Quantitative skills as a graduate learning outcome of university science degree programmes: student performance explored through theplanned-enacted-experiencedcurriculum model

NASA Astrophysics Data System (ADS)

Matthews, Kelly E.; Adams, Peter; Goos, Merrilyn

2016-07-01

Application of mathematical and statistical thinking and reasoning, typically referred to as quantitative skills, is essential for university bioscience students. First, this study developed an assessment task intended to gauge graduating students' quantitative skills. The Quantitative Skills Assessment of Science Students (QSASS) was the result, which examined 10 mathematical and statistical sub-topics. Second, the study established an evidential baseline of students' quantitative skills performance and confidence levels by piloting the QSASS with 187 final-year biosciences students at a research-intensive university. The study is framed within the planned-enacted-experienced curriculum model and contributes to science reform efforts focused on enhancing the quantitative skills of university graduates, particularly in the biosciences. The results found, on average, weak performance and low confidence on the QSASS, suggesting divergence between academics' intentions and students' experiences of learning quantitative skills. Implications for curriculum design and future studies are discussed.

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

ERIC Educational Resources Information Center

Whiteley, Meredith A.; Fenske, Robert H.

1990-01-01

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

An analysis of mathematical connection ability based on student learning style on visualization auditory kinesthetic (VAK) learning model with self-assessment

NASA Astrophysics Data System (ADS)

Apipah, S.; Kartono; Isnarto

2018-03-01

This research aims to analyze the quality of VAK learning with self-assessment toward the ability of mathematical connection performed by students and to analyze students’ mathematical connection ability based on learning styles in VAK learning model with self-assessment. This research applies mixed method type with concurrent embedded design. The subject of this research consists of VIII grade students from State Junior High School 9 Semarang who apply visual learning style, auditory learning style, and kinesthetic learning style. The data of learning style is collected by using questionnaires, the data of mathematical connection ability is collected by performing tests, and the data of self-assessment is collected by using assessment sheets. The quality of learning is qualitatively valued from planning stage, realization stage, and valuation stage. The result of mathematical connection ability test is analyzed quantitatively by mean test, conducting completeness test, mean differentiation test, and mean proportional differentiation test. The result of the research shows that VAK learning model results in well-qualified learning regarded from qualitative and quantitative sides. Students with visual learning style perform the highest mathematical connection ability, students with kinesthetic learning style perform average mathematical connection ability, and students with auditory learning style perform the lowest mathematical connection ability.

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.

Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

NASA Astrophysics Data System (ADS)

Ovan; Waluya, S. B.; Nugroho, S. E.

2018-03-01

This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

Modelling Mathematical Reasoning in Physics Education

ERIC Educational Resources Information Center

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

2012-01-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

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

Pathways to Mathematics: Longitudinal Predictors of Performance

ERIC Educational Resources Information Center

LeFevre, Jo-Anne; Fast, Lisa; Skwarchuk, Sheri-Lynn; Smith-Chant, Brenda L.; Bisanz, Jeffrey; Kamawar, Deepthi; Penner-Wilger, Marcie

2010-01-01

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial…

6 Principles for Quantitative Reasoning and Modeling

ERIC Educational Resources Information Center

Weber, Eric; Ellis, Amy; Kulow, Torrey; Ozgur, Zekiye

2014-01-01

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

PubMed Central

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

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.

Does Writing Have Any Effect on Mathematics Success?

ERIC Educational Resources Information Center

Dündar, Sefa

2016-01-01

In this study, the relationship between mathematics success and the formal properties and contents of the notebooks in which students take notes during mathematics classes have been examined. The exploratory model, in which quantitative and qualitative data are used together, has been used in this study. This study consists of 176 students from 3…

Schoolwide Mathematics Achievement within the Gifted Cluster Grouping Model

ERIC Educational Resources Information Center

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

2012-01-01

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

Modeling Synergistic Drug Inhibition of Mycobacterium tuberculosis Growth in Murine Macrophages

DTIC Science & Technology

2011-01-01

important application of metabolic network modeling is the ability to quantitatively model metabolic enzyme inhibition and predict bacterial growth...describe the extensions of this framework to model drug- induced growth inhibition of M. tuberculosis in macrophages.39 Mathematical framework Fig. 1 shows...starting point, we used the previously developed iNJ661v model to represent the metabolic Fig. 1 Mathematical framework: a set of coupled models used to

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

PubMed

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

2016-10-01

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

Novel mathematic models for quantitative transitivity of quality-markers in extraction process of the Buyanghuanwu decoction.

PubMed

Zhang, Yu-Tian; Xiao, Mei-Feng; Deng, Kai-Wen; Yang, Yan-Tao; Zhou, Yi-Qun; Zhou, Jin; He, Fu-Yuan; Liu, Wen-Long

2018-06-01

Nowadays, to research and formulate an efficiency extraction system for Chinese herbal medicine, scientists have always been facing a great challenge for quality management, so that the transitivity of Q-markers in quantitative analysis of TCM was proposed by Prof. Liu recently. In order to improve the quality of extraction from raw medicinal materials for clinical preparations, a series of integrated mathematic models for transitivity of Q-markers in quantitative analysis of TCM were established. Buyanghuanwu decoction (BYHWD) was a commonly TCMs prescription, which was used to prevent and treat the ischemic heart and brain diseases. In this paper, we selected BYHWD as an extraction experimental subject to study the quantitative transitivity of TCM. Based on theory of Fick's Rule and Noyes-Whitney equation, novel kinetic models were established for extraction of active components. Meanwhile, fitting out kinetic equations of extracted models and then calculating the inherent parameters in material piece and Q-marker quantitative transfer coefficients, which were considered as indexes to evaluate transitivity of Q-markers in quantitative analysis of the extraction process of BYHWD. HPLC was applied to screen and analyze the potential Q-markers in the extraction process. Fick's Rule and Noyes-Whitney equation were adopted for mathematically modeling extraction process. Kinetic parameters were fitted and calculated by the Statistical Program for Social Sciences 20.0 software. The transferable efficiency was described and evaluated by potential Q-markers transfer trajectory via transitivity availability AUC, extraction ratio P, and decomposition ratio D respectively. The Q-marker was identified with AUC, P, D. Astragaloside IV, laetrile, paeoniflorin, and ferulic acid were studied as potential Q-markers from BYHWD. The relative technologic parameters were presented by mathematic models, which could adequately illustrate the inherent properties of raw materials preparation and affection of Q-markers transitivity in equilibrium processing. AUC, P, D for potential Q-markers of AST-IV, laetrile, paeoniflorin, and FA were obtained, with the results of 289.9 mAu s, 46.24%, 22.35%; 1730 mAu s, 84.48%, 1.963%; 5600 mAu s, 70.22%, 0.4752%; 7810 mAu s, 24.29%, 4.235%, respectively. The results showed that the suitable Q-markers were laetrile and paeoniflorin in our study, which exhibited acceptable traceability and transitivity in the extraction process of TCMs. Therefore, these novel mathematic models might be developed as a new standard to control TCMs quality process from raw medicinal materials to product manufacturing. Copyright © 2018 Elsevier GmbH. All rights reserved.

Modeling Scientific Processes with Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

ERIC Educational Resources Information Center

Schuchardt, Anita M.; Schunn, Christian D.

2016-01-01

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

Examining Student Opinions on Computer Use Based on the Learning Styles in Mathematics Education

ERIC Educational Resources Information Center

Ozgen, Kemal; Bindak, Recep

2012-01-01

The purpose of this study is to identify the opinions of high school students, who have different learning styles, related to computer use in mathematics education. High school students' opinions on computer use in mathematics education were collected with both qualitative and quantitative approaches in the study conducted with a survey model. For…

Mathematical modelling and quantitative methods.

PubMed

Edler, L; Poirier, K; Dourson, M; Kleiner, J; Mileson, B; Nordmann, H; Renwick, A; Slob, W; Walton, K; Würtzen, G

2002-01-01

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

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.

Young children's core symbolic and nonsymbolic quantitative knowledge in the prediction of later mathematics achievement.

PubMed

Geary, David C; vanMarle, Kristy

2016-12-01

At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was assessed at the end of preschool (M = 64 months). We used a series of Bayesian and standard regression analyses to winnow this broad set of competencies down to the core subset of quantitative skills that predict later mathematics achievement, controlling other factors. This knowledge included children's fluency in reciting the counting string, their understanding of the cardinal value of number words, and recognition of Arabic numerals, as well as their sensitivity to the relative quantity of 2 collections of objects. The results inform theoretical models of the foundations of children's early quantitative development and have practical implications for the design of early interventions for children at risk for poor long-term mathematics achievement. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Quantitative model analysis with diverse biological data: applications in developmental pattern formation.

PubMed

Pargett, Michael; Umulis, David M

2013-07-15

Mathematical modeling of transcription factor and signaling networks is widely used to understand if and how a mechanism works, and to infer regulatory interactions that produce a model consistent with the observed data. Both of these approaches to modeling are informed by experimental data, however, much of the data available or even acquirable are not quantitative. Data that is not strictly quantitative cannot be used by classical, quantitative, model-based analyses that measure a difference between the measured observation and the model prediction for that observation. To bridge the model-to-data gap, a variety of techniques have been developed to measure model "fitness" and provide numerical values that can subsequently be used in model optimization or model inference studies. Here, we discuss a selection of traditional and novel techniques to transform data of varied quality and enable quantitative comparison with mathematical models. This review is intended to both inform the use of these model analysis methods, focused on parameter estimation, and to help guide the choice of method to use for a given study based on the type of data available. Applying techniques such as normalization or optimal scaling may significantly improve the utility of current biological data in model-based study and allow greater integration between disparate types of data. Copyright © 2013 Elsevier Inc. All rights reserved.

Quantitative assessment model for gastric cancer screening

PubMed Central

Chen, Kun; Yu, Wei-Ping; Song, Liang; Zhu, Yi-Min

2005-01-01

AIM: To set up a mathematic model for gastric cancer screening and to evaluate its function in mass screening for gastric cancer. METHODS: A case control study was carried on in 66 patients and 198 normal people, then the risk and protective factors of gastric cancer were determined, including heavy manual work, foods such as small yellow-fin tuna, dried small shrimps, squills, crabs, mothers suffering from gastric diseases, spouse alive, use of refrigerators and hot food, etc. According to some principles and methods of probability and fuzzy mathematics, a quantitative assessment model was established as follows: first, we selected some factors significant in statistics, and calculated weight coefficient for each one by two different methods; second, population space was divided into gastric cancer fuzzy subset and non gastric cancer fuzzy subset, then a mathematic model for each subset was established, we got a mathematic expression of attribute degree (AD). RESULTS: Based on the data of 63 patients and 693 normal people, AD of each subject was calculated. Considering the sensitivity and specificity, the thresholds of AD values calculated were configured with 0.20 and 0.17, respectively. According to these thresholds, the sensitivity and specificity of the quantitative model were about 69% and 63%. Moreover, statistical test showed that the identification outcomes of these two different calculation methods were identical (P>0.05). CONCLUSION: The validity of this method is satisfactory. It is convenient, feasible, economic and can be used to determine individual and population risks of gastric cancer. PMID:15655813

Using Technology to Balance Algebraic Explorations

ERIC Educational Resources Information Center

Kurz, Terri L.

2013-01-01

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

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

PubMed

Richards, D; Berry, S; Howard, M

2012-01-01

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

The Effects of an Undergraduate Programme of Preschool Teaching on Preservice Teachers' Attitudes Towards Early Mathematics Education in Turkey: A Longitudinal Study

ERIC Educational Resources Information Center

Kesicioglu, Oguz Serdar

2015-01-01

The aim of this study is to set forth preservice teachers' attitudes towards early mathematics education. For this purpose, quantitative and qualitative research methods were used conjunctively and the research was planned in accordance with a "screening model". The longitudinal screening model, one of the screening models, was used in…

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

PubMed

Getto, Philipp; Marciniak-Czochra, Anna

2015-01-01

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

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

PubMed Central

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

2013-01-01

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

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

PubMed

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

2013-10-01

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

Representations and Rafts

ERIC Educational Resources Information Center

Hartweg, Kimberly Sipes

2011-01-01

To build on prior knowledge and mathematical understanding, middle school students need to be given the opportunity to make connections among a variety of representations. Graphs, tables, algebraic formulas, and models are just a few examples of representations that can help students explore quantitative relationships. As a mathematics educator,…

Mathematical modeling of gene expression: a guide for the perplexed biologist

PubMed Central

Ay, Ahmet; Arnosti, David N.

2011-01-01

The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean and differential equation models we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems. PMID:21417596

Quantitative Skills as a Graduate Learning Outcome of University Science Degree Programmes: Student Performance Explored through the "Planned-Enacted-Experienced" Curriculum Model

ERIC Educational Resources Information Center

Matthews, Kelly E.; Adams, Peter; Goos, Merrilyn

2016-01-01

Application of mathematical and statistical thinking and reasoning, typically referred to as quantitative skills, is essential for university bioscience students. First, this study developed an assessment task intended to gauge graduating students' quantitative skills. The Quantitative Skills Assessment of Science Students (QSASS) was the result,…

Ancient Paradoxes Can Extend Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Introductory Life Science Mathematics and Quantitative Neuroscience Courses

ERIC Educational Resources Information Center

Duffus, Dwight; Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an…

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

PubMed

Han, Jinxiang; Huang, Jinzhao

2012-03-01

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

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

NASA Astrophysics Data System (ADS)

Handayani, I.; Januar, R. L.; Purwanto, S. E.

2018-01-01

This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

LECTURES ON DECISION THEORY,

DTIC Science & Technology

These lecture notes deal with the mathematical theory of decision - making , i.e., wihematical models of situations in which there is a set of...individual and group decision - making as a quantitative science, in contrast with a field such as physics, suggests that mathematical theorizing on...phenomena of decision - making is very much an exploratory enterprise and that ex isting models have limited generality and appli cability. The purpose is to

Modeling RNA interference in mammalian cells

PubMed Central

2011-01-01

Background RNA interference (RNAi) is a regulatory cellular process that controls post-transcriptional gene silencing. During RNAi double-stranded RNA (dsRNA) induces sequence-specific degradation of homologous mRNA via the generation of smaller dsRNA oligomers of length between 21-23nt (siRNAs). siRNAs are then loaded onto the RNA-Induced Silencing multiprotein Complex (RISC), which uses the siRNA antisense strand to specifically recognize mRNA species which exhibit a complementary sequence. Once the siRNA loaded-RISC binds the target mRNA, the mRNA is cleaved and degraded, and the siRNA loaded-RISC can degrade additional mRNA molecules. Despite the widespread use of siRNAs for gene silencing, and the importance of dosage for its efficiency and to avoid off target effects, none of the numerous mathematical models proposed in literature was validated to quantitatively capture the effects of RNAi on the target mRNA degradation for different concentrations of siRNAs. Here, we address this pressing open problem performing in vitro experiments of RNAi in mammalian cells and testing and comparing different mathematical models fitting experimental data to in-silico generated data. We performed in vitro experiments in human and hamster cell lines constitutively expressing respectively EGFP protein or tTA protein, measuring both mRNA levels, by quantitative Real-Time PCR, and protein levels, by FACS analysis, for a large range of concentrations of siRNA oligomers. Results We tested and validated four different mathematical models of RNA interference by quantitatively fitting models' parameters to best capture the in vitro experimental data. We show that a simple Hill kinetic model is the most efficient way to model RNA interference. Our experimental and modeling findings clearly show that the RNAi-mediated degradation of mRNA is subject to saturation effects. Conclusions Our model has a simple mathematical form, amenable to analytical investigations and a small set of parameters with an intuitive physical meaning, that makes it a unique and reliable mathematical tool. The findings here presented will be a useful instrument for better understanding RNAi biology and as modelling tool in Systems and Synthetic Biology. PMID:21272352

Gender, Math Confidence, and Grit: Relationships with Quantitative Skills and Performance in an Undergraduate Biology Course

ERIC Educational Resources Information Center

Flanagan, K. M.; Einarson, J.

2017-01-01

In a world filled with big data, mathematical models, and statistics, the development of strong quantitative skills is becoming increasingly critical for modern biologists. Teachers in this field must understand how students acquire quantitative skills and explore barriers experienced by students when developing these skills. In this study, we…

Learning biology through connecting mathematics to scientific mechanisms: Student outcomes and teacher supports

NASA Astrophysics Data System (ADS)

Schuchardt, Anita

Integrating mathematics into science classrooms has been part of the conversation in science education for a long time. However, studies on student learning after incorporating mathematics in to the science classroom have shown mixed results. Understanding the mixed effects of including mathematics in science has been hindered by a historical focus on characteristics of integration tangential to student learning (e.g., shared elements, extent of integration). A new framework is presented emphasizing the epistemic role of mathematics in science. An epistemic role of mathematics missing from the current literature is identified: use of mathematics to represent scientific mechanisms, Mechanism Connected Mathematics (MCM). Building on prior theoretical work, it is proposed that having students develop mathematical equations that represent scientific mechanisms could elevate their conceptual understanding and quantitative problem solving. Following design and implementation of an MCM unit in inheritance, a large-scale quantitative analysis of pre and post implementation test results showed MCM students, compared to traditionally instructed students) had significantly greater gains in conceptual understanding of mathematically modeled scientific mechanisms, and their ability to solve complex quantitative problems. To gain insight into the mechanism behind the gain in quantitative problem solving, a small-scale qualitative study was conducted of two contrasting groups: 1) within-MCM instruction: competent versus struggling problem solvers, and 2) within-competent problem solvers: MCM instructed versus traditionally instructed. Competent MCM students tended to connect their mathematical inscriptions to the scientific phenomenon and to switch between mathematical and scientifically productive approaches during problem solving in potentially productive ways. The other two groups did not. To address concerns about teacher capacity presenting barriers to scalability of MCM approaches, the types and amount of teacher support needed to achieve these types of student learning gains were investigated. In the context of providing teachers with access to educative materials, students achieved learning gains in both areas in the absence of face-to-face teacher professional development. However, maximal student learning gains required the investment of face-to-face professional development. This finding can govern distribution of scarce resources, but does not preclude implementation of MCM instruction even where resource availability does not allow for face-to-face professional development.

Epigenetics meets mathematics: towards a quantitative understanding of chromatin biology.

PubMed

Steffen, Philipp A; Fonseca, João P; Ringrose, Leonie

2012-10-01

How fast? How strong? How many? So what? Why do numbers matter in biology? Chromatin binding proteins are forever in motion, exchanging rapidly between bound and free pools. How do regulatory systems whose components are in constant flux ensure stability and flexibility? This review explores the application of quantitative and mathematical approaches to mechanisms of epigenetic regulation. We discuss methods for measuring kinetic parameters and protein quantities in living cells, and explore the insights that have been gained by quantifying and modelling dynamics of chromatin binding proteins. Copyright © 2012 WILEY Periodicals, Inc.

EPAs Virtual Embryo: Modeling Developmental Toxicity

EPA Science Inventory

Embryogenesis is regulated by concurrent activities of signaling pathways organized into networks that control spatial patterning, molecular clocks, morphogenetic rearrangements and cell differentiation. Quantitative mathematical and computational models are needed to better unde...

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

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

Advancement via Individual Determination: A Model for Equity in Secondary Mathematics

ERIC Educational Resources Information Center

Hodges, Cynthia D.

2013-01-01

This study examined the impact of Advancement Via Individual Determination (AVID) methodologies on the mathematics achievement of African American, European American, and Hispanic students as measured by the State of Texas Assessment of Academic Readiness (STAAR) End of Course (EOC) for Algebra I. This quantitative nonexperimental ex post facto…

The Characterization of Cognitive Processes Involved in Chemical Kinetics Using a Blended Processing Framework

ERIC Educational Resources Information Center

Bain, Kinsey; Rodriguez, Jon-Marc G.; Moon, Alena; Towns, Marcy H.

2018-01-01

Chemical kinetics is a highly quantitative content area that involves the use of multiple mathematical representations to model processes and is a context that is under-investigated in the literature. This qualitative study explored undergraduate student integration of chemistry and mathematics during problem solving in the context of chemical…

A Quantitative Analysis of Methods Used for Avoidance and Acceleration of Developmental Mathematics Sequences in Community College

ERIC Educational Resources Information Center

Travers, Steven T.

2017-01-01

Many developmental mathematics programs at community colleges in recent years have undergone a process of redesign in an attempt increase the historical poor rate of student successful completion of required developmental coursework. Various curriculum and instructional design models that incorporate methods of avoiding and accelerating the…

Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

PubMed

Dinç, Erdal; Ozdemir, Abdil

2005-01-01

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

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

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

PubMed

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

2010-01-01

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

A structural equation modeling analysis of students' understanding in basic mathematics

NASA Astrophysics Data System (ADS)

Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

2017-11-01

This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Fuzzy Performance between Surface Fitting and Energy Distribution in Turbulence Runner

PubMed Central

Liang, Zhongwei; Liu, Xiaochu; Ye, Bangyan; Brauwer, Richard Kars

2012-01-01

Because the application of surface fitting algorithms exerts a considerable fuzzy influence on the mathematical features of kinetic energy distribution, their relation mechanism in different external conditional parameters must be quantitatively analyzed. Through determining the kinetic energy value of each selected representative position coordinate point by calculating kinetic energy parameters, several typical algorithms of complicated surface fitting are applied for constructing microkinetic energy distribution surface models in the objective turbulence runner with those obtained kinetic energy values. On the base of calculating the newly proposed mathematical features, we construct fuzzy evaluation data sequence and present a new three-dimensional fuzzy quantitative evaluation method; then the value change tendencies of kinetic energy distribution surface features can be clearly quantified, and the fuzzy performance mechanism discipline between the performance results of surface fitting algorithms, the spatial features of turbulence kinetic energy distribution surface, and their respective environmental parameter conditions can be quantitatively analyzed in detail, which results in the acquirement of final conclusions concerning the inherent turbulence kinetic energy distribution performance mechanism and its mathematical relation. A further turbulence energy quantitative study can be ensured. PMID:23213287

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,…

The mathematics of movement

USGS Publications Warehouse

Johnson, D.H.

1999-01-01

Review of: Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants. Peter Turchin. 1998. Sinauer Associates, Sunderland, MA. 306 pages. $38.95 (paper).

A Transformative Model for Undergraduate Quantitative Biology Education

ERIC Educational Resources Information Center

Usher, David C.; Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The "BIO2010" report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3)…

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.

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

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

1995-01-01

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

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

DTIC Science & Technology

2016-05-11

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

Examination of Test and Item Statistics from Visual and Verbal Mathematics Questions

ERIC Educational Resources Information Center

Alpayar, Cagla; Gulleroglu, H. Deniz

2017-01-01

The aim of this research is to determine whether students' test performance and approaches to test questions change based on the type of mathematics questions (visual or verbal) administered to them. This research is based on a mixed-design model. The quantitative data are gathered from 297 seventh grade students, attending seven different middle…

Enhancing mathematics teachers' quality through Lesson Study.

PubMed

Lomibao, Laila S

2016-01-01

The efficiency and effectivity of the learning experience is dependent on the teacher quality, thus, enhancing teacher's quality is vital in improving the students learning outcome. Since, the usual top-down one-shot cascading model practice for teachers' professional development in Philippines has been observed to have much information dilution, and the Southeast Asian Ministers of Education Organization demanded the need to develop mathematics teachers' quality standards through the Southeast Asia Regional Standards for Mathematics Teachers (SEARS-MT), thus, an intensive, ongoing professional development model should be provided to teachers. This study was undertaken to determine the impact of Lesson Study on Bulua National High School mathematics teachers' quality level in terms of SEARS-MT dimensions. A mixed method of quantitative-qualitative research design was employed. Results of the analysis revealed that Lesson Study effectively enhanced mathematics teachers' quality and promoted teachers professional development. Teachers positively perceived Lesson Study to be beneficial for them to become a better mathematics teacher.

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

The use of mathematical models to inform influenza pandemic preparedness and response

PubMed Central

Wu, Joseph T; Cowling, Benjamin J

2011-01-01

Summary Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a real-time tool for pandemic control is currently limited by the lack of essential surveillance information such as serologic data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases. PMID:21727183

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

NASA Astrophysics Data System (ADS)

Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

PubMed Central

Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.

2015-01-01

Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372

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

PubMed

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

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

Quantitative Literacy: Geosciences and Beyond

NASA Astrophysics Data System (ADS)

Richardson, R. M.; McCallum, W. G.

2002-12-01

Quantitative literacy seems like such a natural for the geosciences, right? The field has gone from its origin as a largely descriptive discipline to one where it is hard to imagine failing to bring a full range of mathematical tools to the solution of geological problems. Although there are many definitions of quantitative literacy, we have proposed one that is analogous to the UNESCO definition of conventional literacy: "A quantitatively literate person is one who, with understanding, can both read and represent quantitative information arising in his or her everyday life." Central to this definition is the concept that a curriculum for quantitative literacy must go beyond the basic ability to "read and write" mathematics and develop conceptual understanding. It is also critical that a curriculum for quantitative literacy be engaged with a context, be it everyday life, humanities, geoscience or other sciences, business, engineering, or technology. Thus, our definition works both within and outside the sciences. What role do geoscience faculty have in helping students become quantitatively literate? Is it our role, or that of the mathematicians? How does quantitative literacy vary between different scientific and engineering fields? Or between science and nonscience fields? We will argue that successful quantitative literacy curricula must be an across-the-curriculum responsibility. We will share examples of how quantitative literacy can be developed within a geoscience curriculum, beginning with introductory classes for nonmajors (using the Mauna Loa CO2 data set) through graduate courses in inverse theory (using singular value decomposition). We will highlight six approaches to across-the curriculum efforts from national models: collaboration between mathematics and other faculty; gateway testing; intensive instructional support; workshops for nonmathematics faculty; quantitative reasoning requirement; and individual initiative by nonmathematics faculty.

Biological-Mathematical Modeling of Chronic Toxicity.

DTIC Science & Technology

1981-07-22

34Mathematical Model of Uptake and Distribution," Uptake and Distribution of Anesthetic Agents, E. M. Papper and R. J. Kitz (Editors, McGraw-Hill Book Co., Inc...distribution, In: Papper , E.M. and Kltz, R.J.(eds.) Uptake and distribution of anesthetic agents, McGraw- Hill, New York, p. 72 3. Plpleson, W.W...1963) Quantitative prediction of anesthetic concentrations. In: Papper , E.M. and Kitz, R.J. (eds.) Uptake and distribution of anesthetic agents, McGraw

The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

ERIC Educational Resources Information Center

Walters, Charles David

2017-01-01

Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008)…

Disaster metrics: quantitative benchmarking of hospital surge capacity in trauma-related multiple casualty events.

PubMed

Bayram, Jamil D; Zuabi, Shawki; Subbarao, Italo

2011-06-01

Hospital surge capacity in multiple casualty events (MCE) is the core of hospital medical response, and an integral part of the total medical capacity of the community affected. To date, however, there has been no consensus regarding the definition or quantification of hospital surge capacity. The first objective of this study was to quantitatively benchmark the various components of hospital surge capacity pertaining to the care of critically and moderately injured patients in trauma-related MCE. The second objective was to illustrate the applications of those quantitative parameters in local, regional, national, and international disaster planning; in the distribution of patients to various hospitals by prehospital medical services; and in the decision-making process for ambulance diversion. A 2-step approach was adopted in the methodology of this study. First, an extensive literature search was performed, followed by mathematical modeling. Quantitative studies on hospital surge capacity for trauma injuries were used as the framework for our model. The North Atlantic Treaty Organization triage categories (T1-T4) were used in the modeling process for simplicity purposes. Hospital Acute Care Surge Capacity (HACSC) was defined as the maximum number of critical (T1) and moderate (T2) casualties a hospital can adequately care for per hour, after recruiting all possible additional medical assets. HACSC was modeled to be equal to the number of emergency department beds (#EDB), divided by the emergency department time (EDT); HACSC = #EDB/EDT. In trauma-related MCE, the EDT was quantitatively benchmarked to be 2.5 (hours). Because most of the critical and moderate casualties arrive at hospitals within a 6-hour period requiring admission (by definition), the hospital bed surge capacity must match the HACSC at 6 hours to ensure coordinated care, and it was mathematically benchmarked to be 18% of the staffed hospital bed capacity. Defining and quantitatively benchmarking the different components of hospital surge capacity is vital to hospital preparedness in MCE. Prospective studies of our mathematical model are needed to verify its applicability, generalizability, and validity.

Introductory science and mathematics education for 21st-Century biologists.

PubMed

Bialek, William; Botstein, David

2004-02-06

Galileo wrote that "the book of nature is written in the language of mathematics"; his quantitative approach to understanding the natural world arguably marks the beginning of modern science. Nearly 400 years later, the fragmented teaching of science in our universities still leaves biology outside the quantitative and mathematical culture that has come to define the physical sciences and engineering. This strikes us as particularly inopportune at a time when opportunities for quantitative thinking about biological systems are exploding. We propose that a way out of this dilemma is a unified introductory science curriculum that fully incorporates mathematics and quantitative thinking.

An overview of quantitative approaches in Gestalt perception.

PubMed

Jäkel, Frank; Singh, Manish; Wichmann, Felix A; Herzog, Michael H

2016-09-01

Gestalt psychology is often criticized as lacking quantitative measurements and precise mathematical models. While this is true of the early Gestalt school, today there are many quantitative approaches in Gestalt perception and the special issue of Vision Research "Quantitative Approaches in Gestalt Perception" showcases the current state-of-the-art. In this article we give an overview of these current approaches. For example, ideal observer models are one of the standard quantitative tools in vision research and there is a clear trend to try and apply this tool to Gestalt perception and thereby integrate Gestalt perception into mainstream vision research. More generally, Bayesian models, long popular in other areas of vision research, are increasingly being employed to model perceptual grouping as well. Thus, although experimental and theoretical approaches to Gestalt perception remain quite diverse, we are hopeful that these quantitative trends will pave the way for a unified theory. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

On the feasibility of quantitative ultrasonic determination of fracture toughness: A literature review

NASA Technical Reports Server (NTRS)

Fu, L. S.

1980-01-01

The three main topics covered are: (1) fracture toughness and microstructure, (2) quantitative ultrasonic and microstructure; and (3) scattering and related mathematical methods. Literature in these areas is reviewed to give insight to the search of a theoretical foundation for quantitative ultrasonic measurement of fracture toughness. The literature review shows that fracture toughness is inherently related to the microstructure and in particular, it depends upon the spacing of inclusions or second particles and the aspect ratio of second phase particles. There are indications that ultrasonic velocity attenuation measurements can be used to determine fracture toughness. The leads to a review of the mathematical models available in solving boundary value problems related to microstructural factors that govern facture toughness and wave motion. A framework towards the theoretical study for the quantitative determination of fracture toughness is described and suggestions for future research are proposed.

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.

Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models

PubMed Central

Rejniak, Katarzyna A.; Gerlee, Philip

2013-01-01

Summary In this review we summarize our recent efforts using mathematical modeling and computation to simulate cancer invasion, with a special emphasis on the tumor microenvironment. We consider cancer progression as a complex multiscale process and approach it with three single-cell based mathematical models that examine the interactions between tumor microenvironment and cancer cells at several scales. The models exploit distinct mathematical and computational techniques, yet they share core elements and can be compared and/or related to each other. The overall aim of using mathematical models is to uncover the fundamental mechanisms that lend cancer progression its direction towards invasion and metastasis. The models effectively simulate various modes of cancer cell adaptation to the microenvironment in a growing tumor. All three point to a general mechanism underlying cancer invasion: competition for adaptation between distinct cancer cell phenotypes, driven by a tumor microenvironment with scarce resources. These theoretical predictions pose an intriguing experimental challenge: test the hypothesis that invasion is an emergent property of cancer cell populations adapting to selective microenvironment pressure, rather than culmination of cancer progression producing cells with the “invasive phenotype”. In broader terms, we propose that fundamental insights into cancer can be achieved by experimentation interacting with theoretical frameworks provided by computational and mathematical modeling. PMID:18524624

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.

Mathematical Ability of 10-Year-Old Boys and Girls: Genetic and Environmental Etiology of Typical and Low Performance

PubMed Central

Kovas, Yulia; Haworth, Claire M. A.; Petrill, Stephen A.; Plomin, Robert

2009-01-01

The genetic and environmental etiologies of 3 aspects of low mathematical performance (math disability) and the full range of variability (math ability) were compared for boys and girls in a sample of 5,348 children age 10 years (members of 2,674 pairs of same-sex and opposite-sex twins) from the United Kingdom (UK). The measures, which we developed for Web-based testing, included problems from 3 domains of mathematics taught as part of the UK National Curriculum. Using quantitative genetic model-fitting analyses, similar results were found for math disabilities and abilities for all 3 measures: Moderate genetic influence and environmental influence were mainly due to nonshared environmental factors that were unique to the individual, with little influence from shared environment. No sex differences were found in the etiologies of math abilities and disabilities. We conclude that low mathematical performance is the quantitative extreme of the same genetic and environmental factors responsible for variation throughout the distribution. PMID:18064980

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

A Bayesian explanation of the "Uncanny Valley" effect and related psychological phenomena

NASA Astrophysics Data System (ADS)

Moore, Roger K.

2012-11-01

There are a number of psychological phenomena in which dramatic emotional responses are evoked by seemingly innocuous perceptual stimuli. A well known example is the `uncanny valley' effect whereby a near human-looking artifact can trigger feelings of eeriness and repulsion. Although such phenomena are reasonably well documented, there is no quantitative explanation for the findings and no mathematical model that is capable of predicting such behavior. Here I show (using a Bayesian model of categorical perception) that differential perceptual distortion arising from stimuli containing conflicting cues can give rise to a perceptual tension at category boundaries that could account for these phenomena. The model is not only the first quantitative explanation of the uncanny valley effect, but it may also provide a mathematical explanation for a range of social situations in which conflicting cues give rise to negative, fearful or even violent reactions.

A Bayesian explanation of the ‘Uncanny Valley’ effect and related psychological phenomena

PubMed Central

Moore, Roger K.

2012-01-01

There are a number of psychological phenomena in which dramatic emotional responses are evoked by seemingly innocuous perceptual stimuli. A well known example is the ‘uncanny valley’ effect whereby a near human-looking artifact can trigger feelings of eeriness and repulsion. Although such phenomena are reasonably well documented, there is no quantitative explanation for the findings and no mathematical model that is capable of predicting such behavior. Here I show (using a Bayesian model of categorical perception) that differential perceptual distortion arising from stimuli containing conflicting cues can give rise to a perceptual tension at category boundaries that could account for these phenomena. The model is not only the first quantitative explanation of the uncanny valley effect, but it may also provide a mathematical explanation for a range of social situations in which conflicting cues give rise to negative, fearful or even violent reactions. PMID:23162690

The rising impact of mathematical modelling in epidemiology: antibiotic resistance research as a case study

PubMed Central

TEMIME, L.; HEJBLUM, G.; SETBON, M.; VALLERON, A. J.

2008-01-01

SUMMARY Mathematical modelling of infectious diseases has gradually become part of public health decision-making in recent years. However, the developing status of modelling in epidemiology and its relationship with other relevant scientific approaches have never been assessed quantitatively. Herein, using antibiotic resistance as a case study, 60 published models were analysed. Their interactions with other scientific fields are reported and their citation impact evaluated, as well as temporal trends. The yearly number of antibiotic resistance modelling publications increased significantly between 1990 and 2006. This rise cannot be explained by the surge of interest in resistance phenomena alone. Moreover, modelling articles are, on average, among the most frequently cited third of articles from the journal in which they were published. The results of this analysis, which might be applicable to other emerging public health problems, demonstrate the growing interest in mathematical modelling approaches to evaluate antibiotic resistance. PMID:17767792

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

An Evaluation into the Views of Candidate Mathematics Teachers over "Tablet Computers" to be Applied in Secondary Schools

ERIC Educational Resources Information Center

Aksu, Hasan Hüseyin

2014-01-01

This study aims to investigate, in terms of different variables, the views of prospective Mathematics teachers on tablet computers to be used in schools as an outcome of the Fatih Project, which was initiated by the Ministry of National Education. In the study, scanning model, one of the quantitative research methods, was used. In the population…

Differential equations with applications in cancer diseases.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Computational Toxicology (S)

EPA Science Inventory

The emerging field of computational toxicology applies mathematical and computer models and molecular biological and chemical approaches to explore both qualitative and quantitative relationships between sources of environmental pollutant exposure and adverse health outcomes. Th...

Computational model, method, and system for kinetically-tailoring multi-drug chemotherapy for individuals

DOEpatents

Gardner, Shea Nicole

2007-10-23

A method and system for tailoring treatment regimens to individual patients with diseased cells exhibiting evolution of resistance to such treatments. A mathematical model is provided which models rates of population change of proliferating and quiescent diseased cells using cell kinetics and evolution of resistance of the diseased cells, and pharmacokinetic and pharmacodynamic models. Cell kinetic parameters are obtained from an individual patient and applied to the mathematical model to solve for a plurality of treatment regimens, each having a quantitative efficacy value associated therewith. A treatment regimen may then be selected from the plurlaity of treatment options based on the efficacy value.

Data-based mathematical modeling of vectorial transport across double-transfected polarized cells.

PubMed

Bartholomé, Kilian; Rius, Maria; Letschert, Katrin; Keller, Daniela; Timmer, Jens; Keppler, Dietrich

2007-09-01

Vectorial transport of endogenous small molecules, toxins, and drugs across polarized epithelial cells contributes to their half-life in the organism and to detoxification. To study vectorial transport in a quantitative manner, an in vitro model was used that includes polarized MDCKII cells stably expressing the recombinant human uptake transporter OATP1B3 in their basolateral membrane and the recombinant ATP-driven efflux pump ABCC2 in their apical membrane. These double-transfected cells enabled mathematical modeling of the vectorial transport of the anionic prototype substance bromosulfophthalein (BSP) that has frequently been used to examine hepatobiliary transport. Time-dependent analyses of (3)H-labeled BSP in the basolateral, intracellular, and apical compartments of cells cultured on filter membranes and efflux experiments in cells preloaded with BSP were performed. A mathematical model was fitted to the experimental data. Data-based modeling was optimized by including endogenous transport processes in addition to the recombinant transport proteins. The predominant contributions to the overall vectorial transport of BSP were mediated by OATP1B3 (44%) and ABCC2 (28%). Model comparison predicted a previously unrecognized endogenous basolateral efflux process as a negative contribution to total vectorial transport, amounting to 19%, which is in line with the detection of the basolateral efflux pump Abcc4 in MDCKII cells. Rate-determining steps in the vectorial transport were identified by calculating control coefficients. Data-based mathematical modeling of vectorial transport of BSP as a model substance resulted in a quantitative description of this process and its components. The same systems biology approach may be applied to other cellular systems and to different substances.

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

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

Generalizability of New Standards Project, 1993 Pilot Study Tasks in Mathematics. Technical Issues in Procedures To Link State Results to a Common National Standard. Project 2.4 Quantitative Models To Monitor the Status and Progress of Learning and Performance and Their Antecedents.

ERIC Educational Resources Information Center

Linn, Robert L.

The New Standards Project conducted a pilot test of a series of performance-based assessment tasks in mathematics and English language arts at Grades 4 and 8 in the spring of 1993. This paper reports the results of a series of generalizability analyses conducted for a subset of the 1993 pilot study data in mathematics. Generalizability analyses…

Quantitative analysis of transverse bacterial migration induced by chemotaxis in a packed column with structured physical heterogeneity.

PubMed

Wang, Meng; Ford, Roseanne M

2010-01-15

A two-dimensional mathematical model was developed to simulate transport phenomena of chemotactic bacteria in a sand-packed column designed with structured physical heterogeneity in the presence of a localized chemical source. In contrast to mathematical models in previous research work, in which bacteria were typically treated as immobile colloids, this model incorporated a convective-like chemotaxis term to represent chemotactic migration. Consistency between experimental observation and model prediction supported the assertions that (1) dispersion-induced microbial transfer between adjacent conductive zones occurred at the interface and had little influence on bacterial transport in the bulk flow of the permeable layers and (2) the enhanced transverse bacterial migration in chemotactic experiments relative to nonchemotactic controls was mainly due to directed migration toward the chemical source zone. On the basis of parameter sensitivity analysis, chemotactic parameters determined in bulk aqueous fluid were adequate to predict the microbial transport in our intermediate-scale porous media system. Additionally, the analysis of adsorption coefficient values supported the observation of a previous study that microbial deposition to the surface of porous media might be decreased under the effect of chemoattractant gradients. By quantitatively describing bacterial transport and distribution in a heterogeneous system, this mathematical model serves to advance our understanding of chemotaxis and motility effects in granular media systems and provides insights for modeling microbial transport in in situ microbial processes.

A Biologically Constrained, Mathematical Model of Cortical Wave Propagation Preceding Seizure Termination

PubMed Central

González-Ramírez, Laura R.; Ahmed, Omar J.; Cash, Sydney S.; Wayne, C. Eugene; Kramer, Mark A.

2015-01-01

Epilepsy—the condition of recurrent, unprovoked seizures—manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination. PMID:25689136

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

PubMed

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

2012-01-01

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

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

PubMed Central

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

2012-01-01

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

Nonlinear-programming mathematical modeling of coal blending for power plant

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

Tang Longhua; Zhou Junhu; Yao Qiang

At present most of the blending works are guided by experience or linear-programming (LP) which can not reflect the coal complicated characteristics properly. Experimental and theoretical research work shows that most of the coal blend properties can not always be measured as a linear function of the properties of the individual coals in the blend. The authors introduced nonlinear functions or processes (including neural network and fuzzy mathematics), established on the experiments directed by the authors and other researchers, to quantitatively describe the complex coal blend parameters. Finally nonlinear-programming (NLP) mathematical modeling of coal blend is introduced and utilized inmore » the Hangzhou Coal Blending Center. Predictions based on the new method resulted in different results from the ones based on LP modeling. The authors concludes that it is very important to introduce NLP modeling, instead of NL modeling, into the work of coal blending.« less

The Role of Introductory Geosciences in Students' Quantitative Literacy

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Manduca, C.; Baer, E. M.

2006-12-01

Quantitative literacy is more than mathematics; it is about reasoning with data. Colleges and universities have begun to recognize the distinction between mathematics and quantitative literacy, modifying curricula to reflect the need for numerate citizens. Although students may view geology as 'rocks for jocks', the geosciences are truthfully rife with data, making introductory geoscience topics excellent context for developing the quantitative literacy of students with diverse backgrounds. In addition, many news items that deal with quantitative skills, such as the global warming phenomenon, have their basis in the Earth sciences and can serve as timely examples of the importance of quantitative literacy for all students in introductory geology classrooms. Participants at a workshop held in 2006, 'Infusing Quantitative Literacy into Introductory Geoscience Courses,' discussed and explored the challenges and opportunities associated with the inclusion of quantitative material and brainstormed about effective practices for imparting quantitative literacy to students with diverse backgrounds. The tangible results of this workshop add to the growing collection of quantitative materials available through the DLESE- and NSF-supported Teaching Quantitative Skills in the Geosciences website, housed at SERC. There, faculty can find a collection of pages devoted to the successful incorporation of quantitative literacy in introductory geoscience. The resources on the website are designed to help faculty to increase their comfort with presenting quantitative ideas to students with diverse mathematical abilities. A methods section on "Teaching Quantitative Literacy" (http://serc.carleton.edu/quantskills/methods/quantlit/index.html) focuses on connecting quantitative concepts with geoscience context and provides tips, trouble-shooting advice and examples of quantitative activities. The goal in this section is to provide faculty with material that can be readily incorporated into existing introductory geoscience courses. In addition, participants at the workshop (http://serc.carleton.edu/quantskills/workshop06/index.html) submitted and modified more than 20 activities and model courses (with syllabi) designed to use best practices for helping introductory geoscience students to become quantitatively literate. We present insights from the workshop and other sources for a framework that can aid in increasing quantitative literacy of students from a variety of backgrounds in the introductory geoscience classroom.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Mathematical modeling of efficacy and safety for anticancer drugs clinical development.

PubMed

Lavezzi, Silvia Maria; Borella, Elisa; Carrara, Letizia; De Nicolao, Giuseppe; Magni, Paolo; Poggesi, Italo

2018-01-01

Drug attrition in oncology clinical development is higher than in other therapeutic areas. In this context, pharmacometric modeling represents a useful tool to explore drug efficacy in earlier phases of clinical development, anticipating overall survival using quantitative model-based metrics. Furthermore, modeling approaches can be used to characterize earlier the safety and tolerability profile of drug candidates, and, thus, the risk-benefit ratio and the therapeutic index, supporting the design of optimal treatment regimens and accelerating the whole process of clinical drug development. Areas covered: Herein, the most relevant mathematical models used in clinical anticancer drug development during the last decade are described. Less recent models were considered in the review if they represent a standard for the analysis of certain types of efficacy or safety measures. Expert opinion: Several mathematical models have been proposed to predict overall survival from earlier endpoints and validate their surrogacy in demonstrating drug efficacy in place of overall survival. An increasing number of mathematical models have also been developed to describe the safety findings. Modeling has been extensively used in anticancer drug development to individualize dosing strategies based on patient characteristics, and design optimal dosing regimens balancing efficacy and safety.

DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

NASA Technical Reports Server (NTRS)

Hester, Robert L.; Summers, Richard L.; lIescu, Radu; Esters, Joyee; Coleman, Thomas G.

2010-01-01

Mathematical models and simulation are important tools in discovering the key causal relationships governing physiological processes and improving medical intervention when physiological complexity is a central issue. We have developed a model of integrative human physiology called DigitalHuman (DH) consisting of -5000 variables modeling human physiology describing cardiovascular, renal, respiratory, endocrine, neural and metabolic physiology. Users can view time-dependent solutions and interactively introduce perturbations by altering numerical parameters to investigate new hypotheses. The variables, parameters and quantitative relationships as well as all other model details are described in XML text files. All aspects of the model, including the mathematical equations describing the physiological processes are written in XML open source, text-readable files. Model structure is based upon empirical data of physiological responses documented within the peer-reviewed literature. The model can be used to understand proposed physiological mechanisms and physiological interactions that may not be otherwise intUitively evident. Some of the current uses of this model include the analyses of renal control of blood pressure, the central role of the liver in creating and maintaining insulin resistance, and the mechanisms causing orthostatic hypotension in astronauts. Additionally the open source aspect of the modeling environment allows any investigator to add detailed descriptions of human physiology to test new concepts. The model accurately predicts both qualitative and more importantly quantitative changes in clinically and experimentally observed responses. DigitalHuman provides scientists a modeling environment to understand the complex interactions of integrative physiology. This research was supported by.NIH HL 51971, NSF EPSCoR, and NASA

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Mathematical modeling and numerical simulation of the mitotic spindle orientation system.

PubMed

Ibrahim, Bashar

2018-05-21

The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division. Copyright © 2018. Published by Elsevier Inc.

"Standards"-Based Mathematics Curricula and the Promotion of Quantitative Literacy in Elementary School

ERIC Educational Resources Information Center

Wilkins, Jesse L. M.

2015-01-01

Background: Prior research has shown that students taught using "Standards"-based mathematics curricula tend to outperform students on measures of mathematics achievement. However, little research has focused particularly on the promotion of student quantitative literacy (QLT). In this study, the potential influence of the…

Why physics needs mathematics

NASA Astrophysics Data System (ADS)

Rohrlich, Fritz

2011-12-01

Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.

Prospective Middle-School Mathematics Teachers' Quantitative Reasoning and Their Support for Students' Quantitative Reasoning

ERIC Educational Resources Information Center

Kabael, Tangul; Akin, Ayca

2018-01-01

The aim of this research is to examine prospective mathematics teachers' quantitative reasoning, their support for students' quantitative reasoning and the relationship between them, if any. The teaching experiment was used as the research method in this qualitatively designed study. The data of the study were collected through a series of…

Structural equation modeling assessing relationship between mathematics beliefs, teachers' attitudes and teaching practices among novice teachers in Malaysia

NASA Astrophysics Data System (ADS)

Borhan, Noziati; Zakaria, Effandi

2017-05-01

This quantitative study was conducted to investigate the perception level of novice teachers about mathematics belief, teachers' attitude towards mathematics and teaching practices of mathematics in the classroom. In addition, it also aims to identify whether there is a correspondence model with the data obtained and to identify the relationship between the variables of beliefs, attitudes and practices among novice teachers in Malaysia. A total of 263 primary novice teachers throughout the country were involved in this study were selected randomly. Respondents are required to provide a response to the questionnaire of 66 items related to mathematics beliefs, attitudes and practices of the teaching mathematics. There are ten sub-factors which have been established in this instrument for three major constructs using a Likert scale rating of five points. The items of the constructs undergo the exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) procedure involve of unidimensionality test, convergent validity, construct validity and discriminant validity. Descriptive statistics were used to describe the frequency, percentage, the mean and standard deviation for completing some research questions that have been expressed. As for inferential statistical analysis, the researchers used structural equation modeling (SEM) to answer the question of correspondents model and the relationship between these three variables. The results of the study were found that there exist a correspondence measurement and structural model with the data obtained. While the relationship between variable found that mathematics beliefs have a significant influence on teachers' attitudes towards mathematics as well as the relationship between the attitudes with teaching practices. Meanwhile, mathematics belief had no significant relationship with mathematics teaching practices among novice teachers in Malaysia.

A Multidimensional Model for the Identification of Dual-Exceptional Learners

ERIC Educational Resources Information Center

Al-Hroub, Anies

2013-01-01

This research takes mathematics as a model for investigating the definitions, identification, classification and characteristics of a group of gifted student related to the notion of "dual-exceptionality". An extensive process using qualitative and quantitative methods was conducted by a multidisciplinary team to develop and implement a…

Mathematics Prerequisites for Introductory Geoscience Courses: Using Technology to Help Solve the Problem

NASA Astrophysics Data System (ADS)

Burn, H. E.; Wenner, J. M.; Baer, E. M.

2011-12-01

The quantitative components of introductory geoscience courses can pose significant barriers to students. Many academic departments respond by stripping courses of their quantitative components or by attaching prerequisite mathematics courses [PMC]. PMCs cause students to incur additional costs and credits and may deter enrollment in introductory courses; yet, stripping quantitative content from geoscience courses masks the data-rich, quantitative nature of geoscience. Furthermore, the diversity of math skills required in geoscience and students' difficulty with transferring mathematical knowledge across domains suggest that PMCs may be ineffective. Instead, this study explores an alternative strategy -- to remediate students' mathematical skills using online modules that provide students with opportunities to build contextual quantitative reasoning skills. The Math You Need, When You Need It [TMYN] is a set of modular online student resources that address mathematical concepts in the context of the geosciences. TMYN modules are online resources that employ a "just-in-time" approach - giving students access to skills and then immediately providing opportunities to apply them. Each module places the mathematical concept in multiple geoscience contexts. Such an approach illustrates the immediate application of a principle and provides repeated exposure to a mathematical skill, enhancing long-term retention. At the same time, placing mathematics directly in several geoscience contexts better promotes transfer of learning by using similar discourse (words, tools, representations) and context that students will encounter when applying mathematics in the future. This study uses quantitative and qualitative data to explore the effectiveness of TMYN modules in remediating students' mathematical skills. Quantitative data derive from ten geoscience courses that used TMYN modules during the fall 2010 and spring 2011 semesters; none of the courses had a PMC. In all courses, students completed a pretest, the assigned modules, and a posttest. Success in remediation was measured using normalized gain scores, which measures the change in score divided by the maximum possible increase: (posttest-pretest)/(1-pretest). To compare across courses, normalized gain scores were standardized. Additional analysis included disaggregating normalized gain scores by quartiles based on pretest scores. The results were supplemented by qualitative data from faculty interviews and information provided by faculty on a web form upon completion of the course. Results suggest TMYN modules remediate mathematical skills effectively, and that normalized gains tend to be higher for students in the lower quartiles on the pretest. Students indicate finding the modules helpful, though sometimes difficult. Faculty interview data triangulate these findings and provide further evidence that online, modularized remediation is an effective alternative to assigning prerequisite mathematical courses to remediate mathematical skills.

Quantitative structure-property relationship (correlation analysis) of phosphonic acid-based chelates in design of MRI contrast agent.

PubMed

Tiwari, Anjani K; Ojha, Himanshu; Kaul, Ankur; Dutta, Anupama; Srivastava, Pooja; Shukla, Gauri; Srivastava, Rakesh; Mishra, Anil K

2009-07-01

Nuclear magnetic resonance imaging is a very useful tool in modern medical diagnostics, especially when gadolinium (III)-based contrast agents are administered to the patient with the aim of increasing the image contrast between normal and diseased tissues. With the use of soft modelling techniques such as quantitative structure-activity relationship/quantitative structure-property relationship after a suitable description of their molecular structure, we have studied a series of phosphonic acid for designing new MRI contrast agent. Quantitative structure-property relationship studies with multiple linear regression analysis were applied to find correlation between different calculated molecular descriptors of the phosphonic acid-based chelating agent and their stability constants. The final quantitative structure-property relationship mathematical models were found as--quantitative structure-property relationship Model for phosphonic acid series (Model 1)--log K(ML) = {5.00243(+/-0.7102)}- MR {0.0263(+/-0.540)}n = 12 l r l = 0.942 s = 0.183 F = 99.165 quantitative structure-property relationship Model for phosphonic acid series (Model 2)--log K(ML) = {5.06280(+/-0.3418)}- MR {0.0252(+/- .198)}n = 12 l r l = 0.956 s = 0.186 F = 99.256.

Thermodynamic investigation of the interaction between cyclodextrins and preservatives - Application and verification in a mathematical model to determine the needed preservative surplus in aqueous cyclodextrin formulations.

PubMed

Holm, René; Olesen, Niels Erik; Alexandersen, Signe Dalgaard; Dahlgaard, Birgitte N; Westh, Peter; Mu, Huiling

2016-05-25

Preservatives are inactivated when added to conserve aqueous cyclodextrin (CD) formulations due to complex formation between CDs and the preservative. To maintain the desired conservation effect the preservative needs to be added in apparent surplus to account for this inactivation. The purpose of the present work was to establish a mathematical model, which defines this surplus based upon knowledge of stability constants and the minimal concentration of preservation to inhibit bacterial growth. The stability constants of benzoic acid, methyl- and propyl-paraben with different frequently used βCDs were determined by isothermal titration calorimetry. Based upon this knowledge mathematical models were constructed to account for the equilibrium systems and to calculate the required concentration of the preservations, which was evaluated experimentally based upon the USP/Ph. Eur./JP monograph. The mathematical calculations were able to predict the needed concentration of preservation in the presence of CDs; it clearly demonstrated the usefulness of including all underlying chemical equilibria in a mathematical model, such that the formulation design can be based on quantitative arguments. Copyright © 2015 Elsevier B.V. All rights reserved.

Sifting noisy data for truths about noisy systems. Comment on "Extracting physics of life at the molecular level: A review of single-molecule data analyses" by W. Colomb and S.K. Sarkar

NASA Astrophysics Data System (ADS)

Flyvbjerg, Henrik; Mortensen, Kim I.

2015-06-01

With each new aspect of nature that becomes accessible to quantitative science, new needs arise for data analysis and mathematical modeling. The classical example is Tycho Brahe's accurate and comprehensive observations of planets, which made him hire Kepler for his mathematical skills to assist with the data analysis. We all learned what that lead to: Kepler's three laws of planetary motion, phenomenology in purely mathematical form. Newton built on this, and the scientific revolution was over, completed.

Toxicity Estimation Software Tool (TEST)

EPA Science Inventory

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

Playful Physics

NASA Technical Reports Server (NTRS)

Weaver, David

2008-01-01

Effectively communicate qualitative and quantitative information orally and in writing. Explain the application of fundamental physical principles to various physical phenomena. Apply appropriate problem-solving techniques to practical and meaningful problems using graphical, mathematical, and written modeling tools. Work effectively in collaborative groups.

Quantitative Finance

NASA Astrophysics Data System (ADS)

James, Jessica

2017-01-01

Quantitative finance is a field that has risen to prominence over the last few decades. It encompasses the complex models and calculations that value financial contracts, particularly those which reference events in the future, and apply probabilities to these events. While adding greatly to the flexibility of the market available to corporations and investors, it has also been blamed for worsening the impact of financial crises. But what exactly does quantitative finance encompass, and where did these ideas and models originate? We show that the mathematics behind finance and behind games of chance have tracked each other closely over the centuries and that many well-known physicists and mathematicians have contributed to the field.

Mathematic modeling the relationship of bacteria number in a dairy product and the color difference measured by a CCD image sensor

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Zhao, Zhigang; Chen, Dongkui; Liu, Yuping

2005-01-01

Although many methods, such as bacteria plate count, flow cytometry and impedance method have been broadly used in the dairy industry to quantitate bacteria numbers around the world, none of them is a quick, low cost and easy one. In this study, we proposed to apply the color difference theory in this field to establish a mathematic model to quantitate bacteria number in fresh milk. Preliminary testing results not only indicate that the application of the color difference theory to the new system is practical, but also confirm the theoretical relationship between the numbers of bacteria, incubation time and color difference. The proof of the principal study in this article further suggests that the novel method has the potential to replace the traditional methods to determine bacteria numbers for the food industry.

Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

PubMed

Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

2018-03-01

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

Grass Grows, the Cow Eats: A Simple Grazing Systems Model with Emergent Properties

ERIC Educational Resources Information Center

Ungar, Eugene David; Seligman, Noam G.; Noy-Meir, Imanuel

2004-01-01

We describe a simple, yet intellectually challenging model of grazing systems that introduces basic concepts in ecology and systems analysis. The practical is suitable for high-school and university curricula with a quantitative orientation, and requires only basic skills in mathematics and spreadsheet use. The model is based on Noy-Meir's (1975)…

Quantitative dual-probe microdialysis: mathematical model and analysis.

PubMed

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

2002-04-01

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

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

A Quantitative Model of Early Atherosclerotic Plaques Parameterized Using In Vitro Experiments.

PubMed

Thon, Moritz P; Ford, Hugh Z; Gee, Michael W; Myerscough, Mary R

2018-01-01

There are a growing number of studies that model immunological processes in the artery wall that lead to the development of atherosclerotic plaques. However, few of these models use parameters that are obtained from experimental data even though data-driven models are vital if mathematical models are to become clinically relevant. We present the development and analysis of a quantitative mathematical model for the coupled inflammatory, lipid and macrophage dynamics in early atherosclerotic plaques. Our modeling approach is similar to the biologists' experimental approach where the bigger picture of atherosclerosis is put together from many smaller observations and findings from in vitro experiments. We first develop a series of three simpler submodels which are least-squares fitted to various in vitro experimental results from the literature. Subsequently, we use these three submodels to construct a quantitative model of the development of early atherosclerotic plaques. We perform a local sensitivity analysis of the model with respect to its parameters that identifies critical parameters and processes. Further, we present a systematic analysis of the long-term outcome of the model which produces a characterization of the stability of model plaques based on the rates of recruitment of low-density lipoproteins, high-density lipoproteins and macrophages. The analysis of the model suggests that further experimental work quantifying the different fates of macrophages as a function of cholesterol load and the balance between free cholesterol and cholesterol ester inside macrophages may give valuable insight into long-term atherosclerotic plaque outcomes. This model is an important step toward models applicable in a clinical setting.

Exposure Science and the US EPA National Center for Computational Toxicology

EPA Science Inventory

The emerging field of computational toxicology applies mathematical and computer models and molecular biological and chemical approaches to explore both qualitative and quantitative relationships between sources of environmental pollutant exposure and adverse health outcomes. The...

Introductory life science mathematics and quantitative neuroscience courses.

PubMed

Duffus, Dwight; Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses.

The Abstract Selection Task: New Data and an Almost Comprehensive Model

ERIC Educational Resources Information Center

Klauer, Karl Christoph; Stahl, Christoph; Erdfelder, Edgar

2007-01-01

A complete quantitative account of P. Wason's (1966) abstract selection task is proposed. The account takes the form of a mathematical model. It is assumed that some response patterns are caused by inferential reasoning, whereas other responses reflect cognitive processes that affect each card selection separately and independently of other card…

Development of a Model for Some Aspects of University Policy. Technical Report.

ERIC Educational Resources Information Center

Goossens, J. L. M.; And Others

A method to calculate the need for academic staff per faculty, based on educational programs and numbers of students, is described which is based on quantitative relations between programs, student enrollment, and total budget. The model is described schematically and presented in a mathematical form adapted to computer processing. Its application…

QUANTITATIVE STRUCTURE—PROPERTY RELATIONSHIPS FOR ENHANCING PREDICTIONS OF SYNTHETIC ORGANIC CHEMICAL REMOVAL FROM DRINKING WATER BY GRANULAR ACTIVATED CARBON

EPA Science Inventory

A number of mathematical models have been developed to predict activated carbon column performance using single-solute isotherm data as inputs. Many assumptions are built into these models to account for kinetics of adsorption and competition for adsorption sites. This work...

Effectiveness of a Corequisite Delivery Model for Developmental Mathematics

ERIC Educational Resources Information Center

Fair, Katherine Eileen

2017-01-01

The purpose of this quantitative quasi-experimental study is to determine the effectiveness of a corequisite delivery model for developmental math students at a 4-year public institution. Nationally, close to fifty percent of incoming college students are placed in non-credit bearing remedial courses (Complete College America, 2012). Students must…

Logic integer programming models for signaling networks.

PubMed

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

2009-05-01

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

Computer simulation of the metastatic progression.

PubMed

Wedemann, Gero; Bethge, Anja; Haustein, Volker; Schumacher, Udo

2014-01-01

A novel computer model based on a discrete event simulation procedure describes quantitatively the processes underlying the metastatic cascade. Analytical functions describe the size of the primary tumor and the metastases, while a rate function models the intravasation events of the primary tumor and metastases. Events describe the behavior of the malignant cells until the formation of new metastases. The results of the computer simulations are in quantitative agreement with clinical data determined from a patient with hepatocellular carcinoma in the liver. The model provides a more detailed view on the process than a conventional mathematical model. In particular, the implications of interventions on metastasis formation can be calculated.

Complexity-aware simple modeling.

PubMed

Gómez-Schiavon, Mariana; El-Samad, Hana

2018-02-26

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches. Copyright © 2018 Elsevier Ltd. All rights reserved.

Modelling the effect of structural QSAR parameters on skin penetration using genetic programming

NASA Astrophysics Data System (ADS)

Chung, K. K.; Do, D. Q.

2010-09-01

In order to model relationships between chemical structures and biological effects in quantitative structure-activity relationship (QSAR) data, an alternative technique of artificial intelligence computing—genetic programming (GP)—was investigated and compared to the traditional method—statistical. GP, with the primary advantage of generating mathematical equations, was employed to model QSAR data and to define the most important molecular descriptions in QSAR data. The models predicted by GP agreed with the statistical results, and the most predictive models of GP were significantly improved when compared to the statistical models using ANOVA. Recently, artificial intelligence techniques have been applied widely to analyse QSAR data. With the capability of generating mathematical equations, GP can be considered as an effective and efficient method for modelling QSAR data.

The Quantitative Preparation of Future Geoscience Graduate Students

NASA Astrophysics Data System (ADS)

Manduca, C. A.; Hancock, G. S.

2006-12-01

Modern geoscience is a highly quantitative science. In February, a small group of faculty and graduate students from across the country met to discuss the quantitative preparation of geoscience majors for graduate school. The group included ten faculty supervising graduate students in quantitative areas spanning the earth, atmosphere, and ocean sciences; five current graduate students in these areas; and five faculty teaching undergraduate students in the spectrum of institutions preparing students for graduate work. Discussion focused in four key ares: Are incoming graduate students adequately prepared for the quantitative aspects of graduate geoscience programs? What are the essential quantitative skills are that are required for success in graduate school? What are perceived as the important courses to prepare students for the quantitative aspects of graduate school? What programs/resources would be valuable in helping faculty/departments improve the quantitative preparation of students? The participants concluded that strengthening the quantitative preparation of undergraduate geoscience majors would increase their opportunities in graduate school. While specifics differed amongst disciplines, a special importance was placed on developing the ability to use quantitative skills to solve geoscience problems. This requires the ability to pose problems so they can be addressed quantitatively, understand the relationship between quantitative concepts and physical representations, visualize mathematics, test the reasonableness of quantitative results, creatively move forward from existing models/techniques/approaches, and move between quantitative and verbal descriptions. A list of important quantitative competencies desirable in incoming graduate students includes mechanical skills in basic mathematics, functions, multi-variate analysis, statistics and calculus, as well as skills in logical analysis and the ability to learn independently in quantitative ways. Calculus, calculus-based physics, chemistry, statistics, programming and linear algebra were viewed as important course preparation for a successful graduate experience. A set of recommendations for departments and for new community resources includes ideas for infusing quantitative reasoning throughout the undergraduate experience and mechanisms for learning from successful experiments in both geoscience and mathematics. A full list of participants, summaries of the meeting discussion and recommendations are available at http://serc.carleton.edu/quantskills/winter06/index.html. These documents, crafted by a small but diverse group can serve as a starting point for broader community discussion of the quantitative preparation of future geoscience graduate students.

Mathematical model of a DIC position sensing system within an optical trap

NASA Astrophysics Data System (ADS)

Wulff, Kurt D.; Cole, Daniel G.; Clark, Robert L.

2005-08-01

The quantitative study of displacements and forces of motor proteins and processes that occur at the microscopic level and below require a high level of sensitivity. For optical traps, two techniques for position sensing have been accepted and used quite extensively: quadrant photodiodes and an interferometric position sensing technique based on DIC imaging. While quadrant photodiodes have been studied in depth and mathematically characterized, a mathematical characterization of the interferometric position sensor has not been presented to the authors' knowledge. The interferometric position sensing method works off of the DIC imaging capabilities of a microscope. Circularly polarized light is sent into the microscope and the Wollaston prism used for DIC imaging splits the beam into its orthogonal components, displacing them by a set distance determined by the user. The distance between the axes of the beams is set so the beams overlap at the specimen plane and effectively share the trapped microsphere. A second prism then recombines the light beams and the exiting laser light's polarization is measured and related to position. In this paper we outline the mathematical characterization of a microsphere suspended in an optical trap using a DIC position sensing method. The sensitivity of this mathematical model is then compared to the QPD model. The mathematical model of a microsphere in an optical trap can serve as a calibration curve for an experimental setup.

Gender Equity in Mathematics: Beliefs of Students, Parents, and Teachers

ERIC Educational Resources Information Center

Leedy, M. Gail; LaLonde, Donna; Runk, Kristen

2003-01-01

The attitudes about mathematics held by girls and boys participating in a regional mathematics contest, their parents, teachers, and mathematics coaches were investigated. Quantitative data regarding mathematics as a male domain, perception of importance of mathematics, confidence in learning mathematics, effectance motivation, and usefulness of…

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.

On the Edge of Mathematics and Biology Integration: Improving Quantitative Skills in Undergraduate Biology Education

ERIC Educational Resources Information Center

Feser, Jason; Vasaly, Helen; Herrera, Jose

2013-01-01

In this paper, the authors describe how two institutions are helping their undergraduate biology students build quantitative competencies. Incorporation of quantitative skills and reasoning in biology are framed through a discussion of two cases that both concern introductory biology courses, but differ in the complexity of the mathematics and the…

Introductory Life Science Mathematics and Quantitative Neuroscience Courses

PubMed Central

Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses. PMID:20810971

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2016-04-01

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

Analysis of critical thinking ability of VII grade students based on the mathematical anxiety level through learning cycle 7E model

NASA Astrophysics Data System (ADS)

Widyaningsih, E.; Waluya, S. B.; Kurniasih, A. W.

2018-03-01

This study aims to know mastery learning of students’ critical thinking ability with learning cycle 7E, determine whether the critical thinking ability of the students with learning cycle 7E is better than students’ critical thinking ability with expository model, and describe the students’ critical thinking phases based on the mathematical anxiety level. The method is mixed method with concurrent embedded. The population is VII grade students of SMP Negeri 3 Kebumen academic year 2016/2017. Subjects are determined by purposive sampling, selected two students from each level of mathematical anxiety. Data collection techniques include test, questionnaire, interview, and documentation. Quantitative data analysis techniques include mean test, proportion test, difference test of two means, difference test of two proportions and for qualitative data used Miles and Huberman model. The results show that: (1) students’ critical thinking ability with learning cycle 7E achieve mastery learning; (2) students’ critical thinking ability with learning cycle 7E is better than students’ critical thinking ability with expository model; (3) description of students’ critical thinking phases based on the mathematical anxiety level that is the lower the mathematical anxiety level, the subjects have been able to fulfil all of the indicators of clarification, assessment, inference, and strategies phases.

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.

Quantitative Analysis of the Interdisciplinarity of Applied Mathematics.

PubMed

Xie, Zheng; Duan, Xiaojun; Ouyang, Zhenzheng; Zhang, Pengyuan

2015-01-01

The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999-2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.

The mathematics of a successful deconvolution: a quantitative assessment of mixture-based combinatorial libraries screened against two formylpeptide receptors.

PubMed

Santos, Radleigh G; Appel, Jon R; Giulianotti, Marc A; Edwards, Bruce S; Sklar, Larry A; Houghten, Richard A; Pinilla, Clemencia

2013-05-30

In the past 20 years, synthetic combinatorial methods have fundamentally advanced the ability to synthesize and screen large numbers of compounds for drug discovery and basic research. Mixture-based libraries and positional scanning deconvolution combine two approaches for the rapid identification of specific scaffolds and active ligands. Here we present a quantitative assessment of the screening of 32 positional scanning libraries in the identification of highly specific and selective ligands for two formylpeptide receptors. We also compare and contrast two mixture-based library approaches using a mathematical model to facilitate the selection of active scaffolds and libraries to be pursued for further evaluation. The flexibility demonstrated in the differently formatted mixture-based libraries allows for their screening in a wide range of assays.

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

PubMed

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

2011-10-04

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

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

PubMed

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

2012-02-28

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

Partial differential equation models in the socio-economic sciences.

PubMed

Burger, Martin; Caffarelli, Luis; Markowich, Peter A

2014-11-13

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

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

Model of Market Share Affected by Social Media Reputation

NASA Astrophysics Data System (ADS)

Ishii, Akira; Kawahata, Yasuko; Goto, Ujo

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

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.

Analysis and Management of Animal Populations: Modeling, Estimation and Decision Making

USGS Publications Warehouse

Williams, B.K.; Nichols, J.D.; Conroy, M.J.

2002-01-01

This book deals with the processes involved in making informed decisions about the management of animal populations. It covers the modeling of population responses to management actions, the estimation of quantities needed in the modeling effort, and the application of these estimates and models to the development of sound management decisions. The book synthesizes and integrates in a single volume the methods associated with these themes, as they apply to ecological assessment and conservation of animal populations. KEY FEATURES * Integrates population modeling, parameter estimation and * decision-theoretic approaches to management in a single, cohesive framework * Provides authoritative, state-of-the-art descriptions of quantitative * approaches to modeling, estimation and decision-making * Emphasizes the role of mathematical modeling in the conduct of science * and management * Utilizes a unifying biological context, consistent mathematical notation, * and numerous biological examples

The Sampling Issues in Quantitative Research

ERIC Educational Resources Information Center

Delice, Ali

2010-01-01

A concern for generalization dominates quantitative research. For generalizability and repeatability, identification of sample size is essential. The present study investigates 90 qualitative master's theses submitted for the Primary and Secondary School Science and Mathematics Education Departments, Mathematic Education Discipline in 10…

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

PubMed

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

2014-06-01

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

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

THE APPLICATION OF CYBERNETICS IN PEDAGOGY.

ERIC Educational Resources Information Center

ATUTOV, P.R.

THE APPLICATION OF CYBERNETICS TO PEDAGOGY CAN CREATE A PRECISE SCIENCE OF INSTRUCTION AND EDUCATION THROUGH THE TIME-CONSUMING BUT INEVITABLE TRANSITION FROM IDENTIFICATION OF QUALITATIVE RELATIONSHIPS AMONG PEDAGOGICAL OBJECTS TO QUANTITATIVE ANALYSIS OF THESE OBJECTS. THE THEORETICAL UTILITY OF MATHEMATICAL MODELS AND FORMULAE FOR EXPLANATORY…

Dynamic Resource Allocation in Conservation Planning

DTIC Science & Technology

2011-08-01

0932392 and IIS-0953413, the Caltech Center for the Mathematics of Information, and by the US Fish and Wildlife Service. We thank J. Bakker, J. Bush ...Moilanen, A.; Pakkala, T.; and Kuussaari, M. 1996. The quantitative incidence function model and persistence of an endangered butterfly metapopulation

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-01-01

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

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor.

PubMed

Xiu, G H; Jiang, L; Li, P

2001-07-05

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor. Copyright 2001 John Wiley & Sons, Inc.

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

PubMed

Schaid, Daniel J

2010-01-01

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

Are Universities Providing Non-STEM Students the Mathematics Preparation Required by Their Programs?: A Case Study of A Quantitative Literacy Pathway and Vertical Alignment from Remediation to Degree Completion

ERIC Educational Resources Information Center

Allen, Charles

2017-01-01

Informed by Gagne's belief in the necessity of prerequisite knowledge for new learning, and Bruner's Spiral Curriculum Theory, the objective of this case study was to explore the postsecondary pathway from remedial mathematics, through one gateway mathematics course, and into the quantitative literacy requirements of various non-STEM programs of…

Assessing crown fire potential by linking models of surface and crown fire behavior

Treesearch

Joe H. Scott; Elizabeth D. Reinhardt

2001-01-01

Fire managers are increasingly concerned about the threat of crown fires, yet only now are quantitative methods for assessing crown fire hazard being developed. Links among existing mathematical models of fire behavior are used to develop two indices of crown fire hazard-the Torching Index and Crowning Index. These indices can be used to ordinate different forest...

Mathematical Modeling in Support of Military Operational Medicine

DTIC Science & Technology

2006-07-01

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

Parents' Attitudes toward Mathematics and the Influence on Their Students' Attitudes toward Mathematics: A Quantitative Study

ERIC Educational Resources Information Center

Mohr-Schroeder, Margaret J.; Jackson, Christa; Cavalcanti, Maureen; Jong, Cindy; Schroeder, D. Craig; Speler, Lydia G.

2017-01-01

The purpose of this study was to investigate parents' attitudes toward mathematics, their students' attitude toward mathematics, and the influence of the parents' attitude on the students' attitude toward mathematics. Data analyses revealed statistically significant positive correlations between parents' and students' attitudes toward mathematics.…

A Checklist for Successful Quantitative Live Cell Imaging in Systems Biology

PubMed Central

Sung, Myong-Hee

2013-01-01

Mathematical modeling of signaling and gene regulatory networks has provided unique insights about systems behaviors for many cell biological problems of medical importance. Quantitative single cell monitoring has a crucial role in advancing systems modeling of molecular networks. However, due to the multidisciplinary techniques that are necessary for adaptation of such systems biology approaches, dissemination to a wide research community has been relatively slow. In this essay, I focus on some technical aspects that are often under-appreciated, yet critical in harnessing live cell imaging methods to achieve single-cell-level understanding and quantitative modeling of molecular networks. The importance of these technical considerations will be elaborated with examples of successes and shortcomings. Future efforts will benefit by avoiding some pitfalls and by utilizing the lessons collectively learned from recent applications of imaging in systems biology. PMID:24709701

The Mathematics of a Successful Deconvolution: A Quantitative Assessment of Mixture-Based Combinatorial Libraries Screened Against Two Formylpeptide Receptors

PubMed Central

Santos, Radleigh G.; Appel, Jon R.; Giulianotti, Marc A.; Edwards, Bruce S.; Sklar, Larry A.; Houghten, Richard A.; Pinilla, Clemencia

2014-01-01

In the past 20 years, synthetic combinatorial methods have fundamentally advanced the ability to synthesize and screen large numbers of compounds for drug discovery and basic research. Mixture-based libraries and positional scanning deconvolution combine two approaches for the rapid identification of specific scaffolds and active ligands. Here we present a quantitative assessment of the screening of 32 positional scanning libraries in the identification of highly specific and selective ligands for two formylpeptide receptors. We also compare and contrast two mixture-based library approaches using a mathematical model to facilitate the selection of active scaffolds and libraries to be pursued for further evaluation. The flexibility demonstrated in the differently formatted mixture-based libraries allows for their screening in a wide range of assays. PMID:23722730

Prospective elementary teachers' perceptions of the processes of modeling: A case study

NASA Astrophysics Data System (ADS)

Fazio, Claudio; di Paola, Benedetto; Guastella, Ivan

2012-06-01

In this paper we discuss a study on the approaches to modeling of students of the 4-year elementary school teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. factorial analysis of the correspondences and implicative analysis. A qualitative analysis of key words and terms used by students during interviews is also used to examine some aspects that emerged from the quantitative analysis. The students have been classified on the basis of their different epistemological approaches to knowledge construction, and implications between different conceptual strategies used to answer the questionnaire have been highlighted. The study’s conclusions are consistent with previous research, but the use of quantitative data analysis allowed us to classify the students into three “profiles” related to different epistemological approaches to knowledge construction, and to show the implications of the different conceptual strategies used to answer the questionnaire, giving an estimation of the classification or implication “strength.” Some hints on how a course for elementary school physics and mathematics education can be planned to orient the future teachers to the construction of models of explanation are reported.

Exploring the Earth System through online interactive models

NASA Astrophysics Data System (ADS)

Coogan, L. A.

2013-12-01

Upper level Earth Science students commonly have a strong background of mathematical training from Math courses, however their ability to use mathematical models to solve Earth Science problems is commonly limited. Their difficulty comes, in part, because of the nature of the subject matter. There is a large body of background ';conceptual' and ';observational' understanding and knowledge required in the Earth Sciences before in-depth quantification becomes useful. For example, it is difficult to answer questions about geological processes until you can identify minerals and rocks and understand the general geodynamic implications of their associations. However, science is fundamentally quantitative. To become scientists students have to translate their conceptual understanding into quantifiable models. Thus, it is desirable for students to become comfortable with using mathematical models to test hypotheses. With the aim of helping to bridging the gap between conceptual understanding and quantification I have started to build an interactive teaching website based around quantitative models of Earth System processes. The site is aimed at upper-level undergraduate students and spans a range of topics that will continue to grow as time allows. The mathematical models are all built for the students, allowing them to spend their time thinking about how the ';model world' changes in response to their manipulation of the input variables. The web site is divided into broad topics or chapters (Background, Solid Earth, Ocean and Atmosphere, Earth history) and within each chapter there are different subtopic (e.g. Solid Earth: Core, Mantle, Crust) and in each of these individual webpages. Each webpage, or topic, starts with an introduction to the topic, followed by an interactive model that the students can use sliders to control the input to and watch how the results change. This interaction between student and model is guided by a series of multiple choice questions that the student answers and immediately gets feedback whether the answer is correct or not. This way the students can ensure they understand the concepts before moving on. A discussion forum for the students to discuss the topics is in development and each page has a feedback option to allow both numerical (1-10) and written feedback on how useful the webpage was. By the end of exploring any given process students are expected to understand how the different parameters explored by the model interact to control the results. They should appreciate why the controlling equations look the way they do (all equations needed to develop the models are present in the introduction) and how these interact to control the results. While this is no substitute to students undertaking the calculations for themselves this approach allows a much wider range of topics to be explored quantitatively than if the students have to code all models themselves.

Correlated receptor transport processes buffer single-cell heterogeneity

PubMed Central

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

2017-01-01

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

Test-and-treat approach to HIV/AIDS: a primer for mathematical modeling.

PubMed

Nah, Kyeongah; Nishiura, Hiroshi; Tsuchiya, Naho; Sun, Xiaodan; Asai, Yusuke; Imamura, Akifumi

2017-09-05

The public benefit of test-and-treat has induced a need to justify goodness for the public, and mathematical modeling studies have played a key role in designing and evaluating the test-and-treat strategy for controlling HIV/AIDS. Here we briefly and comprehensively review the essence of contemporary understanding of the test-and-treat policy through mathematical modeling approaches and identify key pitfalls that have been identified to date. While the decrease in HIV incidence is achieved with certain coverages of diagnosis, care and continued treatment, HIV prevalence is not necessarily decreased and sometimes the test-and-treat is accompanied by increased long-term cost of antiretroviral therapy (ART). To confront with the complexity of assessment on this policy, the elimination threshold or the effective reproduction number has been proposed for its use in determining the overall success to anticipate the eventual elimination. Since the publication of original model in 2009, key issues of test-and-treat modeling studies have been identified, including theoretical problems surrounding the sexual partnership network, heterogeneities in the transmission dynamics, and realistic issues of achieving and maintaining high treatment coverage in the most hard-to-reach populations. To explicitly design country-specific control policy, quantitative modeling approaches to each single setting with differing epidemiological context would require multi-disciplinary collaborations among clinicians, public health practitioners, laboratory technologists, epidemiologists and mathematical modelers.

76 FR 6795 - Statement of Organization, Functions, and Delegations of Authority; Office of the National...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-02-08

... Coordinator; (2) applies research methodologies to perform evaluation studies of health information technology grant programs; and, (3) applies advanced mathematical or quantitative modeling to the U.S. health care... remaining items in the paragraph accordingly: ``(1) Applying research methodologies to perform evaluation...

Colored Petri net modeling and simulation of signal transduction pathways.

PubMed

Lee, Dong-Yup; Zimmer, Ralf; Lee, Sang Yup; Park, Sunwon

2006-03-01

Presented herein is a methodology for quantitatively analyzing the complex signaling network by resorting to colored Petri nets (CPN). The mathematical as well as Petri net models for two basic reaction types were established, followed by the extension to a large signal transduction system stimulated by epidermal growth factor (EGF) in an application study. The CPN models based on the Petri net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the EGF signaling pathway. The usefulness of Petri nets is demonstrated for the quantitative analysis of the signal transduction pathway. Moreover, the trade-offs between modeling capability and simulation efficiency of this pathway are explored, suggesting that the Petri net model can be invaluable in the initial stage of building a dynamic model.

Effect of viscosity on tear drainage and ocular residence time.

PubMed

Zhu, Heng; Chauhan, Anuj

2008-08-01

An increase in residence time of dry eye medications including artificial tears will likely enhance therapeutic benefits. The drainage rates and the residence time of eye drops depend on the viscosity of the instilled fluids. However, a quantitative understanding of the dependence of drainage rates and the residence time on viscosity is lacking. The current study aims to develop a mathematical model for the drainage of Newtonian fluids and also for power-law non-Newtonian fluids of different viscosities. This study is an extension of our previous study on the mathematical model of tear drainage. The tear drainage model is modified to describe the drainage of Newtonian fluids with viscosities higher than the tear viscosity and power-law non-Newtonian fluids with rheological parameters obtained from fitting experimental data in literature. The drainage rate through canaliculi was derived from the modified drainage model and was incorporated into a tear mass balance to calculate the transients of total solute quantity in ocular fluids and the bioavailability of instilled drugs. For Newtonian fluids, increasing the viscosity does not affect the drainage rate unless the viscosity exceeds a critical value of about 4.4 cp. The viscosity has a maximum impact on drainage rate around a value of about 100 cp. The trends are similar for shear thinning power law fluids. The transients of total solute quantity, and the residence time agrees at least qualitatively with experimental studies. A mathematical model has been developed for the drainage of Newtonian fluids and power-law fluids through canaliculi. The model can quantitatively explain different experimental observations on the effect of viscosity on the residence of instilled fluids on the ocular surface. The current study is helpful for understanding the mechanism of fluid drainage from the ocular surface and for improving the design of dry eye treatments.

A Quantitative Risk Analysis of Deficient Contractor Business System

DTIC Science & Technology

2012-04-30

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

Parent Involvement and the Impact on Student Achievement in Grades 2-5

ERIC Educational Resources Information Center

Thurber, Yvonne Marie

2013-01-01

This quantitative research study examined the relationship between student achievement in reading and mathematics on the STAR (Standardized Test for the Assessment of Reading and Mathematics) and parent involvement in specific character development activities. The research design was quantitative in nature and conducted in two similar elementary…

Digital Native Students: Gender Differences in Mathematics and Gaming

ERIC Educational Resources Information Center

Yong, Su-Ting

2017-01-01

The purpose of this study was to explore gender differences among digital native students in mathematics learning and gaming. A quantitative dominant mixed methods approach was employed in which quantitative surveys [174 students] and qualitative interviews [eight students, eight parents and six teachers] were administered concurrently. Data…

Systems Toxicology: From Basic Research to Risk Assessment

PubMed Central

2014-01-01

Systems Toxicology is the integration of classical toxicology with quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization. Society demands increasingly close scrutiny of the potential health risks associated with exposure to chemicals present in our everyday life, leading to an increasing need for more predictive and accurate risk-assessment approaches. Developing such approaches requires a detailed mechanistic understanding of the ways in which xenobiotic substances perturb biological systems and lead to adverse outcomes. Thus, Systems Toxicology approaches offer modern strategies for gaining such mechanistic knowledge by combining advanced analytical and computational tools. Furthermore, Systems Toxicology is a means for the identification and application of biomarkers for improved safety assessments. In Systems Toxicology, quantitative systems-wide molecular changes in the context of an exposure are measured, and a causal chain of molecular events linking exposures with adverse outcomes (i.e., functional and apical end points) is deciphered. Mathematical models are then built to describe these processes in a quantitative manner. The integrated data analysis leads to the identification of how biological networks are perturbed by the exposure and enables the development of predictive mathematical models of toxicological processes. This perspective integrates current knowledge regarding bioanalytical approaches, computational analysis, and the potential for improved risk assessment. PMID:24446777

Systems toxicology: from basic research to risk assessment.

PubMed

Sturla, Shana J; Boobis, Alan R; FitzGerald, Rex E; Hoeng, Julia; Kavlock, Robert J; Schirmer, Kristin; Whelan, Maurice; Wilks, Martin F; Peitsch, Manuel C

2014-03-17

Systems Toxicology is the integration of classical toxicology with quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization. Society demands increasingly close scrutiny of the potential health risks associated with exposure to chemicals present in our everyday life, leading to an increasing need for more predictive and accurate risk-assessment approaches. Developing such approaches requires a detailed mechanistic understanding of the ways in which xenobiotic substances perturb biological systems and lead to adverse outcomes. Thus, Systems Toxicology approaches offer modern strategies for gaining such mechanistic knowledge by combining advanced analytical and computational tools. Furthermore, Systems Toxicology is a means for the identification and application of biomarkers for improved safety assessments. In Systems Toxicology, quantitative systems-wide molecular changes in the context of an exposure are measured, and a causal chain of molecular events linking exposures with adverse outcomes (i.e., functional and apical end points) is deciphered. Mathematical models are then built to describe these processes in a quantitative manner. The integrated data analysis leads to the identification of how biological networks are perturbed by the exposure and enables the development of predictive mathematical models of toxicological processes. This perspective integrates current knowledge regarding bioanalytical approaches, computational analysis, and the potential for improved risk assessment.

Mathematical modeling of drug release from lipid dosage forms.

PubMed

Siepmann, J; Siepmann, F

2011-10-10

Lipid dosage forms provide an interesting potential for controlled drug delivery. In contrast to frequently used poly(ester) based devices for parenteral administration, they do not lead to acidification upon degradation and potential drug inactivation, especially in the case of protein drugs and other acid-labile active agents. The aim of this article is to give an overview on the current state of the art of mathematical modeling of drug release from this type of advanced drug delivery systems. Empirical and semi-empirical models are described as well as mechanistic theories, considering diffusional mass transport, potentially limited drug solubility and the leaching of other, water-soluble excipients into the surrounding bulk fluid. Various practical examples are given, including lipid microparticles, beads and implants, which can successfully be used to control the release of an incorporated drug during periods ranging from a few hours up to several years. The great benefit of mechanistic mathematical theories is the possibility to quantitatively predict the effects of different formulation parameters and device dimensions on the resulting drug release kinetics. Thus, in silico simulations can significantly speed up product optimization. This is particularly useful if long release periods (e.g., several months) are targeted, since experimental trial-and-error studies are highly time-consuming in these cases. In the future it would be highly desirable to combine mechanistic theories with the quantitative description of the drug fate in vivo, ideally including the pharmacodynamic efficacy of the treatments. Copyright © 2011 Elsevier B.V. All rights reserved.

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.

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.

Mathematical biomarkers for the autonomic regulation of cardiovascular system.

PubMed

Campos, Luciana A; Pereira, Valter L; Muralikrishna, Amita; Albarwani, Sulayma; Brás, Susana; Gouveia, Sónia

2013-10-07

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance.

Mathematical biomarkers for the autonomic regulation of cardiovascular system

PubMed Central

Campos, Luciana A.; Pereira, Valter L.; Muralikrishna, Amita; Albarwani, Sulayma; Brás, Susana; Gouveia, Sónia

2013-01-01

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance. PMID:24109456

A review on principles, theory and practices of 2D-QSAR.

PubMed

Roy, Kunal; Das, Rudra Narayan

2014-01-01

The central axiom of science purports the explanation of every natural phenomenon using all possible logics coming from pure as well as mixed scientific background. The quantitative structure-activity relationship (QSAR) analysis is a study correlating the behavioral manifestation of compounds with their structures employing the interdisciplinary knowledge of chemistry, mathematics, biology as well as physics. Several studies have attempted to mathematically correlate the chemistry and property (physicochemical/ biological/toxicological) of molecules using various computationally or experimentally derived quantitative parameters termed as descriptors. The dimensionality of the descriptors depends on the type of algorithm employed and defines the nature of QSAR analysis. The most interesting feature of predictive QSAR models is that the behavior of any new or even hypothesized molecule can be predicted by the use of the mathematical equations. The phrase "2D-QSAR" signifies development of QSAR models using 2D-descriptors. Such predictor variables are the most widely practised ones because of their simple and direct mathematical algorithmic nature involving no time consuming energy computations and having reproducible operability. 2D-descriptors have a deluge of contributions in extracting chemical attributes and they are also capable of representing the 3D molecular features to some extent; although in no case they should be considered as the ultimate one, since they often suffer from the problems of intercorrelation, insufficient chemical information as well as lack of interpretation. However, by following rational approaches, novel 2D-descriptors may be developed to obviate various existing problems giving potential 2D-QSAR equations, thereby solving the innumerable chemical mysteries still unexplored.

Mathematical modeling of human brain physiological data

NASA Astrophysics Data System (ADS)

Böhm, Matthias; Faltermeier, Rupert; Brawanski, Alexander; Lang, Elmar W.

2013-12-01

Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung , J. Math. Biol.JMBLAJ0303-681210.1007/s00285-005-0343-5 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about 80% of the recordings of ABP together with ICP and the partial oxygen pressure (TiPO2) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.

On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.

An engineering approach to modelling, decision support and control for sustainable systems.

PubMed

Day, W; Audsley, E; Frost, A R

2008-02-12

Engineering research and development contributes to the advance of sustainable agriculture both through innovative methods to manage and control processes, and through quantitative understanding of the operation of practical agricultural systems using decision models. This paper describes how an engineering approach, drawing on mathematical models of systems and processes, contributes new methods that support decision making at all levels from strategy and planning to tactics and real-time control. The ability to describe the system or process by a simple and robust mathematical model is critical, and the outputs range from guidance to policy makers on strategic decisions relating to land use, through intelligent decision support to farmers and on to real-time engineering control of specific processes. Precision in decision making leads to decreased use of inputs, less environmental emissions and enhanced profitability-all essential to sustainable systems.

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

PubMed

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

2018-01-01

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

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.

Modeling the Dynamics of High-Grade Serous Ovarian Cancer Progression for Transvaginal Ultrasound-Based Screening and Early Detection

PubMed Central

Lee, Jung-Min; Levy, Doron

2016-01-01

High-grade serous ovarian cancer (HGSOC) represents the majority of ovarian cancers and accounts for the largest proportion of deaths from the disease. A timely detection of low volume HGSOC should be the goal of any screening studies. However, numerous transvaginal ultrasound (TVU) detection-based population studies aimed at detecting low-volume disease have not yielded reduced mortality rates. A quantitative invalidation of TVU as an effective HGSOC screening strategy is a necessary next step. Herein, we propose a mathematical model for a quantitative explanation on the reported failure of TVU-based screening to improve HGSOC low-volume detectability and overall survival.We develop a novel in silico mathematical assessment of the efficacy of a unimodal TVU monitoring regimen as a strategy aimed at detecting low-volume HGSOC in cancer-positive cases, defined as cases for which the inception of the first malignant cell has already occurred. Our findings show that the median window of opportunity interval length for TVU monitoring and HGSOC detection is approximately 1.76 years. This does not translate into reduced mortality levels or improved detection accuracy in an in silico cohort across multiple TVU monitoring frequencies or detection sensitivities. We demonstrate that even a semiannual, unimodal TVU monitoring protocol is expected to miss detectable HGSOC. Lastly, we find that circa 50% of the simulated HGSOC growth curves never reach the baseline detectability threshold, and that on average, 5–7 infrequent, rate-limiting stochastic changes in the growth parameters are associated with reaching HGSOC detectability and mortality thresholds respectively. Focusing on a malignancy poorly studied in the mathematical oncology community, our model captures the dynamic, temporal evolution of HGSOC progression. Our mathematical model is consistent with recent case reports and prospective TVU screening population studies, and provides support to the empirical recommendation against frequent HGSOC screening. PMID:27257824

Leadership for School Numeracy: How School Leaders' Knowledge and Attitudes Impact Student Mathematics Achievement

ERIC Educational Resources Information Center

Walker-Glenn, Michelle Lynn

2010-01-01

Although most high schools espouse school-wide literacy initiatives, few schools place equal emphasis on numeracy, or quantitative literacy. This lack of attention to quantitative skills is ironic in light of documented deficiencies in student mathematics achievement. While significant research exists regarding best practices for mathematics…

Quantitative modelling of amyloidogenic processing and its influence by SORLA in Alzheimer's disease.

PubMed

Schmidt, Vanessa; Baum, Katharina; Lao, Angelyn; Rateitschak, Katja; Schmitz, Yvonne; Teichmann, Anke; Wiesner, Burkhard; Petersen, Claus Munck; Nykjaer, Anders; Wolf, Jana; Wolkenhauer, Olaf; Willnow, Thomas E

2012-01-04

The extent of proteolytic processing of the amyloid precursor protein (APP) into neurotoxic amyloid-β (Aβ) peptides is central to the pathology of Alzheimer's disease (AD). Accordingly, modifiers that increase Aβ production rates are risk factors in the sporadic form of AD. In a novel systems biology approach, we combined quantitative biochemical studies with mathematical modelling to establish a kinetic model of amyloidogenic processing, and to evaluate the influence by SORLA/SORL1, an inhibitor of APP processing and important genetic risk factor. Contrary to previous hypotheses, our studies demonstrate that secretases represent allosteric enzymes that require cooperativity by APP oligomerization for efficient processing. Cooperativity enables swift adaptive changes in secretase activity with even small alterations in APP concentration. We also show that SORLA prevents APP oligomerization both in cultured cells and in the brain in vivo, eliminating the preferred form of the substrate and causing secretases to switch to a less efficient non-allosteric mode of action. These data represent the first mathematical description of the contribution of genetic risk factors to AD substantiating the relevance of subtle changes in SORLA levels for amyloidogenic processing as proposed for patients carrying SORL1 risk alleles.

Quantitative modelling of amyloidogenic processing and its influence by SORLA in Alzheimer's disease

PubMed Central

Schmidt, Vanessa; Baum, Katharina; Lao, Angelyn; Rateitschak, Katja; Schmitz, Yvonne; Teichmann, Anke; Wiesner, Burkhard; Petersen, Claus Munck; Nykjaer, Anders; Wolf, Jana; Wolkenhauer, Olaf; Willnow, Thomas E

2012-01-01

The extent of proteolytic processing of the amyloid precursor protein (APP) into neurotoxic amyloid-β (Aβ) peptides is central to the pathology of Alzheimer's disease (AD). Accordingly, modifiers that increase Aβ production rates are risk factors in the sporadic form of AD. In a novel systems biology approach, we combined quantitative biochemical studies with mathematical modelling to establish a kinetic model of amyloidogenic processing, and to evaluate the influence by SORLA/SORL1, an inhibitor of APP processing and important genetic risk factor. Contrary to previous hypotheses, our studies demonstrate that secretases represent allosteric enzymes that require cooperativity by APP oligomerization for efficient processing. Cooperativity enables swift adaptive changes in secretase activity with even small alterations in APP concentration. We also show that SORLA prevents APP oligomerization both in cultured cells and in the brain in vivo, eliminating the preferred form of the substrate and causing secretases to switch to a less efficient non-allosteric mode of action. These data represent the first mathematical description of the contribution of genetic risk factors to AD substantiating the relevance of subtle changes in SORLA levels for amyloidogenic processing as proposed for patients carrying SORL1 risk alleles. PMID:21989385

Integrating quantitative thinking into an introductory biology course improves students' mathematical reasoning in biological contexts.

PubMed

Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa

2014-01-01

Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning.

Integrating Quantitative Thinking into an Introductory Biology Course Improves Students’ Mathematical Reasoning in Biological Contexts

PubMed Central

Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa

2014-01-01

Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students’ apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students’ understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students’ inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students’ biology learning. PMID:24591504

Ionic charge distributions of energetic particles from solar flares

NASA Technical Reports Server (NTRS)

Mullan, D. J.; Waldron, W. L.

1986-01-01

The effects which solar flare X-rays have on the charge states of solar cosmic rays is determined quantitatively. Rather than to characterize the charge distribution by temperature alone, it is proposed that the X-ray flux at the acceleration site also is used. The effects of flare X-rays are modeled mathematically.

Comparing South African Female and Male Pre-Service Teachers' Beliefs about the Nature of Mathematics

ERIC Educational Resources Information Center

Spangenberg, Erica Dorethea; Myburgh, Chris

2017-01-01

Girls performing well in mathematics at school do not necessarily enrol for mathematics courses at South African universities. Teachers could be transferring beliefs about the nature of mathematics favouring boys. This paper compared male and female pre-service teachers' beliefs about the nature of mathematics. A quantitative, descriptive research…

Effects of Animated Agents in Web-Based Instruction on Mathematics: Achievement and Attitudes toward Mathematics

ERIC Educational Resources Information Center

Lodree, Anika W.; Moore, Joi L.; Gilbert, Juan E.

2008-01-01

This article summarizes a quantitative study of the effects of animated agents in web-based instruction (WBI) on mathematics achievement and attitudes toward mathematics in postsecondary education. Eighty-one college students who were enrolled in a core mathematic course at a doctoral/research-extensive university in central Alabama participated…

Applying mathematical concepts with hands-on, food-based science curriculum.

PubMed

Roseno, Ashley T; Carraway-Stage, Virginia G; Hoerdeman, Callan; Díaz, Sebastián R; Eugene, Geist; Duffrin, Melani W

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student's mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students' mathematics knowledge while building a foundation for becoming quantitatively literate adults.

Applying mathematical concepts with hands-on, food-based science curriculum

PubMed Central

Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Eugene, Geist; Duffrin, Melani W.

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student’s mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students’ mathematics knowledge while building a foundation for becoming quantitatively literate adults. PMID:26494927

SSBD: a database of quantitative data of spatiotemporal dynamics of biological phenomena

PubMed Central

Tohsato, Yukako; Ho, Kenneth H. L.; Kyoda, Koji; Onami, Shuichi

2016-01-01

Motivation: Rapid advances in live-cell imaging analysis and mathematical modeling have produced a large amount of quantitative data on spatiotemporal dynamics of biological objects ranging from molecules to organisms. There is now a crucial need to bring these large amounts of quantitative biological dynamics data together centrally in a coherent and systematic manner. This will facilitate the reuse of this data for further analysis. Results: We have developed the Systems Science of Biological Dynamics database (SSBD) to store and share quantitative biological dynamics data. SSBD currently provides 311 sets of quantitative data for single molecules, nuclei and whole organisms in a wide variety of model organisms from Escherichia coli to Mus musculus. The data are provided in Biological Dynamics Markup Language format and also through a REST API. In addition, SSBD provides 188 sets of time-lapse microscopy images from which the quantitative data were obtained and software tools for data visualization and analysis. Availability and Implementation: SSBD is accessible at http://ssbd.qbic.riken.jp. Contact: sonami@riken.jp PMID:27412095

The new AP Physics exams: Integrating qualitative and quantitative reasoning

NASA Astrophysics Data System (ADS)

Elby, Andrew

2015-04-01

When physics instructors and education researchers emphasize the importance of integrating qualitative and quantitative reasoning in problem solving, they usually mean using those types of reasoning serially and separately: first students should analyze the physical situation qualitatively/conceptually to figure out the relevant equations, then they should process those equations quantitatively to generate a solution, and finally they should use qualitative reasoning to check that answer for plausibility (Heller, Keith, & Anderson, 1992). The new AP Physics 1 and 2 exams will, of course, reward this approach to problem solving. But one kind of free response question will demand and reward a further integration of qualitative and quantitative reasoning, namely mathematical modeling and sense-making--inventing new equations to capture a physical situation and focusing on proportionalities, inverse proportionalities, and other functional relations to infer what the equation ``says'' about the physical world. In this talk, I discuss examples of these qualitative-quantitative translation questions, highlighting how they differ from both standard quantitative and standard qualitative questions. I then discuss the kinds of modeling activities that can help AP and college students develop these skills and habits of mind.

SSBD: a database of quantitative data of spatiotemporal dynamics of biological phenomena.

PubMed

Tohsato, Yukako; Ho, Kenneth H L; Kyoda, Koji; Onami, Shuichi

2016-11-15

Rapid advances in live-cell imaging analysis and mathematical modeling have produced a large amount of quantitative data on spatiotemporal dynamics of biological objects ranging from molecules to organisms. There is now a crucial need to bring these large amounts of quantitative biological dynamics data together centrally in a coherent and systematic manner. This will facilitate the reuse of this data for further analysis. We have developed the Systems Science of Biological Dynamics database (SSBD) to store and share quantitative biological dynamics data. SSBD currently provides 311 sets of quantitative data for single molecules, nuclei and whole organisms in a wide variety of model organisms from Escherichia coli to Mus musculus The data are provided in Biological Dynamics Markup Language format and also through a REST API. In addition, SSBD provides 188 sets of time-lapse microscopy images from which the quantitative data were obtained and software tools for data visualization and analysis. SSBD is accessible at http://ssbd.qbic.riken.jp CONTACT: sonami@riken.jp. © The Author 2016. Published by Oxford University Press.

Mathematical model to analyze the dissolution behavior of metastable crystals or amorphous drug accompanied with a solid-liquid interface reaction.

PubMed

Hirai, Daiki; Iwao, Yasunori; Kimura, Shin-Ichiro; Noguchi, Shuji; Itai, Shigeru

2017-04-30

Metastable crystals and the amorphous state of poorly water-soluble drugs in solid dispersions (SDs), are subject to a solid-liquid interface reaction upon exposure to a solvent. The dissolution behavior during the solid-liquid interface reaction often shows that the concentration of drugs is supersaturated, with a high initial drug concentration compared with the solubility of stable crystals but finally approaching the latter solubility with time. However, a method for measuring the precipitation rate of stable crystals and/or the potential solubility of metastable crystals or amorphous drugs has not been established. In this study, a novel mathematical model that can represent the dissolution behavior of the solid-liquid interface reaction for metastable crystals or amorphous drug was developed and its validity was evaluated. The theory for this model was based on the Noyes-Whitney equation and assumes that the precipitation of stable crystals at the solid-liquid interface occurs through a first-order reaction. Moreover, two models were developed, one assuming that the surface area of the drug remains constant because of the presence of excess drug in the bulk and the other that the surface area changes in time-dependency because of agglomeration of the drug. SDs of Ibuprofen (IB)/polyvinylpyrrolidone (PVP) were prepared and their dissolution behaviors under non-sink conditions were fitted by the models to evaluate improvements in solubility. The model assuming time-dependent surface area showed good agreement with experimental values. Furthermore, by applying the model to the dissolution profile, parameters such as the precipitation rate and the potential solubility of the amorphous drug were successfully calculated. In addition, it was shown that the improvement in solubility with supersaturation was able to be evaluated quantitatively using this model. Therefore, this mathematical model would be a useful tool to quantitatively determine the supersaturation concentration of a metastable drug from solid dispersions. Copyright © 2017 Elsevier B.V. All rights reserved.

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

PubMed

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

2016-01-01

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

Mathematical Modelling of Allelopathy: IV. Assessment of Contributions of Competition and Allelopathy to Interference by Barley

PubMed Central

Liu, De Li; An, Min; Johnson, I.R.; Lovett, J.V.

2005-01-01

One of the main challenges to the research on allelopathy is technically the separation of allelopathic effect from competition, and quantitatively, the assessment of the contribution of each component to overall interference. A simple mathematical model is proposed to calculate the contribution of allelopathy and competition to interference. As an example of applying the quantitative model to interference by barley (Hordeum vulgare cv. Triumph), the approach used was an addition of allelopathic effect, by an equivalent amount, to the environment of the test plant (white mustard, Sinapis alba), rather than elimination of competition. Experiments were conducted in glasshouse to determine the magnitude of the contributions of allelopathy and competition to interference by barley. The leachates of living barley roots significantly reduced the total dry weight of white mustard. The model involved the calculation of adjusted densities to an equivalent basis for modelling the contribution of allelopathy and competition to total interference. The results showed that allelopathy contributed 40%, 37% and 43% to interference by barley at 6, 12 and 18 white mustard pot−1. The consistency in magnitude of the calculated contribution of allelopathic effect by barley across various densities of receiver plant suggested that the adjusted equivalent density is effective and that the model is able to assess the contribution of each component of interference regardless of the density of receiver plant. PMID:19330162

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

Estimation in the Primary School: Developing a Key Mathematical Skill for Life

ERIC Educational Resources Information Center

Mildenhall, Paula

2016-01-01

Very recently, in the "Australian Association of Mathematics Teachers (AAMT)/Australian Industry Group quantitative report" (2014), concerns were raised that school mathematics is lacking real world application. This report highlighted the gaps between school mathematics and the requirements of the workplace. After interviewing industry…

A Quantitative and Qualitative Study of Math Anxiety among Preservice Teachers

ERIC Educational Resources Information Center

Sloan, Tina Rye

2010-01-01

This project investigated the effects of a standards-based mathematics methods course on the mathematics anxiety levels of preservice teachers. The qualitative portion of the study examined aspects of a math methods course that affected mathematics anxiety levels and the antecedents of mathematics anxiety. Findings revealed a significant…

Mathematical Difficulty: Does Early Intervention Enhance Mathematical Performance?

ERIC Educational Resources Information Center

Graham, Jennifer

2008-01-01

The need to ask educators about their opinions on the subject to what extent early intervention methods enhance mathematical performance is long overdue. The purpose of this quantitative research is to examine the extent to which teachers agree that early intervention methods enhance the mathematical performance of students with mathematical…

Early Foundations for Mathematics Learning and Their Relations to Learning Disabilities.

PubMed

Geary, David C

2013-02-01

Children's quantitative competencies upon entry into school can have lifelong consequences. Children who start behind generally stay behind, and mathematical skills at school completion influence employment prospects and wages in adulthood. I review the current debate over whether early quantitative learning is supported by (a) an inherent system for representing approximate magnitudes, (b) an attentional-control system that enables explicit processing of quantitative symbols, such as Arabic numerals, or (c) the logical problem-solving abilities that facilitate learning of the relations among numerals. Studies of children with mathematical learning disabilities and difficulties have suggested that each of these competencies may be involved, but to different degrees and at different points in the learning process. Clarifying how and when these competencies facilitate early quantitative learning and developing interventions to address their impact on children have the potential to yield substantial benefits for individuals and for society.

[Study on the quantitative evaluation on the degree of TCM basic syndromes often encountered in patients with primary liver cancer].

PubMed

Li, Dong-tao; Ling, Chang-quan; Zhu, De-zeng

2007-07-01

To establish a quantitative model for evaluating the degree of the TCM basic syndromes often encountered in patients with primary liver cancer (PLC). Medical literatures concerning the clinical investigation and TCM syndrome of PLC were collected and analyzed adopting expert-composed symposium method, and the 100 millimeter scaling was applied in combining with scoring on degree of symptoms to establish a quantitative criterion for symptoms and signs degree classification in patients with PLC. Two models, i.e. the additive model and the additive-multiplicative model, were established by using comprehensive analytic hierarchy process (AHP) as the mathematical tool to estimate the weight of the criterion for evaluating basic syndromes in various layers by specialists. Then the two models were verified in clinical practice and the outcomes were compared with that fuzzy evaluated by specialists. Verification on 459 times/case of PLC showed that the coincidence rate between the outcomes derived from specialists with that from the additive model was 84.53 %, and with that from the additive-multificative model was 62.75 %, the difference between the two showed statistical significance (P<0.01). It could be decided that the additive model is the principle model suitable for quantitative evaluation on the degree of TCM basic syndromes in patients with PLC.

Visualization of Problem Solving Related to the Quantitative Composition of Solutions in the Dynamic "GeoGebra" Environment

ERIC Educational Resources Information Center

Kostic, V. Dj.; Jovanovic, V. P. Stankov; Sekulic, T. M.; Takaci, Dj. B.

2016-01-01

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

Young Children's Core Symbolic and Nonsymbolic Quantitative Knowledge in the Prediction of Later Mathematics Achievement

ERIC Educational Resources Information Center

Geary, David C.; vanMarle, Kristy

2016-01-01

At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was…

Contextualising Mathematics Self-Efficacy and Performance among Rural High School Students in the Philippines

ERIC Educational Resources Information Center

Causapin, Mark

2016-01-01

This paper expands the scope of typical quantitative studies on mathematics self-efficacy by including a short ethnography of the students' daily classroom experiences. It attempts to provide a "thicker description" and a context in which these beliefs could be interpreted. Using both qualitative and quantitative sets of data, it is…

Beyond Quantitative Decline: Conceptual Shifts in Adolescents' Development of Interest in Mathematics

ERIC Educational Resources Information Center

Frenzel, Anne C.; Pekrun, Reinhard; Dicke, Anna-Lena; Goetz, Thomas

2012-01-01

Research has shown that the average values for academic interest decrease during adolescence. Looking beyond such quantitative decline, we explored qualitative change of interest in the domain of mathematics across adolescence. Study 1 was based on a longitudinal data set (annual assessments from Grade 5 to Grade 9; N = 3,193). Latent variable…

Myeloma Cell Dynamics in Response to Treatment Supports a Model of Hierarchical Differentiation and Clonal Evolution.

PubMed

Tang, Min; Zhao, Rui; van de Velde, Helgi; Tross, Jennifer G; Mitsiades, Constantine; Viselli, Suzanne; Neuwirth, Rachel; Esseltine, Dixie-Lee; Anderson, Kenneth; Ghobrial, Irene M; San Miguel, Jesús F; Richardson, Paul G; Tomasson, Michael H; Michor, Franziska

2016-08-15

Since the pioneering work of Salmon and Durie, quantitative measures of tumor burden in multiple myeloma have been used to make clinical predictions and model tumor growth. However, such quantitative analyses have not yet been performed on large datasets from trials using modern chemotherapy regimens. We analyzed a large set of tumor response data from three randomized controlled trials of bortezomib-based chemotherapy regimens (total sample size n = 1,469 patients) to establish and validate a novel mathematical model of multiple myeloma cell dynamics. Treatment dynamics in newly diagnosed patients were most consistent with a model postulating two tumor cell subpopulations, "progenitor cells" and "differentiated cells." Differential treatment responses were observed with significant tumoricidal effects on differentiated cells and less clear effects on progenitor cells. We validated this model using a second trial of newly diagnosed patients and a third trial of refractory patients. When applying our model to data of relapsed patients, we found that a hybrid model incorporating both a differentiation hierarchy and clonal evolution best explains the response patterns. The clinical data, together with mathematical modeling, suggest that bortezomib-based therapy exerts a selection pressure on myeloma cells that can shape the disease phenotype, thereby generating further inter-patient variability. This model may be a useful tool for improving our understanding of disease biology and the response to chemotherapy regimens. Clin Cancer Res; 22(16); 4206-14. ©2016 AACR. ©2016 American Association for Cancer Research.

Simulation Of Combat With An Expert System

NASA Technical Reports Server (NTRS)

Provenzano, J. P.

1989-01-01

Proposed expert system predicts outcomes of combat situations. Called "COBRA", combat outcome based on rules for attrition, system selects rules for mathematical modeling of losses and discrete events in combat according to previous experiences. Used with another software module known as the "Game". Game/COBRA software system, consisting of Game and COBRA modules, provides for both quantitative aspects and qualitative aspects in simulations of battles. COBRA intended for simulation of large-scale military exercises, concepts embodied in it have much broader applicability. In industrial research, knowledge-based system enables qualitative as well as quantitative simulations.

Bridging the divide: a model-data approach to Polar and Alpine microbiology.

PubMed

Bradley, James A; Anesio, Alexandre M; Arndt, Sandra

2016-03-01

Advances in microbial ecology in the cryosphere continue to be driven by empirical approaches including field sampling and laboratory-based analyses. Although mathematical models are commonly used to investigate the physical dynamics of Polar and Alpine regions, they are rarely applied in microbial studies. Yet integrating modelling approaches with ongoing observational and laboratory-based work is ideally suited to Polar and Alpine microbial ecosystems given their harsh environmental and biogeochemical characteristics, simple trophic structures, distinct seasonality, often difficult accessibility, geographical expansiveness and susceptibility to accelerated climate changes. In this opinion paper, we explain how mathematical modelling ideally complements field and laboratory-based analyses. We thus argue that mathematical modelling is a powerful tool for the investigation of these extreme environments and that fully integrated, interdisciplinary model-data approaches could help the Polar and Alpine microbiology community address some of the great research challenges of the 21st century (e.g. assessing global significance and response to climate change). However, a better integration of field and laboratory work with model design and calibration/validation, as well as a stronger focus on quantitative information is required to advance models that can be used to make predictions and upscale processes and fluxes beyond what can be captured by observations alone. © FEMS 2016.

Bridging the divide: a model-data approach to Polar and Alpine microbiology

PubMed Central

Bradley, James A.; Anesio, Alexandre M.; Arndt, Sandra

2016-01-01

Advances in microbial ecology in the cryosphere continue to be driven by empirical approaches including field sampling and laboratory-based analyses. Although mathematical models are commonly used to investigate the physical dynamics of Polar and Alpine regions, they are rarely applied in microbial studies. Yet integrating modelling approaches with ongoing observational and laboratory-based work is ideally suited to Polar and Alpine microbial ecosystems given their harsh environmental and biogeochemical characteristics, simple trophic structures, distinct seasonality, often difficult accessibility, geographical expansiveness and susceptibility to accelerated climate changes. In this opinion paper, we explain how mathematical modelling ideally complements field and laboratory-based analyses. We thus argue that mathematical modelling is a powerful tool for the investigation of these extreme environments and that fully integrated, interdisciplinary model-data approaches could help the Polar and Alpine microbiology community address some of the great research challenges of the 21st century (e.g. assessing global significance and response to climate change). However, a better integration of field and laboratory work with model design and calibration/validation, as well as a stronger focus on quantitative information is required to advance models that can be used to make predictions and upscale processes and fluxes beyond what can be captured by observations alone. PMID:26832206

Advanced quantitative measurement methodology in physics education research

NASA Astrophysics Data System (ADS)

Wang, Jing

The ultimate goal of physics education research (PER) is to develop a theoretical framework to understand and improve the learning process. In this journey of discovery, assessment serves as our headlamp and alpenstock. It sometimes detects signals in student mental structures, and sometimes presents the difference between expert understanding and novice understanding. Quantitative assessment is an important area in PER. Developing research-based effective assessment instruments and making meaningful inferences based on these instruments have always been important goals of the PER community. Quantitative studies are often conducted to provide bases for test development and result interpretation. Statistics are frequently used in quantitative studies. The selection of statistical methods and interpretation of the results obtained by these methods shall be connected to the education background. In this connecting process, the issues of educational models are often raised. Many widely used statistical methods do not make assumptions on the mental structure of subjects, nor do they provide explanations tailored to the educational audience. There are also other methods that consider the mental structure and are tailored to provide strong connections between statistics and education. These methods often involve model assumption and parameter estimation, and are complicated mathematically. The dissertation provides a practical view of some advanced quantitative assessment methods. The common feature of these methods is that they all make educational/psychological model assumptions beyond the minimum mathematical model. The purpose of the study is to provide a comparison between these advanced methods and the pure mathematical methods. The comparison is based on the performance of the two types of methods under physics education settings. In particular, the comparison uses both physics content assessments and scientific ability assessments. The dissertation includes three parts. The first part involves the comparison between item response theory (IRT) and classical test theory (CTT). The two theories both provide test item statistics for educational inferences and decisions. The two theories are both applied to Force Concept Inventory data obtained from students enrolled in The Ohio State University. Effort was made to examine the similarity and difference between the two theories, and the possible explanation to the difference. The study suggests that item response theory is more sensitive to the context and conceptual features of the test items than classical test theory. The IRT parameters provide a better measure than CTT parameters for the educational audience to investigate item features. The second part of the dissertation is on the measure of association for binary data. In quantitative assessment, binary data is often encountered because of its simplicity. The current popular measures of association fail under some extremely unbalanced conditions. However, the occurrence of these conditions is not rare in educational data. Two popular association measures, the Pearson's correlation and the tetrachoric correlation are examined. A new method, model based association is introduced, and an educational testing constraint is discussed. The existing popular methods are compared with the model based association measure with and without the constraint. Connections between the value of association and the context and conceptual features of questions are discussed in detail. Results show that all the methods have their advantages and disadvantages. Special attention to the test and data conditions is necessary. The last part of the dissertation is focused on exploratory factor analysis (EFA). The theoretical advantages of EFA are discussed. Typical misunderstanding and misusage of EFA are explored. The EFA is performed on Lawson's Classroom Test of Scientific Reasoning (LCTSR), a widely used assessment on scientific reasoning skills. The reasoning ability structures for U.S. and Chinese students at different educational levels are given by the analysis. A final discussion on the advanced quantitative assessment methodology and the pure mathematical methodology is presented at the end.

Connecting Research to Teaching: Professional Communities: Teachers Supporting Teachers.

ERIC Educational Resources Information Center

Adajian, Lisa Byrd

1996-01-01

Reviews research on importance of strong professional communities for supporting reform. National Center for Research in Mathematical Sciences Education (NCRMSE) found significant correlation between teachers' professional community and reformed mathematics instruction. Urban Mathematics Collaboratives (UMC), Quantitative Understanding: Amplifying…

Modeling virus survival and transport in the subsurface

NASA Astrophysics Data System (ADS)

Yates, Marylynn V.; Yates, S. R.; Wagner, Jan; Gerba, Charles P.

1987-03-01

The significance of viruses as agents of waterborne disease in the United States is just beginning to be recognized. The ability to predict how far viruses can be transported and how long they can remain infective in soil and groundwater is desirable from the standpoint of planning the placement of sources of contamination so that they will not have an impact on drinking-water wells. This, in turn should have the effect of decreasing the number of waterborne disease outbreaks caused by viruses. This article reviews the factors that affect the survival and migration of viruses in soils and groundwater. It also discusses the efforts that have been made to mathematically model the movement of viruses in the subsurface, including the assumptions made by the modelers. At this time, it appears that modeling efforts are constrained by a lack of quantitative information on virus interactions with soil and fluid media, rather than on mathematical solution techniques.

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

NASA Astrophysics Data System (ADS)

Pastres, Roberto; Solidoro, Cosimo

2012-01-01

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

Assessing Strategies Against Gambiense Sleeping Sickness Through Mathematical Modeling

PubMed Central

Rock, Kat S; Ndeffo-Mbah, Martial L; Castaño, Soledad; Palmer, Cody; Pandey, Abhishek; Atkins, Katherine E; Ndung’u, Joseph M; Hollingsworth, T Déirdre; Galvani, Alison; Bever, Caitlin; Chitnis, Nakul; Keeling, Matt J

2018-01-01

Abstract Background Control of gambiense sleeping sickness relies predominantly on passive and active screening of people, followed by treatment. Methods Mathematical modeling explores the potential of 3 complementary interventions in high- and low-transmission settings. Results Intervention strategies that included vector control are predicted to halt transmission most quickly. Targeted active screening, with better and more focused coverage, and enhanced passive surveillance, with improved access to diagnosis and treatment, are both estimated to avert many new infections but, when used alone, are unlikely to halt transmission before 2030 in high-risk settings. Conclusions There was general model consensus in the ranking of the 3 complementary interventions studied, although with discrepancies between the quantitative predictions due to differing epidemiological assumptions within the models. While these predictions provide generic insights into improving control, the most effective strategy in any situation depends on the specific epidemiology in the region and the associated costs. PMID:29860287

Application of a Mathematical Model to Describe the Effects of Chlorpyrifos on Caenorhabditis elegans Development

PubMed Central

Boyd, Windy A.; Smith, Marjolein V.; Kissling, Grace E.; Rice, Julie R.; Snyder, Daniel W.; Portier, Christopher J.; Freedman, Jonathan H.

2009-01-01

Background The nematode Caenorhabditis elegans is being assessed as an alternative model organism as part of an interagency effort to develop better means to test potentially toxic substances. As part of this effort, assays that use the COPAS Biosort flow sorting technology to record optical measurements (time of flight (TOF) and extinction (EXT)) of individual nematodes under various chemical exposure conditions are being developed. A mathematical model has been created that uses Biosort data to quantitatively and qualitatively describe C. elegans growth, and link changes in growth rates to biological events. Chlorpyrifos, an organophosphate pesticide known to cause developmental delays and malformations in mammals, was used as a model toxicant to test the applicability of the growth model for in vivo toxicological testing. Methodology/Principal Findings L1 larval nematodes were exposed to a range of sub-lethal chlorpyrifos concentrations (0–75 µM) and measured every 12 h. In the absence of toxicant, C. elegans matured from L1s to gravid adults by 60 h. A mathematical model was used to estimate nematode size distributions at various times. Mathematical modeling of the distributions allowed the number of measured nematodes and log(EXT) and log(TOF) growth rates to be estimated. The model revealed three distinct growth phases. The points at which estimated growth rates changed (change points) were constant across the ten chlorpyrifos concentrations. Concentration response curves with respect to several model-estimated quantities (numbers of measured nematodes, mean log(TOF) and log(EXT), growth rates, and time to reach change points) showed a significant decrease in C. elegans growth with increasing chlorpyrifos concentration. Conclusions Effects of chlorpyrifos on C. elegans growth and development were mathematically modeled. Statistical tests confirmed a significant concentration effect on several model endpoints. This confirmed that chlorpyrifos affects C. elegans development in a concentration dependent manner. The most noticeable effect on growth occurred during early larval stages: L2 and L3. This study supports the utility of the C. elegans growth assay and mathematical modeling in determining the effects of potentially toxic substances in an alternative model organism using high-throughput technologies. PMID:19753116

Qualitative and quantitative descriptions of glenohumeral motion.

PubMed

Hill, A M; Bull, A M J; Wallace, A L; Johnson, G R

2008-02-01

Joint modelling plays an important role in qualitative and quantitative descriptions of both normal and abnormal joints, as well as predicting outcomes of alterations to joints in orthopaedic practice and research. Contemporary efforts in modelling have focussed upon the major articulations of the lower limb. Well-constrained arthrokinematics can form the basis of manageable kinetic and dynamic mathematical predictions. In order to contain computation of shoulder complex modelling, glenohumeral joint representations in both limited and complete shoulder girdle models have undergone a generic simplification. As such, glenohumeral joint models are often based upon kinematic descriptions of inadequate degrees of freedom (DOF) for clinical purposes and applications. Qualitative descriptions of glenohumeral motion range from the parody of a hinge joint to the complex realism of a spatial joint. In developing a model, a clear idea of intention is required in order to achieve a required application. Clinical applicability of a model requires both descriptive and predictive output potentials, and as such, a high level of validation is required. Without sufficient appreciation of the clinical intention of the arthrokinematic foundation to a model, error is all too easily introduced. Mathematical description of joint motion serves to quantify all relevant clinical parameters. Commonly, both the Euler angle and helical (screw) axis methods have been applied to the glenohumeral joint, although concordance between these methods and classical anatomical appreciation of joint motion is limited, resulting in miscommunication between clinician and engineer. Compounding these inconsistencies in motion quantification is gimbal lock and sequence dependency.

Reporting Qualitative Data Quantitatively: Code-Switching in Mathematics Classrooms

ERIC Educational Resources Information Center

Neo, Kian-Sen; Heng, Buai-Chin

2012-01-01

This article is based on a research investigating the communication in primary mathematics classrooms. One of the research's objectives was to determine what languages were used in the primary mathematics classrooms, and to what extent, do teachers and students resort to code-switching in teaching and learning mathematics. A total of 16 classroom…

Mathematical Interventions for Secondary Students with Learning Disabilities and Mathematics Difficulties: A Meta-Analysis

ERIC Educational Resources Information Center

Jitendra, Asha K.; Lein, Amy E.; Im, Soo-hyun; Alghamdi, Ahmed A.; Hefte, Scott B.; Mouanoutoua, John

2018-01-01

This meta-analysis is the first to provide a quantitative synthesis of empirical evaluations of mathematical intervention programs implemented in secondary schools for students with learning disabilities and mathematics difficulties. Included studies used a treatment-control group design. A total of 19 experimental and quasi-experimental studies…

Assessment in the Context of Mathematics Instruction Reform: The Design of Assessment in the QUASAR Project.

ERIC Educational Resources Information Center

Silver, Edward A.; Lane, Suzanne

Recent reports on mathematics education reform have focused the attention of educational practitioners and policymakers on new goals for mathematics education and new descriptions of mathematical proficiency. QUASAR is a national project (Quantitative Understanding: Amplifying Student Achievement and Reasoning) designed to improve the mathematics…

Prior Decisions and Experiences about Mathematics of Students in Bridging Courses

ERIC Educational Resources Information Center

Gordon, Sue; Nicholas, Jackie

2013-01-01

We report on the survey responses of 51 students attending mathematics bridging courses at a major Australian university, investigating what mathematics, if any, these students had studied in the senior years of schooling and what factors affected their decisions about the level of mathematics chosen. Quantitative findings are augmented by…

Exploring Rural High School Learners' Experience of Mathematics Anxiety in Academic Settings

ERIC Educational Resources Information Center

Hlalele, Dipane

2012-01-01

The purpose of the study was to explore rural high school learners' experience of mathematics anxiety in academic settings. Mathematics anxiety has been found to have an adverse effect on confidence, motivation and achievement. This quantitative study is exploratory and descriptive in nature. The participants were 403 learners doing mathematics in…

Who is afraid of math? Two sources of genetic variance for mathematical anxiety.

PubMed

Wang, Zhe; Hart, Sara Ann; Kovas, Yulia; Lukowski, Sarah; Soden, Brooke; Thompson, Lee A; Plomin, Robert; McLoughlin, Grainne; Bartlett, Christopher W; Lyons, Ian M; Petrill, Stephen A

2014-09-01

Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem solving and achievement. This study investigated the genetic and environmental factors contributing to the observed differences in the anxiety people feel when confronted with mathematical tasks. In addition, the genetic and environmental mechanisms that link mathematical anxiety with math cognition and general anxiety were also explored. Univariate and multivariate quantitative genetic models were conducted in a sample of 514 12-year-old twin siblings. Genetic factors accounted for roughly 40% of the variation in mathematical anxiety, with the remaining being accounted for by child-specific environmental factors. Multivariate genetic analyses suggested that mathematical anxiety was influenced by the genetic and nonfamilial environmental risk factors associated with general anxiety and additional independent genetic influences associated with math-based problem solving. The development of mathematical anxiety may involve not only exposure to negative experiences with mathematics, but also likely involves genetic risks related to both anxiety and math cognition. These results suggest that integrating cognitive and affective domains may be particularly important for mathematics and may extend to other areas of academic achievement. © 2014 The Authors. Journal of Child Psychology and Psychiatry. © 2014 Association for Child and Adolescent Mental Health.

Who’s Afraid of Math? Two Sources of Genetic Variance for Mathematical Anxiety

PubMed Central

Wang, Zhe; Hart, Sara Ann; Kovas, Yulia; Lukowski, Sarah; Soden, Brooke; Thompson, Lee A.; Plomin, Robert; McLoughlin, Grainne; Bartlett, Christopher W.; Lyons, Ian M.; Petrill, Stephen A.

2015-01-01

Background Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem-solving and achievement. The present study investigated the genetic and environmental factors contributing to the observed differences in the anxiety people feel when confronted with mathematical tasks. In addition, the genetic and environmental mechanisms that link mathematical anxiety with math cognition and general anxiety were also explored. Methods Univariate and multivariate quantitative genetic models were conducted in a sample of 514 12-year-old twin siblings. Results Genetic factors accounted for roughly 40% of the variation in mathematical anxiety, with the remaining being accounted for by child-specific environmental factors. Multivariate genetic analyses suggested that mathematical anxiety was influenced by the genetic and non-familial environmental risk factors associated with general anxiety and additional independent genetic influences associated with math-based problem solving. Conclusions The development of mathematical anxiety may involve not only exposure to negative experiences with mathematics, but also likely involves genetic risks related to both anxiety and math cognition. These results suggest that integrating cognitive and affective domains may be particularly important for mathematics, and may extend to other areas of academic achievement. PMID:24611799

Biophysically based mathematical modeling of interstitial cells of Cajal slow wave activity generated from a discrete unitary potential basis.

PubMed

Faville, R A; Pullan, A J; Sanders, K M; Koh, S D; Lloyd, C M; Smith, N P

2009-06-17

Spontaneously rhythmic pacemaker activity produced by interstitial cells of Cajal (ICC) is the result of the entrainment of unitary potential depolarizations generated at intracellular sites termed pacemaker units. In this study, we present a mathematical modeling framework that quantitatively represents the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC operating over the physiological membrane potential range. The mathematical model presented here extends our recently developed biophysically based pacemaker unit modeling framework by including mechanisms necessary for coordinating unitary potential events, such as a T-Type Ca2+ current, Vm-dependent K+ currents, and global Ca2+ diffusion. Model simulations produce spontaneously rhythmic slow wave depolarizations with an amplitude of 65 mV at a frequency of 17.4 cpm. Our model predicts that activity at the spatial scale of the pacemaker unit is fundamental for ICC slow wave generation, and Ca2+ influx from activation of the T-Type Ca2+ current is required for unitary potential entrainment. These results suggest that intracellular Ca2+ levels, particularly in the region local to the mitochondria and endoplasmic reticulum, significantly influence pacing frequency and synchronization of pacemaker unit discharge. Moreover, numerical investigations show that our ICC model is capable of qualitatively replicating a wide range of experimental observations.

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

PubMed

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

2016-04-01

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

Towards a quantitative understanding of oxygen tension and cell density evolution in fibrin hydrogels.

PubMed

Demol, Jan; Lambrechts, Dennis; Geris, Liesbet; Schrooten, Jan; Van Oosterwyck, Hans

2011-01-01

The in vitro culture of hydrogel-based constructs above a critical size is accompanied by problems of unequal cell distribution when diffusion is the primary mode of oxygen transfer. In this study, an experimentally-informed mathematical model was developed to relate cell proliferation and death inside fibrin hydrogels to the local oxygen tension in a quantitative manner. The predictive capacity of the resulting model was tested by comparing its outcomes to the density, distribution and viability of human periosteum derived cells (hPDCs) that were cultured inside fibrin hydrogels in vitro. The model was able to reproduce important experimental findings, such as the formation of a multilayered cell sheet at the hydrogel periphery and the occurrence of a cell density gradient throughout the hydrogel. In addition, the model demonstrated that cell culture in fibrin hydrogels can lead to complete anoxia in the centre of the hydrogel for realistic values of oxygen diffusion and consumption. A sensitivity analysis also identified these two parameters, together with the proliferation parameters of the encapsulated cells, as the governing parameters for the occurrence of anoxia. In conclusion, this study indicates that mathematical models can help to better understand oxygen transport limitations and its influence on cell behaviour during the in vitro culture of cell-seeded hydrogels. Copyright © 2010 Elsevier Ltd. All rights reserved.

Review of Education in Mathematics, Data Science and Quantitative Disciplines: Report to the Group of Eight Universities

ERIC Educational Resources Information Center

Brown, Gavin

2009-01-01

The Reference Committee firmly shares the view that the state of the mathematical sciences and related quantitative disciplines in Australia has deteriorated to a dangerous level, and continues to deteriorate. Accordingly the author decided to structure this Report around a small number of recommendations, some long term and others to address…

Math Across the Community College Curriculum (MAC3): A Successful Path to Quantitative Literacy

ERIC Educational Resources Information Center

Hillyard, Cinnamon; Korey, Jane; Leoni, Deann; Hartzler, Rebecca

2010-01-01

In recent years, mathematical and quantitative arguments have become prominent in the media as well as in politics, business, and science conversations. This has led to multiple calls for mathematics to be more accessible and meaningful to a wider range of the population (AMATYC, 2006; Cerrito, 1996; Cheney, 1989; Cohen, 1982; College Board, 1983;…

The Relationship between Agriculture Knowledge Bases for Teaching and Sources of Knowledge

ERIC Educational Resources Information Center

Rice, Amber H.; Kitchel, Tracy

2015-01-01

The purpose of this study was to describe the agriculture knowledge bases for teaching of agriculture teachers and to see if a relationship existed between years of teaching experience, sources of knowledge, and development of pedagogical content knowledge (PCK), using quantitative methods. A model of PCK from mathematics was utilized as a…

Control of the flow over wing airfoils in transonic regimes by means of force action of surface elements on the flow

NASA Astrophysics Data System (ADS)

Aul'chenko, S. M.; Zamuraev, V. P.

2012-09-01

Mathematical modeling of the effect of force oscillations of surface elements of a wing airfoil on the shock-wave structure of the transonic flow over it is implemented. The qualitative and quantitative effect of the oscillation parameters on the airfoil wave drag is investigated.

Quantitative Methods in Library and Information Science Literature: Descriptive vs. Inferential Statistics.

ERIC Educational Resources Information Center

Brattin, Barbara C.

Content analysis was performed on the top six core journals for 1990 in library and information science to determine the extent of research in the field. Articles (n=186) were examined for descriptive or inferential statistics and separately for the presence of mathematical models. Results show a marked (14%) increase in research for 1990,…

Quantifying falsifiability of scientific theories

NASA Astrophysics Data System (ADS)

Nemenman, Ilya

I argue that the notion of falsifiability, a key concept in defining a valid scientific theory, can be quantified using Bayesian Model Selection, which is a standard tool in modern statistics. This relates falsifiability to the quantitative version of the statistical Occam's razor, and allows transforming some long-running arguments about validity of scientific theories from philosophical discussions to rigorous mathematical calculations.

Service-Learning and Mathematics

ERIC Educational Resources Information Center

Roemer, Cynthia Anne

2009-01-01

Contemporary educational theory has given increased attention to service-learning as valuable pedagogy. Ever-changing technology progress and applications demand a quantitatively literate population, supporting the need for experiential activities in mathematics. This study addresses service-learning pedagogy in mathematics through a study of the…

Forest management and economics

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

Buongiorno, J.; Gilless, J.K.

1987-01-01

This volume provides a survey of quantitative methods, guiding the reader through formulation and analysis of models that address forest management problems. The authors use simple mathematics, graphics, and short computer programs to explain each method. Emphasizing applications, they discuss linear, integer, dynamic, and goal programming; simulation; network modeling; and econometrics, as these relate to problems of determining economic harvest schedules in even-aged and uneven-aged forests, the evaluation of forest policies, multiple-objective decision making, and more.

An Analysis of Final Course Grades in Two Different Entry Level Mathematics Courses between and among First Year College Students with Different Levels of High School Mathematics Preparation

ERIC Educational Resources Information Center

Muir, Carrie

2012-01-01

The purpose of this study was to compare the performance of first year college students with similar high school mathematics backgrounds in two introductory level college mathematics courses, "Fundamentals and Techniques of College Algebra and Quantitative Reasoning and Mathematical Skills," and to compare the performance of students…

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

PubMed

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

1986-01-01

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

Correlating subjective and objective descriptors of ultra high molecular weight wear particles from total joint prostheses.

PubMed

McMullin, Brian T; Leung, Ming-Ying; Shanbhag, Arun S; McNulty, Donald; Mabrey, Jay D; Agrawal, C Mauli

2006-02-01

A total of 750 images of individual ultra-high molecular weight polyethylene (UHMWPE) particles isolated from periprosthetic failed hip, knee, and shoulder arthroplasties were extracted from archival scanning electron micrographs. Particle size and morphology was subsequently analyzed using computerized image analysis software utilizing five descriptors found in ASTM F1877-98, a standard for quantitative description of wear debris. An online survey application was developed to display particle images, and allowed ten respondents to classify particle morphologies according to commonly used terminology as fibers, flakes, or granules. Particles were categorized based on a simple majority of responses. All descriptors were evaluated using a one-way ANOVA and Tukey-Kramer test for all-pairs comparison among each class of particles. A logistic regression model using half of the particles included in the survey was then used to develop a mathematical scheme to predict whether a given particle should be classified as a fiber, flake, or granule based on its quantitative measurements. The validity of the model was then assessed using the other half of the survey particles and compared with human responses. Comparison of the quantitative measurements of isolated particles showed that the morphologies of each particle type classified by respondents were statistically different from one another (p<0.05). The average agreement between mathematical prediction and human respondents was 83.5% (standard error 0.16%). These data suggest that computerized descriptors can be feasibly correlated with subjective terminology, thus providing a basis for a common vocabulary for particle description which can be translated into quantitative dimensions.

Correlating subjective and objective descriptors of ultra high molecular weight wear particles from total joint prostheses

PubMed Central

McMullin, Brian T.; Leung, Ming-Ying; Shanbhag, Arun S.; McNulty, Donald; Mabrey, Jay D.; Agrawal, C. Mauli

2014-01-01

A total of 750 images of individual ultra-high molecular weight polyethylene (UHMWPE) particles isolated from periprosthetic failed hip, knee, and shoulder arthroplasties were extracted from archival scanning electron micrographs. Particle size and morphology was subsequently analyzed using computerized image analysis software utilizing five descriptors found in ASTM F1877-98, a standard for quantitative description of wear debris. An online survey application was developed to display particle images, and allowed ten respondents to classify particle morphologies according to commonly used terminology as fibers, flakes, or granules. Particles were categorized based on a simple majority of responses. All descriptors were evaluated using a one-way ANOVA and Tukey–Kramer test for all-pairs comparison among each class of particles. A logistic regression model using half of the particles included in the survey was then used to develop a mathematical scheme to predict whether a given particle should be classified as a fiber, flake, or granule based on its quantitative measurements. The validity of the model was then assessed using the other half of the survey particles and compared with human responses. Comparison of the quantitative measurements of isolated particles showed that the morphologies of each particle type classified by respondents were statistically different from one another (po0:05). The average agreement between mathematical prediction and human respondents was 83.5% (standard error 0.16%). These data suggest that computerized descriptors can be feasibly correlated with subjective terminology, thus providing a basis for a common vocabulary for particle description which can be translated into quantitative dimensions. PMID:16112725

Teacher Self-Efficacy and the Use of the Internet to Cultivate Mathematics Literacy

ERIC Educational Resources Information Center

Letwinsky, Karim Medico

2012-01-01

The purpose of this quantitative study was to investigate the relationship between mathematics teachers' self-efficacy and the use of technology and the Internet in secondary education classrooms. The focus was on the Internet as a tool to promote mathematics communication and literacy in the online environment. A total of 100 mathematics teachers…

Assessing Senior Secondary School Students' Mathematical Proficiency as Related to Gender and Performance in Mathematics in Nigeria

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.

2017-01-01

The study investigated mathematical proficiency as related to gender and performance in mathematics among 400 Nigerian senior secondary school students from 10 elitist senior secondary schools in Lagos State using the quantitative research method within the blueprint of descriptive survey design. Data collected were analysed using the descriptive…

Assessing Preservice Teachers' Mathematics Cognitive Failures as Related to Mathematics Anxiety and Performance in Undergraduate Calculus

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.; Odogwu, Helen N.

2017-01-01

The study investigated mathematics cognitive failures as related to mathematics anxiety, gender and performance in calculus among 450 preservice teachers from four public universities in the South West geo-political zone of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

Science, Technology, Engineering, and Mathematics (STEM) Curriculum and Seventh Grade Mathematics and Science Achievement

ERIC Educational Resources Information Center

James, Jamie Smith

2014-01-01

The purpose of this quantitative research study was to evaluate to what degree Science, Technology, Engineering and Mathematics (STEM) education influenced mathematics and science achievement of seventh grade students in one Middle Tennessee school district. This research used an independent samples t test at the a = 0.05 level to evaluate…

Biological Surface Adsorption Index of Nanomaterials: Modelling Surface Interactions of Nanomaterials with Biomolecules.

PubMed

Chen, Ran; Riviere, Jim E

2017-01-01

Quantitative analysis of the interactions between nanomaterials and their surrounding environment is crucial for safety evaluation in the application of nanotechnology as well as its development and standardization. In this chapter, we demonstrate the importance of the adsorption of surrounding molecules onto the surface of nanomaterials by forming biocorona and thus impact the bio-identity and fate of those materials. We illustrate the key factors including various physical forces in determining the interaction happening at bio-nano interfaces. We further discuss the mathematical endeavors in explaining and predicting the adsorption phenomena, and propose a new statistics-based surface adsorption model, the Biological Surface Adsorption Index (BSAI), to quantitatively analyze the interaction profile of surface adsorption of a large group of small organic molecules onto nanomaterials with varying surface physicochemical properties, first employing five descriptors representing the surface energy profile of the nanomaterials, then further incorporating traditional semi-empirical adsorption models to address concentration effects of solutes. These Advancements in surface adsorption modelling showed a promising development in the application of quantitative predictive models in biological applications, nanomedicine, and environmental safety assessment of nanomaterials.

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

PubMed

Gibiansky, Leonid; Gibiansky, Ekaterina

2018-02-01

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

Using ‘particle in a box’ models to calculate energy levels in semiconductor quantum well structures

NASA Astrophysics Data System (ADS)

Ebbens, A. T.

2018-07-01

Although infinite potential ‘particle in a box’ models are widely used to introduce quantised energy levels their predictions cannot be quantitatively compared with atomic emission spectra. Here, this problem is overcome by describing how both infinite and finite potential well models can be used to calculate the confined energy levels of semiconductor quantum wells. This is done by using physics and mathematics concepts that are accessible to pre-university students. The results of the models are compared with experimental data and their accuracy discussed.

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.

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.

South Dakota Middle School Mathematics Teachers' Perceptions of Teaching Competencies

ERIC Educational Resources Information Center

Bleecker, Heather A.

2017-01-01

This quantitative research study investigates South Dakota middle school (grades 5-8) mathematics teachers' perceptions of teaching competencies including general pedagogical knowledge (GPK) and mathematical pedagogical content knowledge (MPCK). The study also considered how teacher characteristics relate to teacher competencies. The study…

A Computational Model of the Ionic Currents, Ca2+ Dynamics and Action Potentials Underlying Contraction of Isolated Uterine Smooth Muscle

PubMed Central

Tong, Wing-Chiu; Choi, Cecilia Y.; Karche, Sanjay; Holden, Arun V.; Zhang, Henggui; Taggart, Michael J.

2011-01-01

Uterine contractions during labor are discretely regulated by rhythmic action potentials (AP) of varying duration and form that serve to determine calcium-dependent force production. We have employed a computational biology approach to develop a fuller understanding of the complexity of excitation-contraction (E-C) coupling of uterine smooth muscle cells (USMC). Our overall aim is to establish a mathematical platform of sufficient biophysical detail to quantitatively describe known uterine E-C coupling parameters and thereby inform future empirical investigations of physiological and pathophysiological mechanisms governing normal and dysfunctional labors. From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: currents (L- and T-type), current, an hyperpolarization-activated current, three voltage-gated currents, two -activated current, -activated current, non-specific cation current, - exchanger, - pump and background current. The magnitudes and kinetics of each current system in a spindle shaped single cell with a specified surface area∶volume ratio is described by differential equations, in terms of maximal conductances, electrochemical gradient, voltage-dependent activation/inactivation gating variables and temporal changes in intracellular computed from known fluxes. These quantifications are validated by the reconstruction of the individual experimental ionic currents obtained under voltage-clamp. Phasic contraction is modeled in relation to the time constant of changing . This integrated model is validated by its reconstruction of the different USMC AP configurations (spikes, plateau and bursts of spikes), the change from bursting to plateau type AP produced by estradiol and of simultaneous experimental recordings of spontaneous AP, and phasic force. In summary, our advanced mathematical model provides a powerful tool to investigate the physiological ionic mechanisms underlying the genesis of uterine electrical E-C coupling of labor and parturition. This will furnish the evolution of descriptive and predictive quantitative models of myometrial electrogenesis at the whole cell and tissue levels. PMID:21559514

Metabolic modelling in the development of cell factories by synthetic biology

PubMed Central

Jouhten, Paula

2012-01-01

Cell factories are commonly microbial organisms utilized for bioconversion of renewable resources to bulk or high value chemicals. Introduction of novel production pathways in chassis strains is the core of the development of cell factories by synthetic biology. Synthetic biology aims to create novel biological functions and systems not found in nature by combining biology with engineering. The workflow of the development of novel cell factories with synthetic biology is ideally linear which will be attainable with the quantitative engineering approach, high-quality predictive models, and libraries of well-characterized parts. Different types of metabolic models, mathematical representations of metabolism and its components, enzymes and metabolites, are useful in particular phases of the synthetic biology workflow. In this minireview, the role of metabolic modelling in synthetic biology will be discussed with a review of current status of compatible methods and models for the in silico design and quantitative evaluation of a cell factory. PMID:24688669

Fitness to work of astronauts in conditions of action of the extreme emotional factors

NASA Astrophysics Data System (ADS)

Prisniakova, L. M.

2004-01-01

The theoretical model for the quantitative determination of influence of a level of emotional exertion on the success of human activity is presented. The learning curves of fixed words in the groups with a different level of the emotional exertion are analyzed. The obtained magnitudes of time constant T depending on a type of the emotional exertion are a quantitative measure of the emotional exertion. Time constants could also be of use for a prediction of the characteristic of fitness to work of an astronaut in conditions of extreme factors. The inverse of the sign of influencing on efficiency of activity of the man is detected. The paper offers a mathematical model of the relation between successful activity and motivations or the emotional exertion (Yerkes-Dodson law). Proposed models can serve by the theoretical basis of the quantitative characteristics of an estimation of activity of astronauts in conditions of the emotional factors at a phase of their selection.

Fitness to work of astronauts in conditions of action of the extreme emotional factors.

PubMed

Prisniakova, L M

2004-01-01

The theoretical model for the quantitative determination of influence of a level of emotional exertion on the success of human activity is presented. The learning curves of fixed words in the groups with a different level of the emotional exertion are analyzed. The obtained magnitudes of time constant T depending on a type of the emotional exertion are a quantitative measure of the emotional exertion. Time constants could also be of use for a prediction of the characteristic of fitness to work of an astronaut in conditions of extreme factors. The inverse of the sign of influencing on efficiency of activity of the man is detected. The paper offers a mathematical model of the relation between successful activity and motivations or the emotional exertion (Yerkes-Dodson law). Proposed models can serve by the theoretical basis of the quantitative characteristics of an estimation of activity of astronauts in conditions of the emotional factors at a phase of their selection. Published by Elsevier Ltd on behalf of COSPAR.

Ultrafast quantitation of six quinolones in water samples by second-order capillary electrophoresis data modeling with multivariate curve resolution-alternating least squares.

PubMed

Alcaráz, Mirta R; Vera-Candioti, Luciana; Culzoni, María J; Goicoechea, Héctor C

2014-04-01

This paper presents the development of a capillary electrophoresis method with diode array detector coupled to multivariate curve resolution-alternating least squares (MCR-ALS) to conduct the resolution and quantitation of a mixture of six quinolones in the presence of several unexpected components. Overlapping of time profiles between analytes and water matrix interferences were mathematically solved by data modeling with the well-known MCR-ALS algorithm. With the aim of overcoming the drawback originated by two compounds with similar spectra, a special strategy was implemented to model the complete electropherogram instead of dividing the data in the region as usually performed in previous works. The method was first applied to quantitate analytes in standard mixtures which were randomly prepared in ultrapure water. Then, tap water samples spiked with several interferences were analyzed. Recoveries between 76.7 and 125 % and limits of detection between 5 and 18 μg L(-1) were achieved.

Dissecting Embryonic Stem Cell Self-Renewal and Differentiation Commitment from Quantitative Models.

PubMed

Hu, Rong; Dai, Xianhua; Dai, Zhiming; Xiang, Qian; Cai, Yanning

2016-10-01

To model quantitatively embryonic stem cell (ESC) self-renewal and differentiation by computational approaches, we developed a unified mathematical model for gene expression involved in cell fate choices. Our quantitative model comprised ESC master regulators and lineage-specific pivotal genes. It took the factors of multiple pathways as input and computed expression as a function of intrinsic transcription factors, extrinsic cues, epigenetic modifications, and antagonism between ESC master regulators and lineage-specific pivotal genes. In the model, the differential equations of expression of genes involved in cell fate choices from regulation relationship were established according to the transcription and degradation rates. We applied this model to the Murine ESC self-renewal and differentiation commitment and found that it modeled the expression patterns with good accuracy. Our model analysis revealed that Murine ESC was an attractor state in culture and differentiation was predominantly caused by antagonism between ESC master regulators and lineage-specific pivotal genes. Moreover, antagonism among lineages played a critical role in lineage reprogramming. Our results also uncovered that the ordered expression alteration of ESC master regulators over time had a central role in ESC differentiation fates. Our computational framework was generally applicable to most cell-type maintenance and lineage reprogramming.

Automatic inference of multicellular regulatory networks using informative priors.

PubMed

Sun, Xiaoyun; Hong, Pengyu

2009-01-01

To fully understand the mechanisms governing animal development, computational models and algorithms are needed to enable quantitative studies of the underlying regulatory networks. We developed a mathematical model based on dynamic Bayesian networks to model multicellular regulatory networks that govern cell differentiation processes. A machine-learning method was developed to automatically infer such a model from heterogeneous data. We show that the model inference procedure can be greatly improved by incorporating interaction data across species. The proposed approach was applied to C. elegans vulval induction to reconstruct a model capable of simulating C. elegans vulval induction under 73 different genetic conditions.

Propensity to Leave versus Probability of Leaving: The Relationship between Intrinsic and Extrinsic Satisfaction in the Voluntary Leaving Behavior of IT Professionals

ERIC Educational Resources Information Center

King, Christopher S.

2013-01-01

This dissertation presents a quantitative analysis of the relationship between intrinsic and extrinsic job satisfaction and the voluntary leaving behavior of IT professionals. In addition, the study adds to the validity and reliability of the Udechukwu and Mujtaba Mathematical Turnover Model. Surveyed within the study for their intrinsic and…

Reducing the wave drag of wing airfoils in transonic flow regimes by the force action of airfoil surface elements on the flow

NASA Astrophysics Data System (ADS)

Aul'chenko, S. M.; Zamuraev, V. P.

2012-11-01

Mathematical modeling of the influence of forced oscillations of surface elements of a wing airfoil on the shock-wave structure of transonic flow past it has been carried out. The qualitative and quantitative influence of the oscillation parameters on the wave drag of the airfoil has been investigated.

STEM Education through the Perspectives of Secondary Schools Teachers and School Administrators in Turkey

ERIC Educational Resources Information Center

Çevik, Mustafa; Özgünay, Esma

2018-01-01

The aim of this study is to explore the views of science, mathematics and information technologies teachers working in secondary schools and administrators of the schools, in which these teachers are working, regarding STEM. This research is based on a survey model in which quantitative data tools were used to directly obtain the opinions of…

Multiscale Modeling of Antibody-Drug Conjugates: Connecting Tissue and Cellular Distribution to Whole Animal Pharmacokinetics and Potential Implications for Efficacy.

PubMed

Cilliers, Cornelius; Guo, Hans; Liao, Jianshan; Christodolu, Nikolas; Thurber, Greg M

2016-09-01

Antibody-drug conjugates exhibit complex pharmacokinetics due to their combination of macromolecular and small molecule properties. These issues range from systemic concerns, such as deconjugation of the small molecule drug during the long antibody circulation time or rapid clearance from nonspecific interactions, to local tumor tissue heterogeneity, cell bystander effects, and endosomal escape. Mathematical models can be used to study the impact of these processes on overall distribution in an efficient manner, and several types of models have been used to analyze varying aspects of antibody distribution including physiologically based pharmacokinetic (PBPK) models and tissue-level simulations. However, these processes are quantitative in nature and cannot be handled qualitatively in isolation. For example, free antibody from deconjugation of the small molecule will impact the distribution of conjugated antibodies within the tumor. To incorporate these effects into a unified framework, we have coupled the systemic and organ-level distribution of a PBPK model with the tissue-level detail of a distributed parameter tumor model. We used this mathematical model to analyze new experimental results on the distribution of the clinical antibody-drug conjugate Kadcyla in HER2-positive mouse xenografts. This model is able to capture the impact of the drug-antibody ratio (DAR) on tumor penetration, the net result of drug deconjugation, and the effect of using unconjugated antibody to drive ADC penetration deeper into the tumor tissue. This modeling approach will provide quantitative and mechanistic support to experimental studies trying to parse the impact of multiple mechanisms of action for these complex drugs.

Multiscale Modeling of Antibody Drug Conjugates: Connecting tissue and cellular distribution to whole animal pharmacokinetics and potential implications for efficacy

PubMed Central

Cilliers, Cornelius; Guo, Hans; Liao, Jianshan; Christodolu, Nikolas; Thurber, Greg M.

2016-01-01

Antibody drug conjugates exhibit complex pharmacokinetics due to their combination of macromolecular and small molecule properties. These issues range from systemic concerns, such as deconjugation of the small molecule drug during the long antibody circulation time or rapid clearance from non-specific interactions, to local tumor tissue heterogeneity, cell bystander effects, and endosomal escape. Mathematical models can be used to study the impact of these processes on overall distribution in an efficient manner, and several types of models have been used to analyze varying aspects of antibody distribution including physiologically based pharmacokinetic (PBPK) models and tissue-level simulations. However, these processes are quantitative in nature and cannot be handled qualitatively in isolation. For example, free antibody from deconjugation of the small molecule will impact the distribution of conjugated antibodies within the tumor. To incorporate these effects into a unified framework, we have coupled the systemic and organ-level distribution of a PBPK model with the tissue-level detail of a distributed parameter tumor model. We used this mathematical model to analyze new experimental results on the distribution of the clinical antibody drug conjugate Kadcyla in HER2 positive mouse xenografts. This model is able to capture the impact of the drug antibody ratio (DAR) on tumor penetration, the net result of drug deconjugation, and the effect of using unconjugated antibody to drive ADC penetration deeper into the tumor tissue. This modeling approach will provide quantitative and mechanistic support to experimental studies trying to parse the impact of multiple mechanisms of action for these complex drugs. PMID:27287046

Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

NASA Astrophysics Data System (ADS)

Jovanović, Ivana; Miljanović, Igor

2015-12-01

Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.

In vivo quantitative analysis of Talin turnover in response to force

PubMed Central

Hákonardóttir, Guðlaug Katrín; López-Ceballos, Pablo; Herrera-Reyes, Alejandra Donají; Das, Raibatak; Coombs, Daniel; Tanentzapf, Guy

2015-01-01

Cell adhesion to the extracellular matrix (ECM) allows cells to form and maintain three-dimensional tissue architecture. Cell–ECM adhesions are stabilized upon exposure to mechanical force. In this study, we used quantitative imaging and mathematical modeling to gain mechanistic insight into how integrin-based adhesions respond to increased and decreased mechanical forces. A critical means of regulating integrin-based adhesion is provided by modulating the turnover of integrin and its adhesion complex (integrin adhesion complex [IAC]). The turnover of the IAC component Talin, a known mechanosensor, was analyzed using fluorescence recovery after photobleaching. Experiments were carried out in live, intact flies in genetic backgrounds that increased or decreased the force applied on sites of adhesion. This analysis showed that when force is elevated, the rate of assembly of new adhesions increases such that cell–ECM adhesion is stabilized. Moreover, under conditions of decreased force, the overall rate of turnover, but not the proportion of adhesion complex components undergoing turnover, increases. Using point mutations, we identify the key functional domains of Talin that mediate its response to force. Finally, by fitting a mathematical model to the data, we uncover the mechanisms that mediate the stabilization of ECM-based adhesion during development. PMID:26446844

Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment.

PubMed

Anderson, Alexander R A; Weaver, Alissa M; Cummings, Peter T; Quaranta, Vito

2006-12-01

Emergence of invasive behavior in cancer is life-threatening, yet ill-defined due to its multifactorial nature. We present a multiscale mathematical model of cancer invasion, which considers cellular and microenvironmental factors simultaneously and interactively. Unexpectedly, the model simulations predict that harsh tumor microenvironment conditions (e.g., hypoxia, heterogenous extracellular matrix) exert a dramatic selective force on the tumor, which grows as an invasive mass with fingering margins, dominated by a few clones with aggressive traits. In contrast, mild microenvironment conditions (e.g., normoxia, homogeneous matrix) allow clones with similar aggressive traits to coexist with less aggressive phenotypes in a heterogeneous tumor mass with smooth, noninvasive margins. Thus, the genetic make-up of a cancer cell may realize its invasive potential through a clonal evolution process driven by definable microenvironmental selective forces. Our mathematical model provides a theoretical/experimental framework to quantitatively characterize this selective pressure for invasion and test ways to eliminate it.

Proposing a Formalised Model for Mindful Information Systems Offshoring

NASA Astrophysics Data System (ADS)

Costello, Gabriel J.; Coughlan, Chris; Donnellan, Brian; Gadatsch, Andreas

The central thesis of this chapter is that mathematical economics can provide a novel approach to the examination of offshoring business decisions and provide an impetus for future research in the area. A growing body of research indicates that projected cost savings from IT offshoring projects are not being met. Furthermore, evidence suggests that decision-making processes have been more emotional than rational, and that many offshoring arrangements have been rushed into without adequate analysis of the true costs involved. Building on the concept of mindfulness and mindlessness introduced to the IS literature by Swanson and Ramiller, a cost equation is developed using “deductive reasoning rather than inductive study” in the tradition of mathematical economics. The model endeavours to capture a wide range of both the quantitative and qualitative parameters. Although the economic model is illustrated against the background of a European scenario, the theoretical framework is generic and applicable to organisations in any global location.

A study of stiffness, residual strength and fatigue life relationships for composite laminates

NASA Technical Reports Server (NTRS)

Ryder, J. T.; Crossman, F. W.

1983-01-01

Qualitative and quantitative exploration of the relationship between stiffness, strength, fatigue life, residual strength, and damage of unnotched, graphite/epoxy laminates subjected to tension loading. Clarification of the mechanics of the tension loading is intended to explain previous contradictory observations and hypotheses; to develop a simple procedure to anticipate strength, fatigue life, and stiffness changes; and to provide reasons for the study of more complex cases of compression, notches, and spectrum fatigue loading. Mathematical models are developed based upon analysis of the damage states. Mathematical models were based on laminate analysis, free body type modeling or a strain energy release rate. Enough understanding of the tension loaded case is developed to allow development of a proposed, simple procedure for calculating strain to failure, stiffness, strength, data scatter, and shape of the stress-life curve for unnotched laminates subjected to tension load.

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

Insights from mathematical modeling of renal tubular function.

PubMed

Weinstein, A M

1998-01-01

Mathematical models of proximal tubule have been developed which represent the important solute species within the constraints of known cytosolic concentrations, transport fluxes, and overall epithelial permeabilities. In general, model simulations have been used to assess the quantitative feasibility of what appear to be qualitatively plausible mechanisms, or alternatively, to identify incomplete rationalization of experimental observations. The examples considered include: (1) proximal water reabsorption, for which the lateral interspace is a locus for solute-solvent coupling; (2) ammonia secretion, for which the issue is prioritizing driving forces - transport on the Na+/H+ exchanger, on the Na,K-ATPase, or ammoniagenesis; (3) formate-stimulated NaCl reabsorption, for which simple addition of a luminal membrane chloride/formate exchanger fails to represent experimental observation, and (4) balancing luminal entry and peritubular exit, in which ATP-dependent peritubular K+ channels have been implicated, but appear unable to account for the bulk of proximal tubule cell volume homeostasis.

Establishing Quantitative Within-Subject Confidence Limits For Clinical Stereoroentgenographs

NASA Astrophysics Data System (ADS)

Korn, Edward L.; Baumrind, Sheldon; Chafetz, Neil; Curry, Sean; Moffitt, Francis

1983-07-01

It is now quite clear that under ideal conditions, discrete points can be located on x-ray films with standard deviations of less than 50 i. However, under routine clinical conditions, such considerations as individual variation in anatomy, movement of the subject between exposures, and variations in image quality combine to produce considerable reductions in the confidence which can be placed in quantitative assessments made from stereoroentgenographic films. This paper discusses some considerations involved in designing mathematical models in such a way as to optimize the use of imperfect data in answering specific clinical questions.

Mathematics Anxiety and Mathematics Self-Efficacy in Relation to Medication Calculation Performance in Nurses

ERIC Educational Resources Information Center

Melius, Joyce

2012-01-01

The purpose of this study is to identify and analyze the relationships that exist between mathematics anxiety and nurse self-efficacy for mathematics, and the medication calculation performance of acute care nurses. This research used a quantitative correlational research design and involved a sample of 84 acute care nurses, LVNs and RNs, from a…

A Study of Students' Conceptual, Procedural Knowledge, Logical Thinking and Creativity during the First Year of Tertiary Mathematics

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand; Hulsman, Kees

2015-01-01

This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…

Promoting Social Change through Writing: A Quantitative Study of Research-Based Best Practices in Eighth-Grade Mathematics

ERIC Educational Resources Information Center

Bettencourt, Connie Lynn

2009-01-01

Studies report that U.S. students rank among the lowest in the area of mathematical knowledge of all industrialized countries. Schools in the United States are producing graduates ill-prepared to be successful at jobs which require mathematical competency. To increase mathematical understanding, this study examined the inclusion of writing in…

A Naturalistic Inquiry into the Attitudes toward Mathematics and Mathematics Self-Efficacy Beliefs of Middle School Students

ERIC Educational Resources Information Center

Stramel, Janet K.

2010-01-01

While there has been much quantitative research done in the area of attitudes and self-efficacy beliefs, this study sought hear the voices of the middle school child. Therefore, this qualitative study investigated the attitudes toward mathematics and mathematics self-efficacy beliefs of middle school students in one middle school in western…

Comparing Mathematics Achievement Scores: Face-To-Face versus Online Delivery

ERIC Educational Resources Information Center

Lenderman, Ami

2017-01-01

The purpose of this quantitative study was to explore the relationship between the use of online courseware at Georgia Virtual School as an instructional delivery method and student achievement of 9th and 10th grade mathematics students as measured by Mathematics I and Mathematics II End of Course Test (EOCT) scores. The knowledge of an increase,…

Elementary Teachers' Mathematical Knowledge for Teaching Prerequisite Algebra Concepts

ERIC Educational Resources Information Center

Welder, Rachael M.; Simonsen, Linda M.

2011-01-01

The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…

Using Google Apps to Develop the Mathematical Practices

ERIC Educational Resources Information Center

Layton, Rebecca D.; Cady, Jo Ann; Layton, Christopher A.

2017-01-01

Recent recommendations for the teaching of mathematics place an emphasis on the Common Core's Standards for Mathematical Practice (SMP) (CCSSI 2010). The SMPs emphasize constructing viable arguments, critiquing the ideas of others, reasoning abstractly and quantitatively, and using computational procedures. These skills, including the use of…

Continuum and discrete approach in modeling biofilm development and structure: a review.

PubMed

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

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.

Spatiotemporal Characterization of a Fibrin Clot Using Quantitative Phase Imaging

PubMed Central

Gannavarpu, Rajshekhar; Bhaduri, Basanta; Tangella, Krishnarao; Popescu, Gabriel

2014-01-01

Studying the dynamics of fibrin clot formation and its morphology is an important problem in biology and has significant impact for several scientific and clinical applications. We present a label-free technique based on quantitative phase imaging to address this problem. Using quantitative phase information, we characterized fibrin polymerization in real-time and present a mathematical model describing the transition from liquid to gel state. By exploiting the inherent optical sectioning capability of our instrument, we measured the three-dimensional structure of the fibrin clot. From this data, we evaluated the fractal nature of the fibrin network and extracted the fractal dimension. Our non-invasive and speckle-free approach analyzes the clotting process without the need for external contrast agents. PMID:25386701

Explorations of Metacognition among Academically Talented Middle and High School Mathematics Students

ERIC Educational Resources Information Center

Young, Adena Elizabeth

2010-01-01

The purpose of this dissertation was to examine metacognition among academically talented middle and high school mathematics students from both educational psychology and mathematics education perspectives. A synthesis of the literatures and three studies employing quantitative, qualitative, and mixed methodologies were used to address three…

Educational Neuroscience: New Horizons for Research in Mathematics Education

ERIC Educational Resources Information Center

Campbell, Stephen R.

2006-01-01

This paper outlines an initiative in mathematics education research that aims to augment qualitative methods of research into mathematical cognition and learning with quantitative methods of psychometrics and psychophysiology. Background and motivation are provided for this initiative, which is coming to be referred to as educational neuroscience.…

Student Attrition in Mathematics E-Learning

ERIC Educational Resources Information Center

Smith, Glenn Gordon; Ferguson, David

2005-01-01

Qualitative studies indicate that mathematics does not work well in e-learning. The current study used quantitative methods to investigate more objectively the extent of problems with mathematics in e-learning. The authors used student attrition as a simple measure of student satisfaction and course viability in two studies, one investigating…

Increasing the Diversity of Teachers in Mathematics and Science Partnerships

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Parker, Jana L.; Kitsantas, Anastasia; Bolyard, Johnna J.; Huie, Faye

2009-01-01

This study examines teacher diversity in a federally-funded mathematics and science partnership program. Each of the partnerships in the program provided preservice and/or inservice education for teachers in mathematics, science, or both. Researchers used qualitative and quantitative methods to examine the effect of strategies implemented by the…

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

Mathematics from High School to Community College: Preparation, Articulation, and College Un-Readiness

ERIC Educational Resources Information Center

Jaffe, Louise

2012-01-01

This research studied the role of mathematics as a roadblock to college completion for community college-bound students in California. Using longitudinal quantitative analysis, I observed the educational pipeline between high school and community college and analyzed how different high school mathematics histories predicted readiness, or…

Secondary School Teachers' Conceptions and Their Teaching Practices Using Graphing Calculators

ERIC Educational Resources Information Center

Lee, Jane A.; McDougall, Douglas E.

2010-01-01

This article investigates secondary school teachers' conceptions of mathematics and their teaching practices in the use of graphing calculators in their mathematics classrooms. Case studies on three teacher participants were developed using quantitative and qualitative data that consisted of self-assessments on beliefs in mathematics,…

Influences of Teaching Approaches and Class Size on Undergraduate Mathematical Learning

ERIC Educational Resources Information Center

Olson, Jo Clay; Cooper, Sandy; Lougheed, Tom

2011-01-01

An issue for many mathematics departments is the success rate of precalculus students. In an effort to increase the success rate, this quantitative study investigated how class size and teaching approach influenced student achievement and students' attitudes towards learning mathematics. Students' achievement and their attitudes toward learning…

Mathematical Tasks as a Framework for Reflection: From Research To Practice.

ERIC Educational Resources Information Center

Stein, Mary Kay; Smith, Margaret Schwan

1998-01-01

Describes the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) national reform project aimed at studying and fostering the development and implementation of enhanced mathematics instructional programs. It is a framework for reflection based on mathematical tasks used during classroom instruction and the ways in…

What Is the Relationship between Technology and Mathematics Teaching Anxiety?

ERIC Educational Resources Information Center

Tatar, Enver; Zengin, Yilmaz; Kagizmanli, Türkan Berrin

2015-01-01

The aim of this study is to determine the relationship between pre-service teachers' perceptions regarding technology use in mathematics teaching and their computer literacy levels as well as their mathematics teaching anxiety. The nonexperimental correlational research, which is included in the quantitative research approach, was used in the…

Students' Perceptions of Single-Gender Science and Mathematics Classroom Experiences

ERIC Educational Resources Information Center

Brown, Sherri L.; Ronau, Robert R.

2012-01-01

While participating in single- and mixed-gender science and mathematics classes, ninth-grade urban high school students' (n = 118) academic self-concept, self-efficacy, and school climate perceptions were examined. Their perceptions were measured quantitatively from the Fennema-Sherman Mathematics (modified for Science) Attitude and the Patterns…

Petri net modelling of biological networks.

PubMed

Chaouiya, Claudine

2007-07-01

Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series of extensions, which allow different abstraction levels, from purely qualitative to more complex quantitative models. Noteworthily, each of these models preserves the underlying graph, which depicts the interactions between the biological components. This article intends to present the basics of the approach and to foster the potential role PNs could play in the development of the computational systems biology.

A Study Assessing the Potential of Negative Effects in Interdisciplinary Math–Biology Instruction

PubMed Central

Madlung, Andreas; Bremer, Martina; Himelblau, Edward; Tullis, Alexa

2011-01-01

There is increasing enthusiasm for teaching approaches that combine mathematics and biology. The call for integrating more quantitative work in biology education has led to new teaching tools that improve quantitative skills. Little is known, however, about whether increasing interdisciplinary work can lead to adverse effects, such as the development of broader but shallower skills or the possibility that math anxiety causes some students to disengage in the classroom, or, paradoxically, to focus so much on the mathematics that they lose sight of its application for the biological concepts in the center of the unit at hand. We have developed and assessed an integrative learning module and found disciplinary learning gains to be equally strong in first-year students who actively engaged in embedded quantitative calculations as in those students who were merely presented with quantitative data in the context of interpreting biological and biostatistical results. When presented to advanced biology students, our quantitative learning tool increased test performance significantly. We conclude from our study that the addition of mathematical calculations to the first year and advanced biology curricula did not hinder overall student learning, and may increase disciplinary learning and data interpretation skills in advanced students. PMID:21364099

Biophysically Based Mathematical Modeling of Interstitial Cells of Cajal Slow Wave Activity Generated from a Discrete Unitary Potential Basis

PubMed Central

Faville, R.A.; Pullan, A.J.; Sanders, K.M.; Koh, S.D.; Lloyd, C.M.; Smith, N.P.

2009-01-01

Abstract Spontaneously rhythmic pacemaker activity produced by interstitial cells of Cajal (ICC) is the result of the entrainment of unitary potential depolarizations generated at intracellular sites termed pacemaker units. In this study, we present a mathematical modeling framework that quantitatively represents the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC operating over the physiological membrane potential range. The mathematical model presented here extends our recently developed biophysically based pacemaker unit modeling framework by including mechanisms necessary for coordinating unitary potential events, such as a T-Type Ca2+ current, Vm-dependent K+ currents, and global Ca2+ diffusion. Model simulations produce spontaneously rhythmic slow wave depolarizations with an amplitude of 65 mV at a frequency of 17.4 cpm. Our model predicts that activity at the spatial scale of the pacemaker unit is fundamental for ICC slow wave generation, and Ca2+ influx from activation of the T-Type Ca2+ current is required for unitary potential entrainment. These results suggest that intracellular Ca2+ levels, particularly in the region local to the mitochondria and endoplasmic reticulum, significantly influence pacing frequency and synchronization of pacemaker unit discharge. Moreover, numerical investigations show that our ICC model is capable of qualitatively replicating a wide range of experimental observations. PMID:19527643

Mathematical modeling the radiation effects on humoral immunity

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

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

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

Blood and small intestine cell kinetics under radiation exposures: Mathematical modeling

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

2009-12-01

Mathematical models which describe the dynamics of two vital body systems (hematopoiesis and small intestinal epithelium) in mammals exposed to acute and chronic radiation are developed. These models, based on conventional biological theories, are implemented as systems of nonlinear differential equations. Their variables and constant parameters have clear biological meaning, that provides successful identification and verification of the models in hand. It is shown that the predictions of the models qualitatively and quantitatively agree with the respective experimental data for small laboratory animals (mice, rats) exposed to acute/chronic irradiation in wide ranges of doses and dose rates. The explanation of a number of radiobiological effects, including those of the low-level long-term exposures, is proposed proceeding from the modeling results. All this bears witness to the validity of employment of the developed models, after a proper identification, in investigation and prediction of radiation effects on the hematopoietic and small intestinal epithelium systems in various mammalian species, including humans. In particular, the models can be used for estimating effects of irradiation on astronauts in the long-term space missions, such as Lunar colonies and Mars voyages.

A physiologically based mathematical model of dermal absorption in man.

PubMed

Auton, T R; Westhead, D R; Woollen, B H; Scott, R C; Wilks, M F

1994-01-01

A sound understanding of the mechanisms determining percutaneous absorption is necessary for toxicological risk assessment of chemicals contacting the skin. As part of a programme investigating these mechanisms we have developed a physiologically based mathematical model. The structure of the model parallels the multi-layer structure of the skin, with separate surface, stratum corneum and viable tissue layers. It simulates the effects of partitioning and diffusive transport between the sub-layers, and metabolism in the viable epidermis. In addition the model describes removal processes on the surface of the skin, including the effects of washing and desquamation, and rubbing off onto clothing. This model is applied to data on the penetration of the herbicide fluazifop-butyl through human skin in vivo and in vitro. Part of this dataset is used to estimate unknown model parameter values and the remainder is used to provide a partial validation of the model. Only a small fraction of the applied dose was absorbed through the skin; most of it was removed by washing or onto clothing. The model provides a quantitative description of these loss processes on the skin surface.

Introduction to focus issue: quantitative approaches to genetic networks.

PubMed

Albert, Réka; Collins, James J; Glass, Leon

2013-06-01

All cells of living organisms contain similar genetic instructions encoded in the organism's DNA. In any particular cell, the control of the expression of each different gene is regulated, in part, by binding of molecular complexes to specific regions of the DNA. The molecular complexes are composed of protein molecules, called transcription factors, combined with various other molecules such as hormones and drugs. Since transcription factors are coded by genes, cellular function is partially determined by genetic networks. Recent research is making large strides to understand both the structure and the function of these networks. Further, the emerging discipline of synthetic biology is engineering novel gene circuits with specific dynamic properties to advance both basic science and potential practical applications. Although there is not yet a universally accepted mathematical framework for studying the properties of genetic networks, the strong analogies between the activation and inhibition of gene expression and electric circuits suggest frameworks based on logical switching circuits. This focus issue provides a selection of papers reflecting current research directions in the quantitative analysis of genetic networks. The work extends from molecular models for the binding of proteins, to realistic detailed models of cellular metabolism. Between these extremes are simplified models in which genetic dynamics are modeled using classical methods of systems engineering, Boolean switching networks, differential equations that are continuous analogues of Boolean switching networks, and differential equations in which control is based on power law functions. The mathematical techniques are applied to study: (i) naturally occurring gene networks in living organisms including: cyanobacteria, Mycoplasma genitalium, fruit flies, immune cells in mammals; (ii) synthetic gene circuits in Escherichia coli and yeast; and (iii) electronic circuits modeling genetic networks using field-programmable gate arrays. Mathematical analyses will be essential for understanding naturally occurring genetic networks in diverse organisms and for providing a foundation for the improved development of synthetic genetic networks.

Introduction to Focus Issue: Quantitative Approaches to Genetic Networks

NASA Astrophysics Data System (ADS)

Albert, Réka; Collins, James J.; Glass, Leon

2013-06-01

All cells of living organisms contain similar genetic instructions encoded in the organism's DNA. In any particular cell, the control of the expression of each different gene is regulated, in part, by binding of molecular complexes to specific regions of the DNA. The molecular complexes are composed of protein molecules, called transcription factors, combined with various other molecules such as hormones and drugs. Since transcription factors are coded by genes, cellular function is partially determined by genetic networks. Recent research is making large strides to understand both the structure and the function of these networks. Further, the emerging discipline of synthetic biology is engineering novel gene circuits with specific dynamic properties to advance both basic science and potential practical applications. Although there is not yet a universally accepted mathematical framework for studying the properties of genetic networks, the strong analogies between the activation and inhibition of gene expression and electric circuits suggest frameworks based on logical switching circuits. This focus issue provides a selection of papers reflecting current research directions in the quantitative analysis of genetic networks. The work extends from molecular models for the binding of proteins, to realistic detailed models of cellular metabolism. Between these extremes are simplified models in which genetic dynamics are modeled using classical methods of systems engineering, Boolean switching networks, differential equations that are continuous analogues of Boolean switching networks, and differential equations in which control is based on power law functions. The mathematical techniques are applied to study: (i) naturally occurring gene networks in living organisms including: cyanobacteria, Mycoplasma genitalium, fruit flies, immune cells in mammals; (ii) synthetic gene circuits in Escherichia coli and yeast; and (iii) electronic circuits modeling genetic networks using field-programmable gate arrays. Mathematical analyses will be essential for understanding naturally occurring genetic networks in diverse organisms and for providing a foundation for the improved development of synthetic genetic networks.

Agent-based modeling: case study in cleavage furrow models

PubMed Central

Mogilner, Alex; Manhart, Angelika

2016-01-01

The number of studies in cell biology in which quantitative models accompany experiments has been growing steadily. Roughly, mathematical and computational techniques of these models can be classified as “differential equation based” (DE) or “agent based” (AB). Recently AB models have started to outnumber DE models, but understanding of AB philosophy and methodology is much less widespread than familiarity with DE techniques. Here we use the history of modeling a fundamental biological problem—positioning of the cleavage furrow in dividing cells—to explain how and why DE and AB models are used. We discuss differences, advantages, and shortcomings of these two approaches. PMID:27811328

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.

A New Approach to Predict the Fish Fillet Shelf-Life in Presence of Natural Preservative Agents.

PubMed

Giuffrida, Alessandro; Giarratana, Filippo; Valenti, Davide; Muscolino, Daniele; Parisi, Roberta; Parco, Alessio; Marotta, Stefania; Ziino, Graziella; Panebianco, Antonio

2017-04-13

Three data sets concerning the behaviour of spoilage flora of fillets treated with natural preservative substances (NPS) were used to construct a new kind of mathematical predictive model. This model, unlike other ones, allows expressing the antibacterial effect of the NPS separately from the prediction of the growth rate. This approach, based on the introduction of a parameter into the predictive primary model, produced a good fitting of observed data and allowed characterising quantitatively the increase of shelf-life of fillets.

Using a Prediction Model to Manage Cyber Security Threats.

PubMed

Jaganathan, Venkatesh; Cherurveettil, Priyesh; Muthu Sivashanmugam, Premapriya

2015-01-01

Cyber-attacks are an important issue faced by all organizations. Securing information systems is critical. Organizations should be able to understand the ecosystem and predict attacks. Predicting attacks quantitatively should be part of risk management. The cost impact due to worms, viruses, or other malicious software is significant. This paper proposes a mathematical model to predict the impact of an attack based on significant factors that influence cyber security. This model also considers the environmental information required. It is generalized and can be customized to the needs of the individual organization.

Using a Prediction Model to Manage Cyber Security Threats

PubMed Central

Muthu Sivashanmugam, Premapriya

2015-01-01

Cyber-attacks are an important issue faced by all organizations. Securing information systems is critical. Organizations should be able to understand the ecosystem and predict attacks. Predicting attacks quantitatively should be part of risk management. The cost impact due to worms, viruses, or other malicious software is significant. This paper proposes a mathematical model to predict the impact of an attack based on significant factors that influence cyber security. This model also considers the environmental information required. It is generalized and can be customized to the needs of the individual organization. PMID:26065024

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.

Molecular Descriptors

NASA Astrophysics Data System (ADS)

Consonni, Viviana; Todeschini, Roberto

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

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.

Terminology, concepts, and models in genetic epidemiology.

PubMed

Teare, M Dawn; Koref, Mauro F Santibàñez

2011-01-01

Genetic epidemiology brings together approaches and techniques developed in mathematical genetics and statistics, medical genetics, quantitative genetics, and epidemiology. In the 1980s, the focus was on the mapping and identification of genes where defects had large effects at the individual level. More recently, statistical and experimental advances have made possible to identify and characterise genes associated with small effects at the individual level. In this chapter, we provide a brief outline of the models, concepts, and terminology used in genetic epidemiology.

Tractable Experiment Design via Mathematical Surrogates

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

Williams, Brian J.

This presentation summarizes the development and implementation of quantitative design criteria motivated by targeted inference objectives for identifying new, potentially expensive computational or physical experiments. The first application is concerned with estimating features of quantities of interest arising from complex computational models, such as quantiles or failure probabilities. A sequential strategy is proposed for iterative refinement of the importance distributions used to efficiently sample the uncertain inputs to the computational model. In the second application, effective use of mathematical surrogates is investigated to help alleviate the analytical and numerical intractability often associated with Bayesian experiment design. This approach allows formore » the incorporation of prior information into the design process without the need for gross simplification of the design criterion. Illustrative examples of both design problems will be presented as an argument for the relevance of these research problems.« less

Quantitative Courses in a Liberal Education Program: A Case Study

ERIC Educational Resources Information Center

Wismath, Shelly L.; Mackay, D. Bruce

2012-01-01

This essay argues for the importance of quantitative reasoning skills as part of a liberal education and describes the successful introduction of a mathematics-based quantitative skills course at a small Canadian university. Today's students need quantitative problem-solving skills, to function as adults, professionals, consumers, and citizens in…

A mathematical model for foreign body reactions in 2D.

PubMed

Su, Jianzhong; Gonzales, Humberto Perez; Todorov, Michail; Kojouharov, Hristo; Tang, Liping

2011-02-01

The foreign body reactions are commonly referred to the network of immune and inflammatory reactions of human or animals to foreign objects placed in tissues. They are basic biological processes, and are also highly relevant to bioengineering applications in implants, as fibrotic tissue formations surrounding medical implants have been found to substantially reduce the effectiveness of devices. Despite of intensive research on determining the mechanisms governing such complex responses, few mechanistic mathematical models have been developed to study such foreign body reactions. This study focuses on a kinetics-based predictive tool in order to analyze outcomes of multiple interactive complex reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire period (up to several months). A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of foreign body reaction kinetics. The simulation results have been consistent with experimental data and the model can facilitate quantitative insights for study of foreign body reaction process in general.

Contributions to the study of inductive transducers for measuring the amplitude of vibrations in solid media

NASA Technical Reports Server (NTRS)

Dragan, O.; Galan, N.; Sirbu, A.; Ghita, C.

1974-01-01

The design and construction of inductive transducers for measuring the vibrations in metal bars at ultrasonic frequencies are discussed. Illustrations of the inductive transducers are provided. The quantitative relations that are useful in designing the transducers are analyzed. Mathematical models are developed to substantiate the theoretical considerations. Results obtained with laboratory equipment in testing specified metal samples are included.

Helping Students to Recognize and Evaluate an Assumption in Quantitative Reasoning: A Basic Critical-Thinking Activity with Marbles and Electronic Balance

ERIC Educational Resources Information Center

Slisko, Josip; Cruz, Adrian Corona

2013-01-01

There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively…

Decoding the Principles of Emergence and Resiliency in Biological Collective Systems - A Multi-Scale Approach: Final Report

DTIC Science & Technology

2018-02-15

models and approaches are also valid using other invasive and non - invasive technologies. Finally, we illustrate and experimentally evaluate this...2017 Project Outline q  Pattern formation diversity in wild microbial societies q  Experimental and mathematical analysis methodology q  Skeleton...chemotaxis, nutrient degradation, and the exchange of amino acids between cells. Using both quantitative experimental methods and several theoretical

3-D zebrafish embryo image filtering by nonlinear partial differential equations.

PubMed

Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro

2007-01-01

We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.

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.

Remedial Math Instruction Intervention: Efficacy of Constructivist Practices on Alternative Students with Disabilities Mathematics Achievement

ERIC Educational Resources Information Center

Mbwiri, Francis I.

2017-01-01

Many students with disabilities attending alternative high schools are not improving their mathematics ability scores. Failure to improve their mathematics ability scores has hampered their potential academic success and career prospects, resulting in many students dropping out of schools without graduating. The purpose of this quantitative study…

Teaching Biology through Statistics: Application of Statistical Methods in Genetics and Zoology Courses

ERIC Educational Resources Information Center

Colon-Berlingeri, Migdalisel; Burrowes, Patricia A.

2011-01-01

Incorporation of mathematics into biology curricula is critical to underscore for undergraduate students the relevance of mathematics to most fields of biology and the usefulness of developing quantitative process skills demanded in modern biology. At our institution, we have made significant changes to better integrate mathematics into the…

Equations and Inequalities: Making Mathematics Accessible to All. PISA

ERIC Educational Resources Information Center

Piacentini, Mario; Monticone, Chiara

2016-01-01

More than ever, students need to engage with mathematics concepts, think quantitatively and analytically, and communicate using mathematics. All these skills are central to a young person's preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic…

The Effects of English Language Proficiency and Curricular Pathways: Latina/os' Mathematics Achievement in Secondary Schools

ERIC Educational Resources Information Center

Mosqueda, Eduardo; Maldonado, Saul I.

2013-01-01

This study analyzes nationally-representative quantitative data from the first (2002) and second (2004) waves of the Educational Longitudinal Study to examine the relationship between Latina/o secondary school students' degree of English-language proficiency (ELP), mathematics course-taking measures, and 12th grade mathematics achievement.…

Culture Points: Engaging Students outside the Classroom

ERIC Educational Resources Information Center

Fraboni, Michael; Hartshorn, Kevin

2007-01-01

In the typical first-year mathematics course--whether it be calculus or a general education quantitative proficiency course--we struggle to help students see the relevance of mathematics to their own lives. Particularly in a focused course such as calculus, there is a danger that students see mathematics as an isolated subject, with applications…

Distributed Leadership: Key to Improving Primary Students' Mathematical Knowledge

ERIC Educational Resources Information Center

Larson, Matthew R.; Smith, Wendy M.

2013-01-01

The purpose of this article is to present the findings of a quantitative study focused on primary mathematics teachers who participated in an intensive professional development program and then had leadership responsibility for the implementation of a new primary mathematics curriculum in their district. The study examines the effect of the…

Teacher Efficacy of High School Mathematics Co-Teachers

ERIC Educational Resources Information Center

Rimpola, Raquel C.

2011-01-01

High school mathematics inclusion classes help provide all students the access to rigorous curriculum. This study provides information about the teacher efficacy of high school mathematics co-teachers. It considers the influence of the amount of collaborative planning time on the efficacy of co-teachers. A quantitative research design was used,…

A Study of Early Childhood Mathematics Teaching in the United States and China

ERIC Educational Resources Information Center

Li, Xia; Chi, Liping; DeBey, Mary; Baroody, Arthur J.

2015-01-01

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts.…

Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum

ERIC Educational Resources Information Center

Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…

The Preparedness of Preservice Secondary Mathematics Teachers to Teach Statistics: A Cross-Institutional Mixed Methods Study

ERIC Educational Resources Information Center

Lovett, Jennifer Nickell

2016-01-01

The purpose of this study is to provide researchers, mathematics educators, and statistics educators information about the current state of preservice secondary mathematics teachers' preparedness to teach statistics. To do so, this study employed an explanatory mixed methods design to quantitatively examine the statistical knowledge and statistics…

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

Student’s rigorous mathematical thinking based on cognitive style

NASA Astrophysics Data System (ADS)

Fitriyani, H.; Khasanah, U.

2017-12-01

The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.

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

Role of mechanics in the appearance of oscillatory instability and standing waves of the mechanochemical activity in the Physarum polycephalum plasmodium

NASA Astrophysics Data System (ADS)

Teplov, Vladimir A.

2017-06-01

The modes of continuously distributed mechanochemical self-sustained oscillations (autowaves) exhibited by the Physarum plasmodium under different experimental conditions are reviewed. The role of the stretch-induced activation of contractile oscillations in the spatiotemporal self-organization of the plasmodium is elucidated. Different mathematical models describing contractile autowaves in ectoplasm and the streaming of the endoplasm are considered. Our mathematical models, which are based on the hypothesis of local positive feedback between the deformation and contraction of the contractile apparatus, are also presented. The feedback is mediated through a chemical regulatory system, whose kinetics involves the coupling to the mechanical strain. The mathematical analysis and computer simulations have demonstrated that the solutions of the models agree quantitatively with the experimental data. In particular, the only hydrodynamic interactions between the different parts of the plasmodium via the streaming endoplasm can lead to globally coordinated ectoplasmic contractions and vigorous shuttle endoplasmic streaming. These models, with empirically determined values of the viscoelastic parameters, well simulate the form and duration of the transient contractile processes observed after the isolation of the strands as well as the subsequent excitation of auto-oscillations and their stretch-induced activation under isotonic and isometric conditions.

[A novel approach to NIR spectral quantitative analysis: semi-supervised least-squares support vector regression machine].

PubMed

Li, Lin; Xu, Shuo; An, Xin; Zhang, Lu-Da

2011-10-01

In near infrared spectral quantitative analysis, the precision of measured samples' chemical values is the theoretical limit of those of quantitative analysis with mathematical models. However, the number of samples that can obtain accurately their chemical values is few. Many models exclude the amount of samples without chemical values, and consider only these samples with chemical values when modeling sample compositions' contents. To address this problem, a semi-supervised LS-SVR (S2 LS-SVR) model is proposed on the basis of LS-SVR, which can utilize samples without chemical values as well as those with chemical values. Similar to the LS-SVR, to train this model is equivalent to solving a linear system. Finally, the samples of flue-cured tobacco were taken as experimental material, and corresponding quantitative analysis models were constructed for four sample compositions' content(total sugar, reducing sugar, total nitrogen and nicotine) with PLS regression, LS-SVR and S2 LS-SVR. For the S2 LS-SVR model, the average relative errors between actual values and predicted ones for the four sample compositions' contents are 6.62%, 7.56%, 6.11% and 8.20%, respectively, and the correlation coefficients are 0.974 1, 0.973 3, 0.923 0 and 0.948 6, respectively. Experimental results show the S2 LS-SVR model outperforms the other two, which verifies the feasibility and efficiency of the S2 LS-SVR model.

Effects of single-gender mathematics classrooms on self-perception of mathematical ability and post secondary engineering paths: an Australian case study

NASA Astrophysics Data System (ADS)

Tully, D.; Jacobs, B.

2010-08-01

This study focused on a population of female engineering students, probing the influences of their secondary school experience on their choice to pursue an engineering course of study at university. The motivating question is: Do unique opportunities exist in an all-female secondary school mathematics classroom, which impact a young woman's self-perception of her mathematics ability as well as promote a positive path towards an engineering-based university major? Using both qualitative and quantitative data collection instruments, this study examined a sample of Australian engineering students enrolled at the University of Technology, Sydney (UTS). Demographic statistics show that 40% of UTS' female engineering student population attended a single-gender secondary school, indicating a potential influence of school type (single-gender) on engineering enrolment patterns. Female students were primarily motivated to pursue a post secondary engineering path because of a self-belief that they are good at mathematics. In contrast, male students were more influenced by positive male role models of family members who are practising engineers. In measures of self- perception of mathematical skill and ability, female students from single-gender schools outscored their male engineering counterparts. Additionally, female students seem to benefit from verbal encouragement, contextualisation, same gender problem-solving groups and same gender classroom dynamics.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-08-01

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

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

NASA Astrophysics Data System (ADS)

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies.

PubMed

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

PubMed Central

Lu, Gui-Min; Yu, Jian-Guo

2018-01-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study. PMID:29892347

Analysis of passenger acceptance of commercial flights having characteristics similar to STOL

NASA Technical Reports Server (NTRS)

Kuhlthau, A. R.; Jacobson, I. D.

1973-01-01

Previous work in the development of quantitative models for the prediction of passenger reaction to motion and vehicle environment parameters in flight was extended to include a class of aircraft appropriate for low-density, short-haul service. The results indicate that it is possible to obtain quantitative response inputs from an usually small special test-subject group which will be representative of the general traveling public. Additional data which indicate the importance of comfort as a factor in evaluating ride quality was obtained, and identification of the factors which contribute to judgments regarding comfort level was improved. Seat comfort and seat spacing is very vital in the smaller aircraft. Mathematical modeling applied in conjuction with passenger reaction data was shown to be very useful for establishing ride-quality design criteria.

The Effect of Dynamic Software on Prospective Mathematics Teachers' Perceptions Regarding Information and Communication Technology

ERIC Educational Resources Information Center

Tatar, Enver

2013-01-01

The aim of this study was to determine the effect of dynamic software on prospective mathematics teachers' perception levels regarding information and communication technology (ICT). The study was conducted with senior prospective teachers studying in a department of secondary mathematics education. The data of the study used both quantitative and…

Shortage of Mathematics Teachers in Thai Basic Education Level

ERIC Educational Resources Information Center

Puncreobutr, Vichian; Rattanatumma, Tawachai

2016-01-01

The objective of this study was to identify the reasons for shortage of Mathematics teachers at Thai Basic Education level. This research is both quantitative and qualitative in nature. For the purpose of study, survey was conducted with senior high school students, in order to find out their willingness to pursue mathematics in Bachelor of…

An Evaluation of the Relationship between Classroom Practices and Mathematics Motivation from Student and Teacher Perspectives

ERIC Educational Resources Information Center

Chen, Jinsong

2011-01-01

This study evaluated the relationships between classroom practices and mathematics motivation. The evaluation was given in a specific context, namely eighth grade in U.S. middle schools. Using quantitative methods, the study adopted data from the Trends in International Mathematics and Science Study (TIMSS) 2007 and compared classroom practices…

A Mathematics Education Comparative Analysis of ALEKS Technology and Direct Classroom Instruction

ERIC Educational Resources Information Center

Mertes, Emily Sue

2013-01-01

Assessment and LEarning in Knowledge Spaces (ALEKS), a technology-based mathematics curriculum, was piloted in the 2012-2013 school year at a Minnesota rural public middle school. The goal was to find an equivalent or more effective mathematics teaching method than traditional direct instruction. The purpose of this quantitative study was to…

Cognitive Predictors of Achievement Growth in Mathematics: A 5-Year Longitudinal Study

ERIC Educational Resources Information Center

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of 1st grade quantitative competencies that predict mathematics achievement start point and growth through 5th grade. Measures of number, counting, and arithmetic competencies were administered in early 1st grade and used to predict mathematics achievement through 5th (n = 177), while controlling for…

Influence of Demographic Factors on Students' Beliefs in Learning Mathematics

ERIC Educational Resources Information Center

Tahir, Izah Mohd; Bakar, Nor Mazlina Abu

2009-01-01

Learning mathematics has been recognized by many as important. It does not only develop students' ability to think in quantitative terms but can also enhance skills such as analytical and problem solving skills. However, to enable us to tell our students how important mathematics is we have to understand students' beliefs in learning mathematics…

Teaching Efficacy: Exploring Relationships between Mathematics and Science Self-Efficacy Beliefs, PCK and Domain Knowledge among Preservice Teachers from the United States

ERIC Educational Resources Information Center

Thomson, Margareta Maria; DiFrancesca, Daniell; Carrier, Sarah; Lee, Carrie

2017-01-01

This mixed-methods study investigated the relationships among preservice teachers' efficacy beliefs, pedagogical content knowledge (PCK) and their domain knowledge (DK) as related to mathematics and science teaching. Quantitative results revealed that participants' PCK was significantly correlated with their mathematics and science efficacy…

Aspiring Mathematicians: Students' Views regarding What It Takes to Be Successful in Mathematics

ERIC Educational Resources Information Center

Ampadu, Ernest

2013-01-01

This article explores junior high school students' views regarding what it takes to be successful in mathematics. Qualitative and quantitative methods were employed to collect and analyse data, describe and interpret junior high school students (12-14 years) perceptions about what it takes to be successful in mathematics. 22 students from four…

Quantitative characterization of surface topography using spectral analysis

NASA Astrophysics Data System (ADS)

Jacobs, Tevis D. B.; Junge, Till; Pastewka, Lars

2017-03-01

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography—however, this potential can only be achieved through the accurate, quantitative reconstruction of the PSDs of real-world surfaces.

How predictive quantitative modelling of tissue organisation can inform liver disease pathogenesis.

PubMed

Drasdo, Dirk; Hoehme, Stefan; Hengstler, Jan G

2014-10-01

From the more than 100 liver diseases described, many of those with high incidence rates manifest themselves by histopathological changes, such as hepatitis, alcoholic liver disease, fatty liver disease, fibrosis, and, in its later stages, cirrhosis, hepatocellular carcinoma, primary biliary cirrhosis and other disorders. Studies of disease pathogeneses are largely based on integrating -omics data pooled from cells at different locations with spatial information from stained liver structures in animal models. Even though this has led to significant insights, the complexity of interactions as well as the involvement of processes at many different time and length scales constrains the possibility to condense disease processes in illustrations, schemes and tables. The combination of modern imaging modalities with image processing and analysis, and mathematical models opens up a promising new approach towards a quantitative understanding of pathologies and of disease processes. This strategy is discussed for two examples, ammonia metabolism after drug-induced acute liver damage, and the recovery of liver mass as well as architecture during the subsequent regeneration process. This interdisciplinary approach permits integration of biological mechanisms and models of processes contributing to disease progression at various scales into mathematical models. These can be used to perform in silico simulations to promote unravelling the relation between architecture and function as below illustrated for liver regeneration, and bridging from the in vitro situation and animal models to humans. In the near future novel mechanisms will usually not be directly elucidated by modelling. However, models will falsify hypotheses and guide towards the most informative experimental design. Copyright © 2014 European Association for the Study of the Liver. Published by Elsevier B.V. All rights reserved.

Developing a database for pedestrians' earthquake emergency evacuation in indoor scenarios.

PubMed

Zhou, Junxue; Li, Sha; Nie, Gaozhong; Fan, Xiwei; Tan, Jinxian; Li, Huayue; Pang, Xiaoke

2018-01-01

With the booming development of evacuation simulation software, developing an extensive database in indoor scenarios for evacuation models is imperative. In this paper, we conduct a qualitative and quantitative analysis of the collected videotapes and aim to provide a complete and unitary database of pedestrians' earthquake emergency response behaviors in indoor scenarios, including human-environment interactions. Using the qualitative analysis method, we extract keyword groups and keywords that code the response modes of pedestrians and construct a general decision flowchart using chronological organization. Using the quantitative analysis method, we analyze data on the delay time, evacuation speed, evacuation route and emergency exit choices. Furthermore, we study the effect of classroom layout on emergency evacuation. The database for indoor scenarios provides reliable input parameters and allows the construction of real and effective constraints for use in software and mathematical models. The database can also be used to validate the accuracy of evacuation models.

Experimental methods and transport models for drug delivery across the blood-brain barrier.

PubMed

Fu, Bingmei M

2012-06-01

The blood-brain barrier (BBB) is a dynamic barrier essential for maintaining the micro-environment of the brain. Although the special anatomical features of the BBB determine its protective role for the central nervous system (CNS) from blood-born neurotoxins, however, the BBB extremely limits the therapeutic efficacy of drugs into the CNS, which greatly hinders the treatment of major brain diseases. This review summarized the unique structures of the BBB, described a variety of in vivo and in vitro experimental methods for determining the transport properties of the BBB, e.g., the permeability of the BBB to water, ions, and solutes including nutrients, therapeutic agents and drug carriers, and presented newly developed mathematical models which quantitatively correlate the anatomical structures of the BBB with its barrier functions. Finally, on the basis of the experimental observations and the quantitative models, several strategies for drug delivery through the BBB were proposed.

Experimental Methods and Transport Models for Drug Delivery across the Blood-Brain Barrier

PubMed Central

Fu, Bingmei M

2017-01-01

The blood-brain barrier (BBB) is a dynamic barrier essential for maintaining the micro-environment of the brain. Although the special anatomical features of the BBB determine its protective role for the central nervous system (CNS) from blood-born neurotoxins, however, the BBB extremely limits the therapeutic efficacy of drugs into the CNS, which greatly hinders the treatment of major brain diseases. This review summarized the unique structures of the BBB, described a variety of in vivo and in vitro experimental methods for determining the transport properties of the BBB, e.g., the permeability of the BBB to water, ions, and solutes including nutrients, therapeutic agents and drug carriers, and presented newly developed mathematical models which quantitatively correlate the anatomical structures of the BBB with its barrier functions. Finally, on the basis of the experimental observations and the quantitative models, several strategies for drug delivery through the BBB were proposed. PMID:22201587

Specificity, cross-talk and adaptation in Interferon signaling

NASA Astrophysics Data System (ADS)

Zilman, Anton

Innate immune system is the first line of defense of higher organisms against pathogens. It coordinates the behavior of millions of cells of multiple types, achieved through numerous signaling molecules. This talk focuses on the signaling specificity of a major class of signaling molecules - Type I Interferons - which are also used therapeutically in the treatment of a number of diseases, such as Hepatitis C, multiple sclerosis and some cancers. Puzzlingly, different Interferons act through the same cell surface receptor but have different effects on the target cells. They also exhibit a strange pattern of temporal cross-talk resulting in a serious clinical problem - loss of response to Interferon therapy. We combined mathematical modeling with quantitative experiments to develop a quantitative model of specificity and adaptation in the Interferon signaling pathway. The model resolves several outstanding experimental puzzles and directly affects the clinical use of Type I Interferons in treatment of viral hepatitis and other diseases.

Systems Biology-Driven Hypotheses Tested In Vivo: The Need to Advancing Molecular Imaging Tools.

PubMed

Verma, Garima; Palombo, Alessandro; Grigioni, Mauro; La Monaca, Morena; D'Avenio, Giuseppe

2018-01-01

Processing and interpretation of biological images may provide invaluable insights on complex, living systems because images capture the overall dynamics as a "whole." Therefore, "extraction" of key, quantitative morphological parameters could be, at least in principle, helpful in building a reliable systems biology approach in understanding living objects. Molecular imaging tools for system biology models have attained widespread usage in modern experimental laboratories. Here, we provide an overview on advances in the computational technology and different instrumentations focused on molecular image processing and analysis. Quantitative data analysis through various open source software and algorithmic protocols will provide a novel approach for modeling the experimental research program. Besides this, we also highlight the predictable future trends regarding methods for automatically analyzing biological data. Such tools will be very useful to understand the detailed biological and mathematical expressions under in-silico system biology processes with modeling properties.

Mathematical Model of HIF-1 alpha Pathway, Oxygen Transport and Hypoxia

DTIC Science & Technology

2017-09-01

interpret experimental data in terms of underlying mechanisms. Such experiments, if quantitative , can also be used to calibrate and further parameterize...Wing Air Force Research Laboratory Wright-Patterson AFB OH 45433-5707 STINFO COPY Work Unit Manager MATTIE.DAV ID.R.123010 1880 Digitally signed by...MONITORING AGENCY NAME(S) AND ADDRESS(ES) Air Force Materiel Command* Air Force Research Laboratory 711th Human Performance Wing Human Effectiveness

Heat Exchange with Air and Temperature Profile of a Moving Oversize Tire

NASA Astrophysics Data System (ADS)

Grinchuk, P. S.; Fisenko, S. P.

2016-11-01

A one-dimensional mathematical model of heat transfer in a tire with account for the deformation energy dissipation and heat exchange of a moving tire with air has been developed. The mean temperature profiles are calculated and transition to a stationary thermal regime is considered. The influence of the rate of energy dissipation and of effective thermal conductivity of rubber on the temperature field is investigated quantitatively.

[Applications of mathematical statistics methods on compatibility researches of traditional Chinese medicines formulae].

PubMed

Mai, Lan-Yin; Li, Yi-Xuan; Chen, Yong; Xie, Zhen; Li, Jie; Zhong, Ming-Yu

2014-05-01

The compatibility of traditional Chinese medicines (TCMs) formulae containing enormous information, is a complex component system. Applications of mathematical statistics methods on the compatibility researches of traditional Chinese medicines formulae have great significance for promoting the modernization of traditional Chinese medicines and improving clinical efficacies and optimizations of formulae. As a tool for quantitative analysis, data inference and exploring inherent rules of substances, the mathematical statistics method can be used to reveal the working mechanisms of the compatibility of traditional Chinese medicines formulae in qualitatively and quantitatively. By reviewing studies based on the applications of mathematical statistics methods, this paper were summarized from perspective of dosages optimization, efficacies and changes of chemical components as well as the rules of incompatibility and contraindication of formulae, will provide the references for further studying and revealing the working mechanisms and the connotations of traditional Chinese medicines.

Advances and Computational Tools towards Predictable Design in Biological Engineering

PubMed Central

2014-01-01

The design process of complex systems in all the fields of engineering requires a set of quantitatively characterized components and a method to predict the output of systems composed by such elements. This strategy relies on the modularity of the used components or the prediction of their context-dependent behaviour, when parts functioning depends on the specific context. Mathematical models usually support the whole process by guiding the selection of parts and by predicting the output of interconnected systems. Such bottom-up design process cannot be trivially adopted for biological systems engineering, since parts function is hard to predict when components are reused in different contexts. This issue and the intrinsic complexity of living systems limit the capability of synthetic biologists to predict the quantitative behaviour of biological systems. The high potential of synthetic biology strongly depends on the capability of mastering this issue. This review discusses the predictability issues of basic biological parts (promoters, ribosome binding sites, coding sequences, transcriptional terminators, and plasmids) when used to engineer simple and complex gene expression systems in Escherichia coli. A comparison between bottom-up and trial-and-error approaches is performed for all the discussed elements and mathematical models supporting the prediction of parts behaviour are illustrated. PMID:25161694

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

Thangavelu, Pulari U.; Gupta, Vipul; Dixit, Narendra M., E-mail: narendra@chemeng.iisc.ernet.in

The contest between the host factor APOBEC3G (A3G) and the HIV-1 protein Vif presents an attractive target of intervention. The extent to which the A3G–Vif interaction must be suppressed to tilt the balance in favor of A3G remains unknown. We employed stochastic simulations and mathematical modeling of the within-host dynamics and evolution of HIV-1 to estimate the fraction of progeny virions that must incorporate A3G to render productive infection unsustainable. Using three different approaches, we found consistently that a transition from sustained infection to suppression of productive infection occurred when the latter fraction exceeded ∼0.8. The transition was triggered bymore » A3G-induced hypermutations that led to premature stop codons compromising viral production and was consistent with driving the basic reproductive number, R{sub 0}, below unity. The fraction identified may serve as a quantitative guideline for strategies targeting the A3G–Vif axis. - Highlights: • We perform simulations and mathematical modeling of the role of APOBEC3G in suppressing HIV-1 infection. • In three distinct ways, we estimate that when over 80% of progeny virions carry APOBEC3G, productive HIV-1 infection would be suppressed. • Our estimate of this critical fraction presents quantitative guidelines for strategies targeting the APOBEC3G–Vif axis.« less

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

PubMed Central

de la Fuente, Ildefonso Martínez

2010-01-01

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life. PMID:20957111

[SciELO Public Health: the performance of Cadernos de Saúde Pública and Revista de Saúde Pública].

PubMed

Barata, Rita Barradas

2007-12-01

The aim of this paper was to analyze two Brazilian scientific journals included in the SciELO Library of Public Health, using a group of bibliometric indicators and scrutinizing the articles most viewed. Cadernos de Saúde Pública was accessed 3,743.59 times per month, with an average of 30.31 citations per article. The 50 articles most viewed (6.72 to 524.5 views) were mostly published in Portuguese (92%). 42% were theoretical essays, 20% surveys, and 16% descriptive studies. 42% used argumentative techniques, 34% quantitative techniques, 18% qualitative techniques, and 6% mathematical modeling. The most common themes were: health and work (50%), epidemiology (22%), and environmental health (8%). Revista de Saúde Pública was accessed 1,590.97 times per month, with an average of 26.27 citations per article. The 50 articles most viewed (7.33 and 56.50 views) were all published in Portuguese: 46% were surveys, 14% databases analysis, and 12% systematic reviews. Quantitative techniques were adopted in 66% of such articles, while mathematical modeling was the same as observed in Cadernos de Saúde Pública, as were qualitative techniques. The most common themes were health services organization (22%), nutrition (22%), health and work (18%), epidemiology (12%), and environmental health (12%).

Choices and changes: Eccles' Expectancy-Value model and upper-secondary school students' longitudinal reflections about their choice of a STEM education

NASA Astrophysics Data System (ADS)

Lykkegaard, Eva; Ulriksen, Lars

2016-03-01

During the past 30 years, Eccles' comprehensive social-psychological Expectancy-Value Model of Motivated Behavioural Choices (EV-MBC model) has been proven suitable for studying educational choices related to Science, Technology, Engineering and/or Mathematics (STEM). The reflections of 15 students in their last year in upper-secondary school concerning their choice of tertiary education were examined using quantitative EV-MBC surveys and repeated qualitative interviews. This article presents the analyses of three cases in detail. The analytical focus was whether the factors indicated in the EV-MBC model could be used to detect significant changes in the students' educational choice processes. An important finding was that the quantitative EV-MBC surveys and the qualitative interviews gave quite different results concerning the students' considerations about the choice of tertiary education, and that significant changes in the students' reflections were not captured by the factors of the EV-MBC model. This questions the validity of the EV-MBC surveys. Moreover, the quantitative factors from the EV-MBC model did not sufficiently explain students' dynamical educational choice processes where students in parallel considered several different potential educational trajectories. We therefore call for further studies of the EV-MBC model's use in describing longitudinal choice processes and especially in investigating significant changes.

Elementary metallography

NASA Technical Reports Server (NTRS)

Kazem, Sayyed M.

1992-01-01

Materials and Processes 1 (MET 141) is offered to freshmen by the Mechanical Engineering Department at Purdue University. The goal of MET 141 is to broaden the technical background of students who have not had any college science courses. Hence, applied physics, chemistry, and mathematics are included and quantitative problem solving is involved. In the elementary metallography experiment of this course, the objectives are: (1) introduce the vocabulary and establish outlook; (2) make qualitative observations and quantitative measurements; (3) demonstrate the proper use of equipment; and (4) review basic mathematics and science.

Clinical and mathematical introduction to computer processing of scintigraphic images

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

Goris, M.L.; Briandet, P.A.

The authors state in their preface:''...we believe that there is no book yet available in which computing in nuclear medicine has been approached in a reasonable manner. This book is our attempt to correct the situation.'' The book is divided into four sections: (1) Clinical Applications of Quantitative Scintigraphic Analysis; (2) Mathematical Derivations; (3) Processing Methods of Scintigraphic Images; and (4) The (Computer) System. Section 1 has chapters on quantitative approaches to congenital and acquired heart diseases, nephrology and urology, and pulmonary medicine.

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

NASA Astrophysics Data System (ADS)

Ojha, Lokendra Kumar

2017-07-01

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

Exploring mathematics anxiety and attitude: Mathematics students' experiences

NASA Astrophysics Data System (ADS)

Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

2017-11-01

A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

Spatiotemporal modeling of laser tissue soldering using photothermal nanocomposites.

PubMed

Mushaben, Madaline; Urie, Russell; Flake, Tanner; Jaffe, Michael; Rege, Kaushal; Heys, Jeffrey

2018-02-01

Laser tissue soldering using photothermal solders is a technology that facilitates rapid sealing using heat-induced changes in the tissue and the solder material. The solder material is made of gold nanorods embedded in a protein matrix patch that can be placed over the tissue rupture site and heated with a laser. Although laser tissue soldering is an attractive approach for surgical repair, potential photothermal damage can limit the success of this approach. Development of predictive mathematical models of photothermal effects including cell death, can lead to more efficient approaches in laser-based tissue repair. We describe an experimental and modeling investigation into photothermal solder patches for sealing porcine and mouse cadaver intestine sections using near-infrared laser irradiation. Spatiotemporal changes in temperature were determined at the surface as well as various depths below the patch. A mathematical model, based on the finite element method, predicts the spatiotemporal temperature distribution in the patch and surrounding tissue, as well as concomitant cell death in the tissue is described. For both the porcine and mouse intestine systems, the model predicts temperatures that are quantitatively similar to the experimental measurements with the model predictions of temperature increase often being within a just a few degrees of experimental measurements. This mathematical model can be employed to identify optimal conditions for minimizing healthy cell death while still achieving a strong seal of the ruptured tissue using laser soldering. Lasers Surg. Med. 50:143-152, 2018. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

[Quality assurance of the renal applications software].

PubMed

del Real Núñez, R; Contreras Puertas, P I; Moreno Ortega, E; Mena Bares, L M; Maza Muret, F R; Latre Romero, J M

2007-01-01

The need for quality assurance of all technical aspects of nuclear medicine studies is widely recognised. However, little attention has been paid to the quality assurance of the applications software. Our work reported here aims at verifying the analysis software for processing of renal nuclear medicine studies (renograms). The software tools were used to build a synthetic dynamic model of renal system. The model consists of two phases: perfusion and function. The organs of interest (kidneys, bladder and aortic artery) were simple geometric forms. The uptake of the renal structures was described by mathematic functions. Curves corresponding to normal or pathological conditions were simulated for kidneys, bladder and aortic artery by appropriate selection of parameters. There was no difference between the parameters of the mathematic curves and the quantitative data produced by the renal analysis program. Our test procedure is simple to apply, reliable, reproducible and rapid to verify the renal applications software.

Petri Nets - A Mathematical Formalism to Analyze Chemical Reaction Networks.

PubMed

Koch, Ina

2010-12-17

In this review we introduce and discuss Petri nets - a mathematical formalism to describe and analyze chemical reaction networks. Petri nets were developed to describe concurrency in general systems. We find most applications to technical and financial systems, but since about twenty years also in systems biology to model biochemical systems. This review aims to give a short informal introduction to the basic formalism illustrated by a chemical example, and to discuss possible applications to the analysis of chemical reaction networks, including cheminformatics. We give a short overview about qualitative as well as quantitative modeling Petri net techniques useful in systems biology, summarizing the state-of-the-art in that field and providing the main literature references. Finally, we discuss advantages and limitations of Petri nets and give an outlook to further development. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

PubMed

Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

2014-12-01

A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

Behavioral variability of choices versus structural inconsistency of preferences.

PubMed

Regenwetter, Michel; Davis-Stober, Clintin P

2012-04-01

Theories of rational choice often make the structural consistency assumption that every decision maker's binary strict preference among choice alternatives forms a strict weak order. Likewise, the very concept of a utility function over lotteries in normative, prescriptive, and descriptive theory is mathematically equivalent to strict weak order preferences over those lotteries, while intransitive heuristic models violate such weak orders. Using new quantitative interdisciplinary methodologies, we dissociate the variability of choices from the structural inconsistency of preferences. We show that laboratory choice behavior among stimuli of a classical "intransitivity" paradigm is, in fact, consistent with variable strict weak order preferences. We find that decision makers act in accordance with a restrictive mathematical model that, for the behavioral sciences, is extraordinarily parsimonious. Our findings suggest that the best place to invest future behavioral decision research is not in the development of new intransitive decision models but rather in the specification of parsimonious models consistent with strict weak order(s), as well as heuristics and other process models that explain why preferences appear to be weakly ordered.

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

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

PubMed

Gramatica, Paola; Papa, Ester; Sangion, Alessandro

2018-01-24

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

Simple mathematical law benchmarks human confrontations.

PubMed

Johnson, Neil F; Medina, Pablo; Zhao, Guannan; Messinger, Daniel S; Horgan, John; Gill, Paul; Bohorquez, Juan Camilo; Mattson, Whitney; Gangi, Devon; Qi, Hong; Manrique, Pedro; Velasquez, Nicolas; Morgenstern, Ana; Restrepo, Elvira; Johnson, Nicholas; Spagat, Michael; Zarama, Roberto

2013-12-10

Many high-profile societal problems involve an individual or group repeatedly attacking another - from child-parent disputes, sexual violence against women, civil unrest, violent conflicts and acts of terror, to current cyber-attacks on national infrastructure and ultrafast cyber-trades attacking stockholders. There is an urgent need to quantify the likely severity and timing of such future acts, shed light on likely perpetrators, and identify intervention strategies. Here we present a combined analysis of multiple datasets across all these domains which account for >100,000 events, and show that a simple mathematical law can benchmark them all. We derive this benchmark and interpret it, using a minimal mechanistic model grounded by state-of-the-art fieldwork. Our findings provide quantitative predictions concerning future attacks; a tool to help detect common perpetrators and abnormal behaviors; insight into the trajectory of a 'lone wolf'; identification of a critical threshold for spreading a message or idea among perpetrators; an intervention strategy to erode the most lethal clusters; and more broadly, a quantitative starting point for cross-disciplinary theorizing about human aggression at the individual and group level, in both real and online worlds.

Simple mathematical law benchmarks human confrontations

NASA Astrophysics Data System (ADS)

Johnson, Neil F.; Medina, Pablo; Zhao, Guannan; Messinger, Daniel S.; Horgan, John; Gill, Paul; Bohorquez, Juan Camilo; Mattson, Whitney; Gangi, Devon; Qi, Hong; Manrique, Pedro; Velasquez, Nicolas; Morgenstern, Ana; Restrepo, Elvira; Johnson, Nicholas; Spagat, Michael; Zarama, Roberto

2013-12-01

Many high-profile societal problems involve an individual or group repeatedly attacking another - from child-parent disputes, sexual violence against women, civil unrest, violent conflicts and acts of terror, to current cyber-attacks on national infrastructure and ultrafast cyber-trades attacking stockholders. There is an urgent need to quantify the likely severity and timing of such future acts, shed light on likely perpetrators, and identify intervention strategies. Here we present a combined analysis of multiple datasets across all these domains which account for >100,000 events, and show that a simple mathematical law can benchmark them all. We derive this benchmark and interpret it, using a minimal mechanistic model grounded by state-of-the-art fieldwork. Our findings provide quantitative predictions concerning future attacks; a tool to help detect common perpetrators and abnormal behaviors; insight into the trajectory of a `lone wolf' identification of a critical threshold for spreading a message or idea among perpetrators; an intervention strategy to erode the most lethal clusters; and more broadly, a quantitative starting point for cross-disciplinary theorizing about human aggression at the individual and group level, in both real and online worlds.

Computational technique for stepwise quantitative assessment of equation correctness

NASA Astrophysics Data System (ADS)

Othman, Nuru'l Izzah; Bakar, Zainab Abu

2017-04-01

Many of the computer-aided mathematics assessment systems that are available today possess the capability to implement stepwise correctness checking of a working scheme for solving equations. The computational technique for assessing the correctness of each response in the scheme mainly involves checking the mathematical equivalence and providing qualitative feedback. This paper presents a technique, known as the Stepwise Correctness Checking and Scoring (SCCS) technique that checks the correctness of each equation in terms of structural equivalence and provides quantitative feedback. The technique, which is based on the Multiset framework, adapts certain techniques from textual information retrieval involving tokenization, document modelling and similarity evaluation. The performance of the SCCS technique was tested using worked solutions on solving linear algebraic equations in one variable. 350 working schemes comprising of 1385 responses were collected using a marking engine prototype, which has been developed based on the technique. The results show that both the automated analytical scores and the automated overall scores generated by the marking engine exhibit high percent agreement, high correlation and high degree of agreement with manual scores with small average absolute and mixed errors.

Remote sensing observations for monitoring and mathematical simulations of transboundary air pollutants migration from Siberian mass wildfires to Kazakhstan

NASA Astrophysics Data System (ADS)

Kaipov, I. V.

2017-03-01

Anthropogenic and natural factors have increased the power of wildfires in massive Siberian woodlands. As a consequence, the expansion of burned areas and increase in the duration of the forest fire season have led to the release of significant amounts of gases and aerosols. Therefore, it is important to understand the impact of wildland fires on air quality, atmospheric composition, climate and accurately describe the distribution of combustion products in time and space. The most effective research tool is the regional hydrodynamic model of the atmosphere, coupled with the model of pollutants transport and chemical interaction. Taking into account the meteorological parameters and processes of chemical interaction of impurities, complex use of remote sensing techniques for monitoring massive forest fires and mathematical modeling of long-range transport of pollutants in the atmosphere, allow to evaluate spatial and temporal scale of the phenomenon and calculate the quantitative characteristics of pollutants depending on the height and distance of migration.

A mathematical study of a model for childhood diseases with non-permanent immunity

NASA Astrophysics Data System (ADS)

Moghadas, S. M.; Gumel, A. B.

2003-08-01

Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. Since vaccination is considered to be the most effective strategy against childhood diseases, the development of a framework that would predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial. This paper provides this framework via qualitative and quantitative analysis of a deterministic mathematical model for the transmission dynamics of a childhood disease in the presence of a preventive vaccine that may wane over time. Using global stability analysis of the model, based on constructing a Lyapunov function, it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value. It is also shown that the disease will persist within the population if the coverage level is below this threshold. These results are verified numerically by constructing, and then simulating, a robust semi-explicit second-order finite-difference method.

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.

A computational model of the ionic currents, Ca2+ dynamics and action potentials underlying contraction of isolated uterine smooth muscle.

PubMed

Tong, Wing-Chiu; Choi, Cecilia Y; Kharche, Sanjay; Karche, Sanjay; Holden, Arun V; Zhang, Henggui; Taggart, Michael J

2011-04-29

Uterine contractions during labor are discretely regulated by rhythmic action potentials (AP) of varying duration and form that serve to determine calcium-dependent force production. We have employed a computational biology approach to develop a fuller understanding of the complexity of excitation-contraction (E-C) coupling of uterine smooth muscle cells (USMC). Our overall aim is to establish a mathematical platform of sufficient biophysical detail to quantitatively describe known uterine E-C coupling parameters and thereby inform future empirical investigations of physiological and pathophysiological mechanisms governing normal and dysfunctional labors. From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: Ca2+ currents (L- and T-type), Na+ current, an hyperpolarization-activated current, three voltage-gated K+ currents, two Ca2+-activated K+ current, Ca2+-activated Cl current, non-specific cation current, Na+-Ca2+ exchanger, Na+-K+ pump and background current. The magnitudes and kinetics of each current system in a spindle shaped single cell with a specified surface area:volume ratio is described by differential equations, in terms of maximal conductances, electrochemical gradient, voltage-dependent activation/inactivation gating variables and temporal changes in intracellular Ca2+ computed from known Ca2+ fluxes. These quantifications are validated by the reconstruction of the individual experimental ionic currents obtained under voltage-clamp. Phasic contraction is modeled in relation to the time constant of changing [Ca2+]i. This integrated model is validated by its reconstruction of the different USMC AP configurations (spikes, plateau and bursts of spikes), the change from bursting to plateau type AP produced by estradiol and of simultaneous experimental recordings of spontaneous AP, [Ca2+]i and phasic force. In summary, our advanced mathematical model provides a powerful tool to investigate the physiological ionic mechanisms underlying the genesis of uterine electrical E-C coupling of labor and parturition. This will furnish the evolution of descriptive and predictive quantitative models of myometrial electrogenesis at the whole cell and tissue levels.

Comparing Differences in Math Achievement and Attitudes toward Math in a Sixth Grade Mathematics Enrichment Pilot Program

ERIC Educational Resources Information Center

Tow, Tamara

2011-01-01

High-stakes assessments have encouraged educators to ignore the needs of the top performers. Therefore, the Oakwood School District decided to implement a mathematics pilot enrichment program in order to meet the needs of the advanced mathematics students. As a result, this study used quantitative data to determine if there was a significant…

Affordance Access Matters: Preschool Children's Learning Progressions While Interacting with Touch-Screen Mathematics Apps

ERIC Educational Resources Information Center

Bullock, Emma P.; Shumway, Jessica F.; Watts, Christina M.; Moyer-Packenham, Patricia S.

2017-01-01

The purpose of this study was to contribute to the research on mathematics app use by very young children, and specifically mathematics apps for touch-screen mobile devices that contain virtual manipulatives. The study used a convergent parallel mixed methods design, in which quantitative and qualitative data were collected in parallel, analyzed…

The Effects of Integrating LEGO Robotics into a Mathematics Curriculum to Promote the Development of Proportional Reasoning

ERIC Educational Resources Information Center

Casler-Failing, Shelli L.

2017-01-01

This mixed methods, action research case study sought to investigate the effects of incorporating LEGO robotics into a seventh grade mathematics curriculum focused on the development of proportional reasoning through the lens of Social Constructivist Theory. Quantitative data was collected via pre- and post-tests from the mathematics class of six…

Interdisciplinary Student/Teacher Materials in Energy, the Environment, and the Economy: Mathematics in Energy, Grades 8-9.

ERIC Educational Resources Information Center

Brown, Evelyn; And Others

This publication is part of a series of instructional units produced by NSTA's Project for an Energy-Enriched Curriculum. The teacher's manual and the student guide for a mathematics unit in this series are presented here. This unit attempts to teach students some necessary mathematical skills needed to understand quantitative facts about energy.…

The Effect of Math Anxiety on the Academic Success of Developmental Mathematics Students at a Texas Community College

ERIC Educational Resources Information Center

Fannin-Carroll, Kristen D.

2014-01-01

The purpose of this study was to examine the relationship between math anxiety and academic success of developmental mathematics students at a Texas community college based on age, gender, and level of developmental mathematics program. A quantitative, casual-comparative design was used to determine relationships. A total of 185 developmental…

The Relationship between Multiplication Fact Speed-Recall and Fluency and Higher Level Mathematics Learning with Eighth Grade Middle School Students

ERIC Educational Resources Information Center

Curry, Steven James

2012-01-01

This quantitative study investigated relationships between higher level mathematics learning and multiplication fact fluency, multiplication fact speed-recall, and reading grade equivalency of eighth grade students in Algebra I and Pre-Algebra. Higher level mathematics learning was indicated by an average score of 80% or higher on first and second…

Experiencing teaching and learning quantitative reasoning in a project-based context

NASA Astrophysics Data System (ADS)

Muir, Tracey; Beswick, Kim; Callingham, Rosemary; Jade, Katara

2016-12-01

This paper presents the findings of a small-scale study that investigated the issues and challenges of teaching and learning about quantitative reasoning (QR) within a project-based learning (PjBL) context. Students and teachers were surveyed and interviewed about their experiences of learning and teaching QR in that context in contrast to teaching and learning mathematics in more traditional settings. The grade 9-12 student participants were characterised by a history of disengagement with mathematics and school in general, and the teacher participants were non-mathematics specialist teachers. Both students and teachers were new to the PjBL situation, which resulted in the teaching/learning relationship being a reciprocal one. The findings indicated that students and teachers viewed QR positively, particularly when compared with traditional mathematics teaching, yet tensions were identified for aspects such as implementation of curriculum and integration of relevant mathematics into projects. Both sets of participants identified situations where learning QR was particularly successful, along with concerns or difficulties about integrating QR into project work. The findings have implications for educators, who may need to examine their own approaches to mathematics teaching, particularly in terms of facilitating student engagement with the subject.

Mathematical modeling and simulation in animal health. Part I: Moving beyond pharmacokinetics.

PubMed

Riviere, J E; Gabrielsson, J; Fink, M; Mochel, J

2016-06-01

The application of mathematical modeling to problems in animal health has a rich history in the form of pharmacokinetic modeling applied to problems in veterinary medicine. Advances in modeling and simulation beyond pharmacokinetics have the potential to streamline and speed-up drug research and development programs. To foster these goals, a series of manuscripts will be published with the following goals: (i) expand the application of modeling and simulation to issues in veterinary pharmacology; (ii) bridge the gap between the level of modeling and simulation practiced in human and veterinary pharmacology; (iii) explore how modeling and simulation concepts can be used to improve our understanding of common issues not readily addressed in human pharmacology (e.g. breed differences, tissue residue depletion, vast weight ranges among adults within a single species, interspecies differences, small animal species research where data collection is limited to sparse sampling, availability of different sampling matrices); and (iv) describe how quantitative pharmacology approaches could help understanding key pharmacokinetic and pharmacodynamic characteristics of a drug candidate, with the goal of providing explicit, reproducible, and predictive evidence for optimizing drug development plans, enabling critical decision making, and eventually bringing safe and effective medicines to patients. This study introduces these concepts and introduces new approaches to modeling and simulation as well as clearly articulate basic assumptions and good practices. The driving force behind these activities is to create predictive models that are based on solid physiological and pharmacological principles as well as adhering to the limitations that are fundamental to applying mathematical and statistical models to biological systems. © 2015 John Wiley & Sons Ltd.

[Fuzzy mathematic quantitative law of composing principle in the study of traditional Chinese medicine].

PubMed

Liu, Ming; Gao, Yue; Xiao, Rui; Zhang, Bo-li

2009-01-01

This study is to analyze microcosmic significance of Chinese medicine composing principle "principal, assistant, complement and mediating guide" and it's fuzzy mathematic quantitative law. According to molecular biology and maximal membership principle, fuzzy subset and membership functions were proposed. Using in vivo experiment on the effects of SiWu Decoction and its ingredients on mice with radiation-induced blood deficiency, it is concluded that DiHuang and DangGui belonged to the principal and assistant subset, BaiShao belonged to the contrary complement subset, ChuanXiong belonged to the mediating guide subset by maximal membership principle. It is discussed that traditional Chinese medicine will be consummate medical science when its theory can be described by mathematic language.

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

PubMed

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

2017-04-01

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

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

The development and potential of inverse simulation for the quantitative assessment of helicopter handling qualities

NASA Technical Reports Server (NTRS)

Bradley, Roy; Thomson, Douglas G.

1993-01-01

In this paper it is proposed that inverse simulation can make a positive contribution to the study of handling qualities. It is shown that mathematical descriptions of the MTEs (Mission Task Elements) defined in ADS-33C may be used to drive an inverse simulation thereby generating, from an appropriate mathematical model, the controls and states of a subject helicopter flying it. By presenting the results of such simulations it is shown that, in the context of inverse simulation, the attitude quickness parameters given in ADS-33C are independent of vehicle configuration. An alternative quickness parameter, associated with the control displacements required to fly the MTE is proposed, and some preliminary results are presented.

Mathematics make microbes beautiful, beneficial, and bountiful.

PubMed

Jungck, John R

2012-01-01

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning. Copyright © 2012 Elsevier Inc. All rights reserved.

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

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

[A new method of processing quantitative PCR data].

PubMed

Ke, Bing-Shen; Li, Guang-Yun; Chen, Shi-Min; Huang, Xiang-Yan; Chen, Ying-Jian; Xu, Jun

2003-05-01

Today standard PCR can't satisfy the need of biotechnique development and clinical research any more. After numerous dynamic research, PE company found there is a linear relation between initial template number and cycling time when the accumulating fluorescent product is detectable.Therefore,they developed a quantitative PCR technique to be used in PE7700 and PE5700. But the error of this technique is too great to satisfy the need of biotechnique development and clinical research. A better quantitative PCR technique is needed. The mathematical model submitted here is combined with the achievement of relative science,and based on the PCR principle and careful analysis of molecular relationship of main members in PCR reaction system. This model describes the function relation between product quantity or fluorescence intensity and initial template number and other reaction conditions, and can reflect the accumulating rule of PCR product molecule accurately. Accurate quantitative PCR analysis can be made use this function relation. Accumulated PCR product quantity can be obtained from initial template number. Using this model to do quantitative PCR analysis,result error is only related to the accuracy of fluorescence intensity or the instrument used. For an example, when the fluorescence intensity is accurate to 6 digits and the template size is between 100 to 1,000,000, the quantitative result accuracy will be more than 99%. The difference of result error is distinct using same condition,same instrument but different analysis method. Moreover,if the PCR quantitative analysis system is used to process data, it will get result 80 times of accuracy than using CT method.

A hydroelastic model of hydrocephalus

NASA Astrophysics Data System (ADS)

Smillie, Alan; Sobey, Ian; Molnar, Zoltan

2005-09-01

We combine elements of poroelasticity and of fluid mechanics to construct a mathematical model of the human brain and ventricular system. The model is used to study hydrocephalus, a pathological condition in which the normal flow of the cerebrospinal fluid is disturbed, causing the brain to become deformed. Our model extends recent work in this area by including flow through the aqueduct, by incorporating boundary conditions that we believe accurately represent the anatomy of the brain and by including time dependence. This enables us to construct a quantitative model of the onset, development and treatment of this condition. We formulate and solve the governing equations and boundary conditions for this model and give results that are relevant to clinical observations.

Exploring Phytoplankton Population Investigation Growth to Enhance Quantitative Literacy

ERIC Educational Resources Information Center

Baumgartner, Erin; Biga, Lindsay; Bledsoe, Karen; Dawson, James; Grammer, Julie; Howard, Ava; Snyder, Jeffrey

2015-01-01

Quantitative literacy is essential to biological literacy (and is one of the core concepts in "Vision and Change in Undergraduate Biology Education: A Call to Action"; AAAS 2009). Building quantitative literacy is a challenging endeavor for biology instructors. Integrating mathematical skills into biological investigations can help build…

Comparison of blood flow models and acquisitions for quantitative myocardial perfusion estimation from dynamic CT

NASA Astrophysics Data System (ADS)

Bindschadler, Michael; Modgil, Dimple; Branch, Kelley R.; La Riviere, Patrick J.; Alessio, Adam M.

2014-04-01

Myocardial blood flow (MBF) can be estimated from dynamic contrast enhanced (DCE) cardiac CT acquisitions, leading to quantitative assessment of regional perfusion. The need for low radiation dose and the lack of consensus on MBF estimation methods motivates this study to refine the selection of acquisition protocols and models for CT-derived MBF. DCE cardiac CT acquisitions were simulated for a range of flow states (MBF = 0.5, 1, 2, 3 ml (min g)-1, cardiac output = 3, 5, 8 L min-1). Patient kinetics were generated by a mathematical model of iodine exchange incorporating numerous physiological features including heterogenenous microvascular flow, permeability and capillary contrast gradients. CT acquisitions were simulated for multiple realizations of realistic x-ray flux levels. CT acquisitions that reduce radiation exposure were implemented by varying both temporal sampling (1, 2, and 3 s sampling intervals) and tube currents (140, 70, and 25 mAs). For all acquisitions, we compared three quantitative MBF estimation methods (two-compartment model, an axially-distributed model, and the adiabatic approximation to the tissue homogeneous model) and a qualitative slope-based method. In total, over 11 000 time attenuation curves were used to evaluate MBF estimation in multiple patient and imaging scenarios. After iodine-based beam hardening correction, the slope method consistently underestimated flow by on average 47.5% and the quantitative models provided estimates with less than 6.5% average bias and increasing variance with increasing dose reductions. The three quantitative models performed equally well, offering estimates with essentially identical root mean squared error (RMSE) for matched acquisitions. MBF estimates using the qualitative slope method were inferior in terms of bias and RMSE compared to the quantitative methods. MBF estimate error was equal at matched dose reductions for all quantitative methods and range of techniques evaluated. This suggests that there is no particular advantage between quantitative estimation methods nor to performing dose reduction via tube current reduction compared to temporal sampling reduction. These data are important for optimizing implementation of cardiac dynamic CT in clinical practice and in prospective CT MBF trials.

Querying quantitative logic models (Q2LM) to study intracellular signaling networks and cell-cytokine interactions.

PubMed

Morris, Melody K; Shriver, Zachary; Sasisekharan, Ram; Lauffenburger, Douglas A

2012-03-01

Mathematical models have substantially improved our ability to predict the response of a complex biological system to perturbation, but their use is typically limited by difficulties in specifying model topology and parameter values. Additionally, incorporating entities across different biological scales ranging from molecular to organismal in the same model is not trivial. Here, we present a framework called "querying quantitative logic models" (Q2LM) for building and asking questions of constrained fuzzy logic (cFL) models. cFL is a recently developed modeling formalism that uses logic gates to describe influences among entities, with transfer functions to describe quantitative dependencies. Q2LM does not rely on dedicated data to train the parameters of the transfer functions, and it permits straight-forward incorporation of entities at multiple biological scales. The Q2LM framework can be employed to ask questions such as: Which therapeutic perturbations accomplish a designated goal, and under what environmental conditions will these perturbations be effective? We demonstrate the utility of this framework for generating testable hypotheses in two examples: (i) a intracellular signaling network model; and (ii) a model for pharmacokinetics and pharmacodynamics of cell-cytokine interactions; in the latter, we validate hypotheses concerning molecular design of granulocyte colony stimulating factor. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

An exploration of gender differences in tertiary mathematics

NASA Astrophysics Data System (ADS)

Watson, Jane M.

1989-02-01

Data from 400 students in a tertiary mathematics course were analysed to explore gender differences on a number of variables associated with learning mathematics. It was concluded that while differences did occur on variables associated with confidence, self-concept, test anxiety and quantitative ability indicating a detrimental effect for women, compensating behaviour by women, including increased assignment work and tutorial attendance, resulted in comparable final course performance for women and men. These findings are discussed in light of participation rates of women in mathematics.

Concepts and tools for predictive modeling of microbial dynamics.

PubMed

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

2004-09-01

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

Quantitative three-dimensional analysis of root canal curvature in maxillary first molars using micro-computed tomography.

PubMed

Lee, Jong-Ki; Ha, Byung-Hyun; Choi, Jeong-Ho; Heo, Seok-Mo; Perinpanayagam, Hiran

2006-10-01

In endodontic therapy, access and instrumentation are strongly affected by root canal curvature. However, the few studies that have actually measured curvature are mostly from two-dimensional radiographs. The purpose of this study was to measure the three-dimensional (3D) canal curvature in maxillary first molars using micro-computed tomography (microCT) and mathematical modeling. Extracted maxillary first molars (46) were scanned by microCT (502 image slices/tooth, 1024 X 1024 pixels, voxel size of 19.5 x 19.5 x 39.0 microm) and their canals reconstructed by 3D modeling software. The intersection of major and minor axes in the canal space of each image slice were connected to create an imaginary central axis for each canal. The radius of curvature of the tangential circle was measured and inverted as a measure of curvature using custom-made mathematical modeling software. Root canal curvature was greatest in the apical third and least in the middle third for all canals. The greatest curvatures were in the mesiobuccal (MB) canal (0.76 +/- 0.48 mm(-1)) with abrupt curves, and the least curvatures were in the palatal (P) canal (0.38 +/- 0.34 mm(-1)) with a gradual curve. This study has measured the 3D curvature of root canals in maxillary first molars and reinforced the value of microCT with mathematical modeling.

Metrics for Performance Evaluation of Patient Exercises during Physical Therapy.

PubMed

Vakanski, Aleksandar; Ferguson, Jake M; Lee, Stephen

2017-06-01

The article proposes a set of metrics for evaluation of patient performance in physical therapy exercises. Taxonomy is employed that classifies the metrics into quantitative and qualitative categories, based on the level of abstraction of the captured motion sequences. Further, the quantitative metrics are classified into model-less and model-based metrics, in reference to whether the evaluation employs the raw measurements of patient performed motions, or whether the evaluation is based on a mathematical model of the motions. The reviewed metrics include root-mean square distance, Kullback Leibler divergence, log-likelihood, heuristic consistency, Fugl-Meyer Assessment, and similar. The metrics are evaluated for a set of five human motions captured with a Kinect sensor. The metrics can potentially be integrated into a system that employs machine learning for modelling and assessment of the consistency of patient performance in home-based therapy setting. Automated performance evaluation can overcome the inherent subjectivity in human performed therapy assessment, and it can increase the adherence to prescribed therapy plans, and reduce healthcare costs.

Quantitative approaches to energy and glucose homeostasis: machine learning and modelling for precision understanding and prediction

PubMed Central

Murphy, Kevin G.; Jones, Nick S.

2018-01-01

Obesity is a major global public health problem. Understanding how energy homeostasis is regulated, and can become dysregulated, is crucial for developing new treatments for obesity. Detailed recording of individual behaviour and new imaging modalities offer the prospect of medically relevant models of energy homeostasis that are both understandable and individually predictive. The profusion of data from these sources has led to an interest in applying machine learning techniques to gain insight from these large, relatively unstructured datasets. We review both physiological models and machine learning results across a diverse range of applications in energy homeostasis, and highlight how modelling and machine learning can work together to improve predictive ability. We collect quantitative details in a comprehensive mathematical supplement. We also discuss the prospects of forecasting homeostatic behaviour and stress the importance of characterizing stochasticity within and between individuals in order to provide practical, tailored forecasts and guidance to combat the spread of obesity. PMID:29367240

The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

NASA Astrophysics Data System (ADS)

Walters, Charles David

Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008) related to quantitative reasoning. However, this may prove challenging, as prior to entering the classroom, PSTs often have few opportunities to develop MKT by examining and reflecting on students' thinking. Videos offer one avenue through which such opportunities are possible. In this study, I report on the design of a mini-course for PSTs that featured a series of videos created as part of a proof-of-concept NSF-funded project. These MathTalk videos highlight the ways in which the quantitative reasoning of two high school students developed over time. Using a mixed approach to grounded theory, I analyzed pre- and postinterviews using an extant coding scheme based on the Silverman and Thompson (2008) framework for the development of MKT. This analysis revealed a shift in participants' affect as well as three distinct shifts in their MKT around quantitative reasoning with distances, including shifts in: (a) quantitative reasoning; (b) point of view (decentering); and (c) orientation toward problem solving. Using the four-part focusing framework (Lobato, Hohensee, & Rhodehamel, 2013), I analyzed classroom data to account for how participants' noticing was linked with the shifts in MKT. Notably, their increased noticing of aspects of MKT around quantitative reasoning with distances, which features prominently in the MathTalk videos, seemed to contribute to the emergence of the shifts in MKT. Results from this study link elements of the learning environment to the development of specific facets of MKT around quantitative reasoning with distances. These connections suggest that vicarious experiences with two students' quantitative reasoning over time was critical for participants' development of MKT.

Optical spectroscopy for quantitative sensing in human pancreatic tissues

NASA Astrophysics Data System (ADS)

Wilson, Robert H.; Chandra, Malavika; Lloyd, William; Chen, Leng-Chun; Scheiman, James; Simeone, Diane; McKenna, Barbara; Mycek, Mary-Ann

2011-07-01

Pancreatic adenocarcinoma has a five-year survival rate of only 6%, largely because current diagnostic methods cannot reliably detect the disease in its early stages. Reflectance and fluorescence spectroscopies have the potential to provide quantitative, minimally-invasive means of distinguishing pancreatic adenocarcinoma from normal pancreatic tissue and chronic pancreatitis. The first collection of wavelength-resolved reflectance and fluorescence spectra and time-resolved fluorescence decay curves from human pancreatic tissues was acquired with clinically-compatible instrumentation. Mathematical models of reflectance and fluorescence extracted parameters related to tissue morphology and biochemistry that were statistically significant for distinguishing between pancreatic tissue types. These results suggest that optical spectroscopy has the potential to detect pancreatic disease in a clinical setting.

[Building mathematics in imagination].

PubMed

Patras, Frédéric

2015-01-01

The extraordinary quantitative achievements of contemporary science often hide their qualitative dimension. In mathematics, the understanding of fundamental theoretical phenomena we have got today goes much beyond that achieved in previous periods. This also holds when it comes to the theorisation of mathematical practice.Philosophically, these changes remain largely to be properly analyzed. The present article will address this issue from the point of view of Bachelard's epistemology.

Examination of the Mathematical Problem-Solving Beliefs and Success Levels of Primary School Teacher Candidates through the Variables of Mathematical Success and Gender

ERIC Educational Resources Information Center

Bal, Ayten Pinar

2015-01-01

The aim of this study is to examine the mathematical problem-solving beliefs and problem-solving success levels of primary school teacher candidates through the variables of academic success and gender. The research was designed according to the mixed methods technique in which qualitative and quantitative methods are used together. The working…

A quantitative validated model reveals two phases of transcriptional regulation for the gap gene giant in Drosophila.

PubMed

Hoermann, Astrid; Cicin-Sain, Damjan; Jaeger, Johannes

2016-03-15

Understanding eukaryotic transcriptional regulation and its role in development and pattern formation is one of the big challenges in biology today. Most attempts at tackling this problem either focus on the molecular details of transcription factor binding, or aim at genome-wide prediction of expression patterns from sequence through bioinformatics and mathematical modelling. Here we bridge the gap between these two complementary approaches by providing an integrative model of cis-regulatory elements governing the expression of the gap gene giant (gt) in the blastoderm embryo of Drosophila melanogaster. We use a reverse-engineering method, where mathematical models are fit to quantitative spatio-temporal reporter gene expression data to infer the regulatory mechanisms underlying gt expression in its anterior and posterior domains. These models are validated through prediction of gene expression in mutant backgrounds. A detailed analysis of our data and models reveals that gt is regulated by domain-specific CREs at early stages, while a late element drives expression in both the anterior and the posterior domains. Initial gt expression depends exclusively on inputs from maternal factors. Later, gap gene cross-repression and gt auto-activation become increasingly important. We show that auto-regulation creates a positive feedback, which mediates the transition from early to late stages of regulation. We confirm the existence and role of gt auto-activation through targeted mutagenesis of Gt transcription factor binding sites. In summary, our analysis provides a comprehensive picture of spatio-temporal gene regulation by different interacting enhancer elements for an important developmental regulator. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

A review of presented mathematical models in Parkinson's disease: black- and gray-box models.

PubMed

Sarbaz, Yashar; Pourakbari, Hakimeh

2016-06-01

Parkinson's disease (PD), one of the most common movement disorders, is caused by damage to the central nervous system. Despite all of the studies on PD, the formation mechanism of its symptoms remained unknown. It is still not obvious why damage only to the substantia nigra pars compacta, a small part of the brain, causes a wide range of symptoms. Moreover, the causes of brain damages remain to be fully elucidated. Exact understanding of the brain function seems to be impossible. On the other hand, some engineering tools are trying to understand the behavior and performance of complex systems. Modeling is one of the most important tools in this regard. Developing quantitative models for this disease has begun in recent decades. They are very effective not only in better understanding of the disease, offering new therapies, and its prediction and control, but also in its early diagnosis. Modeling studies include two main groups: black-box models and gray-box models. Generally, in the black-box modeling, regardless of the system information, the symptom is only considered as the output. Such models, besides the quantitative analysis studies, increase our knowledge of the disorders behavior and the disease symptoms. The gray-box models consider the involved structures in the symptoms appearance as well as the final disease symptoms. These models can effectively save time and be cost-effective for the researchers and help them select appropriate treatment mechanisms among all possible options. In this review paper, first, efforts are made to investigate some studies on PD quantitative analysis. Then, PD quantitative models will be reviewed. Finally, the results of using such models are presented to some extent.

The place of words and numbers in psychiatric research.

PubMed

Falissard, Bruno; Révah, Anne; Yang, Suzanne; Fagot-Largeault, Anne

2013-11-18

In recent decades, there has been widespread debate in the human and social sciences regarding the compatibility and the relative merits of quantitative and qualitative approaches in research. In psychiatry, depending on disciplines and traditions, objects of study can be represented either in words or using two types of mathematization. In the latter case, the use of mathematics in psychiatry is most often only local, as opposed to global as in the case of classical mechanics. Relationships between these objects of study can in turn be explored in three different ways: 1/ by a hermeneutic process, 2/ using statistics, the most frequent method in psychiatric research today, 3/ using equations, i.e. using mathematical relationships that are formal and deterministic. The 3 ways of representing entities (with language, locally with mathematics or globally with mathematics) and the 3 ways of expressing the relationships between entities (using hermeneutics, statistics or equations) can be combined in a cross-tabulation, and nearly all nine combinations can be described using examples. A typology of this nature may be useful in assessing which epistemological perspectives are currently dominant in a constantly evolving field such as psychiatry, and which other perspectives still need to be developed. It also contributes to undermining the overly simplistic and counterproductive beliefs that accompany the assumption of a Manichean "quantitative/qualitative" dichotomy. Systematic examination of this set of typologies could be useful in indicating new directions for future research beyond the quantitative/qualitative divide.

The place of words and numbers in psychiatric research

PubMed Central

2013-01-01

In recent decades, there has been widespread debate in the human and social sciences regarding the compatibility and the relative merits of quantitative and qualitative approaches in research. In psychiatry, depending on disciplines and traditions, objects of study can be represented either in words or using two types of mathematization. In the latter case, the use of mathematics in psychiatry is most often only local, as opposed to global as in the case of classical mechanics. Relationships between these objects of study can in turn be explored in three different ways: 1/ by a hermeneutic process, 2/ using statistics, the most frequent method in psychiatric research today, 3/ using equations, i.e. using mathematical relationships that are formal and deterministic. The 3 ways of representing entities (with language, locally with mathematics or globally with mathematics) and the 3 ways of expressing the relationships between entities (using hermeneutics, statistics or equations) can be combined in a cross-tabulation, and nearly all nine combinations can be described using examples. A typology of this nature may be useful in assessing which epistemological perspectives are currently dominant in a constantly evolving field such as psychiatry, and which other perspectives still need to be developed. It also contributes to undermining the overly simplistic and counterproductive beliefs that accompany the assumption of a Manichean “quantitative/qualitative” dichotomy. Systematic examination of this set of typologies could be useful in indicating new directions for future research beyond the quantitative/qualitative divide. PMID:24246064

What Can Other Areas Teach Us about Numeracy?

ERIC Educational Resources Information Center

Ferme, Elizabeth

2014-01-01

Education professionals, regardless of their specialist area, are broadly aware of the importance of numeracy. Internationally, definitions of numeracy (known elsewhere as mathematical literacy or quantitative reasoning), describe "an individual's capacity to formulate, employ and interpret mathematics in a variety of contexts... reasoning…

Resource Allocation Patterns and Student Achievement

ERIC Educational Resources Information Center

James, Lori; Pate, James; Leech, Donald; Martin, Ellice; Brockmeier, Lantry; Dees, Elizabeth

2011-01-01

This quantitative research study was designed to examine the relationship between system resource allocation patterns and student achievement, as measured by eighth grade Criterion-Referenced Competency Test (CRCT) mathematics, eighth grade CRCT reading, eleventh grade Georgia High School Graduation Test (GHSGT) mathematics, eleventh grade and…

Generalizability and Validity of a Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

1996-01-01

Evidence from test results of 3,604 sixth and seventh graders is provided for the generalizability and validity of the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Cognitive Assessment Instrument, which is designed to measure program outcomes and growth in mathematics. (SLD)

Dimensionality of Motion and Binding Valency Govern Receptor-Ligand Kinetics As Revealed by Agent-Based Modeling.

PubMed

Lehnert, Teresa; Figge, Marc Thilo

2017-01-01

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor-ligand binding in the context of antibody-antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors-such as their dimensionality of motion, morphology, and binding valency-on the receptor-ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors.

Dimensionality of Motion and Binding Valency Govern Receptor–Ligand Kinetics As Revealed by Agent-Based Modeling

PubMed Central

Lehnert, Teresa; Figge, Marc Thilo

2017-01-01

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor–ligand binding in the context of antibody–antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors—such as their dimensionality of motion, morphology, and binding valency—on the receptor–ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors. PMID:29250071

Two approaches to improving mental health care: positivist/quantitative versus skill-based/qualitative.

PubMed

Luchins, Daniel

2012-01-01

The quality improvement model currently used in medicine and mental health was adopted from industry, where it developed out of early 20th-century efforts to apply a positivist/quantitative agenda to improving manufacturing. This article questions the application of this model to mental health care. It argues that (1) developing "operational definitions" for something as value-laden as "quality" risks conflating two realms, what we measure with what we value; (2) when measurements that are tied to individuals are aggregated to establish benchmarks and goals, unwarranted mathematical assumptions are made; (3) choosing clinical outcomes is problematic; (4) there is little relationship between process measures and clinical outcomes; and (5) since changes in quality indices do not relate to improved clinical care, management's reliance on such indices provides an illusory sense of control. An alternative model is the older, skill-based/qualitative approach to knowing, which relies on "implicit/ expert" knowledge. These two approaches offer a series of contrasts: quality versus excellence, competence versus expertise, management versus leadership, extrinsic versus intrinsic rewards. The article concludes that we need not totally dispense with the current quality improvement model, but rather should balance quantitative efforts with the older qualitative approach in a mixed methods model.

Research of MPPT for photovoltaic generation based on two-dimensional cloud model

NASA Astrophysics Data System (ADS)

Liu, Shuping; Fan, Wei

2013-03-01

The cloud model is a mathematical representation to fuzziness and randomness in linguistic concepts. It represents a qualitative concept with expected value Ex, entropy En and hyper entropy He, and integrates the fuzziness and randomness of a linguistic concept in a unified way. This model is a new method for transformation between qualitative and quantitative in the knowledge. This paper is introduced MPPT (maximum power point tracking, MPPT) controller based two- dimensional cloud model through analysis of auto-optimization MPPT control of photovoltaic power system and combining theory of cloud model. Simulation result shows that the cloud controller is simple and easy, directly perceived through the senses, and has strong robustness, better control performance.

Agent-based re-engineering of ErbB signaling: a modeling pipeline for integrative systems biology.

PubMed

Das, Arya A; Ajayakumar Darsana, T; Jacob, Elizabeth

2017-03-01

Experiments in systems biology are generally supported by a computational model which quantitatively estimates the parameters of the system by finding the best fit to the experiment. Mathematical models have proved to be successful in reverse engineering the system. The data generated is interpreted to understand the dynamics of the underlying phenomena. The question we have sought to answer is that - is it possible to use an agent-based approach to re-engineer a biological process, making use of the available knowledge from experimental and modelling efforts? Can the bottom-up approach benefit from the top-down exercise so as to create an integrated modelling formalism for systems biology? We propose a modelling pipeline that learns from the data given by reverse engineering, and uses it for re-engineering the system, to carry out in-silico experiments. A mathematical model that quantitatively predicts co-expression of EGFR-HER2 receptors in activation and trafficking has been taken for this study. The pipeline architecture takes cues from the population model that gives the rates of biochemical reactions, to formulate knowledge-based rules for the particle model. Agent-based simulations using these rules, support the existing facts on EGFR-HER2 dynamics. We conclude that, re-engineering models, built using the results of reverse engineering, opens up the possibility of harnessing the power pack of data which now lies scattered in literature. Virtual experiments could then become more realistic when empowered with the findings of empirical cell biology and modelling studies. Implemented on the Agent Modelling Framework developed in-house. C ++ code templates available in Supplementary material . liz.csir@gmail.com. Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Quantitative Literacy across the Curriculum: Integrating Skills from English Composition, Mathematics, and the Substantive Disciplines

ERIC Educational Resources Information Center

Miller, Jane E.

2010-01-01

Quantitative literacy is an important proficiency that pertains to "word problems" from science, history, and other fields. Unfortunately, teaching how to solve such problems often is relegated to math courses alone. This article examines how quantitative literacy also involves concepts and skills from English composition and the substantive…

Integrating Quantitative Thinking into an Introductory Biology Course Improves Students' Mathematical Reasoning in Biological Contexts

ERIC Educational Resources Information Center

Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa

2014-01-01

Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course…

Scientists and Mathematicians Collaborating to Build Quantitative Skills in Undergraduate Science

ERIC Educational Resources Information Center

Rylands, Leanne; Simbag, Vilma; Matthews, Kelly E.; Coady, Carmel; Belward, Shaun

2013-01-01

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better…

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

PubMed Central

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

2012-01-01

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

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

PubMed

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

2012-05-01

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

Tracer kinetics of forearm endothelial function: comparison of an empirical method and a quantitative modeling technique.

PubMed

Zhao, Xueli; Arsenault, Andre; Lavoie, Kim L; Meloche, Bernard; Bacon, Simon L

2007-01-01

Forearm Endothelial Function (FEF) is a marker that has been shown to discriminate patients with cardiovascular disease (CVD). FEF has been assessed using several parameters: the Rate of Uptake Ratio (RUR), EWUR (Elbow-to-Wrist Uptake Ratio) and EWRUR (Elbow-to-Wrist Relative Uptake Ratio). However, the modeling functions of FEF require more robust models. The present study was designed to compare an empirical method with quantitative modeling techniques to better estimate the physiological parameters and understand the complex dynamic processes. The fitted time activity curves of the forearms, estimating blood and muscle components, were assessed using both an empirical method and a two-compartment model. Although correlational analyses suggested a good correlation between the methods for RUR (r=.90) and EWUR (r=.79), but not EWRUR (r=.34), Altman-Bland plots found poor agreement between the methods for all 3 parameters. These results indicate that there is a large discrepancy between the empirical and computational method for FEF. Further work is needed to establish the physiological and mathematical validity of the 2 modeling methods.

Quantitative Assessment of Agricultural Runoff and Soil Erosion Using Mathematical Modeling: Applications in the Mediterranean Region

NASA Astrophysics Data System (ADS)

Arhonditsis, G.; Giourga, C.; Loumou, A.; Koulouri, M.

2002-09-01

Three mathematical models, the runoff curve number equation, the universal soil loss equation, and the mass response functions, were evaluated for predicting nonpoint source nutrient loading from agricultural watersheds of the Mediterranean region. These methodologies were applied to a catchment, the gulf of Gera Basin, that is a typical terrestrial ecosystem of the islands of the Aegean archipelago. The calibration of the model parameters was based on data from experimental plots from which edge-of-field losses of sediment, water runoff, and nutrients were measured. Special emphasis was given to the transport of dissolved and solid-phase nutrients from their sources in the farmers' fields to the outlet of the watershed in order to estimate respective attenuation rates. It was found that nonpoint nutrient loading due to surface losses was high during winter, the contribution being between 50% and 80% of the total annual nutrient losses from the terrestrial ecosystem. The good fit between simulated and experimental data supports the view that these modeling procedures should be considered as reliable and effective methodological tools in Mediterranean areas for evaluating potential control measures, such as management practices for soil and water conservation and changes in land uses, aimed at diminishing soil loss and nutrient delivery to surface waters. Furthermore, the modifications of the general mathematical formulations and the experimental values of the model parameters provided by the study can be used in further application of these methodologies in watersheds with similar characteristics.

Quantitative characterization of genetic parts and circuits for plant synthetic biology.

PubMed

Schaumberg, Katherine A; Antunes, Mauricio S; Kassaw, Tessema K; Xu, Wenlong; Zalewski, Christopher S; Medford, June I; Prasad, Ashok

2016-01-01

Plant synthetic biology promises immense technological benefits, including the potential development of a sustainable bio-based economy through the predictive design of synthetic gene circuits. Such circuits are built from quantitatively characterized genetic parts; however, this characterization is a significant obstacle in work with plants because of the time required for stable transformation. We describe a method for rapid quantitative characterization of genetic plant parts using transient expression in protoplasts and dual luciferase outputs. We observed experimental variability in transient-expression assays and developed a mathematical model to describe, as well as statistical normalization methods to account for, this variability, which allowed us to extract quantitative parameters. We characterized >120 synthetic parts in Arabidopsis and validated our method by comparing transient expression with expression in stably transformed plants. We also tested >100 synthetic parts in sorghum (Sorghum bicolor) protoplasts, and the results showed that our method works in diverse plant groups. Our approach enables the construction of tunable gene circuits in complex eukaryotic organisms.

Modeling Flow in Porous Media with Double Porosity/Permeability.

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Multi-model approach to petroleum resource appraisal using analytic methodologies for probabilistic systems

USGS Publications Warehouse

Crovelli, R.A.

1988-01-01

The geologic appraisal model that is selected for a petroleum resource assessment depends upon purpose of the assessment, basic geologic assumptions of the area, type of available data, time available before deadlines, available human and financial resources, available computer facilities, and, most importantly, the available quantitative methodology with corresponding computer software and any new quantitative methodology that would have to be developed. Therefore, different resource assessment projects usually require different geologic models. Also, more than one geologic model might be needed in a single project for assessing different regions of the study or for cross-checking resource estimates of the area. Some geologic analyses used in the past for petroleum resource appraisal involved play analysis. The corresponding quantitative methodologies of these analyses usually consisted of Monte Carlo simulation techniques. A probabilistic system of petroleum resource appraisal for play analysis has been designed to meet the following requirements: (1) includes a variety of geologic models, (2) uses an analytic methodology instead of Monte Carlo simulation, (3) possesses the capacity to aggregate estimates from many areas that have been assessed by different geologic models, and (4) runs quickly on a microcomputer. Geologic models consist of four basic types: reservoir engineering, volumetric yield, field size, and direct assessment. Several case histories and present studies by the U.S. Geological Survey are discussed. ?? 1988 International Association for Mathematical Geology.

On the limitations of standard statistical modeling in biological systems: a full Bayesian approach for biology.

PubMed

Gomez-Ramirez, Jaime; Sanz, Ricardo

2013-09-01

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist. Copyright © 2013 Elsevier Ltd. All rights reserved.

Developing Geoscience Students' Quantitative Skills

NASA Astrophysics Data System (ADS)

Manduca, C. A.; Hancock, G. S.

2005-12-01

Sophisticated quantitative skills are an essential tool for the professional geoscientist. While students learn many of these sophisticated skills in graduate school, it is increasingly important that they have a strong grounding in quantitative geoscience as undergraduates. Faculty have developed many strong approaches to teaching these skills in a wide variety of geoscience courses. A workshop in June 2005 brought together eight faculty teaching surface processes and climate change to discuss and refine activities they use and to publish them on the Teaching Quantitative Skills in the Geosciences website (serc.Carleton.edu/quantskills) for broader use. Workshop participants in consultation with two mathematics faculty who have expertise in math education developed six review criteria to guide discussion: 1) Are the quantitative and geologic goals central and important? (e.g. problem solving, mastery of important skill, modeling, relating theory to observation); 2) Does the activity lead to better problem solving? 3) Are the quantitative skills integrated with geoscience concepts in a way that makes sense for the learning environment and supports learning both quantitative skills and geoscience? 4) Does the methodology support learning? (e.g. motivate and engage students; use multiple representations, incorporate reflection, discussion and synthesis) 5) Are the materials complete and helpful to students? 6) How well has the activity worked when used? Workshop participants found that reviewing each others activities was very productive because they thought about new ways to teach and the experience of reviewing helped them think about their own activity from a different point of view. The review criteria focused their thinking about the activity and would be equally helpful in the design of a new activity. We invite a broad international discussion of the criteria(serc.Carleton.edu/quantskills/workshop05/review.html).The Teaching activities can be found on the Teaching Quantitative Skills in the Geosciences website (serc.Carleton.edu/quantskills/). In addition to the teaching activity collection (85 activites), this site contains a variety of resources to assist faculty with the methods they use to teach quantitative skills at both the introductory and advanced levels; information about broader efforts in quantitative literacy involving other science disciplines, and a special section of resources for students who are struggling with their quantitative skills. The site is part of the Digital Library for Earth Science Education and has been developed by geoscience faculty in collaboration with mathematicians and mathematics educators with funding from the National Science Foundation.

Assessing Quantitative Learning With The Math You Need When You Need It

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Baer, E. M.; Burn, H.

2008-12-01

We present new data from a pilot project using the The Math You Need, When You Need It (TMYN) web resources in conjunction with several introductory geoscience courses. TMYN is a series of NSF-supported, NAGT-sponsored, web-based modular resources designed to help students learn (or relearn) mathematical skills essential for success in introductory geoscience courses. TMYN presents mathematical topics that are relevant to introductory geoscience based on a survey of more than 75 geoscience faculty members. To date, modules include unit conversions, many aspects of graphing, density calculations, rearranging equations and other simple mathematical concepts commonly used in the geosciences. The modular nature of the resources make it simple to select the units that are appropriate for a given course. In the fall of 2008, nine TMYN modules were tested in three courses taught at Highline Community College (Geology 101) and University of Wisconsin Oshkosh (Physical and Environmental Geology). Over 300 students participated in the study by taking pre- and post-tests and completing modules relevant to their course. Feedback about the use of these modules has been mixed. Initial results confirm anecdotal evidence that students initially have difficulty applying mathematical concepts to geologic problems. Furthermore, pre- test results indicate that, although instructors assume that students can perform simple mathematical manipulations, many students arrive in courses without the skills to apply mathematical concepts in problem solving situations. TMYN resources effectively provide support for learning quantitative problem solving and a mechanism for students to engage in self-teaching. Although we have seen mixed results due to a range of instructor engagement with the material, TMYN can have significant effect on students who are math phobic or "can't do math" because they can work at their own pace to overcome affective obstacles such as fear and dislike of mathematics. TMYN is most effective when instructors make explicit connections between material in the modules and course content. Instructors who participated in the study in Fall 2008 reacted positively to the use of TMYN in introductory geoscience courses because the resources require minimal class and prep time. Furthermore, when instructors can hold students responsible for the quantitative concepts covered with TMYN, they feel more comfortable including quantitative information without significant loss of geologic content.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

The quantum-mechanical approach to construction of quantitative assessments of some documentary information properties (on example of nuclear knowledge)

NASA Astrophysics Data System (ADS)

Lebedev, A. A.; Maksimov, N. V.; Smirnova, E. V.

2017-01-01

The paper presents a model of information interactions, based on a probabilistic concept of meanings. The proposed hypothesis about the wave nature of information and use of quantum mechanics mathematical apparatus allow to consider the phenomena of interference and diffraction with respect to the linguistic variables, and to quantify dynamics of terms in subject areas. Retrospective database INIS IAEA was used as an experimental base.

Quantitative Studies in Planetary Volcanism

NASA Technical Reports Server (NTRS)

Baloga, Stephen M.

2004-01-01

Proxemy Research has a research grant to perform scientific investigations of volcanism and volcanic-related process on other planets. Part of this research involves mathematical modeling of specific volcanic transport processes and the use of terrestrial analogs. This report contains a summary of activities conducted over the time period indicated. In addition, a synopsis of science research conducted during the period is given. A complete listing of publications and scientific abstracts that were presented at scientific conferences is contained in the report.

Computational physiology and the Physiome Project.

PubMed

Crampin, Edmund J; Halstead, Matthew; Hunter, Peter; Nielsen, Poul; Noble, Denis; Smith, Nicolas; Tawhai, Merryn

2004-01-01

Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization--from proteins to cells, tissues, organs and organ systems--these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline.

The Intracellular Trafficking Pathway of Transferrin

PubMed Central

Mayle, Kristine M.; Le, Alexander M.; Kamei, Daniel T.

2011-01-01

Background Transferrin (Tf) is an iron-binding protein that facilitates iron-uptake in cells. Iron-loaded Tf first binds to the Tf receptor (TfR) and enters the cell through clathrin-mediated endocytosis. Inside the cell, Tf is trafficked to early endosomes, delivers iron, and then is subsequently directed to recycling endosomes to be taken back to the cell surface. Scope of Review We aim to review the various methods and techniques that researchers have employed for elucidating the Tf trafficking pathway and the cell-machinery components involved. These experimental methods can be categorized as microscopy, radioactivity, and surface plasmon resonance (SPR). Major Conclusions Qualitative experiments, such as total internal reflectance fluorescence (TIRF), electron, laser-scanning confocal, and spinning-disk confocal microscopy, have been utilized to determine the roles of key components in the Tf trafficking pathway. These techniques allow temporal resolution and are useful for imaging Tf endocytosis and recycling, which occur on the order of seconds to minutes. Additionally, radiolabeling and SPR methods, when combined with mathematical modeling, have enabled researchers to estimate quantitative kinetic parameters and equilibrium constants associated with Tf binding and trafficking. General Significance Both qualitative and quantitative data can be used to analyze the Tf trafficking pathway. The valuable information that is obtained about the Tf trafficking pathway can then be combined with mathematical models to identify design criteria to improve the ability of Tf to deliver anticancer drugs. PMID:21968002

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.

Orchestrating Mathematical Discourse: Affordances and Hindrances for Novice Elementary Teachers

ERIC Educational Resources Information Center

Lee, Carrie Wilkerson

2016-01-01

The purpose of this study was to examine the mathematical discourse within novice elementary teachers' classrooms. More specifically, this study employed a sequential, explanatory mixed methods design to first quantitatively analyze the relationship between teachers' discourse practices and teacher attributes and school context. Next, a…

Gendered Microaggressions in Science, Technology, Engineering, and Mathematics

ERIC Educational Resources Information Center

Yang, Yang; Carroll, Doris Wright

2018-01-01

Women remain underrepresented in both science, technology, engineering, and mathematics (STEM) workforce and academia. In this quantitative study, we focused on female faculty across STEM disciplines and their experiences in higher educational institutions through the lens of microaggressions theory. Two questions were addressed: (a) whether and…

Gender-Related Differential Item Functioning on a Middle-School Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

This study examined gender-related differential item functioning (DIF) using a mathematics performance assessment, the QUASAR Cognitive Assessment Instrument (QCAI), administered to middle school students. The QCAI was developed for the Quantitative Understanding: Amplifying Student Achievement and Reading (QUASAR) project, which focuses on…

Improving Math Success in Higher Education Institutions

ERIC Educational Resources Information Center

Bisk, Richard

2013-01-01

Many students begin higher education unprepared for college-level work in mathematics and must take non-credit developmental courses. Furthermore, many are "math-phobic" and avoid courses, majors and careers that involve quantitative work. Yet science, technology, engineering and mathematics (STEM) fields are among the few job-growth…

Probing the stochastic property of endoreduplication in cell size determination of Arabidopsis thaliana leaf epidermal tissue

PubMed Central

2017-01-01

Cell size distribution is highly reproducible, whereas the size of individual cells often varies greatly within a tissue. This is obvious in a population of Arabidopsis thaliana leaf epidermal cells, which ranged from 1,000 to 10,000 μm2 in size. Endoreduplication is a specialized cell cycle in which nuclear genome size (ploidy) is doubled in the absence of cell division. Although epidermal cells require endoreduplication to enhance cellular expansion, the issue of whether this mechanism is sufficient for explaining cell size distribution remains unclear due to a lack of quantitative understanding linking the occurrence of endoreduplication with cell size diversity. Here, we addressed this question by quantitatively summarizing ploidy profile and cell size distribution using a simple theoretical framework. We first found that endoreduplication dynamics is a Poisson process through cellular maturation. This finding allowed us to construct a mathematical model to predict the time evolution of a ploidy profile with a single rate constant for endoreduplication occurrence in a given time. We reproduced experimentally measured ploidy profile in both wild-type leaf tissue and endoreduplication-related mutants with this analytical solution, further demonstrating the probabilistic property of endoreduplication. We next extended the mathematical model by incorporating the element that cell size is determined according to ploidy level to examine cell size distribution. This analysis revealed that cell size is exponentially enlarged 1.5 times every endoreduplication round. Because this theoretical simulation successfully recapitulated experimentally observed cell size distributions, we concluded that Poissonian endoreduplication dynamics and exponential size-boosting are the sources of the broad cell size distribution in epidermal tissue. More generally, this study contributes to a quantitative understanding whereby stochastic dynamics generate steady-state biological heterogeneity. PMID:28926847

Determining absolute protein numbers by quantitative fluorescence microscopy.

PubMed

Verdaasdonk, Jolien Suzanne; Lawrimore, Josh; Bloom, Kerry

2014-01-01

Biological questions are increasingly being addressed using a wide range of quantitative analytical tools to examine protein complex composition. Knowledge of the absolute number of proteins present provides insights into organization, function, and maintenance and is used in mathematical modeling of complex cellular dynamics. In this chapter, we outline and describe three microscopy-based methods for determining absolute protein numbers--fluorescence correlation spectroscopy, stepwise photobleaching, and ratiometric comparison of fluorescence intensity to known standards. In addition, we discuss the various fluorescently labeled proteins that have been used as standards for both stepwise photobleaching and ratiometric comparison analysis. A detailed procedure for determining absolute protein number by ratiometric comparison is outlined in the second half of this chapter. Counting proteins by quantitative microscopy is a relatively simple yet very powerful analytical tool that will increase our understanding of protein complex composition. © 2014 Elsevier Inc. All rights reserved.

Shape and shear guide sperm cells spiraling upstream

NASA Astrophysics Data System (ADS)

Kantsler, Vasily; Dunkel, Jorn; Goldstein, Raymond E.

2014-11-01

A major puzzle in biology is how mammalian sperm determine and maintain the correct swimming direction during the various phases of the sexual reproduction process. Currently debated mechanisms for sperm long range travel vary from peristaltic pumping to temperature sensing (thermotaxis) and direct response to fluid flow (rheotaxis), but little is known quantitatively about their relative importance. Here, we report the first quantitative experimental study of mammalian sperm rheotaxis. Using microfluidic devices, we investigate systematically the swimming behavior of human and bull sperm over a wide range of physiologically relevant shear rates and viscosities. Our measurements show that the interplay of fluid shear, steric surface-interactions and chirality of the flagellar beat leads to a stable upstream spiraling motion of sperm cells, thus providing a generic and robust rectification mechanism to support mammalian fertilization. To rationalize these findings, we identify a minimal mathematical model that is capable of describing quantitatively the experimental observations.

Ephaptic conduction in a cardiac strand model with 3D electrodiffusion

PubMed Central

Mori, Yoichiro; Fishman, Glenn I.; Peskin, Charles S.

2008-01-01

We study cardiac action potential propagation under severe reduction in gap junction conductance. We use a mathematical model of cellular electrical activity that takes into account both three-dimensional geometry and ionic concentration effects. Certain anatomical and biophysical parameters are varied to see their impact on cardiac action potential conduction velocity. This study uncovers quantitative features of ephaptic propagation that differ from previous studies based on one-dimensional models. We also identify a mode of cardiac action potential propagation in which the ephaptic and gap-junction-mediated mechanisms alternate. Our study demonstrates the usefulness of this modeling approach for electrophysiological systems especially when detailed membrane geometry plays an important role. PMID:18434544

Real-time Social Internet Data to Guide Forecasting Models

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

Del Valle, Sara Y.

Our goal is to improve decision support by monitoring and forecasting events using social media, mathematical models, and quantifying model uncertainty. Our approach is real-time, data-driven forecasts with quantified uncertainty: Not just for weather anymore. Information flow from human observations of events through an Internet system and classification algorithms is used to produce quantitatively uncertain forecast. In summary, we want to develop new tools to extract useful information from Internet data streams, develop new approaches to assimilate real-time information into predictive models, validate approaches by forecasting events, and our ultimate goal is to develop an event forecasting system using mathematicalmore » approaches and heterogeneous data streams.« less

Comparison of Modeling Methods to Determine Liver-to-blood Inocula and Parasite Multiplication Rates During Controlled Human Malaria Infection

PubMed Central

Douglas, Alexander D.; Edwards, Nick J.; Duncan, Christopher J. A.; Thompson, Fiona M.; Sheehy, Susanne H.; O'Hara, Geraldine A.; Anagnostou, Nicholas; Walther, Michael; Webster, Daniel P.; Dunachie, Susanna J.; Porter, David W.; Andrews, Laura; Gilbert, Sarah C.; Draper, Simon J.; Hill, Adrian V. S.; Bejon, Philip

2013-01-01

Controlled human malaria infection is used to measure efficacy of candidate malaria vaccines before field studies are undertaken. Mathematical modeling using data from quantitative polymerase chain reaction (qPCR) parasitemia monitoring can discriminate between vaccine effects on the parasite's liver and blood stages. Uncertainty regarding the most appropriate modeling method hinders interpretation of such trials. We used qPCR data from 267 Plasmodium falciparum infections to compare linear, sine-wave, and normal-cumulative-density-function models. We find that the parameters estimated by these models are closely correlated, and their predictive accuracy for omitted data points was similar. We propose that future studies include the linear model. PMID:23570846

The Music of Mathematics: Toward a New Problem Typology

NASA Astrophysics Data System (ADS)

Quarfoot, David

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

[From clinical judgment to linear regression model.

PubMed

Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O

2013-01-01

When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.

A network-based approach for resistance transmission in bacterial populations.

PubMed

Gehring, Ronette; Schumm, Phillip; Youssef, Mina; Scoglio, Caterina

2010-01-07

Horizontal transfer of mobile genetic elements (conjugation) is an important mechanism whereby resistance is spread through bacterial populations. The aim of our work is to develop a mathematical model that quantitatively describes this process, and to use this model to optimize antimicrobial dosage regimens to minimize resistance development. The bacterial population is conceptualized as a compartmental mathematical model to describe changes in susceptible, resistant, and transconjugant bacteria over time. This model is combined with a compartmental pharmacokinetic model to explore the effect of different plasma drug concentration profiles. An agent-based simulation tool is used to account for resistance transfer occurring when two bacteria are adjacent or in close proximity. In addition, a non-linear programming optimal control problem is introduced to minimize bacterial populations as well as the drug dose. Simulation and optimization results suggest that the rapid death of susceptible individuals in the population is pivotal in minimizing the number of transconjugants in a population. This supports the use of potent antimicrobials that rapidly kill susceptible individuals and development of dosage regimens that maintain effective antimicrobial drug concentrations for as long as needed to kill off the susceptible population. Suggestions are made for experiments to test the hypotheses generated by these simulations.

CCTV Coverage Index Based on Surveillance Resolution and Its Evaluation Using 3D Spatial Analysis

PubMed Central

Choi, Kyoungah; Lee, Impyeong

2015-01-01

We propose a novel approach to evaluating how effectively a closed circuit television (CCTV) system can monitor a targeted area. With 3D models of the target area and the camera parameters of the CCTV system, the approach produces surveillance coverage index, which is newly defined in this study as a quantitative measure for surveillance performance. This index indicates the proportion of the space being monitored with a sufficient resolution to the entire space of the target area. It is determined by computing surveillance resolution at every position and orientation, which indicates how closely a specific object can be monitored with a CCTV system. We present full mathematical derivation for the resolution, which depends on the location and orientation of the object as well as the geometric model of a camera. With the proposed approach, we quantitatively evaluated the surveillance coverage of a CCTV system in an underground parking area. Our evaluation process provided various quantitative-analysis results, compelling us to examine the design of the CCTV system prior to its installation and understand the surveillance capability of an existing CCTV system. PMID:26389909

Developing and Applying Quantitative Skills Maps for STEM Curricula, with a Focus on Different Modes of Learning

ERIC Educational Resources Information Center

Reid, Jackie; Wilkes, Janelle

2016-01-01

Mapping quantitative skills across the science, technology, engineering and mathematics (STEM) curricula will help educators identify gaps and duplication in the teaching, practice and assessment of the necessary skills. This paper describes the development and implementation of quantitative skills mapping tools for courses in STEM at a regional…

Future Directions for The Math You Need, When You Need It: Adaptation and Implementation of Online Student-Centered Tutorials that Remediate Introductory Geoscience-Related Mathematical Skills

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Burn, H.; Baer, E. M.

2009-12-01

Requiring introductory geoscience students to apply mathematical concepts and solve quantitative problems can be an arduous task because these courses tend to attract students with diverse levels of mathematical preparedness. Perhaps more significantly, geoscience instructors grapple with quantitative content because of the difficulties students have transferring their prior mathematical learning to common geological problems. As a result, instructors can choose to eliminate the mathematics, spend valuable class time teaching basic mathematical skills or let students flounder in the hope that they will learn on their own. None of these choices are ideal. Instead, research suggests that introductory geoscience courses are opportune places to increase students’ quantitative abilities but that students need effective support at their own skill level. To provide such support, we developed The Math You Need, When You Need It (TMYN): a set of online geoscience context-rich tutorials that students complete just before they encounter a mathematical or numerical skill in their introductory course. The tutorials are modular; each mathematical topic has a set of pages that students work through toward a final assessment. The 11 modules currently available, including unit conversions, graphing, calculating density, and rearranging equations, touch on quantitative topics that cross a number of geologic contexts. TMYN modules are designed to be stand-alone and flexible - faculty members can choose modules appropriate for their courses and implement them at any time throughout the term. The flexible and adaptable nature of TMYN enables faculty to provide a supportive learning environment that remediates math for those who need it without taking significant classroom time. Since spring 2008, seven instructors at Highline Community College and University of Wisconsin Oshkosh successfully implemented TMYN in six geoscience courses with diverse student audiences. Evaluation of pilot implementations suggests that the flexibility of TYMN is one of its strengths. Specifically, faculty members responded positively to the ability to choose relevant topics and provide students with competence in pertinent mathematical concepts; students liked the supportive, contextual environment and the ability to work at their own pace. And, despite the fact that each implementation varied in the number and type of modules used, the timing of module use, grading stakes, and course size, pre/post test results consistently showed improvement in student skills associated with a given module, suggesting that all implementations were successful. Post-module surveys likewise revealed that both instructors and students found the experience valuable. We present the wide variety of successful implementations with an eye toward exploring future directions for the project, including soliciting new and diverse ways in which other institutions and instructors might adapt and apply TMYN to their own courses.

Introduction to Quantitative Science, a Ninth-Grade Laboratory-Centered Course Stressing Quantitative Observation and Mathematical Analysis of Experimental Results. Final Report.

ERIC Educational Resources Information Center

Badar, Lawrence J.

This report, in the form of a teacher's guide, presents materials for a ninth grade introductory course on Introduction to Quantitative Science (IQS). It is intended to replace a traditional ninth grade general science with a process oriented course that will (1) unify the sciences, and (2) provide a quantitative preparation for the new science…

Developing and applying quantitative skills maps for STEM curricula, with a focus on different modes of learning

NASA Astrophysics Data System (ADS)

Reid, Jackie; Wilkes, Janelle

2016-08-01

Mapping quantitative skills across the science, technology, engineering and mathematics (STEM) curricula will help educators identify gaps and duplication in the teaching, practice and assessment of the necessary skills. This paper describes the development and implementation of quantitative skills mapping tools for courses in STEM at a regional university that offers both on-campus and distance modes of study. Key elements of the mapping project included the identification of key graduate quantitative skills, the development of curriculum mapping tools to record in which unit(s) and at what level of attainment each quantitative skill is taught, practised and assessed, and identification of differences in the way quantitative skills are developed for on-campus and distance students. Particular attention is given to the differences that are associated with intensive schools, which consist of concentrated periods of face-to-face learning over a three-four day period, and are available to distance education students enrolled in STEM units. The detailed quantitative skills mapping process has had an impact on the review of first-year mathematics units, resulted in crucial changes to the curriculum in a number of courses, and contributed to a more integrated approach, and a collective responsibility, to the development of students' quantitative skills for both face-to-face and online modes of learning.

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

A genome-wide association study identifies multiple loci associated with mathematics ability and disability

PubMed Central

Docherty, S J; Davis, O S P; Kovas, Y; Meaburn, E L; Dale, P S; Petrill, S A; Schalkwyk, L C; Plomin, R

2010-01-01

Numeracy is as important as literacy and exhibits a similar frequency of disability. Although its etiology is relatively poorly understood, quantitative genetic research has demonstrated mathematical ability to be moderately heritable. In this first genome-wide association study (GWAS) of mathematical ability and disability, 10 out of 43 single nucleotide polymorphism (SNP) associations nominated from two high- vs. low-ability (n = 600 10-year-olds each) scans of pooled DNA were validated (P < 0.05) in an individually genotyped sample of *2356 individuals spanning the entire distribution of mathematical ability, as assessed by teacher reports and online tests. Although the effects are of the modest sizes now expected for complex traits and require further replication, interesting candidate genes are implicated such as NRCAM which encodes a neuronal cell adhesion molecule. When combined into a set, the 10 SNPs account for 2.9% (F = 56.85; df = 1 and 1881; P = 7.277e–14) of the phenotypic variance. The association is linear across the distribution consistent with a quantitative trait locus (QTL) hypothesis; the third of children in our sample who harbour 10 or more of the 20 risk alleles identified are nearly twice as likely (OR = 1.96; df = 1; P = 3.696e–07) to be in the lowest performing 15% of the distribution. Our results correspond with those of quantitative genetic research in indicating that mathematical ability and disability are influenced by many genes generating small effects across the entire spectrum of ability, implying that more highly powered studies will be needed to detect and replicate these QTL associations. PMID:20039944

A genome-wide association study identifies multiple loci associated with mathematics ability and disability.

PubMed

Docherty, S J; Davis, O S P; Kovas, Y; Meaburn, E L; Dale, P S; Petrill, S A; Schalkwyk, L C; Plomin, R

2010-03-01

Numeracy is as important as literacy and exhibits a similar frequency of disability. Although its etiology is relatively poorly understood, quantitative genetic research has demonstrated mathematical ability to be moderately heritable. In this first genome-wide association study (GWAS) of mathematical ability and disability, 10 out of 43 single nucleotide polymorphism (SNP) associations nominated from two high- vs. low-ability (n = 600 10-year-olds each) scans of pooled DNA were validated (P < 0.05) in an individually genotyped sample of (*)2356 individuals spanning the entire distribution of mathematical ability, as assessed by teacher reports and online tests. Although the effects are of the modest sizes now expected for complex traits and require further replication, interesting candidate genes are implicated such as NRCAM which encodes a neuronal cell adhesion molecule. When combined into a set, the 10 SNPs account for 2.9% (F = 56.85; df = 1 and 1881; P = 7.277e-14) of the phenotypic variance. The association is linear across the distribution consistent with a quantitative trait locus (QTL) hypothesis; the third of children in our sample who harbour 10 or more of the 20 risk alleles identified are nearly twice as likely (OR = 1.96; df = 1; P = 3.696e-07) to be in the lowest performing 15% of the distribution. Our results correspond with those of quantitative genetic research in indicating that mathematical ability and disability are influenced by many genes generating small effects across the entire spectrum of ability, implying that more highly powered studies will be needed to detect and replicate these QTL associations.

Girls in the UK Have Similar Reasons to Boys for Intending to Study Mathematics Post-16 Thanks to the Support and Encouragement They Receive

ERIC Educational Resources Information Center

Mujtaba, Tamjid; Reiss, Michael

2016-01-01

This paper focuses on the aspirations of 13- and 15-year-olds to continue with mathematics after the age of 16 and the association with perceptions of their mathematics education during the academic year 2008/9. A quantitative analysis was undertaken on the views of 12,176 UK students, obtained through surveys, with qualitative case studies on two…

Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support

NASA Technical Reports Server (NTRS)

Cruthirds, John E.

2003-01-01

A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.

Principles of quantitation of viral loads using nucleic acid sequence-based amplification in combination with homogeneous detection using molecular beacons.

PubMed

Weusten, Jos J A M; Carpay, Wim M; Oosterlaken, Tom A M; van Zuijlen, Martien C A; van de Wiel, Paul A

2002-03-15

For quantitative NASBA-based viral load assays using homogeneous detection with molecular beacons, such as the NucliSens EasyQ HIV-1 assay, a quantitation algorithm is required. During the amplification process there is a constant growth in the concentration of amplicons to which the beacon can bind while generating a fluorescence signal. The overall fluorescence curve contains kinetic information on both amplicon formation and beacon binding, but only the former is relevant for quantitation. In the current paper, mathematical modeling of the relevant processes is used to develop an equation describing the fluorescence curve as a function of the amplification time and the relevant kinetic parameters. This equation allows reconstruction of RNA formation, which is characterized by an exponential increase in concentrations as long as the primer concentrations are not rate limiting and by linear growth over time after the primer pool is depleted. During the linear growth phase, the actual quantitation is based on assessing the amplicon formation rate from the viral RNA relative to that from a fixed amount of calibrator RNA. The quantitation procedure has been successfully applied in the NucliSens EasyQ HIV-1 assay.

Modelling Ebola virus dynamics: Implications for therapy.

PubMed

Martyushev, Alexey; Nakaoka, Shinji; Sato, Kei; Noda, Takeshi; Iwami, Shingo

2016-11-01

Ebola virus (EBOV) causes a severe, often fatal Ebola virus disease (EVD), for which no approved antivirals exist. Recently, some promising anti-EBOV drugs, which are experimentally potent in animal models, have been developed. However, because the quantitative dynamics of EBOV replication in humans is uncertain, it remains unclear how much antiviral suppression of viral replication affects EVD outcome in patients. Here, we developed a novel mathematical model to quantitatively analyse human viral load data obtained during the 2000/01 Uganda EBOV outbreak and evaluated the effects of different antivirals. We found that nucleoside analogue- and siRNA-based therapies are effective if a therapy with a >50% inhibition rate is initiated within a few days post-symptom-onset. In contrast, antibody-based therapy requires not only a higher inhibition rate but also an earlier administration, especially for otherwise fatal cases. Our results demonstrate that an appropriate choice of EBOV-specific drugs is required for effective EVD treatment. Copyright © 2016 Elsevier B.V. All rights reserved.

Impact of Summer Recess on Mathematics Learning Retention

ERIC Educational Resources Information Center

Hornack, David

2016-01-01

School administrators across the nation are actively searching for solutions to increase student achievement due in part to the significant amount of knowledge that is lost annually each summer. Mathematical computation skills are especially at-risk. This quantitative research study was designed to investigate the impact of summer recess also…

A Meta-Analysis of Empirical Research on Teaching Students with Mathematics Learning Difficulties

ERIC Educational Resources Information Center

Dennis, Minyi Shih; Sharp, Emily; Chovanes, Jacquelyn; Thomas, Amanda; Burns, Raquel M.; Custer, Beth; Park, Junkoung

2016-01-01

This article quantitatively summarizes experimental and quasi-experimental studies on teaching students with mathematics difficulties (MD) published between 2000 and 2014, research that was available following earlier syntheses. It reports the analysis of effect sizes of 25 intervention studies on participant characteristics, intervention…

The Effect of Cooperative Groups on Math Anxiety

ERIC Educational Resources Information Center

Batton, Melissa

2010-01-01

Research indicates that many students have difficulty with mathematics, which can be attributed to many factors including math anxiety. Students who experience math anxiety have poor attitudes towards mathematics and perform below grade level based on class and statewide assessments. The purpose of this quasi-experimental quantitative study was to…

Merging Mathematics and English: One Approach to Bridging the Disciplines.

ERIC Educational Resources Information Center

Hansbarger, J. Clark; Stewart, Eric Lane

1996-01-01

Discusses two six-week projects for high school students involving qualitative and quantitative research methods to integrate mathematics and English. Students use descriptive statistics and prose to present findings about (1) their school space and (2) daily life for American troops in the Gulf War. (KMC)

The Application of Montessori Method in Learning Mathematics: An Experimental Research

ERIC Educational Resources Information Center

Faryadi, Qais

2017-01-01

The prime objective of this research was to investigate whether the Montessori method of learning helped kindergarten pupils improve their mathematical proficiency, critical thinking and problem-solving skills, besides training them to be responsible learners. Quantitative, qualitative, and observational methods were employed in the investigation.…