMed

Gregory, W M; Richards, M A; Slevin, M L; Souhami, R L

1991-02-15

A mathematical model is presented which seeks to determine, from examination of the response durations of a group of patients with malignant disease, the mean and distribution of the resistant tumor volume. The mean tumor-doubling time and distribution of doubling times are also estimated. The model assumes that in a group of patients there is a log-normal distribution both of resistant disease and of tumor-doubling times and implies that the shapes of certain parts of an actuarial response-duration curve are related to these two factors. The model has been applied to data from two reported acute leukemia trials: (a) a recent acute myelogenous leukemia trial was examined. Close fits were obtained for both the first and second remission-duration curves. The model results suggested that patients with long first remissions had less resistant disease and had tumors with slower growth rates following second line treatment; (b) an historical study of maintenance therapy for acute lymphoblastic leukemia was used to estimate the mean cell-kill (approximately 10(4) cells) achieved with single agent, 6-mercaptopurine. Application of the model may have clinical relevance, for example, in identifying groups of patients likely to benefit from further intensification of treatment.

Quantifying Astronaut Tasks: Robotic Technology and Future Space Suit Design

NASA Technical Reports Server (NTRS)

Newman, Dava

2003-01-01

The primary aim of this research effort was to advance the current understanding of astronauts' capabilities and limitations in space-suited EVA by developing models of the constitutive and compatibility relations of a space suit, based on experimental data gained from human test subjects as well as a 12 degree-of-freedom human-sized robot, and utilizing these fundamental relations to estimate a human factors performance metric for space suited EVA work. The three specific objectives are to: 1) Compile a detailed database of torques required to bend the joints of a space suit, using realistic, multi- joint human motions. 2) Develop a mathematical model of the constitutive relations between space suit joint torques and joint angular positions, based on experimental data and compare other investigators' physics-based models to experimental data. 3) Estimate the work envelope of a space suited astronaut, using the constitutive and compatibility relations of the space suit. The body of work that makes up this report includes experimentation, empirical and physics-based modeling, and model applications. A detailed space suit joint torque-angle database was compiled with a novel experimental approach that used space-suited human test subjects to generate realistic, multi-joint motions and an instrumented robot to measure the torques required to accomplish these motions in a space suit. Based on the experimental data, a mathematical model is developed to predict joint torque from the joint angle history. Two physics-based models of pressurized fabric cylinder bending are compared to experimental data, yielding design insights. The mathematical model is applied to EVA operations in an inverse kinematic analysis coupled to the space suit model to calculate the volume in which space-suited astronauts can work with their hands, demonstrating that operational human factors metrics can be predicted from fundamental space suit information.

Challenges of Electronic Medical Surveillance Systems

DTIC Science & Technology

2004-06-01

More sophisticated approaches, such as regression models and classical autoregressive moving average ( ARIMA ) models that make estimates based on...with those predicted by a mathematical model . The primary benefit of ARIMA models is their ability to correct for local trends in the data so that...works well, for example, during a particularly severe flu season, where prolonged periods of high visit rates are adjusted to by the ARIMA model , thus

Estimating the effects of Cry1F Bt-maize pollen on non-target Lepidoptera using a mathematical model of exposure

PubMed Central

Perry, Joe N; Devos, Yann; Arpaia, Salvatore; Bartsch, Detlef; Ehlert, Christina; Gathmann, Achim; Hails, Rosemary S; Hendriksen, Niels B; Kiss, Jozsef; Messéan, Antoine; Mestdagh, Sylvie; Neemann, Gerd; Nuti, Marco; Sweet, Jeremy B; Tebbe, Christoph C

2012-01-01

In farmland biodiversity, a potential risk to the larvae of non-target Lepidoptera from genetically modified (GM) Bt-maize expressing insecticidal Cry1 proteins is the ingestion of harmful amounts of pollen deposited on their host plants. A previous mathematical model of exposure quantified this risk for Cry1Ab protein. We extend this model to quantify the risk for sensitive species exposed to pollen containing Cry1F protein from maize event 1507 and to provide recommendations for management to mitigate this risk. A 14-parameter mathematical model integrating small- and large-scale exposure was used to estimate the larval mortality of hypothetical species with a range of sensitivities, and under a range of simulated mitigation measures consisting of non-Bt maize strips of different widths placed around the field edge. The greatest source of variability in estimated mortality was species sensitivity. Before allowance for effects of large-scale exposure, with moderate within-crop host-plant density and with no mitigation, estimated mortality locally was <10% for species of average sensitivity. For the worst-case extreme sensitivity considered, estimated mortality locally was 99·6% with no mitigation, although this estimate was reduced to below 40% with mitigation of 24-m-wide strips of non-Bt maize. For highly sensitive species, a 12-m-wide strip reduced estimated local mortality under 1·5%, when within-crop host-plant density was zero. Allowance for large-scale exposure effects would reduce these estimates of local mortality by a highly variable amount, but typically of the order of 50-fold. Mitigation efficacy depended critically on assumed within-crop host-plant density; if this could be assumed negligible, then the estimated effect of mitigation would reduce local mortality below 1% even for very highly sensitive species. Synthesis and applications. Mitigation measures of risks of Bt-maize to sensitive larvae of non-target lepidopteran species can be effective, but depend on host-plant densities which are in turn affected by weed-management regimes. We discuss the relevance for management of maize events where cry1F is combined (stacked) with a herbicide-tolerance trait. This exemplifies how interactions between biota may occur when different traits are stacked irrespective of interactions between the proteins themselves and highlights the importance of accounting for crop management in the assessment of the ecological impact of GM plants. PMID:22496596

Intensity level for exercise training in fibromyalgia by using mathematical models.

PubMed

Lemos, Maria Carolina D; Valim, Valéria; Zandonade, Eliana; Natour, Jamil

2010-03-22

It has not been assessed before whether mathematical models described in the literature for prescriptions of exercise can be used for fibromyalgia syndrome patients. The objective of this paper was to determine how age-predicted heart rate formulas can be used with fibromyalgia syndrome populations as well as to find out which mathematical models are more accurate to control exercise intensity. A total of 60 women aged 18-65 years with fibromyalgia syndrome were included; 32 were randomized to walking training at anaerobic threshold. Age-predicted formulas to maximum heart rate ("220 minus age" and "208 minus 0.7 x age") were correlated with achieved maximum heart rate (HRMax) obtained by spiroergometry. Subsequently, six mathematical models using heart rate reserve (HRR) and age-predicted HRMax formulas were studied to estimate the intensity level of exercise training corresponding to heart rate at anaerobic threshold (HRAT) obtained by spiroergometry. Linear and nonlinear regression models were used for correlations and residues analysis for the adequacy of the models. Age-predicted HRMax and HRAT formulas had a good correlation with achieved heart rate obtained in spiroergometry (r = 0.642; p < 0.05). For exercise prescription in the anaerobic threshold intensity, the percentages were 52.2-60.6% HRR and 75.5-80.9% HRMax. Formulas using HRR and the achieved HRMax showed better correlation. Furthermore, the percentages of HRMax and HRR were significantly higher for the trained individuals (p < 0.05). Age-predicted formulas can be used for estimating HRMax and for exercise prescriptions in women with fibromyalgia syndrome. Karnoven's formula using heart rate achieved in ergometric test showed a better correlation. For the prescription of exercises in the threshold intensity, 52% to 60% HRR or 75% to 80% HRMax must be used in sedentary women with fibromyalgia syndrome and these values are higher and must be corrected for trained patients.

Intensity level for exercise training in fibromyalgia by using mathematical models

PubMed Central

2010-01-01

Background It has not been assessed before whether mathematical models described in the literature for prescriptions of exercise can be used for fibromyalgia syndrome patients. The objective of this paper was to determine how age-predicted heart rate formulas can be used with fibromyalgia syndrome populations as well as to find out which mathematical models are more accurate to control exercise intensity. Methods A total of 60 women aged 18-65 years with fibromyalgia syndrome were included; 32 were randomized to walking training at anaerobic threshold. Age-predicted formulas to maximum heart rate ("220 minus age" and "208 minus 0.7 × age") were correlated with achieved maximum heart rate (HRMax) obtained by spiroergometry. Subsequently, six mathematical models using heart rate reserve (HRR) and age-predicted HRMax formulas were studied to estimate the intensity level of exercise training corresponding to heart rate at anaerobic threshold (HRAT) obtained by spiroergometry. Linear and nonlinear regression models were used for correlations and residues analysis for the adequacy of the models. Results Age-predicted HRMax and HRAT formulas had a good correlation with achieved heart rate obtained in spiroergometry (r = 0.642; p < 0.05). For exercise prescription in the anaerobic threshold intensity, the percentages were 52.2-60.6% HRR and 75.5-80.9% HRMax. Formulas using HRR and the achieved HRMax showed better correlation. Furthermore, the percentages of HRMax and HRR were significantly higher for the trained individuals (p < 0.05). Conclusion Age-predicted formulas can be used for estimating HRMax and for exercise prescriptions in women with fibromyalgia syndrome. Karnoven's formula using heart rate achieved in ergometric test showed a better correlation. For the prescription of exercises in the threshold intensity, 52% to 60% HRR or 75% to 80% HRMax must be used in sedentary women with fibromyalgia syndrome and these values are higher and must be corrected for trained patients. PMID:20307323

Evaluation of leaf wetness duration models for operational use in strawberry disease-warning systems in four US states.

PubMed

Montone, Verona O; Fraisse, Clyde W; Peres, Natalia A; Sentelhas, Paulo C; Gleason, Mark; Ellis, Michael; Schnabel, Guido

2016-11-01

Leaf wetness duration (LWD) plays a key role in disease development and is often used as an input in disease-warning systems. LWD is often estimated using mathematical models, since measurement by sensors is rarely available and/or reliable. A strawberry disease-warning system called "Strawberry Advisory System" (SAS) is used by growers in Florida, USA, in deciding when to spray their strawberry fields to control anthracnose and Botrytis fruit rot. Currently, SAS is implemented at six locations, where reliable LWD sensors are deployed. A robust LWD model would facilitate SAS expansion from Florida to other regions where reliable LW sensors are not available. The objective of this study was to evaluate the use of mathematical models to estimate LWD and time of spray recommendations in comparison to on site LWD measurements. Specific objectives were to (i) compare model estimated and observed LWD and resulting differences in timing and number of fungicide spray recommendations, (ii) evaluate the effects of weather station sensors precision on LWD models performance, and (iii) compare LWD models performance across four states in the USA. The LWD models evaluated were the classification and regression tree (CART), dew point depression (DPD), number of hours with relative humidity equal or greater than 90 % (NHRH ≥90 %), and Penman-Monteith (P-M). P-M model was expected to have the lowest errors, since it is a physically based and thus portable model. Indeed, the P-M model estimated LWD most accurately (MAE <2 h) at a weather station with high precision sensors but was the least accurate when lower precision sensors of relative humidity and estimated net radiation (based on solar radiation and temperature) were used (MAE = 3.7 h). The CART model was the most robust for estimating LWD and for advising growers on fungicide-spray timing for anthracnose and Botrytis fruit rot control and is therefore the model we recommend for expanding the strawberry disease warning beyond Florida, to other locations where weather stations may be deployed with lower precision sensors, and net radiation observations are not available.

Evaluation of leaf wetness duration models for operational use in strawberry disease-warning systems in four US states

NASA Astrophysics Data System (ADS)

Montone, Verona O.; Fraisse, Clyde W.; Peres, Natalia A.; Sentelhas, Paulo C.; Gleason, Mark; Ellis, Michael; Schnabel, Guido

2016-11-01

Leaf wetness duration (LWD) plays a key role in disease development and is often used as an input in disease-warning systems. LWD is often estimated using mathematical models, since measurement by sensors is rarely available and/or reliable. A strawberry disease-warning system called "Strawberry Advisory System" (SAS) is used by growers in Florida, USA, in deciding when to spray their strawberry fields to control anthracnose and Botrytis fruit rot. Currently, SAS is implemented at six locations, where reliable LWD sensors are deployed. A robust LWD model would facilitate SAS expansion from Florida to other regions where reliable LW sensors are not available. The objective of this study was to evaluate the use of mathematical models to estimate LWD and time of spray recommendations in comparison to on site LWD measurements. Specific objectives were to (i) compare model estimated and observed LWD and resulting differences in timing and number of fungicide spray recommendations, (ii) evaluate the effects of weather station sensors precision on LWD models performance, and (iii) compare LWD models performance across four states in the USA. The LWD models evaluated were the classification and regression tree (CART), dew point depression (DPD), number of hours with relative humidity equal or greater than 90 % (NHRH ≥90 %), and Penman-Monteith (P-M). P-M model was expected to have the lowest errors, since it is a physically based and thus portable model. Indeed, the P-M model estimated LWD most accurately (MAE <2 h) at a weather station with high precision sensors but was the least accurate when lower precision sensors of relative humidity and estimated net radiation (based on solar radiation and temperature) were used (MAE = 3.7 h). The CART model was the most robust for estimating LWD and for advising growers on fungicide-spray timing for anthracnose and Botrytis fruit rot control and is therefore the model we recommend for expanding the strawberry disease warning beyond Florida, to other locations where weather stations may be deployed with lower precision sensors, and net radiation observations are not available.

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Estimating in vivo airway surface liquid concentration in trials of inhaled antibiotics.

PubMed

Hasan, M A; Lange, C F

2007-01-01

Antibiotic drugs exhibit concentration dependence in their efficacy. Therefore, ensuring appropriate concentration of these drugs in the relevant body fluid is important for obtaining the desired therapeutic and physiological action. Until recently there had been no suitable method available to measure or estimate concentration of drugs in the human airways resulting from inhaled aerosols or to determine the amount of inhaled antibiotics required to ensure minimum inhibitory concentration of a drug in the airway surface liquid (ASL). In this paper a numerical method is used for estimating local concentration of inhaled pharmaceutical aerosols in different generations of the human tracheobronchial airways. The method utilizes a mathematical lung deposition model to estimate amounts of aerosols depositing in different lung generations, and a recent ASL model along with deposition results to assess the concentration of deposited drugs immediately following inhalation. Examples of concentration estimates for two case studies: one for the antibiotic tobramycin against Pseudomonas aeruginosa, and another for taurolidine against Burkholderia cepacia are presented. The aerosol characteristics, breathing pattern and properties of nebulized solutions were adopted from two recent clinical studies on efficacy of these drugs in cystic fibrosis (CF) patients and from other sources in the literature. While the clinically effective tobramycin showed a concentration higher than the required in vivo concentration, that for the ineffective taurolidine was found to be below the speculated required in vivo concentration. Results of this study thus show that the mathematical ASL model combined with the lung deposition model can be an effective tool for helping decide the optimum dosage of inhaled antibiotic drugs delivered during human clinical trials.

Choosing an Appropriate Modelling Framework for Analysing Multispecies Co-culture Cell Biology Experiments.

PubMed

Markham, Deborah C; Simpson, Matthew J; Baker, Ruth E

2015-04-01

In vitro cell biology assays play a crucial role in informing our understanding of the migratory, proliferative and invasive properties of many cell types in different biological contexts. While mono-culture assays involve the study of a population of cells composed of a single cell type, co-culture assays study a population of cells composed of multiple cell types (or subpopulations of cells). Such co-culture assays can provide more realistic insights into many biological processes including tissue repair, tissue regeneration and malignant spreading. Typically, system parameters, such as motility and proliferation rates, are estimated by calibrating a mathematical or computational model to the observed experimental data. However, parameter estimates can be highly sensitive to the choice of model and modelling framework. This observation motivates us to consider the fundamental question of how we can best choose a model to facilitate accurate parameter estimation for a particular assay. In this work we describe three mathematical models of mono-culture and co-culture assays that include different levels of spatial detail. We study various spatial summary statistics to explore if they can be used to distinguish between the suitability of each model over a range of parameter space. Our results for mono-culture experiments are promising, in that we suggest two spatial statistics that can be used to direct model choice. However, co-culture experiments are far more challenging: we show that these same spatial statistics which provide useful insight into mono-culture systems are insufficient for co-culture systems. Therefore, we conclude that great care ought to be exercised when estimating the parameters of co-culture assays.

A Novel Physiology-Based Mathematical Model to Estimate Red Blood Cell Lifespan in Different Human Age Groups.

PubMed

An, Guohua; Widness, John A; Mock, Donald M; Veng-Pedersen, Peter

2016-09-01

Direct measurement of red blood cell (RBC) survival in humans has improved from the original accurate but limited differential agglutination technique to the current reliable, safe, and accurate biotin method. Despite this, all of these methods are time consuming and require blood sampling over several months to determine the RBC lifespan. For situations in which RBC survival information must be obtained quickly, these methods are not suitable. With the exception of adults and infants, RBC survival has not been extensively investigated in other age groups. To address this need, we developed a novel, physiology-based mathematical model that quickly estimates RBC lifespan in healthy individuals at any age. The model is based on the assumption that the total number of RBC recirculations during the lifespan of each RBC (denoted by N max) is relatively constant for all age groups. The model was initially validated using the data from our prior infant and adult biotin-labeled red blood cell studies and then extended to the other age groups. The model generated the following estimated RBC lifespans in 2-year-old, 5-year-old, 8-year-old, and 10-year-old children: 62, 74, 82, and 86 days, respectively. We speculate that this model has useful clinical applications. For example, HbA1c testing is not reliable in identifying children with diabetes because HbA1c is directly affected by RBC lifespan. Because our model can estimate RBC lifespan in children at any age, corrections to HbA1c values based on the model-generated RBC lifespan could improve diabetes diagnosis as well as therapy in children.

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy.

PubMed

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristeidis; Schwartz, Sorell L; Bies, Robert; Freedman, Immanuel

2018-06-19

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology. Copyright © 2018 Elsevier Ltd. All rights reserved.

Parameters estimation of sandwich beam model with rigid polyurethane foam core

NASA Astrophysics Data System (ADS)

Barbieri, Nilson; Barbieri, Renato; Winikes, Luiz Carlos

2010-02-01

In this work, the physical parameters of sandwich beams made with the association of hot-rolled steel, Polyurethane rigid foam and High Impact Polystyrene, used for the assembly of household refrigerators and food freezers are estimated using measured and numeric frequency response functions (FRFs). The mathematical models are obtained using the finite element method (FEM) and the Timoshenko beam theory. The physical parameters are estimated using the amplitude correlation coefficient and genetic algorithm (GA). The experimental data are obtained using the impact hammer and four accelerometers displaced along the sample (cantilevered beam). The parameters estimated are Young's modulus and the loss factor of the Polyurethane rigid foam and the High Impact Polystyrene.

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.

A Review of the “Bolus Guide,” A New Insulin Bolus Dosing Support Tool Based on Selection of Carbohydrate Ranges

PubMed Central

Pańkowska, Ewa

2010-01-01

In this issue of Journal of Diabetes Science and Technology, Shapira and colleagues present new concepts of carbohydrate load estimation in intensive insulin therapy. By using a mathematical model, they attempt to establish how accurately carbohydrate food content should be maintained in order to keep postprandial blood glucose levels in the recommended range. Their mathematical formula, the “bolus guide” (BG), is verified by simulating prandial insulin dosing and responding to proper blood glucose levels. Different variants such as insulin sensitivity factor, insulin-to-carbohydrate ratio, and target blood glucose were taken into this formula in establishing the calculated proper insulin dose. The new approach presented here estimates the carbohydrate content by rearranging the carbohydrate load instead of the simple point estimation that the current bolus calculators (BCs) use. Computerized estimations show that the BG directives, as compared to a BC, result in more glucose levels above 200 mg/dl and thus indicate less hypoglycemia readings. PMID:20663454

Parameters estimation for reactive transport: A way to test the validity of a reactive model

NASA Astrophysics Data System (ADS)

Aggarwal, Mohit; Cheikh Anta Ndiaye, Mame; Carrayrou, Jérôme

The chemical parameters used in reactive transport models are not known accurately due to the complexity and the heterogeneous conditions of a real domain. We will present an efficient algorithm in order to estimate the chemical parameters using Monte-Carlo method. Monte-Carlo methods are very robust for the optimisation of the highly non-linear mathematical model describing reactive transport. Reactive transport of tributyltin (TBT) through natural quartz sand at seven different pHs is taken as the test case. Our algorithm will be used to estimate the chemical parameters of the sorption of TBT onto the natural quartz sand. By testing and comparing three models of surface complexation, we show that the proposed adsorption model cannot explain the experimental data.

Relationships between autofocus methods for SAR and self-survey techniques for SONAR. [Synthetic Aperture Radar (SAR)

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

Wahl, D.E.; Jakowatz, C.V. Jr.; Ghiglia, D.C.

1991-01-01

Autofocus methods in SAR and self-survey techniques in SONAR have a common mathematical basis in that they both involve estimation and correction of phase errors introduced by sensor position uncertainties. Time delay estimation and correlation methods have been shown to be effective in solving the self-survey problem for towed SONAR arrays. Since it can be shown that platform motion errors introduce similar time-delay estimation problems in SAR imaging, the question arises as to whether such techniques could be effectively employed for autofocus of SAR imagery. With a simple mathematical model for motion errors in SAR, we will show why suchmore » correlation/time-delay techniques are not nearly as effective as established SAR autofocus algorithms such as phase gradient autofocus or sub-aperture based methods. This analysis forms an important bridge between signal processing methodologies for SAR and SONAR. 5 refs., 4 figs.« less

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

NASA Technical Reports Server (NTRS)

Oman, C. M.

1982-01-01

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

The YAV-8B simulation and modeling. Volume 2: Program listing

NASA Technical Reports Server (NTRS)

1983-01-01

Detailed mathematical models of varying complexity representative of the YAV-8B aircraft are defined and documented. These models are used in parameter estimation and in linear analysis computer programs while investigating YAV-8B aircraft handling qualities. Both a six degree of freedom nonlinear model and a linearized three degree of freedom longitudinal and lateral directional model were developed. The nonlinear model is based on the mathematical model used on the MCAIR YAV-8B manned flight simulator. This simulator model has undergone periodic updating based on the results of approximately 360 YAV-8B flights and 8000 hours of wind tunnel testing. Qualified YAV-8B flight test pilots have commented that the handling qualities characteristics of the simulator are quite representative of the real aircraft. These comments are validated herein by comparing data from both static and dynamic flight test maneuvers to the same obtained using the nonlinear program.

High pressure common rail injection system modeling and control.

PubMed

Wang, H P; Zheng, D; Tian, Y

2016-07-01

In this paper modeling and common-rail pressure control of high pressure common rail injection system (HPCRIS) is presented. The proposed mathematical model of high pressure common rail injection system which contains three sub-systems: high pressure pump sub-model, common rail sub-model and injector sub-model is a relative complicated nonlinear system. The mathematical model is validated by the software Matlab and a virtual detailed simulation environment. For the considered HPCRIS, an effective model free controller which is called Extended State Observer - based intelligent Proportional Integral (ESO-based iPI) controller is designed. And this proposed method is composed mainly of the referred ESO observer, and a time delay estimation based iPI controller. Finally, to demonstrate the performances of the proposed controller, the proposed ESO-based iPI controller is compared with a conventional PID controller and ADRC. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

First pass intestinal and liver metabolism of paracetamol in a microfluidic platform coupled with a mathematical modeling as a means of evaluating ADME processes in humans.

PubMed

Prot, Jean Matthieu; Maciel, Luis; Bricks, Thibault; Merlier, Franck; Cotton, Jérôme; Paullier, Patrick; Bois, Fréderic Yves; Leclerc, Eric

2014-10-01

We developed a microfluidic platform to investigate paracetamol intestinal and liver first pass metabolism. This approach was coupled with a mathematical model to estimate intrinsic in vitro parameters and to predict in vivo processes. The kinetic modeling estimated the paracetamol and paracetamol sulfate permeabilities, the sulfate and glucuronide effluxes in the intestine compartment. Based on a gut model, we estimated intrinsic intestinal clearance of between 26 and 77 L/h for paracetamol in humans, a permeability of 10 L/h, and a gut availability between 0.17 and 0.53 (compared to 0.95-1 in vivo). The role played by the liver in paracetamol metabolism was estimated via in vitro intrinsic clearances of 7.6, 13.6, and 11.5 µL/min/10(6) cells for HepG2/C3a, rat primary hepatocytes, and human primary hepatocytes, respectively. Based on a parallel tube model to describe the liver, the paracetamol hepatic clearance, and the paracetamol hepatic availability in humans were estimated at 6.5 mL/min/kg of bodyweight (BDW) and 0.7, respectively (when compared to 5 mL/min/kg of BDW and 0.77 to 0.88 for in vivo values, respectively). The drug availability was predicted ranging between 0.24 and 0.41 (0.88 in vivo). The overall approach provided a first step in an integrated strategy combining in silico/in vitro methods based on microfluidic for evaluating drug absorption, distribution and metabolism processes. © 2014 Wiley Periodicals, Inc.

Estimation of the Level of Cognitive Development of a Preschool Child Using the System of Situations with Mathematical Contents

ERIC Educational Resources Information Center

Gorev, Pavel M.; Bichurina, Svetlana Y.; Yakupova, Rufiya M.; Khairova, Irina V.

2016-01-01

Cognitive development of personality can be considered as one of the key directions of preschool education presented in the world practice, where preschool programs are educational ones, and preschool education is the first level of the general education. Thereby the purpose of the research is to create a model of reliable estimation of cognitive…

Comparison of Chronic and Acute Models of Risk on Mathematics Achievement and Growth

ERIC Educational Resources Information Center

Desjardins, Christopher David; Cutuli, J.J.; Herbers, Janette E.; Chan, Chi-Keung; Hinz, Elizabeth; Heistad, David; Long, Jeffrey D.; Masten, Ann S.

2011-01-01

The rate of poverty for children in the United States is far higher than for other advantaged nations (Payne & Biddle, 1999) with an estimated 13.3 million children, 18% of all children, living below the poverty threshold (U. S. Bureau of the Census, 2008). An estimated 5.8 million children live in extreme poverty where their families earn less…

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

A Primary Classroom Inquiry: Estimating the Height of a Tree

ERIC Educational Resources Information Center

Brown, Natalie; Watson, Jane; Wright, Suzie; Skalicky, Jane

2011-01-01

Measurement is one of the key areas of study in mathematics and features prominently in the "Australian Curriculum: Mathematics" (ACARA, 2010). In this set of investigations requiring students to estimate indirectly the height of a tree they are encouraged to use the "power of mathematical reasoning" and "apply their…

Strategies Students with and without Mathematics Disabilities Use When Estimating Fractions on Number Lines

ERIC Educational Resources Information Center

Zhang, Dake; Stecker, Pamela; Beqiri, Klesti

2017-01-01

We examined faulty strategies with possible underlying misconceptions, as well as execution mistakes, among middle schoolers with and without mathematics disabilities when estimating fractions on number lines. Fifty-one middle schoolers participated in this study, including 27 students with mathematics disabilities. Participants were asked to…

A test and re-estimation of Taylor's empirical capacity-reserve relationship

USGS Publications Warehouse

Long, K.R.

2009-01-01

In 1977, Taylor proposed a constant elasticity model relating capacity choice in mines to reserves. A test of this model using a very large (n = 1,195) dataset confirms its validity but obtains significantly different estimated values for the model coefficients. Capacity is somewhat inelastic with respect to reserves, with an elasticity of 0.65 estimated for open-pit plus block-cave underground mines and 0.56 for all other underground mines. These new estimates should be useful for capacity determinations as scoping studies and as a starting point for feasibility studies. The results are robust over a wide range of deposit types, deposit sizes, and time, consistent with physical constraints on mine capacity that are largely independent of technology. ?? 2009 International Association for Mathematical Geology.

AIR MONITOR SITING BY OBJECTIVE

EPA Science Inventory

A method is developed whereby measured pollutant concentrations can be used in conjunction with a mathematical air quality model to estimate the full spatial and temporal concentration distributions of the pollutants over a given region. The method is based on the application of ...

Health Risk of Exposure to Atmospheric Pollutant Particles

EPA Science Inventory

In relation to multi-component mixture nature of atmospheric PM, this presentation will discuss methods for estimating the respiratory internal dose by experiment and mathematical modeling, limitations of each method and interpretations of the results in the context of health ris...

EFFECTIVENESS OF SOIL AND WATER CONSERVATION PRACTICES FOR POLLUTION CONTROL

EPA Science Inventory

The potential water quality effects and economic implications of soil and water conservation practices (SWCPs) are identified. Method for estimating the effects of SWCPs on pollutant losses from croplands are presented. Mathematical simulation and linear programming models were u...

Computational Control of Flexible Aerospace Systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Investigation into solar drying of potato: effect of sample geometry on drying kinetics and CO2 emissions mitigation.

PubMed

Tripathy, P P

2015-03-01

Drying experiments have been performed with potato cylinders and slices using a laboratory scale designed natural convection mixed-mode solar dryer. The drying data were fitted to eight different mathematical models to predict the drying kinetics, and the validity of these models were evaluated statistically through coefficient of determination (R(2)), root mean square error (RMSE) and reduced chi-square (χ (2)). The present investigation showed that amongst all the mathematical models studied, the Modified Page model was in good agreement with the experimental drying data for both potato cylinders and slices. A mathematical framework has been proposed to estimate the performance of the food dryer in terms of net CO2 emissions mitigation potential along with unit cost of CO2 mitigation arising because of replacement of different fossil fuels by renewable solar energy. For each fossil fuel replaced, the gross annual amount of CO2 as well as net amount of annual CO2 emissions mitigation potential considering CO2 emissions embodied in the manufacture of mixed-mode solar dryer has been estimated. The CO2 mitigation potential and amount of fossil fuels saved while drying potato samples were found to be the maximum for coal followed by light diesel oil and natural gas. It was inferred from the present study that by the year 2020, 23 % of CO2 emissions can be mitigated by the use of mixed-mode solar dryer for drying of agricultural products.

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

PubMed

Boden, Lisa A; McKendrick, Iain J

2017-01-01

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

Placental Volumetry by 2-D Sonography with a New Mathematical Formula: Prospective Study on the Shell of a Spherical Sector Model.

PubMed

Kozinszky, Zoltan; Surányi, Andrea; Péics, Hajnalka; Molnár, András; Pál, Attila

2015-08-01

The aim of this study was to determine the utility of a new mathematical model in volumetric assessment of the placenta using 2-D ultrasound. Placental volumetry was performed in a prospective cross-sectional survey by virtual organ computer-aided analysis (VOCAL) with the help of a shell-off method in 346 uncomplicated pregnancies according to STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) guidelines. Furthermore, placental thickness, length and height were measured with the 2-D technique to estimate placental volume based on the mathematical formula for the volume of "the shell of the spherical sector." Fetal size was also assessed by 2-D sonography. The placental volumes measured by 2-D and 3-D techniques had a correlation of 0.86. In the first trimester, the correlation was 0.82, and later during pregnancy, it was 0.86. Placental volumetry using "the circle-shaped shell of the spherical sector" mathematical model with 2-D ultrasound technique may be introduced into everyday practice to screen for placental volume deviations associated with adverse pregnancy outcome. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Cognitive diagnosis modelling incorporating item response times.

PubMed

Zhan, Peida; Jiao, Hong; Liao, Dandan

2018-05-01

To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy 'and' gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow-up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RTs into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters. © 2017 The British Psychological Society.

A nonlinear SIR with stability

NASA Astrophysics Data System (ADS)

Trisilowati, Darti, I.; Fitri, S.

2014-02-01

The aim of this work is to develop a mathematical model of a nonlinear susceptible-infectious-removed (SIR) epidemic model with vaccination. We analyze the stability of the model by linearizing the model around the equilibrium point. Then, diphtheria data from East Java province is fitted to the model. From these estimated parameters, we investigate which parameters that play important role in the epidemic model. Some numerical simulations are given to illustrate the analytical results and the behavior of the model.

Space shuttle propulsion parameter estimation using optimal estimation techniques

NASA Technical Reports Server (NTRS)

1983-01-01

The first twelve system state variables are presented with the necessary mathematical developments for incorporating them into the filter/smoother algorithm. Other state variables, i.e., aerodynamic coefficients can be easily incorporated into the estimation algorithm, representing uncertain parameters, but for initial checkout purposes are treated as known quantities. An approach for incorporating the NASA propulsion predictive model results into the optimal estimation algorithm was identified. This approach utilizes numerical derivatives and nominal predictions within the algorithm with global iterations of the algorithm. The iterative process is terminated when the quality of the estimates provided no longer significantly improves.

Partitioning of net carbon dioxide flux measured by automatic transparent chamber

NASA Astrophysics Data System (ADS)

Dyukarev, EA

2018-03-01

Mathematical model was developed for describing carbon dioxide fluxes at open sedge-sphagnum fen during growing season. The model was calibrated using the results of observations from automatic transparent chamber and it allows us to estimate autotrophic, heterotrophic and ecosystem respiration fluxes, gross and net primary vegetation production, and the net carbon balance.

Model of Market Share Affected by Social Media Reputation

NASA Astrophysics Data System (ADS)

Ishii, Akira; Kawahata, Yasuko; Goto, Ujo

Proposal of market theory to put the effect of social media into account is presented in this paper. The standard market share model in economics is employed as a market theory and the effect of social media is considered quantitatively using the mathematical model for hit phenomena. Using this model, we can estimate the effect of social media in market share as a simple market model simulation using our proposed method.

Parameter Estimation for Viscoplastic Material Modeling

NASA Technical Reports Server (NTRS)

Saleeb, Atef F.; Gendy, Atef S.; Wilt, Thomas E.

1997-01-01

A key ingredient in the design of engineering components and structures under general thermomechanical loading is the use of mathematical constitutive models (e.g. in finite element analysis) capable of accurate representation of short and long term stress/deformation responses. In addition to the ever-increasing complexity of recent viscoplastic models of this type, they often also require a large number of material constants to describe a host of (anticipated) physical phenomena and complicated deformation mechanisms. In turn, the experimental characterization of these material parameters constitutes the major factor in the successful and effective utilization of any given constitutive model; i.e., the problem of constitutive parameter estimation from experimental measurements.

A novel analytical solution for estimating aquifer properties within a horizontally anisotropic aquifer bounded by a stream

NASA Astrophysics Data System (ADS)

Huang, Yibin; Zhan, Hongbin; Knappett, Peter S. K.

2018-04-01

Past studies modeling stream-aquifer interaction commonly account for vertical anisotropy in hydraulic conductivity, but rarely address horizontal anisotropy, which may exist in certain sedimentary environments. If present, horizontal anisotropy will greatly impact stream depletion and the amount of recharge a pumped aquifer captures from the river. This scenario requires a different and somewhat more sophisticated mathematical approach to model and interpret pumping test results than previous models used to describe captured recharge from rivers. In this study, a new mathematical model is developed to describe the spatiotemporal distribution of drawdown from stream-bank pumping with a well screened across a horizontally anisotropic, confined aquifer, laterally bounded by a river. This new model is used to estimate four aquifer parameters including the magnitude and directions of major and minor principal transmissivities and storativity based on the observed drawdown-time curves within a minimum of three non-collinear observation wells. In order to approve the efficacy of the new model, a MATLAB script file is programmed to conduct a four-parameter inversion to estimate the four parameters of concern. By comparing the results of analytical and numerical inversions, the accuracy of estimated results from both inversions is acceptable, but the MATLAB program sometimes becomes problematic because of the difficulty of separating the local minima from the global minima. It appears that the new analytical model of this study is applicable and robust in estimating parameter values for a horizontally anisotropic aquifer laterally bounded by a stream. Besides that, the new model calculates stream depletion rate as a function of stream-bank pumping. Unique to horizontally anisotropic and homogeneous aquifers, the stream depletion rate at any given pumping rate depends closely on the horizontal anisotropy ratio and the direction of the principle transmissivities relative to the stream-bank.

Thirty Years of Nonparametric Item Response Theory.

ERIC Educational Resources Information Center

Molenaar, Ivo W.

2001-01-01

Discusses relationships between a mathematical measurement model and its real-world applications. Makes a distinction between large-scale data matrices commonly found in educational measurement and smaller matrices found in attitude and personality measurement. Also evaluates nonparametric methods for estimating item response functions and…

BMDExpress Data Viewer: A Visualization Tool to Analyze BMDExpress Datasets(SoTC)

EPA Science Inventory

Background: Benchmark Dose (BMD) modelling is a mathematical approach used to determine where a dose-response change begins to take place relative to controls following chemical exposure. BMDs are being increasingly applied in regulatory toxicology to estimate acceptable exposure...

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

DOT National Transportation Integrated Search

1971-06-01

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

BMDExpress Data Viewer: A Visualization Tool to Analyze BMDExpress Datasets (STC symposium)

EPA Science Inventory

Background: Benchmark Dose (BMD) modelling is a mathematical approach used to determine where a dose-response change begins to take place relative to controls following chemical exposure. BMDs are being increasingly applied in regulatory toxicology to estimate acceptable exposure...

Modeling the Epidemiology of Cholera to Prevent Disease Transmission in Developing Countries

PubMed Central

MUKANDAVIRE, ZINDOGA; MORRIS, J. GLENN

2015-01-01

Cholera remains an important global cause of morbidity and mortality, which is capable of causing periodic epidemic disease. A number of mathematical models have been developed to help in understanding the dynamics of cholera outbreaks and for use as a tool in planning interventions, including vaccination campaigns. We have explored the utility of models in assessing the spread of cholera in the recent epidemics in Zimbabwe and Haiti. In both instances, a mathematical model was formulated and fitted to cumulative cholera cases to estimate the basic reproductive number ℜ0, and the partial reproductive numbers reflecting potential differences in environmental-to-human versus human-to-human transmission were quantified. In Zimbabwe, estimated ℜ0 for the epidemic using aggregated data at the national level was 1.15; in Haiti, it was 1.55. However, when calculated at a provincial/departmental level, estimated basic reproductive numbers were highly heterogeneous, with a range of 1.11 to 2.72 in Zimbabwe and 1.06 to 2.63 in Haiti. Our models suggest that the underlying patterns of cholera transmission varied widely from region to region, with a corresponding variation in the amenability of outbreaks to control measures such as immunization. These data underscore the heterogeneity of transmission dynamics, potentially linked to differences in environment, socio-economic conditions, and cultural practices. They also highlight the potential utility of these types of models in guiding development of public health intervention strategies. PMID:26185087

Longitudinal development of number line estimation and mathematics performance in primary school children.

PubMed

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

2015-06-01

Children's ability to relate number to a continuous quantity abstraction visualized as a number line is widely accepted to be predictive of mathematics achievement. However, a debate has emerged with respect to how children's placements are distributed on this number line across development. In the current study, different models were applied to children's longitudinal number placement data to get more insight into the development of number line representations in kindergarten and early primary school years. In addition, longitudinal developmental relations between number line placements and mathematical achievement, measured with a national test of mathematics, were investigated using cross-lagged panel modeling. A group of 442 children participated in a 3-year longitudinal study (ages 5-8 years) in which they completed a number-to-position task every 6 months. Individual number line placements were fitted to various models, of which a one-anchor power model provided the best fit for many of the placements at a younger age (5 or 6 years) and a two-anchor power model provided better fit for many of the children at an older age (7 or 8 years). The number of children who made linear placements also grew with age. Cross-lagged panel analyses indicated that the best fit was provided with a model in which number line acuity and mathematics performance were mutually predictive of each other rather than models in which one ability predicted the other in a non-reciprocal way. This indicates that number line acuity should not be seen as a predictor of math but that both skills influence each other during the developmental process. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Probabilistic/Fracture-Mechanics Model For Service Life

NASA Technical Reports Server (NTRS)

Watkins, T., Jr.; Annis, C. G., Jr.

1991-01-01

Computer program makes probabilistic estimates of lifetime of engine and components thereof. Developed to fill need for more accurate life-assessment technique that avoids errors in estimated lives and provides for statistical assessment of levels of risk created by engineering decisions in designing system. Implements mathematical model combining techniques of statistics, fatigue, fracture mechanics, nondestructive analysis, life-cycle cost analysis, and management of engine parts. Used to investigate effects of such engine-component life-controlling parameters as return-to-service intervals, stresses, capabilities for nondestructive evaluation, and qualities of materials.

[Effect of the ISS Russian segment configuration on the service module radiation environment].

PubMed

Mitrikas, V G

2011-01-01

Mathematical modeling of variations in the Service module radiation environment as a function of ISS Russian segment configuration was carried out using models of the RS modules and a spherical humanoid phantom. ISS reconfiguration impacted significantly only the phantom brought into the transfer compartment (ExT). The Radiation Safety Service prohibition for cosmonauts to stay in this compartment during solar flare events remains valid. In all other instances, error of dose estimation is higher as compared to dose value estimation with consideration for ISS RS reconfiguration.

Model of continual metabolism species for estimating stability of CELSS and natural ecosystems

NASA Astrophysics Data System (ADS)

Bartsev, S. I.

Estimation of stability range of natural and man-made ecosystems is necessary for effective control of them However traditional ecological models usually underestimate stability of real ecosystems It takes place due to the usage of fixed stoichiometry model of metabolism The objective is in creating theoretical and mathematical models for adequate description of both man-made and natural ecological systems A concept of genetically fixed but metabolically flexible species is considered in the paper According to the concept the total flow of matter through ecological system is supported at almost constant level depending on energy income by flexibility of metabolic organization of genetic species It is shown introducing continual metabolism species extends the range of stability making its estimation more adequate to real ecological systems

A mathematical formula to estimate in vivo thyroid volume from two-dimensional ultrasonography.

PubMed

Trimboli, Pierpaolo; Ruggieri, Massimo; Fumarola, Angela; D'Alò, Michele; Straniero, Andrea; Maiuolo, Amelia; Ulisse, Salvatore; D'Armiento, Massimino

2008-08-01

The determination of thyroid volume (TV) is required for the management of thyroid diseases. Since two-dimensional ultrasonography (2D-US) has become the accepted method for the assessment of TV (2D-US-TV), we verified whether it accurately assesses postsurgical measured TV (PS-TV). In 92 patients who underwent total thyroidectomy by conventional cervicotomy, 2D-US-TV obtained by the ellipsoid volume formula was compared to PS-TV, determined by the Archimedes' principle. Mean 2D-US-TV (23.9 +/- 14.8 mL) was significantly lower than mean PS-TV (33.4 +/- 20.1 mL). Underestimation was observed in 77% of cases, and it was related to gland multinodularity and/or nodular involvement of the isthmus, while 2D-US-TV matched the PS-TV in the remaining 21 cases (23%). A mathematical formula, to estimate PS-TV from US-TV, was derived using a linear model (Calculated-TV = [1.24 x 2D-US-TV]+ 3.66). Calculated-TV (mean value 33.4 +/- 18.3 mL) significantly (p < 0.01) increased from 21 (23%) to 31 (34%) of the cases that matched PS-TV. In addition, it significantly (p < 0.01) decreased from 77% to 27% the percentage of cases where PS-TV was underestimated as well as the range of the disagreement from 245% to 92%. This study shows that 2D-US does not provide an accurate estimation of TV and suggests that it can be improved by a mathematical model different from the ellipsoid model. If confirmed in prospective studies, this may contribute to a more appropriate management of thyroid diseases.

Estimation of the dynamics and rate of transmission of classical swine fever (hog cholera) in wild pigs.

PubMed Central

Hone, J.; Pech, R.; Yip, P.

1992-01-01

Infectious diseases establish in a population of wildlife hosts when the number of secondary infections is greater than or equal to one. To estimate whether establishment will occur requires extensive experience or a mathematical model of disease dynamics and estimates of the parameters of the disease model. The latter approach is explored here. Methods for estimating key model parameters, the transmission coefficient (beta) and the basic reproductive rate (RDRS), are described using classical swine fever (hog cholera) in wild pigs as an example. The tentative results indicate that an acute infection of classical swine fever will establish in a small population of wild pigs. Data required for estimation of disease transmission rates are reviewed and sources of bias and alternative methods discussed. A comprehensive evaluation of the biases and efficiencies of the methods is needed. PMID:1582476

Software for Estimating Costs of Testing Rocket Engines

NASA Technical Reports Server (NTRS)

Hines, Merlon M.

2004-01-01

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Software for Estimating Costs of Testing Rocket Engines

NASA Technical Reports Server (NTRS)

Hines, Merion M.

2002-01-01

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Software for Estimating Costs of Testing Rocket Engines

NASA Technical Reports Server (NTRS)

Hines, Merlon M.

2003-01-01

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Estimation of maximum transdermal flux of nonionized xenobiotics from basic physicochemical determinants

PubMed Central

Milewski, Mikolaj; Stinchcomb, Audra L.

2012-01-01

An ability to estimate the maximum flux of a xenobiotic across skin is desirable both from the perspective of drug delivery and toxicology. While there is an abundance of mathematical models describing the estimation of drug permeability coefficients, there are relatively few that focus on the maximum flux. This article reports and evaluates a simple and easy-to-use predictive model for the estimation of maximum transdermal flux of xenobiotics based on three common molecular descriptors: logarithm of octanol-water partition coefficient, molecular weight and melting point. The use of all three can be justified on the theoretical basis of their influence on the solute aqueous solubility and the partitioning into the stratum corneum lipid domain. The model explains 81% of the variability in the permeation dataset comprised of 208 entries and can be used to obtain a quick estimate of maximum transdermal flux when experimental data is not readily available. PMID:22702370

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

PubMed

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

2016-01-01

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

A critical review of the field application of a mathematical model of malaria eradication

PubMed Central

Nájera, J. A.

1974-01-01

A malaria control field research trial in northern Nigeria was planned with the aid of a computer simulation based on Macdonald's mathematical model of malaria epidemiology. Antimalaria attack was based on a combination of mass drug administration (chloroquine and pyrimethamine) and DDT house spraying. The observed results were at great variance with the predictions of the model. The causes of these discrepancies included inadequate estimation of the model's basic variables, and overestimation, in planning the simulation, of the effects of the attack measures and of the degree of perfection attainable by their application. The discrepancies were to a great extent also due to deficiencies in the model. An analysis is made of those considered to be the most important. It is concluded that research efforts should be encouraged to increase our knowledge of the basic epidemiological factors, their variation and correlations, and to formulate more realistic and useful theoretical models. PMID:4156197

Three-dimensional FLASH Laser Radar Range Estimation via Blind Deconvolution

DTIC Science & Technology

2009-10-01

scene can result in errors due to several factors including the optical spatial impulse response, detector blurring, photon noise , timing jitter, and...estimation error include spatial blur, detector blurring, noise , timing jitter, and inter-sample targets. Unlike previous research, this paper ac- counts...for pixel coupling by defining the range image mathematical model as a 2D convolution between the system spatial impulse response and the object (target

Life Cycle Assessment of Vehicle Lightweighting: Novel Mathematical Methods to Estimate Use-Phase Fuel Consumption.

PubMed

Kim, Hyung Chul; Wallington, Timothy J; Sullivan, John L; Keoleian, Gregory A

2015-08-18

Lightweighting is a key strategy to improve vehicle fuel economy. Assessing the life-cycle benefits of lightweighting requires a quantitative description of the use-phase fuel consumption reduction associated with mass reduction. We present novel methods of estimating mass-induced fuel consumption (MIF) and fuel reduction values (FRVs) from fuel economy and dynamometer test data in the U.S. Environmental Protection Agency (EPA) database. In the past, FRVs have been measured using experimental testing. We demonstrate that FRVs can be mathematically derived from coast down coefficients in the EPA vehicle test database avoiding additional testing. MIF and FRVs calculated for 83 different 2013 MY vehicles are in the ranges 0.22-0.43 and 0.15-0.26 L/(100 km 100 kg), respectively, and increase to 0.27-0.53 L/(100 km 100 kg) with powertrain resizing to retain equivalent vehicle performance. We show how use-phase fuel consumption can be estimated using MIF and FRVs in life cycle assessments (LCAs) of vehicle lightweighting from total vehicle and vehicle component perspectives with, and without, powertrain resizing. The mass-induced fuel consumption model is illustrated by estimating lifecycle greenhouse gas (GHG) emission benefits from lightweighting a grille opening reinforcement component using magnesium or carbon fiber composite for 83 different vehicle models.

Monitoring and Prediction of Precipitable Water Vapor using GPS data in Turkey

NASA Astrophysics Data System (ADS)

Ansari, Kutubuddin; Althuwaynee, Omar F.; Corumluoglu, Ozsen

2016-12-01

Although Global Positioning System (GPS) primarily provide accurate estimates of position, velocity and time of the receiver, as the signals pass through the atmoshphere carrying its signatures, thus offers opportunities for atmoshpheric applications. Precipitable water vapor (PWV) is a vital component of the atmosphere and significantly influences atmospheric processes like rainfall and atmospheric temperature. The developing networks of continuously operating GPS can be used to efficiently estimate PWV. The Turkish Permanent GPS Network (TPGN) is employed to monitor PWV information in Turkey. This work primarily aims to derive long-term data of PWV by using atmospheric path delays observed through continuously operating TPGN from November 2014 to October 2015. A least square mathematical approach was then applied to establish the relation of the observed PWV to rainfall and temperature. The modeled PWV was correlated with PWV estimated from GPS data, with an average correlation of 67.10 %-88.60 %. The estimated root mean square error (RMSE) varied from 2.840 to 6.380, with an average of 4.697. Finally, data of TPGN, rainfall, and temperature were obtained for less than 2 months (November 2015 to December 2015) and assessed to validate the mathematical model. This study provides a basis for determining PWV by using rainfall and temperature data.

Online machining error estimation method of numerical control gear grinding machine tool based on data analysis of internal sensors

NASA Astrophysics Data System (ADS)

Zhao, Fei; Zhang, Chi; Yang, Guilin; Chen, Chinyin

2016-12-01

This paper presents an online estimation method of cutting error by analyzing of internal sensor readings. The internal sensors of numerical control (NC) machine tool are selected to avoid installation problem. The estimation mathematic model of cutting error was proposed to compute the relative position of cutting point and tool center point (TCP) from internal sensor readings based on cutting theory of gear. In order to verify the effectiveness of the proposed model, it was simulated and experimented in gear generating grinding process. The cutting error of gear was estimated and the factors which induce cutting error were analyzed. The simulation and experiments verify that the proposed approach is an efficient way to estimate the cutting error of work-piece during machining process.

Renal parameter estimates in unrestrained dogs

NASA Technical Reports Server (NTRS)

Rader, R. D.; Stevens, C. M.

1974-01-01

A mathematical formulation has been developed to describe the hemodynamic parameters of a conceptualized kidney model. The model was developed by considering regional pressure drops and regional storage capacities within the renal vasculature. Estimation of renal artery compliance, pre- and postglomerular resistance, and glomerular filtration pressure is feasible by considering mean levels and time derivatives of abdominal aortic pressure and renal artery flow. Changes in the smooth muscle tone of the renal vessels induced by exogenous angiotensin amide, acetylcholine, and by the anaesthetic agent halothane were estimated by use of the model. By employing totally implanted telemetry, the technique was applied on unrestrained dogs to measure renal resistive and compliant parameters while the dogs were being subjected to obedience training, to avoidance reaction, and to unrestrained caging.

The impact of temporal sampling resolution on parameter inference for biological transport models.

PubMed

Harrison, Jonathan U; Baker, Ruth E

2018-06-25

Imaging data has become an essential tool to explore key biological questions at various scales, for example the motile behaviour of bacteria or the transport of mRNA, and it has the potential to transform our understanding of important transport mechanisms. Often these imaging studies require us to compare biological species or mutants, and to do this we need to quantitatively characterise their behaviour. Mathematical models offer a quantitative description of a system that enables us to perform this comparison, but to relate mechanistic mathematical models to imaging data, we need to estimate their parameters. In this work we study how collecting data at different temporal resolutions impacts our ability to infer parameters of biological transport models; performing exact inference for simple velocity jump process models in a Bayesian framework. The question of how best to choose the frequency with which data is collected is prominent in a host of studies because the majority of imaging technologies place constraints on the frequency with which images can be taken, and the discrete nature of observations can introduce errors into parameter estimates. In this work, we mitigate such errors by formulating the velocity jump process model within a hidden states framework. This allows us to obtain estimates of the reorientation rate and noise amplitude for noisy observations of a simple velocity jump process. We demonstrate the sensitivity of these estimates to temporal variations in the sampling resolution and extent of measurement noise. We use our methodology to provide experimental guidelines for researchers aiming to characterise motile behaviour that can be described by a velocity jump process. In particular, we consider how experimental constraints resulting in a trade-off between temporal sampling resolution and observation noise may affect parameter estimates. Finally, we demonstrate the robustness of our methodology to model misspecification, and then apply our inference framework to a dataset that was generated with the aim of understanding the localization of RNA-protein complexes.

Analyzing the reliability of mechanical parts in 10 kV aerial transmission lines under ice-coating and wind effects in view of their design features

NASA Astrophysics Data System (ADS)

Doletskaya, L. I.; Solopov, R. V.; Kavchenkov, V. P.; Andreenkov, E. S.

2017-12-01

The physical features of the damage of aerial lines with a voltage of 10 kV under ice and wind loads are examined, mathematical models for estimating the reliability the mechanical part in aerial lines with the application of analytical theoretical methods and corresponding mathematical models taking into account the probabilistic nature of ice and wind loads are described, calculation results on reliability, specific damage and average time for restoration in case of emergency outages of 10 kV high-voltage transmission aerial lines with the use of uninsulated and protected wires are presented.

Estimating the Distance to the Moon--Its Relevance to Mathematics. Core-Plus Mathematics Project.

ERIC Educational Resources Information Center

Stern, David P.

This document features an activity for estimating the distance from the earth to the moon during a solar eclipse based on calculations performed by the ancient Greek astronomer Hipparchus. Historical, mathematical, and scientific details about the calculation are provided. Internet resources for teachers to obtain more information on the subject…

Space structures insulating material's thermophysical and radiation properties estimation

NASA Astrophysics Data System (ADS)

Nenarokomov, A. V.; Alifanov, O. M.; Titov, D. M.

2007-11-01

In many practical situations in aerospace technology it is impossible to measure directly such properties of analyzed materials (for example, composites) as thermal and radiation characteristics. The only way that can often be used to overcome these difficulties is indirect measurements. This type of measurement is usually formulated as the solution of inverse heat transfer problems. Such problems are ill-posed in mathematical sense and their main feature shows itself in the solution instabilities. That is why special regularizing methods are needed to solve them. The experimental methods of identification of the mathematical models of heat transfer based on solving the inverse problems are one of the modern effective solving manners. The objective of this paper is to estimate thermal and radiation properties of advanced materials using the approach based on inverse methods.

Mathematic modeling of the method of measurement relative dielectric permeability

NASA Astrophysics Data System (ADS)

Plotnikova, I. V.; Chicherina, N. V.; Stepanov, A. B.

2018-05-01

The method of measuring relative permittivity’s and the position of the interface between layers of a liquid medium is considered in the article. An electric capacitor is a system consisting of two conductors that are separated by a dielectric layer. It is mathematically proven that at any given time it is possible to obtain the values of the relative permittivity in the layers of the liquid medium and to determine the level of the interface between the layers of the two-layer liquid. The estimation of measurement errors is made.

Towing Tank Tests on a Ram Wing in a Rectangular Guideway

DOT National Transportation Integrated Search

1973-07-01

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

Theory of Visual Attention (TVA) applied to mice in the 5-choice serial reaction time task.

PubMed

Fitzpatrick, C M; Caballero-Puntiverio, M; Gether, U; Habekost, T; Bundesen, C; Vangkilde, S; Woldbye, D P D; Andreasen, J T; Petersen, A

2017-03-01

The 5-choice serial reaction time task (5-CSRTT) is widely used to measure rodent attentional functions. In humans, many attention studies in healthy and clinical populations have used testing based on Bundesen's Theory of Visual Attention (TVA) to estimate visual processing speeds and other parameters of attentional capacity. We aimed to bridge these research fields by modifying the 5-CSRTT's design and by mathematically modelling data to derive attentional parameters analogous to human TVA-based measures. C57BL/6 mice were tested in two 1-h sessions on consecutive days with a version of the 5-CSRTT where stimulus duration (SD) probe length was varied based on information from previous TVA studies. Thereafter, a scopolamine hydrobromide (HBr; 0.125 or 0.25 mg/kg) pharmacological challenge was undertaken, using a Latin square design. Mean score values were modelled using a new three-parameter version of TVA to obtain estimates of visual processing speeds, visual thresholds and motor response baselines in each mouse. The parameter estimates for each animal were reliable across sessions, showing that the data were stable enough to support analysis on an individual level. Scopolamine HBr dose-dependently reduced 5-CSRTT attentional performance while also increasing reward collection latency at the highest dose. Upon TVA modelling, scopolamine HBr significantly reduced visual processing speed at both doses, while having less pronounced effects on visual thresholds and motor response baselines. This study shows for the first time how 5-CSRTT performance in mice can be mathematically modelled to yield estimates of attentional capacity that are directly comparable to estimates from human studies.

Methods to estimate irrigated reference crop evapotranspiration - a review.

PubMed

Kumar, R; Jat, M K; Shankar, V

2012-01-01

Efficient water management of crops requires accurate irrigation scheduling which, in turn, requires the accurate measurement of crop water requirement. Irrigation is applied to replenish depleted moisture for optimum plant growth. Reference evapotranspiration plays an important role for the determination of water requirements for crops and irrigation scheduling. Various models/approaches varying from empirical to physically base distributed are available for the estimation of reference evapotranspiration. Mathematical models are useful tools to estimate the evapotranspiration and water requirement of crops, which is essential information required to design or choose best water management practices. In this paper the most commonly used models/approaches, which are suitable for the estimation of daily water requirement for agricultural crops grown in different agro-climatic regions, are reviewed. Further, an effort has been made to compare the accuracy of various widely used methods under different climatic conditions.

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

PubMed Central

Sun, Xiaodian; Jin, Li; Xiong, Momiao

2008-01-01

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks. PMID:19018286

Heterogeneity in geographical trends of HIV epidemics among key populations in Pakistan: a mathematical modeling study of survey data.

PubMed

Melesse, Dessalegn Y; Shafer, Leigh Anne; Emmanuel, Faran; Reza, Tahira; Achakzai, Baseer K; Furqan, Sofia; Blanchard, James F

2018-06-01

Assessing patterns and trends in new infections is key to better understanding of HIV epidemics, and is best done through monitoring changes in incidence over time. In this study, we examined disparities in geographical trends of HIV epidemics among people who inject drugs (PWIDs), female sex workers (FSWs) and hijra /transgender/male sex workers (H/MSWs), in Pakistan. The UNAIDS Estimation and Projection Package (EPP) mathematical model was used to explore geographical trends in HIV epidemics. Four rounds of mapping and surveillance data collected among key populations (KPs) across 20 cities in Pakistan between 2005-2011 was used for modeling. Empirical estimates of HIV prevalence of each KP in each city were used to fit the model to estimate prevalence and incidence over time. HIV incidence among PWIDs in Pakistan reached its peak in 2011, estimated at 45.3 per 1000 person-years. Incidence was projected to continue to rise from 18.9 in 2015 to 24.3 in 2020 among H/MSWs and from 3.2 in 2015 to 6.3 in 2020 among FSWs. The number of people living with HIV in Pakistan was estimated to steadily increase through at least 2020. HIV incidence peak among PWIDs ranged from 16.2 in 1997 in Quetta to 71.0 in 2010 in Faisalabad (per 1000 person-years). Incidence among H/MSWs may continue to rise through 2020 in all the cities, except in Larkana where it peaked in the early 2000s. In 2015, model estimated incidence among FSWs was 8.1 in Karachi, 6.6 in Larkana, 2.0 in Sukkur and 1.2 in Lahore (per 1000 person-years). There exists significant geographical heterogeneity in patterns and trends of HIV sub-epidemics in Pakistan. Focused interventions and service delivery approaches, different by KP and city, are recommended.

Heterogeneity in geographical trends of HIV epidemics among key populations in Pakistan: a mathematical modeling study of survey data

PubMed Central

Melesse, Dessalegn Y; Shafer, Leigh Anne; Emmanuel, Faran; Reza, Tahira; Achakzai, Baseer K; Furqan, Sofia; Blanchard, James F

2018-01-01

Background Assessing patterns and trends in new infections is key to better understanding of HIV epidemics, and is best done through monitoring changes in incidence over time. In this study, we examined disparities in geographical trends of HIV epidemics among people who inject drugs (PWIDs), female sex workers (FSWs) and hijra/transgender/male sex workers (H/MSWs), in Pakistan. Methods The UNAIDS Estimation and Projection Package (EPP) mathematical model was used to explore geographical trends in HIV epidemics. Four rounds of mapping and surveillance data collected among key populations (KPs) across 20 cities in Pakistan between 2005-2011 was used for modeling. Empirical estimates of HIV prevalence of each KP in each city were used to fit the model to estimate prevalence and incidence over time. Results HIV incidence among PWIDs in Pakistan reached its peak in 2011, estimated at 45.3 per 1000 person-years. Incidence was projected to continue to rise from 18.9 in 2015 to 24.3 in 2020 among H/MSWs and from 3.2 in 2015 to 6.3 in 2020 among FSWs. The number of people living with HIV in Pakistan was estimated to steadily increase through at least 2020. HIV incidence peak among PWIDs ranged from 16.2 in 1997 in Quetta to 71.0 in 2010 in Faisalabad (per 1000 person-years). Incidence among H/MSWs may continue to rise through 2020 in all the cities, except in Larkana where it peaked in the early 2000s. In 2015, model estimated incidence among FSWs was 8.1 in Karachi, 6.6 in Larkana, 2.0 in Sukkur and 1.2 in Lahore (per 1000 person-years). Conclusions There exists significant geographical heterogeneity in patterns and trends of HIV sub-epidemics in Pakistan. Focused interventions and service delivery approaches, different by KP and city, are recommended. PMID:29770215

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

PubMed

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

2011-08-01

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

Estimation of Unsteady Aerodynamic Models from Dynamic Wind Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick; Klein, Vladislav

2011-01-01

Demanding aerodynamic modelling requirements for military and civilian aircraft have motivated researchers to improve computational and experimental techniques and to pursue closer collaboration in these areas. Model identification and validation techniques are key components for this research. This paper presents mathematical model structures and identification techniques that have been used successfully to model more general aerodynamic behaviours in single-degree-of-freedom dynamic testing. Model parameters, characterizing aerodynamic properties, are estimated using linear and nonlinear regression methods in both time and frequency domains. Steps in identification including model structure determination, parameter estimation, and model validation, are addressed in this paper with examples using data from one-degree-of-freedom dynamic wind tunnel and water tunnel experiments. These techniques offer a methodology for expanding the utility of computational methods in application to flight dynamics, stability, and control problems. Since flight test is not always an option for early model validation, time history comparisons are commonly made between computational and experimental results and model adequacy is inferred by corroborating results. An extension is offered to this conventional approach where more general model parameter estimates and their standard errors are compared.

The Specific Features of design and process engineering in branch of industrial enterprise

NASA Astrophysics Data System (ADS)

Sosedko, V. V.; Yanishevskaya, A. G.

2017-06-01

Production output of industrial enterprise is organized in debugged working mechanisms at each stage of product’s life cycle from initial design documentation to product and finishing it with utilization. The topic of article is mathematical model of the system design and process engineering in branch of the industrial enterprise, statistical processing of estimated implementation results of developed mathematical model in branch, and demonstration of advantages at application at this enterprise. During the creation of model a data flow about driving of information, orders, details and modules in branch of enterprise groups of divisions were classified. Proceeding from the analysis of divisions activity, a data flow, details and documents the state graph of design and process engineering was constructed, transitions were described and coefficients are appropriated. To each condition of system of the constructed state graph the corresponding limiting state probabilities were defined, and also Kolmogorov’s equations are worked out. When integration of sets of equations of Kolmogorov the state probability of system activity the specified divisions and production as function of time in each instant is defined. On the basis of developed mathematical model of uniform system of designing and process engineering and manufacture, and a state graph by authors statistical processing the application of mathematical model results was carried out, and also advantage at application at this enterprise is shown. Researches on studying of loading services probability of branch and third-party contractors (the orders received from branch within a month) were conducted. The developed mathematical model of system design and process engineering and manufacture can be applied to definition of activity state probability of divisions and manufacture as function of time in each instant that will allow to keep account of loading of performance of work in branches of the enterprise.

Mathematical Fluid Dynamic Modeling of Plasma Stall-Spin Departure Control

DTIC Science & Technology

2007-04-01

filter (4), is appropriate for further CSN modeling of the vortical flow. The CNS solver reproduces symmetric and asymmetric vortex fields (Figure 11...calculations conducted for laminar flow showed that the CNS solver reproduces symmetric and asymmetric vortex fields and can be used for estimation of the...Galilean-invariant leeward vortex filter. The modified k-F EASM model was incorporated into our CSN solver. Parametric calculations showed that numerical

Flight dynamics analysis and simulation of heavy lift airships. Volume 2: Technical manual

NASA Technical Reports Server (NTRS)

Ringland, R. F.; Tischler, M. B.; Jex, H. R.; Emmen, R. D.; Ashkenas, I. L.

1982-01-01

The mathematical models embodied in the simulation are described in considerable detail and with supporting evidence for the model forms chosen. In addition the trimming and linearization algorithms used in the simulation are described. Appendices to the manual identify reference material for estimating the needed coefficients for the input data and provide example simulation results.

Radiolytic and thermolytic bubble gas hydrogen composition

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

Woodham, W.

This report describes the development of a mathematical model for the estimation of the hydrogen composition of gas bubbles trapped in radioactive waste. The model described herein uses a material balance approach to accurately incorporate the rates of hydrogen generation by a number of physical phenomena and scale the aforementioned rates in a manner that allows calculation of the final hydrogen composition.

Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

NASA Astrophysics Data System (ADS)

Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.

2017-10-01

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.

Mathematical Modeling of Programmatic Requirements for Yaws Eradication

PubMed Central

Mitjà, Oriol; Fitzpatrick, Christopher; Asiedu, Kingsley; Solomon, Anthony W.; Mabey, David C.W.; Funk, Sebastian

2017-01-01

Yaws is targeted for eradication by 2020. The mainstay of the eradication strategy is mass treatment followed by case finding. Modeling has been used to inform programmatic requirements for other neglected tropical diseases and could provide insights into yaws eradication. We developed a model of yaws transmission varying the coverage and number of rounds of treatment. The estimated number of cases arising from an index case (basic reproduction number [R0]) ranged from 1.08 to 3.32. To have 80% probability of achieving eradication, 8 rounds of treatment with 80% coverage were required at low estimates of R0 (1.45). This requirement increased to 95% at high estimates of R0 (2.47). Extending the treatment interval to 12 months increased requirements at all estimates of R0. At high estimates of R0 with 12 monthly rounds of treatment, no combination of variables achieved eradication. Models should be used to guide the scale-up of yaws eradication. PMID:27983500

A Bayes linear Bayes method for estimation of correlated event rates.

PubMed

Quigley, John; Wilson, Kevin J; Walls, Lesley; Bedford, Tim

2013-12-01

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well-known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates. © 2013 Society for Risk Analysis.

Mathematical model of marine diesel engine simulator for a new methodology of self propulsion tests

NASA Astrophysics Data System (ADS)

Izzuddin, Nur; Sunarsih, Priyanto, Agoes

2015-05-01

As a vessel operates in the open seas, a marine diesel engine simulator whose engine rotation is controlled to transmit through propeller shaft is a new methodology for the self propulsion tests to track the fuel saving in a real time. Considering the circumstance, this paper presents the real time of marine diesel engine simulator system to track the real performance of a ship through a computer-simulated model. A mathematical model of marine diesel engine and the propeller are used in the simulation to estimate fuel rate, engine rotating speed, thrust and torque of the propeller thus achieve the target vessel's speed. The input and output are a real time control system of fuel saving rate and propeller rotating speed representing the marine diesel engine characteristics. The self-propulsion tests in calm waters were conducted using a vessel model to validate the marine diesel engine simulator. The simulator then was used to evaluate the fuel saving by employing a new mathematical model of turbochargers for the marine diesel engine simulator. The control system developed will be beneficial for users as to analyze different condition of vessel's speed to obtain better characteristics and hence optimize the fuel saving rate.

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

PubMed

Moray, Neville; Groeger, John; Stanton, Neville

2017-02-01

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

Loss Estimations due to Earthquakes and Secondary Technological Hazards

NASA Astrophysics Data System (ADS)

Frolova, N.; Larionov, V.; Bonnin, J.

2009-04-01

Expected loss and damage assessment due to natural and technological disasters are of primary importance for emergency management just after the disaster, as well as for development and implementation of preventive measures plans. The paper addresses the procedures and simulation models for loss estimations due to strong earthquakes and secondary technological accidents. The mathematical models for shaking intensity distribution, damage to buildings and structures, debris volume, number of fatalities and injuries due to earthquakes and technological accidents at fire and chemical hazardous facilities are considered, which are used in geographical information systems assigned for these purposes. The criteria of technological accidents occurrence are developed on the basis of engineering analysis of past events' consequences. The paper is providing the results of scenario earthquakes consequences estimation and individual seismic risk assessment taking into account the secondary technological hazards at regional and urban levels. The individual risk is understood as the probability of death (or injuries) due to possible hazardous event within one year in a given territory. It is determined through mathematical expectation of social losses taking into account the number of inhabitants in the considered settlement and probability of natural and/or technological disaster.

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

PubMed Central

Boden, Lisa A.; McKendrick, Iain J.

2017-01-01

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

Using Multiple Outcomes of Sexual Behavior to Provide Insights Into Chlamydia Transmission and the Effectiveness of Prevention Interventions in Adolescents.

PubMed

Enns, Eva Andrea; Kao, Szu-Yu; Kozhimannil, Katy Backes; Kahn, Judith; Farris, Jill; Kulasingam, Shalini L

2017-10-01

Mathematical models are important tools for assessing prevention and management strategies for sexually transmitted infections. These models are usually developed for a single infection and require calibration to observed epidemiological trends in the infection of interest. Incorporating other outcomes of sexual behavior into the model, such as pregnancy, may better inform the calibration process. We developed a mathematical model of chlamydia transmission and pregnancy in Minnesota adolescents aged 15 to 19 years. We calibrated the model to statewide rates of reported chlamydia cases alone (chlamydia calibration) and in combination with pregnancy rates (dual calibration). We evaluated the impact of calibrating to different outcomes of sexual behavior on estimated input parameter values, predicted epidemiological outcomes, and predicted impact of chlamydia prevention interventions. The two calibration scenarios produced different estimates of the probability of condom use, the probability of chlamydia transmission per sex act, the proportion of asymptomatic infections, and the screening rate among men. These differences resulted in the dual calibration scenario predicting lower prevalence and incidence of chlamydia compared with calibrating to chlamydia cases alone. When evaluating the impact of a 10% increase in condom use, the dual calibration scenario predicted fewer infections averted over 5 years compared with chlamydia calibration alone [111 (6.8%) vs 158 (8.5%)]. While pregnancy and chlamydia in adolescents are often considered separately, both are outcomes of unprotected sexual activity. Incorporating both as calibration targets in a model of chlamydia transmission resulted in different parameter estimates, potentially impacting the intervention effectiveness predicted by the model.

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

NASA Technical Reports Server (NTRS)

Oman, C. M.

1982-01-01

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

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

NASA Technical Reports Server (NTRS)

Oman, C. M.

1980-01-01

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

A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications.

PubMed

Bogdańska, Magdalena U; Bodnar, Marek; Piotrowska, Monika J; Murek, Michael; Schucht, Philippe; Beck, Jürgen; Martínez-González, Alicia; Pérez-García, Víctor M

2017-01-01

Gliomas are the most frequent type of primary brain tumours. Low grade gliomas (LGGs, WHO grade II gliomas) may grow very slowly for the long periods of time, however they inevitably cause death due to the phenomenon known as the malignant transformation. This refers to the transition of LGGs to more aggressive forms of high grade gliomas (HGGs, WHO grade III and IV gliomas). In this paper we propose a mathematical model describing the spatio-temporal transition of LGGs into HGGs. Our modelling approach is based on two cellular populations with transitions between them being driven by the tumour microenvironment transformation occurring when the tumour cell density grows beyond a critical level. We show that the proposed model describes real patient data well. We discuss the relationship between patient prognosis and model parameters. We approximate tumour radius and velocity before malignant transformation as well as estimate the onset of this process.

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

PubMed

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

2008-10-07

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

Determination of suitable drying curve model for bread moisture loss during baking

NASA Astrophysics Data System (ADS)

Soleimani Pour-Damanab, A. R.; Jafary, A.; Rafiee, S.

2013-03-01

This study presents mathematical modelling of bread moisture loss or drying during baking in a conventional bread baking process. In order to estimate and select the appropriate moisture loss curve equation, 11 different models, semi-theoretical and empirical, were applied to the experimental data and compared according to their correlation coefficients, chi-squared test and root mean square error which were predicted by nonlinear regression analysis. Consequently, of all the drying models, a Page model was selected as the best one, according to the correlation coefficients, chi-squared test, and root mean square error values and its simplicity. Mean absolute estimation error of the proposed model by linear regression analysis for natural and forced convection modes was 2.43, 4.74%, respectively.

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative–quantitative modeling

PubMed Central

Streif, Stefan; Savchenko, Anton; Rumschinski, Philipp; Borchers, Steffen; Findeisen, Rolf

2012-01-01

Summary: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if–then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLabTM-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. Availability: ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/ Contact: stefan.streif@ovgu.de PMID:22451270

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative-quantitative modeling.

PubMed

Streif, Stefan; Savchenko, Anton; Rumschinski, Philipp; Borchers, Steffen; Findeisen, Rolf

2012-05-01

Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if-then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLab(TM)-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/

The Computational Estimation and Instructional Perspectives of Elementary School Teachers

ERIC Educational Resources Information Center

Tsao, Yea-Ling; Pan, Ting-Rung

2013-01-01

The purpose of this study is to investigate teachers' understanding and knowledge of computational estimation, and teaching practice toward to computational estimation. There are six fifth-grade elementary teachers who participated in this study; three teachers with mathematics/ science major and three teachers with non-mathematics/science major.…

A global parallel model based design of experiments method to minimize model output uncertainty.

PubMed

Bazil, Jason N; Buzzard, Gregory T; Rundell, Ann E

2012-03-01

Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.

An operational GLS model for hydrologic regression

USGS Publications Warehouse

Tasker, Gary D.; Stedinger, J.R.

1989-01-01

Recent Monte Carlo studies have documented the value of generalized least squares (GLS) procedures to estimate empirical relationships between streamflow statistics and physiographic basin characteristics. This paper presents a number of extensions of the GLS method that deal with realities and complexities of regional hydrologic data sets that were not addressed in the simulation studies. These extensions include: (1) a more realistic model of the underlying model errors; (2) smoothed estimates of cross correlation of flows; (3) procedures for including historical flow data; (4) diagnostic statistics describing leverage and influence for GLS regression; and (5) the formulation of a mathematical program for evaluating future gaging activities. ?? 1989.

20171015 - Integrating Toxicity, Toxicokinetic, and Exposure Data for Risk-based Chemical Alternatives Assessment (ISES)

EPA Science Inventory

In order to predict the margin between the dose needed for adverse chemical effects and actual human exposure rates, data on hazard, exposure, and toxicokinetics are needed. In vitro methods, biomonitoring, and mathematical modeling have provided initial estimates for many extant...

ELECTROCHEMICAL CHROMIC ACID REGENERATION PROCESS: FITTING OF MEMBRANE TRANSPORT PROPERTIES. (R827125)

EPA Science Inventory

Abstract

A mathematical model was developed to predict changes in contaminant concentrations with time, and to estimate contaminant fluxes due to migration, diffusion, and convection in a laboratory-scale batch electrolysis cell for the regeneration of contaminated har...

Assessing the Benefits of U.S. Customs and Border Protection Regulatory Actions to Reduce Terrorism Risks

DTIC Science & Technology

2012-01-01

conceptual, mathematical , etc.  More formally, models are approximations, representations, or idealizations of selected aspects of the structure...essential – Actuarial estimates inadequate – limited data, great heterogeneity over time & location, conditions change so present & future may not be

Epidemic classification of phytosanitary situations on cereal crops using mathematical modeling

USDA-ARS?s Scientific Manuscript database

Most plant protection researchers and experts divide emerging phytosanitary situations into three classes: epidemic, moderate development of disease, and yield depression. The known principles and methods for estimating these situations (Van der Plank J.E., Kranz J. et al.) do not fully describe th...

Mathematical modeling of nitrous oxide (N2O) emissions from full-scale wastewater treatment plants.

PubMed

Ni, Bing-Jie; Ye, Liu; Law, Yingyu; Byers, Craig; Yuan, Zhiguo

2013-07-16

Mathematical modeling of N2O emissions is of great importance toward understanding the whole environmental impact of wastewater treatment systems. However, information on modeling of N2O emissions from full-scale wastewater treatment plants (WWTP) is still sparse. In this work, a mathematical model based on currently known or hypothesized metabolic pathways for N2O productions by heterotrophic denitrifiers and ammonia-oxidizing bacteria (AOB) is developed and calibrated to describe the N2O emissions from full-scale WWTPs. The model described well the dynamic ammonium, nitrite, nitrate, dissolved oxygen (DO) and N2O data collected from both an open oxidation ditch (OD) system with surface aerators and a sequencing batch reactor (SBR) system with bubbling aeration. The obtained kinetic parameters for N2O production are found to be reasonable as the 95% confidence regions of the estimates are all small with mean values approximately at the center. The model is further validated with independent data sets collected from the same two WWTPs. This is the first time that mathematical modeling of N2O emissions is conducted successfully for full-scale WWTPs. While clearly showing that the NH2OH related pathways could well explain N2O production and emission in the two full-scale plants studied, the modeling results do not prove the dominance of the NH2OH pathways in these plants, nor rule out the possibility of AOB denitrification being a potentially dominating pathway in other WWTPs that are designed or operated differently.

Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

PubMed

Li, Zhiming; Teng, Zhidong; Feng, Xiaomei; Li, Yingke; Zhang, Huiguo

2015-01-01

In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications of the model, we use the recognized infectious and death cases in Guinea to estimate parameters of the model by the least square method. With suitable parameter values, we obtain the estimated value of the basic reproduction number and analyze the sensitivity and uncertainty property by partial rank correlation coefficients.

Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia

NASA Astrophysics Data System (ADS)

Cândea, Doina; Halanay, Andrei; Rǎdulescu, Rodica; Tǎlmaci, Rodica

2017-01-01

We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is to establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. For the most significant parameters of the model which affect the evolution of CML disease during Imatinib treatment we try to estimate the realistic values using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted.

Examples of testing global identifiability of biological and biomedical models with the DAISY software.

PubMed

Saccomani, Maria Pia; Audoly, Stefania; Bellu, Giuseppina; D'Angiò, Leontina

2010-04-01

DAISY (Differential Algebra for Identifiability of SYstems) is a recently developed computer algebra software tool which can be used to automatically check global identifiability of (linear and) nonlinear dynamic models described by differential equations involving polynomial or rational functions. Global identifiability is a fundamental prerequisite for model identification which is important not only for biological or medical systems but also for many physical and engineering systems derived from first principles. Lack of identifiability implies that the parameter estimation techniques may not fail but any obtained numerical estimates will be meaningless. The software does not require understanding of the underlying mathematical principles and can be used by researchers in applied fields with a minimum of mathematical background. We illustrate the DAISY software by checking the a priori global identifiability of two benchmark nonlinear models taken from the literature. The analysis of these two examples includes comparison with other methods and demonstrates how identifiability analysis is simplified by this tool. Thus we illustrate the identifiability analysis of other two examples, by including discussion of some specific aspects related to the role of observability and knowledge of initial conditions in testing identifiability and to the computational complexity of the software. The main focus of this paper is not on the description of the mathematical background of the algorithm, which has been presented elsewhere, but on illustrating its use and on some of its more interesting features. DAISY is available on the web site http://www.dei.unipd.it/ approximately pia/. 2010 Elsevier Ltd. All rights reserved.

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

PubMed

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

2017-02-01

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

Reference breast temperature: proposal of an equation.

PubMed

Souza, Gladis Aparecida Galindo Reisemberger de; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso Neto, Carlos; Neves, Eduardo Borba

2015-01-01

To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies.

Lithium manganese oxide spinel electrodes

NASA Astrophysics Data System (ADS)

Darling, Robert Mason

Batteries based oil intercalation eletrodes are currently being considered for a variety of applications including automobiles. This thesis is concerned with the simulation and experimental investigation of one such system: spinel LiyMn2O4. A mathematical model simulating the behavior of an electrochemical cell containing all intercalation electrode is developed and applied to Li yMn2O4 based systems. The influence of the exchange current density oil the propagation of the reaction through the depth of the electrode is examined theoretically. Galvanostatic cycling and relaxation phenomena on open circuit are simulated for different particle-size distributions. The electrode with uniformly sized particles shows the best performance when the current is on, and relaxes towards equilibrium most quickly. The impedance of a porous electrode containing a particle-size distribution at low frequencies is investigated with all analytic solution and a simplified version of the mathematical model. The presence of the particle-size distribution leads to an apparent diffusion coefficient which has all incorrect concentration dependence. A Li/1 M LiClO4 in propylene carbonate (PC)/ LiyMn 2O4 cell is used to investigate the influence of side reactions oil the current-potential behavior of intercalation electrodes. Slow cyclic voltammograms and self-discharge data are combined to estimate the reversible potential of the host material and the kinetic parameters for the side reaction. This information is then used, together with estimates of the solid-state diffusion coefficient and main-reaction exchange current density, in a mathematical model of the system. Predictions from the model compare favorably with continuous cycling results and galvanostatic experiments with periodic current interruptions. The variation with respect to composition of' the diffusion coefficient of lithium in LiyMn2O4 is estimated from incomplete galvanostatic discharges following open-circult periods. The results compared favorably with those available in the literature. Dynamic Monte Carlo simulations were conducted to investigate the concentration dependence of the diffusion coefficient fundamentally. The dynamic Monte Carlo predictions compare favorably with the experimental data.

Reciprocal Sliding Friction Model for an Electro-Deposited Coating and Its Parameter Estimation Using Markov Chain Monte Carlo Method

PubMed Central

Kim, Kyungmok; Lee, Jaewook

2016-01-01

This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficient during the initial running-in period and steady-state sliding is expressed as a simple linear function. The friction coefficient in the transition to higher friction is described with a mathematical model derived from Kachanov-type damage law. The model parameters are then estimated using the Markov Chain Monte Carlo (MCMC) approach. It is identified that estimated friction coefficients obtained by MCMC approach are in good agreement with measured ones. PMID:28773359

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2006-01-01

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

Determination of the mass transfer limiting step of dye adsorption onto commercial adsorbent by using mathematical models.

PubMed

Marin, Pricila; Borba, Carlos Eduardo; Módenes, Aparecido Nivaldo; Espinoza-Quiñones, Fernando R; de Oliveira, Silvia Priscila Dias; Kroumov, Alexander Dimitrov

2014-01-01

Reactive blue 5G dye removal in a fixed-bed column packed with Dowex Optipore SD-2 adsorbent was modelled. Three mathematical models were tested in order to determine the limiting step of the mass transfer of the dye adsorption process onto the adsorbent. The mass transfer resistance was considered to be a criterion for the determination of the difference between models. The models contained information about the external, internal, or surface adsorption limiting step. In the model development procedure, two hypotheses were applied to describe the internal mass transfer resistance. First, the mass transfer coefficient constant was considered. Second, the mass transfer coefficient was considered as a function of the dye concentration in the adsorbent. The experimental breakthrough curves were obtained for different particle diameters of the adsorbent, flow rates, and feed dye concentrations in order to evaluate the predictive power of the models. The values of the mass transfer parameters of the mathematical models were estimated by using the downhill simplex optimization method. The results showed that the model that considered internal resistance with a variable mass transfer coefficient was more flexible than the other ones and this model described the dynamics of the adsorption process of the dye in the fixed-bed column better. Hence, this model can be used for optimization and column design purposes for the investigated systems and similar ones.

A method of estimating conceptus doses resulting from multidetector CT examinations during all stages of gestation

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

Damilakis, John; Tzedakis, Antonis; Perisinakis, Kostas

Purpose: Current methods for the estimation of conceptus dose from multidetector CT (MDCT) examinations performed on the mother provide dose data for typical protocols with a fixed scan length. However, modified low-dose imaging protocols are frequently used during pregnancy. The purpose of the current study was to develop a method for the estimation of conceptus dose from any MDCT examination of the trunk performed during all stages of gestation. Methods: The Monte Carlo N-Particle (MCNP) radiation transport code was employed in this study to model the Siemens Sensation 16 and Sensation 64 MDCT scanners. Four mathematical phantoms were used, simulatingmore » women at 0, 3, 6, and 9 months of gestation. The contribution to the conceptus dose from single simulated scans was obtained at various positions across the phantoms. To investigate the effect of maternal body size and conceptus depth on conceptus dose, phantoms of different sizes were produced by adding layers of adipose tissue around the trunk of the mathematical phantoms. To verify MCNP results, conceptus dose measurements were carried out by means of three physical anthropomorphic phantoms, simulating pregnancy at 0, 3, and 6 months of gestation and thermoluminescence dosimetry (TLD) crystals. Results: The results consist of Monte Carlo-generated normalized conceptus dose coefficients for single scans across the four mathematical phantoms. These coefficients were defined as the conceptus dose contribution from a single scan divided by the CTDI free-in-air measured with identical scanning parameters. Data have been produced to take into account the effect of maternal body size and conceptus position variations on conceptus dose. Conceptus doses measured with TLD crystals showed a difference of up to 19% compared to those estimated by mathematical simulations. Conclusions: Estimation of conceptus doses from MDCT examinations of the trunk performed on pregnant patients during all stages of gestation can be made using the method developed in the current study.« less

Experimental evaluation of a mathematical model for predicting transfer efficiency of a high volume-low pressure air spray gun.

PubMed

Tan, Y M; Flynn, M R

2000-10-01

The transfer efficiency of a spray-painting gun is defined as the amount of coating applied to the workpiece divided by the amount sprayed. Characterizing this transfer process allows for accurate estimation of the overspray generation rate, which is important for determining a spray painter's exposure to airborne contaminants. This study presents an experimental evaluation of a mathematical model for predicting the transfer efficiency of a high volume-low pressure spray gun. The effects of gun-to-surface distance and nozzle pressure on the agreement between the transfer efficiency measurement and prediction were examined. Wind tunnel studies and non-volatile vacuum pump oil in place of commercial paint were used to determine transfer efficiency at nine gun-to-surface distances and four nozzle pressure levels. The mathematical model successfully predicts transfer efficiency within the uncertainty limits. The least squares regression between measured and predicted transfer efficiency has a slope of 0.83 and an intercept of 0.12 (R2 = 0.98). Two correction factors were determined to improve the mathematical model. At higher nozzle pressure settings, 6.5 psig and 5.5 psig, the correction factor is a function of both gun-to-surface distance and nozzle pressure level. At lower nozzle pressures, 4 psig and 2.75 psig, gun-to-surface distance slightly influences the correction factor, while nozzle pressure has no discernible effect.

Mathematical model of the metabolism of 123I-16-iodo-9-hexadecenoic acid in an isolated rat heart. Validation by comparison with experimental measurements.

PubMed

Dubois, F; Depresseux, J C; Bontemps, L; Demaison, L; Keriel, C; Mathieu, J P; Pernin, C; Marti-Batlle, D; Vidal, M; Cuchet, P

1986-01-01

The aim of the present study was to demonstrate that it is possible to estimate the intracellular metabolism of a fatty acid labelled with iodine using external radioactivity measurements. 123I-16-iodo-9-hexadecenoic acid (IHA) was injected close to the coronary arteries of isolated rat hearts perfused according to the Langendorff technique. The time course of the cardiac radioactivity was measured using an INa crystal coupled to an analyser. The obtained curves were analysed using a four-compartment mathematical model, with the compartments corresponding to the vascular-IHA (O), intramyocardial free-IHA (1), esterified-IHA (2) and iodide (3) pools. Curve analysis using this model demonstrated that, as compared to substrate-free perfusion, the presence of glucose (11 mM) increased IHA storage and decreased its oxidation. These changes were enhanced by the presence of insulin. A comparison of these results with measurements of the radioactivity levels within the various cellular fractions validated our proposed mathematical model. Thus, using only a mathematical analysis of a cardiac time-activity curve, it is possible to obtain quantitative information about IHA distribution in the different intracellular metabolic pathways. This technique is potentially useful for the study of metabolic effects of ischaemia or anoxia, as well as for the study of the influence of various substrates or drugs on IHA metabolism in isolated rat hearts.

Stochastic differential equation (SDE) model of opening gold share price of bursa saham malaysia

NASA Astrophysics Data System (ADS)

Hussin, F. N.; Rahman, H. A.; Bahar, A.

2017-09-01

Black and Scholes option pricing model is one of the most recognized stochastic differential equation model in mathematical finance. Two parameter estimation methods have been utilized for the Geometric Brownian model (GBM); historical and discrete method. The historical method is a statistical method which uses the property of independence and normality logarithmic return, giving out the simplest parameter estimation. Meanwhile, discrete method considers the function of density of transition from the process of diffusion normal log which has been derived from maximum likelihood method. These two methods are used to find the parameter estimates samples of Malaysians Gold Share Price data such as: Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas, and Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas Shariah. Modelling of gold share price is essential since fluctuation of gold affects worldwide economy nowadays, including Malaysia. It is found that discrete method gives the best parameter estimates than historical method due to the smallest Root Mean Square Error (RMSE) value.

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

USGS Publications Warehouse

Bolker, Benjamin M.; Gardner, Beth; Maunder, Mark; Berg, Casper W.; Brooks, Mollie; Comita, Liza; Crone, Elizabeth; Cubaynes, Sarah; Davies, Trevor; de Valpine, Perry; Ford, Jessica; Gimenez, Olivier; Kéry, Marc; Kim, Eun Jung; Lennert-Cody, Cleridy; Magunsson, Arni; Martell, Steve; Nash, John; Nielson, Anders; Regentz, Jim; Skaug, Hans; Zipkin, Elise

2013-01-01

1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

Parameter Estimation in Atmospheric Data Sets

NASA Technical Reports Server (NTRS)

Wenig, Mark; Colarco, Peter

2004-01-01

In this study the structure tensor technique is used to estimate dynamical parameters in atmospheric data sets. The structure tensor is a common tool for estimating motion in image sequences. This technique can be extended to estimate other dynamical parameters such as diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. As a test scenario this technique will be applied to modeled dust data. In this case vertically integrated dust concentrations were used to derive wind information. Those results can be compared to the wind vector fields which served as input to the model. Based on this analysis, a method to compute atmospheric data parameter fields will be presented. .

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.

HIV Model Parameter Estimates from Interruption Trial Data including Drug Efficacy and Reservoir Dynamics

PubMed Central

Luo, Rutao; Piovoso, Michael J.; Martinez-Picado, Javier; Zurakowski, Ryan

2012-01-01

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3–5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients. PMID:22815727

Mathematical Methods for Studying DNA and Protein Interactions

NASA Astrophysics Data System (ADS)

LeGresley, Sarah

Deoxyribnucleic Acid (DNA) damage can lead to health related issues such as developmental disorders, aging, and cancer. It has been estimated that damage rates may be as high as 100,000 per cell per day. Because of the devastating effects that DNA damage can have, DNA repair mechanisms are of great interest yet are not completely understood. To gain a better understanding of possible DNA repair mechanisms, my dissertation focused on mathematical methods for understanding the interactions between DNA and proteins. I developed a damaged DNA model to estimate the probabilities of damaged DNA being located at specific positions. Experiments were then performed that suggested that the damaged DNA may be repositioned. These experimental results were consistent with the model's prediction that damaged DNA has preferred locations. To study how proteins might be moving along the DNA, I studied the use of the uniform motion "n-step" model. The n-step model has been used to determine the kinetics parameters (e.g. rates at which a protein moves along the DNA, how much energy is required to move a protein along a specified amount of DNA, etc.) of proteins moving along the DNA. Monte Carlo methods were used to simulate proteins moving with different types of non-uniform motion (e.g. backward, jumping, etc.) along the DNA. Estimates for the kinetics parameters in the n-step model were found by fitting of the Monte Carlo simulation data. Analysis indicated that non-uniform motion of the protein may lead to over or underestimation of the kinetic parameters of this n-step model.

Theoretical and experimental researches of the liquid evaporation during thermal vacuum influences

NASA Astrophysics Data System (ADS)

Trushlyakov, V.; Panichkin, A.; Prusova, O.; Zharikov, K.; Dron, M.

2018-01-01

The mathematical model of the evaporation process of model liquid with the free surface boundary conditions of the "mirror" type under thermal vacuum influence and the numerical estimates of the evaporation process parameters are developed. An experimental stand, comprising a vacuum chamber, an experimental model tank with a heating element is designed; the experimental data are obtained. A comparative analysis of numerical and experimental results showed their close match.

Conceptions and Images of Mathematics Professors on Teaching Mathematics in School.

ERIC Educational Resources Information Center

Pehkonen, Erkki

1999-01-01

Clarifies what kind of mathematical beliefs are conveyed to student teachers during their studies. Interviews mathematics professors (n=7) from five Finnish universities who were responsible for mathematics teacher education. Professors estimated that teachers' basic knowledge was poor and old-fashioned, requiring improvement, and they emphasized…

Low Dose Radiation Cancer Risks: Epidemiological and Toxicological Models

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

David G. Hoel, PhD

2012-04-19

The basic purpose of this one year research grant was to extend the two stage clonal expansion model (TSCE) of carcinogenesis to exposures other than the usual single acute exposure. The two-stage clonal expansion model of carcinogenesis incorporates the biological process of carcinogenesis, which involves two mutations and the clonal proliferation of the intermediate cells, in a stochastic, mathematical way. The current TSCE model serves a general purpose of acute exposure models but requires numerical computation of both the survival and hazard functions. The primary objective of this research project was to develop the analytical expressions for the survival functionmore » and the hazard function of the occurrence of the first cancer cell for acute, continuous and multiple exposure cases within the framework of the piece-wise constant parameter two-stage clonal expansion model of carcinogenesis. For acute exposure and multiple exposures of acute series, it is either only allowed to have the first mutation rate vary with the dose, or to have all the parameters be dose dependent; for multiple exposures of continuous exposures, all the parameters are allowed to vary with the dose. With these analytical functions, it becomes easy to evaluate the risks of cancer and allows one to deal with the various exposure patterns in cancer risk assessment. A second objective was to apply the TSCE model with varing continuous exposures from the cancer studies of inhaled plutonium in beagle dogs. Using step functions to estimate the retention functions of the pulmonary exposure of plutonium the multiple exposure versions of the TSCE model was to be used to estimate the beagle dog lung cancer risks. The mathematical equations of the multiple exposure versions of the TSCE model were developed. A draft manuscript which is attached provides the results of this mathematical work. The application work using the beagle dog data from plutonium exposure has not been completed due to the fact that the research project did not continue beyond its first year.« less

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

PubMed

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

2013-12-01

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

USING SIMPLE MATHEMATICAL MODELS FOR ESTIMATING IMPACTS TO GROUND WATER AT PETROLEUM RELEASE SITES - WORKSHOP

EPA Science Inventory

Regulators and consultants alike are routinely tasked with predicting potential future impacts to ground water resources from leaking underground storage tank (LUST) sites. Site data is usually sparse, variable, and uncertain at best. However, this type of data can be evaluated ...

ESTIMATION OF INFILTRATION RATE IN THE VADOSE ZONE: APPLICATION OF SELECTED MATHEMATICAL MODELS - VOLUME II

EPA Science Inventory

Movement of water into and through the vadose zone is of great importance to the assessment of contaminant fate and transport, agricultural management, and natural resource protection. The process of water movement is very dynamic, changing dramatically over time and space. Inf...

Can avian reproductive outcomes estimated with MCnest be made more robust using stochastic parameterizations?

EPA Science Inventory

The Markov chain nest productivity model, or MCnest, is a set of algorithms for integrating the results of avian toxicity tests with reproductive life-history data to project the relative magnitude of chemical effects on avian reproduction. The mathematical foundation of MCnest i...

Compensating for estimation smoothing in kriging

USGS Publications Warehouse

Olea, R.A.; Pawlowsky, Vera

1996-01-01

Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator-compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-fr2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well - better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. ?? 1996 International Association for Mathematical Geology.

[Analysis of genetico-demographic structure of rural populations living near the Semipalatinsk nuclear test site].

PubMed

Sviatova, G S; Berezina, G M; Abil'dinova, G Zh

2001-12-01

Rural populations neighboring the Semipalatinsk nuclear test site were used as a model to develop and test an integrated population-genetic approach to analysis of the medical genetic situation and environmental conditions in the areas studied. The contributions of individual factors of population dynamics into the formation of the genetic load were also assessed. The informative values of some genetic markers were estimated. Based on these estimates, a mathematical model was constructed that makes it possible to calculate numerical scores for analysis of the genetic loads in populations differing in environmental exposure.

A simple algorithm to estimate the effective regional atmospheric parameters for thermal-inertia mapping

USGS Publications Warehouse

Watson, K.; Hummer-Miller, S.

1981-01-01

A method based solely on remote sensing data has been developed to estimate those meteorological effects which are required for thermal-inertia mapping. It assumes that the atmospheric fluxes are spatially invariant and that the solar, sky, and sensible heat fluxes can be approximated by a simple mathematical form. Coefficients are determined from least-squares method by fitting observational data to our thermal model. A comparison between field measurements and the model-derived flux shows the type of agreement which can be achieved. An analysis of the limitations of the method is also provided. ?? 1981.

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

PubMed

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

2005-03-15

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

[METHODS OF MATHEMATICAL MODELING IN MORPHOLOGICAL DIAGNOSTICS OF CHORNOBYL FACTOR INFLUENCE ON PROSTATE GLAND OF COAL MINERS-- THE CHERNOBYL DISASTER FIGHTERS].

PubMed

Danylov, Iu V; Motkov, K V; Shevchenko, T I

2014-01-01

The morphometric estimation of parenchyma and stroma condition included the determination of 25 parameters in a prostate gland at 27 persons. The mathematical model of morphogenesis of prostate gland was created by Bayes' method. The method of differential diagnosis of a prostate gland tissues' changes conditioned by the influence of the Chernobyl factor and/or unfavorable terms of the work in underground coal mines have been worked out. Its practical use provides exactness and reliability of the diagnosis (not less than 95%), independence from the level of the qualification and personal experience of the doctor, allows us to unify, optimize and individualize the diagnostic algorithms, answer the requirements of evidential medicine.

[Methods of mathematical modeling in morphological diagnostics of Chernobyl factor influence on the testes of coal miners of Donbas--the Chernobyl disaster fighters].

PubMed

Danylov, Iu V; Motkov, K V; Shevchenko, T I

2014-01-01

The morphometric estimation of parenchyma and stroma condition included the determination of 29 parameters in testicles at 27 persons. The mathematical model of morphogenesis of testicles was created by Bayes' method. The method of differential diagnosis of testicles tissues' changes conditioned by the influence of the Chernobyl factor and/or unfavorable terms of the work in underground coal mines have been worked out. Its practical use provides exactness and reliability of the diagnosis (not less than 95%), independence from the level of the qualification and personal experience of the doctor, allows us to unify, optimize and individualize the diagnostic algorithms, answer the requirements of evidential medicine.

Thermal mathematical modeling and system simulation of Space Shuttle less subsystem

NASA Technical Reports Server (NTRS)

Chao, D. C.; Battley, H. H.; Gallegos, J. J.; Curry, D. M.

1984-01-01

Applications, validation tests, and upgrades of the two- and three-dimensional system level thermal mathematical system simulation models (TMSSM) used for thermal protection system (TPS) analyses are described. The TMSSM were developed as an aid to predicting the performance requirements and configurations of the Shuttle wing leading edge (WLE) and nose cone (NC) TPS tiles. The WLE and its structure were subjected to acoustic, thermal/vacuum, and air loads tests to simulate launch, on-orbit, and re-entry behavior. STS-1, -2 and -5 flight data led to recalibration of on-board instruments and raised estimates of the thermal shock at the NC and WLE. Baseline heating data are now available for the design of future TPS.

Preliminary study of TEC application in cooling system

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Monitoring temperatures in coal conversion and combustion processes via ultrasound

NASA Astrophysics Data System (ADS)

Gopalsami, N.; Raptis, A. C.; Mulcahey, T. P.

1980-02-01

The state of the art of instrumentation for monitoring temperatures in coal conversion and combustion systems is examined. The instrumentation types studied include thermocouples, radiation pyrometers, and acoustical thermometers. The capabilities and limitations of each type are reviewed. A feasibility study of the ultrasonic thermometry is described. A mathematical model of a pulse-echo ultrasonic temperature measurement system is developed using linear system theory. The mathematical model lends itself to the adaptation of generalized correlation techniques for the estimation of propagation delays. Computer simulations are made to test the efficacy of the signal processing techniques for noise-free as well as noisy signals. Based on the theoretical study, acoustic techniques to measure temperature in reactors and combustors are feasible.

A cooperative strategy for parameter estimation in large scale systems biology models.

PubMed

Villaverde, Alejandro F; Egea, Jose A; Banga, Julio R

2012-06-22

Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently. A new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs ("threads") that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results. The cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems.

A cooperative strategy for parameter estimation in large scale systems biology models

PubMed Central

2012-01-01

Background Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently. Results A new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs (“threads”) that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results. Conclusions The cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems. PMID:22727112

Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor.

PubMed

Masić, Alma; Bengtsson, Jessica; Christensson, Magnus

2010-09-01

In this paper we determine the oxygen profile in a biofilm on suspended carriers in two ways: firstly by microelectrode measurements and secondly by a simple mathematical model. The Moving Bed Biofilm Reactor is well-established for wastewater treatment where bacteria grow as a biofilm on the protective surfaces of suspended carriers. The flat shaped BiofilmChip P was developed to allow good conditions for transport of substrates into the biofilm. The oxygen profile was measured in situ the nitrifying biofilm with a microelectrode and it was simulated with a one-dimensional mathematical model. We extended the model by adding a CSTR equation, to connect the reactor to the biofilm through the boundary conditions. We showed the dependence of the thickness of the mass transfer boundary layer on the bulk flow rate. Finally, we estimated the erosion parameter lambda to increase the concordance between the measured and simulated profiles. This lead to a simple empirical relationship between lambda and the flow rate. The data gathered by in situ microelectrode measurements can, together with the mathematical model, be used in predictive modeling and give more insight in the design of new carriers, with the ambition of making process operation more energy efficient. Copyright 2010 Elsevier Inc. All rights reserved.

Quantitative estimation of the cost of parasitic castration in a Helisoma anceps population using a matrix population model.

PubMed

Negovetich, N J; Esch, G W

2008-10-01

Larval trematodes frequently castrate their snail intermediate hosts. When castrated, the snails do not contribute offspring to the population, yet they persist and compete with the uninfected individuals for the available food resources. Parasitic castration should reduce the population growth rate lambda, but the magnitude of this decrease is unknown. The present study attempted to quantify the cost of parasitic castration at the level of the population by mathematically modeling the population of the planorbid snail Helisoma anceps in Charlie's Pond, North Carolina. Analysis of the model identified the life-history trait that most affects lambda, and the degree to which parasitic castration can lower lambda. A period matrix product model was constructed with estimates of fecundity, survival, growth rates, and infection probabilities calculated in a previous study. Elasticity analysis was performed by increasing the values of the life-history traits by 10% and recording the percentage change in lambda. Parasitic castration resulted in a 40% decrease in lambda of H. anceps. Analysis of the model suggests that decreasing the size at maturity was more effective at reducing the cost of castration than increasing survival or growth rates of the snails. The current matrix model was the first to mathematically describe a snail population, and the predictions of the model are in agreement with published research.

IPMP Global Fit - A one-step direct data analysis tool for predictive microbiology.

PubMed

Huang, Lihan

2017-12-04

The objective of this work is to develop and validate a unified optimization algorithm for performing one-step global regression analysis of isothermal growth and survival curves for determination of kinetic parameters in predictive microbiology. The algorithm is incorporated with user-friendly graphical interfaces (GUIs) to develop a data analysis tool, the USDA IPMP-Global Fit. The GUIs are designed to guide the users to easily navigate through the data analysis process and properly select the initial parameters for different combinations of mathematical models. The software is developed for one-step kinetic analysis to directly construct tertiary models by minimizing the global error between the experimental observations and mathematical models. The current version of the software is specifically designed for constructing tertiary models with time and temperature as the independent model parameters in the package. The software is tested with a total of 9 different combinations of primary and secondary models for growth and survival of various microorganisms. The results of data analysis show that this software provides accurate estimates of kinetic parameters. In addition, it can be used to improve the experimental design and data collection for more accurate estimation of kinetic parameters. IPMP-Global Fit can be used in combination with the regular USDA-IPMP for solving the inverse problems and developing tertiary models in predictive microbiology. Published by Elsevier B.V.

Mathematical model of optical signals emitted by electrical discharges occuring in electroinsulating oil

NASA Astrophysics Data System (ADS)

Kozioł, Michał

2017-10-01

The article presents a parametric model describing the registered distributions spectrum of optical radiation emitted by electrical discharges generated in the systems: the needle- needle, the needleplate and in the system for surface discharges. Generation of electrical discharges and registration of the emitted radiation was carried out in three different electrical insulating oils: fabric new, operated (used) and operated with air bubbles. For registration of optical spectra in the range of ultraviolet, visible and near infrared a high resolution spectrophotometer was. The proposed mathematical model was developed in a regression procedure using gauss-sigmoid type function. The dependent variable was the intensity of the recorded optical signals. In order to estimate the optimal parameters of the model an evolutionary algorithm was used. The optimization procedure was performed in Matlab environment. For determination of the matching quality of theoretical parameters of the regression function to the empirical data determination coefficient R2 was applied.

Ultrasensitivity in signaling cascades revisited: Linking local and global ultrasensitivity estimations.

PubMed

Altszyler, Edgar; Ventura, Alejandra C; Colman-Lerner, Alejandro; Chernomoretz, Ariel

2017-01-01

Ultrasensitive response motifs, capable of converting graded stimuli into binary responses, are well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive modules can enhance the system's ultrasensitivity, how a given combination of layers affects a cascade's ultrasensitivity remains an open question for the general case. Here, we introduce a methodology that allows us to determine the presence of sequestration effects and to quantify the relative contribution of each module to the overall cascade's ultrasensitivity. The proposed analysis framework provides a natural link between global and local ultrasensitivity descriptors and it is particularly well-suited to characterize and understand mathematical models used to study real biological systems. As a case study, we have considered three mathematical models introduced by O'Shaughnessy et al. to study a tunable synthetic MAPK cascade, and we show how our methodology can help modelers better understand alternative models.

Simulation of Industrial Wastewater Treatment from the Suspended Impurities into the Flooded Waste Mining Workings

NASA Astrophysics Data System (ADS)

Bondareva, L.; Zakharov, Yu; Goudov, A.

2017-04-01

The paper is dedicated to the mathematical model of slurry wastewater treatment and disposal in a flooded mine working. The goal of the research is to develop and analyze the mathematical model of suspended impurities flow and distribution. Impurity sedimentation model is under consideration. Due to the sediment compaction problem solution domain can be modified. The model allows making a forecast whether volley emission is possible. Numerical simulation results for “Kolchuginskaya” coal mine presented. Impurity concentration diagrams in outflow corresponding to the real full-scale data obtained. Safely operation time mine workings like a wastewater treatment facility are estimated. The carried out calculations demonstrate that the method of industrial wastewater treatment in flooded waste mine workings can be put into practice but it is very important to observe all the processes going on to avoid volley emission of accumulated impurities.

Assessing Strategies Against Gambiense Sleeping Sickness Through Mathematical Modeling

PubMed Central

Rock, Kat S; Ndeffo-Mbah, Martial L; Castaño, Soledad; Palmer, Cody; Pandey, Abhishek; Atkins, Katherine E; Ndung’u, Joseph M; Hollingsworth, T Déirdre; Galvani, Alison; Bever, Caitlin; Chitnis, Nakul; Keeling, Matt J

2018-01-01

Abstract Background Control of gambiense sleeping sickness relies predominantly on passive and active screening of people, followed by treatment. Methods Mathematical modeling explores the potential of 3 complementary interventions in high- and low-transmission settings. Results Intervention strategies that included vector control are predicted to halt transmission most quickly. Targeted active screening, with better and more focused coverage, and enhanced passive surveillance, with improved access to diagnosis and treatment, are both estimated to avert many new infections but, when used alone, are unlikely to halt transmission before 2030 in high-risk settings. Conclusions There was general model consensus in the ranking of the 3 complementary interventions studied, although with discrepancies between the quantitative predictions due to differing epidemiological assumptions within the models. While these predictions provide generic insights into improving control, the most effective strategy in any situation depends on the specific epidemiology in the region and the associated costs. PMID:29860287

Ultrasensitivity in signaling cascades revisited: Linking local and global ultrasensitivity estimations

PubMed Central

Altszyler, Edgar; Ventura, Alejandra C.; Colman-Lerner, Alejandro; Chernomoretz, Ariel

2017-01-01

Ultrasensitive response motifs, capable of converting graded stimuli into binary responses, are well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive modules can enhance the system’s ultrasensitivity, how a given combination of layers affects a cascade’s ultrasensitivity remains an open question for the general case. Here, we introduce a methodology that allows us to determine the presence of sequestration effects and to quantify the relative contribution of each module to the overall cascade’s ultrasensitivity. The proposed analysis framework provides a natural link between global and local ultrasensitivity descriptors and it is particularly well-suited to characterize and understand mathematical models used to study real biological systems. As a case study, we have considered three mathematical models introduced by O’Shaughnessy et al. to study a tunable synthetic MAPK cascade, and we show how our methodology can help modelers better understand alternative models. PMID:28662096

Mathematical modeling of enzyme production using Trichoderma harzianum P49P11 and sugarcane bagasse as carbon source.

PubMed

Gelain, Lucas; da Cruz Pradella, José Geraldo; da Costa, Aline Carvalho

2015-12-01

A mathematical model to describe the kinetics of enzyme production by the filamentous fungus Trichoderma harzianum P49P11 was developed using a low cost substrate as main carbon source (pretreated sugarcane bagasse). The model describes the cell growth, variation of substrate concentration and production of three kinds of enzymes (cellulases, beta-glucosidase and xylanase) in different sugarcane bagasse concentrations (5; 10; 20; 30; 40 gL(-1)). The 10 gL(-1) concentration was used to validate the model and the other to parameter estimation. The model for enzyme production has terms implicitly representing induction and repression. Substrate variation was represented by a simple degradation rate. The models seem to represent well the kinetics with a good fit for the majority of the assays. Validation results indicate that the models are adequate to represent the kinetics for a biotechnological process. Copyright © 2015 Elsevier Ltd. All rights reserved.

Filling in the gaps: estimating numbers of chlamydia tests and diagnoses by age group and sex before and during the implementation of the English National Screening Programme, 2000 to 2012.

PubMed

Chandra, Nastassya L; Soldan, Kate; Dangerfield, Ciara; Sile, Bersabeh; Duffell, Stephen; Talebi, Alireza; Choi, Yoon H; Hughes, Gwenda; Woodhall, Sarah C

2017-02-02

To inform mathematical modelling of the impact of chlamydia screening in England since 2000, a complete picture of chlamydia testing is needed. Monitoring and surveillance systems evolved between 2000 and 2012. Since 2012, data on publicly funded chlamydia tests and diagnoses have been collected nationally. However, gaps exist for earlier years. We collated available data on chlamydia testing and diagnosis rates among 15-44-year-olds by sex and age group for 2000-2012. Where data were unavailable, we applied data- and evidence-based assumptions to construct plausible minimum and maximum estimates and set bounds on uncertainty. There was a large range between estimates in years when datasets were less comprehensive (2000-2008); smaller ranges were seen hereafter. In 15-19-year-old women in 2000, the estimated diagnosis rate ranged between 891 and 2,489 diagnoses per 100,000 persons. Testing and diagnosis rates increased between 2000 and 2012 in women and men across all age groups using minimum or maximum estimates, with greatest increases seen among 15-24-year-olds. Our dataset can be used to parameterise and validate mathematical models and serve as a reference dataset to which trends in chlamydia-related complications can be compared. Our analysis highlights the complexities of combining monitoring and surveillance datasets. This article is copyright of The Authors, 2017.

Quantifying the effect of experimental design choices for in vitro scratch assays.

PubMed

Johnston, Stuart T; Ross, Joshua V; Binder, Benjamin J; Sean McElwain, D L; Haridas, Parvathi; Simpson, Matthew J

2016-07-07

Scratch assays are often used to investigate potential drug treatments for chronic wounds and cancer. Interpreting these experiments with a mathematical model allows us to estimate the cell diffusivity, D, and the cell proliferation rate, λ. However, the influence of the experimental design on the estimates of D and λ is unclear. Here we apply an approximate Bayesian computation (ABC) parameter inference method, which produces a posterior distribution of D and λ, to new sets of synthetic data, generated from an idealised mathematical model, and experimental data for a non-adhesive mesenchymal population of fibroblast cells. The posterior distribution allows us to quantify the amount of information obtained about D and λ. We investigate two types of scratch assay, as well as varying the number and timing of the experimental observations captured. Our results show that a scrape assay, involving one cell front, provides more precise estimates of D and λ, and is more computationally efficient to interpret than a wound assay, with two opposingly directed cell fronts. We find that recording two observations, after making the initial observation, is sufficient to estimate D and λ, and that the final observation time should correspond to the time taken for the cell front to move across the field of view. These results provide guidance for estimating D and λ, while simultaneously minimising the time and cost associated with performing and interpreting the experiment. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

PubMed

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

2018-06-19

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

Determination of minimum enzymatic decolorization time of reactive dye solution by spectroscopic & mathematical approach.

PubMed

Celebi, Mithat; Ozdemir, Zafer Omer; Eroglu, Emre; Altikatoglu, Melda; Guney, Ibrahim

2015-02-01

Synthetic dyes are very important for textile dyeing, paper printing, color photography and petroleum products. Traditional methods of dye removal include biodegradation, precipitation, adsorption, chemical degradation, photo degradation, and chemical coagulation. Dye decolorization with enzymatic reaction is an important issue for several research field (chemistry, environment) In this study, minimum decolorization time of Remazol Brilliant Blue R dye with Horseradish peroxidase enzyme was calculated using with mathematical equation depending on experimental data. Dye decolorization was determined by monitoring the absorbance decrease at the specific maximum wavelength for dye. All experiments were carried out with different initial dye concentrations of Remazol Brilliant Blue R at 25 degrees C constant temperature for 30 minutes. The development of the least squares estimators for a nonlinear model brings about complications not encountered in the case of the linear model. Decolorization times for completely removal of dye were calculated according to equation. It was shown that mathematical equation was conformed exponential curve for dye degradation.

Investigation of the blood behaviour and vascular diseases by using mathematical physic principles

NASA Astrophysics Data System (ADS)

Yardimci, Ahmet; Simsek, Buket

2017-07-01

In this paper we prepare a short survey for using of mathematical physic principles in blood flow and vascular diseases researches. The study of the behavior of blood flow in the blood vessels provides understanding on connection between flow and the development of dieseases such as atherosclerosis, thrombosis, aneurysms etc. and how the flow dynamics is changed under these conditions. Blood flow phenomena are often too complex that it would be possible to describe them entirely analytically, although simple models, such as Poiseuille model, can still provide some insight into blood flow. Blood is not an "ideal fluid" and energy is lost as flowing blood overcomes resistance. Resistance to blood flow is a function of viscosity, vessel radius, and vessel length. So, mathematical Physic principles are useful tools for blood flow research studies. Blood flow is a function of pressure gradient and resistance and resistance to flow can be estimates using Poiseuille's law. Reynold's number can be used to determine whether flow is laminar or turbulent.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

A mathematical model of exposure of non-target Lepidoptera to Bt-maize pollen expressing Cry1Ab within Europe.

PubMed

Perry, J N; Devos, Y; Arpaia, S; Bartsch, D; Gathmann, A; Hails, R S; Kiss, J; Lheureux, K; Manachini, B; Mestdagh, S; Neemann, G; Ortego, F; Schiemann, J; Sweet, J B

2010-05-07

Genetically modified (GM) maize MON810 expresses a Cry1Ab insecticidal protein, derived from Bacillus thuringiensis (Bt), toxic to lepidopteran target pests such as Ostrinia nubilalis. An environmental risk to non-target Lepidoptera from this GM crop is exposure to harmful amounts of Bt-containing pollen deposited on host plants in or near MON810 fields. An 11-parameter mathematical model analysed exposure of larvae of three non-target species: the butterflies Inachis io (L.), Vanessa atalanta (L.) and moth Plutella xylostella (L.), in 11 representative maize cultivation regions in four European countries. A mortality-dose relationship was integrated with a dose-distance relationship to estimate mortality both within the maize MON810 crop and within the field margin at varying distances from the crop edge. Mortality estimates were adjusted to allow for physical effects; the lack of temporal coincidence between the susceptible larval stage concerned and the period over which maize MON810 pollen is shed; and seven further parameters concerned with maize agronomy and host-plant ecology. Sublethal effects were estimated and allowance made for aggregated pollen deposition. Estimated environmental impact was low: in all regions, the calculated mortality rate for worst-case scenarios was less than one individual in every 1572 for the butterflies and one in 392 for the moth.

A mathematical model of exposure of non-target Lepidoptera to Bt-maize pollen expressing Cry1Ab within Europe

PubMed Central

Perry, J. N.; Devos, Y.; Arpaia, S.; Bartsch, D.; Gathmann, A.; Hails, R. S.; Kiss, J.; Lheureux, K.; Manachini, B.; Mestdagh, S.; Neemann, G.; Ortego, F.; Schiemann, J.; Sweet, J. B.

2010-01-01

Genetically modified (GM) maize MON810 expresses a Cry1Ab insecticidal protein, derived from Bacillus thuringiensis (Bt), toxic to lepidopteran target pests such as Ostrinia nubilalis. An environmental risk to non-target Lepidoptera from this GM crop is exposure to harmful amounts of Bt-containing pollen deposited on host plants in or near MON810 fields. An 11-parameter mathematical model analysed exposure of larvae of three non-target species: the butterflies Inachis io (L.), Vanessa atalanta (L.) and moth Plutella xylostella (L.), in 11 representative maize cultivation regions in four European countries. A mortality–dose relationship was integrated with a dose–distance relationship to estimate mortality both within the maize MON810 crop and within the field margin at varying distances from the crop edge. Mortality estimates were adjusted to allow for physical effects; the lack of temporal coincidence between the susceptible larval stage concerned and the period over which maize MON810 pollen is shed; and seven further parameters concerned with maize agronomy and host-plant ecology. Sublethal effects were estimated and allowance made for aggregated pollen deposition. Estimated environmental impact was low: in all regions, the calculated mortality rate for worst-case scenarios was less than one individual in every 1572 for the butterflies and one in 392 for the moth. PMID:20053648

Mathematical analysis of frontal affinity chromatography in particle and membrane configurations.

PubMed

Tejeda-Mansir, A; Montesinos, R M; Guzmán, R

2001-10-30

The scaleup and optimization of large-scale affinity-chromatographic operations in the recovery, separation and purification of biochemical components is of major industrial importance. The development of mathematical models to describe affinity-chromatographic processes, and the use of these models in computer programs to predict column performance is an engineering approach that can help to attain these bioprocess engineering tasks successfully. Most affinity-chromatographic separations are operated in the frontal mode, using fixed-bed columns. Purely diffusive and perfusion particles and membrane-based affinity chromatography are among the main commercially available technologies for these separations. For a particular application, a basic understanding of the main similarities and differences between particle and membrane frontal affinity chromatography and how these characteristics are reflected in the transport models is of fundamental relevance. This review presents the basic theoretical considerations used in the development of particle and membrane affinity chromatography models that can be applied in the design and operation of large-scale affinity separations in fixed-bed columns. A transport model for column affinity chromatography that considers column dispersion, particle internal convection, external film resistance, finite kinetic rate, plus macropore and micropore resistances is analyzed as a framework for exploring further the mathematical analysis. Such models provide a general realistic description of almost all practical systems. Specific mathematical models that take into account geometric considerations and transport effects have been developed for both particle and membrane affinity chromatography systems. Some of the most common simplified models, based on linear driving-force (LDF) and equilibrium assumptions, are emphasized. Analytical solutions of the corresponding simplified dimensionless affinity models are presented. Particular methods for estimating the parameters that characterize the mass-transfer and adsorption mechanisms in affinity systems are described.

A clinically parameterized mathematical model of Shigella immunity to inform vaccine design

PubMed Central

Wahid, Rezwanul; Toapanta, Franklin R.; Simon, Jakub K.; Sztein, Marcelo B.

2018-01-01

We refine and clinically parameterize a mathematical model of the humoral immune response against Shigella, a diarrheal bacteria that infects 80-165 million people and kills an estimated 600,000 people worldwide each year. Using Latin hypercube sampling and Monte Carlo simulations for parameter estimation, we fit our model to human immune data from two Shigella EcSf2a-2 vaccine trials and a rechallenge study in which antibody and B-cell responses against Shigella′s lipopolysaccharide (LPS) and O-membrane proteins (OMP) were recorded. The clinically grounded model is used to mathematically investigate which key immune mechanisms and bacterial targets confer immunity against Shigella and to predict which humoral immune components should be elicited to create a protective vaccine against Shigella. The model offers insight into why the EcSf2a-2 vaccine had low efficacy and demonstrates that at a group level a humoral immune response induced by EcSf2a-2 vaccine or wild-type challenge against Shigella′s LPS or OMP does not appear sufficient for protection. That is, the model predicts an uncontrolled infection of gut epithelial cells that is present across all best-fit model parameterizations when fit to EcSf2a-2 vaccine or wild-type challenge data. Using sensitivity analysis, we explore which model parameter values must be altered to prevent the destructive epithelial invasion by Shigella bacteria and identify four key parameter groups as potential vaccine targets or immune correlates: 1) the rate that Shigella migrates into the lamina propria or epithelium, 2) the rate that memory B cells (BM) differentiate into antibody-secreting cells (ASC), 3) the rate at which antibodies are produced by activated ASC, and 4) the Shigella-specific BM carrying capacity. This paper underscores the need for a multifaceted approach in ongoing efforts to design an effective Shigella vaccine. PMID:29304144

A clinically parameterized mathematical model of Shigella immunity to inform vaccine design.

PubMed

Davis, Courtney L; Wahid, Rezwanul; Toapanta, Franklin R; Simon, Jakub K; Sztein, Marcelo B

2018-01-01

We refine and clinically parameterize a mathematical model of the humoral immune response against Shigella, a diarrheal bacteria that infects 80-165 million people and kills an estimated 600,000 people worldwide each year. Using Latin hypercube sampling and Monte Carlo simulations for parameter estimation, we fit our model to human immune data from two Shigella EcSf2a-2 vaccine trials and a rechallenge study in which antibody and B-cell responses against Shigella's lipopolysaccharide (LPS) and O-membrane proteins (OMP) were recorded. The clinically grounded model is used to mathematically investigate which key immune mechanisms and bacterial targets confer immunity against Shigella and to predict which humoral immune components should be elicited to create a protective vaccine against Shigella. The model offers insight into why the EcSf2a-2 vaccine had low efficacy and demonstrates that at a group level a humoral immune response induced by EcSf2a-2 vaccine or wild-type challenge against Shigella's LPS or OMP does not appear sufficient for protection. That is, the model predicts an uncontrolled infection of gut epithelial cells that is present across all best-fit model parameterizations when fit to EcSf2a-2 vaccine or wild-type challenge data. Using sensitivity analysis, we explore which model parameter values must be altered to prevent the destructive epithelial invasion by Shigella bacteria and identify four key parameter groups as potential vaccine targets or immune correlates: 1) the rate that Shigella migrates into the lamina propria or epithelium, 2) the rate that memory B cells (BM) differentiate into antibody-secreting cells (ASC), 3) the rate at which antibodies are produced by activated ASC, and 4) the Shigella-specific BM carrying capacity. This paper underscores the need for a multifaceted approach in ongoing efforts to design an effective Shigella vaccine.

Gaussian Process Model for Antarctic Surface Mass Balance and Ice Core Site Selection

NASA Astrophysics Data System (ADS)

White, P. A.; Reese, S.; Christensen, W. F.; Rupper, S.

2017-12-01

Surface mass balance (SMB) is an important factor in the estimation of sea level change, and data are collected to estimate models for prediction of SMB on the Antarctic ice sheet. Using Favier et al.'s (2013) quality-controlled aggregate data set of SMB field measurements, a fully Bayesian spatial model is posed to estimate Antarctic SMB and propose new field measurement locations. Utilizing Nearest-Neighbor Gaussian process (NNGP) models, SMB is estimated over the Antarctic ice sheet. An Antarctic SMB map is rendered using this model and is compared with previous estimates. A prediction uncertainty map is created to identify regions of high SMB uncertainty. The model estimates net SMB to be 2173 Gton yr-1 with 95% credible interval (2021,2331) Gton yr-1. On average, these results suggest lower Antarctic SMB and higher uncertainty than previously purported [Vaughan et al. (1999); Van de Berg et al. (2006); Arthern, Winebrenner and Vaughan (2006); Bromwich et al. (2004); Lenaerts et al. (2012)], even though this model utilizes significantly more observations than previous models. Using the Gaussian process' uncertainty and model parameters, we propose 15 new measurement locations for field study utilizing a maximin space-filling, error-minimizing design; these potential measurements are identied to minimize future estimation uncertainty. Using currently accepted Antarctic mass balance estimates and our SMB estimate, we estimate net mass loss [Shepherd et al. (2012); Jacob et al. (2012)]. Furthermore, we discuss modeling details for both space-time data and combining field measurement data with output from mathematical models using the NNGP framework.

From the guest editors.

PubMed

Chowell, Gerardo; Feng, Zhilan; Song, Baojun

2013-01-01

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

A Direct Adaptive Control Approach in the Presence of Model Mismatch

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.; Tao, Gang; Khong, Thuan

2009-01-01

This paper considers the problem of direct model reference adaptive control when the plant-model matching conditions are violated due to abnormal changes in the plant or incorrect knowledge of the plant's mathematical structure. The approach consists of direct adaptation of state feedback gains for state tracking, and simultaneous estimation of the plant-model mismatch. Because of the mismatch, the plant can no longer track the state of the original reference model, but may be able to track a new reference model that still provides satisfactory performance. The reference model is updated if the estimated plant-model mismatch exceeds a bound that is determined via robust stability and/or performance criteria. The resulting controller is a hybrid direct-indirect adaptive controller that offers asymptotic state tracking in the presence of plant-model mismatch as well as parameter deviations.

Implementation of Kalman filter algorithm on models reduced using singular pertubation approximation method and its application to measurement of water level

NASA Astrophysics Data System (ADS)

Rachmawati, Vimala; Khusnul Arif, Didik; Adzkiya, Dieky

2018-03-01

The systems contained in the universe often have a large order. Thus, the mathematical model has many state variables that affect the computation time. In addition, generally not all variables are known, so estimations are needed to measure the magnitude of the system that cannot be measured directly. In this paper, we discuss the model reduction and estimation of state variables in the river system to measure the water level. The model reduction of a system is an approximation method of a system with a lower order without significant errors but has a dynamic behaviour that is similar to the original system. The Singular Perturbation Approximation method is one of the model reduction methods where all state variables of the equilibrium system are partitioned into fast and slow modes. Then, The Kalman filter algorithm is used to estimate state variables of stochastic dynamic systems where estimations are computed by predicting state variables based on system dynamics and measurement data. Kalman filters are used to estimate state variables in the original system and reduced system. Then, we compare the estimation results of the state and computational time between the original and reduced system.

Estimation of Handling Qualities Parameters of the Tu-144 Supersonic Transport Aircraft from Flight Test Data

NASA Technical Reports Server (NTRS)

Curry, Timothy J.; Batterson, James G. (Technical Monitor)

2000-01-01

Low order equivalent system (LOES) models for the Tu-144 supersonic transport aircraft were identified from flight test data. The mathematical models were given in terms of transfer functions with a time delay by the military standard MIL-STD-1797A, "Flying Qualities of Piloted Aircraft," and the handling qualities were predicted from the estimated transfer function coefficients. The coefficients and the time delay in the transfer functions were estimated using a nonlinear equation error formulation in the frequency domain. Flight test data from pitch, roll, and yaw frequency sweeps at various flight conditions were used for parameter estimation. Flight test results are presented in terms of the estimated parameter values, their standard errors, and output fits in the time domain. Data from doublet maneuvers at the same flight conditions were used to assess the predictive capabilities of the identified models. The identified transfer function models fit the measured data well and demonstrated good prediction capabilities. The Tu-144 was predicted to be between level 2 and 3 for all longitudinal maneuvers and level I for all lateral maneuvers. High estimates of the equivalent time delay in the transfer function model caused the poor longitudinal rating.

Use of a mathematical model to estimate tuberculosis transmission risk in an Internet café.

PubMed

Furuya, Hiroyuki; Nagamine, Michiko; Watanabe, Tetsu

2009-03-01

People who live under fragile living conditions may stay overnight in Internet cafés in urban areas. An outbreak of tuberculosis (TB), the routes of which were possibly related to such a facility, has been reported. The purpose of this study was to use a mathematical model to quantify the public health risk of TB infection in such a facility. The reproduction number for airborne infection in an enclosed space (R (A)) was estimated using a Wells-Riley model. First, we estimated R (A) for the TB infection based on the report of the TB outbreak in the Internet café. Second, TB infectious dose, number of days of exposure, and air-exchange rate in the facility were varied to estimate the effect of TB risk settings and environmental factors. We assumed that TB patients and 59 susceptible subjects stayed for 150 days in a room where the air-exchange rate was five per hour. Using the estimated median R (A) of 44.14, the TB infection rate was 74.6%. This result was similar to the epidemiological report that the TB infection rate among employees in the Internet café was 70%. The median R (A) increased linearly as the number of days of exposure increased. The slope of the change in median R (A) divided by the change in the number of days of exposure increased exponentially as air-exchange rate decreased; thus air ventilation in a facility may be essential to prevent TB infection. Appropriate air ventilation in facilities such as Internet cafés is needed as part of a TB-control program in metropolitan areas.

An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

PubMed

Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

2017-04-01

Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

LIFETIME LUNG CANCER RISKS ASSOCIATED WITH INDOOR RADON EXPOSURE BASED ON VARIOUS RADON RISK MODELS FOR CANADIAN POPULATION.

PubMed

Chen, Jing

2017-04-01

This study calculates and compares the lifetime lung cancer risks associated with indoor radon exposure based on well-known risk models in the literature; two risk models are from joint studies among miners and the other three models were developed from pooling studies on residential radon exposure from China, Europe and North America respectively. The aim of this article is to make clear that the various models are mathematical descriptions of epidemiologically observed real risks in different environmental settings. The risk from exposure to indoor radon is real and it is normal that variations could exist among different risk models even when they were applied to the same dataset. The results show that lifetime risk estimates vary significantly between the various risk models considered here: the model based on the European residential data provides the lowest risk estimates, while models based on the European miners and Chinese residential pooling with complete dosimetry give the highest values. The lifetime risk estimates based on the EPA/BEIR-VI model lie within this range and agree reasonably well with the averages of risk estimates from the five risk models considered in this study. © Crown copyright 2016.

Deterministic SLIR model for tuberculosis disease mapping

NASA Astrophysics Data System (ADS)

Aziz, Nazrina; Diah, Ijlal Mohd; Ahmad, Nazihah; Kasim, Maznah Mat

2017-11-01

Tuberculosis (TB) occurs worldwide. It can be transmitted to others directly through air when active TB persons sneeze, cough or spit. In Malaysia, it was reported that TB cases had been recognized as one of the most infectious disease that lead to death. Disease mapping is one of the methods that can be used as the prevention strategies since it can displays clear picture for the high-low risk areas. Important thing that need to be considered when studying the disease occurrence is relative risk estimation. The transmission of TB disease is studied through mathematical model. Therefore, in this study, deterministic SLIR models are used to estimate relative risk for TB disease transmission.

Modelling of seasonal influenza and estimation of the burden in Tunisia.

PubMed

Chlif, S; Aissi, W; Bettaieb, J; Kharroubi, G; Nouira, M; Yazidi, R; El Moussi, A; Maazaoui, L; Slim, A; Salah, A Ben

2016-10-02

The burden of influenza was estimated from surveillance data in Tunisia using epidemiological parameters of transmission with WHO classical tools and mathematical modelling. The incidence rates of influenza-associated influenza-like illness (ILI) per 100 000 were 18 735 in 2012/2013 season; 5536 in 2013/14 and 12 602 in 2014/15. The estimated proportions of influenza-associated ILI in the total outpatient load were 3.16%; 0.86% and 1.98% in the 3 seasons respectively. Distribution of influenza viruses among positive patients was: A(H3N2) 15.5%; A(H1N1)pdm2009 39.2%; and B virus 45.3% in 2014/2015 season. From the estimated numbers of symptomatic cases, we estimated that the critical proportions of the population that should be vaccinated were 15%, 4% and 10% respectively. Running the model for the different values of R0, we quantified the number of symptomatic clinical cases, the clinical attack rates, the symptomatic clinical attack rates and the number of deaths. More realistic versions of this model and improved estimates of parameters from surveillance data will strengthen the estimation of the burden of influenza.

Estimating and Modeling Gene Flow for a Spatially Distributed Species

DTIC Science & Technology

1991-01-01

inherited from each parent’s gamete (sperm or egg) cell. The qsnotype of a diploid individual is the specification of all of its chromosome pairs. It is...sometimes sufficient to model a diploid species as if it were haploid . Haploid individuals have only one of each type of chromosome. We think of a chro...stage for the mathematical models, the necessary genetical terms are collected here. Most organisms are diploid , having chromosome.- in pairs, one

Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks

PubMed Central

Besada, Juan A.

2017-01-01

In this paper, a complete and rigorous mathematical model for secondary surveillance radar systematic errors (biases) is developed. The model takes into account the physical effects systematically affecting the measurement processes. The azimuth biases are calculated from the physical error of the antenna calibration and the errors of the angle determination dispositive. Distance bias is calculated from the delay of the signal produced by the refractivity index of the atmosphere, and from clock errors, while the altitude bias is calculated taking into account the atmosphere conditions (pressure and temperature). It will be shown, using simulated and real data, that adapting a classical bias estimation process to use the complete parametrized model results in improved accuracy in the bias estimation. PMID:28934157

THE SHEFFIELD ALCOHOL POLICY MODEL - A MATHEMATICAL DESCRIPTION.

PubMed

Brennan, Alan; Meier, Petra; Purshouse, Robin; Rafia, Rachid; Meng, Yang; Hill-Macmanus, Daniel; Angus, Colin; Holmes, John

2014-09-30

This methodology paper sets out a mathematical description of the Sheffield Alcohol Policy Model version 2.0, a model to evaluate public health strategies for alcohol harm reduction in the UK. Policies that can be appraised include a minimum price per unit of alcohol, restrictions on price discounting, and broader public health measures. The model estimates the impact on consumers, health services, crime, employers, retailers and government tax revenues. The synthesis of public and commercial data sources to inform the model structure is described. A detailed algebraic description of the model is provided. This involves quantifying baseline levels of alcohol purchasing and consumption by age and gender subgroups, estimating the impact of policies on consumption, for example, using evidence on price elasticities of demand for alcohol, quantification of risk functions relating alcohol consumption to harms including 47 health conditions, crimes, absenteeism and unemployment, and finally monetary valuation of the consequences. The results framework, shown for a minimum price per unit of alcohol, has been used to provide policy appraisals for the UK government policy-makers. In discussion and online appendix, we explore issues around valuation and scope, limitations of evidence/data, how the framework can be adapted to other countries and decisions, and ongoing plans for further development. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd.

Estimation of hepatitis C virus infections resulting from vertical transmission in Egypt.

PubMed

Benova, Lenka; Awad, Susanne F; Miller, F DeWolfe; Abu-Raddad, Laith J

2015-03-01

Despite having the highest hepatitis C virus (HCV) prevalence in the world, the ongoing level of HCV incidence in Egypt and its drivers are poorly understood. Whereas HCV mother-to-child infection is a well-established transmission route, there are no estimates of HCV infections resulting from vertical transmission for any country, including Egypt. The aim of this study was to estimate the absolute number of new HCV infections resulting from vertical transmission in Egypt. We developed a conceptual framework of HCV vertical transmission, expressed in terms of a mathematical model and based on maternal HCV antibody and viremia. The mathematical model estimated the number of HCV vertical infections nationally and for six subnational areas. Applying two vertical transmission risk estimates to the 2008 Egyptian birth cohort, we estimated that between 3,080 and 5,167 HCV infections resulted from vertical transmission among children born in 2008. HCV vertical transmission may account for half of incident cases in the <5-year age group. Disproportionately higher proportions of vertical infections were estimated in Lower Rural and Upper Rural subnational areas. This geographical clustering was a result of higher-area-level HCV prevalence among women and higher fertility rates. Vertical transmission is one of the primary HCV infection routes among children<5 years in Egypt. The absolute number of vertical transmissions and the young age at infection highlight a public health concern. These findings also emphasize the need to quantify the relative contributions of other transmission routes to HCV incidence in Egypt. © 2014 The Authors. Hepatology published by Wiley Periodicals, Inc., on behalf of the American Association for the Study of Liver Diseases.

[Flavouring estimation of quality of grape wines with use of methods of mathematical statistics].

PubMed

Yakuba, Yu F; Khalaphyan, A A; Temerdashev, Z A; Bessonov, V V; Malinkin, A D

2016-01-01

The questions of forming of wine's flavour integral estimation during the tasting are discussed, the advantages and disadvantages of the procedures are declared. As investigating materials we used the natural white and red wines of Russian manufactures, which were made with the traditional technologies from Vitis Vinifera, straight hybrids, blending and experimental wines (more than 300 different samples). The aim of the research was to set the correlation between the content of wine's nonvolatile matter and wine's tasting quality rating by mathematical statistics methods. The content of organic acids, amino acids and cations in wines were considered as the main factors influencing on the flavor. Basically, they define the beverage's quality. The determination of those components in wine's samples was done by the electrophoretic method «CAPEL». Together with the analytical checking of wine's samples quality the representative group of specialists simultaneously carried out wine's tasting estimation using 100 scores system. The possibility of statistical modelling of correlation of wine's tasting estimation based on analytical data of amino acids and cations determination reasonably describing the wine's flavour was examined. The statistical modelling of correlation between the wine's tasting estimation and the content of major cations (ammonium, potassium, sodium, magnesium, calcium), free amino acids (proline, threonine, arginine) and the taking into account the level of influence on flavour and analytical valuation within fixed limits of quality accordance were done with Statistica. Adequate statistical models which are able to predict tasting estimation that is to determine the wine's quality using the content of components forming the flavour properties have been constructed. It is emphasized that along with aromatic (volatile) substances the nonvolatile matter - mineral substances and organic substances - amino acids such as proline, threonine, arginine influence on wine's flavour properties. It has been shown the nonvolatile components contribute in organoleptic and flavour quality estimation of wines as aromatic volatile substances but they take part in forming the expert's evaluation.

Estimating parameter of influenza transmission using regularized least square

NASA Astrophysics Data System (ADS)

Nuraini, N.; Syukriah, Y.; Indratno, S. W.

2014-02-01

Transmission process of influenza can be presented in a mathematical model as a non-linear differential equations system. In this model the transmission of influenza is determined by the parameter of contact rate of the infected host and susceptible host. This parameter will be estimated using a regularized least square method where the Finite Element Method and Euler Method are used for approximating the solution of the SIR differential equation. The new infected data of influenza from CDC is used to see the effectiveness of the method. The estimated parameter represents the contact rate proportion of transmission probability in a day which can influence the number of infected people by the influenza. Relation between the estimated parameter and the number of infected people by the influenza is measured by coefficient of correlation. The numerical results show positive correlation between the estimated parameters and the infected people.

Kinetics and mechanism of olefin catalytic hydroalumination by organoaluminum compounds

NASA Astrophysics Data System (ADS)

Koledina, K. F.; Gubaidullin, I. M.

2016-05-01

The complex reaction mechanism of α-olefin catalytic hydroalumination by alkylalanes is investigated via mathematical modeling that involves plotting the kinetic models for the individual reactions that make up a complex system and a separate study of their principles. Kinetic parameters of olefin catalytic hydroalumination are estimated. Activation energies of the possible steps of the schemes of complex reaction mechanisms are compared and possible reaction pathways are determined.

Thermodynamic analysis of biofuels as fuels for high temperature fuel cells

NASA Astrophysics Data System (ADS)

Milewski, Jarosław; Bujalski, Wojciech; Lewandowski, Janusz

2011-11-01

Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.

Thermodynamic analysis of biofuels as fuels for high temperature fuel cells

NASA Astrophysics Data System (ADS)

Milewski, Jarosław; Bujalski, Wojciech; Lewandowski, Janusz

2013-02-01

Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.

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

PubMed

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

2007-02-01

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

Mathematical model of organic substrate degradation in solid waste windrow composting.

PubMed

Seng, Bunrith; Kristanti, Risky Ayu; Hadibarata, Tony; Hirayama, Kimiaki; Katayama-Hirayama, Keiko; Kaneko, Hidehiro

2016-01-01

Organic solid waste composting is a complex process that involves many coupled physical, chemical and biological mechanisms. To understand this complexity and to ease in planning, design and management of the composting plant, mathematical model for simulation is usually applied. The aim of this paper is to develop a mathematical model of organic substrate degradation and its performance evaluation in solid waste windrow composting system. The present model is a biomass-dependent model, considering biological growth processes under the limitation of moisture, oxygen and substrate contents, and temperature. The main output of this model is substrate content which was divided into two categories: slowly and rapidly degradable substrates. To validate the model, it was applied to a laboratory scale windrow composting of a mixture of wood chips and dog food. The wastes were filled into a cylindrical reactor of 6 cm diameter and 1 m height. The simulation program was run for 3 weeks with 1 s stepwise. The simulated results were in reasonably good agreement with the experimental results. The MC and temperature of model simulation were found to be matched with those of experiment, but limited for rapidly degradable substrates. Under anaerobic zone, the degradation of rapidly degradable substrate needs to be incorporated into the model to achieve full simulation of a long period static pile composting. This model is a useful tool to estimate the changes of substrate content during composting period, and acts as a basic model for further development of a sophisticated model.

Mathematical model of marine diesel engine simulator for a new methodology of self propulsion tests

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

Izzuddin, Nur; Sunarsih,; Priyanto, Agoes

As a vessel operates in the open seas, a marine diesel engine simulator whose engine rotation is controlled to transmit through propeller shaft is a new methodology for the self propulsion tests to track the fuel saving in a real time. Considering the circumstance, this paper presents the real time of marine diesel engine simulator system to track the real performance of a ship through a computer-simulated model. A mathematical model of marine diesel engine and the propeller are used in the simulation to estimate fuel rate, engine rotating speed, thrust and torque of the propeller thus achieve the targetmore » vessel’s speed. The input and output are a real time control system of fuel saving rate and propeller rotating speed representing the marine diesel engine characteristics. The self-propulsion tests in calm waters were conducted using a vessel model to validate the marine diesel engine simulator. The simulator then was used to evaluate the fuel saving by employing a new mathematical model of turbochargers for the marine diesel engine simulator. The control system developed will be beneficial for users as to analyze different condition of vessel’s speed to obtain better characteristics and hence optimize the fuel saving rate.« less

Measuring Forest Area Loss Over Time Using FIA Plots and Satellite Imagery

Treesearch

Michael L. Hoppus; Andrew J. Lister

2005-01-01

How accurately can FIA plots, scattered at 1 per 6,000 acres, identify often rare forest land loss, estimated at less than 1 percent per year in the Northeast? Here we explore this question mathematically, empirically, and by comparing FIA plot estimates of forest change with satellite image based maps of forest loss. The mathematical probability of exactly estimating...

Estimation of parameters of constant elasticity of substitution production functional model

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi

2017-11-01

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

An evolutionary morphological approach for software development cost estimation.

PubMed

Araújo, Ricardo de A; Oliveira, Adriano L I; Soares, Sergio; Meira, Silvio

2012-08-01

In this work we present an evolutionary morphological approach to solve the software development cost estimation (SDCE) problem. The proposed approach consists of a hybrid artificial neuron based on framework of mathematical morphology (MM) with algebraic foundations in the complete lattice theory (CLT), referred to as dilation-erosion perceptron (DEP). Also, we present an evolutionary learning process, called DEP(MGA), using a modified genetic algorithm (MGA) to design the DEP model, because a drawback arises from the gradient estimation of morphological operators in the classical learning process of the DEP, since they are not differentiable in the usual way. Furthermore, an experimental analysis is conducted with the proposed model using five complex SDCE problems and three well-known performance metrics, demonstrating good performance of the DEP model to solve SDCE problems. Copyright © 2012 Elsevier Ltd. All rights reserved.

Motion and Structure Estimation of Manoeuvring Objects in Multiple- Camera Image Sequences

DTIC Science & Technology

1992-11-01

and Speckert [23], Gennery [24], Hallman [25], Legters and Young [26], Stuller and Krishnamurthy [27], Wu et al. [381, Matthies, Kanade, and Szeliski...26] G.R. Legters , T.Y. Young, "A mathematical model for computer image track- ing," IEEE Transactions on Pattern Analysis and Machine Intelligence

Calculating Irradiance For Photosynthesis In The Ocean

NASA Technical Reports Server (NTRS)

Collins, Donald J.; Davis, Curtiss O.; Booth, C. Rockwell; Kiefer, Dale A.; Stallings, Casson

1990-01-01

Mathematical model predicts available and usable irradiances. Yields estimates of irradiance available for photosynthesis (Epar) and irradiance usable for photosynthesis (Epur) as functions of depth in ocean. Describes Epur and Epar in terms of spectral parameters measured remotely (from satellites or airplanes). These irradiances useful in studies of photosynthetic productivity of phytoplankton in euphotic layer.

Estimating potential stylet penetration of southern green stink bug (Hemiptera: Pentatomidae) - A mathematical modeling approach

USDA-ARS?s Scientific Manuscript database

Southern green stink bugs, Nezara viridula (L.), and related species are significant pests of cotton in the U.S. Cotton Belt. Using their stylets, adults introduce disease pathogens of cotton into cotton bolls, and preliminary data indicates nymphs can also ingest these pathogens. Data is lacking ...

Science Achievement Gaps Begin Very Early, Persist, and Are Largely Explained by Modifiable Factors

ERIC Educational Resources Information Center

Morgan, Paul L.; Farkas, George; Hillemeier, Marianne M.; Maczuga, Steve

2016-01-01

We examined the age of onset, over-time dynamics, and mechanisms underlying science achievement gaps in U.S. elementary and middle schools. To do so, we estimated multilevel growth models that included as predictors children's own general knowledge, reading and mathematics achievement, behavioral self-regulation, sociodemographics, other child-…

Application of mathematical model methods for optimization tasks in construction materials technology

NASA Astrophysics Data System (ADS)

Fomina, E. V.; Kozhukhova, N. I.; Sverguzova, S. V.; Fomin, A. E.

2018-05-01

In this paper, the regression equations method for design of construction material was studied. Regression and polynomial equations representing the correlation between the studied parameters were proposed. The logic design and software interface of the regression equations method focused on parameter optimization to provide the energy saving effect at the stage of autoclave aerated concrete design considering the replacement of traditionally used quartz sand by coal mining by-product such as argillite. The mathematical model represented by a quadric polynomial for the design of experiment was obtained using calculated and experimental data. This allowed the estimation of relationship between the composition and final properties of the aerated concrete. The surface response graphically presented in a nomogram allowed the estimation of concrete properties in response to variation of composition within the x-space. The optimal range of argillite content was obtained leading to a reduction of raw materials demand, development of target plastic strength of aerated concrete as well as a reduction of curing time before autoclave treatment. Generally, this method allows the design of autoclave aerated concrete with required performance without additional resource and time costs.

Estimating the force of measles virus infection from hospitalised cases in Lusaka, Zambia.

PubMed

Scott, Susana; Mossong, Joel; Moss, William J; Cutts, Felicity T; Kasolo, Francis; Sinkala, Moses; Cousens, Simon

2004-12-21

Estimates of the force of infection (the rate at which susceptible individuals acquire infection) are essential for modelling the transmission dynamics of infectious diseases and can be a useful tool in evaluating mass vaccination strategies. Few estimates exist of the force of infection of measles virus in sub-Saharan Africa. A mathematical model was applied to age-specific recorded hospital admissions between September 1996 and September 1999 to estimate the force of measles virus infection in Lusaka, Zambia. The average force of infection was estimated to be 20% per year (95% confidence intervals (CI) 16.5, 23.5) which was insensitive to varying assumptions about vaccine coverage. The force of infection varied from year to year (P < 0.001) reflecting the cyclic pattern of measles incidence. The estimated probability of a case being hospitalised decreased with age, consistent with less severe disease in older children. Estimates of the force of infection using routinely available data were consistent with those based upon serological surveys in other sub-Saharan African countries.

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

Thangavelu, Pulari U.; Gupta, Vipul; Dixit, Narendra M., E-mail: narendra@chemeng.iisc.ernet.in

The contest between the host factor APOBEC3G (A3G) and the HIV-1 protein Vif presents an attractive target of intervention. The extent to which the A3G–Vif interaction must be suppressed to tilt the balance in favor of A3G remains unknown. We employed stochastic simulations and mathematical modeling of the within-host dynamics and evolution of HIV-1 to estimate the fraction of progeny virions that must incorporate A3G to render productive infection unsustainable. Using three different approaches, we found consistently that a transition from sustained infection to suppression of productive infection occurred when the latter fraction exceeded ∼0.8. The transition was triggered bymore » A3G-induced hypermutations that led to premature stop codons compromising viral production and was consistent with driving the basic reproductive number, R{sub 0}, below unity. The fraction identified may serve as a quantitative guideline for strategies targeting the A3G–Vif axis. - Highlights: • We perform simulations and mathematical modeling of the role of APOBEC3G in suppressing HIV-1 infection. • In three distinct ways, we estimate that when over 80% of progeny virions carry APOBEC3G, productive HIV-1 infection would be suppressed. • Our estimate of this critical fraction presents quantitative guidelines for strategies targeting the APOBEC3G–Vif axis.« less

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study.

PubMed

MacLean, Adam L; Harrington, Heather A; Stumpf, Michael P H; Byrne, Helen M

2016-01-01

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women.

PubMed

Higa, M N; Silva, E; Neves, V F C; Catai, A M; Gallo, L; Silva de Sá, M F

2007-04-01

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 +/- 2.63 years old) and 16 postmenopausal (57 +/- 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg(-1) min(-1)), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg(-1) min(-1)) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (rs = 0.75) and VCO2 (rs = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

Mathematical modeling the radiation effects on humoral immunity

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

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

State observer for synchronous motors

DOEpatents

Lang, Jeffrey H.

1994-03-22

A state observer driven by measurements of phase voltages and currents for estimating the angular orientation of a rotor of a synchronous motor such as a variable reluctance motor (VRM). Phase voltages and currents are detected and serve as inputs to a state observer. The state observer includes a mathematical model of the electromechanical operation of the synchronous motor. The characteristics of the state observer are selected so that the observer estimates converge to the actual rotor angular orientation and velocity, winding phase flux linkages or currents.

Quantification of the rates of resynchronization of heart rate with body temperature rhythms in man following a photoperiod shift

NASA Technical Reports Server (NTRS)

Hetherington, N. W.; Rosenblatt, L. S.; Higgins, E. A.; Winget, C. M.

1973-01-01

A mathematical model previously presented by Rosenblatt et al. (1973) for estimating the rates of resynchronization of individual biorhythms following transmeridian flights or photoperiod shifts is extended to estimation of rates at which two biorythms resynchronize with respect to each other. Such quantification of the rate of restoration of the initial phase relationship of the two biorhythms is pointed out as a valuable tool in the study of internal desynchronosis.

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

A model for estimating pathogen variability in shellfish and predicting minimum depuration times.

PubMed

McMenemy, Paul; Kleczkowski, Adam; Lees, David N; Lowther, James; Taylor, Nick

2018-01-01

Norovirus is a major cause of viral gastroenteritis, with shellfish consumption being identified as one potential norovirus entry point into the human population. Minimising shellfish norovirus levels is therefore important for both the consumer's protection and the shellfish industry's reputation. One method used to reduce microbiological risks in shellfish is depuration; however, this process also presents additional costs to industry. Providing a mechanism to estimate norovirus levels during depuration would therefore be useful to stakeholders. This paper presents a mathematical model of the depuration process and its impact on norovirus levels found in shellfish. Two fundamental stages of norovirus depuration are considered: (i) the initial distribution of norovirus loads within a shellfish population and (ii) the way in which the initial norovirus loads evolve during depuration. Realistic assumptions are made about the dynamics of norovirus during depuration, and mathematical descriptions of both stages are derived and combined into a single model. Parameters to describe the depuration effect and norovirus load values are derived from existing norovirus data obtained from U.K. harvest sites. However, obtaining population estimates of norovirus variability is time-consuming and expensive; this model addresses the issue by assuming a 'worst case scenario' for variability of pathogens, which is independent of mean pathogen levels. The model is then used to predict minimum depuration times required to achieve norovirus levels which fall within possible risk management levels, as well as predictions of minimum depuration times for other water-borne pathogens found in shellfish. Times for Escherichia coli predicted by the model all fall within the minimum 42 hours required for class B harvest sites, whereas minimum depuration times for norovirus and FRNA+ bacteriophage are substantially longer. Thus this study provides relevant information and tools to assist norovirus risk managers with future control strategies.

Fluorescence of bioaerosols: mathematical model including primary fluorescing and absorbing molecules in bacteria.

PubMed

Hill, Steven C; Pan, Yong-Le; Williamson, Chatt; Santarpia, Joshua L; Hill, Hanna H

2013-09-23

This paper describes a mathematical model of fluorescent biological particles composed of bacteria, viruses, or proteins. The fluorescent and/or light absorbing molecules included in the model are amino acids (tryptophan, etc.); nucleic acids (DNA, RNA, etc.); coenzymes (nicotinamide adenine dinucleotides, flavins, and vitamins B₆ and K and variants of these); and dipicolinates. The concentrations, absorptivities, and fluorescence quantum yields are estimated from the literature, often with large uncertainties. The bioparticles in the model are spherical and homogeneous. Calculated fluorescence cross sections for particles excited at 266, 280, and 355 nm are compared with measured values from the literature for several bacteria, bacterial spores and albumins. The calculated 266- and 280-nm excited fluorescence is within a factor of 3.2 of the measurements for the vegetative cells and proteins, but overestimates the fluorescence of spores by a factor of 10 or more. This is the first reported modeling of the fluorescence of bioaerosols in which the primary fluorophores and absorbing molecules are included.

Latent tuberculosis infection in foreign-born communities: Import vs. transmission in The Netherlands derived through mathematical modelling

PubMed Central

Kloet, Serieke; Cobelens, Frank; Bootsma, Martin

2018-01-01

While tuberculosis (TB) represents a significant disease burden worldwide, low-incidence countries strive to reach the WHO target of pre-elimination by 2035. Screening for TB in immigrants is an important component of the strategy to reduce the TB burden in low-incidence settings. An important option is the screening and preventive treatment of latent TB infection (LTBI). Whether this policy is worthwhile depends on the extent of transmission within the country, and introduction of new cases through import. Mathematical transmission models of TB have been used to identify key parameters in the epidemiology of TB and estimate transmission rates. An important application has also been to investigate the consequences of policy scenarios. Here, we formulate a mathematical model for TB transmission within the Netherlands to estimate the size of the pool of latent infections, and to determine the share of importation–either through immigration or travel- versus transmission within the Netherlands. We take into account importation of infections due to immigration, and travel to the country of origin, focusing on the three ethnicities most represented among foreign-born TB cases (after exclusion of those overrepresented among asylum seekers): Moroccans, Turkish and Indonesians. We fit a system of ordinary differential equations to the data from the Netherlands Tuberculosis Registry on (extra-)pulmonary TB cases from 1995–2013. We estimate that about 27% of Moroccans, 25% of Indonesians, and 16% of Turkish, are latently infected. Furthermore, we find that for all three foreign-born communities, immigration is the most important source of LTBI, but the extent of within-country transmission is much lower (about half) for the Turkish and Indonesian communities than for the Moroccan. This would imply that contact investigation would have a greater yield in the latter community than in the former. Travel remains a minor factor contributing LTBI, suggesting that targeting returning travelers might be less effective at preventing LTBI than immigrants upon entry in the country. PMID:29444122

Latent tuberculosis infection in foreign-born communities: Import vs. transmission in The Netherlands derived through mathematical modelling.

PubMed

Korthals Altes, Hester; Kloet, Serieke; Cobelens, Frank; Bootsma, Martin

2018-01-01

While tuberculosis (TB) represents a significant disease burden worldwide, low-incidence countries strive to reach the WHO target of pre-elimination by 2035. Screening for TB in immigrants is an important component of the strategy to reduce the TB burden in low-incidence settings. An important option is the screening and preventive treatment of latent TB infection (LTBI). Whether this policy is worthwhile depends on the extent of transmission within the country, and introduction of new cases through import. Mathematical transmission models of TB have been used to identify key parameters in the epidemiology of TB and estimate transmission rates. An important application has also been to investigate the consequences of policy scenarios. Here, we formulate a mathematical model for TB transmission within the Netherlands to estimate the size of the pool of latent infections, and to determine the share of importation-either through immigration or travel- versus transmission within the Netherlands. We take into account importation of infections due to immigration, and travel to the country of origin, focusing on the three ethnicities most represented among foreign-born TB cases (after exclusion of those overrepresented among asylum seekers): Moroccans, Turkish and Indonesians. We fit a system of ordinary differential equations to the data from the Netherlands Tuberculosis Registry on (extra-)pulmonary TB cases from 1995-2013. We estimate that about 27% of Moroccans, 25% of Indonesians, and 16% of Turkish, are latently infected. Furthermore, we find that for all three foreign-born communities, immigration is the most important source of LTBI, but the extent of within-country transmission is much lower (about half) for the Turkish and Indonesian communities than for the Moroccan. This would imply that contact investigation would have a greater yield in the latter community than in the former. Travel remains a minor factor contributing LTBI, suggesting that targeting returning travelers might be less effective at preventing LTBI than immigrants upon entry in the country.

Patient-based estimation of organ dose for a population of 58 adult patients across 13 protocol categories

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

Sahbaee, Pooyan, E-mail: psahbae@ncsu.edu; Segars, W. Paul; Samei, Ehsan

2014-07-15

Purpose: This study aimed to provide a comprehensive patient-specific organ dose estimation across a multiplicity of computed tomography (CT) examination protocols. Methods: A validated Monte Carlo program was employed to model a common CT system (LightSpeed VCT, GE Healthcare). The organ and effective doses were estimated from 13 commonly used body and neurological CT examination. The dose estimation was performed on 58 adult computational extended cardiac-torso phantoms (35 male, 23 female, mean age 51.5 years, mean weight 80.2 kg). The organ dose normalized by CTDI{sub vol} (h factor) and effective dose normalized by the dose length product (DLP) (k factor)more » were calculated from the results. A mathematical model was derived for the correlation between the h and k factors with the patient size across the protocols. Based on this mathematical model, a dose estimation iPhone operating system application was designed and developed to be used as a tool to estimate dose to the patients for a variety of routinely used CT examinations. Results: The organ dose results across all the protocols showed an exponential decrease with patient body size. The correlation was generally strong for the organs which were fully or partially located inside the scan coverage (Pearson sample correlation coefficient (r) of 0.49). The correlation was weaker for organs outside the scan coverage for which distance between the organ and the irradiation area was a stronger predictor of dose to the organ. For body protocols, the effective dose before and after normalization by DLP decreased exponentially with increasing patient's body diameter (r > 0.85). The exponential relationship between effective dose and patient's body diameter was significantly weaker for neurological protocols (r < 0.41), where the trunk length was a slightly stronger predictor of effective dose (0.15 < r < 0.46). Conclusions: While the most accurate estimation of a patient dose requires specific modeling of the patient anatomy, a first order approximation of organ and effective doses from routine CT scan protocols can be reasonably estimated using size specific factors. Estimation accuracy is generally poor for organ outside the scan range and for neurological protocols. The dose calculator designed in this study can be used to conveniently estimate and report the dose values for a patient across a multiplicity of CT scan protocols.« less

Modeling the Declining Positivity Rates for Human Immunodeficiency Virus Testing in New York State.

PubMed

Martin, Erika G; MacDonald, Roderick H; Smith, Lou C; Gordon, Daniel E; Lu, Tao; OʼConnell, Daniel A

2015-01-01

New York health care providers have experienced declining percentages of positive human immunodeficiency virus (HIV) tests among patients. Furthermore, observed positivity rates are lower than expected on the basis of the national estimate that one-fifth of HIV-infected residents are unaware of their infection. We used mathematical modeling to evaluate whether this decline could be a result of declining numbers of HIV-infected persons who are unaware of their infection, a measure that is impossible to measure directly. A stock-and-flow mathematical model of HIV incidence, testing, and diagnosis was developed. The model includes stocks for uninfected, infected and unaware (in 4 disease stages), and diagnosed individuals. Inputs came from published literature and time series (2006-2009) for estimated new infections, newly diagnosed HIV cases, living diagnosed cases, mortality, and diagnosis rates in New York. Primary model outcomes were the percentage of HIV-infected persons unaware of their infection and the percentage of HIV tests with a positive result (HIV positivity rate). In the base case, the estimated percentage of unaware HIV-infected persons declined from 14.2% in 2006 (range, 11.9%-16.5%) to 11.8% in 2010 (range, 9.9%-13.1%). The HIV positivity rate, assuming testing occurred independent of risk, was 0.12% in 2006 (range, 0.11%-0.15%) and 0.11% in 2010 (range, 0.10%-0.13%). The observed HIV positivity rate was more than 4 times the expected positivity rate based on the model. HIV test positivity is a readily available indicator, but it cannot distinguish causes of underlying changes. Findings suggest that the percentage of unaware HIV-infected New Yorkers is lower than the national estimate and that the observed HIV test positivity rate is greater than expected if infected and uninfected individuals tested at the same rate, indicating that testing efforts are appropriately targeting undiagnosed cases.

Anomaly Detection in Test Equipment via Sliding Mode Observers

NASA Technical Reports Server (NTRS)

Solano, Wanda M.; Drakunov, Sergey V.

2012-01-01

Nonlinear observers were originally developed based on the ideas of variable structure control, and for the purpose of detecting disturbances in complex systems. In this anomaly detection application, these observers were designed for estimating the distributed state of fluid flow in a pipe described by a class of advection equations. The observer algorithm uses collected data in a piping system to estimate the distributed system state (pressure and velocity along a pipe containing liquid gas propellant flow) using only boundary measurements. These estimates are then used to further estimate and localize possible anomalies such as leaks or foreign objects, and instrumentation metering problems such as incorrect flow meter orifice plate size. The observer algorithm has the following parts: a mathematical model of the fluid flow, observer control algorithm, and an anomaly identification algorithm. The main functional operation of the algorithm is in creating the sliding mode in the observer system implemented as software. Once the sliding mode starts in the system, the equivalent value of the discontinuous function in sliding mode can be obtained by filtering out the high-frequency chattering component. In control theory, "observers" are dynamic algorithms for the online estimation of the current state of a dynamic system by measurements of an output of the system. Classical linear observers can provide optimal estimates of a system state in case of uncertainty modeled by white noise. For nonlinear cases, the theory of nonlinear observers has been developed and its success is mainly due to the sliding mode approach. Using the mathematical theory of variable structure systems with sliding modes, the observer algorithm is designed in such a way that it steers the output of the model to the output of the system obtained via a variety of sensors, in spite of possible mismatches between the assumed model and actual system. The unique properties of sliding mode control allow not only control of the model internal states to the states of the real-life system, but also identification of the disturbance or anomaly that may occur.

Sundanese Ethnomathematics: Mathematical Activities in Estimating, Measuring, and Making Patterns

ERIC Educational Resources Information Center

Muhtadi, Dedi; Sukirwan; Warsito; Prahmana, Rully Charitas Indra

2017-01-01

Mathematics is a form of culture integrated in all aspects of society, wherever there are, including the sundanese ethnic communities. This enables the mathematical concepts embedded in cultural practices and recognizes that all people develop a special way of doing mathematics called ethnomathematics activities. Sundanese ethnomathematics is…

Estimation in the Primary School: Developing a Key Mathematical Skill for Life

ERIC Educational Resources Information Center

Mildenhall, Paula

2016-01-01

Very recently, in the "Australian Association of Mathematics Teachers (AAMT)/Australian Industry Group quantitative report" (2014), concerns were raised that school mathematics is lacking real world application. This report highlighted the gaps between school mathematics and the requirements of the workplace. After interviewing industry…

Reference breast temperature: proposal of an equation

PubMed Central

de Souza, Gladis Aparecida Galindo Reisemberger; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso, Carlos; Neves, Eduardo Borba

2015-01-01

ABSTRACT Objective To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Methods Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. Results We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. Conclusion The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies. PMID:26761549

Predictability and preparedness in influenza control.

PubMed

Smith, Derek J

2006-04-21

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

Modelling the growth and ethanol production of Brettanomyces bruxellensis at different glucose concentrations.

PubMed

Aguilar-Uscanga, M G; Garcia-Alvarado, Y; Gomez-Rodriguez, J; Phister, T; Delia, M L; Strehaiano, P

2011-08-01

To study the effect of glucose concentrations on the growth by Brettanomyces bruxellensis yeast strain in batch experiments and develop a mathematical model for kinetic behaviour analysis of yeast growing in batch culture. A Matlab algorithm was developed for the estimation of model parameters. Glucose fermentation by B. bruxellensis was studied by varying its concentration (5, 9.3, 13.8, 16.5, 17.6 and 21.4%). The increase in substrate concentration up to a certain limit was accompanied by an increase in ethanol and biomass production; at a substrate concentration of 50-138 g l(-1), the ethanol and biomass production were 24, 59 and 6.3, 11.4 g l(-1), respectively. However, an increase in glucose concentration to 165 g l(-1) led to a drastic decrease in product formation and substrate utilization. The model successfully simulated the batch kinetic observed in all cases. The confidence intervals were also estimated at each phase at a 0.95 probability level in a t-Student distribution for f degrees of freedom. The maximum ethanol and biomass yields were obtained with an initial glucose concentration of 138 g l(-1). These experiments illustrate the importance of using a mathematical model applied to kinetic behaviour on glucose concentration by B. bruxellensis. © 2011 The Authors. Letters in Applied Microbiology © 2011 The Society for Applied Microbiology.

Combining fuzzy mathematics with fuzzy logic to solve business management problems

NASA Astrophysics Data System (ADS)

Vrba, Joseph A.

1993-12-01

Fuzzy logic technology has been applied to control problems with great success. Because of this, many observers fell that fuzzy logic is applicable only in the control arena. However, business management problems almost never deal with crisp values. Fuzzy systems technology--a combination of fuzzy logic, fuzzy mathematics and a graphical user interface--is a natural fit for developing software to assist in typical business activities such as planning, modeling and estimating. This presentation discusses how fuzzy logic systems can be extended through the application of fuzzy mathematics and the use of a graphical user interface to make the information contained in fuzzy numbers accessible to business managers. As demonstrated through examples from actual deployed systems, this fuzzy systems technology has been employed successfully to provide solutions to the complex real-world problems found in the business environment.

Validation Methods Research for Fault-Tolerant Avionics and Control Systems Sub-Working Group Meeting. CARE 3 peer review

NASA Technical Reports Server (NTRS)

Trivedi, K. S. (Editor); Clary, J. B. (Editor)

1980-01-01

A computer aided reliability estimation procedure (CARE 3), developed to model the behavior of ultrareliable systems required by flight-critical avionics and control systems, is evaluated. The mathematical models, numerical method, and fault-tolerant architecture modeling requirements are examined, and the testing and characterization procedures are discussed. Recommendations aimed at enhancing CARE 3 are presented; in particular, the need for a better exposition of the method and the user interface is emphasized.

N-mix for fish: estimating riverine salmonid habitat selection via N-mixture models

USGS Publications Warehouse

Som, Nicholas A.; Perry, Russell W.; Jones, Edward C.; De Juilio, Kyle; Petros, Paul; Pinnix, William D.; Rupert, Derek L.

2018-01-01

Models that formulate mathematical linkages between fish use and habitat characteristics are applied for many purposes. For riverine fish, these linkages are often cast as resource selection functions with variables including depth and velocity of water and distance to nearest cover. Ecologists are now recognizing the role that detection plays in observing organisms, and failure to account for imperfect detection can lead to spurious inference. Herein, we present a flexible N-mixture model to associate habitat characteristics with the abundance of riverine salmonids that simultaneously estimates detection probability. Our formulation has the added benefits of accounting for demographics variation and can generate probabilistic statements regarding intensity of habitat use. In addition to the conceptual benefits, model application to data from the Trinity River, California, yields interesting results. Detection was estimated to vary among surveyors, but there was little spatial or temporal variation. Additionally, a weaker effect of water depth on resource selection is estimated than that reported by previous studies not accounting for detection probability. N-mixture models show great promise for applications to riverine resource selection.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

PubMed

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

PubMed Central

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N. V.

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test. PMID:23469172

Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.

PubMed

Hack, C Eric

2006-04-17

Physiologically based toxicokinetic (PBTK) and toxicodynamic (TD) models of bromate in animals and humans would improve our ability to accurately estimate the toxic doses in humans based on available animal studies. These mathematical models are often highly parameterized and must be calibrated in order for the model predictions of internal dose to adequately fit the experimentally measured doses. Highly parameterized models are difficult to calibrate and it is difficult to obtain accurate estimates of uncertainty or variability in model parameters with commonly used frequentist calibration methods, such as maximum likelihood estimation (MLE) or least squared error approaches. The Bayesian approach called Markov chain Monte Carlo (MCMC) analysis can be used to successfully calibrate these complex models. Prior knowledge about the biological system and associated model parameters is easily incorporated in this approach in the form of prior parameter distributions, and the distributions are refined or updated using experimental data to generate posterior distributions of parameter estimates. The goal of this paper is to give the non-mathematician a brief description of the Bayesian approach and Markov chain Monte Carlo analysis, how this technique is used in risk assessment, and the issues associated with this approach.

Economic communication model set

NASA Astrophysics Data System (ADS)

Zvereva, Olga M.; Berg, Dmitry B.

2017-06-01

This paper details findings from the research work targeted at economic communications investigation with agent-based models usage. The agent-based model set was engineered to simulate economic communications. Money in the form of internal and external currencies was introduced into the models to support exchanges in communications. Every model, being based on the general concept, has its own peculiarities in algorithm and input data set since it was engineered to solve the specific problem. Several and different origin data sets were used in experiments: theoretic sets were estimated on the basis of static Leontief's equilibrium equation and the real set was constructed on the basis of statistical data. While simulation experiments, communication process was observed in dynamics, and system macroparameters were estimated. This research approved that combination of an agent-based and mathematical model can cause a synergetic effect.

A model of human decision making in multiple process monitoring situations

NASA Technical Reports Server (NTRS)

Greenstein, J. S.; Rouse, W. B.

1982-01-01

Human decision making in multiple process monitoring situations is considered. It is proposed that human decision making in many multiple process monitoring situations can be modeled in terms of the human's detection of process related events and his allocation of attention among processes once he feels event have occurred. A mathematical model of human event detection and attention allocation performance in multiple process monitoring situations is developed. An assumption made in developing the model is that, in attempting to detect events, the human generates estimates of the probabilities that events have occurred. An elementary pattern recognition technique, discriminant analysis, is used to model the human's generation of these probability estimates. The performance of the model is compared to that of four subjects in a multiple process monitoring situation requiring allocation of attention among processes.

Blood and small intestine cell kinetics under radiation exposures: Mathematical modeling

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

2009-12-01

Mathematical models which describe the dynamics of two vital body systems (hematopoiesis and small intestinal epithelium) in mammals exposed to acute and chronic radiation are developed. These models, based on conventional biological theories, are implemented as systems of nonlinear differential equations. Their variables and constant parameters have clear biological meaning, that provides successful identification and verification of the models in hand. It is shown that the predictions of the models qualitatively and quantitatively agree with the respective experimental data for small laboratory animals (mice, rats) exposed to acute/chronic irradiation in wide ranges of doses and dose rates. The explanation of a number of radiobiological effects, including those of the low-level long-term exposures, is proposed proceeding from the modeling results. All this bears witness to the validity of employment of the developed models, after a proper identification, in investigation and prediction of radiation effects on the hematopoietic and small intestinal epithelium systems in various mammalian species, including humans. In particular, the models can be used for estimating effects of irradiation on astronauts in the long-term space missions, such as Lunar colonies and Mars voyages.

A physiologically based mathematical model of dermal absorption in man.

PubMed

Auton, T R; Westhead, D R; Woollen, B H; Scott, R C; Wilks, M F

1994-01-01

A sound understanding of the mechanisms determining percutaneous absorption is necessary for toxicological risk assessment of chemicals contacting the skin. As part of a programme investigating these mechanisms we have developed a physiologically based mathematical model. The structure of the model parallels the multi-layer structure of the skin, with separate surface, stratum corneum and viable tissue layers. It simulates the effects of partitioning and diffusive transport between the sub-layers, and metabolism in the viable epidermis. In addition the model describes removal processes on the surface of the skin, including the effects of washing and desquamation, and rubbing off onto clothing. This model is applied to data on the penetration of the herbicide fluazifop-butyl through human skin in vivo and in vitro. Part of this dataset is used to estimate unknown model parameter values and the remainder is used to provide a partial validation of the model. Only a small fraction of the applied dose was absorbed through the skin; most of it was removed by washing or onto clothing. The model provides a quantitative description of these loss processes on the skin surface.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer

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

Liu, Yifang; Lee, Chi-Guhn; Chan, Timothy C. Y., E-mail: tcychan@mie.utoronto.ca

2014-02-15

Purpose: To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy. Methods: The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxelsmore » on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity. Results: The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict. Conclusions: By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer.« less

DAISY: a new software tool to test global identifiability of biological and physiological systems.

PubMed

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D'Angiò, Leontina

2007-10-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

Characterizing Topology of Probabilistic Biological Networks.

PubMed

Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2013-09-06

Biological interactions are often uncertain events, that may or may not take place with some probability. Existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. Here, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. We develop a method that accurately describes the degree distribution of such networks. We also extend our method to accurately compute the joint degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. It also helps us find an adequate mathematical model using maximum likelihood estimation. Our results demonstrate that power law and log-normal models best describe degree distributions for probabilistic networks. The inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected.

Physical disintegration of toilet papers in wastewater systems: experimental analysis and mathematical modeling.

PubMed

Eren, Beytullah; Karadagli, Fatih

2012-03-06

Physical disintegration of representative toilet papers was investigated in this study to assess their disintegration potential in sewer systems. Characterization of toilet papers from different parts of the world indicated two main categories as premium and average quality. Physical disintegration experiments were conducted with representative products from each category according to standard protocols with improvements. The experimental results were simulated by mathematical model to estimate best-fit values of disintegration rate coefficients and fractional distribution ratios. Our results from mathematical modeling and experimental work show that premium products release more amounts of small fibers and disintegrate more slowly than average ones. Comparison of the toilet papers with the tampon applicators studied previously indicates that premium quality toilet papers present significant potential to persist in sewer pipes. Comparison of turbulence level in our experimental setup with those of partial flow conditions in sewer pipes indicates that drains and small sewer pipes are critical sections where disintegration of toilet papers will be limited. For improvement, requirements for minimum pipe slopes may be increased to sustain transport and disintegration of flushable products in small pipes. In parallel, toilet papers can be improved to disintegrate rapidly in sewer systems, while they meet consumer expectations.

The mathematical model of dynamic stabilization system for autonomous car

NASA Astrophysics Data System (ADS)

Saikin, A. M.; Buznikov, S. E.; Shabanov, N. S.; Elkin, D. S.

2018-02-01

Leading foreign companies and domestic enterprises carry out extensive researches and developments in the field of control systems for autonomous cars and in the field of improving driver assistance systems. The search for technical solutions, as a rule, is based on heuristic methods and does not always lead to satisfactory results. The purpose of this research is to formalize the road safety problem in the terms of modern control theory, to construct the adequate mathematical model for solving it, including the choice of software and hardware environment. For automatic control of the object, it is necessary to solve the problem of dynamic stabilization in the most complete formulation. The solution quality of the problem on a finite time interval is estimated by the value of the quadratic functional. Car speed, turn angle and additional yaw rate (during car drift or skidding) measurements are performed programmatically by the original virtual sensors. The limit speeds at which drift, skidding or rollover begins are calculated programmatically taking into account the friction coefficient identified in motion. The analysis of the results confirms both the adequacy of the mathematical models and the algorithms and the possibility of implementing the system in the minimal technical configuration.

Analytic modeling of aerosol size distributions

NASA Technical Reports Server (NTRS)

Deepack, A.; Box, G. P.

1979-01-01

Mathematical functions commonly used for representing aerosol size distributions are studied parametrically. Methods for obtaining best fit estimates of the parameters are described. A catalog of graphical plots depicting the parametric behavior of the functions is presented along with procedures for obtaining analytical representations of size distribution data by visual matching of the data with one of the plots. Examples of fitting the same data with equal accuracy by more than one analytic model are also given.

Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments

NASA Astrophysics Data System (ADS)

Zia, R. K. P.; Dong, J. J.; Schmittmann, B.

2011-07-01

The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes.

Optimization of CW Fiber Lasers With Strong Nonlinear Cavity Dynamics

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A unifying framework for marginalized random intercept models of correlated binary outcomes

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian M.

2013-01-01

We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized random intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts. PMID:25342871

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

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

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

Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

NASA Astrophysics Data System (ADS)

Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

2017-12-01

This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

Rainfall estimation with TFR model using Ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Asyiqotur Rohmah, Nabila; Apriliani, Erna

2018-03-01

Rainfall fluctuation can affect condition of other environment, correlated with economic activity and public health. The increasing of global average temperature is influenced by the increasing of CO2 in the atmosphere, which caused climate change. Meanwhile, the forests as carbon sinks that help keep the carbon cycle and climate change mitigation. Climate change caused by rainfall intensity deviations can affect the economy of a region, and even countries. It encourages research on rainfall associated with an area of forest. In this study, the mathematics model that used is a model which describes the global temperatures, forest cover, and seasonal rainfall called the TFR (temperature, forest cover, and rainfall) model. The model will be discretized first, and then it will be estimated by the method of Ensemble Kalman Filter (EnKF). The result shows that the more ensembles used in estimation, the better the result is. Also, the accurateness of simulation result is influenced by measurement variable. If a variable is measurement data, the result of simulation is better.

Time Estimation Deficits in Childhood Mathematics Difficulties

ERIC Educational Resources Information Center

Hurks, Petra P. M.; van Loosbroek, Erik

2014-01-01

Time perception has not been comprehensively examined in mathematics difficulties (MD). Therefore, verbal time estimation, production, and reproduction were tested in 13 individuals with MD and 16 healthy controls, matched for age, sex, and intellectual skills. Individuals with MD performed comparably to controls in time reproduction, but showed a…

Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

NASA Astrophysics Data System (ADS)

Podlipenko, Yu. K.; Shestopalov, Yu. V.

2017-09-01

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

Incorporation of diffusion-weighted magnetic resonance imaging data into a simple mathematical model of tumor growth

NASA Astrophysics Data System (ADS)

Atuegwu, N. C.; Colvin, D. C.; Loveless, M. E.; Xu, L.; Gore, J. C.; Yankeelov, T. E.

2012-01-01

We build on previous work to show how serial diffusion-weighted MRI (DW-MRI) data can be used to estimate proliferation rates in a rat model of brain cancer. Thirteen rats were inoculated intracranially with 9L tumor cells; eight rats were treated with the chemotherapeutic drug 1,3-bis(2-chloroethyl)-1-nitrosourea and five rats were untreated controls. All animals underwent DW-MRI immediately before, one day and three days after treatment. Values of the apparent diffusion coefficient (ADC) were calculated from the DW-MRI data and then used to estimate the number of cells in each voxel and also for whole tumor regions of interest. The data from the first two imaging time points were then used to estimate the proliferation rate of each tumor. The proliferation rates were used to predict the number of tumor cells at day three, and this was correlated with the corresponding experimental data. The voxel-by-voxel analysis yielded Pearson's correlation coefficients ranging from -0.06 to 0.65, whereas the region of interest analysis provided Pearson's and concordance correlation coefficients of 0.88 and 0.80, respectively. Additionally, the ratio of positive to negative proliferation values was used to separate the treated and control animals (p <0.05) at an earlier point than the mean ADC values. These results further illustrate how quantitative measurements of tumor state obtained non-invasively by imaging can be incorporated into mathematical models that predict tumor growth.

Single-lens stereovision system using a prism: position estimation of a multi-ocular prism.

PubMed

Cui, Xiaoyu; Lim, Kah Bin; Zhao, Yue; Kee, Wei Loon

2014-05-01

In this paper, a position estimation method using a prism-based single-lens stereovision system is proposed. A multifaced prism was considered as a single optical system composed of few refractive planes. A transformation matrix which relates the coordinates of an object point to its coordinates on the image plane through the refraction of the prism was derived based on geometrical optics. A mathematical model which is able to denote the position of an arbitrary faces prism with only seven parameters is introduced. This model further extends the application of the single-lens stereovision system using a prism to other areas. Experimentation results are presented to prove the effectiveness and robustness of our proposed model.

Self-Deferral, HIV Infection, and the Blood Supply: Evaluating an AIDS Intervention.

ERIC Educational Resources Information Center

Kaplan, Edward H.; Novick, Alvin

1990-01-01

This paper evaluates the effectiveness of self-deferral, a social screen implemented to protect the U.S. blood supply from human immunodeficiency virus (HIV) infection prior to the advent of laboratory testing. Mathematical models are developed to estimate the number of infectious transfusions ultimately leading to AIDS prior to self-deferral.…