The Particle/Wave-in-a-Box Model in Dutch Secondary Schools

ERIC Educational Resources Information Center

Hoekzema, Dick; van den Berg, Ed; Schooten, Gert; van Dijk, Leo

2007-01-01

The combination of mathematical and conceptual difficulties makes teaching quantum physics at secondary schools a precarious undertaking. With many of the conceptual difficulties being unavoidable, simplifying the mathematics becomes top priority. The particle/wave-in-a-box provides a teaching model which includes many aspects of serious …

Optimization of a new mathematical model for bacterial growth

USDA-ARS?s Scientific Manuscript database

The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...

Mathematical models for optimization of the centrifugal stage of a refrigerating compressor

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

Nuzhdin, A.S.

1987-09-01

The authors describe a general approach to the creating of mathematical models of energy and head losses in the flow part of the centrifugal compressor. The mathematical model of the pressure head and efficiency of a two-section stage proposed in this paper is meant for determining its characteristics for the assigned geometric dimensions and for optimizing by variance calculations. Characteristic points on the plot of velocity distribution over the margin of the vanes of the impeller and the diffuser of the centrifugal stage with a combined diffuser are presented. To assess the reliability of the mathematical model the authors comparedmore » some calculated data with the experimental ones.« less

Assessing Attitudes toward Mathematics across Teacher Education Contexts

ERIC Educational Resources Information Center

Jong, Cindy; Hodges, Thomas E.

2015-01-01

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

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

Understanding intratumor heterogeneity by combining genome analysis and mathematical modeling.

PubMed

Niida, Atsushi; Nagayama, Satoshi; Miyano, Satoru; Mimori, Koshi

2018-04-01

Cancer is composed of multiple cell populations with different genomes. This phenomenon called intratumor heterogeneity (ITH) is supposed to be a fundamental cause of therapeutic failure. Therefore, its principle-level understanding is a clinically important issue. To achieve this goal, an interdisciplinary approach combining genome analysis and mathematical modeling is essential. For example, we have recently performed multiregion sequencing to unveil extensive ITH in colorectal cancer. Moreover, by employing mathematical modeling of cancer evolution, we demonstrated that it is possible that this ITH is generated by neutral evolution. In this review, we introduce recent advances in a research field related to ITH and also discuss strategies for exploiting novel findings on ITH in a clinical setting. © 2018 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.

Mathematical Modeling and Analysis of a Wide Bandwidth Bipolar Power Supply for the Fast Correctors in the APS Upgrade

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

Song, Byeong M.; Wang, Ju

This paper presents the mathematical modeling and analysis of a wide bandwidth bipolar power supply for the fast correctors in the APS Upgrade. A wide bandwidth current regulator with a combined PI and phase-lead compensator has been newly proposed, analyzed, and simulated through both a mathematical model and a physical electronic circuit model using MATLAB and PLECS. The proposed regulator achieves a bandwidth with a -1.23dB attenuation and a 32.40° phase-delay at 10 kHz for a small signal less than 1% of the DC scale. The mathematical modeling and design, simulation results of a fast corrector power supply control systemmore » are presented in this paper.« less

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.

Professional Development for Secondary School Mathematics Teachers: A Peer Mentoring Model

ERIC Educational Resources Information Center

Kensington-Miller, Barbara

2012-01-01

Professional development is important for all teachers, and in low socio-economic schools where the challenges of teaching are greater this need is crucial. A model involving a combination of one-on-one peer mentoring integrated with group peer mentoring was piloted with experienced mathematics teachers of senior students in low socio-economic…

Manual of phosphoric acid fuel cell stack three-dimensional model and computer program

NASA Technical Reports Server (NTRS)

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

1984-01-01

A detailed distributed mathematical model of phosphoric acid fuel cell stack have been developed, with the FORTRAN computer program, for analyzing the temperature distribution in the stack and the associated current density distribution on the cell plates. Energy, mass, and electrochemical analyses in the stack were combined to develop the model. Several reasonable assumptions were made to solve this mathematical model by means of the finite differences numerical method.

Mathematical model and stability analysis of fluttering and autorotation of an articulated plate into a flow

NASA Astrophysics Data System (ADS)

Rostami, Ali Bakhshandeh; Fernandes, Antonio Carlos

2018-03-01

This paper is dedicated to develop a mathematical model that can simulate nonlinear phenomena of a hinged plate which places into the fluid flow (1 DOF). These phenomena are fluttering (oscillation motion), autorotation (continuous rotation) and chaotic motion (combination of fluttering and autorotation). Two mathematical models are developed for 1 DOF problem using two eminent mathematical models which had been proposed for falling plates (3 DOF). The procedures of developing these models are elaborated and then these results are compared to experimental data. The best model in the simulation of the phenomena is chosen for stability and bifurcation analysis. Based on these analyses, this model shows a transcritical bifurcation and as a result, the stability diagram and threshold are presented. Moreover, an analytical expression is given for finding the boundary of bifurcation from the fluttering to the autorotation.

A Novel Approach to Develop the Lower Order Model of Multi-Input Multi-Output System

NASA Astrophysics Data System (ADS)

Rajalakshmy, P.; Dharmalingam, S.; Jayakumar, J.

2017-10-01

A mathematical model is a virtual entity that uses mathematical language to describe the behavior of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines like physics, biology, and electrical engineering as well as in the social sciences like economics, sociology and political science. Physicists, Engineers, Computer scientists, and Economists use mathematical models most extensively. With the advent of high performance processors and advanced mathematical computations, it is possible to develop high performing simulators for complicated Multi Input Multi Ouptut (MIMO) systems like Quadruple tank systems, Aircrafts, Boilers etc. This paper presents the development of the mathematical model of a 500 MW utility boiler which is a highly complex system. A synergistic combination of operational experience, system identification and lower order modeling philosophy has been effectively used to develop a simplified but accurate model of a circulation system of a utility boiler which is a MIMO system. The results obtained are found to be in good agreement with the physics of the process and with the results obtained through design procedure. The model obtained can be directly used for control system studies and to realize hardware simulators for boiler testing and operator training.

Fighting Cancer with Mathematics and Viruses.

PubMed

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

2017-08-23

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

Fighting Cancer with Mathematics and Viruses

PubMed Central

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

2017-01-01

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

Chikungunya Virus: In Vitro Response to Combination Therapy With Ribavirin and Interferon Alfa 2a.

PubMed

Gallegos, Karen M; Drusano, George L; D Argenio, David Z; Brown, Ashley N

2016-10-15

We evaluated the antiviral activities of ribavirin (RBV) and interferon (IFN) alfa as monotherapy and combination therapy against chikungunya virus (CHIKV). Vero cells were infected with CHIKV in the presence of RBV and/or IFN alfa, and viral production was quantified by plaque assay. A mathematical model was fit to the data to identify drug interactions for effect. We ran simulations using the best-fit model parameters to predict the antiviral activity associated with clinically relevant regimens of RBV and IFN alfa as combination therapy. The model predictions were validated using the hollow fiber infection model (HFIM) system. RBV and IFN alfa were effective against CHIKV as monotherapy at supraphysiological concentrations. However, RBV and IFN alfa were highly synergistic for antiviral effect when administered as combination therapy. Simulations with our mathematical model predicted that a standard clinical regimen of RBV plus IFN alfa would inhibit CHIKV burden by 2.5 log10 following 24 hours of treatment. In the HFIM system, RBV plus IFN alfa at clinical exposures resulted in a 2.1-log10 decrease in the CHIKV burden following 24 hours of therapy. These findings validate the prediction made by the mathematical model. These studies illustrate the promise of RBV plus IFN alfa as a potential therapeutic strategy for the treatment of CHIKV infections. © The Author 2016. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail journals.permissions@oup.com.

Connecting Biology and Mathematics: First Prepare the Teachers

PubMed Central

2010-01-01

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers. PMID:20810951

A mathematical model for CTL effect on a latently infected cell inclusive HIV dynamics and treatment

NASA Astrophysics Data System (ADS)

Tarfulea, N. E.

2017-10-01

This paper investigates theoretically and numerically the effect of immune effectors, such as the cytotoxic lymphocyte (CTL), in modeling HIV pathogenesis (via a newly developed mathematical model); our results suggest the significant impact of the immune response on the control of the virus during primary infection. Qualitative aspects (including positivity, boundedness, stability, uncertainty, and sensitivity analysis) are addressed. Additionally, by introducing drug therapy, we analyze numerically the model to assess the effect of treatment consisting of a combination of several antiretroviral drugs. Our results show that the inclusion of the CTL compartment produces a higher rebound for an individual's healthy helper T-cell compartment than drug therapy alone. Furthermore, we quantitatively characterize successful drugs or drug combination scenarios.

Statistical models of lunar rocks and regolith

NASA Technical Reports Server (NTRS)

Marcus, A. H.

1973-01-01

The mathematical, statistical, and computational approaches used in the investigation of the interrelationship of lunar fragmental material, regolith, lunar rocks, and lunar craters are described. The first two phases of the work explored the sensitivity of the production model of fragmental material to mathematical assumptions, and then completed earlier studies on the survival of lunar surface rocks with respect to competing processes. The third phase combined earlier work into a detailed statistical analysis and probabilistic model of regolith formation by lithologically distinct layers, interpreted as modified crater ejecta blankets. The fourth phase of the work dealt with problems encountered in combining the results of the entire project into a comprehensive, multipurpose computer simulation model for the craters and regolith. Highlights of each phase of research are given.

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

PubMed

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

2015-02-01

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

Long Term Persistence of Preschool Intervention on Children's Mathematical Development: Results from the German Model Project "Kindergarten of the Future in Bavaria"

ERIC Educational Resources Information Center

Lehrl, Simone; Kluczniok, Katharina; Rossbach, Hans-Guenther; Anders, Yvonne

2017-01-01

The present study examines how attending the German model project "Kindergarten of the Future in Bavaria" (KiDZ), which provided 138 children (aged 3 to 6) with traditional preschool stimulation combined with cognitive and domain-specific stimulation, is associated with children's competencies in mathematics over time to age 12 compared…

JSEM: A Framework for Identifying and Evaluating Indicators.

ERIC Educational Resources Information Center

Hyman, Jeffrey B.; Leibowitz, Scott G.

2001-01-01

Presents an approach to identifying and evaluating combinations of indicators when the mathematical relationships between the indicators and an endpoint may not be quantified, a limitation common to many ecological assessments. Uses the framework of Structural Equation Modeling (SEM), which combines path analysis with measurement model, to…

Are Three Sheets Enough? Using Toilet Paper to Teach Science and Mathematics

ERIC Educational Resources Information Center

Woolverton, Christopher J.; Woolverton, Lyssa N.

2006-01-01

Toilet paper (TP) composition and physical characteristics were used to model scientific investigations that combined several "National Science Education Standards." Experiments with TP permitted the integration of TP history, societal change resulting from invention, mathematics (including geometry and statistics), germ theory, and personal…

Separating Cognitive and Content Domains in Mathematical Competence

ERIC Educational Resources Information Center

Harks, Birgit; Klieme, Eckhard; Hartig, Johannes; Leiss, Dominik

2014-01-01

The present study investigates the empirical separability of mathematical (a) content domains, (b) cognitive domains, and (c) content-specific cognitive domains. There were 122 items representing two content domains (linear equations vs. theorem of Pythagoras) combined with two cognitive domains (modeling competence vs. technical competence)…

Modeling combination HCV prevention among HIV-infected men who have sex with men and people who inject drugs

PubMed Central

Martin, Natasha K.; Skaathun, Britt; Vickerman, Peter; Stuart, David

2017-01-01

Background People who inject drugs (PWID) and HIV-infected men who have sex with men (MSM) are key risk groups for hepatitis C virus (HCV) transmission. Mathematical modeling studies can help elucidate what level and combination of prevention intervention scale-up is required to control or eliminate epidemics among these key populations. Methods We discuss the evidence surrounding HCV prevention interventions and provide an overview of the mathematical modeling literature projecting the impact of scaled-up HCV prevention among PWID and HIV-infected MSM. Results Harm reduction interventions such as opiate substitution therapy and needle and syringe programs are effective in reducing HCV incidence among PWID. Modeling and limited empirical data indicate HCV treatment could additionally be used for prevention. No studies have evaluated the effectiveness of behavior change interventions to reduce HCV incidence among MSM, but existing interventions to reduce HIV risk could be effective. Mathematical modeling and empirical data indicates that scale-up of harm reduction could reduce HCV transmission, but in isolation is unlikely to eliminate HCV among PWID. By contrast, elimination is possibly achievable through combination scale-up of harm reduction and HCV treatment. Similarly, among HIV-infected MSM, eliminating the emerging epidemics will likely require HCV treatment scale-up in combination with additional interventions to reduce HCV-related risk behaviors. Conclusions Elimination of HCV will likely require combination prevention efforts among both PWID and HIV-infected MSM populations. Further empirical research is required to validate HCV treatment as prevention among these populations, and to identify effective behavioral interventions to reduce HCV incidence among MSM. PMID:28534885

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

PubMed

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

2018-06-01

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

Differentiated Success: Combining Theories to Explain Learning

ERIC Educational Resources Information Center

Jorgensen, Robyn; Larkin, Kevin

2015-01-01

This paper explores the value of different paradigms to explain dispositions towards mathematics among primary school students from different social backgrounds. As part of a larger project designed to elicit students' thinking and attitudes towards mathematics, we seek to develop an explanatory model for the socially-differentiated outcomes in…

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school.

PubMed

Cerda, Gamal; Pérez, Carlos; Navarro, José I; Aguilar, Manuel; Casas, José A; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students' level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

The Dynamics of Drug Resistance: A Mathematical Perspective

PubMed Central

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Mathematical modeling of reflectance and intrinsic fluorescence for cancer detection in human pancreatic tissue

NASA Astrophysics Data System (ADS)

Wilson, Robert H.; Chandra, Malavika; Scheiman, James; Simeone, Diane; McKenna, Barbara; Purdy, Julianne; Mycek, Mary-Ann

2009-02-01

Pancreatic adenocarcinoma has a five-year survival rate of only 4%, largely because an effective procedure for early detection has not been developed. In this study, mathematical modeling of reflectance and fluorescence spectra was utilized to quantitatively characterize differences between normal pancreatic tissue, pancreatitis, and pancreatic adenocarcinoma. Initial attempts at separating the spectra of different tissue types involved dividing fluorescence by reflectance, and removing absorption artifacts by applying a "reverse Beer-Lambert factor" when the absorption coefficient was modeled as a linear combination of the extinction coefficients of oxy- and deoxy-hemoglobin. These procedures demonstrated the need for a more complete mathematical model to quantitatively describe fluorescence and reflectance for minimally-invasive fiber-based optical diagnostics in the pancreas.

Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.

2015-01-01

We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.

A Mathematical Model for Continuous Fiber Reinforced Thermoplastic Composite in Melt Impregnation

NASA Astrophysics Data System (ADS)

Ren, Feng; Yu, Yang; Yang, Jianjun; Xin, Chunling; He, Yadong

2017-06-01

Through the combination of Reynolds equation and Darcy's law, a mathematical model was established to calculate the pressure distribution in wedge area, which contributed to the forecast effect of processing parameters on impregnation degree of the fiber bundle. The experiments were conducted to verify the capacity of the proposed model with satisfactory results, which means that the model is effective in predicting the influence of processing parameters on impregnation. From the mathematical model, it was known that the impregnation degree of the fiber bundle would be improved by increasing the processing temperature, number and radius of pins, or decreasing the pulling speed and the center distance of pins, which provided a possible solution to the difficulty of melt with high viscosity in melt impregnation and optimization of impregnation processing.

What Diagrams Argue in Late Imperial Chinese Combinatorial Texts.

PubMed

Bréard, Andrea

2015-01-01

Attitudes towards diagrammatic reasoning and visualization in mathematics were seldom spelled out in texts from pre-modern China, although illustrations figure prominently in mathematical literature since the eleventh century. Taking the sums of finite series and their combinatorial interpretation as a case study, this article investigates the epistemological function of illustrations from the eleventh to the nineteenth century that encode either the mathematical objects themselves or represent their related algorithms. It particularly focuses on the two illustrations given in Wang Lai's (1768-1813) Mathematical Principles of Sequential Combinations, arguing that they reflect a specific mode of nineteenth-century mathematical argumentative practice and served as a heuristic model for later authors.

The development of a combined mathematical model to forecast the incidence of hepatitis E in Shanghai, China.

PubMed

Ren, Hong; Li, Jian; Yuan, Zheng-An; Hu, Jia-Yu; Yu, Yan; Lu, Yi-Han

2013-09-08

Sporadic hepatitis E has become an important public health concern in China. Accurate forecasting of the incidence of hepatitis E is needed to better plan future medical needs. Few mathematical models can be used because hepatitis E morbidity data has both linear and nonlinear patterns. We developed a combined mathematical model using an autoregressive integrated moving average model (ARIMA) and a back propagation neural network (BPNN) to forecast the incidence of hepatitis E. The morbidity data of hepatitis E in Shanghai from 2000 to 2012 were retrieved from the China Information System for Disease Control and Prevention. The ARIMA-BPNN combined model was trained with 144 months of morbidity data from January 2000 to December 2011, validated with 12 months of data January 2012 to December 2012, and then employed to forecast hepatitis E incidence January 2013 to December 2013 in Shanghai. Residual analysis, Root Mean Square Error (RMSE), normalized Bayesian Information Criterion (BIC), and stationary R square methods were used to compare the goodness-of-fit among ARIMA models. The Bayesian regularization back-propagation algorithm was used to train the network. The mean error rate (MER) was used to assess the validity of the combined model. A total of 7,489 hepatitis E cases was reported in Shanghai from 2000 to 2012. Goodness-of-fit (stationary R2=0.531, BIC= -4.768, Ljung-Box Q statistics=15.59, P=0.482) and parameter estimates were used to determine the best-fitting model as ARIMA (0,1,1)×(0,1,1)12. Predicted morbidity values in 2012 from best-fitting ARIMA model and actual morbidity data from 2000 to 2011 were used to further construct the combined model. The MER of the ARIMA model and the ARIMA-BPNN combined model were 0.250 and 0.176, respectively. The forecasted incidence of hepatitis E in 2013 was 0.095 to 0.372 per 100,000 population. There was a seasonal variation with a peak during January-March and a nadir during August-October. Time series analysis suggested a seasonal pattern of hepatitis E morbidity in Shanghai, China. An ARIMA-BPNN combined model was used to fit the linear and nonlinear patterns of time series data, and accurately forecast hepatitis E infections.

Mathematical (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters

PubMed Central

Baten, Elke; Desoete, Annemie

2018-01-01

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. PMID:29867645

Mathematical (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters.

PubMed

Baten, Elke; Desoete, Annemie

2018-01-01

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers' experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school

PubMed Central

Cerda, Gamal; Pérez, Carlos; Navarro, José I.; Aguilar, Manuel; Casas, José A.; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students’ performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain. PMID:26441739

A Categorization Model for Educational Values of the History of Mathematics. An Empirical Study

NASA Astrophysics Data System (ADS)

Wang, Xiao-qin; Qi, Chun-yan; Wang, Ke

2017-11-01

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the history of mathematics by combining the objectives of high school mathematics curriculum in China. This framework includes six dimensions: the harmony of knowledge, the beauty of ideas or methods, the pleasure of inquiries, the improvement of capabilities, the charm of cultures, and the availability of moral education. The results show that this framework better explained the all-educational values of the history of mathematics that all teaching cases showed. Therefore, the framework can guide teachers to better integrate the history of mathematics into teaching.

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

PubMed

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

2011-01-01

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

Respiratory protective device design using control system techniques

NASA Technical Reports Server (NTRS)

Burgess, W. A.; Yankovich, D.

1972-01-01

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

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

Current advancements and challenges in soil-root interactions modelling

NASA Astrophysics Data System (ADS)

Schnepf, Andrea; Huber, Katrin; Abesha, Betiglu; Meunier, Felicien; Leitner, Daniel; Roose, Tiina; Javaux, Mathieu; Vanderborght, Jan; Vereecken, Harry

2015-04-01

Roots change their surrounding soil chemically, physically and biologically. This includes changes in soil moisture and solute concentration, the exudation of organic substances into the rhizosphere, increased growth of soil microorganisms, or changes in soil structure. The fate of water and solutes in the root zone is highly determined by these root-soil interactions. Mathematical models of soil-root systems in combination with non-invasive techniques able to characterize root systems are a promising tool to understand and predict the behaviour of water and solutes in the root zone. With respect to different fields of applications, predictive mathematical models can contribute to the solution of optimal control problems in plant recourse efficiency. This may result in significant gains in productivity, efficiency and environmental sustainability in various land use activities. Major challenges include the coupling of model parameters of the relevant processes with the surrounding environment such as temperature, nutrient concentration or soil water content. A further challenge is the mathematical description of the different spatial and temporal scales involved. This includes in particular the branched structures formed by root systems or the external mycelium of mycorrhizal fungi. Here, reducing complexity as well as bridging between spatial scales is required. Furthermore, the combination of experimental and mathematical techniques may advance the field enormously. Here, the use of root system, soil and rhizosphere models is presented through a number of modelling case studies, including image based modelling of phosphate uptake by a root with hairs, model-based optimization of root architecture for phosphate uptake from soil, upscaling of rhizosphere models, modelling root growth in structured soil, and the effect of root hydraulic architecture on plant water uptake efficiency and drought resistance.

Current Advancements and Challenges in Soil-Root Interactions Modelling

NASA Astrophysics Data System (ADS)

Schnepf, A.; Huber, K.; Abesha, B.; Meunier, F.; Leitner, D.; Roose, T.; Javaux, M.; Vanderborght, J.; Vereecken, H.

2014-12-01

Roots change their surrounding soil chemically, physically and biologically. This includes changes in soil moisture and solute concentration, the exudation of organic substances into the rhizosphere, increased growth of soil microorganisms, or changes in soil structure. The fate of water and solutes in the root zone is highly determined by these root-soil interactions. Mathematical models of soil-root systems in combination with non-invasive techniques able to characterize root systems are a promising tool to understand and predict the behaviour of water and solutes in the root zone. With respect to different fields of applications, predictive mathematical models can contribute to the solution of optimal control problems in plant recourse efficiency. This may result in significant gains in productivity, efficiency and environmental sustainability in various land use activities. Major challenges include the coupling of model parameters of the relevant processes with the surrounding environment such as temperature, nutrient concentration or soil water content. A further challenge is the mathematical description of the different spatial and temporal scales involved. This includes in particular the branched structures formed by root systems or the external mycelium of mycorrhizal fungi. Here, reducing complexity as well as bridging between spatial scales is required. Furthermore, the combination of experimental and mathematical techniques may advance the field enormously. Here, the use of root system, soil and rhizosphere models is presented through a number of modelling case studies, including image based modelling of phosphate uptake by a root with hairs, model-based optimization of root architecture for phosphate uptake from soil, upscaling of rhizosphere models, modelling root growth in structured soil, and the effect of root hydraulic architecture on plant water uptake efficiency and drought resistance.

An evidential reasoning extension to quantitative model-based failure diagnosis

NASA Technical Reports Server (NTRS)

Gertler, Janos J.; Anderson, Kenneth C.

1992-01-01

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

Computer modeling of heat pipe performance

NASA Technical Reports Server (NTRS)

Peterson, G. P.

1983-01-01

A parametric study of the defining equations which govern the steady state operational characteristics of the Grumman monogroove dual passage heat pipe is presented. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests on actual prototypes.

Research on NC laser combined cutting optimization model of sheet metal parts

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Zhang, Y. L.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

The optimization problem for NC laser combined cutting of sheet metal parts was taken as the research object in this paper. The problem included two contents: combined packing optimization and combined cutting path optimization. In the problem of combined packing optimization, the method of “genetic algorithm + gravity center NFP + geometric transformation” was used to optimize the packing of sheet metal parts. In the problem of combined cutting path optimization, the mathematical model of cutting path optimization was established based on the parts cutting constraint rules of internal contour priority and cross cutting. The model played an important role in the optimization calculation of NC laser combined cutting.

Some considerations concerning the theory of combined toxicity: a case study of subchronic experimental intoxication with cadmium and lead.

PubMed

Varaksin, Anatoly N; Katsnelson, Boris A; Panov, Vladimir G; Privalova, Larisa I; Kireyeva, Ekaterina P; Valamina, Irene E; Beresneva, Olga Yu

2014-02-01

Rats were exposed intraperitoneally (3 times a week up to 20 injections) to either Cadmium and Lead salts in doses equivalent to their 0.05 LD50 separately or combined in the same or halved doses. Toxic effects were assessed by more than 40 functional, biochemical and morphometric indices. We analysed the results obtained aiming at determination of the type of combined toxicity using either common sense considerations based on descriptive statistics or two mathematical models based (a) on ANOVA and (b) on Mathematical Theory of Experimental Design, which correspond, respectively, to the widely recognised paradigms of effect additivity and dose additivity. Nevertheless, these approaches have led us unanimously to the following conclusions: (1) The above paradigms are virtually interchangeable and should be regarded as different methods of modelling the combined toxicity rather than as reflecting fundamentally differing processes. (2) Within both models there exist not merely three traditionally used types of combined toxicity (additivity, subadditivity and superadditivity) but at least 10 variants of it depending on exactly which effect is considered and on its level, as well as on the dose levels and their ratio. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Contextual Approach with Guided Discovery Learning and Brain Based Learning in Geometry Learning

NASA Astrophysics Data System (ADS)

Kartikaningtyas, V.; Kusmayadi, T. A.; Riyadi

2017-09-01

The aim of this study was to combine the contextual approach with Guided Discovery Learning (GDL) and Brain Based Learning (BBL) in geometry learning of junior high school. Furthermore, this study analysed the effect of contextual approach with GDL and BBL in geometry learning. GDL-contextual and BBL-contextual was built from the steps of GDL and BBL that combined with the principles of contextual approach. To validate the models, it uses quasi experiment which used two experiment groups. The sample had been chosen by stratified cluster random sampling. The sample was 150 students of grade 8th in junior high school. The data were collected through the student’s mathematics achievement test that given after the treatment of each group. The data analysed by using one way ANOVA with different cell. The result shows that GDL-contextual has not different effect than BBL-contextual on mathematics achievement in geometry learning. It means both the two models could be used in mathematics learning as the innovative way in geometry learning.

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.

Discrete structures in continuum descriptions of defective crystals

PubMed Central

2016-01-01

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of ‘plastic strain variables’, which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. PMID:27002070

The HIV Cure Research Agenda: The Role of Mathematical Modelling and Cost-Effectiveness Analysis.

PubMed

Freedberg, Kenneth A; Possas, Cristina; Deeks, Steven; Ross, Anna Laura; Rosettie, Katherine L; Di Mascio, Michele; Collins, Chris; Walensky, Rochelle P; Yazdanpanah, Yazdan

The research agenda towards an HIV cure is building rapidly. In this article, we discuss the reasons for and methodological approach to using mathematical modeling and cost-effectiveness analysis in this agenda. We provide a brief description of the proof of concept for cure and the current directions of cure research. We then review the types of clinical economic evaluations, including cost analysis, cost-benefit analysis, and cost-effectiveness analysis. We describe the use of mathematical modeling and cost-effectiveness analysis early in the HIV epidemic as well as in the era of combination antiretroviral therapy. We then highlight the novel methodology of Value of Information analysis and its potential role in the planning of clinical trials. We close with recommendations for modeling and cost-effectiveness analysis in the HIV cure agenda.

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.

Mathematical models for exploring different aspects of genotoxicity and carcinogenicity databases.

PubMed

Benigni, R; Giuliani, A

1991-12-01

One great obstacle to understanding and using the information contained in the genotoxicity and carcinogenicity databases is the very size of such databases. Their vastness makes them difficult to read; this leads to inadequate exploitation of the information, which becomes costly in terms of time, labor, and money. In its search for adequate approaches to the problem, the scientific community has, curiously, almost entirely neglected an existent series of very powerful methods of data analysis: the multivariate data analysis techniques. These methods were specifically designed for exploring large data sets. This paper presents the multivariate techniques and reports a number of applications to genotoxicity problems. These studies show how biology and mathematical modeling can be combined and how successful this combination is.

Mathematical Modelling and Analysis of the Tumor Treatment Regimens with Pulsed Immunotherapy and Chemotherapy

PubMed Central

Pang, Liuyong; Shen, Lin; Zhao, Zhong

2016-01-01

To begin with, in this paper, single immunotherapy, single chemotherapy, and mixed treatment are discussed, and sufficient conditions under which tumor cells will be eliminated ultimately are obtained. We analyze the impacts of the least effective concentration and the half-life of the drug on therapeutic results and then find that increasing the least effective concentration or extending the half-life of the drug can achieve better therapeutic effects. In addition, since most types of tumors are resistant to common chemotherapy drugs, we consider the impact of drug resistance on therapeutic results and propose a new mathematical model to explain the cause of the chemotherapeutic failure using single drug. Based on this, in the end, we explore the therapeutic effects of two-drug combination chemotherapy, as well as mixed immunotherapy with combination chemotherapy. Numerical simulations indicate that combination chemotherapy is very effective in controlling tumor growth. In comparison, mixed immunotherapy with combination chemotherapy can achieve a better treatment effect. PMID:26997972

Mathematical Modelling and Analysis of the Tumor Treatment Regimens with Pulsed Immunotherapy and Chemotherapy.

PubMed

Pang, Liuyong; Shen, Lin; Zhao, Zhong

2016-01-01

To begin with, in this paper, single immunotherapy, single chemotherapy, and mixed treatment are discussed, and sufficient conditions under which tumor cells will be eliminated ultimately are obtained. We analyze the impacts of the least effective concentration and the half-life of the drug on therapeutic results and then find that increasing the least effective concentration or extending the half-life of the drug can achieve better therapeutic effects. In addition, since most types of tumors are resistant to common chemotherapy drugs, we consider the impact of drug resistance on therapeutic results and propose a new mathematical model to explain the cause of the chemotherapeutic failure using single drug. Based on this, in the end, we explore the therapeutic effects of two-drug combination chemotherapy, as well as mixed immunotherapy with combination chemotherapy. Numerical simulations indicate that combination chemotherapy is very effective in controlling tumor growth. In comparison, mixed immunotherapy with combination chemotherapy can achieve a better treatment effect.

Modeling small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models.

PubMed

Salgia, Ravi; Mambetsariev, Isa; Hewelt, Blake; Achuthan, Srisairam; Li, Haiqing; Poroyko, Valeriy; Wang, Yingyu; Sattler, Martin

2018-05-25

Mathematical cancer models are immensely powerful tools that are based in part on the fractal nature of biological structures, such as the geometry of the lung. Cancers of the lung provide an opportune model to develop and apply algorithms that capture changes and disease phenotypes. We reviewed mathematical models that have been developed for biological sciences and applied them in the context of small cell lung cancer (SCLC) growth, mutational heterogeneity, and mechanisms of metastasis. The ultimate goal is to develop the stochastic and deterministic nature of this disease, to link this comprehensive set of tools back to its fractalness and to provide a platform for accurate biomarker development. These techniques may be particularly useful in the context of drug development research, such as combination with existing omics approaches. The integration of these tools will be important to further understand the biology of SCLC and ultimately develop novel therapeutics.

Integrated Modeling of Complex Optomechanical Systems

NASA Astrophysics Data System (ADS)

Andersen, Torben; Enmark, Anita

2011-09-01

Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.

Epidemics of panic during a bioterrorist attack--a mathematical model.

PubMed

Radosavljevic, Vladan; Radunovic, Desanka; Belojevic, Goran

2009-09-01

A bioterrorist attacks usually cause epidemics of panic in a targeted population. We have presented epidemiologic aspect of this phenomenon as a three-component model--host, information on an attack and social network. We have proposed a mathematical model of panic and counter-measures as the function of time in a population exposed to a bioterrorist attack. The model comprises ordinary differential equations and graphically presented combinations of the equations parameters. Clinically, we have presented a model through a sequence of psychic conditions and disorders initiated by an act of bioterrorism. This model might be helpful for an attacked community to timely and properly apply counter-measures and to minimize human mental suffering during a bioterrorist attack.

Discrete structures in continuum descriptions of defective crystals.

PubMed

Parry, G P

2016-04-28

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of 'plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. © 2016 The Author(s).

To the Greatest Lengths: Al Qaeda, Proximity and Recruitment Risk

DTIC Science & Technology

2010-12-01

activity (Boba, 2005, pp. 218–219). On the complex end of this spectrum, density mapping uses mathematical formulas to determine degrees of criminal...area. These calculations "combines actuarial risk prediction with environmental criminology to assign risk values to places according to their...translated records, and the compilation of distance variables are correct. 46 2. Model Mathematically , the formula for this test is

Experimental advances and preliminary mathematical modeling of the Swiss-roll mixed-reactant direct borohydride fuel cell

NASA Astrophysics Data System (ADS)

Aziznia, Amin; Oloman, Colin W.; Gyenge, Előd L.

2014-11-01

The Swiss-roll single-cell mixed reactant (SR-MRFC) borohydride - oxygen fuel cell equipped with Pt/carbon cloth 3D anode and either MnO2 or Ag gas-diffusion cathodes is investigated by a combination of experimental studies and preliminary mathematical modeling of the polarization curve. We investigate the effects of four variables: cathode side metallic mesh fluid distributor, separator type (Nafion 112® vs. Viledon®), cathode catalyst (MnO2 vs. Ag), and the hydrophilic pore volume fraction of the gas-diffusion cathode. Using a two-phase feed of alkaline borohydride solution (1 M NaBH4 - 2 M NaOH) and O2 gas in an SR-MRFC equipped with Pt/C 3D anode, MnO2 gas diffusion cathode, Viledon® porous diaphragm, expanded mesh cathode-side fluid distributor, the maximum superficial power density is 2230 W m-2 at 323 K and 105 kPa(abs). The latter superficial power density is almost 3.5 times higher than our previously reported superficial power density for the same catalyst combinations. Furthermore, with a Pt anode and Ag cathode catalyst combination, a superficial power density of 2500 W m-2 is achieved with superior performance durability compared to the MnO2 cathode. The fuel cell results are substantiated by impedance spectroscopy analysis and preliminary mathematical model predictions based on mixed potential theory.

Mathematical Modeling of Cellular Cross-Talk Between Endothelial and Tumor Cells Highlights Counterintuitive Effects of VEGF-Targeted Therapies.

PubMed

Jain, Harsh; Jackson, Trachette

2018-05-01

Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the expression of pro-angiogenic growth factors, including members of the vascular endothelial growth factor (VEGF) family of ligands. VEGF ligands are overexpressed in a wide variety of solid tumors and therefore have inspired optimism that inhibition of the different axes of the VEGF pathway-alone or in combination-would represent powerful anti-angiogenic therapies for most cancer types. When considering treatments that target VEGF and its receptors, it is difficult to tease out the differential anti-angiogenic and anti-tumor effects of all combinations experimentally because tumor cells and vascular endothelial cells are engaged in a dynamic cross-talk that impacts key aspects of tumorigenesis, independent of angiogenesis. Here we develop a mathematical model that connects intracellular signaling responsible for both endothelial and tumor cell proliferation and death to population-level cancer growth and angiogenesis. We use this model to investigate the effect of bidirectional communication between endothelial cells and tumor cells on treatments targeting VEGF and its receptors both in vitro and in vivo. Our results underscore the fact that in vitro therapeutic outcomes do not always translate to the in vivo situation. For example, our model predicts that certain therapeutic combinations result in antagonism in vivo that is not observed in vitro. Mathematical modeling in this direction can shed light on the mechanisms behind experimental observations that manipulating VEGF and its receptors is successful in some cases but disappointing in others.

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

PubMed

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

2009-06-01

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

Energy-technological complex with reactor for torrefaction

NASA Astrophysics Data System (ADS)

Kuzmina, J. S.; Director, L. B.; Zaichenko, V. M.

2016-11-01

To eliminate shortcomings of raw plant materials pelletizing process with thermal treatment (low-temperature pyrolysis or torrefaction) can be applied. This paper presents a mathematical model of energy-technological complex (ETC) for combined production of heat, electricity and solid biofuels torrefied pellets. According to the structure the mathematical model consists of mathematical models of main units of ETC and the relationships between them and equations of energy and material balances. The equations describe exhaust gas straining action through a porous medium formed by pellets. Decomposition rate of biomass was calculated by using the gross-reaction diagram, which is responsible for the disintegration of raw material. A mathematical model has been tested according to bench experiments on one reactor module. From nomographs, designed for a particular configuration of ETC it is possible to determine the basic characteristics of torrefied pellets (rate of weight loss, heating value and heat content) specifying only two parameters (temperature and torrefaction time). It is shown that the addition of reactor for torrefaction to gas piston engine can improve the energy efficiency of power plant.

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

How to mathematically optimize drug regimens using optimal control.

PubMed

Moore, Helen

2018-02-01

This article gives an overview of a technique called optimal control, which is used to optimize real-world quantities represented by mathematical models. I include background information about the historical development of the technique and applications in a variety of fields. The main focus here is the application to diseases and therapies, particularly the optimization of combination therapies, and I highlight several such examples. I also describe the basic theory of optimal control, and illustrate each of the steps with an example that optimizes the doses in a combination regimen for leukemia. References are provided for more complex cases. The article is aimed at modelers working in drug development, who have not used optimal control previously. My goal is to make this technique more accessible in the biopharma community.

Mathematical modeling to predict residential solid waste generation.

PubMed

Benítez, Sara Ojeda; Lozano-Olvera, Gabriela; Morelos, Raúl Adalberto; Vega, Carolina Armijo de

2008-01-01

One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R(2) were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.

INTEGRATION OF AN ECONOMY UNDER IMPERFECT COMPETITION WITH A TWELVE-CELL ECOLOGICAL MODEL

EPA Science Inventory

This report documents the scientific research work done to date on developing a generalized mathematical model depicting a combined economic-ecological-social system with the goal of making it available to the scientific community. The model is preliminary and has not been tested...

Challenges for Complex Microbial Ecosystems: Combination of Experimental Approaches with Mathematical Modeling

PubMed Central

Haruta, Shin; Yoshida, Takehito; Aoi, Yoshiteru; Kaneko, Kunihiko; Futamata, Hiroyuki

2013-01-01

In the past couple of decades, molecular ecological techniques have been developed to elucidate microbial diversity and distribution in microbial ecosystems. Currently, modern techniques, represented by meta-omics and single cell observations, are revealing the incredible complexity of microbial ecosystems and the large degree of phenotypic variation. These studies propound that microbiological techniques are insufficient to untangle the complex microbial network. This minireview introduces the application of advanced mathematical approaches in combination with microbiological experiments to microbial ecological studies. These combinational approaches have successfully elucidated novel microbial behaviors that had not been recognized previously. Furthermore, the theoretical perspective also provides an understanding of the plasticity, robustness and stability of complex microbial ecosystems in nature. PMID:23995424

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.

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition.

PubMed

Simeoni, Chiara; Dinicola, Simona; Cucina, Alessandra; Mascia, Corrado; Bizzarri, Mariano

2018-01-01

In this report, we aim at presenting a viable strategy for the study of Epithelial-Mesenchymal Transition (EMT) and its opposite Mesenchymal-Epithelial Transition (MET) by means of a Systems Biology approach combined with a suitable Mathematical Modeling analysis. Precisely, it is shown how the presence of a metastable state, that is identified at a mesoscopic level of description, is crucial for making possible the appearance of a phase transition mechanism in the framework of fast-slow dynamics for Ordinary Differential Equations (ODEs).

Feasibility of wake vortex monitoring systems for air terminals

NASA Technical Reports Server (NTRS)

Wilson, D. J.; Shrider, K. R.; Lawrence, T. R.

1972-01-01

Wake vortex monitoring systems, especially those using laser Doppler sensors, were investigated. The initial phases of the effort involved talking with potential users (air traffic controllers, pilots, etc.) of a wake vortex monitoring system to determine system requirements from the user's viewpoint. These discussions involved the volumes of airspace to be monitored for vortices, and potential methods of using the monitored vortex data once the data are available. A subsequent task led to determining a suitable mathematical model of the vortex phenomena and developing a mathematical model of the laser Doppler sensor for monitoring the vortex flow field. The mathematical models were used in combination to help evaluate the capability of laser Doppler instrumentation in monitoring vortex flow fields both in the near vicinity of the sensor (within 1 kilometer and at long ranges(10 kilometers).

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.

FILTRATION MODEL FOR COAL FLY ASH WITH GLASS FABRICS

EPA Science Inventory

The report describes a new mathematical model for predicting woven glass filter performance with coal fly ash aerosols from utility boilers. Its data base included: an extensive bench- and pilot-scale laboratory investigation of several dust/fabric combinations; field data from t...

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.

Molecular Mechanics and Dynamics Characterization of an "in silico" Mutated Protein: A Stand-Alone Lab Module or Support Activity for "in vivo" and "in vitro" Analyses of Targeted Proteins

ERIC Educational Resources Information Center

Chiang, Harry; Robinson, Lucy C.; Brame, Cynthia J.; Messina, Troy C.

2013-01-01

Over the past 20 years, the biological sciences have increasingly incorporated chemistry, physics, computer science, and mathematics to aid in the development and use of mathematical models. Such combined approaches have been used to address problems from protein structure-function relationships to the workings of complex biological systems.…

An Evaluation Model Applied to a Mathematics-Methods Program Involving Three Characteristics of Teaching Style and Their Relationship to Pupil Achievement. Teacher Education Forum; Volume 3, Number 4.

ERIC Educational Resources Information Center

Dodd, Carol Ann

This study explores a technique for evaluating teacher education programs in terms of teaching competencies, as applied to the Indiana University Mathematics Methods Program (MMP). The evaluation procedures formulated for the study include a process product design in combination with a modification of Pophan's performance test paradigm and Gage's…

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression.

PubMed

Saitou, Takashi; Imamura, Takeshi

2016-01-01

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation. © 2015 Japanese Society of Developmental Biologists.

Mathematical modeling of vesicle drug delivery systems 2: targeted vesicle interactions with cells, tumors, and the body.

PubMed

Ying, Chong T; Wang, Juntian; Lamm, Robert J; Kamei, Daniel T

2013-02-01

Vesicles have been studied for several years in their ability to deliver drugs. Mathematical models have much potential in reducing time and resources required to engineer optimal vesicles, and this review article summarizes these models that aid in understanding the ability of targeted vesicles to bind and internalize into cancer cells, diffuse into tumors, and distribute in the body. With regard to binding and internalization, radiolabeling and surface plasmon resonance experiments can be performed to determine optimal vesicle size and the number and type of ligands conjugated. Binding and internalization properties are also inputs into a mathematical model of vesicle diffusion into tumor spheroids, which highlights the importance of the vesicle diffusion coefficient and the binding affinity of the targeting ligand. Biodistribution of vesicles in the body, along with their half-life, can be predicted with compartmental models for pharmacokinetics that include the effect of targeting ligands, and these predictions can be used in conjunction with in vivo models to aid in the design of drug carriers. Mathematical models can prove to be very useful in drug carrier design, and our hope is that this review will encourage more investigators to combine modeling with quantitative experimentation in the field of vesicle-based drug delivery.

Neural signatures of co-occurring reading and mathematical difficulties.

PubMed

Skeide, Michael A; Evans, Tanya M; Mei, Edward Z; Abrams, Daniel A; Menon, Vinod

2018-06-19

Impaired abilities in multiple domains is common in children with learning difficulties. Co-occurrence of low reading and mathematical abilities (LRLM) appears in almost every second child with learning difficulties. However, little is known regarding the neural bases of this combination. Leveraging a unique and tightly controlled sample including children with LRLM, isolated low reading ability (LR), and isolated low mathematical ability (LM), we uncover a distinct neural signature in children with co-occurring low reading and mathematical abilities differentiable from LR and LM. Specifically, we show that LRLM is neuroanatomically distinct from both LR and LM based on reduced cortical folding of the right parahippocampal gyrus, a medial temporal lobe region implicated in visual associative learning. LRLM children were further distinguished from LR and LM by patterns of intrinsic functional connectivity between parahippocampal gyrus and brain circuitry underlying reading and numerical quantity processing. Our results critically inform cognitive and neural models of LRLM by implicating aberrations in both domain-specific and domain-general brain regions involved in reading and mathematics. More generally, our results provide the first evidence for distinct multimodal neural signatures associated with LRLM, and suggest that this population displays an independent phenotype of learning difficulty that cannot be explained simply as a combination of isolated low reading and mathematical abilities. © 2018 John Wiley & Sons Ltd.

Controlling Release Kinetics of PLG Microspheres Using a Manufacturing Technique

NASA Astrophysics Data System (ADS)

Berchane, Nader

2005-11-01

Controlled drug delivery offers numerous advantages compared with conventional free dosage forms, in particular: improved efficacy and patient compliance. Emulsification is a widely used technique to entrap drugs in biodegradable microspheres for controlled drug delivery. The size of the formed microspheres has a significant influence on drug release kinetics. Despite the advantages of controlled drug delivery, previous attempts to achieve predetermined release rates have seen limited success. This study develops a tool to tailor desired release kinetics by combining microsphere batches of specified mean diameter and size distribution. A fluid mechanics based correlation that predicts the average size of Poly(Lactide-co-Glycolide) [PLG] microspheres from the manufacturing technique, is constructed and validated by comparison with experimental results. The microspheres produced are accurately represented by the Rosin-Rammler mathematical distribution function. A mathematical model is formulated that incorporates the microsphere distribution function to predict the release kinetics from mono-dispersed and poly-dispersed populations. Through this mathematical model, different release kinetics can be achieved by combining different sized populations in different ratios. The resulting design tool should prove useful for the pharmaceutical industry to achieve designer release kinetics.

Experimental design and modelling approach to evaluate efficacy of β-lactam/β-lactamase inhibitor combinations.

PubMed

Sy, S K B; Derendorf, H

2017-07-29

A β-lactamase inhibitor (BLI) confers susceptibility of β-lactamase-expressing multidrug resistant (MDR) organisms to the partnering β-lactam (BL). To discuss the experimental design and modelling strategies for two-drug combinations, using ceftazidime- and aztreonam-avibactam combinations, as examples. The information came from several publications on avibactam in vitro time-kill studies and corresponding pharmacodynamic models. The experimental design to optimally gather crucial information from constant-concentration time-kill studies is to use an agile matrix of two-drug concentration combinations that cover 0.25- to 4-fold BL minimum inhibitory concentration (MIC) relative to the BLI concentrations to be tested against the particular isolate. This shifting agile design can save substantial costs and resources, without sacrificing crucial information needed for model development. The complex synergistic BL/BLI interaction is quantitatively explored using a semi-mechanistic pharmacokinetic-pharmacodynamic (PK/PD) mathematical model that accounts for antimicrobial activities in the combination, bacteria-mediated BL degradation and inhibition of BL degradation by BLI. A predictive mathematical formulation for the two-drug killing effects preserves the correlation between the model-derived EC 50 of BL and the BL MIC. The predictive value of PK/PD model is evaluated against external data that were not used for model development, including but not limited to in vitro hollow fibre and in vivo murine infection models. As a framework for translational predictions, the goal of this modelling strategy is to significantly decrease the decision-making time by running clinical trial simulations with MIC-substituted EC 50 function for isolates of comparable susceptibility through established correlation between BL MIC and EC 50 values. Copyright © 2017 European Society of Clinical Microbiology and Infectious Diseases. Published by Elsevier Ltd. All rights reserved.

A Novel Integrated Ecological Model for the study of Sustainability

EPA Science Inventory

In recent years, there has been a growing interest among various sections of the society in the study of sustainability. Recently, a generalized mathematical model depicting a combined economic-ecological-social system has been proposed to help in the formal study of sustainabili...

In Vitro Activity of MK-7655, a Novel β-Lactamase Inhibitor, in Combination with Imipenem against Carbapenem-Resistant Gram-Negative Bacteria

PubMed Central

Hirsch, Elizabeth B.; Ledesma, Kimberly R.; Chang, Kai-Tai; Schwartz, Michael S.; Motyl, Mary R.

2012-01-01

Carbapenem-resistant bacteria represent a significant treatment challenge due to the lack of active antimicrobials available. MK-7655 is a novel β-lactamase inhibitor under clinical development. We investigated the combined killing activity of imipenem and MK-7655 against four imipenem-resistant bacterial strains, using a mathematical model previously evaluated in our laboratory. Time-kill studies (TKS) were conducted with imipenem and MK-7655 against a KPC-2-producing Klebsiella pneumoniae isolate (KP6339) as well as 3 Pseudomonas aeruginosa isolates (PA24226, PA24227, and PA24228) with OprD porin deletions and overexpression of AmpC. TKS were performed using 25 clinically achievable concentration combinations in a 5-by-5 array. Bacterial burden at 24 h was determined in triplicate by quantitative culture and mathematically modeled using a three-dimensional response surface. Mathematical model assessments were evaluated experimentally using clinically relevant dosing regimens of imipenem, with or without MK-7655, in a hollow-fiber infection model (HFIM). The combination of imipenem and MK-7655 was synergistic for all strains. Interaction indices were as follows: for KP6339, 0.50 (95% confidence interval [CI], 0.42 to 0.58); for PA24226, 0.60 (95% CI, 0.58 to 0.62); for PA24227, 0.70 (95% CI, 0.66 to 0.74); and for PA24228, 0.55 (95% CI, 0.49 to 0.61). In the HFIM, imipenem plus MK-7655 considerably reduced the bacterial burden at 24 h, while failure with imipenem alone was seen against all isolates. Sustained suppression of bacterial growth at 72 h was achieved with simulated doses of 500 mg imipenem plus 500 mg MK-7655 in 2 (KP6339 and PA24227) strains, and it was achieved in an additional strain (PA24228) when the imipenem dose was increased to 1,000 mg. Additional studies are being conducted to determine the optimal dose and combinations to be used in clinical investigations. PMID:22526311

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

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

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

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

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

Online Professional Development: Combining Best Practices from Teacher, Technology and Distance Education

ERIC Educational Resources Information Center

Signer, Barbara

2008-01-01

This article provides a model of online professional development that is consistent with recommendations from the fields of teacher education, technology staff development and online learning. A graduate mathematics education course designed and implemented using the model is presented to exemplify the model's core components and interactions. The…

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..

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

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

The Reciprocal Internal/External Frame of Reference Model Using Grades and Test Scores

ERIC Educational Resources Information Center

Möller, Jens; Zimmermann, Friederike; Köller, Olaf

2014-01-01

Background: The reciprocal I/E model (RI/EM) combines the internal/external frame of reference model (I/EM) with the reciprocal effects model (REM). The RI/EM extends the I/EM longitudinally and the REM across domains. The model predicts that, within domains, mathematics and verbal achievement (VACH) and academic self-concept have positive effects…

Dimensionless Analysis and Numerical Modeling of Rebalancing Phenomena During Levitation

NASA Astrophysics Data System (ADS)

Gao, Lei; Shi, Zhe; Li, Donghui; McLean, Alexander; Chattopadhyay, Kinnor

2016-06-01

Electromagnetic levitation (EML) has proved to be a powerful tool for research activities in areas pertaining to materials physics and engineering. The customized EML setups in various fields, ranging from solidification to nanomaterial manufacturing, require the designing of stable levitation systems. Since the elevated droplet is opaque, the most effective way to research on EML is mathematical modeling. In the present study, a 3D model was built to investigate the rebalancing phenomenon causing instabilities during droplet melting. A mathematical model modified based on Hooke's law (spring) was proposed to describe the levitation system. This was combined with dimensionless analysis to investigate the generation of levitation forces as it will significantly affect the behavior of the spring model.

Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques - project status and first results

NASA Astrophysics Data System (ADS)

Schmidt, M.; Hugentobler, U.; Jakowski, N.; Dettmering, D.; Liang, W.; Limberger, M.; Wilken, V.; Gerzen, T.; Hoque, M.; Berdermann, J.

2012-04-01

Near real-time high resolution and high precision ionosphere models are needed for a large number of applications, e.g. in navigation, positioning, telecommunications or astronautics. Today these ionosphere models are mostly empirical, i.e., based purely on mathematical approaches. In the DFG project 'Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques (MuSIK)' the complex phenomena within the ionosphere are described vertically by combining the Chapman electron density profile with a plasmasphere layer. In order to consider the horizontal and temporal behaviour the fundamental target parameters of this physics-motivated approach are modelled by series expansions in terms of tensor products of localizing B-spline functions depending on longitude, latitude and time. For testing the procedure the model will be applied to an appropriate region in South America, which covers relevant ionospheric processes and phenomena such as the Equatorial Anomaly. The project connects the expertise of the three project partners, namely Deutsches Geodätisches Forschungsinstitut (DGFI) Munich, the Institute of Astronomical and Physical Geodesy (IAPG) of the Technical University Munich (TUM) and the German Aerospace Center (DLR), Neustrelitz. In this presentation we focus on the current status of the project. In the first year of the project we studied the behaviour of the ionosphere in the test region, we setup appropriate test periods covering high and low solar activity as well as winter and summer and started the data collection, analysis, pre-processing and archiving. We developed partly the mathematical-physical modelling approach and performed first computations based on simulated input data. Here we present information on the data coverage for the area and the time periods of our investigations and we outline challenges of the multi-dimensional mathematical-physical modelling approach. We show first results, discuss problems in modelling and possible solution strategies and finally, we address open questions.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach.

PubMed

Barnes, Marcia A; Stubbs, Allison; Raghubar, Kimberly P; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M; Smith-Chant, Brenda

2011-05-01

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Mathematical Skills in 3- and 5-Year-Olds with Spina Bifida and Their Typically Developing Peers: A Longitudinal Approach

PubMed Central

Barnes, Marcia A.; Stubbs, Allison; Raghubar, Kimberly P.; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M.; Smith-Chant, Brenda

2011-01-01

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual–spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual–spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual–spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder. PMID:21418718

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

PubMed

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

2017-04-01

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

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

2011-12-17

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

CEASAW: A User-Friendly Computer Environment Analysis for the Sawmill Owner

Treesearch

Guillermo Mendoza; William Sprouse; Philip A. Araman; William G. Luppold

1991-01-01

Improved spreadsheet software capabilities have brought optimization to users with little or no background in mathematical programming. Better interface capabilities of spreadsheet models now make it possible to combine optimization models with a spreadsheet system. Sawmill production and inventory systems possess many features that make them suitable application...

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

Koizumi, Yoshiki; Nakajim, Syo; Ohash, Hirofumi

Cell culture study combing a mathematical model and computer simulation quantifies the anti-hepatitis C virus drug efficacy at any concentrations and any combinations in preclinical settings, and can obtain rich basic evidences for selecting optimal treatments prior to costly clinical trials.

Kinematic analysis of asymmetric folds in competent layers using mathematical modelling

NASA Astrophysics Data System (ADS)

Aller, J.; Bobillo-Ares, N. C.; Bastida, F.; Lisle, R. J.; Menéndez, C. O.

2010-08-01

Mathematical 2D modelling of asymmetric folds is carried out by applying a combination of different kinematic folding mechanisms: tangential longitudinal strain, flexural flow and homogeneous deformation. The main source of fold asymmetry is discovered to be due to the superimposition of a general homogeneous deformation on buckle folds that typically produces a migration of the hinge point. Forward modelling is performed mathematically using the software 'FoldModeler', by the superimposition of simple shear or a combination of simple shear and irrotational strain on initial buckle folds. The resulting folds are Ramsay class 1C folds, comparable to those formed by symmetric flattening, but with different length of limbs and layer thickness asymmetry. Inverse modelling is made by fitting the natural fold to a computer-simulated fold. A problem of this modelling is the search for the most appropriate homogeneous deformation to be superimposed on the initial fold. A comparative analysis of the irrotational and rotational deformations is made in order to find the deformation which best simulates the shapes and attitudes of natural folds. Modelling of recumbent folds suggests that optimal conditions for their development are: a) buckling in a simple shear regime with a sub-horizontal shear direction and layering gently dipping towards this direction; b) kinematic amplification due to superimposition of a combination of simple shear and irrotational strain with a sub-vertical maximum shortening direction for the latter component. The modelling shows that the amount of homogeneous strain necessary for the development of recumbent folds is much less when an irrotational strain component is superimposed at this stage that when the superimposed strain is only simple shear. In nature, the amount of the irrotational strain component probably increases during the development of the fold as a consequence of the increasing influence of the gravity due to the tectonic superimposition of rocks.

Understanding electricity generation in osmotic microbial fuel cells through integrated experimental investigation and mathematical modeling.

PubMed

Qin, Mohan; Ping, Qingyun; Lu, Yaobin; Abu-Reesh, Ibrahim M; He, Zhen

2015-11-01

Osmotic microbial fuel cells (OsMFCs) are a new type of MFCs with integrating forward osmosis (FO). However, it is not well understood why electricity generation is improved in OsMFCs compared to regular MFCs. Herein, an approach integrating experimental investigation and mathematical model was adopted to address the question. Both an OsMFC and an MFC achieved similar organic removal efficiency, but the OsMFC generated higher current than the MFC with or without water flux, resulting from the lower resistance of FO membrane. Combining NaCl and glucose as a catholyte demonstrated that the catholyte conductivity affected the electricity generation in the OsMFC. A mathematical model of OsMFCs was developed and validated with the experimental data. The model predicated the variation of internal resistance with increasing water flux, and confirmed the importance of membrane resistance. Increasing water flux with higher catholyte conductivity could decrease the membrane resistance. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

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

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

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

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.

Improving operating room efficiency by applying bin-packing and portfolio techniques to surgical case scheduling.

PubMed

Van Houdenhoven, Mark; van Oostrum, Jeroen M; Hans, Erwin W; Wullink, Gerhard; Kazemier, Geert

2007-09-01

An operating room (OR) department has adopted an efficient business model and subsequently investigated how efficiency could be further improved. The aim of this study is to show the efficiency improvement of lowering organizational barriers and applying advanced mathematical techniques. We applied advanced mathematical algorithms in combination with scenarios that model relaxation of various organizational barriers using prospectively collected data. The setting is the main inpatient OR department of a university hospital, which sets its surgical case schedules 2 wk in advance using a block planning method. The main outcome measures are the number of freed OR blocks and OR utilization. Lowering organizational barriers and applying mathematical algorithms can yield a 4.5% point increase in OR utilization (95% confidence interval 4.0%-5.0%). This is obtained by reducing the total required OR time. Efficient OR departments can further improve their efficiency. The paper shows that a radical cultural change that comprises the use of mathematical algorithms and lowering organizational barriers improves OR utilization.

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

NASA Astrophysics Data System (ADS)

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

2014-10-01

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

How to Combine Collaboration Scripts and Heuristic Worked Examples to Foster Mathematical Argumentation--When Working Memory Matters

ERIC Educational Resources Information Center

Schwaighofer, Matthias; Vogel, Freydis; Kollar, Ingo; Ufer, Stefan; Strohmaier, Anselm; Terwedow, Ilka; Ottinger, Sarah; Reiss, Kristina; Fischer, Frank

2017-01-01

Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners…

Hydrogen production by the hyperthermophilic bacterium Thermotoga maritima Part II: modeling and experimental approaches for hydrogen production.

PubMed

Auria, Richard; Boileau, Céline; Davidson, Sylvain; Casalot, Laurence; Christen, Pierre; Liebgott, Pierre Pol; Combet-Blanc, Yannick

2016-01-01

Thermotoga maritima is a hyperthermophilic bacterium known to produce hydrogen from a large variety of substrates. The aim of the present study is to propose a mathematical model incorporating kinetics of growth, consumption of substrates, product formations, and inhibition by hydrogen in order to predict hydrogen production depending on defined culture conditions. Our mathematical model, incorporating data concerning growth, substrates, and products, was developed to predict hydrogen production from batch fermentations of the hyperthermophilic bacterium, T. maritima . It includes the inhibition by hydrogen and the liquid-to-gas mass transfer of H 2 , CO 2 , and H 2 S. Most kinetic parameters of the model were obtained from batch experiments without any fitting. The mathematical model is adequate for glucose, yeast extract, and thiosulfate concentrations ranging from 2.5 to 20 mmol/L, 0.2-0.5 g/L, or 0.01-0.06 mmol/L, respectively, corresponding to one of these compounds being the growth-limiting factor of T. maritima . When glucose, yeast extract, and thiosulfate concentrations are all higher than these ranges, the model overestimates all the variables. In the window of the model validity, predictions of the model show that the combination of both variables (increase in limiting factor concentration and in inlet gas stream) leads up to a twofold increase of the maximum H 2 -specific productivity with the lowest inhibition. A mathematical model predicting H 2 production in T. maritima was successfully designed and confirmed in this study. However, it shows the limit of validity of such mathematical models. Their limit of applicability must take into account the range of validity in which the parameters were established.

Multiscale Mathematical Modeling in Dental Tissue Engineering: Toward Computer-Aided Design of a Regenerative System Based on Hydroxyapatite Granules, Focussing on Early and Mid-Term Stiffness Recovery

PubMed Central

Scheiner, Stefan; Komlev, Vladimir S.; Gurin, Alexey N.; Hellmich, Christian

2016-01-01

We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall conglomerate-type scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions. In this context, the question arises how the compound stiffness is driven by the key design parameters of the tissue engineering system: macroporosity, crack density, as well as scaffold resorption/bone formation rates. We here tackle this question by combining the latest state-of-the-art mathematical modeling techniques in the field of multiscale micromechanics, into an unprecedented suite of highly efficient, semi-analytically defined computation steps resolving several levels of hierarchical organization, from the millimeter- down to the nanometer-scale. This includes several types of homogenization schemes, namely such for porous polycrystals with elongated solid elements, for cracked matrix-inclusion composites, as well as for assemblies of coated spherical compounds. Together with the experimentally known stiffnesses of hydroxyapatite crystals and mandibular bone tissue, the new mathematical model suggests that early stiffness recovery (i.e., within several weeks) requires total avoidance of microcracks in the hydroxyapatite scaffolds, while mid-term stiffness recovery (i.e., within several months) is additionally promoted by provision of small granule sizes, in combination with high bone formation and low scaffold resorption rates. PMID:27708584

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation.

PubMed

Chisholm, Rebecca H; Lorenzi, Tommaso; Clairambault, Jean

2016-11-01

Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Modeling Tumor Clonal Evolution for Drug Combinations Design.

PubMed

Zhao, Boyang; Hemann, Michael T; Lauffenburger, Douglas A

2016-03-01

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

Mathematical Modeling – The Impact of Cooling Water Temperature Upsurge on Combined Cycle Power Plant Performance and Operation

NASA Astrophysics Data System (ADS)

Indra Siswantara, Ahmad; Pujowidodo, Hariyotejo; Darius, Asyari; Ramdlan Gunadi, Gun Gun

2018-03-01

This paper presents the mathematical modeling analysis on cooling system in a combined cycle power plant. The objective of this study is to get the impact of cooling water upsurge on plant performance and operation, using Engineering Equation Solver (EES™) tools. Power plant installed with total power capacity of block#1 is 505.95 MWe and block#2 is 720.8 MWe, where sea water consumed as cooling media at two unit condensers. Basic principle of analysis is heat balance calculation from steam turbine and condenser, concern to vacuum condition and heat rate values. Based on the result shown graphically, there were impact the upsurge of cooling water to increase plant heat rate and vacuum pressure in condenser so ensued decreasing plant efficiency and causing possibility steam turbine trip as back pressure raised from condenser.

Effect of Multiple Delays in an Eco-Epidemiological Model with Strong Allee Effect

NASA Astrophysics Data System (ADS)

Ghosh, Kakali; Biswas, Santanu; Samanta, Sudip; Tiwari, Pankaj Kumar; Alshomrani, Ali Saleh; Chattopadhyay, Joydev

In the present article, we make an attempt to investigate the effect of two time delays, logistic delay and gestation delay, on an eco-epidemiological model. In the proposed model, strong Allee effect is considered in the growth term of the prey population. We incorporate two time lags and inspect elementary mathematical characteristic of the proposed model such as boundedness, uniform persistence, stability and Hopf-bifurcation for all possible combinations of both delays at the interior equilibrium point of the system. We observe that increase in gestation delay leads to chaotic solutions through the limit cycle. We also observe that the Allee effect play a major role in controlling the chaos. We execute several numerical simulations to illustrate the proposed mathematical model and our analytical findings.

CORRECTING FOR MEASUREMENT ERROR IN LATENT VARIABLES USED AS PREDICTORS*

PubMed Central

Schofield, Lynne Steuerle

2015-01-01

This paper represents a methodological-substantive synergy. A new model, the Mixed Effects Structural Equations (MESE) model which combines structural equations modeling and item response theory is introduced to attend to measurement error bias when using several latent variables as predictors in generalized linear models. The paper investigates racial and gender disparities in STEM retention in higher education. Using the MESE model with 1997 National Longitudinal Survey of Youth data, I find prior mathematics proficiency and personality have been previously underestimated in the STEM retention literature. Pre-college mathematics proficiency and personality explain large portions of the racial and gender gaps. The findings have implications for those who design interventions aimed at increasing the rates of STEM persistence among women and under-represented minorities. PMID:26977218

Approach to Computer Implementation of Mathematical Model of 3-Phase Induction Motor

NASA Astrophysics Data System (ADS)

Pustovetov, M. Yu

2018-03-01

This article discusses the development of the computer model of an induction motor based on the mathematical model in a three-phase stator reference frame. It uses an approach that allows combining during preparation of the computer model dual methods: means of visual programming circuitry (in the form of electrical schematics) and logical one (in the form of block diagrams). The approach enables easy integration of the model of an induction motor as part of more complex models of electrical complexes and systems. The developed computer model gives the user access to the beginning and the end of a winding of each of the three phases of the stator and rotor. This property is particularly important when considering the asymmetric modes of operation or when powered by the special circuitry of semiconductor converters.

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.

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

Review on experiment-based two- and three-dimensional models for wound healing

PubMed Central

Gefen, Amit

2016-01-01

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers. PMID:27708762

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

PubMed

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

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

A mixed integer program to model spatial wildfire behavior and suppression placement decisions

Treesearch

Erin J. Belval; Yu Wei; Michael Bevers

2015-01-01

Wildfire suppression combines multiple objectives and dynamic fire behavior to form a complex problem for decision makers. This paper presents a mixed integer program designed to explore integrating spatial fire behavior and suppression placement decisions into a mathematical programming framework. Fire behavior and suppression placement decisions are modeled using...

Digital computer simulation of inductor-energy-storage dc-to-dc converters with closed-loop regulators

NASA Technical Reports Server (NTRS)

Ohri, A. K.; Owen, H. A.; Wilson, T. G.; Rodriguez, G. E.

1974-01-01

The simulation of converter-controller combinations by means of a flexible digital computer program which produces output to a graphic display is discussed. The procedure is an alternative to mathematical analysis of converter systems. The types of computer programming involved in the simulation are described. Schematic diagrams, state equations, and output equations are displayed for four basic forms of inductor-energy-storage dc to dc converters. Mathematical models are developed to show the relationship of the parameters.

Interactions of elevation, aspect, and slope in models of forest species composition and productivity

Treesearch

Albert R. Stage; Christian Salas

2007-01-01

We present a linear model for the interacting effects of elevation, aspect, and slope for use in predicting forest productivity or species composition. The model formulation we propose integrates interactions of these three factors in a mathematical expression representing their combined effect in terms of a cosine function of aspect with a phase shift and amplitude...

Mathematical modeling of high-pH chemical flooding

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

Bhuyan, D.; Lake, L.W.; Pope, G.A.

1990-05-01

This paper describes a generalized compositional reservoir simulator for high-pH chemical flooding processes. This simulator combines the reaction chemistry associated with these processes with the extensive physical- and flow-property modeling schemes of an existing micellar/polymer flood simulator, UTCHEM. Application of the model is illustrated for cases from a simple alkaline preflush to surfactant-enhanced alkaline-polymer flooding.

Electrochemical carbon dioxide concentrator: Math model

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

[Study on the epidemiological characteristics and incidence trend of scarlet fever in Shanghai, 2005-2012].

PubMed

Ren, Hong; Wang, Ye; Chen, Ming-liang; Yuan, Zheng-an; Li, Yan-ting; Huang, Pu; Hu, Jia-yu

2013-07-01

To systemically analyze the epidemiological characteristics, molecular markers of circulating group A Streptococcus (GAS) isolates and the incidence trend of scarlet fever in Shanghai from 2005 to 2012 as well as to explore the practice of GAS isolates surveillance program and the combined mathematical model in the early warning of scarlet fever. The morbidity series of scarlet fever were retrieved to analyze and fit the combined mathematical model which comprised an autoregressive integrated moving average (ARIMA) model and a neural network. GAS isolates surveillances programs were implemented on community healthy population, using the emm typing and superantigens detecting method in Shanghai during the epidemic period of scarlet fever in 2008, 2010 and 2012. The standardized prevalence of GAS isolates was estimated with the demographic data. From 2005 to 2012, there were a total of 9410 scarlet fever cases reported in Shanghai including local registered residents and immigrant population, showing that the distribution of patients as sporadic. The morbidity kept rising with seasonal and periodical variations and the peak was in 2011. The average morbidity was 6.012 per 100 000 persons. Morbidity in the the suburban was significantly higher than that in the urban areas. Children at 4 to 8 years old were easy to be involved. The mean error rate of single ARIMA model,ARIMA-GRNN and back propagation artificial neural network combined model were 0.268, 0.432 and 0.131 respectively. The predicted incidence of scarlet fever in 2013 would keep fluctuating within a narrow range from 0.446 to 3.467 per 100 000 persons. A total number of 4409 throat swab samples were collected through the GAS isolates surveillance programs in 2008, 2010 and 2012. The standardized prevalence of GAS isolates in each year were 0.000%, 0.000% and 1.092%. 18 GAS isolates were identified and 15 isolates (83.33%)belonged to emm 12.0. The morbidity of scarlet fever would continue to maintain an upward trend in Shanghai and the techniques used in GAS isolates surveillance program and in the combined mathematical model could be applied for the early warning system on scarlet fever.

Selected National Cancer Institute Breast Cancer Research Topics | NIH MedlinePlus the Magazine

MedlinePlus

... effective treatments for these women. The Integrative Cancer Biology Program combines experimental and clinical research with mathematical modeling to gain new insights into cancer biology, prevention, diagnostics, and treatments. Multiple centers are developing ...

75 FR 3375 - School Improvement Grants; American Recovery and Reinvestment Act of 2009 (ARRA); Title I of the...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-21

... ESEA in reading/language arts and mathematics combined; and (3) is no higher achieving on the State's...)(3) of the ESEA in reading/language arts and mathematics combined; and (3) either is no higher... mathematics combined; and (3) does not meet the requirements to be a Tier I or Tier II school. Thus, a Tier...

Predicting gene regulatory networks by combining spatial and temporal gene expression data in Arabidopsis root stem cells

PubMed Central

de Luis Balaguer, Maria Angels; Fisher, Adam P.; Clark, Natalie M.; Fernandez-Espinosa, Maria Guadalupe; Möller, Barbara K.; Weijers, Dolf; Williams, Cranos; Lorenzo, Oscar; Sozzani, Rosangela

2017-01-01

Identifying the transcription factors (TFs) and associated networks involved in stem cell regulation is essential for understanding the initiation and growth of plant tissues and organs. Although many TFs have been shown to have a role in the Arabidopsis root stem cells, a comprehensive view of the transcriptional signature of the stem cells is lacking. In this work, we used spatial and temporal transcriptomic data to predict interactions among the genes involved in stem cell regulation. To accomplish this, we transcriptionally profiled several stem cell populations and developed a gene regulatory network inference algorithm that combines clustering with dynamic Bayesian network inference. We leveraged the topology of our networks to infer potential major regulators. Specifically, through mathematical modeling and experimental validation, we identified PERIANTHIA (PAN) as an important molecular regulator of quiescent center function. The results presented in this work show that our combination of molecular biology, computational biology, and mathematical modeling is an efficient approach to identify candidate factors that function in the stem cells. PMID:28827319

Modeling and optimization of a hybrid solar combined cycle (HYCS)

NASA Astrophysics Data System (ADS)

Eter, Ahmad Adel

2011-12-01

The main objective of this thesis is to investigate the feasibility of integrating concentrated solar power (CSP) technology with the conventional combined cycle technology for electric generation in Saudi Arabia. The generated electricity can be used locally to meet the annual increasing demand. Specifically, it can be utilized to meet the demand during the hours 10 am-3 pm and prevent blackout hours, of some industrial sectors. The proposed CSP design gives flexibility in the operation system. Since, it works as a conventional combined cycle during night time and it switches to work as a hybrid solar combined cycle during day time. The first objective of the thesis is to develop a thermo-economical mathematical model that can simulate the performance of a hybrid solar-fossil fuel combined cycle. The second objective is to develop a computer simulation code that can solve the thermo-economical mathematical model using available software such as E.E.S. The developed simulation code is used to analyze the thermo-economic performance of different configurations of integrating the CSP with the conventional fossil fuel combined cycle to achieve the optimal integration configuration. This optimal integration configuration has been investigated further to achieve the optimal design of the solar field that gives the optimal solar share. Thermo-economical performance metrics which are available in the literature have been used in the present work to assess the thermo-economic performance of the investigated configurations. The economical and environmental impact of integration CSP with the conventional fossil fuel combined cycle are estimated and discussed. Finally, the optimal integration configuration is found to be solarization steam side in conventional combined cycle with solar multiple 0.38 which needs 29 hectare and LEC of HYCS is 63.17 $/MWh under Dhahran weather conditions.

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

PubMed

Anderies, John M

2015-02-01

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

A mathematical and experimental simulation of the hematological response to weightlessness

NASA Technical Reports Server (NTRS)

Kimzey, S. L.; Leonard, J. I.; Johnson, P. C.

1979-01-01

A mathematical model of erythropoiesis control was used to simulate the effects of bedrest and zero-g on the circulating red cell mass. The model incorporates the best current understanding of the dynamics of red cell production and destruction and the associated feedback regulation. Specifically studied were the hemodynamic responses of a 28-day bedrest study devised to simulate Skylab experience. The results support the hypothesis that red cell loss during supine bedrest is a normal physiological feedback process in response to hemoconcentration enhanced tissue oxygenation and suppression of red cell production. Model simulation suggested the possibilities that this period was marked by some combination of increased oxygen-hemoglobin affinity, small reduction in mean red cell life span, ineffective erythropoiesis, or abnormal reticulocytosis.

Avian Influenza spread and transmission dynamics

USGS Publications Warehouse

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

2015-01-01

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

New and practical mathematical model of membrane fouling in an aerobic submerged membrane bioreactor.

PubMed

Zuthi, Mst Fazana Rahman; Guo, Wenshan; Ngo, Huu Hao; Nghiem, Duc Long; Hai, Faisal I; Xia, Siqing; Li, Jianxin; Li, Jixiang; Liu, Yi

2017-08-01

This study aimed to develop a practical semi-empirical mathematical model of membrane fouling that accounts for cake formation on the membrane and its pore blocking as the major processes of membrane fouling. In the developed model, the concentration of mixed liquor suspended solid is used as a lumped parameter to describe the formation of cake layer including the biofilm. The new model considers the combined effect of aeration and backwash on the foulants' detachment from the membrane. New exponential coefficients are also included in the model to describe the exponential increase of transmembrane pressure that typically occurs after the initial stage of an MBR operation. The model was validated using experimental data obtained from a lab-scale aerobic sponge-submerged membrane bioreactor (MBR), and the simulation of the model agreed well with the experimental findings. Copyright © 2017 Elsevier Ltd. All rights reserved.

Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: A mathematical model

PubMed Central

Friedman, Avner

2017-01-01

In this paper we consider a combination therapy of cancer. One drug is a vaccine which activates dendritic cells so that they induce more T cells to infiltrate the tumor. The other drug is a checkpoint inhibitor, which enables the T cells to remain active against the cancer cells. The two drugs are positively correlated in the sense that an increase in the amount of each drug results in a reduction in the tumor volume. We consider the question whether a treatment with combination of the two drugs at certain levels is preferable to a treatment by one of the drugs alone at ‘roughly’ twice the dosage level; if that is the case, then we say that there is a positive ‘synergy’ for this combination of dosages. To address this question, we develop a mathematical model using a system of partial differential equations. The variables include dendritic and cancer cells, CD4+ and CD8+ T cells, IL-12 and IL-2, GM-CSF produced by the vaccine, and a T cell checkpoint inhibitor associated with PD-1. We use the model to explore the efficacy of the two drugs, separately and in combination, and compare the simulations with data from mouse experiments. We next introduce the concept of synergy between the drugs and develop a synergy map which suggests in what proportion to administer the drugs in order to achieve the maximum reduction of tumor volume under the constraint of maximum tolerated dose. PMID:28542574

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

Combined electrochemical, heat generation, and thermal model for large prismatic lithium-ion batteries in real-time applications

NASA Astrophysics Data System (ADS)

Farag, Mohammed; Sweity, Haitham; Fleckenstein, Matthias; Habibi, Saeid

2017-08-01

Real-time prediction of the battery's core temperature and terminal voltage is very crucial for an accurate battery management system. In this paper, a combined electrochemical, heat generation, and thermal model is developed for large prismatic cells. The proposed model consists of three sub-models, an electrochemical model, heat generation model, and thermal model which are coupled together in an iterative fashion through physicochemical temperature dependent parameters. The proposed parameterization cycles identify the sub-models' parameters separately by exciting the battery under isothermal and non-isothermal operating conditions. The proposed combined model structure shows accurate terminal voltage and core temperature prediction at various operating conditions while maintaining a simple mathematical structure, making it ideal for real-time BMS applications. Finally, the model is validated against both isothermal and non-isothermal drive cycles, covering a broad range of C-rates, and temperature ranges [-25 °C to 45 °C].

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

A Mathematical Model for Pathogen Cross-Contamination Dynamics during the Postharvest Processing of Leafy Greens.

PubMed

Mokhtari, Amir; Oryang, David; Chen, Yuhuan; Pouillot, Regis; Van Doren, Jane

2018-01-08

We developed a probabilistic mathematical model for the postharvest processing of leafy greens focusing on Escherichia coli O157:H7 contamination of fresh-cut romaine lettuce as the case study. Our model can (i) support the investigation of cross-contamination scenarios, and (ii) evaluate and compare different risk mitigation options. We used an agent-based modeling framework to predict the pathogen prevalence and levels in bags of fresh-cut lettuce and quantify spread of E. coli O157:H7 from contaminated lettuce to surface areas of processing equipment. Using an unbalanced factorial design, we were able to propagate combinations of random values assigned to model inputs through different processing steps and ranked statistically significant inputs with respect to their impacts on selected model outputs. Results indicated that whether contamination originated on incoming lettuce heads or on the surface areas of processing equipment, pathogen prevalence among bags of fresh-cut lettuce and batches was most significantly impacted by the level of free chlorine in the flume tank and frequency of replacing the wash water inside the tank. Pathogen levels in bags of fresh-cut lettuce were most significantly influenced by the initial levels of contamination on incoming lettuce heads or surface areas of processing equipment. The influence of surface contamination on pathogen prevalence or levels in fresh-cut bags depended on the location of that surface relative to the flume tank. This study demonstrates that developing a flexible yet mathematically rigorous modeling tool, a "virtual laboratory," can provide valuable insights into the effectiveness of individual and combined risk mitigation options. © 2018 The Authors Risk Analysis published by Wiley Periodicals, Inc. on behalf of Society for Risk Analysis.

Modeling Tumor Clonal Evolution for Drug Combinations Design

PubMed Central

Zhao, Boyang; Hemann, Michael T.; Lauffenburger, Douglas A.

2016-01-01

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs. PMID:28435907

Rapid detection and non-subjective characterisation of infectious bronchitis virus isolates using high-resolution melt curve analysis and a mathematical model.

PubMed

Hewson, Kylie; Noormohammadi, Amir H; Devlin, Joanne M; Mardani, Karim; Ignjatovic, Jagoda

2009-01-01

Infectious bronchitis virus (IBV) is a coronavirus that causes upper respiratory, renal and/or reproductive diseases with high morbidity in poultry. Classification of IBV is important for implementation of vaccination strategies to control the disease in commercial poultry. Currently, the lengthy process of sequence analysis of the IBV S1 gene is considered the gold standard for IBV strain identification, with a high nucleotide identity (e.g. > or =95%) indicating related strains. However, this gene has a high propensity to mutate and/or undergo recombination, and alone it may not be reliable for strain identification. A real-time polymerase chain reaction (RT-PCR) combined with high-resolution melt (HRM) curve analysis was developed based on the 3'UTR of IBV for rapid detection and classification of IBV from commercial poultry. HRM curves generated from 230 to 435-bp PCR products of several IBV strains were subjected to further analysis using a mathematical model also developed during this study. It was shown that a combination of HRM curve analysis and the mathematical model could reliably group 189 out of 190 comparisons of pairs of IBV strains in accordance with their 3'UTR and S1 gene identities. The newly developed RT-PCR/HRM curve analysis model could detect and rapidly identify novel and vaccine-related IBV strains, as confirmed by S1 gene and 3'UTR nucleotide sequences. This model is a rapid, reliable, accurate and non-subjective system for detection of IBVs in poultry flocks.

Simulating physiological interactions in a hybrid system of mathematical models.

PubMed

Kretschmer, Jörn; Haunsberger, Thomas; Drost, Erick; Koch, Edmund; Möller, Knut

2014-12-01

Mathematical models can be deployed to simulate physiological processes of the human organism. Exploiting these simulations, reactions of a patient to changes in the therapy regime can be predicted. Based on these predictions, medical decision support systems (MDSS) can help in optimizing medical therapy. An MDSS designed to support mechanical ventilation in critically ill patients should not only consider respiratory mechanics but should also consider other systems of the human organism such as gas exchange or blood circulation. A specially designed framework allows combining three model families (respiratory mechanics, cardiovascular dynamics and gas exchange) to predict the outcome of a therapy setting. Elements of the three model families are dynamically combined to form a complex model system with interacting submodels. Tests revealed that complex model combinations are not computationally feasible. In most patients, cardiovascular physiology could be simulated by simplified models decreasing computational costs. Thus, a simplified cardiovascular model that is able to reproduce basic physiological behavior is introduced. This model purely consists of difference equations and does not require special algorithms to be solved numerically. The model is based on a beat-to-beat model which has been extended to react to intrathoracic pressure levels that are present during mechanical ventilation. The introduced reaction to intrathoracic pressure levels as found during mechanical ventilation has been tuned to mimic the behavior of a complex 19-compartment model. Tests revealed that the model is able to represent general system behavior comparable to the 19-compartment model closely. Blood pressures were calculated with a maximum deviation of 1.8 % in systolic pressure and 3.5 % in diastolic pressure, leading to a simulation error of 0.3 % in cardiac output. The gas exchange submodel being reactive to changes in cardiac output showed a resulting deviation of less than 0.1 %. Therefore, the proposed model is usable in combinations where cardiovascular simulation does not have to be detailed. Computing costs have been decreased dramatically by a factor 186 compared to a model combination employing the 19-compartment model.

Modeling of transient heat pipe operation

NASA Technical Reports Server (NTRS)

Colwell, G. T.; Hartley, J. G.

1986-01-01

Mathematical models and associated solution procedures which can be used to design heat pipe cooled structures for use on hypersonic vehicles are being developed. The models should also have the capability to predict off-design performance for a variety of operating conditions. It is expected that the resulting models can be used to predict startup behavior of liquid metal heat pipes to be used in reentry vehicles, hypersonic aircraft, and space nuclear reactors. Work to date related to numerical solutions of governing differential equations for the outer shell and the combination capillary structure and working fluid is summarized. Finite element numerical equations using both implicit, explicit, and combination methods were examined.

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

Measuring and modeling salience with the theory of visual attention.

PubMed

Krüger, Alexander; Tünnermann, Jan; Scharlau, Ingrid

2017-08-01

For almost three decades, the theory of visual attention (TVA) has been successful in mathematically describing and explaining a wide variety of phenomena in visual selection and recognition with high quantitative precision. Interestingly, the influence of feature contrast on attention has been included in TVA only recently, although it has been extensively studied outside the TVA framework. The present approach further develops this extension of TVA's scope by measuring and modeling salience. An empirical measure of salience is achieved by linking different (orientation and luminance) contrasts to a TVA parameter. In the modeling part, the function relating feature contrasts to salience is described mathematically and tested against alternatives by Bayesian model comparison. This model comparison reveals that the power function is an appropriate model of salience growth in the dimensions of orientation and luminance contrast. Furthermore, if contrasts from the two dimensions are combined, salience adds up additively.

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

PubMed

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

2018-02-01

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

Thermal modeling of phase change solidification in thermal control devices including natural convection effects

NASA Technical Reports Server (NTRS)

Ukanwa, A. O.; Stermole, F. J.; Golden, J. O.

1972-01-01

Natural convection effects in phase change thermal control devices were studied. A mathematical model was developed to evaluate natural convection effects in a phase change test cell undergoing solidification. Although natural convection effects are minimized in flight spacecraft, all phase change devices are ground tested. The mathematical approach to the problem was to first develop a transient two-dimensional conduction heat transfer model for the solidification of a normal paraffin of finite geometry. Next, a transient two-dimensional model was developed for the solidification of the same paraffin by a combined conduction-natural-convection heat transfer model. Throughout the study, n-hexadecane (n-C16H34) was used as the phase-change material in both the theoretical and the experimental work. The models were based on the transient two-dimensional finite difference solutions of the energy, continuity, and momentum equations.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-01-01

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

Does lake size matter? Combining morphology and process modeling to examine the contribution of lake classes to population-scale processes

USGS Publications Warehouse

Winslow, Luke A.; Read, Jordan S.; Hanson, Paul C.; Stanley, Emily H.

2014-01-01

With lake abundances in the thousands to millions, creating an intuitive understanding of the distribution of morphology and processes in lakes is challenging. To improve researchers’ understanding of large-scale lake processes, we developed a parsimonious mathematical model based on the Pareto distribution to describe the distribution of lake morphology (area, perimeter and volume). While debate continues over which mathematical representation best fits any one distribution of lake morphometric characteristics, we recognize the need for a simple, flexible model to advance understanding of how the interaction between morphometry and function dictates scaling across large populations of lakes. These models make clear the relative contribution of lakes to the total amount of lake surface area, volume, and perimeter. They also highlight the critical thresholds at which total perimeter, area and volume would be evenly distributed across lake size-classes have Pareto slopes of 0.63, 1 and 1.12, respectively. These models of morphology can be used in combination with models of process to create overarching “lake population” level models of process. To illustrate this potential, we combine the model of surface area distribution with a model of carbon mass accumulation rate. We found that even if smaller lakes contribute relatively less to total surface area than larger lakes, the increasing carbon accumulation rate with decreasing lake size is strong enough to bias the distribution of carbon mass accumulation towards smaller lakes. This analytical framework provides a relatively simple approach to upscaling morphology and process that is easily generalizable to other ecosystem processes.

Therminator: Configuring the Underlying Statistical Mechanics Model

DTIC Science & Technology

2003-12-01

1502, Oct. 7–10, 2002. [13] Ralph P . Grimaldi , Discrete and Combinational Mathematics, 4th Edition, Addison Wesley Longman, New York, 2000. [14...Eagle Co-Advisor John P . Powers Chairman, Department of Electrical and Computer Engineering Peter J. Denning Chairman, Department of...

Collaborative Research: Atmospheric Pressure Microplasma Chemistry-Photon Synergies Final Report

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

Graves, David

Combining the effects of low temperature, atmospheric pressure microplasmas and microplasma photon sources shows greatly expanded range of applications of each of them. The plasma sources create active chemical species and these can be activated further by addition of photons and associated photochemistry. There are many ways to combine the effects of plasma chemistry and photochemistry, especially if there are multiple phases present. The project combines construction of appropriate test experimental systems, various spectroscopic diagnostics and mathematical modeling.

Reduced modeling of signal transduction – a modular approach

PubMed Central

Koschorreck, Markus; Conzelmann, Holger; Ebert, Sybille; Ederer, Michael; Gilles, Ernst Dieter

2007-01-01

Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties. PMID:17854494

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Mathematical Modeling and Optimization of Gaseous Fuel Processing as a Basic Technology for Long-distance Energy Transportation: The Use of Methanol and Dimethyl Ether as Energy Carriers.

NASA Astrophysics Data System (ADS)

Tyurina, E. A.; Mednikov, A. S.

2017-11-01

The paper presents the results of studies on the perspective technologies of natural gas conversion to synthetic liquid fuel (SLF) at energy-technology installations for combined production of SLF and electricity based on their detailed mathematical models. The technologies of the long-distance transport of energy of natural gas from large fields to final consumers are compared in terms of their efficiency. This work was carried out at Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences and supported by Russian Science Foundation via grant No 16-19-10174

Diffusion-Based Design of Multi-Layered Ophthalmic Lenses for Controlled Drug Release

PubMed Central

Pimenta, Andreia F. R.; Serro, Ana Paula; Paradiso, Patrizia; Saramago, Benilde

2016-01-01

The study of ocular drug delivery systems has been one of the most covered topics in drug delivery research. One potential drug carrier solution is the use of materials that are already commercially available in ophthalmic lenses for the correction of refractive errors. In this study, we present a diffusion-based mathematical model in which the parameters can be adjusted based on experimental results obtained under controlled conditions. The model allows for the design of multi-layered therapeutic ophthalmic lenses for controlled drug delivery. We show that the proper combination of materials with adequate drug diffusion coefficients, thicknesses and interfacial transport characteristics allows for the control of the delivery of drugs from multi-layered ophthalmic lenses, such that drug bursts can be minimized, and the release time can be maximized. As far as we know, this combination of a mathematical modelling approach with experimental validation of non-constant activity source lamellar structures, made of layers of different materials, accounting for the interface resistance to the drug diffusion, is a novel approach to the design of drug loaded multi-layered contact lenses. PMID:27936138

Modeling and optimization of dough recipe for breadsticks

NASA Astrophysics Data System (ADS)

Krivosheev, A. Yu; Ponomareva, E. I.; Zhuravlev, A. A.; Lukina, S. I.; Alekhina, N. N.

2018-05-01

During the work, the authors studied the combined effect of non-traditional raw materials on indicators of quality breadsticks, mathematical methods of experiment planning were applied. The main factors chosen were the dosages of flaxseed flour and grape seed oil. The output parameters were the swelling factor of the products and their strength. Optimization of the formulation composition of the dough for bread sticks was carried out by experimental- statistical methods. As a result of the experiment, mathematical models were constructed in the form of regression equations, adequately describing the process of studies. The statistical processing of the experimental data was carried out by the criteria of Student, Cochran and Fisher (with a confidence probability of 0.95). A mathematical interpretation of the regression equations was given. Optimization of the formulation of the dough for bread sticks was carried out by the method of uncertain Lagrange multipliers. The rational values of the factors were determined: the dosage of flaxseed flour - 14.22% and grape seed oil - 7.8%, ensuring the production of products with the best combination of swelling ratio and strength. On the basis of the data obtained, a recipe and a method for the production of breadsticks "Idea" were proposed (TU (Russian Technical Specifications) 9117-443-02068106-2017).

Evaluating the efficacies of Maximum Tolerated Dose and metronomic chemotherapies: A mathematical approach

NASA Astrophysics Data System (ADS)

Guiraldello, Rafael T.; Martins, Marcelo L.; Mancera, Paulo F. A.

2016-08-01

We present a mathematical model based on partial differential equations that is applied to understand tumor development and its response to chemotherapy. Our primary aim is to evaluate comparatively the efficacies of two chemotherapeutic protocols, Maximum Tolerated Dose (MTD) and metronomic, as well as two methods of drug delivery. Concerning therapeutic outcomes, the metronomic protocol proves more effective in prolonging the patient's life than MTD. Moreover, a uniform drug delivery method combined with the metronomic protocol is the most efficient strategy to reduce tumor density.

General model and control of an n rotor helicopter

NASA Astrophysics Data System (ADS)

Sidea, A. G.; Yding Brogaard, R.; Andersen, N. A.; Ravn, O.

2014-12-01

The purpose of this study was to create a dynamic, nonlinear mathematical model of a multirotor that would be valid for different numbers of rotors. Furthermore, a set of Single Input Single Output (SISO) controllers were implemented for attitude control. Both model and controllers were tested experimentally on a quadcopter. Using the combined model and controllers, simple system simulation and control is possible, by replacing the physical values for the individual systems.

A Mathematical Model for Reactions During Top-Blowing in the AOD Process: Validation and Results

NASA Astrophysics Data System (ADS)

Visuri, Ville-Valtteri; Järvinen, Mika; Kärnä, Aki; Sulasalmi, Petri; Heikkinen, Eetu-Pekka; Kupari, Pentti; Fabritius, Timo

2017-06-01

In earlier work, a fundamental mathematical model was proposed for side-blowing operation in the argon oxygen decarburization (AOD) process. In the preceding part "Derivation of the Model," a new mathematical model was proposed for reactions during top-blowing in the AOD process. In this model it was assumed that reactions occur simultaneously at the surface of the cavity caused by the gas jet and at the surface of the metal droplets ejected from the metal bath. This paper presents validation and preliminary results with twelve industrial heats. In the studied heats, the last combined-blowing stage was altered so that oxygen was introduced from the top lance only. Four heats were conducted using an oxygen-nitrogen mixture (1:1), while eight heats were conducted with pure oxygen. Simultaneously, nitrogen or argon gas was blown via tuyères in order to provide mixing that is comparable to regular practice. The measured carbon content varied from 0.4 to 0.5 wt pct before the studied stage to 0.1 to 0.2 wt pct after the studied stage. The results suggest that the model is capable of predicting changes in metal bath composition and temperature with a reasonably high degree of accuracy. The calculations indicate that the top slag may supply oxygen for decarburization during top-blowing. Furthermore, it is postulated that the metal droplets generated by the shear stress of top-blowing create a large mass exchange area, which plays an important role in enabling the high decarburization rates observed during top-blowing in the AOD process. The overall rate of decarburization attributable to top-blowing in the last combined-blowing stage was found to be limited by the mass transfer of dissolved carbon.

Mathematical models for the early detection and treatment of colorectal cancer.

PubMed

Harper, P R; Jones, S K

2005-05-01

Colorectal cancer is a major cause of death for men and women in the Western world. When the cancer is detected through an awareness of the symptoms by a patient, typically it is at an advanced stage. It is possible to detect cancer at an early stage through screening and the marked differences in survival for early and late stages provide the incentive for the primary prevention or early detection of colorectal cancer. This paper considers mathematical models for colorectal cancer screening together with models for the treatment of patients. Illustrative results demonstrate that detailed attention to the processes involved in diseases, interventions and treatment enable us to combine data and expert knowledge from various sources. Thus a detailed operational model is a very useful tool in helping to make decisions about screening at national and local levels.

Mathematical modelling of thin layer hot air drying of apricot with combined heat and power dryer.

PubMed

Faal, Saeed; Tavakoli, Teymor; Ghobadian, Barat

2015-05-01

In this study thermal energy of an engine was used to dry apricot. For this purpose, experiments were conducted on thin layer drying apricot with combined heat and power dryer, in a laboratory dryer. The drying experiments were carried out for four levels of engine output power (25 %, 50 %, 75 % and full load), producing temperatures of 50, 60, 70, and 80 ° C in drying chamber respectively. The air velocity in drying chamber was about 0.5 ± 0.05 m/s. Different mathematical models were evaluated to predict the behavior of apricot drying in a combined heat and power dryer. Conventional statistical equations namely modeling efficiency (EF), Root mean square error (RMSE) and chi-square (χ2) were also used to determine the most suitable model. Assessments indicated that the Logarithmic model considering the values of EF = 0.998746, χ 2 = 0.000120 and RMSE = 0.004772, shows the best treatment of drying apricot with combined heat and power dryer among eleven models were used in this study. The average values of effective diffusivity ranged 1.6260 × 10(-9) to 4.3612 × 10(-9) m2/s for drying apricot at air temperatures between 50 and 80 °C and at the air flow rate of 0.5 ± 0.05 m/s; the values of Deff increased with the increase of drying temperature the effective diffusivities in the second falling rate period were about eight times greater than that in the first falling rate period.

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

NASA Technical Reports Server (NTRS)

Pennline, James A.

2009-01-01

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research.

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

PubMed Central

Saadati, Farzaneh; Ahmad Tarmizi, Rohani

2015-01-01

Because students’ ability to use statistics, which is mathematical in nature, is one of the concerns of educators, embedding within an e-learning system the pedagogical characteristics of learning is ‘value added’ because it facilitates the conventional method of learning mathematics. Many researchers emphasize the effectiveness of cognitive apprenticeship in learning and problem solving in the workplace. In a cognitive apprenticeship learning model, skills are learned within a community of practitioners through observation of modelling and then practice plus coaching. This study utilized an internet-based Cognitive Apprenticeship Model (i-CAM) in three phases and evaluated its effectiveness for improving statistics problem-solving performance among postgraduate students. The results showed that, when compared to the conventional mathematics learning model, the i-CAM could significantly promote students’ problem-solving performance at the end of each phase. In addition, the combination of the differences in students' test scores were considered to be statistically significant after controlling for the pre-test scores. The findings conveyed in this paper confirmed the considerable value of i-CAM in the improvement of statistics learning for non-specialized postgraduate students. PMID:26132553

CFD Modeling of Flow, Temperature, and Concentration Fields in a Pilot-Scale Rotary Hearth Furnace

NASA Astrophysics Data System (ADS)

Liu, Ying; Su, Fu-Yong; Wen, Zhi; Li, Zhi; Yong, Hai-Quan; Feng, Xiao-Hong

2014-01-01

A three-dimensional mathematical model for simulation of flow, temperature, and concentration fields in a pilot-scale rotary hearth furnace (RHF) has been developed using a commercial computational fluid dynamics software, FLUENT. The layer of composite pellets under the hearth is assumed to be a porous media layer with CO source and energy sink calculated by an independent mathematical model. User-defined functions are developed and linked to FLUENT to process the reduction process of the layer of composite pellets. The standard k-ɛ turbulence model in combination with standard wall functions is used for modeling of gas flow. Turbulence-chemistry interaction is taken into account through the eddy-dissipation model. The discrete ordinates model is used for modeling of radiative heat transfer. A comparison is made between the predictions of the present model and the data from a test of the pilot-scale RHF, and a reasonable agreement is found. Finally, flow field, temperature, and CO concentration fields in the furnace are investigated by the model.

Applying theoretical premises of binary toxicity mathematical modeling to combined impacts of chemical plus physical agents (A case study of moderate subchronic exposures to fluoride and static magnetic field).

PubMed

Katsnelson, B A; Tsepilov, N A; Panov, V G; Sutunkova, M P; Varaksin, A N; Gurvich, V B; Minigalieva, I A; Valamina, I E; Makeyev, O H; Meshtcheryakova, E Y

2016-09-01

Sodium fluoride solution was injected i.p. to rats at a dose equivalent to 0.1 LD50 three times a week up to 18 injections. Two thirds of these rats and of the sham-injected ones were exposed to the whole body impact of a 25 mT static magnetic field for 2 or 4 h a day, 5 times a week. For mathematical analysis of the effects they produced in combination, we used a response surface model. This analysis demonstrated that (like in combined toxicity) the combined adverse action of a chemical plus a physical agent was characterized by a diversity of types depending not only on particular effects these types were assessed for but on their level as well. From this point of view, the indices for which at least one statistically significant effect was observed could be classified as identifying (1) single-factor action; (2) additivity; (3) synergism; (4) antagonism (both subadditive unidirectional action and all variants of contradirectional action). Although the classes (2) and (3) taken together encompass a smaller part of the indices, the biological importance of some of them renders the combination of agents studied as posing a higher health risk than that associated with each them acting alone. Copyright © 2016 Elsevier Ltd. All rights reserved.

Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

NASA Astrophysics Data System (ADS)

Ekici, Can

2016-05-01

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

A mathematical proof and example that Bayes's Theorem is fundamental to actuarial estimates of sexual recidivism risk.

PubMed

Donaldson, Theodore; Wollert, Richard

2008-06-01

Expert witnesses in sexually violent predator (SVP) cases often rely on actuarial instruments to make risk determinations. Many questions surround their use, however. Bayes's Theorem holds much promise for addressing these questions. Some experts nonetheless claim that Bayesian analyses are inadmissible in SVP cases because they are not accepted by the relevant scientific community. This position is illogical because Bayes's Theorem is simply a probabilistic restatement of the way that frequency data are combined to arrive at whatever recidivism rates are paired with each test score in an actuarial table. This article presents a mathematical proof and example validating this assertion. The advantages and implications of a logic model that combines Bayes's Theorem and the null hypothesis are also discussed.

Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties.

PubMed

Hoffmann, Anna; Scherrer, Alexander; Küfer, Karl-Heinz

2015-01-01

Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model. Copyright © 2014 Elsevier Inc. All rights reserved.

Fluid structure interaction model for biological systems in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Aziz, Asim; Shoaib, Muhammad

2016-06-01

In the present paper a one-dimensional mathematical model of a cerebral aneurysm is considered. The model combines the interaction between the arterial wall structure, blood pressure and the cerebral spinal fluid (CSF) that is around the aneurysm. CSF is considered electrically conducting in the presence of a uniform magnetic field. Therefore, it may be possible to control pressure and its flow behavior by using an appropriate magnetic field. Hence, such studies have potential for the treatment of Cerebral aneurysms, diseases of heart and blood vessels. The modeled mathematical equations are solved algebraically and the displacement of the arterial wall is plotted to visualize the wall movement. It is evident from the graphs the inclusion of magnetic field reduce the movement of the arterial wall and in turn prevent the rupture of the cerebral aneurysm. The solution is also investigated using computational tools for various other parameters involve in the model.

Analysis of geologic terrain models for determination of optimum SAR sensor configuration and optimum information extraction for exploration of global non-renewable resources. Pilot study: Arkansas Remote Sensing Laboratory, part 1, part 2, and part 3

NASA Technical Reports Server (NTRS)

Kaupp, V. H.; Macdonald, H. C.; Waite, W. P.; Stiles, J. A.; Frost, F. S.; Shanmugam, K. S.; Smith, S. A.; Narayanan, V.; Holtzman, J. C. (Principal Investigator)

1982-01-01

Computer-generated radar simulations and mathematical geologic terrain models were used to establish the optimum radar sensor operating parameters for geologic research. An initial set of mathematical geologic terrain models was created for three basic landforms and families of simulated radar images were prepared from these models for numerous interacting sensor, platform, and terrain variables. The tradeoffs between the various sensor parameters and the quantity and quality of the extractable geologic data were investigated as well as the development of automated techniques of digital SAR image analysis. Initial work on a texture analysis of SEASAT SAR imagery is reported. Computer-generated radar simulations are shown for combinations of two geologic models and three SAR angles of incidence.

Phosphoric acid fuel cell power plant system performance model and computer program

NASA Technical Reports Server (NTRS)

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

1984-01-01

A FORTRAN computer program was developed for analyzing the performance of phosphoric acid fuel cell power plant systems. Energy mass and electrochemical analysis in the reformer, the shaft converters, the heat exchangers, and the fuel cell stack were combined to develop a mathematical model for the power plant for both atmospheric and pressurized conditions, and for several commercial fuels.

Geocaching: Finding Mathematics in a Global Treasure Hunt

ERIC Educational Resources Information Center

Bragg, Leicha A.

2014-01-01

If you love taking mathematics lessons outdoors, then you will love this article. Leicha Bragg describes geocaching, which combines technology, treasure hunting and mathematics, and results in purposeful, authentic and engaging mathematics.

Predictive models of control strategies involved in containing indoor airborne infections.

PubMed

Chen, S-C; Chang, C-F; Liao, C-M

2006-12-01

Recently developed control measure modeling approaches for containing airborne infections, including engineering controls with respiratory protection and public health interventions, are readily amenable to an integrated-scale analysis. Here we show that such models can be derived from an integrated-scale analysis generated from three different types of functional relationship: Wells-Riley mathematical model, competing-risks model, and Von Foerster equation, both of the key epidemiological determinants involved and of the functional connections between them. We examine mathematically the impact of engineering control measures such as enhanced air exchange and air filtration rates with personal masking combined with public health interventions such as vaccination, isolation, and contact tracing in containing the spread of indoor airborne infections including influenza, chickenpox, measles, and severe acute respiratory syndrome (SARS). If enhanced engineering controls could reduce the basic reproductive number (R0) below 1.60 for chickenpox and 3 for measles, our simulations show that in such a prepared response with public health interventions would have a high probability of containing the indoor airborne infections. Combinations of engineering control measures and public health interventions could moderately contain influenza strains with an R0 as high as 4. Our analysis indicates that effective isolation of symptomatic patients with low-efficacy contact tracing is sufficient to control a SARS outbreak. We suggest that a valuable added dimension to public health inventions could be provided by systematically quantifying transmissibility and proportion of asymptomatic infection of indoor airborne infection. Practical Implications We have developed a flexible mathematical model that can help determine the best intervention strategies for containing indoor airborne infections. The approach presented here is scalable and can be extended to include additional control efficacies. If a newly emergent airborne infection should appear, the model could be quickly calibrated to data and intervention options at the early stage of the outbreak. Data could be provided from the field to estimate value of R0, the serial interval between cases, the distributions of the latent, incubation, and infectious periods, case fatality rates, and secondary spread within important mixing groups. The combination of enhanced engineering control measures and assigned effective public health interventions would have a high probability for containing airborne infection.

Combination therapeutics of Nilotinib and radiation in acute lymphoblastic leukemia as an effective method against drug-resistance.

PubMed

Kaveh, Kamran; Takahashi, Yutaka; Farrar, Michael A; Storme, Guy; Guido, Marcucci; Piepenburg, Jamie; Penning, Jackson; Foo, Jasmine; Leder, Kevin Z; Hui, Susanta K

2017-07-01

Philadelphia chromosome-positive (Ph+) acute lymphoblastic leukemia (ALL) is characterized by a very poor prognosis and a high likelihood of acquired chemo-resistance. Although tyrosine kinase inhibitor (TKI) therapy has improved clinical outcome, most ALL patients relapse following treatment with TKI due to the development of resistance. We developed an in vitro model of Nilotinib-resistant Ph+ leukemia cells to investigate whether low dose radiation (LDR) in combination with TKI therapy overcome chemo-resistance. Additionally, we developed a mathematical model, parameterized by cell viability experiments under Nilotinib treatment and LDR, to explain the cellular response to combination therapy. The addition of LDR significantly reduced drug resistance both in vitro and in computational model. Decreased expression level of phosphorylated AKT suggests that the combination treatment plays an important role in overcoming resistance through the AKT pathway. Model-predicted cellular responses to the combined therapy provide good agreement with experimental results. Augmentation of LDR and Nilotinib therapy seems to be beneficial to control Ph+ leukemia resistance and the quantitative model can determine optimal dosing schedule to enhance the effectiveness of the combination therapy.

MAX meets ADAM: a dosimetric comparison between a voxel-based and a mathematical model for external exposure to photons

NASA Astrophysics Data System (ADS)

Kramer, R.; Vieira, J. W.; Khoury, H. J.; Lima, F. de Andrade

2004-03-01

The International Commission on Radiological Protection intends to revise the organ and tissue equivalent dose conversion coefficients published in various reports. For this purpose the mathematical human medical internal radiation dose (MIRD) phantoms, actually in use, have to be replaced by recently developed voxel-based phantoms. This study investigates the dosimetric consequences, especially with respect to the effective male dose, if not only a MIRD phantom is replaced by a voxel phantom, but also if the tissue compositions and the radiation transport codes are changed. This task will be resolved by systematically replacing in the mathematical ADAM/GSF exposure model, first the radiation transport code, then the tissue composition and finally the phantom anatomy, in order to arrive at the voxel-based MAX/EGS4 exposure model. The results show that the combined effect of these replacements can decrease the effective male dose by up to 25% for external exposures to photons for incident energies above 30 keV for different field geometries, mainly because of increased shielding by a heterogeneous skeleton and by the overlying adipose and muscle tissue, and also because of the positions internal organs have in a realistically designed human body compared to their positions in the mathematically constructed phantom.

Image-based quantification and mathematical modeling of spatial heterogeneity in ESC colonies.

PubMed

Herberg, Maria; Zerjatke, Thomas; de Back, Walter; Glauche, Ingmar; Roeder, Ingo

2015-06-01

Pluripotent embryonic stem cells (ESCs) have the potential to differentiate into cells of all three germ layers. This unique property has been extensively studied on the intracellular, transcriptional level. However, ESCs typically form clusters of cells with distinct size and shape, and establish spatial structures that are vital for the maintenance of pluripotency. Even though it is recognized that the cells' arrangement and local interactions play a role in fate decision processes, the relations between transcriptional and spatial patterns have not yet been studied. We present a systems biology approach which combines live-cell imaging, quantitative image analysis, and multiscale, mathematical modeling of ESC growth. In particular, we develop quantitative measures of the morphology and of the spatial clustering of ESCs with different expression levels and apply them to images of both in vitro and in silico cultures. Using the same measures, we are able to compare model scenarios with different assumptions on cell-cell adhesions and intercellular feedback mechanisms directly with experimental data. Applying our methodology to microscopy images of cultured ESCs, we demonstrate that the emerging colonies are highly variable regarding both morphological and spatial fluorescence patterns. Moreover, we can show that most ESC colonies contain only one cluster of cells with high self-renewing capacity. These cells are preferentially located in the interior of a colony structure. The integrated approach combining image analysis with mathematical modeling allows us to reveal potential transcription factor related cellular and intercellular mechanisms behind the emergence of observed patterns that cannot be derived from images directly. © 2015 International Society for Advancement of Cytometry.

Modeling combination therapy for breast cancer with BET and immune checkpoint inhibitors.

PubMed

Lai, Xiulan; Stiff, Andrew; Duggan, Megan; Wesolowski, Robert; Carson, William E; Friedman, Avner

2018-05-07

CTLA-4 is an immune checkpoint expressed on active anticancer T cells. When it combines with its ligand B7 on dendritic cells, it inhibits the activity of the T cells. The Bromo- and Extra-Terminal (BET) protein family includes proteins that regulate the expression of key oncogenes and antiapoptotic proteins. BET inhibitor (BETi) has been shown to reduce the expression of MYC by suppressing its transcription factors and to down-regulate the hypoxic transcriptome response to VEGF-A. This paper develops a mathematical model of the treatment of cancer by combination therapy of BETi and CTLA-4 inhibitor. The model shows that the two drugs are positively correlated in the sense that the tumor volume decreases as the dose of each of the drugs is increased. The model also considers the effect of the combined therapy on levels of myeloid-derived suppressor cells (MDSCs) and the overexpression of TNF-[Formula: see text], which may predict gastrointestinal side effects of the combination.

Utility and translatability of mathematical modeling, cell culture and small and large animal models in magnetic nanoparticle hyperthermia cancer treatment research

NASA Astrophysics Data System (ADS)

Hoopes, P. J.; Petryk, Alicia A.; Misra, Adwiteeya; Kastner, Elliot J.; Pearce, John A.; Ryan, Thomas P.

2015-03-01

For more than 50 years, hyperthermia-based cancer researchers have utilized mathematical models, cell culture studies and animal models to better understand, develop and validate potential new treatments. It has been, and remains, unclear how and to what degree these research techniques depend on, complement and, ultimately, translate accurately to a successful clinical treatment. In the past, when mathematical models have not proven accurate in a clinical treatment situation, the initiating quantitative scientists (engineers, mathematicians and physicists) have tended to believe the biomedical parameters provided to them were inaccurately determined or reported. In a similar manner, experienced biomedical scientists often tend to question the value of mathematical models and cell culture results since those data typically lack the level of biologic and medical variability and complexity that are essential to accurately study and predict complex diseases and subsequent treatments. Such quantitative and biomedical interdependence, variability, diversity and promise have never been greater than they are within magnetic nanoparticle hyperthermia cancer treatment. The use of hyperthermia to treat cancer is well studied and has utilized numerous delivery techniques, including microwaves, radio frequency, focused ultrasound, induction heating, infrared radiation, warmed perfusion liquids (combined with chemotherapy), and, recently, metallic nanoparticles (NP) activated by near infrared radiation (NIR) and alternating magnetic field (AMF) based platforms. The goal of this paper is to use proven concepts and current research to address the potential pathobiology, modeling and quantification of the effects of treatment as pertaining to the similarities and differences in energy delivered by known external delivery techniques and iron oxide nanoparticles.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Identification of Nascent Memory CD8 T Cells and Modeling of Their Ontogeny.

PubMed

Crauste, Fabien; Mafille, Julien; Boucinha, Lilia; Djebali, Sophia; Gandrillon, Olivier; Marvel, Jacqueline; Arpin, Christophe

2017-03-22

Primary immune responses generate short-term effectors and long-term protective memory cells. The delineation of the genealogy linking naive, effector, and memory cells has been complicated by the lack of phenotypes discriminating effector from memory differentiation stages. Using transcriptomics and phenotypic analyses, we identify Bcl2 and Mki67 as a marker combination that enables the tracking of nascent memory cells within the effector phase. We then use a formal approach based on mathematical models describing the dynamics of population size evolution to test potential progeny links and demonstrate that most cells follow a linear naive→early effector→late effector→memory pathway. Moreover, our mathematical model allows long-term prediction of memory cell numbers from a few early experimental measurements. Our work thus provides a phenotypic means to identify effector and memory cells, as well as a mathematical framework to investigate their genealogy and to predict the outcome of immunization regimens in terms of memory cell numbers generated. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Modelling of sedimentation and remobilization in in-line storage sewers for stormwater treatment.

PubMed

Frehmann, T; Flores, C; Luekewille, F; Mietzel, T; Spengler, B; Geiger, W F

2005-01-01

A special arrangement of combined sewer overflow tanks is the in-line storage sewer with downstream discharge (ISS-down). This layout has the advantage that, besides the sewer system, no other structures are required for stormwater treatment. The verification of the efficiency with respect to the processes of sedimentation and remobilization of sediment within the in-line storage sewer with downstream discharge is carried out in a combination of a field and a pilot plant study. The model study was carried out using a pilot plant model scaled 1:13. The following is intended to present some results of the pilot plant study and the mathematical empirical modelling of the sedimentation and remobilization process.

Removal of antibiotics in a parallel-plate thin-film-photocatalytic reactor: Process modeling and evolution of transformation by-products and toxicity.

PubMed

Özkal, Can Burak; Frontistis, Zacharias; Antonopoulou, Maria; Konstantinou, Ioannis; Mantzavinos, Dionissios; Meriç, Süreyya

2017-10-01

Photocatalytic degradation of sulfamethoxazole (SMX) antibiotic has been studied under recycling batch and homogeneous flow conditions in a thin-film coated immobilized system namely parallel-plate (PPL) reactor. Experimentally designed, statistically evaluated with a factorial design (FD) approach with intent to provide a mathematical model takes into account the parameters influencing process performance. Initial antibiotic concentration, UV energy level, irradiated surface area, water matrix (ultrapure and secondary treated wastewater) and time, were defined as model parameters. A full of 2 5 experimental design was consisted of 32 random experiments. PPL reactor test experiments were carried out in order to set boundary levels for hydraulic, volumetric and defined defined process parameters. TTIP based thin-film with polyethylene glycol+TiO 2 additives were fabricated according to pre-described methodology. Antibiotic degradation was monitored by High Performance Liquid Chromatography analysis while the degradation products were specified by LC-TOF-MS analysis. Acute toxicity of untreated and treated SMX solutions was tested by standard Daphnia magna method. Based on the obtained mathematical model, the response of the immobilized PC system is described with a polynomial equation. The statistically significant positive effects are initial SMX concentration, process time and the combined effect of both, while combined effect of water matrix and irradiated surface area displays an adverse effect on the rate of antibiotic degradation by photocatalytic oxidation. Process efficiency and the validity of the acquired mathematical model was also verified for levofloxacin and cefaclor antibiotics. Immobilized PC degradation in PPL reactor configuration was found capable of providing reduced effluent toxicity by simultaneous degradation of SMX parent compound and TBPs. Copyright © 2017. Published by Elsevier B.V.

The Transition to Formal Thinking in Mathematics

ERIC Educational Resources Information Center

Tall, David

2008-01-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

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.

Contribution of Auditory Learning Style to Students’ Mathematical Connection Ability

NASA Astrophysics Data System (ADS)

Karlimah; Risfiani, F.

2017-09-01

This paper presents the results of the research on the relation of mathematical concept with mathematics, other subjects, and with everyday life. This research reveals study result of the students who had auditory learning style and correlates it with their ability of mathematical connection. In this research, the researchers used a combination model or sequential exploratory design method, which is the use of qualitative and quantitative research methods in sequence. The result proves that giving learning facilities which are not suitable for the class whose students have the auditory learning style results in the barely sufficient math connection ability. The average mathematical connection ability of the auditory students was initially in the medium level of qualification. Then, the improvement in the form of the varied learning that suited the auditory learning style still showed the average ability of mathematical connection in medium level of qualification. Nevertheless, there was increase in the frequency of students in the medium level of qualification and decrease in the very low and low level of qualification. This suggests that the learning facilities, which are appropriate for the student’s auditory learning style, contribute well enough to the students’ mathematical connection ability. Therefore, the mathematics learning for students who have an auditory learning style should consist of particular activity that is understanding the concepts of mathematics and their relations.

Hybrid model based unified scheme for endoscopic Cerenkov and radio-luminescence tomography: Simulation demonstration

NASA Astrophysics Data System (ADS)

Wang, Lin; Cao, Xin; Ren, Qingyun; Chen, Xueli; He, Xiaowei

2018-05-01

Cerenkov luminescence imaging (CLI) is an imaging method that uses an optical imaging scheme to probe a radioactive tracer. Application of CLI with clinically approved radioactive tracers has opened an opportunity for translating optical imaging from preclinical to clinical applications. Such translation was further improved by developing an endoscopic CLI system. However, two-dimensional endoscopic imaging cannot identify accurate depth and obtain quantitative information. Here, we present an imaging scheme to retrieve the depth and quantitative information from endoscopic Cerenkov luminescence tomography, which can also be applied for endoscopic radio-luminescence tomography. In the scheme, we first constructed a physical model for image collection, and then a mathematical model for characterizing the luminescent light propagation from tracer to the endoscopic detector. The mathematical model is a hybrid light transport model combined with the 3rd order simplified spherical harmonics approximation, diffusion, and radiosity equations to warrant accuracy and speed. The mathematical model integrates finite element discretization, regularization, and primal-dual interior-point optimization to retrieve the depth and the quantitative information of the tracer. A heterogeneous-geometry-based numerical simulation was used to explore the feasibility of the unified scheme, which demonstrated that it can provide a satisfactory balance between imaging accuracy and computational burden.

An integrated theoretical-experimental approach to accelerate translational tissue engineering.

PubMed

Coy, Rachel H; Evans, Owen R; Phillips, James B; Shipley, Rebecca J

2018-01-01

Implantable devices utilizing bioengineered tissue are increasingly showing promise as viable clinical solutions. The design of bioengineered constructs is currently directed according to the results of experiments that are used to test a wide range of different combinations and spatial arrangements of biomaterials, cells and chemical factors. There is an outstanding need to accelerate the design process and reduce financial costs, whilst minimizing the required number of animal-based experiments. These aims could be achieved through the incorporation of mathematical modelling as a preliminary design tool. Here we focus on tissue-engineered constructs for peripheral nerve repair, which are designed to aid nerve and blood vessel growth and repair after peripheral nerve injury. We offer insight into the role that mathematical modelling can play within tissue engineering, and motivate the use of modelling as a tool capable of improving and accelerating the design of nerve repair constructs in particular. Specific case studies are presented in order to illustrate the potential of mathematical modelling to direct construct design. Copyright © 2016 The Authors Journal of Tissue Engineering and Regenerative Medicine Published by John Wiley & Sons Ltd. Copyright © 2016 The Authors Journal of Tissue Engineering and Regenerative Medicine Published by John Wiley & Sons Ltd.

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.

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

PubMed Central

Wu, Jianhong; Yan, Ping; Archibald, Chris

2007-01-01

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

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

PubMed

Wu, Jianhong; Yan, Ping; Archibald, Chris

2007-10-23

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

Mathematical Model of Cardiovascular and Metabolic Responses to Umbilical Cord Occlusions in Fetal Sheep.

PubMed

Wang, Qiming; Gold, Nathan; Frasch, Martin G; Huang, Huaxiong; Thiriet, Marc; Wang, Xiaogang

2015-12-01

Fetal acidemia during labor is associated with an increased risk of brain injury and lasting neurological deficits. This is in part due to the repetitive occlusions of the umbilical cord (UCO) induced by uterine contractions. Whereas fetal heart rate (FHR) monitoring is widely used clinically, it fails to detect fetal acidemia. Hence, new approaches are needed for early detection of fetal acidemia during labor. We built a mathematical model of the UCO effects on FHR, mean arterial blood pressure (MABP), oxygenation and metabolism. Mimicking fetal experiments, our in silico model reproduces salient features of experimentally observed fetal cardiovascular and metabolic behavior including FHR overshoot, gradual MABP decrease and mixed metabolic and respiratory acidemia during UCO. Combined with statistical analysis, our model provides valuable insight into the labor-like fetal distress and guidance for refining FHR monitoring algorithms to improve detection of fetal acidemia and cardiovascular decompensation.

Propriomuscular coding of kinaesthetic sensation. Experimental approach and mathematical modelling.

PubMed

Gilhodes, J C; Coiton, Y; Roll, J P; Ans, B

1993-01-01

The role of propriomuscular information in kinaesthetic sensation was studied. Experiments were carried out on human subjects in whom kinaesthetic illusions were induced by applying tendon vibration with a variable frequency. Six patterns of frequency modulation were used, four of which had an arbitrary form and the other two mimicked natural Ia discharges. The results show that the shape of the illusory movements recorded depended on the type of vibratory pattern used. A mathematical model for the propriomuscular information decoding process is proposed. It takes into account both the agonist and antagonist muscle spindle populations as sources of kinaesthetic information and is based on the assumption that position and velocity information are additively combined. The experimental data show a good fit with the theoretical data obtained by means of model simulation, thus validating our initial hypothesis. Various aspects of the experimental results and the hypotheses involved in the model are discussed.

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.

A mathematical model to describe the nonlinear elastic properties of the gastrocnemius tendon of chickens.

PubMed

Foutz, T L

1991-03-01

A phenomenological model was developed to describe the nonlinear elastic behavior of the avian gastrocnemius tendon. Quasistatic uniaxial tensile tests were used to apply a deformation and resulting load on the tendon at a deformation rate of 5 mm/min. Plots of deformation versus load indicated a nonlinear loading response. By calculating engineering stress and engineering strain, the experimental data were normalized for tendon shape. The elastic response was determined from stress-strain curves and was found to vary with engineering strain. The response to the applied engineering strain could best be described by a mathematical model that combined a linear function and a nonlinear function. Three parameters in the model were developed to represent the nonlinear elastic behavior of the tendon, thereby allowing analysis of elasticity without prior knowledge of engineering strain. This procedure reduced the amount of data needed for the statistical analysis of nonlinear elasticity.

Allocation of surgical procedures to operating rooms.

PubMed

Ozkarahan, I

1995-08-01

Reduction of health care costs is of paramount importance in our time. This paper is a part of the research which proposes an expert hospital decision support system for resource scheduling. The proposed system combines mathematical programming, knowledge base, and database technologies, and what is more, its friendly interface is suitable for any novice user. Operating rooms in hospitals represent big investments and must be utilized efficiently. In this paper, first a mathematical model similar to job shop scheduling models is developed. The model loads surgical cases to operating rooms by maximizing room utilization and minimizing overtime in a multiple operating room setting. Then a prototype expert system which replaces the expertise of the operations research analyst for the model, drives the modelbase, database, and manages the user dialog is developed. Finally, an overview of the sequencing procedures for operations within an operating room is also presented.

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

Microgravity Investigation of Capillary Driven Imbibition

NASA Astrophysics Data System (ADS)

Dushin, V. R.; Nikitin, V. F.; Smirnov, N. N.; Skryleva, E. I.; Tyurenkova, V. V.

2018-05-01

The goal of the present paper is to investigate the capillary driven filtration in porous media under microgravity conditions. New mathematical model that allows taking into account the blurring of the front due to the instability of the displacement that is developing at the front is proposed. The constants in the mathematical model were selected on the basis of the experimental data on imbibition into unsaturated porous media under microgravity conditions. The flow under the action of a combination of capillary forces and a constant pressure drop or a constant flux is considered. The effect of capillary forces and the type of wettability of the medium on the displacement process is studied. A criterion in which case the capillary effects are insignificant and can be neglected is established.

Advances in electrophoretic separations

NASA Technical Reports Server (NTRS)

Snyder, R. S.; Rhodes, P. H.

1984-01-01

Free fluid electrophoresis is described using laboratory and space experiments combined with extensive mathematical modeling. Buoyancy driven convective flows due to thermal and concentration gradients are absent in the reduced gravity environment of space. The elimination of convection in weightlessness offers possible improvements in electrophoresis and other separation methods which occur in fluid media. The mathematical modeling suggests new ways of doing electrophoresis in space and explains various phenomena observed during past experiments. The extent to which ground based separation techniques are limited by gravity induced convection is investigated and space experiments are designed to evaluate specific characteristics of the fluid/particle environment. A series of experiments are proposed that require weightlessness and apparatus is developed that can be used to carry out these experiments in the near future.

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-01-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

Cognitive Rationality and Its Logic-Mathematical Language

ERIC Educational Resources Information Center

Masalova, Svetlana

2012-01-01

The article deals with the cognitive (flexible) rationality, combining rational and irrational moments of the scientific search of the cognizing subject. Linguo-cognitive model of the concept as the flexible regulative rationality reveals the activity of the cognitive processes and the mentality of the epistemological-ontic subject, its leading…

Pendulum Rides, Rotations and the Coriolis Effect

ERIC Educational Resources Information Center

Pendrill, Ann-Marie; Modig, Conny

2018-01-01

An amusement park is full of examples that can be made into challenging problems for students, combining mathematical modelling with video analysis, as well as measurements in the rides. Traditional amusement ride related textbook problems include free-fall, circular motion, pendula and energy conservation in roller coasters, where the moving…

Carnegie Learning Curricula and Cognitive Tutor[R] Software. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

The combination of "Carnegie Learning Curricula and Cognitive Tutor[R] Software" merges algebra textbooks with interactive software developed around an artificial intelligence model that identifies strengths and weaknesses in an individual student's mastery of mathematical concepts. The software customizes prompts to focus on areas in…

Cognitive Tutor[R] Algebra I. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then customizes prompts…

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

PubMed

Garnier, Alain; Gaillet, Bruno

2015-12-01

Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.

Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model

PubMed Central

Faggiano, Elena; Boffano, Carlo; Acerbi, Francesco; Ciarletta, Pasquale

2015-01-01

Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner. In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data. The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient’s prognosis. PMID:26186462

Tuberculosis Control in South African Gold Mines: Mathematical Modeling of a Trial of Community-Wide Isoniazid Preventive Therapy

PubMed Central

Vynnycky, Emilia; Sumner, Tom; Fielding, Katherine L.; Lewis, James J.; Cox, Andrew P.; Hayes, Richard J.; Corbett, Elizabeth L.; Churchyard, Gavin J.; Grant, Alison D.; White, Richard G.

2015-01-01

A recent major cluster randomized trial of screening, active disease treatment, and mass isoniazid preventive therapy for 9 months during 2006–2011 among South African gold miners showed reduced individual-level tuberculosis incidence but no detectable population-level impact. We fitted a dynamic mathematical model to trial data and explored 1) factors contributing to the lack of population-level impact, 2) the best-achievable impact if all implementation characteristics were increased to the highest level achieved during the trial (“optimized intervention”), and 3) how tuberculosis might be better controlled with additional interventions (improving diagnostics, reducing treatment delay, providing isoniazid preventive therapy continuously to human immunodeficiency virus–positive people, or scaling up antiretroviral treatment coverage) individually and in combination. We found the following: 1) The model suggests that a small proportion of latent infections among human immunodeficiency virus–positive people were cured, which could have been a key factor explaining the lack of detectable population-level impact. 2) The optimized implementation increased impact by only 10%. 3) Implementing additional interventions individually and in combination led to up to 30% and 75% reductions, respectively, in tuberculosis incidence after 10 years. Tuberculosis control requires a combination prevention approach, including health systems strengthening to minimize treatment delay, improving diagnostics, increased antiretroviral treatment coverage, and effective preventive treatment regimens. PMID:25792607

Preface.

PubMed

Friedman, Avner; Lachowicz, Mirosław; Ledzewicz, Urszula; Piotrowska, Monika Joanna; Szymanska, Zuzanna

2017-02-01

This volume was inspired by the topics presented at the international conference "Micro and Macro Systems in Life Sciences" which was held on Jun 8-12, 2015 in Będlewo, Poland. System biology is an approach which tries to understand how micro systems, at the molecular and cellular levels, affect macro systems such as organs, tissue and populations. Thus it is not surprising that a major theme of this volume evolves around cancer and its treatment. Articles on this topic include models for tumor induced angiogenesis, without and with delays, metastatic niche of the bone marrow, drug resistance and metronomic chemotherapy, and virotherapy of glioma. Methods range from dynamical systems to optimal control. Another well represented topic of this volume is mathematical modeling in epidemiology. Mathematical approaches to modeling and control of more specific diseases like malaria, Ebola or human papillomavirus are discussed as well as a more general approaches to the SEIR, and even more general class of models in epidemiology, by using the tools of optimal control and optimization. The volume also brings up challenges in mathematical modeling of other diseases such as tuberculosis. Partial differential equations combined with numerical approaches are becoming important tools in modeling not only tumor growth and treatment, but also other diseases, such as fibrosis of the liver, and atherosclerosis and its associated blood flow dynamics, and our volume presents a state of the art approach on these topics. Understanding mathematics behind the cell motion, appearance of the special patterns in various cell populations, and age structured mutations are among topics addressed inour volume. A spatio-temporal models of synthetic genetic oscillators brings the analysis to the gene level which is the focus of much of current biological research. Mathematics can help biologists to explain the collective behavior of bacterial, a topic that is also presented here. Finally some more across the discipline topics are being addresses, which can appear as a challenge in studying problems in systems biology on all, macro, meso and micro levels. They include numerical approaches to stochastic wave equation arising in modeling Brownian motion, discrete velocity models, many particle approximations as well as very important aspect on the connection between discrete measurement and the construction of the models for various phenomena, particularly the one involving delays. With the variety of biological topics and their mathematical approaches we very much hope that the reader of the Mathematical Biosciences and Engineering will find this volume interesting and inspirational for their own research.

Uncharted waters: Bivalves of midway atoll and integrating mathematics into biology education

NASA Astrophysics Data System (ADS)

McCully, Kristin M.

To protect and conserve the Earth's biodiversity and ecosystem services, it is important not only to understand and conserve species and ecosystems, but also to instill an understanding and appreciation for biodiversity and ecosystem services in the next generations of both scientists and citizens. Thus, this dissertation combines research into the ecology and identity of large bivalves at Midway Atoll in the Northwestern Hawaiian Islands (NWHI) with research on pedagogical strategies for integrating mathematics into undergraduate biology education. The NWHI is one of the few remaining large, mainly intact, predator-dominated coral reef ecosystems and one of the world's largest marine protected areas. Previous bivalve studies focused on the black-lipped pearl oyster, Pinctada margaritifera, which was heavily harvested in the late 1920s, has not recovered, and is now a candidate species for restoration. First, I combined remote sensing, geographic information systems, SCUBA, and mathematical modeling to quantify the abundance, spatial distributions, and filtration capacity of large epifaunal bivalves at Midway Atoll. These bivalves are most abundant on the forereef outside the atoll, but densities are much lower than reported on other reefs, and Midway's bivalves are unlikely to affect plankton abundance and productivity inside the lagoon. Second, I used molecular techniques and phylogenetic reconstructions to identify pearl oysters (Pinctada) from Midway Atoll as P. maculata , a species not previously reported in Hawaii. As a small morphologically cryptic species, P. maculata may be a native species that has not been collected previously, a native species that has been identified incorrectly as the morphologically similar P. radiata, or it may be a recent introduction or natural range extension from the western Pacific. Finally, I review science education literature integrating mathematics into undergraduate biology curricula, and then present and evaluate a computer inquiry module using learner-centered teaching strategies to introduce structured population (matrix) models in an upper-division ecology course. Using pre- and post-test surveys and student interviews, I concluded that students accomplished the module's learning goals: to use matrix models to assess and protect populations and to better appreciate the importance and uses of mathematics in ecology and conservation.

Enhancing student engagement through the affordances of mobile technology: a 21st century learning perspective on Realistic Mathematics Education

NASA Astrophysics Data System (ADS)

Bray, Aibhín; Tangney, Brendan

2016-03-01

Several recent curriculum reforms aim to address the shortfalls traditionally associated with mathematics education through increased emphasis on higher-order-thinking and collaborative skills. Some stakeholders, such as the US National Council of Teachers of Mathematics and the UK Joint Mathematical Council, advocate harnessing the affordances of digital technology in conjunction with social constructivist pedagogies, contextual scenarios, and/or approaches aligned with Realistic Mathematics Education (RME). However, it can be difficult to create technology-mediated, collaborative and contextual activities within a conventional classroom setting. This paper explores how a combination of a transformative, mobile technology-mediated approach, RME, and a particular model of 21st century learning facilitates the development of mathematics learning activities with the potential to increase student engagement and confidence. An explanatory case study with multiple embedded units and a pre-experimental design was conducted with a total of 54 students in 3 schools over 25 hours of class time. Results from student interviews, along with pre-test/post-test analysis of questionnaires, suggest that the approach has the potential to increase student engagement with, and confidence in, mathematics. This paper expands on these results, proposing connections between aspects of the activity design and their impact on student attitudes and behaviours.

Hobbes on natural philosophy as "True Physics" and mixed mathematics.

PubMed

Adams, Marcus P

2016-04-01

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mathematical modeling and fluorescence imaging to study the Ca2+ turnover in skinned muscle fibers.

PubMed Central

Uttenweiler, D; Weber, C; Fink, R H

1998-01-01

A mathematical model was developed for the simulation of the spatial and temporal time course of Ca2+ ion movement in caffeine-induced calcium transients of chemically skinned muscle fiber preparations. Our model assumes cylindrical symmetry and quantifies the radial profile of Ca2+ ion concentration by solving the diffusion equations for Ca2+ ions and various mobile buffers, and the rate equations for Ca2+ buffering (mobile and immobile buffers) and for the release and reuptake of Ca2+ ions by the sarcoplasmic reticulum (SR), with a finite-difference algorithm. The results of the model are compared with caffeine-induced spatial Ca2+ transients obtained from saponin skinned murine fast-twitch fibers by fluorescence photometry and imaging measurements using the ratiometric dye Fura-2. The combination of mathematical modeling and digital image analysis provides a tool for the quantitative description of the total Ca2+ turnover and the different contributions of all interacting processes to the overall Ca2+ transient in skinned muscle fibers. It should thereby strongly improve the usage of skinned fibers as quantitative assay systems for many parameters of the SR and the contractile apparatus helping also to bridge the gap to the intact muscle fiber. PMID:9545029

Mathematical model to predict drivers' reaction speeds.

PubMed

Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L

2012-02-01

Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions.

In Vivo Bioluminescence Tomography for Monitoring Breast Tumor Growth and Metastatic Spreading: Comparative Study and Mathematical Modeling

PubMed Central

Mollard, Séverine; Fanciullino, Raphaelle; Giacometti, Sarah; Serdjebi, Cindy; Benzekry, Sebastien; Ciccolini, Joseph

2016-01-01

This study aimed at evaluating the reliability and precision of Diffuse Luminescent Imaging Tomography (DLIT) for monitoring primary tumor and metastatic spreading in breast cancer mice, and to develop a biomathematical model to describe the collected data. Using orthotopic mammary fat pad model of breast cancer (MDAMB231-Luc) in mice, we monitored tumor and metastatic spreading by three-dimensional (3D) bioluminescence and cross-validated it with standard bioluminescence imaging, caliper measurement and necropsy examination. DLIT imaging proved to be reproducible and reliable throughout time. It was possible to discriminate secondary lesions from the main breast cancer, without removing the primary tumor. Preferential metastatic sites were lungs, peritoneum and lymph nodes. Necropsy examinations confirmed DLIT measurements. Marked differences in growth profiles were observed, with an overestimation of the exponential phase when using a caliper as compared with bioluminescence. Our mathematical model taking into account the balance between living and necrotic cells proved to be able to reproduce the experimental data obtained with a caliper or DLIT imaging, because it could discriminate proliferative living cells from a more composite mass consisting of tumor cells, necrotic cell, or inflammatory tissues. DLIT imaging combined with mathematical modeling could be a powerful and informative tool in experimental oncology. PMID:27812027

Mathematical models and qualities of shredded Thai-style instant rice under a combined gas-fired infrared and air convection drying

NASA Astrophysics Data System (ADS)

Nachaisin, Mali; Teeta, Suminya; Deejing, Konlayut; Pharanat, Wanida

2017-09-01

Instant food is a product produced for convenience for consumer. Qualities are an important attribute of food materials reflecting consumer acceptance. The most problem of instant rice is casehardening during drying process resulted in the longer rehydration time. The objective of this research was to study the qualities of shredded Thai-style instant rice under a combined gas-fired infrared and air convection drying. Additionally, the mathematical models for gas-fired infrared assisted thin-layer drying of shredded Thai-style rice for traditional was investigated. The thin-layer drying of shredded Thai-style rice was carried out under gas-fired infrared intensities of 1000W/m2, air temperatures of 70°C and air velocities of 1 m/s. The drying occurred in the falling rate of drying period. The Page model was found to satisfactorily describe the drying behavior of shredded Thai-style rice, providing the highest R2 (0.997) and the lowest MBE and RMSE (0.01 and 0.18) respectively. A 9 point hedonic test showed in softness and color, but odor and overall acceptance were very similar.

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets — Part A: Mathematical Model and the Influence of Dimple Radius

NASA Astrophysics Data System (ADS)

Ming, Tingzhen; Cai, Cunjin; Yang, Wei; Shen, Wenqing; Gan, Ting

2018-06-01

With increasing heat fluxes caused by electronic components, dimples have attracted wide attention by researchers and have been applied to microchannel heat sink in modern advanced cooling technologies. In this work, the combination of dimples, impinging jets and microchannel heat sink was proposed to improve the heat transfer performance on a cooling surface with a constant heat flux 500 W/cm2. A mathematical model was advanced for numerically analyzing the fluid flow and heat transfer characteristics of a microchannel heat sink with impinging jets and dimples (MHSIJD), and the velocity distribution, pressure drop, and thermal performance of MHSIJD were analyzed by varying the radii of dimples. The results showed that the combination of dimples and MHSIJ can achieve excellent heat transfer performance; for the MHSIJD model in this work, the maximum and average temperatures can be as low as 320 K and 305 K, respectively when mass flow rate is 30 g/s; when dimple radius is larger than 0.195 mm, both the heat transfer coefficient and the overall performance h/ΔP of MHSIJD are higher than those of MHSIJ.

Historical mathematics in the French eighteenth century.

PubMed

Richards, Joan L

2006-12-01

At least since the seventeenth century, the strange combination of epistemological certainty and ontological power that characterizes mathematics has made it a major focus of philosophical, social, and cultural negotiation. In the eighteenth century, all of these factors were at play as mathematical thinkers struggled to assimilate and extend the analysis they had inherited from the seventeenth century. A combination of educational convictions and historical assumptions supported a humanistic mathematics essentially defined by its flexibility and breadth. This mathematics was an expression of l'esprit humain, which was unfolding in a progressive historical narrative. The French Revolution dramatically altered the historical and educational landscapes that had supported this eighteenth-century approach, and within thirty years Augustin Louis Cauchy had radically reconceptualized and restructured mathematics to be rigorous rather than narrative.

Temporal Subtraction of Digital Breast Tomosynthesis Images for Improved Mass Detection

DTIC Science & Technology

2008-10-01

K. Fishman and B. M. W. Tsui, "Development of a computer-generated model for the coronary arterial tree based on multislice CT and morphometric data...mathematical models based on geometric primitives8-22. Bakic et al created synthetic x-ray mammograms using a 3D simulated breast tissue model consisting of...utilized a combination of voxel matrices and geometric primitives to create a breast phantom that includes the breast surface, the duct system, and

Applying multibeam sonar and mathematical modeling for mapping seabed substrate and biota of offshore shallows

NASA Astrophysics Data System (ADS)

Herkül, Kristjan; Peterson, Anneliis; Paekivi, Sander

2017-06-01

Both basic science and marine spatial planning are in a need of high resolution spatially continuous data on seabed habitats and biota. As conventional point-wise sampling is unable to cover large spatial extents in high detail, it must be supplemented with remote sensing and modeling in order to fulfill the scientific and management needs. The combined use of in situ sampling, sonar scanning, and mathematical modeling is becoming the main method for mapping both abiotic and biotic seabed features. Further development and testing of the methods in varying locations and environmental settings is essential for moving towards unified and generally accepted methodology. To fill the relevant research gap in the Baltic Sea, we used multibeam sonar and mathematical modeling methods - generalized additive models (GAM) and random forest (RF) - together with underwater video to map seabed substrate and epibenthos of offshore shallows. In addition to testing the general applicability of the proposed complex of techniques, the predictive power of different sonar-based variables and modeling algorithms were tested. Mean depth, followed by mean backscatter, were the most influential variables in most of the models. Generally, mean values of sonar-based variables had higher predictive power than their standard deviations. The predictive accuracy of RF was higher than that of GAM. To conclude, we found the method to be feasible and with predictive accuracy similar to previous studies of sonar-based mapping.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2014-01-01

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

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

DTIC Science & Technology

2013-03-01

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

Leveraging Hypoxia-Activated Prodrugs to Prevent Drug Resistance in Solid Tumors.

PubMed

Lindsay, Danika; Garvey, Colleen M; Mumenthaler, Shannon M; Foo, Jasmine

2016-08-01

Experimental studies have shown that one key factor in driving the emergence of drug resistance in solid tumors is tumor hypoxia, which leads to the formation of localized environmental niches where drug-resistant cell populations can evolve and survive. Hypoxia-activated prodrugs (HAPs) are compounds designed to penetrate to hypoxic regions of a tumor and release cytotoxic or cytostatic agents; several of these HAPs are currently in clinical trial. However, preliminary results have not shown a survival benefit in several of these trials. We hypothesize that the efficacy of treatments involving these prodrugs depends heavily on identifying the correct treatment schedule, and that mathematical modeling can be used to help design potential therapeutic strategies combining HAPs with standard therapies to achieve long-term tumor control or eradication. We develop this framework in the specific context of EGFR-driven non-small cell lung cancer, which is commonly treated with the tyrosine kinase inhibitor erlotinib. We develop a stochastic mathematical model, parametrized using clinical and experimental data, to explore a spectrum of treatment regimens combining a HAP, evofosfamide, with erlotinib. We design combination toxicity constraint models and optimize treatment strategies over the space of tolerated schedules to identify specific combination schedules that lead to optimal tumor control. We find that (i) combining these therapies delays resistance longer than any monotherapy schedule with either evofosfamide or erlotinib alone, (ii) sequentially alternating single doses of each drug leads to minimal tumor burden and maximal reduction in probability of developing resistance, and (iii) strategies minimizing the length of time after an evofosfamide dose and before erlotinib confer further benefits in reduction of tumor burden. These results provide insights into how hypoxia-activated prodrugs may be used to enhance therapeutic effectiveness in the clinic.

Development of the CCP-200 mathematical model for Syzran CHPP using the Thermolib software package

NASA Astrophysics Data System (ADS)

Usov, S. V.; Kudinov, A. A.

2016-04-01

Simplified cycle diagram of the CCP-200 power generating unit of Syzran CHPP containing two gas turbines PG6111FA with generators, two steam recovery boilers KUP-110/15-8.0/0.7-540/200, and one steam turbine Siemens SST-600 (one-cylinder with two variable heat extraction units of 60/75 MW in heatextraction and condensing modes, accordingly) with S-GEN5-100 generators was presented. Results of experimental guarantee tests of the CCP-200 steam-gas unit are given. Brief description of the Thermolib application for the MatLab Simulink software package is given. Basic equations used in Thermolib for modeling thermo-technical processes are given. Mathematical models of gas-turbine plant, heat-recovery steam generator, steam turbine and integrated plant for power generating unit CCP-200 of Syzran CHPP were developed with the help of MatLab Simulink and Thermolib. The simulation technique at different ambient temperature values was used in order to get characteristics of the developed mathematical model. Graphic comparison of some characteristics of the CCP-200 simulation model (gas temperature behind gas turbine, gas turbine and combined cycle plant capacity, high and low pressure steam consumption and feed water consumption for high and low pressure economizers) with actual characteristics of the steam-gas unit received at experimental (field) guarantee tests at different ambient temperature are shown. It is shown that the chosen degrees of complexity, characteristics of the CCP-200 simulation model, developed by Thermolib, adequately correspond to the actual characteristics of the steam-gas unit received at experimental (field) guarantee tests; this allows considering the developed mathematical model as adequate and acceptable it for further work.

Landsat test of diffuse reflectance models for aquatic suspended solids measurement

NASA Technical Reports Server (NTRS)

Munday, J. C., Jr.; Alfoldi, T. T.

1979-01-01

Landsat radiance data were used to test mathematical models relating diffuse reflectance to aquatic suspended solids concentration. Digital CCT data for Landsat passes over the Bay of Fundy, Nova Scotia were analyzed on a General Electric Co. Image 100 multispectral analysis system. Three data sets were studied separately and together in all combinations with and without solar angle correction. Statistical analysis and chromaticity analysis show that a nonlinear relationship between Landsat radiance and suspended solids concentration is better at curve-fitting than a linear relationship. In particular, the quasi-single-scattering diffuse reflectance model developed by Gordon and coworkers is corroborated. The Gordon model applied to 33 points of MSS 5 data combined from three dates produced r = 0.98.

Unlocking Mathematics Teaching. Second Edition

ERIC Educational Resources Information Center

Koshy, Valsa, Ed.; Murray, Jean, Ed.

2011-01-01

Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

Exploring Collective Mathematical Creativity in Elementary School

ERIC Educational Resources Information Center

Levenson, Esther

2011-01-01

This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked,…

Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication

ERIC Educational Resources Information Center

Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.

2014-01-01

This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities resulted…

Projection model for flame chemiluminescence tomography based on lens imaging

NASA Astrophysics Data System (ADS)

Wan, Minggang; Zhuang, Jihui

2018-04-01

For flame chemiluminescence tomography (FCT) based on lens imaging, the projection model is essential because it formulates the mathematical relation between the flame projections captured by cameras and the chemiluminescence field, and, through this relation, the field is reconstructed. This work proposed the blurry-spot (BS) model, which takes more universal assumptions and has higher accuracy than the widely applied line-of-sight model. By combining the geometrical camera model and the thin-lens equation, the BS model takes into account perspective effect of the camera lens; by combining ray-tracing technique and Monte Carlo simulation, it also considers inhomogeneous distribution of captured radiance on the image plane. Performance of these two models in FCT was numerically compared, and results showed that using the BS model could lead to better reconstruction quality in wider application ranges.

Model verification of mixed dynamic systems. [POGO problem in liquid propellant rockets

NASA Technical Reports Server (NTRS)

Chrostowski, J. D.; Evensen, D. A.; Hasselman, T. K.

1978-01-01

A parameter-estimation method is described for verifying the mathematical model of mixed (combined interactive components from various engineering fields) dynamic systems against pertinent experimental data. The model verification problem is divided into two separate parts: defining a proper model and evaluating the parameters of that model. The main idea is to use differences between measured and predicted behavior (response) to adjust automatically the key parameters of a model so as to minimize response differences. To achieve the goal of modeling flexibility, the method combines the convenience of automated matrix generation with the generality of direct matrix input. The equations of motion are treated in first-order form, allowing for nonsymmetric matrices, modeling of general networks, and complex-mode analysis. The effectiveness of the method is demonstrated for an example problem involving a complex hydraulic-mechanical system.

Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Clements, Douglas H., Ed.; DiBiase, Ann-Marie, Ed.; Sarama, Julie, Ed.

2004-01-01

This book brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's…

[Multi-mathematical modelings for compatibility optimization of Jiangzhi granules].

PubMed

Yang, Ming; Zhang, Li; Ge, Yingli; Lu, Yanliu; Ji, Guang

2011-12-01

To investigate into the method of "multi activity index evaluation and combination optimized of mult-component" for Chinese herbal formulas. According to the scheme of uniform experimental design, efficacy experiment, multi index evaluation, least absolute shrinkage, selection operator (LASSO) modeling, evolutionary optimization algorithm, validation experiment, we optimized the combination of Jiangzhi granules based on the activity indexes of blood serum ALT, ALT, AST, TG, TC, HDL, LDL and TG level of liver tissues, ratio of liver tissue to body. Analytic hierarchy process (AHP) combining with criteria importance through intercriteria correlation (CRITIC) for multi activity index evaluation was more reasonable and objective, it reflected the information of activity index's order and objective sample data. LASSO algorithm modeling could accurately reflect the relationship between different combination of Jiangzhi granule and the activity comprehensive indexes. The optimized combination of Jiangzhi granule showed better values of the activity comprehensive indexed than the original formula after the validation experiment. AHP combining with CRITIC can be used for multi activity index evaluation and LASSO algorithm, it is suitable for combination optimized of Chinese herbal formulas.

Fluid Flow and Solidification Under Combined Action of Magnetic Fields and Microgravity

NASA Technical Reports Server (NTRS)

Li, B. Q.; Shu, Y.; Li, K.; deGroh, H. C.

2002-01-01

Mathematical models, both 2-D and 3-D, are developed to represent g-jitter induced fluid flows and their effects on solidification under combined action of magnetic fields and microgravity. The numerical model development is based on the finite element solution of governing equations describing the transient g-jitter driven fluid flows, heat transfer and solutal transport during crystal growth with and without an applied magnetic field in space vehicles. To validate the model predictions, a ground-based g-jitter simulator is developed using the oscillating wall temperatures where timely oscillating fluid flows are measured using a laser PIV system. The measurements are compared well with numerical results obtained from the numerical models. Results show that a combined action derived from magnetic damping and microgravity can be an effective means to control the melt flow and solutal transport in space single crystal growth systems.

Persisting mathematics and science high school teachers: A Q-methodology study

NASA Astrophysics Data System (ADS)

Robbins-Lavicka, Michelle M.

There is a lack of qualified mathematics and science teachers at all levels of education in Arkansas. Lasting teaching initiative programs are needed to address retention so qualified teachers remain in the classroom. The dearth of studies regarding why mathematics and science teachers persist in the classroom beyond the traditional 5-year attrition period led this Q-methodological study to evaluate the subjective perceptions of persistent mathematics and science teachers to determine what makes them stay. This study sought to understand what factors persisting mathematics and science teachers used to explain their persistence in the classroom beyond 5 years and what educational factors contributed to persisting mathematics and science teachers. Q-methodology combines qualitative and quantitative techniques and provided a systematic means to investigate personal beliefs by collecting a concourse, developing a Q-sample and a person-sample, conducting a Q-sorting process, and analyzing the data. The results indicated that to encourage longevity within mathematics and science classrooms (a) teachers should remain cognizant of their ability to influence student attitudes toward teaching; (b) administrators should provide support for teachers and emphasize the role and importance of professional development; and (c) policy makers should focus their efforts and resources on developing recruitment plans, including mentorship programs, while providing and improving financial compensation. Significantly, the findings indicate that providing mentorship and role models at every level of mathematics and science education will likely encourage qualified teachers to remain in the mathematics and science classrooms, thus increasing the chance of positive social change.

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

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

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

The combined effects of longitudinal heat conduction, flow nonuniformity and temperature nonuniformity in crossflow plate-fin heat exchangers

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

Ranganayakulu, C.; Seetharamu, K.N.

An analysis of a crossflow plate-fin compact heat exchanger, accounting for the combined effects of two-dimensional longitudinal heat conduction through the exchanger wall and nonuniform inlet fluid flow and temperature distribution is carried out using a finite element method. A mathematical equation is developed to generate different types of fluid flow/temperature maldistribution models considering the possible deviations in fluid flow. Using these models, the exchanger effectiveness and its deterioration due to the combined effects of longitudinal heat conduction, flow nonuniformity and temperature nonuniformity are calculated for various design and operating conditions of the exchanger. It was found that the performancemore » variations are quite significant in some typical applications.« less

Magic in the machine: a computational magician's assistant.

PubMed

Williams, Howard; McOwan, Peter W

2014-01-01

A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required. The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced. Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact. In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect. We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London.

Visual and Vestibular Determinants of Perceived Eye-Level

NASA Technical Reports Server (NTRS)

Cohen, Malcolm Martin

2003-01-01

Both gravitational and optical sources of stimulation combine to determine the perceived elevations of visual targets. The ways in which these sources of stimulation combine with one another in operational aeronautical environments are critical for pilots to make accurate judgments of the relative altitudes of other aircraft and of their own altitude relative to the terrain. In a recent study, my colleagues and I required eighteen observers to set visual targets at their apparent horizon while they experienced various levels of G(sub z) in the human centrifuge at NASA-Ames Research Center. The targets were viewed in darkness and also against specific background optical arrays that were oriented at various angles with respect to the vertical; target settings were lowered as Gz was increased; this effect was reduced when the background optical array was visible. Also, target settings were displaced in the direction that the background optical array was pitched. Our results were attributed to the combined influences of otolith-oculomotor mechanisms that underlie the elevator illusion and visual-oculomotor mechanisms (optostatic responses) that underlie the perceptual effects of viewing pitched optical arrays that comprise the background. In this paper, I present a mathematical model that describes the independent and combined effects of G(sub z) intensity and the orientation and structure of background optical arrays; the model predicts quantitative deviations from normal accurate perceptions of target localization under a variety of conditions. Our earlier experimental results and the mathematical model are described in some detail, and the effects of viewing specific optical arrays under various gravitational-inertial conditions encountered in aeronautical environments are discussed.

A combined theoretical and in vitro modeling approach for predicting the magnetic capture and retention of magnetic nanoparticles in vivo

PubMed Central

David, Allan E.; Cole, Adam J.; Chertok, Beata; Park, Yoon Shin; Yang, Victor C.

2011-01-01

Magnetic nanoparticles (MNP) continue to draw considerable attention as potential diagnostic and therapeutic tools in the fight against cancer. Although many interacting forces present themselves during magnetic targeting of MNP to tumors, most theoretical considerations of this process ignore all except for the magnetic and drag forces. Our validation of a simple in vitro model against in vivo data, and subsequent reproduction of the in vitro results with a theoretical model indicated that these two forces do indeed dominate the magnetic capture of MNP. However, because nanoparticles can be subject to aggregation, and large MNP experience an increased magnetic force, the effects of surface forces on MNP stability cannot be ignored. We accounted for the aggregating surface forces simply by measuring the size of MNP retained from flow by magnetic fields, and utilized this size in the mathematical model. This presumably accounted for all particle-particle interactions, including those between magnetic dipoles. Thus, our “corrected” mathematical model provided a reasonable estimate of not only fractional MNP retention, but also predicted the regions of accumulation in a simulated capillary. Furthermore, the model was also utilized to calculate the effects of MNP size and spatial location, relative to the magnet, on targeting of MNPs to tumors. This combination of an in vitro model with a theoretical model could potentially assist with parametric evaluations of magnetic targeting, and enable rapid enhancement and optimization of magnetic targeting methodologies. PMID:21295085

Effect of substrate material selection on polychromatic integral diffraction efficiency for multilayer diffractive optics in oblique incident situation

NASA Astrophysics Data System (ADS)

Zhang, Bo; Cui, Qingfeng; Piao, Mingxu

2018-05-01

The effect of substrate material selection for multilayer diffractive optical elements (MLDOEs) on polychromatic integral diffraction efficiency (PIDE) is studied in the oblique incident situation. A mathematical model of substrate material selection is proposed to obtain the high PIDE with large incident angle. The extended expression of the microstructure heights with consideration of incident angle is deduced to calculate the PIDE difference Δ η bar(λ) for different substrate material combinations. The smaller value of Δ η bar(λ) indicates the more optimal substrate material combination in a wide incident angle range. Based on the deduced mathematical model, different MLDOEs are analyzed in visible and infrared wavebands. The results show that the three-layer DOEs can be applied in larger incident angle situation than the double-layer DOEs in visible waveband. When the two substrate materials are the same, polycarbonate (PC) is more reasonable than poly(methyl methacrylate) (PMMA) as the middle filling optical material for the three-layer DOEs. In the infrared waveband, the PIDE decreases in the LWIR are obviously smaller than that in the MWIR for the same substrate material combination, and the PIDE cannot be calculated when the incident angle larger than critical angle. The analysis results can be used to guide the hybrid optical system design with MLDOEs.

Traffic Flow Density Distribution Based on FEM

NASA Astrophysics Data System (ADS)

Ma, Jing; Cui, Jianming

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

Neuroprotective Drug for Nerve Trauma Revealed Using Artificial Intelligence.

PubMed

Romeo-Guitart, David; Forés, Joaquim; Herrando-Grabulosa, Mireia; Valls, Raquel; Leiva-Rodríguez, Tatiana; Galea, Elena; González-Pérez, Francisco; Navarro, Xavier; Petegnief, Valerie; Bosch, Assumpció; Coma, Mireia; Mas, José Manuel; Casas, Caty

2018-01-30

Here we used a systems biology approach and artificial intelligence to identify a neuroprotective agent for the treatment of peripheral nerve root avulsion. Based on accumulated knowledge of the neurodegenerative and neuroprotective processes that occur in motoneurons after root avulsion, we built up protein networks and converted them into mathematical models. Unbiased proteomic data from our preclinical models were used for machine learning algorithms and for restrictions to be imposed on mathematical solutions. Solutions allowed us to identify combinations of repurposed drugs as potential neuroprotective agents and we validated them in our preclinical models. The best one, NeuroHeal, neuroprotected motoneurons, exerted anti-inflammatory properties and promoted functional locomotor recovery. NeuroHeal endorsed the activation of Sirtuin 1, which was essential for its neuroprotective effect. These results support the value of network-centric approaches for drug discovery and demonstrate the efficacy of NeuroHeal as adjuvant treatment with surgical repair for nervous system trauma.

Robust Fuzzy Logic Stabilization with Disturbance Elimination

PubMed Central

Danapalasingam, Kumeresan A.

2014-01-01

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

Modeling Viral Spread

PubMed Central

Graw, Frederik; Perelson, Alan S.

2016-01-01

The way in which a viral infection spreads within a host is a complex process that is not well understood. Different viruses, such as human immunodeficiency virus type 1 and hepatitis C virus, have evolved different strategies, including direct cell-to-cell transmission and cell-free transmission, to spread within a host. To what extent these two modes of transmission are exploited in vivo is still unknown. Mathematical modeling has been an essential tool to get a better systematic and quantitative understanding of viral processes that are difficult to discern through strictly experimental approaches. In this review, we discuss recent attempts that combine experimental data and mathematical modeling in order to determine and quantify viral transmission modes. We also discuss the current challenges for a systems-level understanding of viral spread, and we highlight the promises and challenges that novel experimental techniques and data will bring to the field. PMID:27618637

Mathematical models of immune effector responses to viral infections: Virus control versus the development of pathology

NASA Astrophysics Data System (ADS)

Wodarz, Dominik

2005-12-01

This article reviews mathematical models which have investigated the importance of lytic and non-lytic immune responses for the control of viral infections. Lytic immune responses fight the virus by killing infected cells, while non-lytic immune responses fight the virus by inhibiting viral replication while leaving the infected cell alive. The models suggest which types or combinations of immune responses are required to resolve infections which vary in their characteristics, such as the rate of viral replication and the rate of virus-induced target cell death. This framework is then applied to persistent infections and viral evolution. It is investigated how viral evolution and antigenic escape can influence the relative balance of lytic and non-lytic responses over time, and how this might correlate with the transition from an asymptomatic infection to pathology. This is discussed in the specific context of hepatitis C virus infection.

Equation Discovery for Model Identification in Respiratory Mechanics of the Mechanically Ventilated Human Lung

NASA Astrophysics Data System (ADS)

Ganzert, Steven; Guttmann, Josef; Steinmann, Daniel; Kramer, Stefan

Lung protective ventilation strategies reduce the risk of ventilator associated lung injury. To develop such strategies, knowledge about mechanical properties of the mechanically ventilated human lung is essential. This study was designed to develop an equation discovery system to identify mathematical models of the respiratory system in time-series data obtained from mechanically ventilated patients. Two techniques were combined: (i) the usage of declarative bias to reduce search space complexity and inherently providing the processing of background knowledge. (ii) A newly developed heuristic for traversing the hypothesis space with a greedy, randomized strategy analogical to the GSAT algorithm. In 96.8% of all runs the applied equation discovery system was capable to detect the well-established equation of motion model of the respiratory system in the provided data. We see the potential of this semi-automatic approach to detect more complex mathematical descriptions of the respiratory system from respiratory data.

Mathematics Career Simulations: An Invitation

ERIC Educational Resources Information Center

Sinn, Robb; Phipps, Marnie

2013-01-01

A simulated academic career was combined with inquiry-based learning in an upper-division undergraduate mathematics course. Concepts such as tenure, professional conferences and journals were simulated. Simulation procedures were combined with student-led, inquiry-based classroom formats. A qualitative analysis (ethnography) describes the culture…

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

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

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

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

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

A Necessary Condition for Coexistence of Autocatalytic Replicators in a Prebiotic Environment

PubMed Central

Hernandez, Andres F.; Grover, Martha A.

2013-01-01

A necessary, but not sufficient, mathematical condition for the coexistence of short replicating species is presented here. The mathematical condition is obtained for a prebiotic environment, simulated as a fed-batch reactor, which combines monomer recycling, variable reaction order and a fixed monomer inlet flow with two replicator types and two monomer types. An extensive exploration of the parameter space in the model validates the robustness and efficiency of the mathematical condition, with nearly 1.7% of parameter sets meeting the condition and half of those exhibiting sustained coexistence. The results show that it is possible to generate a condition of coexistence, where two replicators sustain a linear growth simultaneously for a wide variety of chemistries, under an appropriate environment. The presence of multiple monomer types is critical to sustaining the coexistence of multiple replicator types. PMID:25369813

A necessary condition for coexistence of autocatalytic replicators in a prebiotic environment.

PubMed

Hernandez, Andres F; Grover, Martha A

2013-07-24

A necessary, but not sufficient, mathematical condition for the coexistence of short replicating species is presented here. The mathematical condition is obtained for a prebiotic environment, simulated as a fed-batch reactor, which combines monomer recycling, variable reaction order and a fixed monomer inlet flow with two replicator types and two monomer types. An extensive exploration of the parameter space in the model validates the robustness and efficiency of the mathematical condition, with nearly 1.7% of parameter sets meeting the condition and half of those exhibiting sustained coexistence. The results show that it is possible to generate a condition of coexistence, where two replicators sustain a linear growth simultaneously for a wide variety of chemistries, under an appropriate environment. The presence of multiple monomer types is critical to sustaining the coexistence of multiple replicator types.

Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map

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

Kanakoglou, K.; School of Physics, Nuclear and Elementary Particle Physics Department, Aristotle University of Thessaloniki; Daskaloyannis, C.

The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation-theoretic property of transferring invariably the super-Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, whilemore » the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.« less

Gain dependent self-phasing in a two-core coherently combined fiber laser.

PubMed

Kunkel, W Minster; Leger, James R

2018-04-16

The influence of the Kramers-Kronig phase is demonstrated in a coherently combined fiber laser where other passive phasing mechanisms such as wavelength tuning have been suppressed. A mathematical model is developed to predict the lasing supermode and is supported by experimental measurements of the gain, phase, and power. The results show that the difference in Kramers-Kronig phase arising from a difference in gain between the two arms partially compensates for an externally applied phase error.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

PubMed

Laomettachit, Teeraphan; Chen, Katherine C; Baumann, William T; Tyson, John J

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a "standard component" modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with "standard components" can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

PubMed Central

Laomettachit, Teeraphan; Chen, Katherine C.; Baumann, William T.

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast. PMID:27187804

Predicting the safety and efficacy of buffer therapy to raise tumour pHe: an integrative modelling study.

PubMed

Martin, N K; Robey, I F; Gaffney, E A; Gillies, R J; Gatenby, R A; Maini, P K

2012-03-27

Clinical positron emission tomography imaging has demonstrated the vast majority of human cancers exhibit significantly increased glucose metabolism when compared with adjacent normal tissue, resulting in an acidic tumour microenvironment. Recent studies demonstrated reducing this acidity through systemic buffers significantly inhibits development and growth of metastases in mouse xenografts. We apply and extend a previously developed mathematical model of blood and tumour buffering to examine the impact of oral administration of bicarbonate buffer in mice, and the potential impact in humans. We recapitulate the experimentally observed tumour pHe effect of buffer therapy, testing a model prediction in vivo in mice. We parameterise the model to humans to determine the translational safety and efficacy, and predict patient subgroups who could have enhanced treatment response, and the most promising combination or alternative buffer therapies. The model predicts a previously unseen potentially dangerous elevation in blood pHe resulting from bicarbonate therapy in mice, which is confirmed by our in vivo experiments. Simulations predict limited efficacy of bicarbonate, especially in humans with more aggressive cancers. We predict buffer therapy would be most effectual: in elderly patients or individuals with renal impairments; in combination with proton production inhibitors (such as dichloroacetate), renal glomular filtration rate inhibitors (such as non-steroidal anti-inflammatory drugs and angiotensin-converting enzyme inhibitors), or with an alternative buffer reagent possessing an optimal pK of 7.1-7.2. Our mathematical model confirms bicarbonate acts as an effective agent to raise tumour pHe, but potentially induces metabolic alkalosis at the high doses necessary for tumour pHe normalisation. We predict use in elderly patients or in combination with proton production inhibitors or buffers with a pK of 7.1-7.2 is most promising.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints.

PubMed

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M

2016-10-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. Copyright © 2016. Published by Elsevier Ltd.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

PubMed Central

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M.

2017-01-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. PMID:27544910

Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools

NASA Astrophysics Data System (ADS)

Okokpujie, Imhade Princess; Ikumapayi, Omolayo M.; Okonkwo, Ugochukwu C.; Salawu, Enesi Y.; Afolalu, Sunday A.; Dirisu, Joseph O.; Nwoke, Obinna N.; Ajayi, Oluseyi O.

2017-12-01

In recent machining operation, tool life is one of the most demanding tasks in production process, especially in the automotive industry. The aim of this paper is to study tool wear on HSS in end milling of aluminium 6061 alloy. The experiments were carried out to investigate tool wear with the machined parameters and to developed mathematical model using response surface methodology. The various machining parameters selected for the experiment are spindle speed (N), feed rate (f), axial depth of cut (a) and radial depth of cut (r). The experiment was designed using central composite design (CCD) in which 31 samples were run on SIEG 3/10/0010 CNC end milling machine. After each experiment the cutting tool was measured using scanning electron microscope (SEM). The obtained optimum machining parameter combination are spindle speed of 2500 rpm, feed rate of 200 mm/min, axial depth of cut of 20 mm, and radial depth of cut 1.0mm was found out to achieved the minimum tool wear as 0.213 mm. The mathematical model developed predicted the tool wear with 99.7% which is within the acceptable accuracy range for tool wear prediction.

Quantum dots as contrast agents for endoscopy: mathematical modeling and experimental validation of the optimal excitation wavelength

NASA Astrophysics Data System (ADS)

Roy, Mathieu; DaCosta, Ralph S.; Weersink, Robert; Netchev, George; Davidson, Sean R. H.; Chan, Warren; Wilson, Brian C.

2007-02-01

Our group is investigating the use of ZnS-capped CdSe quantum dot (QD) bioconjugates combined with fluorescence endoscopy for improved early cancer detection in the esophagus, colon and lung. A major challenge in using fluorescent contrast agents in vivo is to extract the relevant signal from the tissue autofluorescence (AF). Our studies are aimed at maximizing the QD signal to AF background ratio (SBR) to facilitate detection. This work quantitatively evaluates the effect of the excitation wavelength on the SBR, using both experimental measurements and mathematical modeling. Experimental SBR measurements were done by imaging QD solutions placed onto (surface) or embedded in (sub-surface) ex vivo murine tissue samples (brain, kidney, liver, lung), using a polymethylmethacrylate (PMMA) microchannel phantom. The results suggest that the maximum contrast is reached when the excitation wavelength is set at 400+/-20 μm for the surface configuration. For the sub-surface configuration, the optimal excitation wavelength varies with the tissue type and QD emission wavelengths. Our mathematical model, based on an approximation to the diffusion equation, successfully predicts the optimal excitation wavelength for the surface configuration, but needs further modifications to be accurate in the sub-surface configuration.

Refining the quantitative pathway of the Pathways to Mathematics model.

PubMed

Sowinski, Carla; LeFevre, Jo-Anne; Skwarchuk, Sheri-Lynn; Kamawar, Deepthi; Bisanz, Jeffrey; Smith-Chant, Brenda

2015-03-01

In the current study, we adopted the Pathways to Mathematics model of LeFevre et al. (2010). In this model, there are three cognitive domains--labeled as the quantitative, linguistic, and working memory pathways--that make unique contributions to children's mathematical development. We attempted to refine the quantitative pathway by combining children's (N=141 in Grades 2 and 3) subitizing, counting, and symbolic magnitude comparison skills using principal components analysis. The quantitative pathway was examined in relation to dependent numerical measures (backward counting, arithmetic fluency, calculation, and number system knowledge) and a dependent reading measure, while simultaneously accounting for linguistic and working memory skills. Analyses controlled for processing speed, parental education, and gender. We hypothesized that the quantitative, linguistic, and working memory pathways would account for unique variance in the numerical outcomes; this was the case for backward counting and arithmetic fluency. However, only the quantitative and linguistic pathways (not working memory) accounted for unique variance in calculation and number system knowledge. Not surprisingly, only the linguistic pathway accounted for unique variance in the reading measure. These findings suggest that the relative contributions of quantitative, linguistic, and working memory skills vary depending on the specific cognitive task. Copyright © 2014 Elsevier Inc. All rights reserved.

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Microenvironmental influence on microtumour infiltration patterns: 3D-mathematical modelling supported by in vitro studies.

PubMed

Luján, Emmanuel; Soto, Daniela; Rosito, María S; Soba, Alejandro; Guerra, Liliana N; Calvo, Juan C; Marshall, Guillermo; Suárez, Cecilia

2018-05-09

Mathematical modelling approaches have become increasingly abundant in cancer research. Tumour infiltration extent and its spatial organization depend both on the tumour type and stage and on the bio-physicochemical characteristics of the microenvironment. This sets a complex scenario that often requires a multidisciplinary and individually adjusted approach. The ultimate goal of this work is to present an experimental/numerical combined method for the development of a three-dimensional mathematical model with the ability to reproduce the growth and infiltration patterns of a given avascular microtumour in response to different microenvironmental conditions. The model is based on a diffusion-convection reaction equation that considers logistic proliferation, volumetric growth, a rim of proliferative cells at the tumour surface, and invasion with diffusive and convective components. The parameter values of the model were fitted to experimental results while radial velocity and diffusion coefficients were made spatially variable in a case-specific way through the introduction of a shape function and a diffusion-limited-aggregation (DLA)-derived fractal matrix, respectively, according to the infiltration pattern observed. The in vitro model consists of multicellular tumour spheroids (MTSs) of an epithelial mammary tumour cell line (LM3) immersed in a collagen I gel matrix with a standard culture medium ("naive" matrix) or a conditioned medium from adipocytes or preadipocytes ("conditioned" matrix). It was experimentally determined that both adipocyte and preadipocyte conditioned media had the ability to change the MTS infiltration pattern from collective and laminar to an individual and atomized one. Numerical simulations were able to adequately reproduce qualitatively and quantitatively both kinds of infiltration patterns, which were determined by area quantification, analysis of fractal dimensions and lacunarity, and Bland-Altman analysis. These results suggest that the combined approach presented here could be established as a new framework with interesting potential applications at both the basic and clinical levels in the oncology area.

Trends in modeling Biomedical Complex Systems

PubMed Central

Milanesi, Luciano; Romano, Paolo; Castellani, Gastone; Remondini, Daniel; Liò, Petro

2009-01-01

In this paper we provide an introduction to the techniques for multi-scale complex biological systems, from the single bio-molecule to the cell, combining theoretical modeling, experiments, informatics tools and technologies suitable for biological and biomedical research, which are becoming increasingly multidisciplinary, multidimensional and information-driven. The most important concepts on mathematical modeling methodologies and statistical inference, bioinformatics and standards tools to investigate complex biomedical systems are discussed and the prominent literature useful to both the practitioner and the theoretician are presented. PMID:19828068

The measurement of enhancement in mathematical abilities as a result of joint cognitive trainings in numerical and visual- spatial skills: A preliminary study

NASA Astrophysics Data System (ADS)

Agus, M.; Mascia, M. L.; Fastame, M. C.; Melis, V.; Pilloni, M. C.; Penna, M. P.

2015-02-01

A body of literature shows the significant role of visual-spatial skills played in the improvement of mathematical skills in the primary school. The main goal of the current study was to investigate the impact of a combined visuo-spatial and mathematical training on the improvement of mathematical skills in 146 second graders of several schools located in Italy. Participants were presented single pencil-and-paper visuo-spatial or mathematical trainings, computerised version of the above mentioned treatments, as well as a combined version of computer-assisted and pencil-and-paper visuo-spatial and mathematical trainings, respectively. Experimental groups were presented with training for 3 months, once a week. All children were treated collectively both in computer-assisted or pencil-and-paper modalities. At pre and post-test all our participants were presented with a battery of objective tests assessing numerical and visuo-spatial abilities. Our results suggest the positive effect of different types of training for the empowerment of visuo-spatial and numerical abilities. Specifically, the combination of computerised and pencil-and-paper versions of visuo-spatial and mathematical trainings are more effective than the single execution of the software or of the pencil-and-paper treatment.

Evaluation of an Integrated Curriculum in Physics, Mathematics, Engineering, and Chemistry

NASA Astrophysics Data System (ADS)

Beichner, Robert

1997-04-01

An experimental, student centered, introductory curriculum called IMPEC (for Integrated Mathematics, Physics, Engineering, and Chemistry curriculum) is in its third year of pilot-testing at NCSU. The curriculum is taught by a multidisciplinary team of professors using a combination of traditional lecturing and alternative instructional methods including cooperative learning, activity-based class sessions, and extensive use of computer modeling, simulations, and the world wide web. This talk will discuss the research basis for our design and implementation of the curriculum, the qualitative and quantitative methods we have been using to assess its effectiveness, and the educational outcomes we have noted so far.

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

[New trends in the evaluation of mathematics learning disabilities. The role of metacognition].

PubMed

Miranda-Casas, A; Acosta-Escareño, G; Tarraga-Minguez, R; Fernández, M I; Rosel-Remírez, J

2005-01-15

The current trends in the evaluation of mathematics learning disabilities (MLD), based on cognitive and empirical models, are oriented towards combining procedures involving the criteria and the evaluation of cognitive and metacognitive processes, associated to performance in mathematical tasks. The objective of this study is to analyse the metacognitive skills of prediction and evaluation in performing maths tasks and to compare metacognitive performance among pupils with MLD and younger pupils without MLD, who have the same level of mathematical performance. Likewise, we analyse these pupils' desire to learn. Subjects and methods. We compare a total of 44 pupils from the second cycle of primary education (8-10 years old) with and without mathematics learning disabilities. Significant differences are observed between pupils with and without mathematics learning disabilities in their capacity to predict and assess all of the tasks evaluated. As regards their 'desire to learn', no significant differences were found between pupils with and without MLD, which indicated that those with MLD assess their chances of successfully performing maths tasks in the same way as those without MLD. Finally, the findings reveal a similar metacognitive profile in pupils with MLD and the younger pupils with no mathematics learning disabilities. In future studies we consider it important to analyse the influence of the socio-affective belief system in the use of metacognitive skills.

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

Mathematical model of silicon smelting process basing on pelletized charge from technogenic raw materials

NASA Astrophysics Data System (ADS)

Nemchinova, N. V.; Tyutrin, A. A.; Salov, V. M.

2018-03-01

The silicon production process in the electric arc reduction furnaces (EAF) is studied using pelletized charge as an additive to the standard on the basis of the generated mathematical model. The results obtained due to the model will contribute to the analysis of the charge components behavior during melting with the achievement of optimum final parameters of the silicon production process. The authors proposed using technogenic waste as a raw material for the silicon production in a pelletized form using liquid glass and aluminum production dust from the electrostatic precipitators as a binder. The method of mathematical modeling with the help of the ‘Selector’ software package was used as a basis for the theoretical study. A model was simulated with the imitation of four furnace temperature zones and a crystalline silicon phase (25 °C). The main advantage of the created model is the ability to analyze the behavior of all burden materials (including pelletized charge) in the carbothermic process. The behavior analysis is based on the thermodynamic probability data of the burden materials interactions in the carbothermic process. The model accounts for 17 elements entering the furnace with raw materials, electrodes and air. The silicon melt, obtained by the modeling, contained 91.73 % wt. of the target product. The simulation results showed that in the use of the proposed combined charge, the recovery of silicon reached 69.248 %, which is in good agreement with practical data. The results of the crystalline silicon chemical composition modeling are compared with the real silicon samples of chemical analysis data, which showed the results of convergence. The efficiency of the mathematical modeling methods in the studying of the carbothermal silicon obtaining process with complex interphase transformations and the formation of numerous intermediate compounds using a pelletized charge as an additive to the traditional one is shown.

Effects of methyl mercury in combination with polychlorinated biphenyls and brominated flame retardants on the uptake of glutamate in rat brain synaptosomes: a mathematical approach for the study of mixtures.

PubMed

Stavenes Andersen, Ingrid; Voie, Oyvind Albert; Fonnum, Frode; Mariussen, Espen

2009-11-01

Regulatory limit values for toxicants are in general determined by the toxicology of the single compounds. However, little is known about their combined effects. Methyl mercury (MeHg), polychlorinated biphenyls (PCBs), and brominated flame retardants (BFRs) are dominant contaminants in the environment and food. MeHg is a well known neurotoxicant, especially affecting the developing brain. There is increasing evidence that PCB and BFRs also have neurotoxic effects. An enhanced effect of these toxicants, due to either synergistic or additive effects, would be considered as a risk for the fetal development. Here we studied the combinatorial effects of MeHg in combination with PCB or BFR on the reuptake of glutamate in synaptosomes. To provide the optimal conclusion regarding type of interaction, we have analyzed the data using two mathematical models, the Löewe model of additivity and Bliss' model of independent action. Binary and ternary mixtures in different proportions were made. The toxicants had primarily additive effects, as shown with both models, although tendencies towards synergism were observed. MeHg was by far the most potent inhibitor of uptake with an EC(50) value of 0.33 microM. A reconstituted mixture from a relevant fish sample was made in order to elucidate which chemical was responsible for the observed effect. Some interaction was experienced between PCB and MeHg, but in general MeHg seemed to explain the observed effect. We also show that mixture effects should not be assessed by effect addition.

Energy evaluation of protection effectiveness of anti-vibration gloves.

PubMed

Hermann, Tomasz; Dobry, Marian Witalis

2017-09-01

This article describes an energy method of assessing protection effectiveness of anti-vibration gloves on the human dynamic structure. The study uses dynamic models of the human and the glove specified in Standard No. ISO 10068:2012. The physical models of human-tool systems were developed by combining human physical models with a power tool model. The combined human-tool models were then transformed into mathematical models from which energy models were finally derived. Comparative energy analysis was conducted in the domain of rms powers. The energy models of the human-tool systems were solved using numerical simulation implemented in the MATLAB/Simulink environment. The simulation procedure demonstrated the effectiveness of the anti-vibration glove as a method of protecting human operators of hand-held power tools against vibration. The desirable effect is achieved by lowering the flow of energy in the human-tool system when the anti-vibration glove is employed.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

ERIC Educational Resources Information Center

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Reading and Mathematics Bound Together: Creating a Home Environment for Preschool Learning

ERIC Educational Resources Information Center

Godwin, Amber J.; Rupley, William H.; Capraro, Robert M.; Capraro, Mary Margaret

2016-01-01

The combination of mathematics and reading in family reading time can positively impact children's ability to make sense of representations in both mathematics and reading. Four families volunteered to participate in this field based inquiry to learn how to integrate mathematics and reading in parent-supported activities. Four parents and their…

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

PubMed

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

2016-04-08

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

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

PubMed Central

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

2016-01-01

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

The Role of PS Ability and RC Skill in Predicting Growth Trajectories of Mathematics Achievement

ERIC Educational Resources Information Center

Vista, Alvin

2016-01-01

There are relatively few studies in Australia and South-East Asian region that combine investigating models of math growth trajectories with predictors such as reasoning ability and reading comprehension skills. Math achievement is one of the major components of overall academic achievement and it is important to determine what factors (especially…

Handling Math Expressions in Economics: Recoding Spreadsheet Teaching Tool of Growth Models

ERIC Educational Resources Information Center

Moro-Egido, Ana I.; Pedauga, Luis E.

2017-01-01

In the present paper, we develop a teaching methodology for economic theory. The main contribution of this paper relies on combining the interactive characteristics of spreadsheet programs such as Excel and Unicode plain-text linear format for mathematical expressions. The advantage of Unicode standard rests on its ease for writing and reading…

A State-By-State Policy Analysis of STEM Education for K-12 Public Schools

ERIC Educational Resources Information Center

Carmichael, Courtney C.

2017-01-01

For practitioners and policy makers across the nation, STEM education has a vague definition. This study looks at how all 50 states define STEM education in policy, using four models: (a) Disciplinary STEM (Science, Technology, Engineering, Mathematics); (b) Integrated STEM focusing on combining two or more disciplines to produce critical…

Investigating alternative solutions for adsorption-contact drying when burning vegetable wastes

NASA Astrophysics Data System (ADS)

Golubkovich, A. V.

2007-06-01

Results are presented from investigation of three alternative solutions for adsorption-contact drying: combined (with cooling by means of outdoor air), with afterburning of combustible matters, and with limited adsorption of moisture using solid products of fuel combustion. Mathematical models and simplified expressions for calculating the time taken for the fuel drying to proceed are proposed.

A Model of MTSS: Integrating Precision Teaching of Mathematics and a Multi-Level Assessment System in a Generative Classroom

ERIC Educational Resources Information Center

Weisenburgh-Snyder, Amy B.; Malmquist, Susan K.; Robbins, Joanne K.; Lipshin, Alison M.

2015-01-01

In the generative classroom, teachers provide well-designed learning environments that result in the combination, recombination, and reorganization of repertoires such that new untaught repertoires are likely to occur. One component that can contribute to such generativity is Precision Teaching (PT), a frequency building instructional…

Opportunities and constraints of presently used thermal manikins for thermo-physiological simulation of the human body.

PubMed

Psikuta, Agnes; Kuklane, Kalev; Bogdan, Anna; Havenith, George; Annaheim, Simon; Rossi, René M

2016-03-01

Combining the strengths of an advanced mathematical model of human physiology and a thermal manikin is a new paradigm for simulating thermal behaviour of humans. However, the forerunners of such adaptive manikins showed some substantial limitations. This project aimed to determine the opportunities and constraints of the existing thermal manikins when dynamically controlled by a mathematical model of human thermal physiology. Four thermal manikins were selected and evaluated for their heat flux measurement uncertainty including lateral heat flows between manikin body parts and the response of each sector to the frequent change of the set-point temperature typical when using a physiological model for control. In general, all evaluated manikins are suitable for coupling with a physiological model with some recommendations for further improvement of manikin dynamic performance. The proposed methodology is useful to improve the performance of the adaptive manikins and help to provide a reliable and versatile tool for the broad research and development domain of clothing, automotive and building engineering.

Mathematical modeling of a single stage ultrasonically assisted distillation process.

PubMed

Mahdi, Taha; Ahmad, Arshad; Ripin, Adnan; Abdullah, Tuan Amran Tuan; Nasef, Mohamed M; Ali, Mohamad W

2015-05-01

The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor-liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor-liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol-ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system. Copyright © 2014 Elsevier B.V. All rights reserved.

Shoreline as a controlling factor in commercial shrimp production

NASA Technical Reports Server (NTRS)

Faller, K. H. (Principal Investigator)

1978-01-01

An ecological model was developed that relates marsh detritus export and shrimp production, based on the hypothesis that the shoreline is a controlling factor in the production of shrimp through regulation of detritus export from the marsh. LANDSAT data were used to develop measurements of shoreline length and area of marsh having more than 5.0 km shoreline/sq km for the coast of Louisiana, demonstrating the capability of remote sensing to provide important geographic information. These factors were combined with published tidal ranges and salinities to develop a mathematical model that predicted shrimp production for nine geographic units of the Louisiana coast, as indicated by the long term average commercial shrimp yield. The mathematical model relating these parameters and the shrimp production is consistent with an energy flow model describing the interaction of detritus producing marshlands with shrimp nursery grounds and inshore shrimping areas. The analysis supports the basic hypothesis and further raises the possibility of applications to coastal zone management requirements.

Grip Forces During Object Manipulation: Experiment, Mathematical Model & Validation

PubMed Central

Slota, Gregory P.; Latash, Mark L.; Zatsiorsky, Vladimir M.

2011-01-01

When people transport handheld objects, they change the grip force with the object movement. Circular movement patterns were tested within three planes at two different rates (1.0, 1.5 Hz), and two diameters (20, 40 cm). Subjects performed the task reasonably well, matching frequencies and dynamic ranges of accelerations within expectations. A mathematical model was designed to predict the applied normal forces from kinematic data. The model is based on two hypotheses: (a) the grip force changes during movements along complex trajectories can be represented as the sum of effects of two basic commands associated with the parallel and orthogonal manipulation, respectively; (b) different central commands are sent to the thumb and virtual finger (Vf- four fingers combined). The model predicted the actual normal forces with a total variance accounted for of better than 98%. The effects of the two components of acceleration—along the normal axis and the resultant acceleration within the shear plane—on the digit normal forces are additive. PMID:21735245

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Research on biophysical evaluation of the human vestibular system

NASA Technical Reports Server (NTRS)

Young, L. R.

1974-01-01

The human vestibular function was studied by the combined approach of advanced measurement and mathematical modelling. Fundamental measurements of some physical properties of endolymph and perilymph, combined with nystagmus measurements and fluid mechanical analysis of semicircular canal function furthered the theory of canal mechanical response to angular acceleration, caloric stimulation and relating linear acceleration. The effects of adaptation seen at low frequency angular stimulation were studied and modelled to remove some shortcomings of the torsion pendulum models. Otolith function was also studied experimentally and analytically, leading to a new set of models for subjective orientation. Applications to special problems of space, including the case of rotating spacecraft were investigated and the interaction of visual and vestibular cues and their relation to proprioceptive information was explored relative to postural control.

A new mathematical neck model for a low-velocity rear-end impact dummy: evaluation of components influencing head kinematics.

PubMed

Linder, A

2000-03-01

A mathematical model of a new rear-end impact dummy neck was implemented using MADYMO. The main goal was to design a model with a human-like response of the first extension motion in the crash event. The new dummy neck was modelled as a series of rigid bodies (representing the seven cervical vertebrae and the uppermost thoracic element, T1) connected by pin joints, and supplemented by two muscle substitutes. The joints had non-linear stiffness characteristics and the muscle elements possessed both elastic stiffness and damping properties. The new model was compared with two neck models with the same number of vertebrae, but without muscle substitutes. The properties of the muscle substitutes and the need of these were evaluated by using three different modified neck models. The motion of T1 in the simulations was prescribed using displacement data obtained from volunteer tests. In a sensitivity analysis of the mathematical model the influence of different factors on the head-neck kinematics was evaluated. The neck model was validated against kinematics data from volunteer tests: linear displacement, angular displacement, and acceleration of the head relative to the upper torso at 7 km/h velocity change. The response of the new model was within the corridor of the volunteer tests for the main part of the time history plot. This study showed that a combination of elastic stiffness and damping in the muscle substitutes, together with a non-linear joint stiffness, resulted in a head-neck response similar to human volunteers, and superior to that of other tested neck models.

Simulating Microbial Community Patterning Using Biocellion

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

Kang, Seung-Hwa; Kahan, Simon H.; Momeni, Babak

2014-04-17

Mathematical modeling and computer simulation are important tools for understanding complex interactions between cells and their biotic and abiotic environment: similarities and differences between modeled and observed behavior provide the basis for hypothesis forma- tion. Momeni et al. [5] investigated pattern formation in communities of yeast strains engaging in different types of ecological interactions, comparing the predictions of mathematical modeling and simulation to actual patterns observed in wet-lab experiments. However, simu- lations of millions of cells in a three-dimensional community are ex- tremely time-consuming. One simulation run in MATLAB may take a week or longer, inhibiting exploration of the vastmore » space of parameter combinations and assumptions. Improving the speed, scale, and accu- racy of such simulations facilitates hypothesis formation and expedites discovery. Biocellion is a high performance software framework for ac- celerating discrete agent-based simulation of biological systems with millions to trillions of cells. Simulations of comparable scale and accu- racy to those taking a week of computer time using MATLAB require just hours using Biocellion on a multicore workstation. Biocellion fur- ther accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. Biocellion targets computational biologists who have mathematical modeling backgrounds and basic C++ programming skills. This chap- ter describes the necessary steps to adapt the original Momeni et al.'s model to the Biocellion framework as a case study.« less

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.

Prediction of inspiratory flow shapes during sleep with a mathematic model of upper airway forces.

PubMed

Aittokallio, Tero; Gyllenberg, Mats; Saaresranta, Tarja; Polo, Olli

2003-11-01

To predict the airflow dynamics during sleep using a mathematic model that incorporates a number of static and dynamic upper airway forces, and to compare the numerical results to clinical flow data recorded from patients with sleep-disordered breathing on and off various treatment options. Upper airway performance was modeled in virtual subjects characterized by parameter settings that describe common combinations of risk factors predisposing to upper airway collapse during sleep. The treatments effect were induced by relevant changes of the initial parameter values. Computer simulations at our website (http://www.utu.fi/ml/sovmat/bio/). Risk factors considered in the simulation settings were sex, obesity, pharyngeal collapsibility, and decreased phasic activity of pharyngeal muscles. The effects of weight loss, pharyngeal surgery, nasal continuous positive airway pressure, and respiratory stimulation on the inspiratory flow characteristics were tested with the model. Numerical predictions were investigated by means of 3 measurable inspiratory airflow characteristics: initial slope, total volume, and flow shape. The model was able to reproduce the inspiratory flow shape characteristics that have previously been described in the literature. Simulation results also supported the observations that a multitude of factors underlie the pharyngeal collapse and, therefore, certain medical therapies that are effective in some conditions may prove ineffective in others. A mathematic model integrating the current knowledge of upper airway physiology is able to predict individual treatment responses. The model provides a framework for designing novel and potentially feasible treatment alternatives for sleep-disordered breathing.

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

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.

Embedding Number-Combinations Practice Within Word-Problem Tutoring

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas

2012-01-01

Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems. PMID:22661880

Embedding Number-Combinations Practice Within Word-Problem Tutoring.

PubMed

Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas

2010-09-01

Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Comparison of different two-pathway models for describing the combined effect of DO and nitrite on the nitrous oxide production by ammonia-oxidizing bacteria.

PubMed

Lang, Longqi; Pocquet, Mathieu; Ni, Bing-Jie; Yuan, Zhiguo; Spérandio, Mathieu

2017-02-01

The aim of this work is to compare the capability of two recently proposed two-pathway models for predicting nitrous oxide (N 2 O) production by ammonia-oxidizing bacteria (AOB) for varying ranges of dissolved oxygen (DO) and nitrite. The first model includes the electron carriers whereas the second model is based on direct coupling of electron donors and acceptors. Simulations are confronted to extensive sets of experiments (43 batches) from different studies with three different microbial systems. Despite their different mathematical structures, both models could well and similarly describe the combined effect of DO and nitrite on N 2 O production rate and emission factor. The model-predicted contributions for nitrifier denitrification pathway and hydroxylamine pathway also matched well with the available isotopic measurements. Based on sensitivity analysis, calibration procedures are described and discussed for facilitating the future use of those models.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Modeling the Formation of Transverse Weld during Billet-on-Billet Extrusion

PubMed Central

Mahmoodkhani, Yahya; Wells, Mary; Parson, Nick; Jowett, Chris; Poole, Warren

2014-01-01

A comprehensive mathematical model of the hot extrusion process for aluminum alloys has been developed and validated. The plasticity module was developed using a commercial finite element package, DEFORM-2D, a transient Lagrangian model which couples the thermal and deformation phenomena. Validation of the model against industrial data indicated that it gave excellent predictions of the pressure during extrusion. The finite element predictions of the velocity fields were post-processed to calculate the thickness of the surface cladding as one billet is fed in after another through the die (i.e., the transverse weld). The mathematical model was then used to assess the effect a change in feeder dimensions would have on the shape, thickness and extent of the transverse weld during extrusion. Experimental measurements for different combinations of billet materials show that the model is able to accurately predict the transverse weld shape as well as the clad surface layer to thicknesses of 50 μm. The transverse weld is significantly affected by the feeder geometry shape, but the effects of ram speed, billet material and temperature on the transverse weld dimensions are negligible. PMID:28788629

Analysis of satellite multibeam antennas’ performances

NASA Astrophysics Data System (ADS)

Sterbini, Guido

2006-07-01

In this work, we discuss the application of frequency reuse's concept in satellite communications, stressing the importance for a design-oriented mathematical model as first step for dimensioning antenna systems. We consider multibeam reflector antennas. The first part of the work consists in reorganizing, making uniform and completing the models already developed in the scientific literature. In doing it, we adopt the multidimensional Taylor development formalism. For computing the spillover efficiency of the antenna, we consider different feed's illuminations and we propose a completely original mathematical model, obtained by the interpolation of simulator results. The second part of the work is dedicated to characterize the secondary far field pattern. Combining this model together with the information on the cellular coverage geometry is possible to evaluate the isolation and the minimum directivity on the cell. As third part, in order to test the model and its analysis and synthesis capabilities, we implement a software tool that helps the designer in the rapid tuning of the fundamental quantities for the optimization of the performance: the proposed model shows an optimum agreement with the results of the simulations.

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

PubMed

Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz

2016-04-01

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

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Combined biofouling and scaling in membrane feed channels: a new modeling approach.

PubMed

Radu, A I; Bergwerff, L; van Loosdrecht, M C M; Picioreanu, C

2015-01-01

A mathematical model was developed for combined fouling due to biofilms and mineral precipitates in membrane feed channels with spacers. Finite element simulation of flow and solute transport in two-dimensional geometries was coupled with a particle-based approach for the development of a composite (cells and crystals) foulant layer. Three fouling scenarios were compared: biofouling only, scaling only and combined fouling. Combined fouling causes a quicker flux decline than the summed flux deterioration when scaling and biofouling act independently. The model results indicate that the presence of biofilms leads to more mineral formation due to: (1) an enhanced degree of saturation for salts next to the membrane and within the biofilm; and (2) more available surface for nucleation to occur. The impact of biofilm in accelerating gypsum precipitation depends on the composition of the feed water (eg the presence of NaCl) and the kinetics of crystal nucleation and growth. Interactions between flow, solute transport and biofilm-induced mineralization are discussed.

Integration of multiple theories for the simulation of laser interference lithography processes

NASA Astrophysics Data System (ADS)

Lin, Te-Hsun; Yang, Yin-Kuang; Fu, Chien-Chung

2017-11-01

The periodic structure of laser interference lithography (LIL) fabrication is superior to other lithography technologies. In contrast to traditional lithography, LIL has the advantages of being a simple optical system with no mask requirements, low cost, high depth of focus, and large patterning area in a single exposure. Generally, a simulation pattern for the periodic structure is obtained through optical interference prior to its fabrication through LIL. However, the LIL process is complex and combines the fields of optical and polymer materials; thus, a single simulation theory cannot reflect the real situation. Therefore, this research integrates multiple theories, including those of optical interference, standing waves, and photoresist characteristics, to create a mathematical model for the LIL process. The mathematical model can accurately estimate the exposure time and reduce the LIL process duration through trial and error.

Integration of multiple theories for the simulation of laser interference lithography processes.

PubMed

Lin, Te-Hsun; Yang, Yin-Kuang; Fu, Chien-Chung

2017-11-24

The periodic structure of laser interference lithography (LIL) fabrication is superior to other lithography technologies. In contrast to traditional lithography, LIL has the advantages of being a simple optical system with no mask requirements, low cost, high depth of focus, and large patterning area in a single exposure. Generally, a simulation pattern for the periodic structure is obtained through optical interference prior to its fabrication through LIL. However, the LIL process is complex and combines the fields of optical and polymer materials; thus, a single simulation theory cannot reflect the real situation. Therefore, this research integrates multiple theories, including those of optical interference, standing waves, and photoresist characteristics, to create a mathematical model for the LIL process. The mathematical model can accurately estimate the exposure time and reduce the LIL process duration through trial and error.

Locality of the Thomas-Fermi-von Weizsäcker Equations

NASA Astrophysics Data System (ADS)

Nazar, F. Q.; Ortner, C.

2017-06-01

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

Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation

PubMed Central

Day, Judy D.; Metes, Diana M.; Vodovotz, Yoram

2015-01-01

A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient’s (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression. PMID:26441988

A mathematical model for the transmission of Schistosoma japonicum in consideration of seasonal water level fluctuations of Poyang Lake in Jiangxi, China.

PubMed

Xiang, Jian; Chen, Honggen; Ishikawa, Hirofumi

2013-04-01

Poyang Lake, the largest fresh water lake in China, is the major transmission site of Schistosoma japonicum in China. Epidemics of schistosomiasis japonica have threatened the health of residents and stunted social-economic development there. This article aims at evaluating the effect of various control measures against schistosomiasis: selective mass treatment (ST), targeted mass treatment (TT), mass treatment for animal reservoirs (MT), and health education (HE), on reduction of the prevalence through simulations based on a mathematical model. We proposed a mathematical model, which is a system of ordinary differential equations for the transmission of S. japonicum among humans, bovines, and snails. The model takes into account the seasonal variation of the water level of Poyang Lake that is caused by the backflow of the Yangtze River and inflow from five small rivers, which influences the transmission of S. japonicum. For the purpose of dealing with the age-specific prevalence and intensity of infection, the human population was classified into four age categories in the model. We carried out several simulations resulting from the execution of ST and TT for elementary school children (E Sch), and combinations of ST, MT, and HE. The simulations indicated that all of the control measures only for humans had a trend of revival after interruption, and a combination of ST and MT has a significant effect on reducing human infection. Although TT and HE had a significant effect on the prevalence in the E Sch group, it had little effect on the overall human population. The simulations indicate that measures targeted to bovines such as chemotherapy besides humans will be vital to eliminate the transmission of S. japonicum in the Poyang Lake region. Moreover, it is desirable to improve health education for fishermen and herdsmen. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Nanoparticle-mediated drug delivery to treat infections in the female reproductive tract: evaluation of experimental systems and the potential for mathematical modeling.

PubMed

Sims, Lee B; Frieboes, Hermann B; Steinbach-Rankins, Jill M

2018-01-01

A variety of drug-delivery platforms have been employed to deliver therapeutic agents across cervicovaginal mucus (CVM) and the vaginal mucosa, offering the capability to increase the longevity and retention of active agents to treat infections of the female reproductive tract (FRT). Nanoparticles (NPs) have been shown to improve retention, diffusion, and cell-specific targeting via specific surface modifications, relative to other delivery platforms. In particular, polymeric NPs represent a promising option that has shown improved distribution through the CVM. These NPs are typically fabricated from nontoxic, non-inflammatory, US Food and Drug Administration-approved polymers that improve biocompatibility. This review summarizes recent experimental studies that have evaluated NP transport in the FRT, and highlights research areas that more thoroughly and efficiently inform polymeric NP design, including mathematical modeling. An overview of the in vitro, ex vivo, and in vivo NP studies conducted to date - whereby transport parameters are determined, extrapolated, and validated - is presented first. The impact of different NP design features on transport through the FRT is summarized, and gaps that exist due to the limitations of iterative experimentation alone are identified. The potential of mathematical modeling to complement the characterization and evaluation of diffusion and transport of delivery vehicles and active agents through the CVM and mucosa is discussed. Lastly, potential advancements combining experimental and mathematical knowledge are suggested to inform next-generation NP designs, such that infections in the FRT may be more effectively treated.

Underwater terrain-aided navigation system based on combination matching algorithm.

PubMed

Li, Peijuan; Sheng, Guoliang; Zhang, Xiaofei; Wu, Jingqiu; Xu, Baochun; Liu, Xing; Zhang, Yao

2018-07-01

Considering that the terrain-aided navigation (TAN) system based on iterated closest contour point (ICCP) algorithm diverges easily when the indicative track of strapdown inertial navigation system (SINS) is large, Kalman filter is adopted in the traditional ICCP algorithm, difference between matching result and SINS output is used as the measurement of Kalman filter, then the cumulative error of the SINS is corrected in time by filter feedback correction, and the indicative track used in ICCP is improved. The mathematic model of the autonomous underwater vehicle (AUV) integrated into the navigation system and the observation model of TAN is built. Proper matching point number is designated by comparing the simulation results of matching time and matching precision. Simulation experiments are carried out according to the ICCP algorithm and the mathematic model. It can be concluded from the simulation experiments that the navigation accuracy and stability are improved with the proposed combinational algorithm in case that proper matching point number is engaged. It will be shown that the integrated navigation system is effective in prohibiting the divergence of the indicative track and can meet the requirements of underwater, long-term and high precision of the navigation system for autonomous underwater vehicles. Copyright © 2017. Published by Elsevier Ltd.

Growth Processes and Formal Logic. Comments on History and Mathematics Regarded as Combined Educational Tools

ERIC Educational Resources Information Center

Seltman, Muriel; Seltman, P. E. J.

1978-01-01

The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)

Are College Student Success Courses Effective Corequisites to Developmental Mathematics in Community Colleges?

ERIC Educational Resources Information Center

Reilly, Karen L.

2014-01-01

The purpose of this study was to examine the differences in the achievement rates of developmental mathematics students when a student success course was taken in combination with mathematics. The study investigated changes that occurred in the developmental mathematics completion rates of the learners by examining age and the course sequence of…

Hybrid Task Design: Connecting Learning Opportunities Related to Critical Thinking and Statistical Thinking

ERIC Educational Resources Information Center

Kuntze, Sebastian; Aizikovitsh-Udi, Einav; Clarke, David

2017-01-01

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

The mechanical properties of stored red blood cells measured by a convenient microfluidic approach combining with mathematic model.

PubMed

Wang, Ying; You, Guoxing; Chen, Peipei; Li, Jianjun; Chen, Gan; Wang, Bo; Li, Penglong; Han, Dong; Zhou, Hong; Zhao, Lian

2016-03-01

The mechanical properties of red blood cells (RBCs) are critical to the rheological and hemodynamic behavior of blood. Although measurements of the mechanical properties of RBCs have been studied for many years, the existing methods, such as ektacytometry, micropipette aspiration, and microfluidic approaches, still have limitations. Mechanical changes to RBCs during storage play an important role in transfusions, and so need to be evaluated pre-transfusion, which demands a convenient and rapid detection method. We present a microfluidic approach that focuses on the mechanical properties of single cell under physiological shear flow and does not require any high-end equipment, like a high-speed camera. Using this method, the images of stretched RBCs under physical shear can be obtained. The subsequent analysis, combined with mathematic models, gives the deformability distribution, the morphology distribution, the normalized curvature, and the Young's modulus (E) of the stored RBCs. The deformability index and the morphology distribution show that the deformability of RBCs decreases significantly with storage time. The normalized curvature, which is defined as the curvature of the cell tail during stretching in flow, suggests that the surface charge of the stored RBCs decreases significantly. According to the mathematic model, which derives from the relation between shear stress and the adherent cells' extension ratio, the Young's moduli of the stored RBCs are also calculated and show significant increase with storage. Therefore, the present method is capable of representing the mechanical properties and can distinguish the mechanical changes of the RBCs during storage. The advantages of this method are the small sample needed, high-throughput, and easy-use, which make it promising for the quality monitoring of RBCs.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Mathematical analysis of antiretroviral therapy aimed at HIV-1 eradication or maintenance of low viral loads.

PubMed

Wein, L M; D'Amato, R M; Perelson, A S

1998-05-07

Motivated by the ability of combinations of antiretroviral agents to sustain viral suppression in HIV-1-infected individuals, we analyse the transient and steady-state behavior of a mathematical model of HIV-1 dynamics in vivo in order to predict whether these drug regimens can eradicate HIV-1 or maintain viral loads at low levels. The model incorporates two cell types (CD4+ T cells and a long-lived pool of cells), two strains of virus (drug-sensitive wild type and drug-resistant mutant) and two types of antiretroviral agents (reverse transcriptase and protease inhibitors). The transient behavior of the cells and virus and the eventual eradication of the virus are determined primarily by the strength of the combination therapy against the mutant strain and the maximum achievable increase in the uninfected CD4+ T cell concentration. We also predict, if the parameters of the model remain constant during therapy, that less intensive maintenance regimens will be unable to maintain low viral loads for extensive periods of time. However, if the reduction in viral load produced by therapy reduces the state of activation of the immune system, the number of cells susceptible for HIV-1 infection may decrease even though total CD4+ T cells increase. Our model predicts that if this occurs strong inductive therapy that reduces viral load followed by weaker maintenance regimes may succeed.

Mathematical modelling of the antibiotic-induced morphological transition of Pseudomonas aeruginosa

PubMed Central

Keen, Emma; Smith, David J.

2018-01-01

Here we formulate a mechanistic mathematical model to describe the growth dynamics of P. aeruginosa in the presence of the β-lactam antibiotic meropenem. The model is mechanistic in the sense that carrying capacity is taken into account through the dynamics of nutrient availability rather than via logistic growth. In accordance with our experimental results we incorporate a sub-population of cells, differing in morphology from the normal bacillary shape of P. aeruginosa bacteria, which we assume have immunity from direct antibiotic action. By fitting this model to experimental data we obtain parameter values that give insight into the growth of a bacterial population that includes different cell morphologies. The analysis of two parameters sets, that produce different long term behaviour, allows us to manipulate the system theoretically in order to explore the advantages of a shape transition that may potentially be a mechanism that allows P. aeruginosa to withstand antibiotic effects. Our results suggest that inhibition of this shape transition may be detrimental to bacterial growth and thus suggest that the transition may be a defensive mechanism implemented by bacterial machinery. In addition to this we provide strong theoretical evidence for the potential therapeutic strategy of using antimicrobial peptides (AMPs) in combination with meropenem. This proposed combination therapy exploits the shape transition as AMPs induce cell lysis by forming pores in the cytoplasmic membrane, which becomes exposed in the spherical cells. PMID:29481562

Interaction Analysis of Longevity Interventions Using Survival Curves.

PubMed

Nowak, Stefan; Neidhart, Johannes; Szendro, Ivan G; Rzezonka, Jonas; Marathe, Rahul; Krug, Joachim

2018-01-06

A long-standing problem in ageing research is to understand how different factors contributing to longevity should be expected to act in combination under the assumption that they are independent. Standard interaction analysis compares the extension of mean lifespan achieved by a combination of interventions to the prediction under an additive or multiplicative null model, but neither model is fundamentally justified. Moreover, the target of longevity interventions is not mean life span but the entire survival curve. Here we formulate a mathematical approach for predicting the survival curve resulting from a combination of two independent interventions based on the survival curves of the individual treatments, and quantify interaction between interventions as the deviation from this prediction. We test the method on a published data set comprising survival curves for all combinations of four different longevity interventions in Caenorhabditis elegans . We find that interactions are generally weak even when the standard analysis indicates otherwise.

Interaction Analysis of Longevity Interventions Using Survival Curves

PubMed Central

Nowak, Stefan; Neidhart, Johannes; Szendro, Ivan G.; Rzezonka, Jonas; Marathe, Rahul; Krug, Joachim

2018-01-01

A long-standing problem in ageing research is to understand how different factors contributing to longevity should be expected to act in combination under the assumption that they are independent. Standard interaction analysis compares the extension of mean lifespan achieved by a combination of interventions to the prediction under an additive or multiplicative null model, but neither model is fundamentally justified. Moreover, the target of longevity interventions is not mean life span but the entire survival curve. Here we formulate a mathematical approach for predicting the survival curve resulting from a combination of two independent interventions based on the survival curves of the individual treatments, and quantify interaction between interventions as the deviation from this prediction. We test the method on a published data set comprising survival curves for all combinations of four different longevity interventions in Caenorhabditis elegans. We find that interactions are generally weak even when the standard analysis indicates otherwise. PMID:29316622

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

Magic in the machine: a computational magician's assistant

PubMed Central

Williams, Howard; McOwan, Peter W.

2014-01-01

A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required. The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced. Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact. In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect. We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London. PMID:25452736

7 CFR 800.85 - Inspection of grain in combined lots.

Code of Federal Regulations, 2010 CFR

2010-01-01

... REGULATIONS Inspection Methods and Procedures § 800.85 Inspection of grain in combined lots. (a) General. The...) Weighted or mathematical average. Official factor and official criteria information shown on a certificate... section, be based on the weighted or mathematical averages of the analysis of the sublots in the lot and...

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

PubMed

Konstorum, Anna; Vella, Anthony T; Adler, Adam J; Laubenbacher, Reinhard C

2017-06-01

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development. © 2017 The Author(s).

Automatic protein structure solution from weak X-ray data

NASA Astrophysics Data System (ADS)

Skubák, Pavol; Pannu, Navraj S.

2013-11-01

Determining new protein structures from X-ray diffraction data at low resolution or with a weak anomalous signal is a difficult and often an impossible task. Here we propose a multivariate algorithm that simultaneously combines the structure determination steps. In tests on over 140 real data sets from the protein data bank, we show that this combined approach can automatically build models where current algorithms fail, including an anisotropically diffracting 3.88 Å RNA polymerase II data set. The method seamlessly automates the process, is ideal for non-specialists and provides a mathematical framework for successfully combining various sources of information in image processing.

Toxicodynamic and toxicokinetic descriptors of combined chromium (VI) and nickel toxicity.

PubMed

Minigaliyeva, Ilzira A; Katsnelson, Boris A; Privalova, Larisa I; Gurvich, Vladimir B; Panov, Vladimir G; Varaksin, Anatoly N; Makeyev, Oleg H; Sutunkova, Marina P; Loginova, Nadezhda V; Kireyeva, Ekaterina P; Grigoryeva, Ekaterina V; Slyshkina, Tatyana V; Ganebnykh, Eugenia V; Grebenkina, Svetlana V

2014-01-01

After repeated intraperitoneal injections of nickel and chromium (VI) salts to rats, we found, and confirmed by mathematical modeling, that their combined subchronic toxicity can either be of additive type or depart from it (predominantly toward subadditivity) depending on the effect assessed. Against the background of moderate systemic toxicity, the combination under study proved to possess a marked additive genotoxicity assessed by means of the random amplification of polymorphic DNA test. We also demonstrated that chromium and nickel reciprocally influenced the retention of these metals in some organs (especially in the spleen) but not their urinary excretion in this study. © The Author(s) 2014.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Shop Math for the Metal Trades. Combination Welder Apprentice, Machinist Helper, Precision Metal Finisher, Sheet Metal Worker Apprentice. A Report on Metal Trades Industry Certified, Single-Concept, Mathematical Learning Projects to Eliminate Student Math Fears.

ERIC Educational Resources Information Center

Newton, Lawrence R.

This project (1) identifies basic and functional mathematics skills (shop mathematics skills), (2) provides pretests on these functional mathematics skills, and (3) provides student learning projects (project sheets) that prepare metal trades students to read, understand, and apply mathematics and measuring skills that meet entry-level job…

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Graphical function mapping as a new way to explore cause-and-effect chains

USGS Publications Warehouse

Evans, Mary Anne

2016-01-01

Graphical function mapping provides a simple method for improving communication within interdisciplinary research teams and between scientists and nonscientists. This article introduces graphical function mapping using two examples and discusses its usefulness. Function mapping projects the outcome of one function into another to show the combined effect. Using this mathematical property in a simpler, even cartoon-like, graphical way allows the rapid combination of multiple information sources (models, empirical data, expert judgment, and guesses) in an intuitive visual to promote further discussion, scenario development, and clear communication.

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities

PubMed Central

Chu, Felicia W.; vanMarle, Kristy; Geary, David C.

2016-01-01

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement. PMID:27252675

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities.

PubMed

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2016-01-01

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement.

How intergenerational interaction affects attitude-behavior inconsistency.

PubMed

Sekiguchi, Takuya; Nakamaru, Mayuko

2014-04-07

Social norms play an important role in maintaining social order, but at the same time, they can act as a constraint that compels people to take specific actions which run contrary to their attitudes. This paper treats the latter case: we investigate conditions in which attitude-behavior inconsistency persists, constructing mathematical models combining evolutionary games and cultural transmissions. In particular, we focus on the effect of intergenerational interactions. Our models show that both information about others' attitude (e.g., through social surveys) and the combination of intra- and inter-generational interactions are key factors to generate the situation where all people adopt the same behavior but different people have different attitudes. Copyright © 2013 Elsevier Ltd. All rights reserved.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

ERIC Educational Resources Information Center

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Application of Stochastic Learning Theory to Elementary Arithmetic Exercises. Technical Report No. 302. Psychology and Education Series.

ERIC Educational Resources Information Center

Wagner, William J.

The application of a linear learning model, which combines learning theory with a structural analysis of the exercises given to students, to an elementary mathematics curriculum is examined. Elementary arithmetic items taken by about 100 second-grade students on 26 weekly tests form the data base. Weekly predictions of group performance on…

Examining dolphin hydrodynamics provides clues to calf-loss during tuna fishing

PubMed Central

Moore, Pete

2004-01-01

A combination of mathematical modeling and direct observation of the swimming behavior of dolphin mother-calf pairs has shown how the calf can gain much of the energy required for swimming if it is positioned correctly relative to the mother, a situation that may be disrupted during the chases that result from tuna-fishing practices. PMID:15132739

Coupled oscillators and Feynman's three papers

NASA Astrophysics Data System (ADS)

Kim, Y. S.

2007-05-01

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.

Pendulum rides, rotations and the Coriolis effect

NASA Astrophysics Data System (ADS)

Pendrill, Ann-Marie; Modig, Conny

2018-07-01

An amusement park is full of examples that can be made into challenging problems for students, combining mathematical modelling with video analysis, as well as measurements in the rides. Traditional amusement ride related textbook problems include free-fall, circular motion, pendula and energy conservation in roller coasters, where the moving bodies are typically considered point-like. However, an amusement park can offer many more examples that are useful in physics and engineering education, many of them with strong mathematical content. This paper analyses forces on riders in a large rotating pendulum ride, where the Coriolis effect is sufficiently large to be visible in accelerometer data from the rides and leads to different ride experiences in different positions.

Impact of Using History of Mathematics on Students' Mathematics Attitude: A Meta-Analysis Study

ERIC Educational Resources Information Center

Bütüner, Suphi Onder

2015-01-01

The main objective of hereby study is to unearth the big picture, reaching studies about influence of using history of mathematics on attitude of mathematics among students. 6 studies with a total effect size of 14 that comply with coding protocol and comprise statistical values necessary for meta-analysis are combined via meta-analysis method…

Pulsatile blood flow in elastic artery with model aneurysm

NASA Astrophysics Data System (ADS)

Nikolov, N.; Radev, St.; Tabakova, S.

2017-11-01

The mathematical modeling and numerical simulations are expected to play an important role to predict the genesis of different cardiovascular diseases, such as the formation and rupture of aneurysms. In the present work, the numerical solutions of the oscillatory blood flow are constructed for an elastic artery with a model aneurysm by use of the software ANSYS. It is observed that the artery elastic strain behaves in a different way: stably or unstably depending on the different combinations between the flow parameter (outlet pressure) and the elastic modulus of the artery wall.

Plant architecture, growth and radiative transfer for terrestrial and space environments

NASA Technical Reports Server (NTRS)

Norman, John M.; Goel, Narendra S.

1993-01-01

The overall objective of this research was to develop a hardware implemented model that would incorporate realistic and dynamic descriptions of canopy architecture in physiologically based models of plant growth and functioning, with an emphasis on radiative transfer while accommodating other environmental constraints. The general approach has five parts: a realistic mathematical treatment of canopy architecture, a methodology for combining this general canopy architectural description with a general radiative transfer model, the inclusion of physiological and environmental aspects of plant growth, inclusion of plant phenology, and integration.

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

PubMed

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

2014-01-01

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

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400

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

Oginni, B.M.; Bronson, F.L.; Field, M.B.

2012-07-01

Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extensionmore » to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can now be used for quickly and accurately evaluating efficiencies for wider range of gamma-ray spectroscopy applications. (authors)« less

Online Mathematics Homework Increases Student Achievement

ERIC Educational Resources Information Center

Roschelle, Jeremy; Feng, Mingyu; Murphy, Robert F.; Mason, Craig A.

2016-01-01

In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework…

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

Mathematical analysis of compressive/tensile molecular and nuclear structures

NASA Astrophysics Data System (ADS)

Wang, Dayu

Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H2; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the "island of stability" for the current and extended periodic table were studied.

Mathematical modeling of the fermentation of acid-hydrolyzed pyrolytic sugars to ethanol by the engineered strain Escherichia coli ACCC 11177.

PubMed

Chang, Dongdong; Yu, Zhisheng; Islam, Zia Ul; Zhang, Hongxun

2015-05-01

Pyrolysate from waste cotton was acid hydrolyzed and detoxified to yield pyrolytic sugars, which were fermented to ethanol by the strain Escherichia coli ACCC 11177. Mathematical models based on the fermentation data were also constructed. Pyrolysate containing an initial levoglucosan concentration of 146.34 g/L gave a glucose yield of 150 % after hydrolysis, suggesting that other compounds were hydrolyzed to glucose as well. Ethyl acetate-based extraction of bacterial growth inhibitors with an ethyl acetate/hydrolysate ratio of 1:0.5 enabled hydrolysate fermentation by E. coli ACCC 11177, without a standard absorption treatment. Batch processing in a fermenter exhibited a maximum ethanol yield and productivity of 0.41 g/g and 0.93 g/L·h(-1), respectively. The cell growth rate (r x ) was consistent with a logistic equation [Formula: see text], which was determined as a function of cell growth (X). Glucose consumption rate (r s ) and ethanol formation rate (r p ) were accurately validated by the equations [Formula: see text] and [Formula: see text], respectively. Together, our results suggest that combining mathematical models with fermenter fermentation processes can enable optimized ethanol production from cellulosic pyrolysate with E. coli. Similar approaches may facilitate the production of other commercially important organic substances.

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.

Decision Support for the Capacity Management of Bronchoscopy Devices: Optimizing the Cost-Efficient Mix of Reusable and Single-Use Devices Through Mathematical Modeling.

PubMed

Edenharter, Günther M; Gartner, Daniel; Pförringer, Dominik

2017-06-01

Increasing costs of material resources challenge hospitals to stay profitable. Particularly in anesthesia departments and intensive care units, bronchoscopes are used for various indications. Inefficient management of single- and multiple-use systems can influence the hospitals' material costs substantially. Using mathematical modeling, we developed a strategic decision support tool to determine the optimum mix of disposable and reusable bronchoscopy devices in the setting of an intensive care unit. A mathematical model with the objective to minimize costs in relation to demand constraints for bronchoscopy devices was formulated. The stochastic model decides whether single-use, multi-use, or a strategically chosen mix of both device types should be used. A decision support tool was developed in which parameters for uncertain demand such as mean, standard deviation, and a reliability parameter can be inserted. Furthermore, reprocessing costs per procedure, procurement, and maintenance costs for devices can be parameterized. Our experiments show for which demand pattern and reliability measure, it is efficient to only use reusable or disposable devices and under which circumstances the combination of both device types is beneficial. To determine the optimum mix of single-use and reusable bronchoscopy devices effectively and efficiently, managers can enter their hospital-specific parameters such as demand and prices into the decision support tool.The software can be downloaded at: https://github.com/drdanielgartner/bronchomix/.

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

2017-12-01

The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

PubMed Central

Zenker, Sven; Rubin, Jonathan; Clermont, Gilles

2007-01-01

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information. PMID:17997590

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

Modelling multiscale aspects of colorectal cancer

NASA Astrophysics Data System (ADS)

van Leeuwen, Ingeborg M. M.; Byrne, Helen M.; Johnston, Matthew D.; Edwards, Carina M.; Chapman, S. Jonathan; Bodmer, Walter F.; Maini, Philip K.

2008-01-01

Colorectal cancer (CRC) is responsible for nearly half a million deaths annually world-wide [11]. We present a series of mathematical models describing the dynamics of the intestinal epithelium and the kinetics of the molecular pathway most commonly mutated in CRC, the Wnt signalling network. We also discuss how we are coupling such models to build a multiscale model of normal and aberrant guts. This will enable us to combine disparate experimental and clinical data, to investigate interactions between phenomena taking place at different levels of organisation and, eventually, to test the efficacy of new drugs on the system as a whole.

Using network biology to bridge pharmacokinetics and pharmacodynamics in oncology.

PubMed

Kirouac, D C; Onsum, M D

2013-09-04

If mathematical modeling is to be used effectively in cancer drug development, future models must take into account both the mechanistic details of cellular signal transduction networks and the pharmacokinetics (PK) of drugs used to inhibit their oncogenic activity. In this perspective, we present an approach to building multiscale models that capture systems-level architectural features of oncogenic signaling networks, and describe how these models can be used to design combination therapies and identify predictive biomarkers in silico.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e71; doi:10.1038/psp.2013.38; published online 4 September 2013.

Description of bioremediation of soils using the model of a multistep system of microorganisms

NASA Astrophysics Data System (ADS)

Lubysheva, A. I.; Potashev, K. A.; Sofinskaya, O. A.

2018-01-01

The paper deals with the development of a mathematical model describing the interaction of a multi-step system of microorganisms in soil polluted with oil products. Each step in this system uses products of vital activity of the previous step to feed. Six different models of the multi-step system are considered. The equipping of the models with coefficients was carried out from the condition of minimizing the residual of the calculated and experimental data using an original algorithm based on the Levenberg-Marquardt method in combination with the Monte Carlo method for the initial approximation finding.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Complex Study of the Physical Properties of Reticulated Vitreous Carbon

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.

2015-01-01

We give an example of using a two-level identifi cation system incorporating an augmented mathematical model covering the structure, the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. The model, when combined with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little studied characteristics of the above materials. We present some of the results of investigations of reticulated vitreous carbon confirming the possibility of using it in a number of engineering applications.

Cell signaling heterogeneity is modulated by both cell-intrinsic and -extrinsic mechanisms: An integrated approach to understanding targeted therapy.

PubMed

Kim, Eunjung; Kim, Jae-Young; Smith, Matthew A; Haura, Eric B; Anderson, Alexander R A

2018-03-01

During the last decade, our understanding of cancer cell signaling networks has significantly improved, leading to the development of various targeted therapies that have elicited profound but, unfortunately, short-lived responses. This is, in part, due to the fact that these targeted therapies ignore context and average out heterogeneity. Here, we present a mathematical framework that addresses the impact of signaling heterogeneity on targeted therapy outcomes. We employ a simplified oncogenic rat sarcoma (RAS)-driven mitogen-activated protein kinase (MAPK) and phosphoinositide 3-kinase-protein kinase B (PI3K-AKT) signaling pathway in lung cancer as an experimental model system and develop a network model of the pathway. We measure how inhibition of the pathway modulates protein phosphorylation as well as cell viability under different microenvironmental conditions. Training the model on this data using Monte Carlo simulation results in a suite of in silico cells whose relative protein activities and cell viability match experimental observation. The calibrated model predicts distributional responses to kinase inhibitors and suggests drug resistance mechanisms that can be exploited in drug combination strategies. The suggested combination strategies are validated using in vitro experimental data. The validated in silico cells are further interrogated through an unsupervised clustering analysis and then integrated into a mathematical model of tumor growth in a homogeneous and resource-limited microenvironment. We assess posttreatment heterogeneity and predict vast differences across treatments with similar efficacy, further emphasizing that heterogeneity should modulate treatment strategies. The signaling model is also integrated into a hybrid cellular automata (HCA) model of tumor growth in a spatially heterogeneous microenvironment. As a proof of concept, we simulate tumor responses to targeted therapies in a spatially segregated tissue structure containing tumor and stroma (derived from patient tissue) and predict complex cell signaling responses that suggest a novel combination treatment strategy.

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

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

PubMed

Livni, Joseph; Stone, Lewi

2015-03-01

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

Using Computational and Mechanical Models to Study Animal Locomotion

PubMed Central

Miller, Laura A.; Goldman, Daniel I.; Hedrick, Tyson L.; Tytell, Eric D.; Wang, Z. Jane; Yen, Jeannette; Alben, Silas

2012-01-01

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.” PMID:22988026

Dynamic Performance Comparison for MPPT-PV Systems using Hybrid Pspice/Matlab Simulation

NASA Astrophysics Data System (ADS)

Aouchiche, N.; Becherif, M.; HadjArab, A.; Aitcheikh, M. S.; Ramadan, H. S.; Cheknane, A.

2016-10-01

The power generated by solar photovoltaic (PV) module depends on the surrounding irradiance and temperature. This paper presents a hybrid Matlab™/Pspice™ simulation model of PV system, combined with Cadence software SLPS. The hybridization is performed in order to gain the advantages of both simulation tools such as accuracy and efficiency in both Pspice electronic circuit and Matlab™ mathematical modelling respectively. For this purpose, the PV panel and the boost converter are developed using Pspice™ and hybridized with the mathematical Matlab™ model of maximum power point method controller (MPPT) through SLPS. The main objective is verify the significance of using the proposed hybrid simulation techniques in comparing the different MPPT algorithms such as the perturbation and observation (P&O), incremental of conductance (Inc-Cond) and counter reaction voltage using pilot cell (Pilot-Cell). Various simulations are performed under different atmospheric conditions in order to evaluate the dynamic behaviour for the system under study in terms of stability, efficiency and rapidity.

A Computational Framework for Bioimaging Simulation.

PubMed

Watabe, Masaki; Arjunan, Satya N V; Fukushima, Seiya; Iwamoto, Kazunari; Kozuka, Jun; Matsuoka, Satomi; Shindo, Yuki; Ueda, Masahiro; Takahashi, Koichi

2015-01-01

Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge in the mathematical form of biochemical reaction networks and understanding how higher level functions emerge from the combined action of biomolecules. However, there still remain formidable challenges in bridging the gap between bioimaging and mathematical modeling. Generally, measurements using fluorescence microscopy systems are influenced by systematic effects that arise from stochastic nature of biological cells, the imaging apparatus, and optical physics. Such systematic effects are always present in all bioimaging systems and hinder quantitative comparison between the cell model and bioimages. Computational tools for such a comparison are still unavailable. Thus, in this work, we present a computational framework for handling the parameters of the cell models and the optical physics governing bioimaging systems. Simulation using this framework can generate digital images of cell simulation results after accounting for the systematic effects. We then demonstrate that such a framework enables comparison at the level of photon-counting units.

Temporal characteristics of botulinum neurotoxin therapy

PubMed Central

Lebeda, Frank J; Cer, Regina Z; Stephens, Robert M; Mudunuri, Uma

2010-01-01

Botulinum neurotoxin is a pharmaceutical treatment used for an increasing number of neurological and non-neurological indications, symptoms and diseases. Despite the wealth of clinical reports that involve the timing of the therapeutic effects of this toxin, few studies have attempted to integrate these data into unified models. Secondary reactions have also been examined including the development of adverse events, resistance to repeated applications, and nerve terminal sprouting. Our primary intent for conducting this review was to gather relevant pharmacodynamic data from suitable biomedical literature regarding botulinum neurotoxins via the use of automated data-mining techniques. We envision that mathematical models will ultimately be of value to those who are healthcare decision makers and providers, as well as clinical and basic researchers. Furthermore, we hypothesize that the combination of this computer-intensive approach with mathematical modeling will predict the percentage of patients who will favorably or adversely respond to this treatment and thus will eventually assist in developing the increasingly important area of personalized medicine. PMID:20021324

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

Integrated PK-PD and agent-based modeling in oncology.

PubMed

Wang, Zhihui; Butner, Joseph D; Cristini, Vittorio; Deisboeck, Thomas S

2015-04-01

Mathematical modeling has become a valuable tool that strives to complement conventional biomedical research modalities in order to predict experimental outcome, generate new medical hypotheses, and optimize clinical therapies. Two specific approaches, pharmacokinetic-pharmacodynamic (PK-PD) modeling, and agent-based modeling (ABM), have been widely applied in cancer research. While they have made important contributions on their own (e.g., PK-PD in examining chemotherapy drug efficacy and resistance, and ABM in describing and predicting tumor growth and metastasis), only a few groups have started to combine both approaches together in an effort to gain more insights into the details of drug dynamics and the resulting impact on tumor growth. In this review, we focus our discussion on some of the most recent modeling studies building on a combined PK-PD and ABM approach that have generated experimentally testable hypotheses. Some future directions are also discussed.

Integrated PK-PD and Agent-Based Modeling in Oncology

PubMed Central

Wang, Zhihui; Butner, Joseph D.; Cristini, Vittorio

2016-01-01

Mathematical modeling has become a valuable tool that strives to complement conventional biomedical research modalities in order to predict experimental outcome, generate new medical hypotheses, and optimize clinical therapies. Two specific approaches, pharmacokinetic-pharmacodynamic (PK-PD) modeling, and agent-based modeling (ABM), have been widely applied in cancer research. While they have made important contributions on their own (e.g., PK-PD in examining chemotherapy drug efficacy and resistance, and ABM in describing and predicting tumor growth and metastasis), only a few groups have started to combine both approaches together in an effort to gain more insights into the details of drug dynamics and the resulting impact on tumor growth. In this review, we focus our discussion on some of the most recent modeling studies building on a combined PK-PD and ABM approach that have generated experimentally testable hypotheses. Some future directions are also discussed. PMID:25588379

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

PubMed

Ganusov, Vitaly V

2016-01-01

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

Generalizing Prototype Theory: A Formal Quantum Framework

PubMed Central

Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro

2016-01-01

Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436

Robust Combining of Disparate Classifiers Through Order Statistics

NASA Technical Reports Server (NTRS)

Tumer, Kagan; Ghosh, Joydeep

2001-01-01

Integrating the outputs of multiple classifiers via combiners or meta-learners has led to substantial improvements in several difficult pattern recognition problems. In this article we investigate a family of combiners based on order statistics, for robust handling of situations where there are large discrepancies in performance of individual classifiers. Based on a mathematical modeling of how the decision boundaries are affected by order statistic combiners, we derive expressions for the reductions in error expected when simple output combination methods based on the the median, the maximum and in general, the ith order statistic, are used. Furthermore, we analyze the trim and spread combiners, both based on linear combinations of the ordered classifier outputs, and show that in the presence of uneven classifier performance, they often provide substantial gains over both linear and simple order statistics combiners. Experimental results on both real world data and standard public domain data sets corroborate these findings.

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

PubMed

Huang, Lihan; Hwang, Andy; Phillips, John

2011-10-01

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

Mechanistic, Mathematical Model to Predict the Dynamics of Tissue Genesis in Bone Defects via Mechanical Feedback and Mediation of Biochemical Factors

PubMed Central

Moore, Shannon R.; Saidel, Gerald M.; Knothe, Ulf; Knothe Tate, Melissa L.

2014-01-01

The link between mechanics and biology in the generation and the adaptation of bone has been well studied in context of skeletal development and fracture healing. Yet, the prediction of tissue genesis within - and the spatiotemporal healing of - postnatal defects, necessitates a quantitative evaluation of mechano-biological interactions using experimental and clinical parameters. To address this current gap in knowledge, this study aims to develop a mechanistic mathematical model of tissue genesis using bone morphogenetic protein (BMP) to represent of a class of factors that may coordinate bone healing. Specifically, we developed a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteal progenitor cells within a long bone defect surrounded by periosteum and stabilized via an intramedullary nail. The emergent material properties and mechanical environment associated with nascent tissue genesis influence the strain stimulus sensed by progenitor cells within the periosteum. Using a mechanical finite element model, periosteal surface strains are predicted as a function of emergent, nascent tissue properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and tissue production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of endochondral tissue regeneration, assessed as areas of cartilage and mineralized bone, as functions of radial distance from the periosteum and time. Comparing model results to histological outcomes from two previous studies of periosteum-mediated bone regeneration in a common ovine model, it was shown that mechanistic models incorporating mechanical feedback successfully predict patterns (spatial) and trends (temporal) of bone tissue regeneration. The novel model framework presented here integrates a mechanistic feedback system based on the mechanosensitivity of periosteal progenitor cells, which allows for modeling and prediction of tissue regeneration on multiple length and time scales. Through combination of computational, physical and engineering science approaches, the model platform provides a means to test new hypotheses in silico and to elucidate conditions conducive to endogenous tissue genesis. Next generation models will serve to unravel intrinsic differences in bone genesis by endochondral and intramembranous mechanisms. PMID:24967742

Summer Camp of Mathematical Modeling in China

ERIC Educational Resources Information Center

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Phased array feed design technology for Large Aperture Microwave Radiometer (LAMR) Earth observations

NASA Technical Reports Server (NTRS)

Schuman, H. K.

1992-01-01

An assessment of the potential and limitations of phased array antennas in space-based geophysical precision radiometry is described. Mathematical models exhibiting the dependence of system and scene temperatures and system sensitivity on phased array antenna parameters and components such as phase shifters and low noise amplifiers (LNA) are developed. Emphasis is given to minimum noise temperature designs wherein the LNA's are located at the array level, one per element or subarray. Two types of combiners are considered: array lenses (space feeds) and corporate networks. The result of a survey of suitable components and devices is described. The data obtained from that survey are used in conjunction with the mathematical models to yield an assessment of effective array antenna noise temperature for representative geostationary and low Earth orbit systems. Practical methods of calibrating a space-based, phased array radiometer are briefly addressed as well.

A Measuring System for Well Logging Attitude and a Method of Sensor Calibration

PubMed Central

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-01-01

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°. PMID:24859028

Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem

PubMed Central

Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi

2013-01-01

Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem. PMID:23935429

A novel no-reference objective stereoscopic video quality assessment method based on visual saliency analysis

NASA Astrophysics Data System (ADS)

Yang, Xinyan; Zhao, Wei; Ye, Long; Zhang, Qin

2017-07-01

This paper proposes a no-reference objective stereoscopic video quality assessment method with the motivation that making the effect of objective experiments close to that of subjective way. We believe that the image regions with different visual salient degree should not have the same weights when designing an assessment metric. Therefore, we firstly use GBVS algorithm to each frame pairs and separate both the left and right viewing images into the regions with strong, general and week saliency. Besides, local feature information like blockiness, zero-crossing and depth are extracted and combined with a mathematical model to calculate a quality assessment score. Regions with different salient degree are assigned with different weights in the mathematical model. Experiment results demonstrate the superiority of our method compared with the existed state-of-the-art no-reference objective Stereoscopic video quality assessment methods.

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

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

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

NASA Astrophysics Data System (ADS)

Shorts, Vincient F.

1994-09-01

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

[Application of a mathematical algorithm for the detection of electroneuromyographic results in the pathogenesis study of facial dyskinesia].

PubMed

Gribova, N P; Iudel'son, Ia B; Golubev, V L; Abramenkova, I V

2003-01-01

To carry out a differential diagnosis of two facial dyskinesia (FD) models--facial hemispasm (FH) and facial paraspasm (FP), a combined program of electroneuromyographic (ENMG) examination has been created, using statistical analyses, including that for objects identification based on hybrid neural network with the application of adaptive fuzzy logic method and standard statistics programs (Wilcoxon, Student statistics). In FH, a lesion of peripheral facial neuromotor apparatus with augmentation of functions of inter-neurons in segmental and upper segmental stem levels predominated. In FP, primary afferent strengthening in mimic muscles was accompanied by increased motor neurons activity and reciprocal augmentation of inter-neurons, inhibiting motor portion of V pair. Mathematical algorithm for ENMG results recognition worked out in the study provides a precise differentiation of two FD models and opens possibilities for differential diagnosis of other facial motor disorders.

A measuring system for well logging attitude and a method of sensor calibration.

PubMed

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-05-23

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°.

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

NASA Astrophysics Data System (ADS)

Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

2004-08-01

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

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

PubMed Central

Ganusov, Vitaly V.

2016-01-01

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

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

Controlling acrylamide in French fry and potato chip models and a mathematical model of acrylamide formation: acrylamide: acidulants, phytate and calcium.

PubMed

Park, Yeonhwa; Yang, Heewon; Storkson, Jayne M; Albright, Karen J; Liu, Wei; Lindsay, Robert C; Pariza, Michael W

2005-01-01

We previously reported that in potato chip and French fry models, the formation of acrylamide can be reduced by controlling pH during processing steps, either by organic (acidulants) or inorganic acids. Use of phytate, a naturally occurring chelator, with or without Ca++ (or divalent ions), can reduce acrylamide formation in both models. However, since phytate itself is acidic, the question remains as to whether the effect of phytate is due to pH alone or to additional effects. In the French fry model, the effects on acrylamide formation of pH, phytate, and/or Ca++ in various combinations were tested in either blanching or soaking (after blanching) steps. All treatments significantly reduced acrylamide levels compared to control. Among variables tested, pH may be the single most important factor for reducing acrylamide levels, while there were independent effects of phytate and/or Ca++ in this French fry model. We also developed a mathematical formula to estimate the final concentration of acrylamide in a potato chip model, using variables that can affect acrylamide formation: glucose and asparagine concentrations, cut potato surface area and shape, cooking temperature and time, and other processing conditions.

Effectiveness of combination packages for HIV-1 prevention in sub-Saharan Africa depends on partnership network structure: a mathematical modelling study.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina; Cassels, Susan

2016-12-01

Combination packages for HIV prevention can leverage the effectiveness of biomedical and behavioural elements to lower disease incidence with realistic targets for individual and population risk reduction. We investigated how sexual network structures can maximise the effectiveness of a package targeting sexually active adults in sub-Saharan Africa (SSA) with intervention components for medical male circumcision (MMC) and sexual partnership concurrency (having >1 ongoing partner). Network-based mathematical models of HIV type 1 (HIV-1) transmission dynamics among heterosexual couples were used to explore how changes to MMC alone and in combination with changes to concurrency impacted endemic HIV-1 prevalence and incidence. Starting from a base model parameterised from empirical data from West Africa, we simulated the prevalence of circumcision from 10% to 90% and concurrency was modelled at four discrete levels corresponding to values observed across SSA. MMC and concurrency could contribute to the empirical variation in HIV-1 disease prevalence across SSA. Small reductions in concurrency resulted in large declines in HIV-1 prevalence. Scaling up circumcision in low-concurrency settings yields a greater relative benefit, but the absolute number of infections averted depends on both the circumcision coverage and baseline incidence. Epidemic extinction with this package will require substantial scale-up of MMC in low-concurrency settings. Dynamic sexual network structure should be considered in the design and targeting of MMC within combination HIV-1 prevention packages. Realistic levels of coverage for these packages within southern Africa could lead to a reduction of incidence to the low levels observed in western Africa, and possibly, epidemic extinction. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

Identification of line-specific strategies for improving carotenoid production in synthetic maize through data-driven mathematical modeling.

PubMed

Comas, Jorge; Benfeitas, Rui; Vilaprinyo, Ester; Sorribas, Albert; Solsona, Francesc; Farré, Gemma; Berman, Judit; Zorrilla, Uxue; Capell, Teresa; Sandmann, Gerhard; Zhu, Changfu; Christou, Paul; Alves, Rui

2016-09-01

Plant synthetic biology is still in its infancy. However, synthetic biology approaches have been used to manipulate and improve the nutritional and health value of staple food crops such as rice, potato and maize. With current technologies, production yields of the synthetic nutrients are a result of trial and error, and systematic rational strategies to optimize those yields are still lacking. Here, we present a workflow that combines gene expression and quantitative metabolomics with mathematical modeling to identify strategies for increasing production yields of nutritionally important carotenoids in the seed endosperm synthesized through alternative biosynthetic pathways in synthetic lines of white maize, which is normally devoid of carotenoids. Quantitative metabolomics and gene expression data are used to create and fit parameters of mathematical models that are specific to four independent maize lines. Sensitivity analysis and simulation of each model is used to predict which gene activities should be further engineered in order to increase production yields for carotenoid accumulation in each line. Some of these predictions (e.g. increasing Zmlycb/Gllycb will increase accumulated β-carotenes) are valid across the four maize lines and consistent with experimental observations in other systems. Other predictions are line specific. The workflow is adaptable to any other biological system for which appropriate quantitative information is available. Furthermore, we validate some of the predictions using experimental data from additional synthetic maize lines for which no models were developed. © 2016 The Authors The Plant Journal © 2016 John Wiley & Sons Ltd.

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

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

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

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

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

Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx.

PubMed

Elemans, Coen P H; Muller, Mees; Larsen, Ole Naesbye; van Leeuwen, Johan L

2009-04-01

Birdsong has developed into one of the important models for motor control of learned behaviour and shows many parallels with speech acquisition in humans. However, there are several experimental limitations to studying the vocal organ - the syrinx - in vivo. The multidisciplinary approach of combining experimental data and mathematical modelling has greatly improved the understanding of neural control and peripheral motor dynamics of sound generation in birds. Here, we present a simple mechanical model of the syrinx that facilitates detailed study of vibrations and sound production. Our model resembles the 'starling resistor', a collapsible tube model, and consists of a tube with a single membrane in its casing, suspended in an external pressure chamber and driven by various pressure patterns. With this design, we can separately control 'bronchial' pressure and tension in the oscillating membrane and generate a wide variety of 'syllables' with simple sweeps of the control parameters. We show that the membrane exhibits high frequency, self-sustained oscillations in the audio range (>600 Hz fundamental frequency) using laser Doppler vibrometry, and systematically explore the conditions for sound production of the model in its control space. The fundamental frequency of the sound increases with tension in three membranes with different stiffness and mass. The lower-bound fundamental frequency increases with membrane mass. The membrane vibrations are strongly coupled to the resonance properties of the distal tube, most likely because of its reflective properties to sound waves. Our model is a gross simplification of the complex morphology found in birds, and more closely resembles mathematical models of the syrinx. Our results confirm several assumptions underlying existing mathematical models in a complex geometry.

Democratizing Access to Core Mathematics across Grades 9-12

ERIC Educational Resources Information Center

Hegedus, Stephen; Dalton, Sara; Brookstein, Arden; Tapper, John; Heller, Eric

2011-01-01

The authors' proposed work builds upon 12+ years of research collectively known as the "SimCalc Projects." SimCalc Connected MathWorlds (SCM) combines two innovative technological ingredients to address core mathematical ideas in deep and sustainable ways for mathematics learners. Software that addresses content issues through dynamic…

Design Features of Pedagogically-Sound Software in Mathematics.

ERIC Educational Resources Information Center

Haase, Howard; And Others

Weaknesses in educational software currently available in the domain of mathematics are discussed. A technique that was used for the design and production of mathematics software aimed at improving problem-solving skills which combines sound pedagogy and innovative programming is presented. To illustrate the design portion of this technique, a…

Deepening Prospective Mathematics Teachers' Diagnostic Judgments: Interplay of Videos, Focus Questions and Didactic Categories

ERIC Educational Resources Information Center

Prediger, Susanne; Zindel, Carina

2017-01-01

This article combines different conceptualizations of teachers' diagnostic competence in listening to students' mathematical thinking processes on the levels of general perspectives, noticed aspects and activated didactic categories. An empirical study of 159 prospective mathematics teachers' diagnostic judgments investigated how these levels are…

Geometric Mean--What Does It Mean?

ERIC Educational Resources Information Center

Kalder, Robin S.

2012-01-01

The National Council of Teachers of Mathematics and numerous mathematics educators promote the combination of conceptual understanding and procedural learning in the successful instruction of mathematics. Despite this, when geometric mean is taught in a typical American geometry class, it is taught as a process only despite the many connections…

Working Memory in Children with Reading Disabilities and/or Mathematical Disabilities

ERIC Educational Resources Information Center

De Weerdt, Frauke; Desoete, Annemie; Roeyers, Herbert

2013-01-01

Elementary school children with reading disabilities (RD; "n" = 17), mathematical disabilities (MD; "n" = 22), or combined reading and mathematical disabilities (RD+MD; "n" = 28) were compared to average achieving (AA; "n" = 45) peers on working memory measures. On all working memory components, 2 (RD vs. no…

An Effective Solution to Discover Synergistic Drugs for Anti-Cerebral Ischemia from Traditional Chinese Medicinal Formulae

PubMed Central

Lu, Peng; Chen, Chang; Fu, Meihong; Fang, Jing; Gao, Jian; Zhu, Li; Liang, Rixin; Shen, Xin; Yang, Hongjun

2013-01-01

Recently, the pharmaceutical industry has shifted to pursuing combination therapies that comprise more than one active ingredient. Interestingly, combination therapies have been used for more than 2500 years in traditional Chinese medicine (TCM). Understanding optimal proportions and synergistic mechanisms of multi-component drugs are critical for developing novel strategies to combat complex diseases. A new multi-objective optimization algorithm based on least angle regression-partial least squares was proposed to construct the predictive model to evaluate the synergistic effect of the three components of a novel combination drug Yi-qi-jie-du formula (YJ), which came from clinical TCM prescription for the treatment of encephalopathy. Optimal proportion of the three components, ginsenosides (G), berberine (B) and jasminoidin (J) was determined via particle swarm optimum. Furthermore, the combination mechanisms were interpreted using PLS VIP and principal components analysis. The results showed that YJ had optimal proportion 3(G): 2(B): 0.5(J), and it yielded synergy in the treatment of rats impaired by middle cerebral artery occlusion induced focal cerebral ischemia. YJ with optimal proportion had good pharmacological effects on acute ischemic stroke. The mechanisms study demonstrated that the combination of G, B and J could exhibit the strongest synergistic effect. J might play an indispensable role in the formula, especially when combined with B for the acute stage of stroke. All these data in this study suggested that in the treatment of acute ischemic stroke, besides restoring blood supply and protecting easily damaged cells in the area of the ischemic penumbra as early as possible, we should pay more attention to the removal of the toxic metabolites at the same time. Mathematical system modeling may be an essential tool for the analysis of the complex pharmacological effects of multi-component drug. The powerful mathematical analysis method could greatly improve the efficiency in finding new combination drug from TCM. PMID:24236065

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

ERIC Educational Resources Information Center

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

Detecting Strengths and Weaknesses in Learning Mathematics through a Model Classifying Mathematical Skills

ERIC Educational Resources Information Center

Karagiannakis, Giannis N.; Baccaglini-Frank, Anna E.; Roussos, Petros

2016-01-01

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

Modeling the Combined Terrorist-Narcotics Trafficker Threat to National Security

DTIC Science & Technology

2012-05-01

views expressed in this article are those of the authors and do not reflect the official policy or position of the National Defense University...Mason University. Dr. Woodcock was Chief Scientist , Vice President, and Director of the Advanced Mathematics Program, BAE SYSTEMS-Portal Solutions...this relationship. In some cases, both organizations need the same facilitators: improve financial gains, expand geographical domains, provide common

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

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

Optimization of controlled processes in combined-cycle plant (new developments and researches)

NASA Astrophysics Data System (ADS)

Tverskoy, Yu S.; Muravev, I. K.

2017-11-01

All modern complex technical systems, including power units of TPP and nuclear power plants, work in the system-forming structure of multifunctional APCS. The development of the modern APCS mathematical support allows bringing the automation degree to the solution of complex optimization problems of equipment heat-mass-exchange processes in real time. The difficulty of efficient management of a binary power unit is related to the need to solve jointly at least three problems. The first problem is related to the physical issues of combined-cycle technologies. The second problem is determined by the criticality of the CCGT operation to changes in the regime and climatic factors. The third problem is related to a precise description of a vector of controlled coordinates of a complex technological object. To obtain a joint solution of this complex of interconnected problems, the methodology of generalized thermodynamic analysis, methods of the theory of automatic control and mathematical modeling are used. In the present report, results of new developments and studies are shown. These results allow improving the principles of process control and the automatic control systems structural synthesis of power units with combined-cycle plants that provide attainable technical and economic efficiency and operational reliability of equipment.

Numerical Modeling of Nonlinear Thermodynamics in SMA Wires

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

Reynolds, D R; Kloucek, P

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associatedmore » with such materials.« less

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

NASA Astrophysics Data System (ADS)

Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

2016-02-01

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

Binary logistic regression-Instrument for assessing museum indoor air impact on exhibits.

PubMed

Bucur, Elena; Danet, Andrei Florin; Lehr, Carol Blaziu; Lehr, Elena; Nita-Lazar, Mihai

2017-04-01

This paper presents a new way to assess the environmental impact on historical artifacts using binary logistic regression. The prediction of the impact on the exhibits during certain pollution scenarios (environmental impact) was calculated by a mathematical model based on the binary logistic regression; it allows the identification of those environmental parameters from a multitude of possible parameters with a significant impact on exhibitions and ranks them according to their severity effect. Air quality (NO 2 , SO 2 , O 3 and PM 2.5 ) and microclimate parameters (temperature, humidity) monitoring data from a case study conducted within exhibition and storage spaces of the Romanian National Aviation Museum Bucharest have been used for developing and validating the binary logistic regression method and the mathematical model. The logistic regression analysis was used on 794 data combinations (715 to develop of the model and 79 to validate it) by a Statistical Package for Social Sciences (SPSS 20.0). The results from the binary logistic regression analysis demonstrated that from six parameters taken into consideration, four of them present a significant effect upon exhibits in the following order: O 3 >PM 2.5 >NO 2 >humidity followed at a significant distance by the effects of SO 2 and temperature. The mathematical model, developed in this study, correctly predicted 95.1 % of the cumulated effect of the environmental parameters upon the exhibits. Moreover, this model could also be used in the decisional process regarding the preventive preservation measures that should be implemented within the exhibition space. The paper presents a new way to assess the environmental impact on historical artifacts using binary logistic regression. The mathematical model developed on the environmental parameters analyzed by the binary logistic regression method could be useful in a decision-making process establishing the best measures for pollution reduction and preventive preservation of exhibits.

Applying mathematical models to predict resident physician performance and alertness on traditional and novel work schedules.

PubMed

Klerman, Elizabeth B; Beckett, Scott A; Landrigan, Christopher P

2016-09-13

In 2011 the U.S. Accreditation Council for Graduate Medical Education began limiting first year resident physicians (interns) to shifts of ≤16 consecutive hours. Controversy persists regarding the effectiveness of this policy for reducing errors and accidents while promoting education and patient care. Using a mathematical model of the effects of circadian rhythms and length of time awake on objective performance and subjective alertness, we quantitatively compared predictions for traditional intern schedules to those that limit work to ≤ 16 consecutive hours. We simulated two traditional schedules and three novel schedules using the mathematical model. The traditional schedules had extended duration work shifts (≥24 h) with overnight work shifts every second shift (including every third night, Q3) or every third shift (including every fourth night, Q4) night; the novel schedules had two different cross-cover (XC) night team schedules (XC-V1 and XC-V2) and a Rapid Cycle Rotation (RCR) schedule. Predicted objective performance and subjective alertness for each work shift were computed for each individual's schedule within a team and then combined for the team as a whole. Our primary outcome was the amount of time within a work shift during which a team's model-predicted objective performance and subjective alertness were lower than that expected after 16 or 24 h of continuous wake in an otherwise rested individual. The model predicted fewer hours with poor performance and alertness, especially during night-time work hours, for all three novel schedules than for either the traditional Q3 or Q4 schedules. Three proposed schedules that eliminate extended shifts may improve performance and alertness compared with traditional Q3 or Q4 schedules. Predicted times of worse performance and alertness were at night, which is also a time when supervision of trainees is lower. Mathematical modeling provides a quantitative comparison approach with potential to aid residency programs in schedule analysis and redesign.

Improving Control of Tuberculosis in Low-Burden Countries: Insights from Mathematical Modeling

PubMed Central

White, Peter J.; Abubakar, Ibrahim

2016-01-01

Tuberculosis control and elimination remains a challenge for public health even in low-burden countries. New technology and novel approaches to case-finding, diagnosis, and treatment are causes for optimism but they need to be used cost-effectively. This in turn requires improved understanding of the epidemiology of TB and analysis of the effectiveness and cost-effectiveness of different interventions. We describe the contribution that mathematical modeling can make to understanding epidemiology and control of TB in different groups, guiding improved approaches to public health interventions. We emphasize that modeling is not a substitute for collecting data but rather is complementary to empirical research, helping determine what are the key questions to address to maximize the public-health impact of research, helping to plan studies, and making maximal use of available data, particularly from surveillance, and observational studies. We provide examples of how modeling and related empirical research inform policy and discuss how a combination of these approaches can be used to address current questions of key importance, including use of whole-genome sequencing, screening and treatment for latent infection, and combating drug resistance. PMID:27199896

Revisiting Bevacizumab + Cytotoxics Scheduling Using Mathematical Modeling: Proof of Concept Study in Experimental Non-Small Cell Lung Carcinoma.

PubMed

Imbs, Diane-Charlotte; El Cheikh, Raouf; Boyer, Arnaud; Ciccolini, Joseph; Mascaux, Céline; Lacarelle, Bruno; Barlesi, Fabrice; Barbolosi, Dominique; Benzekry, Sébastien

2018-01-01

Concomitant administration of bevacizumab and pemetrexed-cisplatin is a common treatment for advanced nonsquamous non-small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC-bearing mice. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.

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

PubMed

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

2011-01-01

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

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

Multidisciplinary insight into clonal expansion of HTLV-1-infected cells in adult T-cell leukemia via modeling by deterministic finite automata coupled with high-throughput sequencing.

PubMed

Farmanbar, Amir; Firouzi, Sanaz; Park, Sung-Joon; Nakai, Kenta; Uchimaru, Kaoru; Watanabe, Toshiki

2017-01-31

Clonal expansion of leukemic cells leads to onset of adult T-cell leukemia (ATL), an aggressive lymphoid malignancy with a very poor prognosis. Infection with human T-cell leukemia virus type-1 (HTLV-1) is the direct cause of ATL onset, and integration of HTLV-1 into the human genome is essential for clonal expansion of leukemic cells. Therefore, monitoring clonal expansion of HTLV-1-infected cells via isolation of integration sites assists in analyzing infected individuals from early infection to the final stage of ATL development. However, because of the complex nature of clonal expansion, the underlying mechanisms have yet to be clarified. Combining computational/mathematical modeling with experimental and clinical data of integration site-based clonality analysis derived from next generation sequencing technologies provides an appropriate strategy to achieve a better understanding of ATL development. As a comprehensively interdisciplinary project, this study combined three main aspects: wet laboratory experiments, in silico analysis and empirical modeling. We analyzed clinical samples from HTLV-1-infected individuals with a broad range of proviral loads using a high-throughput methodology that enables isolation of HTLV-1 integration sites and accurate measurement of the size of infected clones. We categorized clones into four size groups, "very small", "small", "big", and "very big", based on the patterns of clonal growth and observed clone sizes. We propose an empirical formal model based on deterministic finite state automata (DFA) analysis of real clinical samples to illustrate patterns of clonal expansion. Through the developed model, we have translated biological data of clonal expansion into the formal language of mathematics and represented the observed clonality data with DFA. Our data suggest that combining experimental data (absolute size of clones) with DFA can describe the clonality status of patients. This kind of modeling provides a basic understanding as well as a unique perspective for clarifying the mechanisms of clonal expansion in ATL.

Predicting the safety and efficacy of buffer therapy to raise tumour pHe: an integrative modelling study

PubMed Central

Martin, N K; Robey, I F; Gaffney, E A; Gillies, R J; Gatenby, R A; Maini, P K

2012-01-01

Background: Clinical positron emission tomography imaging has demonstrated the vast majority of human cancers exhibit significantly increased glucose metabolism when compared with adjacent normal tissue, resulting in an acidic tumour microenvironment. Recent studies demonstrated reducing this acidity through systemic buffers significantly inhibits development and growth of metastases in mouse xenografts. Methods: We apply and extend a previously developed mathematical model of blood and tumour buffering to examine the impact of oral administration of bicarbonate buffer in mice, and the potential impact in humans. We recapitulate the experimentally observed tumour pHe effect of buffer therapy, testing a model prediction in vivo in mice. We parameterise the model to humans to determine the translational safety and efficacy, and predict patient subgroups who could have enhanced treatment response, and the most promising combination or alternative buffer therapies. Results: The model predicts a previously unseen potentially dangerous elevation in blood pHe resulting from bicarbonate therapy in mice, which is confirmed by our in vivo experiments. Simulations predict limited efficacy of bicarbonate, especially in humans with more aggressive cancers. We predict buffer therapy would be most effectual: in elderly patients or individuals with renal impairments; in combination with proton production inhibitors (such as dichloroacetate), renal glomular filtration rate inhibitors (such as non-steroidal anti-inflammatory drugs and angiotensin-converting enzyme inhibitors), or with an alternative buffer reagent possessing an optimal pK of 7.1–7.2. Conclusion: Our mathematical model confirms bicarbonate acts as an effective agent to raise tumour pHe, but potentially induces metabolic alkalosis at the high doses necessary for tumour pHe normalisation. We predict use in elderly patients or in combination with proton production inhibitors or buffers with a pK of 7.1–7.2 is most promising. PMID:22382688

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets.

PubMed

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

Motivation: Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana . We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models.

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets

PubMed Central

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

Motivation: Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana. We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models. PMID:28713420

Infrared image enhancement based on the edge detection and mathematical morphology

NASA Astrophysics Data System (ADS)

Zhang, Linlin; Zhao, Yuejin; Dong, Liquan; Liu, Xiaohua; Yu, Xiaomei; Hui, Mei; Chu, Xuhong; Gong, Cheng

2010-11-01

The development of the un-cooled infrared imaging technology from military necessity. At present, It is widely applied in industrial, medicine, scientific and technological research and so on. The infrared radiation temperature distribution of the measured object's surface can be observed visually. The collection of infrared images from our laboratory has following characteristics: Strong spatial correlation, Low contrast , Poor visual effect; Without color or shadows because of gray image , and has low resolution; Low definition compare to the visible light image; Many kinds of noise are brought by the random disturbances of the external environment. Digital image processing are widely applied in many areas, it can now be studied up close and in detail in many research field. It has become one kind of important means of the human visual continuation. Traditional methods for image enhancement cannot capture the geometric information of images and tend to amplify noise. In order to remove noise and improve visual effect. Meanwhile, To overcome the above enhancement issues. The mathematical model of FPA unit was constructed based on matrix transformation theory. According to characteristics of FPA, Image enhancement algorithm which combined with mathematical morphology and edge detection are established. First of all, Image profile is obtained by using the edge detection combine with mathematical morphological operators. And then, through filling the template profile by original image to get the ideal background image, The image noise can be removed on the base of the above method. The experiments show that utilizing the proposed algorithm can enhance image detail and the signal to noise ratio.

Network and Atomistic Simulations Unveil the Structural Determinants of Mutations Linked to Retinal Diseases

PubMed Central

Mariani, Simona; Dell'Orco, Daniele; Felline, Angelo; Raimondi, Francesco; Fanelli, Francesca

2013-01-01

A number of incurable retinal diseases causing vision impairments derive from alterations in visual phototransduction. Unraveling the structural determinants of even monogenic retinal diseases would require network-centered approaches combined with atomistic simulations. The transducin G38D mutant associated with the Nougaret Congenital Night Blindness (NCNB) was thoroughly investigated by both mathematical modeling of visual phototransduction and atomistic simulations on the major targets of the mutational effect. Mathematical modeling, in line with electrophysiological recordings, indicates reduction of phosphodiesterase 6 (PDE) recognition and activation as the main determinants of the pathological phenotype. Sub-microsecond molecular dynamics (MD) simulations coupled with Functional Mode Analysis improve the resolution of information, showing that such impairment is likely due to disruption of the PDEγ binding cavity in transducin. Protein Structure Network analyses additionally suggest that the observed slight reduction of theRGS9-catalyzed GTPase activity of transducin depends on perturbed communication between RGS9 and GTP binding site. These findings provide insights into the structural fundamentals of abnormal functioning of visual phototransduction caused by a missense mutation in one component of the signaling network. This combination of network-centered modeling with atomistic simulations represents a paradigm for future studies aimed at thoroughly deciphering the structural determinants of genetic retinal diseases. Analogous approaches are suitable to unveil the mechanism of information transfer in any signaling network either in physiological or pathological conditions. PMID:24009494

Force-induced bone growth and adaptation: A system theoretical approach to understanding bone mechanotransduction

NASA Astrophysics Data System (ADS)

Maldonado, Solvey; Findeisen, Rolf

2010-06-01

The modeling, analysis, and design of treatment therapies for bone disorders based on the paradigm of force-induced bone growth and adaptation is a challenging task. Mathematical models provide, in comparison to clinical, medical and biological approaches an structured alternative framework to understand the concurrent effects of the multiple factors involved in bone remodeling. By now, there are few mathematical models describing the appearing complex interactions. However, the resulting models are complex and difficult to analyze, due to the strong nonlinearities appearing in the equations, the wide range of variability of the states, and the uncertainties in parameters. In this work, we focus on analyzing the effects of changes in model structure and parameters/inputs variations on the overall steady state behavior using systems theoretical methods. Based on an briefly reviewed existing model that describes force-induced bone adaptation, the main objective of this work is to analyze the stationary behavior and to identify plausible treatment targets for remodeling related bone disorders. Identifying plausible targets can help in the development of optimal treatments combining both physical activity and drug-medication. Such treatments help to improve/maintain/restore bone strength, which deteriorates under bone disorder conditions, such as estrogen deficiency.

Mathematical and computational approaches can complement experimental studies of host-pathogen interactions.

PubMed

Kirschner, Denise E; Linderman, Jennifer J

2009-04-01

In addition to traditional and novel experimental approaches to study host-pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host-pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or 'in silico' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host-pathogen interactions.

Mathematical modeling of degradation for bulk-erosive polymers: applications in tissue engineering scaffolds and drug delivery systems.

PubMed

Chen, Yuhang; Zhou, Shiwei; Li, Qing

2011-03-01

The degradation of polymeric biomaterials, which are widely exploited in tissue engineering and drug delivery systems, has drawn significant attention in recent years. This paper aims to develop a mathematical model that combines stochastic hydrolysis and mass transport to simulate the polymeric degradation and erosion process. The hydrolysis reaction is modeled in a discrete fashion by a fundamental stochastic process and an additional autocatalytic effect induced by the local carboxylic acid concentration in terms of the continuous diffusion equation. Illustrative examples of microparticles and tissue scaffolds demonstrate the applicability of the model. It is found that diffusive transport plays a critical role in determining the degradation pathway, whilst autocatalysis makes the degradation size dependent. The modeling results show good agreement with experimental data in the literature, in which the hydrolysis rate, polymer architecture and matrix size actually work together to determine the characteristics of the degradation and erosion processes of bulk-erosive polymer devices. The proposed degradation model exhibits great potential for the design optimization of drug carriers and tissue scaffolds. Copyright © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

ERIC Educational Resources Information Center

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

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.

Evaluation of the hydrological flow paths in a gravel bed filter modeling a horizontal subsurface flow wetland by using a multi-tracer experiment.

PubMed

Birkigt, Jan; Stumpp, Christine; Małoszewski, Piotr; Nijenhuis, Ivonne

2018-04-15

In recent years, constructed wetland systems have become into focus as means of cost-efficient organic contaminant management. Wetland systems provide a highly reactive environment in which several removal pathways of organic chemicals may be present at the same time; however, specific elimination processes and hydraulic conditions are usually separately investigated and thus not fully understood. The flow system in a three dimensional pilot-scale horizontal subsurface constructed wetland was investigated applying a multi-tracer test combined with a mathematical model to evaluate the flow and transport processes. The results indicate the existence of a multiple flow system with two distinct flow paths through the gravel bed and a preferential flow at the bottom transporting 68% of tracer mass resulting from the inflow design of the model wetland system. There the removal of main contaminant chlorobenzene was up to 52% based on different calculation approaches. Determined retention times in the range of 22d to 32.5d the wetland has a heterogeneous flow pattern. Differences between simulated and measured tracer concentrations in the upper sediment indicate diffusion dominated processes due to stagnant water zones. The tracer study combining experimental evaluation with mathematical modeling demonstrated the complexity of flow and transport processes in the constructed wetlands which need to be taken into account during interpretation of the determining attenuation processes. Copyright © 2017 Elsevier B.V. All rights reserved.

The study of precision measurement of pelvis spatial structure

NASA Astrophysics Data System (ADS)

Ma, Xiang; Ouyang, Jianfei; Qu, Xinghua

2010-03-01

Osteometry is fundamental for anthropometry. It provides the key technology and value to the study of palaeoanthropology, medicine, and criminal investigation. The traditional osteometry that has been widely accepted and used since 18th century has no longer met the information demand for modern research and application. It is significant and necessary to create an advanced 3-dimensional osteometry technique for anthropometry. This paper presents a new quick and accurate method to measure human pelvis through mathematical modeling. The pelvis is a complex combination of bones, which consists of three connected parts: hipbones, sacrum, and coccyx. There are over 40 items to be measured for the 1-dimension characteristics. In this paper, a combined measuring technology is developed for pelvis measurement. It uses machine vision systems and a portable measuring arm to obtain key geometry parameters of the pelvis. The mathematics models of the pelvis spatial structure and its parts are created through the process of data collecting, digging, assembling, and modeling. The experiment shows that the proposed technology can meet traditional osteometry and obtain entire 1D geometric parameters of the pelvis, such as maximum breadth and height, diameter of obstetric conjugata, inclination angle, and sakralneigungswinkel, etc. at the same time after modeling. Besides making the measurements above, the proposed technology can measure the geometry characteristics of pelvis and its parts, such as volume, surface area, curvature, and spatial structure, which are almost impossible for traditional technology. The overall measuring error is less than 0.1mm.

Multiscale Multilevel Approach to Solution of Nanotechnology Problems

NASA Astrophysics Data System (ADS)

Polyakov, Sergey; Podryga, Viktoriia

2018-02-01

The paper is devoted to a multiscale multilevel approach for the solution of nanotechnology problems on supercomputer systems. The approach uses the combination of continuum mechanics models and the Newton dynamics for individual particles. This combination includes three scale levels: macroscopic, mesoscopic and microscopic. For gas-metal technical systems the following models are used. The quasihydrodynamic system of equations is used as a mathematical model at the macrolevel for gas and solid states. The system of Newton equations is used as a mathematical model at the mesoand microlevels; it is written for nanoparticles of the medium and larger particles moving in the medium. The numerical implementation of the approach is based on the method of splitting into physical processes. The quasihydrodynamic equations are solved by the finite volume method on grids of different types. The Newton equations of motion are solved by Verlet integration in each cell of the grid independently or in groups of connected cells. In the framework of the general methodology, four classes of algorithms and methods of their parallelization are provided. The parallelization uses the principles of geometric parallelism and the efficient partitioning of the computational domain. A special dynamic algorithm is used for load balancing the solvers. The testing of the developed approach was made by the example of the nitrogen outflow from a balloon with high pressure to a vacuum chamber through a micronozzle and a microchannel. The obtained results confirm the high efficiency of the developed methodology.

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Adaptive nonlinear control for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Black, William S.

We present the background and motivation for ground vehicle autonomy, and focus on uses for space-exploration. Using a simple design example of an autonomous ground vehicle we derive the equations of motion. After providing the mathematical background for nonlinear systems and control we present two common methods for exactly linearizing nonlinear systems, feedback linearization and backstepping. We use these in combination with three adaptive control methods: model reference adaptive control, adaptive sliding mode control, and extremum-seeking model reference adaptive control. We show the performances of each combination through several simulation results. We then consider disturbances in the system, and design nonlinear disturbance observers for both single-input-single-output and multi-input-multi-output systems. Finally, we show the performance of these observers with simulation results.

Mathematical modeling of HIV prevention measures including pre-exposure prophylaxis on HIV incidence in South Korea.

PubMed

Kim, Sun Bean; Yoon, Myoungho; Ku, Nam Su; Kim, Min Hyung; Song, Je Eun; Ahn, Jin Young; Jeong, Su Jin; Kim, Changsoo; Kwon, Hee-Dae; Lee, Jeehyun; Smith, Davey M; Choi, Jun Yong

2014-01-01

Multiple prevention measures have the possibility of impacting HIV incidence in South Korea, including early diagnosis, early treatment, and pre-exposure prophylaxis (PrEP). We investigated how each of these interventions could impact the local HIV epidemic, especially among men who have sex with men (MSM), who have become the major risk group in South Korea. A mathematical model was used to estimate the effects of each these interventions on the HIV epidemic in South Korea over the next 40 years, as compared to the current situation. We constructed a mathematical model of HIV infection among MSM in South Korea, dividing the MSM population into seven groups, and simulated the effects of early antiretroviral therapy (ART), early diagnosis, PrEP, and combination interventions on the incidence and prevalence of HIV infection, as compared to the current situation that would be expected without any new prevention measures. Overall, the model suggested that the most effective prevention measure would be PrEP. Even though PrEP effectiveness could be lessened by increased unsafe sex behavior, PrEP use was still more beneficial than the current situation. In the model, early diagnosis of HIV infection was also effectively decreased HIV incidence. However, early ART did not show considerable effectiveness. As expected, it would be most effective if all interventions (PrEP, early diagnosis and early treatment) were implemented together. This model suggests that PrEP and early diagnosis could be a very effective way to reduce HIV incidence in South Korea among MSM.

Mathematical Modeling of HIV Prevention Measures Including Pre-Exposure Prophylaxis on HIV Incidence in South Korea

PubMed Central

Kim, Sun Bean; Yoon, Myoungho; Ku, Nam Su; Kim, Min Hyung; Song, Je Eun; Ahn, Jin Young; Jeong, Su Jin; Kim, Changsoo; Kwon, Hee-Dae; Lee, Jeehyun; Smith, Davey M.; Choi, Jun Yong

2014-01-01

Background Multiple prevention measures have the possibility of impacting HIV incidence in South Korea, including early diagnosis, early treatment, and pre-exposure prophylaxis (PrEP). We investigated how each of these interventions could impact the local HIV epidemic, especially among men who have sex with men (MSM), who have become the major risk group in South Korea. A mathematical model was used to estimate the effects of each these interventions on the HIV epidemic in South Korea over the next 40 years, as compared to the current situation. Methods We constructed a mathematical model of HIV infection among MSM in South Korea, dividing the MSM population into seven groups, and simulated the effects of early antiretroviral therapy (ART), early diagnosis, PrEP, and combination interventions on the incidence and prevalence of HIV infection, as compared to the current situation that would be expected without any new prevention measures. Results Overall, the model suggested that the most effective prevention measure would be PrEP. Even though PrEP effectiveness could be lessened by increased unsafe sex behavior, PrEP use was still more beneficial than the current situation. In the model, early diagnosis of HIV infection was also effectively decreased HIV incidence. However, early ART did not show considerable effectiveness. As expected, it would be most effective if all interventions (PrEP, early diagnosis and early treatment) were implemented together. Conclusions This model suggests that PrEP and early diagnosis could be a very effective way to reduce HIV incidence in South Korea among MSM. PMID:24662776

The Interrelationships of Mathematical Precursors in Kindergarten

PubMed Central

Cirino, Paul T.

2011-01-01

This study evaluated the interrelations among cognitive precursors across quantitative, linguistic, and spatial attention domains that have been implicated for math achievement in young children. The dimensionality of the quantity precursors was evaluated in 286 Kindergarteners via latent variable techniques, and the contribution of precursors from each domain was established for small sums addition. Results showed a five factor structure for the quantity precursors with the major distinction between nonsymbolic and symbolic tasks. The overall model demonstrated good fit, and strong predictive power (R2 = 55%) for addition number combinations. Linguistic and spatial attention domains showed indirect relationships with outcomes, with their effects mediated by symbolic quantity measures. These results have implications for the measurement of mathematical precursors, and yield promise for predicting future math performance. PMID:21194711

Automating FEA programming

NASA Technical Reports Server (NTRS)

Sharma, Naveen

1992-01-01

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

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

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

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

Learning How to Represent Mathematics on Paper

ERIC Educational Resources Information Center

Meaney, Tamsin; Trinick, Tony; Fairhall, Uenuku

2009-01-01

These authors have been working with a school in New Zealand that teaches mathematics, in the Maori language. In the last two years, the focus has been on improving the quantity and the quality of writing in mathematics. For the authors, "writing" meant using words, diagrams, symbols and graphs, either individually or in combination.…

Mathematics: A Practical View. Volume I, Teacher Edition. Applied Basic Curriculum Series.

ERIC Educational Resources Information Center

Evaluation, Dissemination and Assessment Center, Dallas.

The activities in this volume of practical mathematics are intended for the intermediate grades. The manual contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate…

Mathematics and Global Perspectives: A Working Team.

ERIC Educational Resources Information Center

Schwartz, Richard H.

1980-01-01

Ways in which mathematics and global education can be combined are described. Following a discussion of the need for having a citizenry capable of analyzing global issues, methods of infusing global education into the mathematics curriculum and math into the social studies curriculum are offered. Half of the document consists of eight sample…

A Framework for Mathematical Thinking: The Case of Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

Mathematical Rigor in the Common Core

ERIC Educational Resources Information Center

Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin

2013-01-01

A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…

Infographics and Mathematics: A Mechanism for Effective Learning in the Classroom

ERIC Educational Resources Information Center

Sudakov, Ivan; Bellsky, Thomas; Usenyuk, Svetlana; Polyakova, Victoria V.

2016-01-01

This work discusses the creation and use of infographics in an undergraduate mathematics course. Infographics are a visualization of information that combines data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from…

Teaching Multidigit Multiplication: Combining Multiple Frameworks to Analyse a Class Episode

ERIC Educational Resources Information Center

Clivaz, Stéphane

2017-01-01

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher's mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and…

Prediction of passenger ride quality in a multifactor environment

NASA Technical Reports Server (NTRS)

Dempsey, T. K.; Leatherwood, J. D.

1976-01-01

A model being developed, permits the understanding and prediction of passenger discomfort in a multifactor environment with particular emphasis upon combined noise and vibration. The model has general applicability to diverse transportation systems and provides a means of developing ride quality design criteria as well as a diagnostic tool for identifying the vibration and/or noise stimuli causing discomfort. Presented are: (1) a review of the basic theoretical and mathematical computations associated with the model, (2) a discussion of methodological and criteria investigations for both the vertical and roll axes of vibration, (3) a description of within-axis masking of discomfort responses for the vertical axis, thereby allowing prediction of the total discomfort due to any random vertical vibration, (4) a discussion of initial data on between-axis masking, and (5) discussion of a study directed towards extension of the vibration model to the more general case of predicting ride quality in the combined noise and vibration environments.

Solubility of Naproxen in Polyethylene Glycol 200 + Water Mixtures at Various Temperatures

PubMed Central

Panahi-Azar, Vahid; Soltanpour, Shahla; Martinez, Fleming; Jouyban, Abolghasem

2015-01-01

The solubility of naproxen in binary mixtures of polyethylene glycol 200 (PEG 200) + water at the temperature range from 298.0 K to 318.0 K were reported. The combinations of Jouyban-Acree model + van’t Hoff and Jouyban-Acree model + partial solubility parameters were used to predict the solubility of naproxen in PEG 200 + water mixtures at different temperatures. Combination of Jouyban-Acree model with van’t Hoff equation can be used to predict solubility in PEG 200 + water with only four solubility data in mono-solvents. The obtained solubility calculation errors vary from ~ 17 % up to 35 % depend on the number of required input data. Non-linear enthalpy-entropy compensation was found for naproxen in the investigated solvent system and the Jouyban−Acree model provides reasonably accurate mathematical descriptions of the thermodynamic data of naproxen in the investigated binary solvent systems. PMID:26664370

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.